urban wind energy: empirical optimization of high-rise building roof

URBAN WIND ENERGY: EMPIRICAL

OPTIMIZATION OF HIGH-RISE

BUILDING ROOF SHAPE FOR THE

WIND ENERGY EXPLOITATION

Ph.D. THESIS

Francisco Toja Silva

Escuela Técnica Superior de Ingenieros Aeronáuticos

Universidad Politécnica de Madrid

2015

TEXiS v.1.0.

This document is prepared to be printed on both sides.

URBAN WIND ENERGY:

EMPIRICAL OPTIMIZATION OF

HIGH-RISE BUILDING ROOF

SHAPE FOR THE WIND

ENERGY EXPLOITATION

A Thesis presented for the Doctor in Aerospace Engineering degree by

Francisco Toja Silva

Supervisors

Dr. Oscar López García

Dr. Jorge Navarro Montesinos

Escuela Técnica Superior de Ingenieros Aeronáuticos

Universidad Politécnica de Madrid

2015

Copyright c© Francisco Toja Silva

To you, and nobody else.

Acknowledgements

If you're not having fun, you're doingsomething wrong.

Groucho Marx

The author wants to acknowledge all the people cited in this Chapter.The present Thesis is dedicated to:

- The reader. You are the actual purpose of this document. I hope itwill be interesting and useful for you.

- The Energy and Environment Research Center (CIEMAT) for the PhDfellowship that made possible the development of the present Thesis. Asincere acknowledgement for making true my dream of progressing in theresearch career towards a new stage. I am aware of the eort that thesociety made funding my career, and I must deserve it bringing all the bestwith the highest motivation and ethical principles in my present and futurework.

- The School of Aeronautics of the UPM for giving me the opportunityto defend this PhD Thesis in Aerospace Engineering.

- My supervisors Oscar and Jorge for the support given. Also to Ignacio,the Director of the Wind Energy Unit of the CIEMAT. I had freedom duringthe Thesis development. It was a privilege because I could focus on the topicsreally interesting and motivating for me. It carried out hard diculties,but thanks to these diculties I have improved not only my scientic andtechnical skills but also my management and transferable skills. I want toreally acknowledge them, they where there when I needed them.

- Mari and Lulila for being on my side in my life. The hard eort toreach the excellence in research is much easier in the best company.

- My work mates at the CIEMATAnne, Carmen, Fernando, Luis, Manuel,Pablo, Pedro and Vadim. A special mention to Dani, for the knowledgetransferred, his patience and the support given. Also a very special mentionto Alfredo and Julien for the excellent knowledge transferred and for givingme the opportunity of leaning from their high-level scientic experience.

- My work mates and personal friends at the Fraunhofer IWES Bastian,

vii

viii Acknowledgements

Bernhard, Michael, Jose, Thais, etc.; for the very good experience of workingwith them and the very good moments together. I felt at home in Olden-burg. A very special mention to Carlos for the very much signicant andappreciated support given, decisive for the success of this Thesis.

- My family and my personal friends Alba, Alberto, Andrea, Candelarias,Carles, Concepción, David, Eduardo, Eric, Franciscos, Isabel, Ismaeles, Juli-eta, Julio, Laura, Lluís, Luis, María Jesús, Mariela, Marc, Mirta, Queralt,Raúl, Rosa, Ruben, Tomás, etc.

I apologize the rest of the people not explicitly mentioned above. Thiswork is also dedicated to them.

Abstract

The clear and present danger of climatechange means we cannot burn our way

to prosperity. We already rely too heavilyon fossil fuels. We need to nd a new,sustainable path to the future we want.We need a clean industrial revolution.

Ban Ki-moon

Resumen en Castellano

El programa Europeo HORIZON2020 en Futuras Ciudades Inteligentes es-tablece como objetivo que el 20% de la energía eléctrica sea generada a partirde fuentes renovables. Este objetivo implica la necesidad de potenciar la ge-neración de energía eólica en todos los ámbitos. La energía eólica reducedrásticamente las emisiones de gases de efecto invernadero y evita los ries-gos geo-políticos asociados al suministro e infraestructuras energéticas, asícomo la dependencia energética de otras regiones. Además, la generación deenergía distribuida (generación en el punto de consumo) presenta signica-tivas ventajas en términos de elevada eciencia energética y estimulación dela economía. El sector de la edicación representa el 40% del consumo en-ergético total de la Unión Europea. La reducción del consumo energético eneste área es, por tanto, una prioridad de acuerdo con los objetivos 20-20-20en eciencia energética. La Directiva 2010/31/EU del Parlamento Europeoy del Consejo de 19 de mayo de 2010 sobre el comportamiento energético deedicaciones contempla la instalación de sistemas de suministro energéticoa partir de fuentes renovables en las edicaciones de nuevo diseño. Actual-mente existe una escasez de conocimiento cientíco y tecnológico acerca dela geometría óptima de las edicaciones para la explotación de la energíaeólica en entornos urbanos.

El campo tecnológico de estudio de la presente Tesis Doctoral es la ge-neración de energía eólica en entornos urbanos. Especícamente, la opti-mización de la geometría de las cubiertas de edicaciones desde el punto devista de la explotación del recurso energético eólico. Debido a que el ujo

ix

x Abstract

del viento alrededor de las edicaciones es exhaustivamente investigado enesta Tesis empleando herramientas de simulación numérica, la mecánica deuidos computacional (CFD en inglés) y la aerodinámica de edicacionesson los campos cientícos de estudio.

El objetivo central de esta Tesis Doctoral es obtener una geometría dealtas prestaciones (u óptima) para la explotación de la energía eólica en cu-biertas de edicaciones de gran altura. Este objetivo es alcanzado medianteun análisis exhaustivo de la inuencia de la forma de la cubierta del edicioen el ujo del viento desde el punto de vista de la explotación energética delrecurso eólico empleando herramientas de simulación numérica (CFD). Adi-cionalmente, la geometría de la edicación convencional (edicio prismático)es estudiada, y el posicionamiento adecuado para los diferentes tipos de aero-generadores es propuesto. La compatibilidad entre el aprovechamiento delas energías solar fotovoltaica y eólica también es analizado en este tipo deedicaciones. La investigación prosigue con la optimización de la geometríade la cubierta. La metodología con la que se obtiene la geometría óptimaconsta de las siguientes etapas:

- Vericación de los resultados de las geometrías previamente estudia-das en la literatura. Las geometrías básicas que se someten a examen son:cubierta plana, a dos aguas, inclinada, abovedada y esférica.

- Análisis de la inuencia de la forma de las aristas de la cubierta sobreel ujo del viento. Esta tarea se lleva a cabo mediante la comparación delos resultados obtenidos para la arista convencional (esquina sencilla) conun parapeto, un voladizo y una esquina curva.

- Análisis del acoplamiento entre la cubierta y los cerramientos verticales(paredes) mediante la comparación entre diferentes variaciones de una cu-bierta esférica en una edicación de gran altura: cubierta esférica estudiadaen la literatura, cubierta esférica integrada geométricamente con las paredes(planta cuadrada en el suelo) y una cubierta esférica acoplada a una paredcilíndrica. El comportamiento del ujo sobre la cubierta es estudiado tam-bién considerando la posibilidad de la variación en la dirección del vientoincidente.

- Análisis del efecto de las proporciones geométricas del edicio sobre elujo en la cubierta.

- Análisis del efecto de la presencia de edicaciones circundantes sobreel ujo del viento en la cubierta del edicio objetivo.

Las contribuciones de la presente Tesis Doctoral pueden resumirse en:- Se demuestra que los modelos de turbulencia RANS obtienen mejores

resultados para la simulación del viento alrededor de edicaciones empleandolos coecientes propuestos por Crespo y los propuestos por Bechmann ySørensen que empleando los coecientes estándar.

- Se demuestra que la estimación de la energía cinética turbulenta del

Abstract xi

ujo empleando modelos de turbulencia RANS puede ser validada mante-niendo el enfoque en la cubierta de la edicación.

- Se presenta una nueva modicación del modelo de turbulencia Durbink − ε que reproduce mejor la distancia de recirculación del ujo de acuerdocon los resultados experimentales.

- Se demuestra una relación lineal entre la distancia de recirculación enuna cubierta plana y el factor constante involucrado en el cálculo de la escalade tiempo de la velocidad turbulenta. Este resultado puede ser empleadopor la comunidad cientíca para la mejora del modelado de la turbulencia endiversas herramientas computacionales (OpenFOAM, Fluent, CFX, etc.).

- La compatibilidad entre las energías solar fotovoltaica y eólica en cu-biertas de edicaciones es analizada. Se demuestra que la presencia de losmódulos solares provoca un descenso en la intensidad de turbulencia.

- Se demuestran conictos en el cambio de escala entre simulaciones deedicaciones a escala real y simulaciones de modelos a escala reducida (túnelde viento). Se demuestra que para respetar las limitaciones de similitud(número de Reynolds) son necesarias mediciones en edicaciones a escalareal o experimentos en túneles de viento empleando agua como uido, espe-cialmente cuando se trata con geometrías complejas, como es el caso de losmódulos solares.

- Se determina el posicionamiento más adecuado para los diferentes tiposde aerogeneradores tomando en consideración la velocidad e intensidad deturbulencia del ujo. El posicionamiento de aerogeneradores es investigadoen las geometrías de cubierta más habituales (plana, a dos aguas, inclinada,abovedada y esférica).

- Las formas de aristas más habituales (esquina, parapeto, voladizo ycurva) son analizadas, así como su efecto sobre el ujo del viento en lacubierta de un edicio de gran altura desde el punto de vista del aprovecha-miento eólico.

- Se propone una geometría óptima (o de altas prestaciones) para elaprovechamiento de la energía eólica urbana. Esta optimización incluye:vericación de las geometrías estudiadas en el estado del arte, análisis dela inuencia de las aristas de la cubierta en el ujo del viento, estudio delacoplamiento entre la cubierta y las paredes, análisis de sensibilidad delgrosor de la cubierta, exploración de la inuencia de las proporciones ge-ométricas de la cubierta y el edicio, e investigación del efecto de las edi-caciones circundantes (considerando diferentes alturas de los alrededores)sobre el ujo del viento en la cubierta del edicio objetivo. Las investiga-ciones comprenden el análisis de la velocidad, la energía cinética turbulentay la intensidad de turbulencia en todos los casos.

xii Abstract

Abstract in English

The HORIZON2020 European program in Future Smart Cities aims to have20% of electricity produced by renewable sources. This goal implies the ne-cessity to enhance the wind energy generation, both with large and smallwind turbines. Wind energy drastically reduces carbon emissions and avoidsgeo-political risks associated with supply and infrastructure constraints, aswell as energy dependence from other regions. Additionally, distributed en-ergy generation (generation at the consumption site) oers signicant ben-ets in terms of high energy eciency and stimulation of the economy. Thebuildings sector represents 40% of the European Union total energy con-sumption. Reducing energy consumption in this area is therefore a pri-ority under the 20-20-20 objectives on energy eciency. The Directive2010/31/EU of the European Parliament and of the Council of 19 May 2010on the energy performance of buildings aims to consider the installationof renewable energy supply systems in new designed buildings. Nowadays,there is a lack of knowledge about the optimum building shape for urbanwind energy exploitation.

The technological eld of study of the present Thesis is the wind en-ergy generation in urban environments. Specically, the improvement of thebuilding-roof shape with a focus on the wind energy resource exploitation.Since the wind ow around buildings is exhaustively investigated in thisThesis using numerical simulation tools, both computational uid dynamics(CFD) and building aerodynamics are the scientic elds of study.

The main objective of this Thesis is to obtain an improved (or optimum)shape of a high-rise building for the wind energy exploitation on the roof. Toachieve this objective, an analysis of the inuence of the building shape onthe behaviour of the wind ow on the roof from the point of view of the windenergy exploitation is carried out using numerical simulation tools (CFD).Additionally, the conventional building shape (prismatic) is analysed, andthe adequate positions for dierent kinds of wind turbines are proposed. Thecompatibility of both photovoltaic-solar and wind energies is also analysedfor this kind of buildings. The investigation continues with the building-roof optimization. The methodology for obtaining the optimum high-risebuilding roof shape involves the following stages:

- Verication of the results of previous building-roof shapes studied inthe literature. The basic shapes that are compared are: at, pitched, shed,vaulted and spheric.

- Analysis of the inuence of the roof-edge shape on the wind ow. Thistask is carried out by comparing the results obtained for the conventionaledge shape (simple corner) with a railing, a cantilever and a curved edge.

- Analysis of the roof-wall coupling by testing dierent variations of aspherical roof on a high-rise building: spherical roof studied in the litera-

Abstract xiii

ture, spherical roof geometrically integrated with the walls (squared-plant)and spherical roof with a cylindrical wall. The ow behaviour on the roofaccording to the variation of the incident wind direction is commented.

- Analysis of the eect of the building aspect ratio on the ow.- Analysis of the surrounding buildings eect on the wind ow on the

target building roof.The contributions of the present Thesis can be summarized as follows:- It is demonstrated that RANS turbulence models obtain better results

for the wind ow around buildings using the coecients proposed by Crespoand those proposed by Bechmann and Sørensen than by using the standardones.

- It is demonstrated that RANS turbulence models can be validated forturbulent kinetic energy focusing on building roofs.

- A new modication of the Durbin k − ε turbulence model is proposedin order to obtain a better agreement of the recirculation distance betweenCFD simulations and experimental results.

- A linear relationship between the recirculation distance on a at roofand the constant factor involved in the calculation of the turbulence velocitytime scale is demonstrated. This discovery can be used by the researchcommunity in order to improve the turbulence modeling in dierent solvers(OpenFOAM, Fluent, CFX, etc.).

- The compatibility of both photovoltaic-solar and wind energies onbuilding roofs is demonstrated. A decrease of turbulence intensity due tothe presence of the solar panels is demonstrated.

- Scaling issues are demonstrated between full-scale buildings and wind-tunnel reduced-scale models. The necessity of respecting the similitude con-straints is demonstrated. Either full-scale measurements or wind-tunnel ex-periments using water as a medium are needed in order to accurately repro-duce the wind ow around buildings, specially when dealing with complexshapes (as solar panels, etc.).

- The most adequate position (most adequate roof region) for the dif-ferent kinds of wind turbines is highlighted attending to both velocity andturbulence intensity. The wind turbine positioning was investigated for themost habitual kind of building-roof shapes (at, pitched, shed, vaulted andspherical).

- The most habitual roof-edge shapes (simple edge, railing, cantileverand curved) were investigated, and their eect on the wind ow on a high-rise building roof were analysed from the point of view of the wind energyexploitation.

- An optimum building-roof shape is proposed for the urban wind energyexploitation. Such optimization includes: state-of-the-art roof shapes test,analysis of the inuence of the roof-edge shape on the wind ow, study of the

xiv Abstract

roof-wall coupling, sensitivity analysis of the roof width, exploration of theaspect ratio of the building-roof shape and investigation of the eect of theneighbouring buildings (considering dierent surrounding heights) on thewind ow on the target building roof. The investigations comprise analysisof velocity, turbulent kinetic energy and turbulence intensity for all the cases.

Contents

Acknowledgements vii

Abstract ix

Nomenclature xxxi

1 Introduction 1

1.1 Scientic and technological elds of study . . . . . . . . . . . 11.2 Objectives and methodology . . . . . . . . . . . . . . . . . . . 11.3 Why empirical? . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Research scope . . . . . . . . . . . . . . . . . . . . . . . . . . 31.5 Justication of this investigation . . . . . . . . . . . . . . . . 51.6 A review of urban wind energy . . . . . . . . . . . . . . . . . 7

1.6.1 A basic concept of the wind ow on building roofs . . 91.6.2 Wind energy exploitation in large structures . . . . . . 111.6.3 Wind energy exploitation in buildings . . . . . . . . . 13

Bibliography notes . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2 CWE applied to building aerodynamics 31

2.1 Basic aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.2 The atmospheric boundary layer . . . . . . . . . . . . . . . . 362.3 Governing equations of the ow and turbulence modeling . . 402.4 Building aerodynamics . . . . . . . . . . . . . . . . . . . . . . 442.5 Hardware used for the simulations . . . . . . . . . . . . . . . 492.6 Validation of RANS turbulence models . . . . . . . . . . . . . 51

2.6.1 Flat roof building model in wind tunnel . . . . . . . . 512.6.2 Curved-roof building model in wind tunnel . . . . . . 73

2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Bibliography notes . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

3 Compatibility of solar and wind energy systems 81

xv

xvi Index

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813.2 Complementary validation . . . . . . . . . . . . . . . . . . . . 823.3 Description of the cases and simulation details . . . . . . . . . 843.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 88

3.4.1 Reynolds number similarity constraints . . . . . . . . . 933.4.2 Solution verication . . . . . . . . . . . . . . . . . . . 963.4.3 Wind energy exploitation and wind turbine positioning 97


4 Building-roof shape optimization 103

4.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 1034.2 State-of-the-art roof shapes . . . . . . . . . . . . . . . . . . . 104

4.2.1 Description of the cases . . . . . . . . . . . . . . . . . 1054.2.2 Simulation results . . . . . . . . . . . . . . . . . . . . 1054.2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 110

4.3 Inuence of the roof-edge shape on the wind ow . . . . . . . 1124.3.1 Description of the cases . . . . . . . . . . . . . . . . . 1124.3.2 Simulation results . . . . . . . . . . . . . . . . . . . . 1144.3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 119

4.4 Wall-roof coupling analysis . . . . . . . . . . . . . . . . . . . 1204.4.1 Description of the cases . . . . . . . . . . . . . . . . . 1204.4.2 Simulation results . . . . . . . . . . . . . . . . . . . . 1214.4.3 Solution verication . . . . . . . . . . . . . . . . . . . 1254.4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 125

4.5 Sensitivity analysis of the roof width . . . . . . . . . . . . . . 1274.5.1 Description of the cases . . . . . . . . . . . . . . . . . 1274.5.2 Results and discussion . . . . . . . . . . . . . . . . . . 1284.5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 131

4.6 Analysis of the building aspect ratio . . . . . . . . . . . . . . 1324.6.1 Description of the cases . . . . . . . . . . . . . . . . . 1324.6.2 Results and discussion . . . . . . . . . . . . . . . . . . 1334.6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 136

4.7 Inuence of the surrounding buildings . . . . . . . . . . . . . 1364.7.1 Description of the cases . . . . . . . . . . . . . . . . . 1364.7.2 Results and discussion . . . . . . . . . . . . . . . . . . 1394.7.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 144


5 Concluding remarks 151

Index xvii

5.1 Final conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 1515.1.1 Contributions of this Thesis . . . . . . . . . . . . . . . 1515.1.2 Conclusions from the investigations . . . . . . . . . . . 153

5.2 Suggestions for further works . . . . . . . . . . . . . . . . . . 156

Bibliography 159

A RBF-based immersed boundary method 179

A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179A.2 RBF interpolation from an arbitrarily scattered set of nodes . 182A.3 Imposition of Dirichlet boundary conditions . . . . . . . . . . 185

A.3.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . 187A.3.2 Results and discussion . . . . . . . . . . . . . . . . . . 189

A.4 Treatment of Neumann boundary conditions . . . . . . . . . . 192A.4.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . 193A.4.2 Results and discussion . . . . . . . . . . . . . . . . . . 195

A.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198Bibliography notes . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

B Curriculum Vitae 201

B.1 Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201B.2 Publications and patents . . . . . . . . . . . . . . . . . . . . . 202B.3 Conferences, congresses and seminars . . . . . . . . . . . . . . 204B.4 Research experience, fellowships and awards . . . . . . . . . . 204B.5 Complementary education . . . . . . . . . . . . . . . . . . . . 205B.6 Complementary work experience . . . . . . . . . . . . . . . . 207B.7 Computational skills . . . . . . . . . . . . . . . . . . . . . . . 208B.8 Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

List of Figures

1.1 Diagram of the methodology (milestones) followed for obtain-ing and analysing an optimum building-roof shape for theurban wind energy exploitation. Deliverables: article 1 isToja-Silva et al. (2015d), article 2 is Toja-Silva et al. (2015b),article 3 is Toja-Silva et al. (2015c) and article 4 is Toja-Silvaet al. (2015a). . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Example of sound levels vs. wind speed for small wind tur-bines (Pantazopoulou (2009)). . . . . . . . . . . . . . . . . . . 8

1.3 Diagram of the simulation case (left) and a symmetric build-ing with a large length with respect to its height (right). Thesimulation comprises the central length of the building. . . . . 10

1.4 Instantaneous velocity (m/s) maps obtained in the simulationfor incident wind velocities of 1, 2, 4 and 10 m/s (from left toright and from the top to the bottom). . . . . . . . . . . . . . 11

1.5 Wind turbines at the Bolte Bridge in Melbourne (Australia).(Oppenheim (2004)) . . . . . . . . . . . . . . . . . . . . . . . 12

1.6 Examples of building-augmented wind turbines (BAWT). . . 14

1.7 Horizontal axis wind turbine (HAWT) in the urban environ-ment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.8 Diuser-augmented wind turbine (DAWT). . . . . . . . . . . 15

1.9 Superposition of a HAWT over the air ow for an incidentvelocity of 1 m/s. . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.10 Hybrid VAWT generator (Darrieus and Savonius). . . . . . . 17

1.11 Power coecients CP vs. the specic velocity λ for three tur-bines: HAWT, Darrieus and H-rotor (Eriksson et al. (2008a)). 18

1.12 Giromill wind turbine with ve blades. . . . . . . . . . . . . . 19

1.13 Power coecient of a Giromill wind turbine with two (left)and three (right) blades (Howell et al. (2010)). . . . . . . . . . 19

1.14 Power coecients Cp (in %) vs. the specic velocity λ forthree types of blades, Giromill wind turbine with four blades(El-Samanoudy et al. (2010)). . . . . . . . . . . . . . . . . . . 20

xix

xx List of figures

1.15 Superposition of a VAWT over the air ow for an incidentvelocity of 1 m/s. . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.16 Helical Darrieus wind turbine. . . . . . . . . . . . . . . . . . . 211.17 Power coecient for various solidities, helical Darrieus wind

turbine (Kirke and Lazauskas (2011)). . . . . . . . . . . . . . 221.18 Flexible Darrieus wind turbine in both horizontal (left) and

vertical (right) positions (Sharpe and Proven (2010)). . . . . . 231.19 Superposition of a horizontal Darrieus wind turbine for an

incident velocity of 1 m/s. . . . . . . . . . . . . . . . . . . . . 241.20 Power vs. rotation speed for various wind velocities, exible

Darrieus wind turbine (Sharpe and Proven (2010)). . . . . . . 241.21 Power coecient Cp of the Savonius wind turbine (D'Alessandro

et al. (2010)). . . . . . . . . . . . . . . . . . . . . . . . . . . . 251.22 Extremely low-cost Savonius wind turbine (left), and a dia-

gram of a Savonius wind turbine with two blades and a de-ector sheet (right) (Mohamed et al. (2010)). . . . . . . . . . 25

1.23 Power coecient of a Savonius wind turbine with two (left)and three (right) blades with and without a deector sheet(Mohamed et al. (2010)). . . . . . . . . . . . . . . . . . . . . . 26

1.24 Helical Savonius wind turbine with three blades. . . . . . . . 261.25 Coecients of power, torque and static torque for a two-blade

Savonius wind turbine with both helical and conventionalblades (Kamoji et al. (2009)). . . . . . . . . . . . . . . . . . . 27

1.26 Vertical-axis resistance-type wind turbine (Müller et al. (2009)). 281.27 Eciency of vertical-axis resistance-type wind turbines (Müller

et al. (2009)). . . . . . . . . . . . . . . . . . . . . . . . . . . . 281.28 Ducted wind turbine on the edge of the building roof (Grant

et al. (2008)). . . . . . . . . . . . . . . . . . . . . . . . . . . . 291.29 Power coecient vs. the dierential pressure coecient of a

ducted wind turbine for various values of the speed coecient(Grant et al. (2008)). . . . . . . . . . . . . . . . . . . . . . . . 29

1.30 Superposition of a ducted wind turbine on the edge of thebuilding roof for an incident velocity of 1 m/s. . . . . . . . . . 30

2.1 Representation of turbulence in water ows, Leonardo daVinci 1508-1509 (Werne (2015)). . . . . . . . . . . . . . . . . 33

2.2 Transition from laminar to turbulent ow at the cigarettesmoke (adapted from Tompitak (2015)). . . . . . . . . . . . . 34

2.3 Flow over an obstacle inside a channel with Re = 800. Notethat velocity is appreciated inside the obstacle, because animmersed boundary method has been used in a DNS CFDcode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

List of figures xxi

2.4 Transition from laminar to turbulent ow in a boundary layer.The characteristic sublayers are shown: viscous sublayer, buerlayer and turbulent region. (Comsol (2015)) . . . . . . . . . . 35

2.5 Diagram of the layers of Earth's atmosphere, showing heightsof characteristic atmospheric phenomena (Encyclopædia Bri-tannica (2015)). . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.6 Diagram of the meteorological phenomena and their respec-tive time and length scale, and the most usual classicationof the meteorogical scales (Geostationary Operational Envi-ronmental Satellites R Series (2015)). . . . . . . . . . . . . . . 38

2.7 Diagram of the time-evolution of the atmosphere (Garratt(1994)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.8 Schematic diagram showing the three regimes of wind owover an obstacle array, and the proportions to which eachregime applies. (Oke (1988)) . . . . . . . . . . . . . . . . . . . 45

2.9 Wind-ow pattern around an isolated building in 2D and 3D.Legend: (1) ow over building, (2) oncoming ow, (3) owfrom stagnation point over building, (4) ow from stagnationpoint around vertical building edges, (5) downow from stag-nation point, (6) standing vortex (base vortex or horseshoevortex), (7) stagnation ow in front of building near groundlevel, (8) corner streams (vortex wrapping around corners),(9) ow around building sides at ground level (adding to cor-ner streams), (10) recirculation ow behind the building, (11)stagnation region behind building at ground level, (12) re-stored ow direction, (13) large vortices behind building and(16) small vortices in shear layer. . . . . . . . . . . . . . . . . 46

2.10 Instantaneous vortex generated by a slender prismatic obsta-cle: (a) top view and (b) lateral view. (Joubert et al. (2015)) 47

2.11 Diagram of the corner roof vortices appearing when the in-cident wind direction is oblique to the walls. (Peterka andCernak (1976)) . . . . . . . . . . . . . . . . . . . . . . . . . . 47

2.12 Examples of pressure elds in recirculation regions on the roof. 48

2.13 Diagram of the case of study. All dimensions are in m. . . . . 53

2.14 Inlet proles: mean streamwise velocity (a), turbulent kineticenergy (b) and turbulent dissipation (c). The points repre-sent the inlet proles used at the experiment of Meng andHibi (1998), and the solid lines are the numerical inlets of thesimulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

2.15 Vertical section of the rened mesh obtained using snappy-HexMesh with close to 3.1M cells. . . . . . . . . . . . . . . . . 55

xxii List of figures

2.16 Diagram of the axes (V1-V6) at the vertical section of thecentral part of the domain, for the comparison of the results.All lengths are in meters. . . . . . . . . . . . . . . . . . . . . 56

2.17 Sensitivity analysis for the recirculation distance XR by vary-ing the constant factor in the denition of TD (Eq. (2.20)). . 58

2.18 Comparison of the turbulent kinetic energy [m2/s2] at thevertical section at the center of the domain, using the modelswith HRk ≥ 66%. . . . . . . . . . . . . . . . . . . . . . . . . . 61

2.19 Detail of the rened meshes obtained for the convergenceanalysis, using the snappyHexMesh application of OpenFOAM. 62

2.20 Diagram of the regions of the building roof for the ow anal-ysis. All lengths are in meters. . . . . . . . . . . . . . . . . . 64

2.21 Vertical proles comparison for U (left) and k (right) at theupstream region of the building, using the RANS models thatsuccessfully pass the validation. . . . . . . . . . . . . . . . . . 65

2.22 Vertical proles comparison for U (left) and k (right) at thecentral region of the building roof, using the RANS modelsthat successfully pass the validation. . . . . . . . . . . . . . . 67

2.23 Vertical proles comparison for U (left) and k (right) at thedownstream region of the building, using the RANS modelsthat successfully pass the validation. . . . . . . . . . . . . . . 68

2.24 Wind turbine positioning diagrams: (A) Most appropriatewind energy exploitation systems at the dierent regions ofthe building roof. The vector eld is the velocity, the back-ground colormap is turbulence intensity (TI) and the boldline (in magenta) is an isocontour of the isoline correspond-ing to TI = 0.15. (B) Ducted wind turbine at the upstreamcorner of the roof into the pressure eld. . . . . . . . . . . . . 70

2.25 Isosurfaces of TI = 0.15 (in grey colour) for a normal inci-dent wind direction (0) and an oblique wind direction (45).HAWT can be placed above the isosurface. Below this region,VAWT must be considered. Dark red represents the building,green the ground and blue the sky. . . . . . . . . . . . . . . . 71

2.26 Diagram of the wind-tunnel geometry and the axes V1-V3 forthe validation of the results. All lengths are in meters. . . . . 73

2.27 Inlet wind proles for the curved-roof validation case: meanstreamwise velocity (U), turbulent kinetic energy (k) and tur-bulent dissipation (ε). The points represent the inlet prolesused at the experiment of Ntinas et al. (2014), and the solidlines are the numerical inlets of the simulations. . . . . . . . . 75

2.28 Vertical section of the rened mesh obtained using snappy-HexMesh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

List of figures xxiii

2.29 Vertical section at the center of the domain of the U and kelds around the building. . . . . . . . . . . . . . . . . . . . . 76

2.30 Comparison of U and k at the vertical section at the centerof the domain. . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.1 Diagram of the validation of the innite-span array of solarpanels. The AXIS indicates the points where the data iscompared for the validation. All values are dimensionless,expressed as multiples of the width of the plate W = 1 m. . . 83

3.2 Comparison between numerical and experimental values forvalidation using the experimental data of Fage and Johansen(1927). All values are dimensionless: distances with respectto the innite array widthW and velocity with respect to thefree-stream velocity U∞ (inlet velocity). . . . . . . . . . . . . 84

3.3 Diagram of the computational domain of the full-scale build-ing. All values are in meters. . . . . . . . . . . . . . . . . . . 85

3.4 Diagram of the geometry of the 41.75 kW photovoltaic facilitywith a tilt angle of 10, at full scale. . . . . . . . . . . . . . . 86

3.5 Diagram of the geometry of the 30.36 kW photovoltaic facilitywith a tilt angle of 30, at full scale. . . . . . . . . . . . . . . 87

3.6 Vertical section of the rened meshes obtained using snappy-HexMesh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

3.7 Diagram of the axes (V1-V4) at the vertical section of thecentral part of the domain, for the comparison of the results.All lengths are dimensionless. . . . . . . . . . . . . . . . . . . 89

3.8 Comparison of the velocity at the vertical section at the centerof the domain, for the full-scale model. Note that some series(10 in V2 and V3) do not have values close to the roof,because the solar panels (including the support structure) llthis space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

3.9 Comparison of turbulent kinetic energy at the vertical sectionat the center of the domain, for the full-scale model. . . . . . 92

3.10 Streamlines that show the recirculation vortices on the rooffor the 30 raised panels, at the full-scale model. . . . . . . . 93

3.11 Comparison of the velocity at the vertical section at the centerof the domain, for the reduced-scale model. . . . . . . . . . . 94

3.12 Comparison of turbulent kinetic energy at the vertical sectionat the center of the domain, for the reduced-scale model. . . . 95

3.13 Streamlines that show the recirculation vortices on the rooffor raised panels in unfavourable position, at the reduced-scalemodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

xxiv List of figures

3.14 Comparison of velocity at the vertical section at the center ofthe domain using 3 dierent meshes. Case of raised panels inunfavourable position. . . . . . . . . . . . . . . . . . . . . . . 98

3.15 Comparison of turbulence kinetic energy at the vertical sec-tion at the center of the domain using 3 dierent meshes.Case of raised panels in unfavourable position. . . . . . . . . . 99

3.16 Vertical proles of turbulence intensity up and downstreamof the roof considering dierent incident wind directions forthe raised solar panels, until the threshold TI = 0.15. . . . . . 100

3.17 Turbulence intensity eld around the building and detail of aVAWT in horizontal position upstream. The grey line repre-sents the threshold TI = 0.15 for the installation of HAWT(above) and VAWT (below), and the vectorial eld is the ve-locity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

4.1 Central vertical section detail of the dierent roof shapes in-vestigated. The red AXIS indicates the points where thedata is compared between the dierent cases. . . . . . . . . . 106

4.2 Vertical section detail of the rened meshes obtained usingsnappyHexMesh for the state-of-the-art analysis. . . . . . . . 107

4.3 Comparison of speed-up, nondimensional TKE and TI for thestate-of-the-art roof shapes analysis at the vertical axis on thecenter of the roof. . . . . . . . . . . . . . . . . . . . . . . . . . 108

4.4 Comparison of speed-up (U/Uref ) and TI elds on the rooffor the state-of-the-art cases: sharp roofs. . . . . . . . . . . . 109

4.5 Comparison of speed-up (U/Uref ) and TI elds on the rooffor the state-of-the-art cases: curved roofs. . . . . . . . . . . . 110

4.6 Examples of the dierent roof-edges tested. . . . . . . . . . . 112

4.7 Central vertical section detail of the dierent roof-edge shapesinvestigated. The red axes V1-V4 indicate the points wherethe data is compared between the dierent cases. Note thatthe axes V1 and V4 start from the normal height of the roofalso for the curved edge, although both upstream and down-stream edges of the roof are 1 m below in this case. Addition-ally, note that the axes V1 and V4 start from 1 m above thenormal roof height for the railing due to the presence of thiselement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

4.8 Vertical section detail of the rened meshes obtained usingsnappyHexMesh. . . . . . . . . . . . . . . . . . . . . . . . . . 114

4.9 Comparison of the speed-up (U/Uref ) at the vertical sectionon the center of the domain. . . . . . . . . . . . . . . . . . . . 115

List of figures xxv

4.10 Comparison of the nondimensional TKE (k/U2ref ) at the ver-

tical section on the center of the domain. . . . . . . . . . . . . 116

4.11 Comparison of TI below the limit of TI < 0.15 at the verticalsection on the center of the domain. . . . . . . . . . . . . . . 117

4.12 Comparison of speed-up (U/Uref ) and TI elds on the roof. . 118

4.13 Comparison of speed-up (U/Uref ) and TI elds on the roof. . 119

4.14 Vertical section detail of the rened meshes obtained usingsnappyHexMesh for the additional spheric roofs. . . . . . . . 121

4.15 Comparison of speed-up, nondimensional TKE and TI for thewall-roof coupling analysis at the vertical axis on the centerof the roof. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

4.16 Comparison of speed-up (U/Uref ) and TI elds for the wall-roof coupling analysis of the spheric roofs. . . . . . . . . . . . 123

4.17 Transversal elds of speed-up (U/Uref ) and TI for vaultedand cylindrical wall-spheric roof. . . . . . . . . . . . . . . . . 124

4.18 Detail of the 3 dierent meshes used for the solution verication.125

4.19 Comparison of speed-up and nondimensional TKE on the cen-ter of the roof using 3 dierent meshes for the solution veri-cation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

4.20 Diagram of the dierent roof-shapes investigated for the sen-sitivity analysis of the roof width (r). . . . . . . . . . . . . . . 127

4.21 Vertical section detail of the rened mesh obtained usingsnappyHexMesh for the sensitivity analysis of the roof width. 128

4.22 Comparison of speed-up, nondimensional TKE and TI for theroof width analysis at the vertical axis on the center of the roof.129

4.23 Maximum values of speed-up (U/Uref ) and nondimensionalTKE (k/U2

ref ) for the dierent roof widths investigated. . . . 130

4.24 Comparison of speed-up (U/Uref ) and TI elds for the roofwidth analysis: thinner width shapes. . . . . . . . . . . . . . . 131

4.25 Comparison of speed-up (U/Uref ) and TI elds for the roofwidth analysis: wider width shapes. . . . . . . . . . . . . . . . 132

4.26 Diagram of the dierent aspect ratios (AR) investigated. . . . 133

4.27 Vertical section detail of the rened mesh obtained usingsnappyHexMesh for the dierent aspect ratios tested. Theaspect ratio (AR) and the number of mesh cells are also indi-cated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

4.28 Comparison of speed-up, nondimensional TKE and TI for theaspect ratio analysis at the vertical axis on the center of theroof. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135


ref ) for the dierent aspect ratios investigated. . . 136

xxvi List of figures

4.30 Comparison of speed-up (U/Uref ) vector eld and TI = 0.15isosurface for the dierent aspect ratios. . . . . . . . . . . . . 137

4.31 Diagram of the computational domain for the surrounding-buildings eect analysis. All values are in meters. The con-guration shown corresponds to h/H = 0.5, as an example. . 138

4.32 Diagram of the dierent aspect ratio buildings. The congu-ration shown corresponds to h/H = 0.5, as an example. . . . 139

4.33 Vertical section detail of the rened mesh obtained usingsnappyHexMesh for the surrounding buildings analysis (shortsurrounding buildings). . . . . . . . . . . . . . . . . . . . . . . 140

4.34 Vertical section detail of the rened mesh obtained usingsnappyHexMesh for the surrounding buildings analysis (tallsurrounding buildings). . . . . . . . . . . . . . . . . . . . . . . 141

4.35 Comparison of the speed-up (U/Uref ) for the surrounding-buildings inuence analysis at the vertical axis on the centerof the roof. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

4.36 Comparison of the nondimensional TKE (k/U2ref ) for the surrounding-

buildings inuence analysis at the vertical axis on the centerof the roof. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

4.37 Comparison of TI below the limit of TI < 0.15 for thesurrounding-buildings inuence analysis at the vertical axison the center of the roof. . . . . . . . . . . . . . . . . . . . . . 143

4.38 Comparison of the maximum speed-up (U/Uref ) and the TIthreshold height for the surrounding-buildings inuence anal-ysis at the vertical axis on the center of the roof. . . . . . . . 144


ref ) for the surrounding-buildings inuence analy-sis considering the dierent aspect ratios investigated. . . . . 145

4.40 Comparison of speed-up (U/Uref ) and TI elds for h/H = 0.25.146



4.43 Comparison of speed-up (U/Uref ) and TI elds for h/H = 1. 149

A.1 Norm of the interpolation error at the Lagrangian points forthe case described in 3.1. Red squares: interpolation error;solid line: ∆x (1st order); dashed line: ∆x2 (2nd order). . . . 185

A.2 Diagram of the interpolation support. . . . . . . . . . . . . . 187

A.3 Mean velocity and vorticity contours at ReD = 30. . . . . . . 190

A.4 Instantaneous velocity and vorticity contours at ReD = 185. . 191

A.5 Shape parameters of the wake formed at Re = 30 (Pinelli etal. (2010)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

List of figures xxvii

A.6 Norm of the interpolation error at the immersed surface fora Dirichlet boundary condition. Red squares: error u; blueasterisks: error v; solid line: ∆x (1st order); dashed line: ∆x2

(2nd order). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193A.7 Final temperature eld T (x, y). External boundary condi-

tions: TN = 100, TS = 25, TW = 75 and the right hand sidewall is considered adiabatic. . . . . . . . . . . . . . . . . . . . 196

A.8 Streamwise section of the temperature eld at the center ofthe domain. Red line: without considering the adiabatic em-bedded surface. Black line: considering the adiabatic embed-ded surface. Blue line: body conformal case. . . . . . . . . . . 196

A.9 Normal derivative of the closest temperature eld outside thevertical wall, in front of the height. Red circles: withoutconsidering the adiabatic embedded surface. Black squares:considering the adiabatic embedded surface. . . . . . . . . . . 197

A.10 Norm of the interpolation error of the derivative at the im-mersed surface. Red squares: derivative error; solid line: ∆x(1st order); dashed line: ∆x2 (2nd order). . . . . . . . . . . . 198

A.11 Temperature eld T (x, y). External boundary conditions:TN = 100, TS = 25, TW = 75 and TE = 50. . . . . . . . . . . 198

List of Tables

1.1 Water consumption of various energy technologies (Saidur etal. (2011)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2 Water consumption of various energy technologies (Saidur etal. (2011)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.3 Improvements to increase the performance of Savonius windturbines (D'Alessandro et al. (2010)). . . . . . . . . . . . . . . 22

2.1 Main dierences between the ABL and the free atmosphere(Blocken (2014b)). . . . . . . . . . . . . . . . . . . . . . . . . 37

2.2 Boundary conditions imposed at each boundary of the do-main following Architectural Institute of Japan (2013) andTominaga et al. (2008). Nomenclature: iP= Inlet prole, zG= zeroGradient, C = Calculated, fV = xedValue, wF = wallfunction, sP = Symmetry plane. . . . . . . . . . . . . . . . . 53

2.3 RANS turbulence models tested. . . . . . . . . . . . . . . . . 56

2.4 Tested coecients of the linear k − ε models. . . . . . . . . . 56

2.5 Comparison of the results using dierent RANS models: Reat-tachment distance relative to the roof length (XR) of the re-circulation vortex on the building roof and hit rate (HR) forthe variables U and k. The values that do not pass the valida-tion process are in red colour, and the results obtained withthe modication of the Durbin turbulence model proposed inthis Thesis are in blue colour. . . . . . . . . . . . . . . . . . . 59

2.6 Main parameters of the mesh renement using the snappyHexMeshapplication of OpenFOAM, and values obtained for the hitrates (HR). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

2.7 Boundary conditions imposed at each boundary of the do-main for the curved roof validation. Nomenclature: C = Cal-culated, fV = xedValue, iP = Inlet prole, sl = slip, sP =Symmetry plane, wF = wall function, zG = zeroGradient. . . 74

xxix

xxx List of tables

2.8 Hit rates (HR) for the variables U and k at the dierentRANS models tested for the curved roof. The results ob-tained with the modication of the Durbin turbulence modelproposed in this Thesis are in blue colour. . . . . . . . . . . . 78

A.1 Comparison of the main parameters of the wake and the dragcoecient at ReD = 30 with other works and experimentaldata. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

A.2 Comparison of the Strouhal number and the drag coecientat ReD = 185 with other works and experimental data. . . . . 192

Nomenclature

ABL . . . . . . . . . . Atmospheric Boundary Layer

AD . . . . . . . . . . . . Absolute maximum admissible deviation from the experi-mental data

p . . . . . . . . . . . . . . Mean pressure [Pa]

BAWT . . . . . . . . Building-Augmented Wind Turbine

C . . . . . . . . . . . . . . Calculated

CAD . . . . . . . . . . Computer-Aided Design

CBL . . . . . . . . . . Convective Boundary Layer

cP . . . . . . . . . . . . . Mean pressure coecient [-]

Cε1 . . . . . . . . . . . . Closure constant k − ε model [-]

Cε2 . . . . . . . . . . . . Closure constant k − ε model [-]

CFD . . . . . . . . . . Computational Fluid Dynamics

CIEMAT . . . . . Centro de Investigaciones Energéticas, Medioambientales yTecnológicas

Cµ . . . . . . . . . . . . . Model coecient turbulence model (proportional number)[-]

CP . . . . . . . . . . . . Power coecient [-]

CPU . . . . . . . . . . Central Processing Unit

CWE . . . . . . . . . Computational Wind Engineering

DAWT . . . . . . . . Diuser-Augmented Wind Turbine

DDN . . . . . . . . . . DataDirect Networks

DDR . . . . . . . . . . Double Data Rate

xxxi

xxxii Nomenclature

δij . . . . . . . . . . . . . Kronecker Delta function

D . . . . . . . . . . . . . Building-base diameter [m]

DIC . . . . . . . . . . . Diagonal Incomplete-Cholesky

DILU . . . . . . . . . Diagonal Incomplete LU

DNS . . . . . . . . . . Direct Numerical Simulation

ε . . . . . . . . . . . . . . Turbulence dissipation [m2/s3]

EU . . . . . . . . . . . . European Union

EXPi . . . . . . . . . Experimental value

FC . . . . . . . . . . . . Fibre Channel

fV . . . . . . . . . . . . xedValue

GAMG . . . . . . . Generalised Geometric-Algebraic Multi-Grid

GCI . . . . . . . . . . . Grid convergence index [%]

H . . . . . . . . . . . . . Building height [m]

HAWT . . . . . . . . Horizontal-Axis Wind Turbine

h . . . . . . . . . . . . . . Height of the surrounding buildings [m]

HPC . . . . . . . . . . High Performance Cluster

HR . . . . . . . . . . . . Hit rate [%]

HRk . . . . . . . . . . . Hit rate for k [%]

HRU . . . . . . . . . . Hit rate for U [%]

iP . . . . . . . . . . . . . Inlet prole

k . . . . . . . . . . . . . . Turbulent kinetic energy [m2/s2]

κ . . . . . . . . . . . . . . Von Karman constant [-]

KL . . . . . . . . . . . . Kato-Launder

KLY . . . . . . . . . . Kato-Launder-Yap

L . . . . . . . . . . . . . . Characteristic length of the problem [m]

λ . . . . . . . . . . . . . . Tip-speed ratio [-]

Nomenclature xxxiii

LES . . . . . . . . . . . Large-Eddy Simulation

LU . . . . . . . . . . . . Lower Upper (factorization)

M . . . . . . . . . . . . . Millions

MMK . . . . . . . . . Murakami-Mochida-Kondo

MPI . . . . . . . . . . . Message Passing Interface

µ . . . . . . . . . . . . . . Dynamic viscosity [Pa·s]

NBL . . . . . . . . . . Nocturnal Boundary Layer

N . . . . . . . . . . . . . Total number of cells

ν . . . . . . . . . . . . . . Kinematic viscosity [m2/s]

νt . . . . . . . . . . . . . . Kinematic eddy viscosity [m2/s]

ω . . . . . . . . . . . . . . Specic rate of dissipation (of k) [m2/s2]

PBiCG . . . . . . . . Preconditioned Bi-Conjugate Gradient

p . . . . . . . . . . . . . . Convergence rate [-]

P∞ . . . . . . . . . . . . Free-stream pressure [Pa]

Pk . . . . . . . . . . . . . Production of k [m2/s3]

P . . . . . . . . . . . . . . Pressure eld [Pa]

RAM . . . . . . . . . . Random-Access Memory

RANS . . . . . . . . . Reynolds-Averaged Navier-Stokes

RD . . . . . . . . . . . . Relative maximum admissible deviation from the experi-mental data

Re . . . . . . . . . . . . . Reynolds number [-]

u′iu′j . . . . . . . . . . . Reynolds stresses [m2/s2]

ρ . . . . . . . . . . . . . . Fluid density [kg/m3]

RNG . . . . . . . . . . Re-Normalisation Group

r . . . . . . . . . . . . . . Building roof height [m]

S . . . . . . . . . . . . . . Modulus of the rate of strain tensor [-]

SATA . . . . . . . . . Serial AT (Advanced Technology) Attachment

xxxiv Nomenclature

SFS . . . . . . . . . . . Self-certifying File System

σε . . . . . . . . . . . . . Dissipation Prandtl number [-]

σk . . . . . . . . . . . . . Kinetic energy Prandtl number [-]

SIMi . . . . . . . . . . Simulation value

SKE . . . . . . . . . . Standard k − ε

sl . . . . . . . . . . . . . Slip (boundary condition)

sP . . . . . . . . . . . . . Symmetry plane

SST . . . . . . . . . . . Shear Stress Transport

STL . . . . . . . . . . . Stereolithography

Sε . . . . . . . . . . . . . Source of ε [m2/s4]

TD . . . . . . . . . . . . Turbulence velocity time scale adopted for the Durbin tur-bulence model [s]

TI . . . . . . . . . . . . . Turbulence intensity [-]

T . . . . . . . . . . . . . . Turbulence velocity time scale [s]

TKE . . . . . . . . . . Turbulent kinetic energy [m2/s2]

U . . . . . . . . . . . . . . Streamwise velocity [m/s]

U∗ . . . . . . . . . . . . . Frictional velocity [m/s]

U∞ . . . . . . . . . . . . Free-stream velocity (reference velocity) [m/s]

URANS . . . . . . . Unsteady Reynolds-Averaged Navier-Stokes

Uref . . . . . . . . . . . Reference velocity [m/s]

U/Uref . . . . . . . . Speed-up ratio [-]

Ω . . . . . . . . . . . . . . Vorticity scale [-]

VAWT . . . . . . . . Vertical-Axis Wind Turbine

wF . . . . . . . . . . . . Wall function

W . . . . . . . . . . . . . Innite solar array width for validation [m]

XR . . . . . . . . . . . . Recirculation (or reattachment) distance on the roof [-]

yn . . . . . . . . . . . . . Normal distance to the nearest wall [m]

Nomenclature xxxv

z . . . . . . . . . . . . . . Independent variable measuring the height above ground[m]

z0 . . . . . . . . . . . . . Roughness height [m]

zG . . . . . . . . . . . . zeroGradient

zref . . . . . . . . . . . . Reference height [m]

Chapter 1

Introduction

Discovery is seeing what everybody elsehas seen, and thinking what nobody else

has thought.

Albert Szent-Györgyi

1.1 Scientic and technological elds of study

The technological eld of study of the present Thesis is the wind energygeneration in urban environments. Specically, the improvement of thebuilding-roof shape with a focus on the wind energy resource exploitation.Since the wind ow around buildings is exhaustively investigated using nu-merical simulation tools, both computational uid dynamics (CFD) andbuilding aerodynamics are the scientic elds of study of this Thesis.

1.2 Objectives and methodology

The main objective of this Thesis is to obtain an improved (or optimum)shape of a high-rise building for the wind energy exploitation on the roof,and the analysis of the behaviour of this shape in an urban environment.To achieve this nal objective, an analysis of the inuence of the buildingshape on the behaviour of the wind ow on the roof from the point of viewof the wind energy exploitation is carried out using numerical simulationtools (CFD).

Figure 1.1 shows the methodology followed for obtaining and analysingthe optimum shape, and the deliverables (journal articles) derived from themilestones reached. Initially, the conventional building shape (prismatic) isanalysed, and the adequate positions for dierent kinds of wind turbines areproposed. A curved roof is also simulated with validation purposes. The

1

2 Chapter 1. Introduction

compatibility of both photovoltaic-solar and wind energies is also analysedfor a conventional at roof. This compatibility is analysed for both a wind-tunnel reduced scale model and a full-scale building, and some scaling issuesare observed and reported.

Figure 1.1: Diagram of the methodology (milestones) followed for obtainingand analysing an optimum building-roof shape for the urban wind energyexploitation. Deliverables: article 1 is Toja-Silva et al. (2015d), article 2 isToja-Silva et al. (2015b), article 3 is Toja-Silva et al. (2015c) and article 4is Toja-Silva et al. (2015a).

The methodology for obtaining the optimum high-rise building roof shapecontinue with the analysis of a full-scale building by carrying out the follow-ing stages:

- Verication of the results of previous building-roof shapes studied atthe literature. The basic shapes that are compared are: at, pitched, shed,vaulted and spheric.

1.3. Why empirical? 3

- Analysis of the inuence of the roof-edge shape on the wind ow. Thistask is carried out by comparing the results obtained for the conventionaledge shape (simple corner) with a railing, a cantilever and a curved edge.

- Analysis of the roof-wall coupling by testing dierent variations of aspherical roof on a high-rise building: spherical roof studied at the litera-ture, spherical roof geometrically integrated with the walls (squared-plant)and spherical roof with a cylindrical wall. The ow behaviour on the roofaccording to the variation of the incident wind direction is commented.

- Analysis of the eect of the building aspect ratio on the ow.The behaviour of the optimum shape previously obtained for an isolated

building is analysed in an urban environment, by investigating the eect ofthe surrounding buildings (with dierent heights) on the wind ow on thetarget building roof.

1.3 Why empirical?

The title of the thesis is Urban wind energy: empirical optimization of high-rise building roof shape for the wind energy exploitation. The question hereis: why the optimization must be empirical?

Optimal design methods involving the solution of an adjoint system ofequations (adjoint method) are often used in Computational Fluid Dynamics(CFD), particularly for aeronautical applications (Giles and Pierce (2000)).The most common use of the adjoint method is shape optimization prob-lems related to the design of airfoils, wings, compressor-turbine blades, etc.The objective of the application of such method is lift maximization, dragminimization, control of ow separation, etc. (Kampolis et al. (2015))

In the present case, the objectives of the optimization are speed-up maxi-mization and the turbulence intensity minimization. Both objectives are notrelated to the building surface but to the surrounding uid eld. This is oneof the reasons why the adjoint method is not used. Additionally, there aremany subjective restrictions to the optimum building shape (aesthetics, fea-sibility, habitability, etc.). Therefore, neither the adjoint method nor otherdeterministic mathematical optimization method known today (Théveninand Janiga (2008)) can be used in the present case. The optimization mustbe based on empirical sensitivity analyses. This empirical optimization iscarried out by means of numerical experimentation with accurately validatedCFD tools.

1.4 Research scope

Urban wind energy is a very large eld of study, and it is necessary todene a limited scope for the investigations. Therefore, the constraints due


to the assumptions done have to be considered. In the following, the globalassumptions (concerning to the general outline) are commented, whereas thespecic assumptions for each task are explained in their respective Chapter.

The most important constraint is that this investigation focuses on thewind ow around buildings, excluding the consideration of the wind tur-bine eect on the ow. Only the available wind resource is obtained, andboth amount and quality of the wind resource are analysed. The wind owaround the building may change due to the presence of the wind turbinebut, nevertheless, the advantages of a building-roof shape with respect tothe others should not be altered. This is, the advantages of a roof shape withrespect to another will remain after considering the wind turbine. Note thatthe objective of this Thesis is to identify the best building-roof shape forthe wind energy exploitation, but not to bring an energy production valuebecause, among other things, it will depend on the dimensions of the realbuilding and on the wind resource in the actual site. It is recommendedfor further investigations the simulation of wind turbines on the optimumroof obtained, in order to analyse the eect of the wind turbine on the ow.Due to the complex geometry involved in such kind of projects, actuatordisk or actuator line wind turbine models can be used. Additionally, a newimmersed boundary method has been developed in a parallel project withinthe framework of this Thesis. This new method has been implemented intoa Direct Numerical Simulation (DNS) code and, in the medium term, it canbe implemented into a LES or RANS code for dealing with complex geome-tries and/or moving boundaries associated to exible wind turbine blades.This immersed boundary method is presented in Annex A.

The wind turbines positioning on the roof is recommended according tothe European Wind Turbine Standards II (Pierik et al. (1999)). The atmo-spheric wind turbulence is one of the main eects causing fatigue damage onwind turbine components (Mouzakis et al. (1999)), and Pierik et al. (1999)stat that when the turbulence intensity (TI) exceeds 15% the fatigue loadson the conventional wind turbines (HAWT) have to be re-evaluated based onthe actual conditions at the site. Therefore, it is assumed in this Thesis thata new concept of Horizontal Axis Wind Turbine (HAWT) or a Vertical AxisWind Turbine (VAWT) should be used in this situation (TI > 0.15). Theterminology in this Thesis for referring to these wind turbines is VAWT, al-though it may include new designs and conceptual HAWT specially designedfor high turbulence environments.

Another very important assumption is a neutrally stratied atmosphericboundary layer (explained in detail in Chapter 2). Other states of the at-mospheric boundary layer befall, but this state is the most frequent whendealing with high wind phenomena. This is, the wind does not use to behigh when the atmospheric boundary layer is not neutrally stratied andvice versa. Unstable atmospheric conditions are associated with thermal

1.5. Justication of this investigation 5

processes (such natural convection) that do not take place with high windconditions. Therefore, it is convenient to consider a neutrally stratied at-mospheric boundary layer from the wind energy exploitation point of view.Additionally, this is the assumption on which almost all wind tunnel testingand most of the CFD simulations in computational wind engineering rely(Blocken (2014b)).

The turbulence modelling and the computational settings are validatedusing wind-tunnel experimental data. The Reynolds number obtained inwind-tunnel experiments is two orders of magnitude lower than the obtainedin full scale buildings. It implies that the similitude constraints are not ade-quately satised. Actually, scaling issues are reported and analysed in Chap-ter 3. However, the research community accept such validations because thelarge amount of the CFD simulations are validated using wind-tunnel ex-perimental data. Nevertheless, full-scale experimental measurements arerecommended as further works in order to conrm the results of the presentinvestigations.

Two-equation steady-state RANS turbulence modelling is used to per-form the CFD simulations. This is deeply discussed and justied in Chapter2. The main reason is that DNS of the wind ow around a real-scaled build-ing geometry is unapproachable, and Large-Eddy Simulation (LES) presentsan agreement with experimental data better than RANS but its computa-tional cost is very high for real-scaled geometries, especially in the case ofthe wind ow around buildings (Franke et al. (2007)).

Regarding the directional sensitivity, the at roof building (with andwithout solar panels) is analysed considering 8 dierent incident wind direc-tions, although most of the attention is focused on the normal-wall direction.The state-of-the art roof shapes and the edges analyses are carried out onlyconsidering an incident wind direction normal to the main plane, accordingto the most advantageous position. This is because it is an intermediatetask. However, the eect of dierent incident wind directions in the mostinteresting shapes is commented. The optimum building-roof shape hasthe same behaviour for all the incident wind directions and, therefore, it isnot necessary to analyse them. The surrounding buildings (for the optimalbuilding-roof shape analysis) can show dierent results for dierent wind di-rections. Since a general pattern is used, the most disadvantageous positionis used for these buildings.

1.5 Justication of this investigation

The HORIZON2020 (European Commission (2015)) in Future Smart Citiesaims to have 20% of electricity produced by renewable sources. This goalimplies the necessity to enhance the wind energy generation, both with large


and small wind turbines. Wind energy drastically reduces carbon emissionsand avoids geo-political risks associated with supply and infrastructure con-straints, as well as energy dependence from other regions.

Large wind turbines are very ecient when they are installed in big windfarms but small wind turbines in the urban environment are still unused,what supposes a waste of an important energy resource (Walker (2011)).Additionally, distributed energy generation (generation at the consumptionsite) oers signicant benets in terms of high energy eciency, lower emis-sion of pollutants, reduced energy dependence and stimulation of the econ-omy (Chicco and Mancarella (2009)). The main reasons of the waste of theurban wind energy resource are the lack of research works related to theresource availability assessment and to a certain lack of societal acceptance.The COST Action TU1304 (WINERCOST (2015)) has as a principal ob-jective to collect the existing expertise on Building-Integrated-Wind EnergyTechnology and to investigate eective adoption methods for enabling theconcept of Smart Future City. The dissemination is focused in particular onthe societal acceptance. One of the most signicant aspects of this lack ofsocietal acceptance is due to the customers disappointment regarding the dif-ference between the expected and the real energy generated. This dierenceoccurs because the performance of the wind turbines are calculated underideal conditions in at terrain, conditions very dierent than the real con-ditions in the urban environment. Another important aspect for the socialacceptance is the visual impact, avoided by considering the wind turbinesduring the architectural design of the buildings.

The buildings sector represents 40% of the European Union (EU) totalenergy consumption. Reducing energy consumption in this area is there-fore a priority under the 20-20-20 objectives on energy eciency (Eu-ropean Commission (2008)). The Directive 2010/31/EU of the EuropeanParliament and of the Council of 19 May 2010 on the energy performanceof buildings (European Union (2010)) contributes to achieving this aim byproposing guiding principles for Member States regarding the energy per-formance of buildings. It implies the setting of minimum requirements forthe design of new buildings. They shall comply with these requirementsand undergo a feasibility study before construction starts, looking at the in-stallation of renewable energy supply systems and other sustainable systems(European Union (2010)).

To the best of the author's knowledge, the only precedent of an exhaus-tive analysis of the most appropriate building shape for the wind energyexploitation on building roofs is the work of Abohela (2012), who studiedsimple geometric roof shapes: at, domed, gabled, pyramidal, barrel vaultedand wedged. Therefore, there is a lack of knowledge about the optimumbuilding shape. One of the aims of this Thesis is to extend studies like theone mentioned above, and to study more complex shapes.

1.6. A review of urban wind energy 7

The buildings aspect ratio is studied in the literature mainly for pollu-tant dispersion (Tong and Leung (2012)) and thermal performance (Inaniciand Demirbilek (2000); Memon et al. (2010)) purposes. There are some il-lustrative estimations of the wind resource (wind energy maps) in real citiessuch Barcelona (Ajuntament de Barcelona (2015)). These maps can bringan estimation of the resource, but they do not bring feasible wind resourcedata for a specic building roof region. Therefore, an additional analysisof the target building must be carried out considering the surroundings.Some authors have analysed a target building considering the surroundingsfor natural ventilation problems. These studies included specic surround-ing buildings for a particular case (van Hoo and Blocken (2010b,a)) and ageneric pattern of surrounding buildings (Ramponi et al. (2015)), as in thepresent case. In the present Thesis, an investigation of the both building as-pect ratio and surrounding buildings eects for the optimum shape obtainedis presented.

1.6 A review of urban wind energy

The largest amount of the wind energy power growth comes from at-terraininstallations. However, the urban environment has a great potential for windpower that has not been harnessed (Walker (2011)). In urban areas, there isa multiplication factor of the wind speed because of the presence of buildings,but the turbulence intensity and the multidirectionality severely increase,which is an aspect that requires special attention (Grautho (19901991);Ledo et al. (2011); Lu and Ip (2009); Bahaj et al. (2007)). Additionally,these installations increase the protability of the external surfaces, i.e., theroof and the walls, which currently serve only to enclose the building.

Another advantage of exploiting wind energy in urban environments isits proximity to the consumption points (distributed electric power genera-tion) that entails signicant benets in terms of high energy eciency, loweremissions (of pollutants), reduced energy dependence and stimulation of theeconomy (Chicco and Mancarella (2009)). The optimization of distributedgeneration involves voltage prole improvements, the reduction of electricenergy ow in power lines (with the associated reduction of energy lossesin power lines and electric devices), and the increase of the energy sourceavailability (El-Ela et al. (2010)). The reduction of greenhouse gas emissionsis another signicant factor (Ackermann et al. (2001)).

Water consumption, a limited resource in some regions, is reduced withthe exploitation of wind power. Table 1.1 shows a comparison of waterconsumption associated with various energy technologies.

Despite the great positive impact of wind power, this energy source hasdisadvantages. One of the shortcomings is the visual impact. However,


Technology Liters/kWhNuclear 2.30Coal 1.90Oil 1.60Combined cycle gas 0.95Wind 0.004Solar 0.110

Table 1.1: Water consumption of various energy technologies (Saidur et al.(2011)).

urban buildings and their auxiliary facilities (e.g., chimneys and aerials)share the visual impact with the wind turbines, minimising it. Additionally,the wind generators can be architecturally integrated.

Noise emissions, both audible and infrasound, are a signicant environ-mental factor to consider. Most of the noise pollution comes from conversionand generation machinery, although the blades of horizontal-axis wind tur-bines (HAWT (Horizontal-Axis Wind Turbine)) also cause noise when theyinteract with the tower structure, especially with leeward working condi-tions (Grautho (19901991)). At high wind velocities, the noise due to theforced circulation of the wind around the building and its associated facili-ties is higher than the noise generated by the wind turbine (Pantazopoulou(2009)), gure 1.2.

Figure 1.2: Example of sound levels vs. wind speed for small wind turbines(Pantazopoulou (2009)).


Wind-powered generators also generate infrasound (with frequencies above16 Hz) and low frequency vibrations that can be transmitted to the buildingstructure. These vibrations can be tolerated by industrial buildings, butthey can cause problems in residential buildings (Grautho (19901991)).This aspect highly varies depending on both the generator and the buildingcharacteristics, and it must be analysed case by case.

The impact of wind turbines on birds is very important in at-terrainwind facilities (Saidur et al. (2011); Bansal et al. (2002)), but its reper-cussions are smaller in urban environments because of other anthropogenicfactors that have a greater impact.

Wind power can also aect TV and radio reception (Saidur et al. (2011);Bansal et al. (2002); Dabis and Chignell (1999)). This is due to the periodicmodulation of the electromagnetic elds by means of reection, absorptionand dispersion by the blades (Saidur et al. (2011)). In urban environments,this impact is lower because of the building dimensions, which are usuallylarger than wind turbines. Any mobile or stationary structure generates in-terference with electromagnetic signals (Bansal et al. (2002)). However, boththe low power and size of urban wind turbines lessen this impact becausethe intensity of the interference has a direct relationship with the obstaclesize (Dabis and Chignell (1999)).

Following Grautho (19901991), mechanical safety is also a fundamen-tal aspect to consider. For each wind turbine, an analysis of the resistance tofatigue of both the structural (including the building structure) and mobilecomponents (especially the blades) must be conducted. The detachmentof a blade (or a part of it) can cause a very serious accident because ofthe substantial momentum. However, the probability of a blade breaking,striking a person and causing injuries (independent of the distance it cov-ers) is extremely low, and the author did not advise establishing a safetyperimeter around the wind turbine outside of the facility. Grautho (19901991) advises establishing a safety perimeter only in the case of hazardousindustries.

1.6.1 A basic concept of the wind ow on building roofs

As a prelude of the more detailed review of building aerodynamics done inChapter 2 (Section 2.4), a qualitative 2D simulation of the wind circula-tion around a vertical section of a long-short building is conducted usingthe computational uid dynamics software Ansys Fluent-Workbench (usingURANS (Unsteady Reynolds-Averaged Navier-Stokes)), in order to com-ment the inuence of the multidirectional urban wind on the dierent typesof wind turbines. A at roof is chosen since, according to Ledo et al. (2011),the power density available in a at roof is the highest of the most commonroof types (pitched, pyramidal, etc.). A concentration factor of the wind is


caused by the building shape, and it can increase the local mean velocityof the wind from 1.5 to 2 times and the power density 3-8 times in certainzones of the building roof (Lu and Ip (2009)).

Figure 1.3 shows a diagram of the simulation case. The geometry istested for homogeneous incident wind velocities (U) of 1, 2, 4 and 10 m/s.Standard values are used for both air density (ρ) and viscosity (µ). Tovalidate the results, the central length of a symmetric building with a length(L) much larger than its height (H), or L >>> H, must be considered,as shown in gure 1.3. In the urban environment, the turbulence intensityand the multidirectional character of the wind are more important than theincident velocity.

Figure 1.3: Diagram of the simulation case (left) and a symmetric build-ing with a large length with respect to its height (right). The simulationcomprises the central length of the building.

Figure 1.4 shows instantaneous velocity maps obtained for incident windvelocities of 1, 2, 4 and 10 m/s. The simulation results show that the airow is highly unstable and multidirectional. A local intensication factor isclearly observed close to the building surfaces that can multiply the incidentwind velocity by 6 in certain zones.

A vortex is formed on the building roof that is very sensitive to theincident velocity variation and is clearly dened for lower incident velocities.For higher incident velocities, both dragging and dispersion of this vortexare observed. Above approximately 2 m/s, the vortices on the roof areprojected upward. Likewise, a vortex appears in front of the upstream wallof the building.

Results obtained in other studies such as those from Ledo et al. (2011),Lu and Ip (2009), Abohela et al. (2013) or Watson (2009) validate the resultsof this simulation. A stable atmosphere was assumed in these simulations(Ledo et al. (2011); Lu and Ip (2009); Abohela et al. (2013); Watson (2009)),although additional strong disturbances appear in actual cases. In the highlyvariable conditions of the actual urban wind, with sudden changes in boththe direction and the velocity in a very short time, the turbulence develop-ment is high. This is one of the reasons why the qualitative analysis of thewind turbine behaviour under urban wind conditions is of great interest.


Figure 1.4: Instantaneous velocity (m/s) maps obtained in the simulationfor incident wind velocities of 1, 2, 4 and 10 m/s (from left to right and fromthe top to the bottom).

To analyse the multidirectional wind conditions that the turbines aresubjected to on a building roof, the turbine sections are superimposed onthe velocity eld obtained from the simulation. To obtain a clearer graphicrepresentation, the map of the velocity distribution for an incident windvelocity of 1 m/s is used because the vortex on the building roof is clearlydened. Analogous conclusions are obtained with other conditions (velocityand direction) of the incident wind.

1.6.2 Wind energy exploitation in large structures

Large structures (such as bridges and oil platforms) can be considered asintermediate applications between at terrain and the urban environment.That is, the structure disturbs the air ow although the external environmentcan be at terrain. Oppenheim (2004) describes a representative exampleof wind turbine integration into a structure, specically the Bolte Bridge inMelbourne (Australia). This study (Oppenheim (2004)) shows the resultsof the analysis of three options:


i) The rst option is a vertical-axis wind turbine (VAWT) with a ca-pacity of 0.6 MW installed between two columns of the bridge structure(gure 1.5a). According to Oppenheim, the main advantage of the VAWTis aesthetic. VAWT within this power range present considerable technicaldiculties, and they are not produced on a commercial scale. Oppenheim(2004) estimates that this turbine can generate 2 GWh/year and reduce CO2

emissions by 3000 t/year.ii) The second option is a diuser-augmented wind turbine (DAWT), also

installed between two columns of the structure (gure 1.5b). According toOppenheim (2004), this option is also aesthetically attractive, but it presentstechnical diculties because of the impossibility of changing the direction.The power generated by this turbine is unacceptably low because of the xeddirection of the rotor (Oppenheim (2004)).

iii) The third option is a horizontal-axis wind turbine (HAWT) with acapacity of 2 MW installed above the bridge structure (gure 1.5c). Thisoption is the most technically viable, and the power generated is the highestof the three options, estimated to be 8 GWh/year, the equivalent to 10,500t/year of CO2 emissions saved or 210,000 t in the 20 years of operation ofthe wind turbine. This proposal is also economically feasible, with a returnperiod of 8-9 years and a prot in the 20 years of operation of 10 milliondollars (Oppenheim (2004)).

(a) VAWT. (b) DAWT. (c) HAWT.

Figure 1.5: Wind turbines at the Bolte Bridge in Melbourne (Australia).(Oppenheim (2004))

The case of the wind energy exploitation with large structures is simi-


lar to at-terrain applications regarding wind characteristics. Hence, theHAWT installation is advantageous because of the higher power coecient(performance) under unidirectional wind conditions.

1.6.3 Wind energy exploitation in buildings

As explained above, the wind has a signicant irregularity (undergoing aconcentration eect in certain zones) and high-intensity turbulence in ur-ban environments. With these considerations, the previous studies thatassumed at terrain do not apply. This presents an opportunity for innova-tion and development because innovative alternatives are required for windenergy exploitation in high building density zones. Several authors suchas Dayan (2006) and Mertens (2002) mention the suitability of the VAWTin this environment because of its higher eciency under turbulent windconditions (Oppenheim (2004); Dayan (2006); Mertens (2002); Holdsworth(2009a,b,c)). The main alternatives for wind energy exploitation in urbansettings are analysed in the following.

1.6.3.1 Building-augmented wind turbines (BAWT)

Mertens (2002) describes the advantages of the architectural integration ofwind turbines into buildings, showing how the building can be designedto generate a multiplication factor of the wind to enhance wind energyexploitation. These are referred to as building-augmented wind turbines(BAWT (Building-Augmented Wind Turbine)). Although the strict mean-ing of this expression covers several methods of building wind exploitation,the most representative sense is that in which the wind turbines are inte-grated into the building morphology. The main advantages are the aestheticfactor and the wind power concentration. In contrast, the single directionof both the wind concentration conguration and the wind turbine (direc-tion consistent with town-planning criteria) causes substantial waste whenthe wind direction diers from that of the design. The high cost is also adrawback.

Stankovic et al. (2009) presents a review of the urban wind energy wherethe last innovative designs of building integrated wind energy exploitationsystems are shown. These buildings were specically designed in order toincrease the wind speed in certain regions for the wind energy harvesting.One physical case of BAWT is the rst skyscraper with integrated windturbines, the Bahrain World Trade Center (see gure 1.6a). Three horizontalaxis wind turbines (HAWT) are placed between two buildings. Althoughthe buildings are designed in such manner that the wind is always normal tothe HAWT plane, the system has some technical problems due to vibrationsinduced by the turbulence to the HAWT. Additionally, the energy harvested


can be increased a 15-30% by changing the position of the buildings (TU/e(2014)). That shows the necessity of an eective research in this eld. Theproject WEB (Campbell et al. (2001)) analyzes a conguration similar to theBahrain WTC, aerodynamically improved (see gure 1.6b). There is also aphysical case of wind energy harvesting through building passages, the PearlRiver Tower Frechette and Gilchrist (2008) in Guangzhou (China), shownin gure 1.6c. The architects state that a model of the building has beentested in a wind tunnel, but there are not any publication with the results.A similar case is the Strata Tower in London (see gure 1.6d), where thewind turbines are integrated in the roof rather than in the building body.

(a) Bahrain WTC. (b) WEB. (c) Pearl River Tower. (d) Strata Tower.

Figure 1.6: Examples of building-augmented wind turbines (BAWT).

1.6.3.2 Horizontal-axis wind turbines (HAWT)

HAWT (gure 1.7) have lower performance under high-turbulence conditions(Oppenheim (2004); Dayan (2006); Mertens (2002); Holdsworth (2009a,b,c);Eriksson et al. (2008b)), and they are mainly recommended for very openareas or isolated buildings (Syngellakis et al. (2006)). The high variability ofthe wind direction in the urban environment is an additional disadvantagebecause with lower wind velocities, the start-up time is greater (Wright andWood (2004)). The wind turbine must be installed at a greater height asits swept area increases to reduce the exposure to turbulence (Syngellakis etal. (2006)). Consequently, this kind of wind turbine is more appropriate forinstallations on large structures (as mentioned above) or in zones with lowbuilding densities.

Using wind diusers, HAWT can operate with lower wind velocities, andthey can better resist turbulence (Wang et al. (2008b,a)). This type ofwind turbine is called a diuser-augmented wind turbine (DAWT (Diuser-Augmented Wind Turbine)). Wang et al. (2008b,a) comment that by using


Figure 1.11: Power coecients CP vs. the specic velocity λ for threeturbines: HAWT, Darrieus and H-rotor (Eriksson et al. (2008a)).

H-rotor Darrieus HAWTBlade prole Simple Complicated ComplicatedYaw mechanism needed No No YesPitch mechanism possible Yes No YesTower Yes No YesGuy wires Optional Yes NoNoise Low Moderate HighBlade area Moderate Large SmallGenerator position On ground On ground On top of towerBlade load Moderate Low HighSelf-starting No No YesTower interference Small Small LargeFoundation Moderate Simple ExtensiveOverall structure Simple Simple Complicated

Table 1.2: Water consumption of various energy technologies (Saidur et al.(2011)).

and expensive (Kirke and Lazauskas (2011)). This study concludes that thelower solidity of the blades increases both peak eciency and tip-speed ratio,as shown in gure 1.17.

Sharpe and Proven (2010) propose a Darrieus wind turbine with exibleblades. This wind turbine can be installed either vertically or horizontally,as shown in gure 1.18. The streamlined support structure performs thefunction of wind concentration (Watson (2009); Sharpe and Proven (2010)).


Figure 1.14: Power coecients Cp (in %) vs. the specic velocity λ for threetypes of blades, Giromill wind turbine with four blades (El-Samanoudy etal. (2010)).

D'Alessandro et al. (2010) conducted a study of the Savonius wind tur-bine. Compared with other wind turbines, it has a lower power coecient(gure 1.21), although it has advantages in that it is self-starting and doesnot have to change direction (omnidirectional) (D'Alessandro et al. (2010)).Another great advantage is that it is extremely simple to construct, andhence it can be extremely low-cost (recycled containers, pipes or barrels canbe used in its construction). This feature would be very attractive in zoneswith extremely low economic resources (gure 1.22). The possibility of usingrecycled materials confers to this technology a highly sustainable character.

The modications of Savonius wind turbines that increase the powercoecient have an important role, especially the variation of the number ofblades, the interposition of obstacles and the helical shape (D'Alessandro etal. (2010); Mohamed et al. (2010)).

Mohamed et al. (2010) present an analysis of Savonius wind turbineswith two and three blades and with a deector sheet (gure 1.22). Theresults show that the deector sheet installation increases the wind turbineeciency considerably (gure 1.23) and that the power coecient is higherin the case of the rotor with two blades.

Kamoji et al. (2009) conducted a study of the helical Savonius wind tur-bine (gures 1.24 and 1.25) show that both the power and torque coecientsare slightly higher in the helical design than in the traditional Savonius un-


Figure 1.17: Power coecient for various solidities, helical Darrieus windturbine (Kirke and Lazauskas (2011)).

gles (gure 1.25). The main disadvantage is the higher complexity of theconstruction, which implies a cost increase (Mohamed et al. (2010)).

As mentioned previously, the low coecient of power of the Savoniusrotor is the most important disadvantage; hence, the improvement of thisfactor is important to the development of this technology (D'Alessandro etal. (2010); Mohamed et al. (2010)). In Table 1.3, a summary of the mainimprovements to increase the performance of the Savonius rotor is shown.

Design modication Gain CommentsHelical rotors Improvement of static torque Complex design and high costDeector plate 20% No further details since 1992Twisted-blade 27% relative Complex design and high costGuide-box tunnel 50% (3 blades) Complex designModied Savonius 60% in static torque Expected vibration problemGuide vanes Depends on wind speed Problems for large tip-speedObstacle plate 15% on peak value Small parameter space used

Table 1.3: Improvements to increase the performance of Savonius wind tur-bines (D'Alessandro et al. (2010)).

Müller et al. (2009) propose a vertical-axis, resistance-type wind turbine


Figure 1.21: Power coecient Cp of the Savonius wind turbine (D'Alessandroet al. (2010)).

Figure 1.22: Extremely low-cost Savonius wind turbine (left), and a diagramof a Savonius wind turbine with two blades and a deector sheet (right)(Mohamed et al. (2010)).

wind turbine can only operate with a perpendicular wind direction.Figure 1.30 shows the superposition of a ducted wind turbine on the

edge of the building roof for an incident velocity of 1 m/s. The representedconditions are appropriate for turbine operation, although this kind of windturbine can only operate with a perpendicular wind direction, as in thesimulation.

Bibliography notes 27

Figure 1.25: Coecients of power, torque and static torque for a two-bladeSavonius wind turbine with both helical and conventional blades (Kamoji etal. (2009)).


Figure 1.28: Ducted wind turbine on the edge of the building roof (Grantet al. (2008)).

Figure 1.29: Power coecient vs. the dierential pressure coecient of aducted wind turbine for various values of the speed coecient (Grant et al.(2008)).

Chapter 2

Computational windengineering applied to buildingaerodynamics

All models are wrong, but some modelsare useful.

George Edward Pelham Box

2.1 Basic aspects

A very interesting and instructive introduction to uid mechanics, compu-tational wind engineering and its application to building aerodynamics canbe found in Blocken (2014b).

According to Anderson (1995), Computational Fluid Dynamics (CFD) isthe art of replacing the integrals or the partial derivatives (as the case maybe) in the Navier-Stokes equations by discretized algebraic forms, which inturn are solved to obtain numbers for the ow eld values at discrete pointsin time and/or space. It is important to mention that CFD is a tool thatallows to solve ow problems that do not have known analytical solutionsand cannot be solved in any other way (Blocken (2014b)). Actually, one ofthe Millennium Problems (Clay Mathematics Institute (2015)) consists intodemonstrate that a general analytical solution to the Navier-Stokes equa-tions exists, and that such solution is unique. The governing equations ofthe ow (Navier-Stokes equations) are explained in Section 2.3. The advan-tages of using CFD are: relatively inexpensive and fast, provides completeinformation in the whole domain, allows parametric studies (very importantin the present case), no similarity constraints and allows numerical experi-ments. On the other hand, the disadvantages are: accuracy and reliability

31

32 Chapter 2. CWE applied to building aerodynamics

are concerns, results are very sensitive to a large number of congurationparameters and verication and validation are required.

There are just few examples of laminar ows involved in real processes, asthe oil ow within a bearing (Couette ow). Therefore, the laminar ows areoften used with academical proposes. The turbulence is almost ubiquitous inboth natural and articial processes, from the movement of the atmosphericair or clouds to the ow within pipes or around airfoils. Therefore, theunderstanding of the turbulence mechanisms, and how to control it, has agreat importance in aerospace, energy, chemical engineering, environmentalsciences and the rest of uid dynamics related elds, including buildingaerodynamics, the topic of the present thesis.

The rst person that observed and described the turbulence phenom-ena was probably Leonardo da Vinci (gure 2.1), and many famous scien-tists have worked on the problem of turbulence (Leonhard Euler, HermannLudwig Ferdinand von Helmholtz, William Thompson (Lord Kelvin), LordRayleigh, Andrey Nikolayevich Kolmogorov, etc.).

A very important similarity parameter for the ow characterization isthe Reynolds (Re) number (Rott (1990)), that expresses the ratio of inertial(resistant to change or motion) forces to viscous (heavy and gluey) forces(National Aeronautics & Space Administration (2015)). The Reynolds num-ber is

Re =ρUL

µ≡ UL

ν, (2.1)

where ρ is the density, µ viscosity, ν kinematic viscosity and U and L arethe characteristic velocity and length of the problem, respectively.

When the Reynolds number increases, the laminar ow becomes tur-bulent going through a transitional regime, because of instabilities appear-ing. From the mathematical point of view, these instabilities appear in theNavier-Stokes equations, mainly due to the nonlinear terms, in the form ofbifurcations. This is, in a bifurcation point a very small change at the inputvariables can leads to completely dierent results. When the critical thresh-old is crossed, small disturbances in the ow eld tend to grow at any pointwith respect to time (absolute instability) or at a uid particle with respectto its movement within the ow (convective instability) (Biswas and Eswaran(2010)). A good example of the transition from laminar to turbulent owcan be appreciated by the observing the cigarette smoke (gure 2.2). Fig-ure 2.3 shows an example of a transitional ow, ow over an obstacle insidea channel with a Reynolds number of 800. Additionally, gure 2.4 show adiagram of the transition process in a boundary layer, and the characteristicsublayers (viscous sublayer, buer layer and turbulent region).

According to Tennekes and Lumley (1972), the main characteristics ofthe turbulent ows are:

2.1. Basic aspects 33

Figure 2.1: Representation of turbulence in water ows, Leonardo da Vinci1508-1509 (Werne (2015)).

Re = 800


turbulence is essentially dissipative. The kinetic energy is converted intointernal energy by viscous shear stress. Therefore, a continuous supply ofenergy is required to sustain the turbulent ow. Otherwise, the turbulencedecays rapidly.

- Continuum. Turbulence is a continuum phenomenon governed by theuid mechanics equations, where even the smallest eddy scales are far largerthan any molecular scale.

In Computational Wind Engineering (CWE), and especially in buildingaerodynamics, the ow is always turbulent. A comprehensive review ofCWE, including history and future perspectives, can be found in Blocken(2014a). The wind ow around buildings is very complex. Murakami (1998)outlines the main diculties in CWE:

- The high Reynolds numbers that require high grid resolutions, espe-cially in near-wall regions as well as accurate wall functions.

- The complex nature of the ow eld with impingement, separation andvortex shedding.

- The numerical diculties associated with the ow at sharp edges, withconsequences for the discretization schemes.

- The inow (and outow) boundary conditions.

2.2 The atmospheric boundary layer

According to the World Meteorological Organization (2015), the Atmo-spheric Boundary Layer (ABL) is the portion of the atmosphere where theEarth's surface (land or water) has a direct inuence. It represents aroundthe 10% of the troposphere (100 m - 3 km). Figure 2.5 shows a diagram ofthe whole atmosphere.

The ABL is very complex, and it is continuously investigated. A deepdescription of the ABL can be found at the literature (Garratt (1994);Kaimal and Finnigan (1994); Stull (1988); Panofsky and Dutton (1984);Plate (1982); Whiteman (2000)). The ABL is characterized by the turbu-lent nature of the ow that reinforces the mixing mechanisms that tends tohomogenize the properties of the uid ow (wind). At the top of the ABL(free atmosphere), the wind is approximately laminar (geostrophic wind).At the ground surface, the wind speed reduces to zero. Therefore, it takesplace a wind shear that dynamically produces turbulence. Table 2.1 presentsthe main dierences between the ABL and the free atmosphere.

The scales of atmospheric motion range from the short length and timeto the decadal and planetary-scale circulations. Figure 2.6 shows some me-teorological phenomena and their respective time and length scale, and themost usual classication of the meteorogical scales:

- Synoptic scale (L > 2000 km): Scale of largest cyclones.

2.2. The atmospheric boundary layer 37

Figure 2.5: Diagram of the layers of Earth's atmosphere, showing heights ofcharacteristic atmospheric phenomena (Encyclopædia Britannica (2015)).

Atmospheric boundary layer Free atmosphereDepth Variable 100 m - 3 km Less variable 8 - 18 kmMean wind speed Near-logarithmic in surface layer Nearly geostrophicTurbulence Present over entire depth Laminar to low/sporadic turbulenceVertical transport Turbulence dominated Mean wind dominated, slow vertical transportDispersion Rapid vertical and horizontal Molecular diusion, rapid horizontal transport

Table 2.1: Main dierences between the ABL and the free atmosphere(Blocken (2014b)).

- Mesoscale (2 km < L < 2000 km): Weather systems, mesocyclones,orographic eects, land-sea breezes, cloud structures, etc.

- Microscale (L < 2 - 10 km): Mixing and dilution, surface heat and masstransfer, near-ground turbulence eects and building aerodynamics. This isthe meteorological scale considered at all the investigations carried out atthe present thesis.

When there is a dierence between the temperature of the surface andthe temperature of the air, a heat ux is created within the ABL. Theseuxes cause three general states of the ABL: unstable, stable and neutral.In the unstable ABL, the temperature of the surface is higher than the tem-perature of the air. Buoyancy forces compound the mechanical eects andintense turbulence is generated. Some coherent structures can be frequently


Figure 2.6: Diagram of the meteorological phenomena and their respectivetime and length scale, and the most usual classication of the meteorogicalscales (Geostationary Operational Environmental Satellites R Series (2015)).

identied within the unstable ABL, such as convective cells or warm parcels(convective boundary layer, CBL). The unstable ABL occurs generally dur-ing the day when the solar heating is important. In the stable ABL, thetemperature of the surface is lower than the temperature of the air. Thethermal eects in that case counteract the motions induced by mechanicalturbulence. The wind is generally weak near the surface and a maximumis often found at the top of the temperature inversion zone. The stableABL usually occurs during the night (nocturnal boundary layer, NBL). Fig-ure 2.7 shows a diagram of the time-evolution of the atmosphere. In theneutral ABL, the temperature of the surface is equal to the temperature ofthe air, and the vertical wind follows a logarithmic prole. Above it, theCoriolis force becomes important and the wind speed increases to becomeequal to the geostrophic wind in the free atmosphere, both in direction and

U =U∗κ

ln

(z + z0z0

),

k =U2∗√Cµ

ε =U3∗

κ(z + z0),


where κ is von Karman's constant, z0 is the roughness length, Uref is thereference height and zref is the reference height. These are the referencevalues in order to calculate U∗ by using Eq. (2.2).

2.3 Governing equations of the ow and turbulence

modeling

The Direct Numerical Simulation (DNS) of the wind ow around a real-scaled building geometry is unapproachable. Therefore, some simplifying as-sumptions must be made. There are two main numerical approaches of owmodelling: Large-Eddy Simulation (LES) and Reynolds Averaged Navier-Stokes Equations (RANS). The LES consists in the modelling of the nearwall ow by using space ltered equations (Pope (2000); Sagaut (2006)).LES presents an agreement with experimental data better than RANS, butits computational cost is very high for real-scaled geometries, especially inthe case of the wind ow around buildings (Franke et al. (2007)). Theother main ow modelling technique consists in the solution of the RANSequations. Currently, state-of-the-art RANS modelling involves the use oftwo-equation closures for the purposes of wind energy resource assessmentover (moderately) complex terrain. A recent comparison of models for thebenchmark case of Bolund can be found in Sumner (2012).

The steady-state RANS equations for an incompressible uid withoutbody forces can be written as (Cheng et al. (2003))

∂ui∂xi

= 0 (2.5)

for the mass conservation, and for the momentum conservation

∂(uiuj)

∂xj= −1

ρ

∂p

∂xi+

∂

∂xj

(ν∂ui∂xj− u′iu′j

), (2.6)

where p is the mean pressure and ρ and ν are the uid density and kinematicviscosity, respectively. The Reynolds stresses (u′iu

′j) must be prescribed in

terms of the mean ow values. Considering the Boussinesq linear isotropiceddy-viscosity hypothesis (linear relationship between the turbulent stressesand the mean velocity gradients), the statistical turbulence closure modelyields

−u′iu′j = 2νtSij −2

3kδij , (2.7)

where

Sij =1

2

(∂ui∂xj

+∂uj∂xi

)(2.8)

2.3. Governing equations of the ow and turbulence modeling 41

is the strain rate tensor, νt is the kinematic eddy viscosity, δij is the Kro-necker Delta function and k = 1

2u′iu′i is the turbulent kinetic energy. The

equations for the turbulent kinetic energy and the turbulence dissipation rate(ε) are necessary to solve all the unknowns. These equations, in steady-stateform without considering buoyancy, are

∂(ujk)

∂xj=

∂

∂xj

[(ν +

νtσk

)∂k

∂xj

]+ Pk − ε (2.9)

and

∂(ujε)

∂xj=

∂

∂xj

[(ν +

νtσε

)∂ε

∂xj

]+ Cε1

ε

kPk − Cε2

ε2

k, (2.10)

where Pk is the production of k, and σk and σε (Prandtl numbers), Cε1 andCε2 are closure constants. The production of k in the standard k− ε model(SKE) is

Pk = νtS2, (2.11)

where S is the modulus of the rate of strain tensor and

νt = Cµk2

ε, (2.12)

where Cµ is the proportional number, another constant parameter.There are some modications of the SKE model, developed to improve

the accuracy of the results, especially the overestimation of the turbulentkinetic energy in the impinging region of blu bodies. Launder and Kato(1993) (KL model) propose the calculation of Pk as a function of the strainrate scale (S) and the vorticity scale (Ω),

Pk = νtSΩ. (2.13)

However, the KL model has a mathematical inconsistency in the mod-elling of −u′iu′j and Pk, between Eqs. (2.7) and (2.13). Furthermore, the KLmodel overestimates Pk (comparing with SKE) when Ω/S > 1. To correctthese problems, Tsuchiya et al. (1997) introduced the Murakami-Mochida-Kondo (MMK) model that adds a modication to the expression for νt,

νt =Cµk

2Ω

εS, (2.14)

only applicable when Ω/S < 1. Otherwise, Eq. (2.12) is applicable, as inthe SKE model.


Durbin (1996) proposed another k−ε modication to correct the k over-estimation in the SKE model by calculating νt related to the turbulencevelocity time scale (T ),

νt = CµkT. (2.15)

Since in the SKE model k/ε is adopted for T , the proposed bound onthe time scale of Durbin (1996) is

T = min(TSKE , TD), (2.16)

where

TSKE = k/ε (2.17)

and

TD =1

3CµS

√3

2. (2.18)

There are variations of the TD variable in the Durbin model. Tominagaet al. (2008) use

TD =1

CµS√

3. (2.19)

According to Durbin (1996), Eq. (2.18) can be modied to obtain agree-ment with experimental data. In the present case, we have empirically foundthe following expression (explained in detail in Section 5.1.2.1) to obtainagreement of the recirculation distance on the building roof with the exper-imental data:

TD =32

45CµS. (2.20)

Yap (1987) also proposed a correction to the k − ε model. It consists inthe addition of a source term Sε to the right hand side of epsilon equation,Eq. (2.10). The added source term is

Sε = 0.83ε2

k

(k1.5

εle− 1

)(k1.5

εle

)2

, (2.21)

where

le = C−0.75µ κyn, (2.22)

2.3. Governing equations of the ow and turbulence modeling 43

where yn is the normal distance to the nearest wall. Yap's correction isusually applied together with the KL model (called KLY) (Kato and Launder(1993)).

Yakhot and Smith (1992) developed the k − ε Re-Normalisation Group(RNG) model, also by adding a term (<) to the right hand side of Eq. (2.10),

< =Cµη

3(

1− ηη0

)1 + βη3

ε2

k, (2.23)

where η = Sk/ε and the rest of the parameters are constants of the model(Yakhot and Smith (1992); Kim and Baik (2004)).

Besides the k−ε models described previously, we also consider the k−ωshear stress transport (SST) (Menter (1994)) model. This model follows thek−ω approach at the near-wall region, and switches to the k− ε away fromthe surface. The steady state transport equations of the k − ω SST modelwithout source terms are

∂(ρujk)

∂xj=

∂

∂xj

(Γk

∂k

∂xj

)+ Pk − Yk (2.24)

and

∂(ρujω)

∂xj=

∂

∂xj

(Γω

∂ω

∂xj

)+ Pω − Yω +Dω, (2.25)

where ω is the specic dissipation, Γk and Γω are the eective diusivitiesof k and ω, respectively, Pk is the generation of k due to mean velocitygradients, Pω is the generation of ω, Yk and Yω are the dissipations of k andω, respectively, and Dω is the cross-diusion term.

Additionally to the linear models described above, we also consider theNonlinear k − ε Shih (Shih et al. (1993)) model. The non-linear eddy vis-cosity models, in general, have been developed to improve the Boussinesqapproximation adopted in the linear eddy viscosity turbulence models keep-ing the stability and applicability conditions. The Nonlinear k − ε Shihmodel consists in the addition of the quadratic term to Eq. (2.7). Thequadratic Reynolds stresses equation yields

−u′iu′j = 2νtSij −2

3kδij − C1νt

k

ε

(SikSkj −

1

3SklSklδij

), (2.26)

where C1 is an empirical coecient.


2.4 Building aerodynamics

An extensive review on urban aerodynamics can be found in Aynsley et al.(2011). They introduce historic considerations: from the Egyptians wherethe houses for workers shielded the houses for ocials from hot desert winds(Aynsley et al. (1977)) and Romans (Vitruvius (1960)) to more modern citiesas Buenos Aires, the new towns in the Industrial Revolution in Sweden andNew York (Olgyay (1992)) where the comfort of all the citizens was pur-sued. Contemporary considerations in wind engineering are also explained:urban hurricane and tornado shelters (Cochran and Peterka (1999)), pedes-trian level winds (Koppes (1970); Irwin (1981); Stathopoulos et al. (1992)),urban design for breeze penetration (Comrie (2000); Saitoh et al. (1996)),winter wind shielding (Stathopoulos et al. (1994)), natural ventilation of low(Lee (1998)) and high-rise buildings (Potangaroa (2001)), dispersion of ur-ban airborne pollutants using both boundary layer wind tunnels (Changnon(1992)) and CFD tools (Johnson (1999)) and, nally, urban wind power isvery briey commented. Some issues that arise when integrating wind tur-bines into buildings are commented: noise and vibration from turbines, needto direct wind from varying directions, accurate location of turbines to catchhigher wind speeds and aesthetics.

Hanna and Britter (2002) explain the wind ow and the gas transportand dispersion at industrial and urban sites. The methods for characterizingthe eects of the surface roughness obstacles on the ow are explained indetail. Three dierent regimes of wind ow over an obstacle array are pre-sented according to the proportions of the roughness elements, as it is shownin gure 2.8. According to this classication, the surrounding buildings (gen-eral pattern for the representation of an urban environment) considered inChapter 4 are in wake interference or skimming ow depending on theirheight in each case, avoiding the case of isolated roughness ow because theisolated building is extensively studied previously.

As stated above, the present Thesis aims to identify the most adequatebasic geometrical shapes that maximize the speed-up and minimize the tur-bulence intensity on high-rise building roofs, for the purpose of urban windenergy exploitation. Craighead (2009) presents a detailed denition and de-scription of high-rise buildings, that are classied as buildings higher than23-30 m or 5-10 stories. High-rise buildings are considered because theirpotential for the wind energy exploitation is higher, since the wind resourceavailability increases with the height according to the logarithmic velocitywind prole explained in Section 2.2.

The wind ow around basic prismatic building shapes was studied byseveral researchers (Beranek and van Koten (1979); Martinuzzi and Tropea(1993); Tominaga et al. (2008); Joubert et al. (2015)). Figure 2.9 shows thewind-ow pattern around an isolated building in both 2D and 3D. The re-

2.4. Building aerodynamics 45

Figure 2.8: Schematic diagram showing the three regimes of wind ow overan obstacle array, and the proportions to which each regime applies. (Oke(1988))

circulation on the roof (a very important feature mentioned throughout thisThesis) is shown in gure 2.9a. Figure 2.10 shows the instantaneous vor-tices appearing around a slender prismatic obstacle. Additionally, obliquesincident wind directions were also studied (He and Song (1997); Richards etal. (2007)). The oblique incident wind causes the corner roof vortices shownin gure 2.11. All the recirculations are caused by the pressure dierencebetween the impingement wall (positive) and the roof (negative, specially in


the recirculation regions). Figure 2.12 shows examples of pressure elds inrecirculation regions on the roof.

(a) 2D (Blocken (2014b))

(b) 3D (Beranek and van Koten (1979))

Figure 2.9: Wind-ow pattern around an isolated building in 2D and 3D.Legend: (1) ow over building, (2) oncoming ow, (3) ow from stagnationpoint over building, (4) ow from stagnation point around vertical buildingedges, (5) downow from stagnation point, (6) standing vortex (base vortexor horseshoe vortex), (7) stagnation ow in front of building near groundlevel, (8) corner streams (vortex wrapping around corners), (9) ow aroundbuilding sides at ground level (adding to corner streams), (10) recirculationow behind the building, (11) stagnation region behind building at groundlevel, (12) restored ow direction, (13) large vortices behind building and(16) small vortices in shear layer.

Basic building shapes are simulated in the following (Section 5.1.2.1) for acarefully validation of the turbulence modelling by comparing the simulationresults with wind-tunnel experimental measurements. The rst case is the

2.4. Building aerodynamics 47

Figure 2.10: Instantaneous vortex generated by a slender prismatic obstacle:(a) top view and (b) lateral view. (Joubert et al. (2015))

Figure 2.11: Diagram of the corner roof vortices appearing when the incidentwind direction is oblique to the walls. (Peterka and Cernak (1976))


(a) Pressure distribution around a cube and isosurface vortex struc-tures (Lim et al. (2009)). The blue and dark green colours indicatethree-dimensional contours of positive and negative pressures, withpressure coecient values of 0.06 and -0.9, respectively. The lightgreen contour denotes vortex isocontour.

(b) Mean pressure coecient on the roof surface with an obliqueincident wind (Peterka and Cernak (1976))

Figure 2.12: Examples of pressure elds in recirculation regions on the roof.

2.5. Hardware used for the simulations 49

benchmark case A of the Architectural Institute of Japan (2013). Thisbenchmark case is an isolated building of aspect ratio 1:1:2 placed withinan atmospheric boundary layer, tested in a wind tunnel by Meng and Hibi(1998). Other prestigious researchers (Tominaga et al. (2008); Gousseau etal. (2013)) have used this case for the validation of their simulation toolsand models. The turbulence models that better reproduce the wind ow onthe roof are validated twice over by comparing the simulation results withthose obtained from the wind-tunnel experiment carried out by Ntinas et al.(2014). The geometry of this additional validation consists in a curved-roofbuilding.

2.5 Hardware used for the simulations

The CFD simulations required for the development of this Ph.D. Thesis wereperformed in the Euler supercomputer (Centro de Investigaciones Energé-ticas Medioambientales y Tecnológicas (2015)) at the CIEMAT ResearchCenter. The CFD simulations were usually performed using 64 processors(8 nodes).

The Euler supercomputing system is constituted by a group of calcula-tion nodes organised as a High Performance Cluster (HPC). These calcula-tion nodes are interconnected by means of a high speed Inniband and bya complementary standard gigabit Ethernet. The Inniband net supportsthe intercommunication of the processes that work in a collaborative format dierent nodes simultaneously in MPI processes. Additionally, it bringshigh speed access to the parallel les system. The Ethernet connects thecluster with the local net systems. The users access and the les edition,compilation and submission is carried out using 2 servers organised in load-balancing cluster mode. Another 2 servers organised in high-availabilitycluster mode manage, monitor and control the whole system. The storagesystem is constituted by 6 servers connected to both Ininiband and Ether-net, with a gross disk volume of 60 TB. The management software is Lustre,organised as a parallel les system. The main characteristics of the Eulersupercomputer are:

- Calculation nodes. 144 blades, with these characteristics:

CPU: 2 Xeon 5450 quadcore 3.0 GHz. (8 cores by node = 1152 cores).

RAM: 2 GB by core.

Cache: 3 MB by core.

Disk: 146 GB by node.

Ethernet: double connection gigabit.


Inniband: double connection 4X DDR.

Linpack rpeak: 13.8 Tops.

- Management nodes. 2 nodes in high-availability cluster. Each node:

CPU: 2 Xeon 5355 quadcore 2.66 GHz.

RAM: 2 GB by core.


Disk: 2 x 146 GB by node.



External disk booth: 3TB gross.

- Interactive access nodes. 2 nodes in load-balancing cluster. Each node:


RAM: 2 GB by core.





- Storage. Parallel storage system, Lustre, constituted by 2 metadata serversand 4 data servers. Each one:


RAM: 2 GB by core.





- Disk booth for Lustre:

Metadata: 1 booth DDN EF2915 with 36 x 300GB disks FC. Total = 10.8TB.

2.6. Validation of RANS turbulence models 51

Data: 1 booth DDN S2A9550 with 120 x 500GB disks SATA. Total = 60TB.

- Inniband:

Star connection 4X DDR full non-blocking.

Central commutator: SFS 7024D with 180 active ports (max. 288 ports)local commutators at chassis blades: 18 x Dell Cisco/TopSpin M7000.

- Ethernet:

Local commutators at chassis blades: 18 x Dell PowerConnect M6220. Thesecommutators are interconnected in stack mode of 48 Gbps.

Central commutators: 4 x PowerConnect 6248.

2.6 Validation of RANS turbulence models

As stated above, basic building shapes are simulated for a carefully validationof the turbulence modelling by comparing the simulation results with wind-tunnel experimental measurements. The rst case is the benchmark caseA of the Architectural Institute of Japan (2013). This benchmark case is aat-roof isolated building placed within an atmospheric boundary layer. Theturbulence models that better reproduce the wind ow on the roof in the rstvalidation (at roof) are validated twice over by comparing the simulationresults with those obtained from the wind-tunnel experiment carried out byNtinas et al. (2014). The geometry of this additional validation consistsin a curved-roof building. This section is crucial in order to decide whichturbulence model use for the CFD simulations of the cases of study.

2.6.1 Flat roof building model in wind tunnel

The choice of the turbulence model is a compromise between the accuracyand the computational cost. Since the purpose of computational wind engi-neering (CWE) analysis is to extend the conclusions to real-scale cases, andthe computational cost of LES with real-scale geometries is too expensivenowadays (Franke et al. (2007); Sumner et al. (2010)), there is a necessityof a better parametrisation of turbulence models used in RANS modellingto eectively deal with real-scale cases. In agreement with this, the mainobjective of the present work is to determine the best 2-equation turbulencemodels from the point of view of the urban wind energy exploitation. To dothis, some k − ε and k − ω models are tested performing simulations withthe free, open source CFD software package OpenFOAM (2013). In orderto compare the simulation results with experimental values, the benchmark


case A of the Architectural Institute of Japan (2013) is used. This bench-mark case is an isolated building of aspect ratio 1:1:2 tested in a wind tunnelby Meng and Hibi (1998).

A similar study was undertaken by Tominaga et al. (2008) using bothlinear RANS (KL, MMK and Durbin's revised k−ε) and LES models, and byShao et al. (2012) using non-linear RANS models (Shih, Craft and Ehrhard).Gousseau et al. (2013) and Kono and Kogaki (2013) performed LES simu-lations (using the Smagorinsky model) for the same building studied in thepresent investigation, obtaining better agreement with experimental data athigher computational cost. This is the reason why RANS models (especiallyin combination with the k − ε model) are widely used in industrial appli-cations for complex cases. These previous studies (Tominaga et al. (2008);Shao et al. (2012)) analysed the whole ow (including upstream and down-stream) but were not focussed on the ow behavior on the building rooffrom the point of view of wind energy exploitation. Steady RANS simula-tions are not always in good agreement with experimental results becauseow unsteadiness due to the vortex shedding behind the building is not wellreproduced (Tominaga et al. (2008)). In this work, we test dierent turbu-lence models, focusing on reproducing experimental measurements for bothvelocity and turbulence kinetic energy on the building roof. Therefore, thepresent investigation is aimed at bringing useful information about the ac-curacy of dierent 2-equation turbulence models for the wind energy assess-ment in the dierent regions of the building roof, since dierent 2-equationturbulence models have dierent degrees of reliability under particular owconditions (detachment, reattachment, recirculation, etc.).

2.6.1.1 Description of the case study and simulation details

The case study is the benchmark case A of the Architectural Institute ofJapan (2013). This benchmark case is an isolated building of aspect ratio1:1:2 placed within an atmospheric boundary layer, tested in a wind tunnelby Meng and Hibi (1998). Figure 2.13 shows the geometry of the prob-lem. Other investigations (such Tominaga et al. (2008) and Gousseau etal. (2013)) describe the geometry in dimensionless units, but in the presentinvestigation the real dimensions of the wind tunnel are specied becausethe results dier signicantly with the domain size (especially k) due to thevariation of the Re number (see Chapter 3 for a deeper discussion aboutsimilarity constraints and scaling issues).

We perform the simulations in OpenFOAM (2013). Table 2.2 presentsthe boundary conditions imposed for all the variables at each boundary of thesimulation domain. The inlet proles, used in the wind tunnel experiment ofMeng and Hibi (1998), are shown in Figure 2.14. They are set in OpenFOAMwith the utility setDiscreteFields (2013). The wall functions are standard


Figure 2.13: Diagram of the case of study. All dimensions are in m.

functions of OpenFOAM.

U k ε νt p

Inlet iP iP iP C zGOutlet zG zG zG C fV zeroGround fV zero kqR wF epsilon wF nutk rough wF zGBuilding fV zero kqR wF epsilon wF nutk wF zGSky fV zero kqr wF epsilon wF nutk rough wF zGSides sP sP sP sP sP

Table 2.2: Boundary conditions imposed at each boundary of the domainfollowing Architectural Institute of Japan (2013) and Tominaga et al. (2008).Nomenclature: iP= Inlet prole, zG = zeroGradient, C = Calculated, fV =xedValue, wF = wall function, sP = Symmetry plane.

The steady-state simpleFoam solver for incompressible turbulent ow isused to solve the partial dierential equations. For the spatial discretizationof dierential operators, the Gaussian integration was used with dierent in-terpolation schemes. The 2nd order linear interpolation was applied for Gra-dient terms, the 2nd order upwind interpolation for Divergence terms, whilefor the Laplacian terms the 2nd order linear interpolation was used with ex-plicit non-orthogonal correction (Rákai et al. (2014); Balogh et al. (2012)).Regarding the linear system solvers, generalised geometric-algebraic multi-grid solver (GAMG) with DIC smoother is used for the pressure, and pre-conditioned bi-conjugate gradient solver for asymmetric matrices (PBiCG)with diagonal incomplete LU (DILU) preconditioner is used for the rest of


1 2 3 4 5 6 7U (m/s)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

z (m

)

Exp. inletNum. inlet

(a) U

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7k (m2 /s2 )

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

z (m

)


(b) k

10-2 10-1 100 101 102

ǫ (m2 /s3 )

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

z (m

)


(c) ε

Figure 2.14: Inlet proles: mean streamwise velocity (a), turbulent kineticenergy (b) and turbulent dissipation (c). The points represent the inletproles used at the experiment of Meng and Hibi (1998), and the solid linesare the numerical inlets of the simulations.

variables. Second order accurate numerical schemes (both central dierenc-ing and upwind) must be used at least in order to avoid problems with falsediusion (Rákai et al. (2014); Balogh et al. (2012); Bakker (2015); ANSYS(2015)).

Regarding the mesh, the external domain (inlet, outlet, ground, sky andsides in Figure 2.13) is implemented using the conventional blockMesh appli-cation of OpenFOAM (Figure 2.15a) with a grading of 4 in vertical direction.The building geometry, previously designed with a CAD tool and saved inSTL format, is embedded into the external mesh using the snappyHexMesh

application. The snappyHexMesh application is an adaptative renementmeshing utility of OpenFOAM very appropriate to mesh complex geome-tries, such as buildings with dierent shapes from stereolithography (STL)CAD les (OpenFOAM (2013); snappyHexMesh (2013); snappyHexMesh-Dict (2013)). This allows to deal with any building shape. The mesh aroundthe building is rened and adapted to its shape. The application allows todene independent renement boxes but, in the present case, the renementis applied around the building surfaces. The renement distance around thebuilding surfaces is 0.16m in this case. Figure 2.19 shows the nal meshobtained. The total number of cells in the nal mesh is close to 3.1M.

2.6.1.2 Validation results

Since this investigation focuses on wind energy exploitation, we concentrateour analysis on the building roof, avoiding a discussion about the recircula-


(a) Vertical section of the external mesh. (b) General view of the nal mesh.

(c) Detail of the nal mesh.

Figure 2.15: Vertical section of the rened mesh obtained using snappy-HexMesh with close to 3.1M cells.

tion downstream of the building. Hence, the comparison of the mean windvelocity (U) and turbulent kinetic energy (k) with the experimental resultsobtained by Meng and Hibi (1998) is carried out at the vertical axes lo-cated at the central plane of the domain according to the diagram shown inFigure 2.16.

We test the RANS turbulence models shown in Table 2.3. Dierentmodel coecients values are also tested (Table 2.4) for the linear k−ε mod-els (except RGN, that uses the analytically determined values for the modelconstants reported in the literature (Yakhot and Smith (1992))). The stan-dard coecients used for industrial ows are compared with those proposedby Crespo et al. (1985) and by Bechmann and Sørensen (2010). The coef-cients that dier from the standard ones are Cµ, Cε1 and κ. Crespo et al.(1985) tailored the standard model constants with the atmospheric measure-ments of Panofsky and Dutton (1984). Bechmann and Sørensen (2010) useCµ = 0.03, the appropriate value for atmospheric ows, and the standardvalue κ = 0.40. The constant Cε1 is calculated using the expression

Cε1 = Cε2 −κ2√Cµσε

, (2.27)

which is derived assuming balance between viscous dissipation and shear


Figure 2.16: Diagram of the axes (V1-V6) at the vertical section of thecentral part of the domain, for the comparison of the results. All lengthsare in meters.

production in the surface layer (Bechmann and Sørensen (2010)).

Turbulence model VariantLinear k − ε Standard (SKE)Linear k − ε Durbin (Durbin (1996))Linear k − ε Durbin-Tominaga (Tominaga et al. (2008))Linear k − ε Durbin-NewLinear k − ε Murakami-Mochida-Kondo (MMK) (Tsuchiya et al. (1997))Linear k − ε Re-normalisation group (RNG) (Yakhot and Smith (1992); Kim and Baik (2004))Linear k − ε Yap (Yap (1987))Nonlinear k − ε Shih (Shih et al. (1993))k − ω SST Shear stress transport (SST) (Menter (1994))

Table 2.3: RANS turbulence models tested.

Cµ Cε1 Cε2 σk σε κ

Std. coecients 0.09 1.44 1.92 1.0 1.3 0.40Crespo et al. (1985) 0.0333 1.176 1.92 1.0 1.3 0.42Bechmann and Sørensen (2010) 0.03 1.21 1.92 1.0 1.3 0.40

Table 2.4: Tested coecients of the linear k − ε models.

The analysis of the results can focus on either qualitative or quantita-tive aspects. The qualitative aspects focus on the behaviour of the wind


ow on the roof, and the quantitative aspects focus on the accuracy of thedata compared with the experimental values. It is important to mentionthis because some models have very good quantitative results although theycannot reproduce well the recirculation on the building roof. This is becauseof experimental data in the size of recirculation vortex is not available (thelower points at the vertical proles V2-V4 of Figure 2.16 are above the re-circulation). The opposite situation also takes place. For example, the SKEmodel using the coecients proposed by Bechmann and Sørensen (2010)matches the same recirculation distance found by the experiment, but themodel does not pass the validation for k.

Before presenting the qualitative results for all the models tested, itis appropriate to explain how we have modied the Durbin model. TheDurbin model is based on the imposition of the Realizability constraint2k ≥ 〈u′αu′α〉 ≥ 0 via a bound on the time scale T (where summation isnot taken in 〈u′αu′α〉). The stagnation anomaly with impinging ows in theSKE model is addressed by relating the eddy viscosity νt to the turbulencevelocity scale 〈v′2〉 and its time scale T . This procedure leads to a reductionof the k overestimation at the impingement wall and to the reproduction ofthe recirculation ow on the roof. Although this overestimation is signi-cantly reduced, it still remains. Another feature is that this model tends tooverestimate the recirculation length both on the roof and beyond the build-ing (Durbin (1996)). According to Durbin (1996), the factors appearing inEq. (2.18) are the maximum in order to strictly apply the Realizabilityconstraint and they can be modied to obtain agreement with experimentaldata, but he clearly states that this issue is beyond the scope of his arti-cle. In the present investigation, using the coecients proposed by Crespoet al. (1985), we have empirically found that the recirculation length XR

can be exactly matched by relaxing the Realizability constraint proposed byDurbin (1996). Note that other authors, as Tominaga et al. (2008), havealso relaxed the Realizability constraint (see Eq. (2.19)). The coecients ofCrespo et al. (1985) are used because the hit rates are higher than those ob-tained using the standard coecients with each version of the Durbin model.Additionally, the recirculation distance XR is closer the experimental valuethan using the coecients proposed by Bechmann and Sørensen (2010), asis shown in Table 2.5. In order to determine the optimum constant factorfor the calculation of TD, we have carried out a sensibility analysis of XR,obtaining Eq. (2.20) as the best alternative. Figure 2.17 shows the valuestested and the corresponding result for XR. Note that the relationship be-tween the constant factors in TD expression (2.20) and XR is linear, as isconrmed by the empirical values that have been determined by means ofCFD simulations.

The most important aspects for the qualitative analysis are the winddirection and the recirculation distance. The wind direction at each region of


0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75Constant factor in TD

0.50

0.55

0.60

0.65

0.70

0.75

XR

Empirical valuesDurbin limitTominagaPresent case - optimumLinear

Figure 2.17: Sensitivity analysis for the recirculation distance XR by varyingthe constant factor in the denition of TD (Eq. (2.20)).

the building roof is analysed in section 4.2. Regarding the recirculation of theow, the comparison of the simulation results obtained for the reattachmentdistance (XR), relative to the roof length, of the recirculation vortex onthe building roof is presented in Table 2.5. As is well known, the SKEmodel cannot predict well the reverse ow on the building roof due to itsoverprediction of the turbulent kinetic energy at the impingement regionof the windward wall (Shao et al. (2012)) and, because of that, the useof SKE is not recommended to estimate the wind behaviour in the urbanenvironment (Franke et al. (2007); Architectural Institute of Japan (2013)).Using the SKE with the coecients of Bechmann and Sørensen (2010), thesame value of XR from the experiment of Meng and Hibi (1998) is obtained,although the case is not successfully validated for k. The Durbin model usedby Tominaga et al. (2008) with the coecients proposed by Crespo et al.(1985) overestimates XR by only 15.4%, giving the closest agreement withthe experimental data among the dierent models tested. Additionally, theMMK model using the coecients of Crespo et al. (1985) overestimates XR

by a 17.3% and the original Durbin with standard coecients underestimatesit by a 17.3%. The Durbin model with the TD proposed in Eq (2.20) showsthe best agreement using the coecients of Crespo et al. (1985), reaching


the same value than the experiment of Meng and Hibi (1998), XR = 0.52.Therefore, these models are the most appropriate to estimate the behaviourof the wind ow over a building roof with a qualitative approach. BothNonlinear Shih and k−ω SST models overestimate the recirculation beyondthe roof. This is in agreement with Shao et al. (2012). All the k− ε modelstested present a better agreement with the experimental data of Meng andHibi (1998) by using the coecients proposed by Crespo et al. (1985) andby Bechmann and Sørensen (2010) than by using the standard coecients.

RANS model Coecients XR HRU HRkSKE Standard 0.16 87.5% 43.8%SKE Crespo 0.36 87.5% 56.3%SKE Bechmann 0.52 87.5% 62.5%RNG Standard 0.62 87.5% 68.8%MMK Crespo 0.61 87.5% 93.8%MMK Bechmann 0.84 87.5% 93.8%Durbin Standard 0.43 87.5% 75.0%Durbin Crespo 0.72 93.8% 87.5%Durbin Bechmann 0.86 87.5% 87.5%Durbin-Tominaga Standard 0.29 87.5% 56.3%Durbin-Tominaga Crespo 0.60 87.5% 75.0%Durbin-Tominaga Bechmann 0.74 87.5% 75.0%Durbin-New Crespo 0.52 87.5% 75.0%Yap Standard 0.40 87.5% 43.8%Yap Bechmann 0.74 81.3% 75.0%Nonlinear Shih Standard >1 87.5% 68.8%k − ω SST Standard >1 87.5% 43.8%Experimental (Meng and Hibi (1998)) 0.52

Table 2.5: Comparison of the results using dierent RANS models: Reat-tachment distance relative to the roof length (XR) of the recirculation vortexon the building roof and hit rate (HR) for the variables U and k. The val-ues that do not pass the validation process are in red colour, and the resultsobtained with the modication of the Durbin turbulence model proposed inthis Thesis are in blue colour.

Table 2.5 also shows the hit rates (HR) for streamwise velocity (U)and the turbulent kinetic energy (k). These hit rates, evaluated at thevertical axes V2-V5 (four axes) of Figure 2.16 (building roof), are calculatedaccording to Santiago et al. (2007) by using the equation

HR =1

n

n∑i=1

Ni, (2.28)


where n is the total number of points compared (note that, in this case,n = 16 because 4 experimental values are available from each vertical axis),and

Ni = 1 if

∣∣∣∣SIMi − EXPiEXPi

∣∣∣∣ ≤ RD or |SIMi − EXPi| ≤ AD

Ni = 0 else ,(2.29)

where SIMi and EXPi are the simulation and experimental values, andRD and AD are the relative and absolute maximum admissible deviationfrom the experimental data, respectively. These values are RD = 0.25 andAD = 0.05 and AD = 0.017 for U and k, respectively (Santiago et al.(2007)). According to Schlünzen et al. (2004), the values of the hit ratethat allow to consider the validation work as successful are HR ≥ 66%when comparing with wind-tunnel experimental values (as in this case) andHR ≥ 95% when comparing with analytical solutions. In this case, allthe models reach streamwise velocity hit rates higher than 80%, which is areasonably good result. The most important diculty for the RANS modelsis to estimate the turbulent kinetic energy. In this case, the only modelsthat reach hit rates above 66% are the RNG (with standard coecients),MMK (with Crespo and Bechmann coecients), all the Durbin variations(with Crespo and Bechmann coecients, and the original Durbin model alsowith standard coecients), Yap (with Bechmann coecients) and NonlinearShih.

The most important aspects of the quantitative analysis are the accuracyof the streamwise velocity and turbulent kinetic energy. All the modelstested successfully passed the validation for U and, therefore, the criticalpoint for the RANS models is to accurately predict the turbulent kineticenergy. Figure 2.18 shows a comparison of the turbulent kinetic energy forthe models that successfully pass the validation for k. The highest values ofk at the impingement region of the windward wall (shown in red), are alwaysoverestimated at the upstream corner. However, these higher values are alsofound on the central region of the building roof, in better agreement with theexperimental results. The results using the MMK model (with Bechmanncoecients) present the best agreement with the experimental data from thequalitative point of view, showing peak values of k only on the central part ofthe roof. The MMK model avoids the overestimation of the production termof k (Pk) by using both strain rate scale S and vorticity scale Ω (instead ofonly S, as in the SKE model) in the calculation of Pk when Ω < S. Theoriginal Durbin models (with Crespo and Bechmann coecients) and theMMK-Crespo also show a qualitatively good result, since the peak valuesaround the upstream edge have a lower magnitude than on the central region.All the models that successfully pass the validation for k are exhaustively


analysed below, focussing on the accuracy of the dierent models at thedierent regions of the building roof.

(a) Durbin-Standard (b) Durbin-Crespo (c) Durbin-Bechmann

(d) Durbin-Tominaga-Crespo

(e) Durbin-Tominaga-Bechmann

(f) RNG-Standard

(g) MMK-Crespo (h) MMK-Bechmann (i) Yap-Bechmann

(j) Nonlinear Shih-Standard

(k) Durbin-New-Crespo (l) Exp. Tominaga et al.(2008)

Figure 2.18: Comparison of the turbulent kinetic energy [m2/s2] at the ver-tical section at the center of the domain, using the models with HRk ≥ 66%.


2.6.1.3 Grid dependency study

In order to check the order of convergence of the solutions, the new variationof the Durbin model proposed in this investigation (the best results found) isanalysed using 3 dierent meshes: coarse, medium-size (the size used for thecomparison of the models) and ne mesh. The renement distances aroundthe building surfaces are controlled by the snappyHexMesh application ofOpenFOAM. Table 2.6 presents the main parameters used, and Figure 2.19shows a detail of the nal meshes obtained. Table 2.6 also shows the hitrates obtained at the 3 cases. The hit rate obtained for U is the same in allcases, but the validation requirement for k is only reached with medium-sizeand ne meshes.

Coarse mesh Medium-size mesh Fine meshRenement distance 0.01 0.16 0.32Total number of cells 1.7M 3.1M 9.8MHRU 87.5% 87.5% 87.5%HRk 68.8% 75.0% 81.3%

Table 2.6: Main parameters of the mesh renement using the snappyHexMeshapplication of OpenFOAM, and values obtained for the hit rates (HR).

(a) Coarse mesh, 1.7M cells. (b) Medium-size mesh, 3.1Mcells.

(c) Fine mesh, 9.8M cells.

Figure 2.19: Detail of the rened meshes obtained for the convergence anal-ysis, using the snappyHexMesh application of OpenFOAM.

To check the order of convergence of the numerical scheme, the gridconvergence index (GCI) is calculated according to Roache (1998) by usingthe total number of cells (N) and the hit rate of k (HRk). Since we use 3dierent meshes, the grid convergence index is

GCI = 1.25|e21|rp21 − 1

, (2.30)


where the relative error is

e21 =HRk,2 −HRk,1

HRk,1, (2.31)

the eective grid renement ratio for a 3-dimensional unstructured grid is

r21 =

(N1

N2

)1/3

, (2.32)

and the observed convergence rate p is

p =

∣∣∣ln ∣∣∣HRk,3−HRk,2

HRk,2−HRk,1

∣∣∣+ q(p)∣∣∣

ln r21, (2.33)

where

q(p) = ln

(rp21 − srp32 − s

), (2.34)

where

s = sign

(HRk,3 −HRk,2HRk,2 −HRk,1

). (2.35)

Note that the system of Eqs. (2.33) and (2.34) must be solved by meansof an iterative procedure, starting with q = 1. The subscripts 1, 2 and 3above refer to the ne, medium-size and coarse meshes, respectively. Sincethe obtained convergence rate is p = 2.23, second order convergence is ob-served in this case, and the error band obtained is close to the asymptoticvalue of the solution because the grid convergence index is GCI21 = 0.0577(5.77%).

2.6.1.4 Behaviour of the dierent models at dierent regions of

the building roof

Since the dierent models analysed show dierent agreement with the ex-perimental data in the dierent regions of the building roof, it is convenientto divide the roof into dierent regions according to the characteristics ofthe ow, in order to recommend the most appropriate model to deal witheach specic problem. Therefore, the building roof is divided into 3 re-gions: upstream corner, central region and downstream corner of the roof(Figure 2.20). The upstream corner of the roof corresponds to the impinge-ment region, the central region corresponds to the recirculation area and thedownstream corner corresponds to the leaving ow region. In what follows,the most appropriate models to estimate the velocity and turbulent kineticenergy at each region are identied.


Figure 2.20: Diagram of the regions of the building roof for the ow analysis.All lengths are in meters.

Upstream corner of the roof

Figures 2.21a and 2.21c show the velocity proles obtained around theupstream corner of the building roof (vertical axes shown in Figure 2.16),using the RANS models that successfully pass the validation, comparedwith the experimental data of Meng and Hibi (1998). The agreement of thevelocity proles with the experimental results is reasonably good. The worstoption to estimate the velocity upstream is the Nonlinear model of Shih etal. (1993).

Figures 2.21b and 2.21d show the turbulent kinetic energy proles ob-tained around the upstream corner of the building roof (vertical axes shownin Figure 2.16), using the RANS models that successfully pass the valida-tion, compared with the experimental data of Meng and Hibi (1998). Thebest models to estimate the turbulent kinetic energy upstream are the MMKand Nonlinear Shih. At the upstream edge, only the Nonlinear Shih modelshows a reasonably good result. The rest of the models clearly overestimatek at z < 0.22 m. Due to the relaxation of the Realizability constraint,the modied Durbin model proposed in the present investigation shows thehighest overestimation at the impingement region, although it shows an ex-cellent agreement with the experimental data at the center and downstreamregions, as will be seen later.

For the estimation of both U and k upstream, the best RANS modelsare the MMK ones, obtaining hit rates of HRU = 92.9% and HRk = 71.4%


at this region for U and k, respectively.

−2 −1 0 1 2 3 4 5 6U (m/s)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

z (m

)

(a) UV 1

0.0 0.5 1.0 1.5 2.0 2.5k (m2 /s2 )

0.00

0.05

0.10

0.15

0.20

0.25

0.30

z (m

)

(b) kV 1

0 1 2 3 4 5 6U (m/s)

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

z (m

)

(c) UV 2

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0k (m2 /s2 )

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

z (m

)

Exp.RNGYap-BechmannMMK-BechmannDurbin-Tominaga-CrespoDurbin-Tominaga-BechmannNonlinear ShihDurbin-New-CrespoDurbin-BechmannDurbin-StandardDurbin-CrespoMMK-Crespo

(d) kV 2

Figure 2.21: Vertical proles comparison for U (left) and k (right) at theupstream region of the building, using the RANS models that successfullypass the validation.

Central region of the roof

Figures 2.22a and 2.22c show the velocity proles obtained at the cen-tral region of the building roof (vertical axes shown in Figure 2.16), usingthe RANS models that successfully pass the validation, compared with theexperimental data of Meng and Hibi (1998). All the models show a rea-sonably good agreement with the experimental data, reaching hit rates ofHRU = 75− 87.5%. The Nonlinear Shih model shows the worst behaviour.


However, there is an uncertainty regarding the velocity in the recirculationbecause the experimental results are only presented from the top of the vor-tex, and the maximum velocity below (negative horizontal component) isnot provided by the experimental results. The reattachment distance (XR)is the only variable available to analyse the qualitative behaviour of the re-circulation ow. From the qualitative point of view, the best agreement isobtained with the new modication proposed for the Durbin model, yield-ing exactly the same value of the reattachment distance obtained at theexperiment of Meng and Hibi (1998). It is important to mention that theNonlinear Shih model clearly overestimates the reattachment distance.

Figures 2.22b and 2.22d show the turbulent kinetic energy prolesobtained at the central region of the building roof (vertical axes shown inFigure 2.16), using the RANS models that successfully pass the validation,compared with the experimental data of Meng and Hibi (1998). The Non-linear Shih model clearly underestimates k at z < 0.18 m up to 60%. Therest of the models show a reasonably good agreement with the experimentalresults. At the lower height of the region (z < 0.18 m) RNG and the originalDurbin (with standard coecients) models underestimate k by 15%. Therest of the models overestimate k by a similar amount. The best modelto estimate k at the central region of the roof is the MMK, that reaches aHRk = 100%.

Downstream corner of the roof

Figures 2.23a and 2.23c show the velocity proles obtained around thedownstream corner of the building roof (vertical axes shown in Figure 2.16),using the RANS models that successfully pass the validation, comparedwith the experimental data of Meng and Hibi (1998). The agreement withthe experimental results is reasonably good for all the models. The worsebehaviour is observed for the Nonlinear Shih proles, where U is notablyunderestimated due to the recirculation overestimation.

Figures 2.23b and 2.23d show the turbulent kinetic energy prolesobtained around the downstream corner of the building roof (vertical axesshown in Figure 2.16), using the RANS models that successfully pass thevalidation, compared with the experimental data of Meng and Hibi (1998).Nonlinear Shih, RNG and the original Durbin (with standard coecients)models clearly underestimate k. The rest of the models show a reasonablygood agreement with the experimental data, especially MMK (with Crespocoecients), the new modied version of Durbin (with Crespo coecients)and Yap (with Bechmann coecients). The exception is downstream of thebuilding (close to the vertical wall of the building), where RNG and theoriginal Durbin (with standard coecients) present the best agreement.


−2 −1 0 1 2 3 4 5 6U (m/s)

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

z (m

)


(a) UV 3

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0k (m2 /s2 )

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

z (m

)

(b) kV 3

−2 −1 0 1 2 3 4 5 6U (m/s)

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

z (m

)

(c) UV 4

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0k (m2 /s2 )

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

z (m

)

(d) kV 4

Figure 2.22: Vertical proles comparison for U (left) and k (right) at thecentral region of the building roof, using the RANS models that successfullypass the validation.

2.6.1.5 Wind energy exploitation and wind turbines positioning

Dening the concentration factor of the wind as the increase of the velocityaround the building compared to the freestream inlet velocity at the heightof the building (Lu and Ip (2009)), a concentration factor of the wind of6-20% on the building roof is appreciated at the vertical axes V2-V5. How-ever, atmospheric wind turbulence is one of the main eects causing fatiguedamage on wind turbine components (Mouzakis et al. (1999)). Accordingto the European Wind Turbine Standards II (Pierik et al. (1999)), when theturbulence intensity exceeds 15% the fatigue loads on the conventional wind


−1 0 1 2 3 4 5 6U (m/s)

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

z (m

)


(a) UV 5

0.0 0.5 1.0 1.5 2.0 2.5 3.0k (m2 /s2 )

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

z (m

)(b) kV 5

−1 0 1 2 3 4 5 6U (m/s)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

z (m

)

(c) UV 6

0.0 0.5 1.0 1.5 2.0 2.5 3.0k (m2 /s2 )

0.00

0.05

0.10

0.15

0.20

0.25

0.30

z (m

)

(d) kV 6

Figure 2.23: Vertical proles comparison for U (left) and k (right) at thedownstream region of the building, using the RANS models that successfullypass the validation.

turbines have to be re-evaluated based on the actual conditions at the site.It implies that a new concept of Horizontal Axis Wind Turbine (HAWT)or a Vertical Axis Wind Turbine (VAWT) should be used in this situation.Therefore, a value of TI = 0.15 is used as a maximum admissible for conven-tional HAWT. Figure 2.24a shows a diagram with the most adequate typeof wind turbine for each region, plotted on top of the turbulence intensitymap and the velocity eld. The bold line represents the limit between themost appropriate area for HAWT and vertical axis wind turbines (VAWT).The most appropriate areas to install HAWT are above z/H = 0.19 fromthe roof surface upstream and above z/H = 0.31 downstream. It is recom-


mended to incline the horizontal axis of the HAWT 5 downwards at theupstream region below z/H = 0.31. Below these heights, the installation ofa VAWT is more appropriate since it is not aected by the wind directionuctuations (Kooiman and Tullis (2010)) and it resists better the velocityuctuations of the wind (Carpman (2011)). Additionally, the VAWT canbe installed in horizontal position (see gure 2.24a) at the central-upstreamregion close to the roof surface, in order to take the most of the recirculationof the ow. That is, the VAWT in horizontal position can exploit the posi-tive streamwise velocity up and the negative streamwise velocity down and,additionally, it can exploit the circular ow upstream or downstream of theturbine. More investigations are needed to better understand the behaviourof the VAWT in strongly turbulent environments.

Another very interesting application for the wind energy exploitation atthe upstream corner of the building roof is the use of a ducted wind turbine(Toja-Silva et al. (2013)). This kind of wind turbine takes the most ofthe pressure dierence between the vertical wall and the roof, with positiveand negative pressures, respectively. Depending on the dierential pressurecoecient, power coecient values close to 1 can be reached (Grant et al.(2008)). Figure 2.24b shows a diagram of the turbine position into thepressure eld.

High wind situations (wind speed > 3 m/s) as the one studied in thispaper show a well dened circulation pattern and a predominant wind di-rection (Whiteman (2000); Jiménez and Dudhia (2013)). However, in orderto make the conclusions of this section more general, and independent of theincident wind direction, we also consider an oblique incident wind direction(45). Figure 2.25 shows a comparison between the threshold of TI = 0.15for a normal incident wind direction (0) and an oblique one (45). For theoblique wind direction, the HAWT can be placed above z/H = 0.14 andz/H = 0.27 at upstream and downstream edges, respectively. Below theseheights, VAWT must be considered. Since the threshold of TI = 0.15 islower everywhere, the heights obtained for the normal incident wind (mostunfavourable case) are conservative values for a general wind direction case.Therefore, we conclude that, in general, an HAWT can be placed abovez/H = 0.31 anywhere at the roof, regardless of the incident wind direction.The situation investigated in this section is an isolated building but, sincethe inlet prole is highly turbulent (as shown in gure 2.14b), our conclusionsare also valid for a building surrounded by smaller buildings.

2.6.1.6 Conclusions of this work

In this investigation, CFD simulations of the wind ow around a singlebuilding were performed with OpenFOAM using several RANS turbulencemodels, and the results were compared with the experimental results of a


(a) Turbine positioning

(b) Ducted wind turbine

Figure 2.24: Wind turbine positioning diagrams: (A) Most appropriate windenergy exploitation systems at the dierent regions of the building roof. Thevector eld is the velocity, the background colormap is turbulence intensity(TI) and the bold line (in magenta) is an isocontour of the isoline corre-sponding to TI = 0.15. (B) Ducted wind turbine at the upstream corner ofthe roof into the pressure eld.


(a) Normal incident wind (0) (b) Oblique incident wind (45)

Figure 2.25: Isosurfaces of TI = 0.15 (in grey colour) for a normal incidentwind direction (0) and an oblique wind direction (45). HAWT can beplaced above the isosurface. Below this region, VAWT must be considered.Dark red represents the building, green the ground and blue the sky.

wind tunnel benchmark case. The behaviour of the dierent RANS modelswere analysed at dierent regions of the building roof (upstream, down-stream and central region of the roof), and the most appropriate modelswere identied for each situation both qualitatively and quantitatively.

On the qualitative side, the Durbin model with the TD form proposedin Eq. (2.20) showed a perfect agreement with the experimental data forrecirculation distance. Additionally, Durbin-Tominaga (with Crespo coe-cients), MMK (with Crespo coecients) and original Durbin (with standardcoecients) models showed a reasonable agreement with the experiment.The SKE model (with Bechmann coecients) also matched the same valueof the recirculation distance obtained by the experiment, but it is not suc-cessfully validated for k. Both Nonlinear Shih and k − ω SST models over-estimate the recirculation beyond the roof. All the k−ε models tested showa better agreement with the experimental data by using the coecients pro-posed by Crespo et al. (1985) and by Bechmann and Sørensen (2010) thanby using the standard coecients.

For the quantitative analysis, the hit rate is calculated. All the modelssuccessfully passed the validation threshold (HR > 66%) for the streamwisevelocity (U) but, for the turbulent kinetic energy (k) only the RNG (withstandard coecients), MMK (with Crespo and Bechmann coecients), allthe Durbin variations (with Crespo and Bechmann coecients, and the orig-inal Durbin model also with standard coecients), Yap (with Bechmanncoecients) and Nonlinear Shih passed the validation.

In order to check the order of convergence of the solutions, the hit rate for


k obtained with the new Durbin TD proposed in this investigation is analysedfor 3 dierent meshes: coarse, medium-size and ne mesh (1.7M, 3.1M and9.8M cells, respectively). The observed convergence rate is p = 2.23 and thegrid convergence index is GCI = 0.0577 (5.77%).

Regarding the behaviour of the RANS models at the dierent regionsof the building roof, at the upstream region of the roof the best agreementwith experimental data for both U and k is achieved using the MMK model(with both Crespo and Bechmann coecients). At the central region ofthe roof there is an uncertainly regarding the velocity in the recirculationzone because the experimental data do not include the negative horizontalcomponent of velocity. The reattachment distance (XR) is the only dataavailable to analyse the qualitative behaviour of the recirculation. Fromthis qualitative point of view, the best agreement is obtained with the newmodication of the Durbin model (with Crespo coecients), yielding exactlythe same value than the experimental one. At the central region of theroof the best agreement for k is obtained with the MMK model (with bothCrespo and Bechmann coecients) that reach a HRk = 100%, althoughthe rest of the linear turbulence models show a reasonably good agreement.At the downstream region of the building roof (on the downstream edge),MMK (with Crespo coecients), the new modied version of Durbin (withCrespo coecients) and Yap (with Bechmann coecients) show the bestagreement for both U and k. The Durbin model with the proposed form ofTD and Crespo coecients gave the best results from a global point of view,both qualitatively and quantitatively. Additionally, the MMK model (withCrespo coecients) gave the best quantitative results and a reasonably goodqualitative agreement with the experimental data.

The analysis of the turbines positioning is based in the turbulent kineticenergy, limited up to a turbulence intensity TI < 0.15 for HAWT, from afatigue loads preventing point of view. According to that, the most appropri-ate areas found to install HAWT are above z/H = 0.19 from the roof surfaceupstream and above z/H = 0.31 downstream. It is recommended to inclinethe horizontal axis of the HAWT 5 downwards at the upstream region belowz/H = 0.31. The installation of VAWT is recommended below these heights.The installation of a VAWT in horizontal position at the central-upstreamregion close to the roof surface was also considered, to make the most ofthe recirculation of the ow. Additionally, the installation of a ducted windturbine at the upstream corner of the building roof, in order to make themost of the pressure dierence between the vertical wall (positive) and theroof surface (negative), is also interesting. Although high wind situations asthe one studied in this paper show a predominant wind direction, in orderto make the conclusions of this paper more general, and independent of theincident wind direction, we also consider an oblique incident wind direction.The results show that HAWT can be placed above z/H = 0.14, z/H = 0.27

TI = 0.15

z/H = 0.31

HR ≥ 75%

ρ =−3 ν = 1.57× 10−5 2 −1

U k ε


U k ε νt p

Inlet iP iP iP C zGOutlet zG zG zG C fV zeroGround fV zero kqR wF epsilon wF nutk rough wF zGBuilding fV zero kqR wF epsilon wF nutk wF zGSky sl sl sl C zGSides sP sP sP sP sP

Table 2.7: Boundary conditions imposed at each boundary of the domain forthe curved roof validation. Nomenclature: C = Calculated, fV = xedValue,iP = Inlet prole, sl = slip, sP = Symmetry plane, wF = wall function, zG= zeroGradient.

tions according to Richards and Hoxey (1993), we use also this methodologyin order to validate it by comparing the simulation results with the exper-imental data obtained by Ntinas et al. (2014). We consider the referencevalues used in the experiment: averaged wind velocity (U) inlet and the tur-bulent kinetic energy reference value of k = 0.011264 m2 s−2. Notice that weuse the logarithmic inlet wind prole for U (according to Richards and Hoxey(1993)) instead of the exponential prole reported from the experiment (seegure 2.27a). Since values of ε are not reported from the experiment, theentire inlet wind prole (gure 2.27c) is dened according to Richards andHoxey (1993). As it is shown below, the validation is successful and theagreement between the simulation results and the experimental values isreasonably good.

A background mesh is constructed using the structured blockMesh appli-cation with a grading of 4 in the vertical direction and the building geometry,previously designed with a CAD tool and saved in STL format, is embeddedinto the background mesh using the snappyHexMesh application of Open-FOAM (snappyHexMesh (2013); snappyHexMeshDict (2013)). The mesharound the building is rened and adapted to its shape. The renementdistance around the building surfaces is 0.1 m. The nal number of cells is6.5M. Figure 2.28 shows the nal mesh obtained.

2.6.2.2 Simulation results

For a qualitative analysis, gure 2.29 shows U and k elds around the build-ing roof. A small recirculation vortex appears at the down corner (betweenthe wall and the ground) of the impingement wall, and a highest vortex ap-pears downstream. This downstream vortex starts from the detached owon the roof, that takes place at the center-downstream region. On the roof,k presents the highest values at the center-upstream region.


0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45U (m/s)

0.0

0.1

0.2

0.3

0.4

0.5

z (m

)

Exp. NtinasNum. inlet

(a) U

0.007 0.008 0.009 0.010 0.011 0.012 0.013k (m2 /s2 )

0.0

0.1

0.2

0.3

0.4

0.5

z (m

)

Num. inlet

(b) k

10-5 10-4 10-3 10-2 10-1

ǫ (m2 /s3 )

0.0

0.1

0.2

0.3

0.4

0.5

z (m

)

Num. inlet

(c) ε

Figure 2.27: Inlet wind proles for the curved-roof validation case: meanstreamwise velocity (U), turbulent kinetic energy (k) and turbulent dissi-pation (ε). The points represent the inlet proles used at the experimentof Ntinas et al. (2014), and the solid lines are the numerical inlets of thesimulations.

The quantitative analysis is carried out by comparing the results of Uand k with the dierent turbulence models with the experimental results ofNtinas et al. (2014) at the vertical axes located at the central plane of thedomain according to the diagram shown in gure 2.26.

Figures 2.30a, 2.30b and 2.30c show a comparison of vertical proles ofU at the dierent roof positions for all the situations described in gure 2.26.


(a) General view mesh, 6.5M cells (b) Detail of the renement area

Figure 2.28: Vertical section of the rened mesh obtained using snappy-HexMesh.

(a) U eld (b) k eld

Figure 2.29: Vertical section at the center of the domain of the U and kelds around the building.

Figure 2.30d shows a comparison of vertical proles of k at the verticalaxis V3 (gure 2.26), the only position with available experimental data.Since the Re number is low, both U an k are overestimated by all themodels, although all the models are successfully validated for U and k.Table 2.8 presents the hit rates obtained at each case, calculated with thesame procedure than for the at roof (Eqs. (2.28-2.29)). All the turbulencemodels are successfully validated by U with a hit rate of HRU = 94.8%,except for the MMK model with the coecients proposed by Crespo et al.(1985) that has obtained a HRk = 96.1%, the best agreement with theexperimental data. This better agreement is observed in the reproductionof the recirculation ow at the downstream region of the roof. For k, all theturbulence models are successfully validated with a hit rate of HRk = 100%.Note that the dierence between the values in gure 2.30d is very small,although a clear overestimation is appreciated. The models that betteragree with the experimental results are MMK, Yap, Durbin (original) and,in the last position, the Durbin models used by Tominaga and the new


modication proposed in this Thesis (Toja-Silva et al. (2015d)). Therefore,the MMK turbulence model clearly show the best behaviour from the modelstested in the present case.

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45U (m/s)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

z (m

)

Exp.Durbin-CrespoDurbin-BechmannMMK-BechmannDurbin-Tominaga-CrespoDurbin-Tominaga-BechmannYap-BechmannDurbin-New-CrespoDurbin-StandardMMK-Crespo

(a) UV 1

0.0 0.1 0.2 0.3 0.4 0.5U (m/s)

0.05

0.10

0.15

0.20

0.25

0.30

z (m

)

(b) UV 2

−0.1 0.0 0.1 0.2 0.3 0.4 0.5U (m/s)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

z (m

)

(c) UV 3

0.000 0.005 0.010 0.015 0.020k (m2 /s2 )

0.00

0.05

0.10

0.15

0.20

0.25

0.30

z (m

)

(d) kV 3

Figure 2.30: Comparison of U and k at the vertical section at the center ofthe domain.

2.6.2.3 Conclusions of this work

The k − ε RANS turbulence models successfully validated with hit ratesof HR ≥ 75% for the at roof are validated twice over for a curved-roofbuilding model. The simulation results are compared with those obtainedat the wind-tunnel experiment carried out by Ntinas et al. (2014).

Due to the low Re number, both U an k are overestimated by all the


RANS model Coecients HRU HRkDurbin (Durbin (1996)) Standard 94.8% 100%Durbin (Durbin (1996)) Crespo et al. (1985) 94.8% 100%Durbin (Durbin (1996)) Bechmann and Sørensen (2010) 94.8% 100%MMK (Tsuchiya et al. (1997)) Crespo et al. (1985) 96.1% 100%MMK (Tsuchiya et al. (1997)) Bechmann and Sørensen (2010) 94.8% 100%Durbin-Tominaga (Tominaga et al. (2008)) Crespo et al. (1985) 94.8% 100%Durbin-Tominaga (Tominaga et al. (2008)) Bechmann and Sørensen (2010) 94.8% 100%Yap (Yap (1987)) Bechmann and Sørensen (2010) 94.8% 100%Durbin-New (Toja-Silva et al. (2015d)) Crespo et al. (1985) 94.8% 100%

Table 2.8: Hit rates (HR) for the variables U and k at the dierent RANSmodels tested for the curved roof. The results obtained with the modicationof the Durbin turbulence model proposed in this Thesis are in blue colour.

models. However, the dierences between the simulation results and theexperimental values are low and all the models are successfully validated forboth U and k, with hit rates of HRU = 94.8% and HRk = 100%, with theonly exemption of the MMK model with Crespo coecients that reached aHRU = 96.1%.

From the results obtained in this Section, it can be concluded that theMMK k − ε turbulence model with Crespo coecients is the most accuratemodel for the analysis of the wind ow on complex-geometry building roofsthat include curved surfaces. The following models can also be used: MMK(with Bechmann coecients), Yap (with Bechmann coecients), the origi-nal Durbin (with standard, Crespo and Bechmann coecients), the Durbin-Tominaga (with Crespo and Bechmann coecients) and the new modica-tion of the Durbin model presented in this thesis (with Crespo coecients).

2.7 Conclusions

At the introduction of this Chapter, the basics aspects of the computationalwind engineering are commented, and the mean issues related to the atmo-spheric boundary layer are explained, including the inlet wind proles usedin the full-scale CFD simulations.

Afterwards, the governing equations of the ow are presented and theturbulence modeling is discussed. Complementarily to the existent models,that are cited, a new modication of the Durbin k − ε turbulence model isproposed. This new modication proposed better agrees with the experi-mental results, as is demonstrated at the following validation.

The rst validation carried out consists in CFD simulations of the window around a single building, that were performed with OpenFOAM usingseveral RANS turbulence models. The results were compared with the ex-

2.7. Conclusions 79

perimental results of a wind-tunnel benchmark case (Meng and Hibi (1998)).The behavior of the dierent RANS models were analysed at dierent regionsof the building roof, and the most appropriate models were identied for eachsituation both qualitatively and quantitatively. On the qualitative side, thenew modied Durbin model showed a perfect agreement with the experimen-tal data for recirculation distance. Additionally, Durbin-Tominaga (withCrespo coecients), MMK (with Crespo coecients) and original Durbin(with standard coecients) models showed a reasonable agreement with theexperiment. The SKE model (with Bechmann coecients) also matched thesame value of the recirculation distance obtained by the experiment, but itis not successfully validated for TKE. All the k − ε models tested show abetter agreement with the experimental data by using the coecients pro-posed by Crespo et al. (1985) and by Bechmann and Sørensen (2010) thanby using the standard coecients. For the quantitative analysis, the hit rateis calculated. All the models successfully passed the validation threshold forU but, for k only the RNG (with standard coecients), MMK (with Cre-spo and Bechmann coecients), all the Durbin variations (with Crespo andBechmann coecients, and the original Durbin model also with standard co-ecients), Yap (with Bechmann coecients) and Nonlinear Shih passed thevalidation. The new modied Durbin model with Crespo coecients gavethe best results from a global point of view, both qualitatively and quanti-tatively. Additionally, the MMK model (with Crespo coecients) gave thebest quantitative results and a reasonably good qualitative agreement withthe experimental data.

The analysis of the turbines positioning for the at roof is based in theturbulent kinetic energy, limited up to a turbulence intensity TI < 0.15for HAWT. According to that, the most appropriate areas to install HAWTwere identied and discussed. An oblique incident wind direction was alsoconsidered. The results show that HAWT can be placed above z/H = 0.31everywhere at the investigated case, regardless of the incident wind direction.The situation investigated corresponds to an isolated building but, since theinlet prole is highly turbulent, this rule can also be applied to a buildingsurrounded by smaller buildings. The installation of a VAWT in horizontalposition at the central-upstream region close to the roof surface was alsoconsidered, to make the most of the recirculation of the ow. Additionally,the installation of a ducted wind turbine at the upstream corner of thebuilding roof, in order to make the most of the pressure dierence betweenthe vertical wall and the roof surface, is also interesting.

The k − ε RANS turbulence models successfully validated for the at-roof building with hit rates of HR ≥ 75% were validated twice at a curved-roof building case. The CFD simulation results were compared with thoseobtained at the wind-tunnel experiment carried out by Ntinas et al. (2014).All the tested models successfully passed the validation procedure for U and


k. The MMK model (with Crespo coecients) obtained the highest hit ratefor U .

From the results obtained in this Chapter, it can be concluded that Yap,Durbin and MMK k−ε turbulence models can be used to accurately analysethe wind ow on complex-geometry building roofs that include both sharpedand curved surfaces.

Although the MMK turbulence model (with Crespo coecients) showsthe best behaviour in both cases, the new modication of the Durbin modelpresented in this chapter is recommended to be used in further simulationsbecause it has been empirically found a higher numerical stability whendealing with very complex geometries (for example with solar panels in nextchapter). Additionally, the MMK model (with Crespo coecients) tends toslightly underestimate TKE, and the new modied Durbin tends to slightlyoverestimate it. Therefore, it is recommended the use of the new modiedDurbin model (with Crespo coecients) in order to bring more conserva-tive results, what is very important for being used in real facilities becausethe real buildings have more roughness elements than the considered in theherein presented studies (antennas, ornamental elements, odd edges, birds,etc.).

In order to be rigorous regarding the extrapolation of the results toa real case, there is a need to carry out benchmark cases similar to thatanalysed in this investigation but with a full-scale geometry. The dierencein the Re number reached may cause substantial dierences on the roof ow.Additionally, we only analysed the regions on the central symmetry axis ofthe roofs, because the experimental data is only available at these positions.

Bibliography notes

Part of the content of Sections 2.3 and 5.1.2.1 has been published in Toja-Silva et al. (2015d) and Toja-Silva et al. (2015c).

Chapter 3

On the compatibility ofphotovoltaic-solar and windenergy exploitation systems onbuilding roofs

The important thing is not to stopquestioning.

Albert Einstein

3.1 Introduction

The complementarity of dierent technologies and the stability of powergeneration is a crucial point for the use of renewable energy sources (Hongand Chen (2014); Cheng et al. (2007)). Solar and wind energies vary withtime and energy management systems are usually necessary to adapt thetime of energy conversion with the demand prole. However, both energysources can be considered complementary. This complementarity varies withthe daily solar cycle and the season. Solar irradiation is available during theday and during the night the wind energy supply is at its highest. In general,the availability of solar power is higher than wind in the summer, while theopposite is true in the winter (q. Liu and x. Wang (2009)). In a wind-solarhybrid system, one source of energy can oset the shortfall of the other(Huang et al. (2015)), yielding a more stable generation system. Therefore,the motivation of the present Chapter is to verify the compatibility of bothwind and photovoltaic solar energy devices on a building roof from the pointof view of the wind ow dynamics.

Some authors have carried out studies of ground-mounted (Shademan

81

82 Chapter 3. Compatibility of solar and wind energy systems

et al. (2014); Aly and Bitsuamlak (2013)) and roof-mounted (Stathopou-los et al. (2014); Kopp et al. (2012); Pratt and Kopp (2013)) solar panels.These previous investigations focussed on the wind loads over the solar ar-rays (pressure coecients). To the author knowledge, only the work of Prattand Kopp (2013) presents data (velocity and Reynolds stresses) of the window on the roof of a low-rise building. Complementarily, in the present in-vestigation the focus is on a high-rise building, since the potential for bothphotovoltaic and wind energy devices is higher because the incident windvelocity is expected to be higher (considering exponential incident wind pro-les) and the possibility of shadows caused by the neighbouring buildings islower than in the case of a low-rise building (assuming that the neighbour-ing buildings are lower or at the same height). The denition of a high-risebuilding includes buildings higher than 23-30 m (or 5-10 stories) (Craighead(2009)).

This Chapter presents an analysis of the inuence of roof-mounted solarpanels on the wind energy exploitation, by studying the behavior of veloc-ity (U) and turbulent kinetic energy (k) on the roof and comparing bothvariables in a at roof (without solar panels) with those in the same roofwith solar panels installed. Two cases are analysed: the wind-tunnel at-roof reduced model studied in Chapter 2 (Toja-Silva et al. (2015d)) and anenlarged version of this building, blown up by a factor of 250 to match realscale dimensions. We use the new modication of the Durbin turbulencemodel explained and validated in Chapter 2 (Toja-Silva et al. (2015d)), thatfocussed on the characteristics of the ow (velocity, turbulent kinetic en-ergy, detachment, reattachment, recirculation, etc.) on the roof. The opensource CFD software package OpenFOAM (2013) is used for the numericalinvestigation.

3.2 Complementary validation

In order to guarantee a rigorous result, an additional validation is carriedout using the modied Durbin k−ε turbulence model with the parameters ofCrespo et al. (1985). A single innite-span array of solar panels (at plate) isvalidated according to the experiment of Fage and Johansen (1927). This pi-oneer experiment is commonly used in recent investigations (Amandolese etal. (2013); Abiola-Ogedengbe et al. (2015); Jubayer and Hangan (2014)) forcomparison and validation purposes. Although recent experiments (Abiola-Ogedengbe et al. (2015)) deal with the wind ow around solar arrays, theyfocus on the surface pressure eld, and Fage and Johansen (1927) is veryuseful for the present investigation because it also brings values of the ve-locity eld around the at plate. This article also brings information aboutthe mean pressure coecient and about the vortices frequency, dimensions,

3.2. Complementary validation 83

speed, etc.The size of the computational domain follows the specications of Bosch

and Rodi (1996) in order to minimize blockage issues. Figure 3.1 showsa diagram of the geometry. The axis where the simulation velocities arecompared with the experimental data is indicated as AXIS in the picture.The slip boundary condition is imposed at the top, bottom and two sidewalls, assuming them as far-eld free stream-surfaces. A no-slip boundarycondition is applied on the plate. A uniform velocity of U∞ = 1 m s−1 and auniform turbulent kinetic energy k = 0.002 m2 s−2 are set at the inlet. Theunstructured mesh is constructed using the snappyHexMesh application ofOpenFOAM (snappyHexMesh (2013); snappyHexMeshDict (2013)), whichresulted in around 6.4M cells. The corresponding Reynolds number basedon the plate length is Re = 7× 104.

Figure 3.1: Diagram of the validation of the innite-span array of solarpanels. The AXIS indicates the points where the data is compared for thevalidation. All values are dimensionless, expressed as multiples of the widthof the plate W = 1 m.

Figure 3.2a shows a comparison between numerical and experimentalresults for U at the vertical axis shown in gure 3.1. A hit rate of HRU =90.9% is reached. This hit rate indicates a very good agreement betweenthe present simulation and the experimental results, specially near the solararray. Since the hit rate is higher than 66%, the validation can be consideredsuccessful (Schlünzen et al. (2004)).

Figure 3.2b shows the distribution of the mean pressure coecient cp =2(P−P∞)/(ρU2

∞) along the at plate surface. The symbol P∞ means the


free-stream pressure, U∞ is the free-stream velocity (or reference velocity)and ρ is the density. A hit rate of HRcp = 70.4% is reached. This hit rateindicates a reasonably good agreement between the present simulation andthe experimental results. This agreement is very good at the windward faceof the solar array, but it is worse at the leeward face due to, on one hand,the well known diculty for the RANS models to accurately reproduce therecirculation of the ow behind a sharp body (Toja-Silva et al. (2015d);Tominaga et al. (2008)) and, on the other hand, to the actual edge shapeof the solar array at the experiment of Fage and Johansen (1927) (notethat it is a pioneer experiment from the year 1927). Other authors haveobtained in recent experiments (Abiola-Ogedengbe et al. (2015)) and simu-lations (Jubayer and Hangan (2014)) similar dierences with the experimentof Fage and Johansen (1927) in the mean pressure coecient distribution atthe leeward face of the at plate. Nevertheless, since the hit rate is higherthan 66%, the validation can also be considered successful for cP (Schlünzenet al. (2004)).

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6U/Uoo

6.64

6.66

6.68

6.70

6.72

6.74

6.76

6.78

6.80

z/W

Exp. FageNumerical

(a) U/U∞ vs. z/W at AXIS.

5.6 5.8 6.0 6.2 6.4x/W

−1.0

−0.5

0.0

0.5

1.0

1.5

c p

Exp. FageNumerical

(b) cp vs. x/W at the at plate surface.

Figure 3.2: Comparison between numerical and experimental values for val-idation using the experimental data of Fage and Johansen (1927). All valuesare dimensionless: distances with respect to the innite array width W andvelocity with respect to the free-stream velocity U∞ (inlet velocity).

3.3 Description of the cases and simulation details

The inuence of roof-mounted solar panels on the wind energy potential isanalyzed by comparing both velocity and turbulent kinetic energy in a atroof (without solar panels) with those in the same roof with solar panels

3.3. Description of the cases and simulation details 85

installed. The base building is the benchmark case A of the ArchitecturalInstitute of Japan (2013), analysed at full-scale. The height of the full-scalebuilding is H = 40 m and the length of the sides is 20 m. Figure 3.3 showsthe domain and dimensions of the full-scale building. The domain is set ac-cording to Best Practice Guidelines (Franke et al. (2007)). According to Hall(1997), Cowan et al. (1997) and Scaperdas and Gilham (2004), for a singlebuilding a distance of 5H between the inow boundary and the building isrecommended if the approach ow proles are well known. However, Bartziset al. (2004) recommends 8H if the inlet ow proles are not available inorder to allow a realistic ow development. As in the present case the inletwind proles for the full-scale building are calculated according to Richardsand Hoxey (1993) (explained below), a constant value is set for k at thewhole height. Therefore, we use a distance of 8H between the inlet bound-ary and the building. The solar panels used in this study are the modelSunpower X21-345 Sunpower (2014). The solar power plants studied in thischapter are designed according to the Spanish regulations (Instituto para laDiversicación y Ahorro de la Energía (2011)). Two designs are considered:

Figure 3.3: Diagram of the computational domain of the full-scale building.All values are in meters.

(i) With a tilt angle of 10. In this case, the T-10 structure (Sunpower(2015)) is used. This system is specially designed for at roofs where isnot allowed to drill for xing the solar panels support structure, as at roofdecking (Tegral (2015); GreenSpec (2015)). The total peak power of thephotovoltaic plant obtained with this design is 41.75 kW. Figure 3.4 showsa detailed diagram of the geometry of this photovoltaic facility at full scale.

(ii) With a tilt angle of 30. As an example, this is the optimum tiltangle at the North-Mediterranean region. The separation between the solarpanels arrays is calculated according to the Spanish regulations (Instituto


(a) 3D view. Advantageous (red) and un-favourable (blue) incident wind directions andthe corresponding vertical axes V1-V4 areshown.

(b) Solar panels detail.

Figure 3.4: Diagram of the geometry of the 41.75 kW photovoltaic facilitywith a tilt angle of 10, at full scale.

para la Diversicación y Ahorro de la Energía (2011)). The total peak powerof the photovoltaic plant obtained with this design is 30.36 kW. Figure 3.5shows a detailed diagram of the geometry of this photovoltaic facility. Addi-tionally, the same facility was tested with the solar panels installed at 0.3 mheight above the roof (gure 3.5c). This raised panels conguration is alsotested because it is a common form of installation (Eco-Hi-Solar (2014)),and dierences in the behaviour of the ow are expected due to the gapbetween the solar arrays and the roof surface under the panels.

In both cases (10 and 30), the wind direction will be tested at the pre-dictably most advantageous and unfavourable directions. This is, from leftand right hand side of the vertical section in gures 3.4b, 3.5b and 3.5c, re-spectively. Note that the names advantageous and unfavourable refer tothe most/least aerodynamic positions according to the inlet wind direction,independently from its appropriateness for the application.

The simulations are performed in OpenFOAM (2013). The same speci-cations explained in Chapter 2 are used for the full-scale building: boundaryconditions, numerical schemes, etc. The only exception is the top bound-ary condition (sky), where the slip boundary condition is imposed in thefull-scale case. The inlet proles used for the full-scale cases are calculatedaccording to Richards and Hoxey (1993), using the equations

U =U∗κ

ln

(z + z0

z0

), (3.1)

3.3. Description of the cases and simulation details 87

(a) 3D view. Advantageous (red) and unfavourable(blue) incident wind directions and the correspondingvertical axes V1-V4 are shown.

(b) Detail panels close to the roof surface. (c) Detail raised panels.

Figure 3.5: Diagram of the geometry of the 30.36 kW photovoltaic facilitywith a tilt angle of 30, at full scale.

k =U2∗√Cµ

(3.2)

and

ε =U3∗

κ(z + z0), (3.3)

where z0 = 0.01 m, and Uref = 4.4 m s−1 and zref = H = 40 m areconsidered as reference values in order to calculate U∗ by using Eq. (3.1).The turbulence model used is the modication of the Durbin k− ε proposedin Chapter 2 (Toja-Silva et al. (2015d)), and the coecients used are thoseproposed by Crespo et al. (1985).

Regarding the mesh, a background mesh is constructed using the struc-tured blockMesh application with a grading of 4 in the vertical direction.


The building geometry (with the solar panels included), previously designedwith a CAD tool and saved in STL format, is embedded into the backgroundmesh using the snappyHexMesh application of OpenFOAM (snappyHexMesh(2013); snappyHexMeshDict (2013)). This allows to deal with any buildingshape. The mesh around the building is rened and adapted to its shape.Renement is applied around the building surfaces. The renement distancearound the building surfaces is 80 m. Figure 3.6 shows the nal meshes ob-tained for the empty roof and for the roof with solar panels with a tilt angleof 10 and 30 (close and raised from the roof), respectively.

(a) General view mesh empty roof, 6.7Mcells.

(b) Detail of 10 inclined solar panels, meshwith 6.9M cells.

(c) Detail of 30 solar panels, mesh with7.1M cells.

(d) Detail of 30 raised solar panels, meshwith 7.1M cells.

Figure 3.6: Vertical section of the rened meshes obtained using snappy-HexMesh.

3.4 Results and discussion

In what follows, the simulation results for the 4 cases (10, 30 close andraised and empty roof) are presented, and the inuence of the presence ofthe roof-mounted solar panels on the wind ow is discussed. Additionally,the characteristics of the wind ow in all cases are analysed and compared,

3.4. Results and discussion 89

bringing an assessment of the possibility of the wind energy exploitationand identifying the most appropriate kind of wind turbine for dierent partsof the roof. The analysis of the results can focus on either quantitative orqualitative aspects. Quantitative aspects focus on an accurate study of thedata at the vertical axes shown in gure 3.7, and qualitative aspects focuson the behavior of the wind ow on the roof (recirculation, wind direction,etc.).

Figure 3.7: Diagram of the axes (V1-V4) at the vertical section of the cen-tral part of the domain, for the comparison of the results. All lengths aredimensionless.

The quantitative analysis is carried out by comparing U and k betweenthe 4 cases (including most advantageous and unfavourable situations) atthe vertical axes located at the central plane of the domain according tothe diagram shown in gure 3.7. For the analysis below, note that theheight of the solar panels for the full-scale model is 0.27 m, 0.52 m and0.82 m (z/H = 1.007, z/H = 1.013 and z/H = 1.02) for 10 and 30

close and raised from the roof, respectively. Note that, from this Chapter,the reference for heights is the ground, corresponding z/H = 1 to the roofsurface.

Figure 3.8 shows the comparison of vertical proles of the velocity atthe dierent roof positions described in gure 3.7. It is observed that, ingeneral, the raised panels tend to reduce the velocity and the rest of thecases, particularly 30, tend to increase it. At V1, U decreases by 10% for the


raised panels, and increases by 10% for 10 in advantageous position and 30

in unfavourable position and by 19% for the 30 in advantageous position, atz/H < 1.18. The major dierence is just above the arrays (z/H = 1.007) inall cases. At V2, the U prole for the raised panels in advantageous positionis similar to the prole of the empty roof. At z/H < 1.13, U decreases forthe raised panels in unfavourable position and slightly increases in all theother cases. The highest increase is noticed for 30 in advantageous position.At V3, the U prole of the raised panels in advantageous position followsrather the same values than for the empty roof, U is drastically reduceduntil a 174% for the raised panels in unfavourable position at z/H < 1.18,due to a massive recirculation of the ow, and is increased until a 97% atz/H < 1.15 for 30 in advantageous position. It slightly increases for therest of the cases. At V4, U is reduced for the raised panels in unfavourableposition until a 36% at z/H < 1.23 and shows a slight deviation at the restof the cases.

Figure 3.9 shows the comparison of vertical proles of the turbulencekinetic energy at the dierent roof positions described in gure 3.7. Sur-prisingly, the turbulent kinetic energy decreases due to the presence of thesolar panels and the decrease is, in general, more pronounced for higher tiltangles, and even higher if the solar panels are raised from the roof. Thisresult is surprising since previous authors (Kopp et al. (2012)) assumed thatthe turbulence might increase due to the presence of obstacles on the roof,including solar panels. However, our result is validated with the experimentof Pratt and Kopp (2013), who found a decrease of the Reynolds Stresses,agreeing with the results of the present investigation. The decrease of theturbulent kinetic energy may be due to the damping (or cushion) eect ofthe recirculation vortices between the solar arrays (gure 3.10). In the caseof the raised panels, the recirculation ow between the panels and the roofsurface increases such damping eect. However, the raised panels, partic-ularly in unfavourable position, show a particular behaviour at the centerand downstream, where k increases at medium heights. This phenomenon(analysed below) is caused by the interaction between the vortices of neigh-bouring solar arrays. In what follows, the comparison rates are taken at thehighest value of k for the empty roof (peak value). At V1, k is reduced forthe raised panels up to a maximum rate of 5% for the advantageous position.It increases for the rest of the cases, until a maximum rate of 5% for the 30

in unfavourable position. At V2, k is reduced in all cases at z/H = 1.12until a maximum rate of 24% for the raised panels in advantageous posi-tion. At V3, k is reduced for the raised panels in unfavourable position atz/H < 1.11 until 63%. The value of k clearly decreases at the rest of thecases at z/H < 1.13 until a maximum rate of 19% for the case of the raisedpanels in advantageous position. The value of k for the raised panels isslightly higher than for the empty roof at 1.13 < z/H < 1.28. At V4, k is


0.0 0.2 0.4 0.6 0.8 1.0 1.2U/Uref

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H

Empty10-advantageous10-unfavourable30-advantagous30-unfavourable30-advantagous-up30-unfavourable-up

(a) V1

−0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2U/Uref

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H

(b) V2

−0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2U/Uref

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H

(c) V3

−0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2U/Uref

1.00

1.05

1.10

1.15

1.20

z/H

(d) V4

Figure 3.8: Comparison of the velocity at the vertical section at the centerof the domain, for the full-scale model. Note that some series (10 in V2 andV3) do not have values close to the roof, because the solar panels (includingthe support structure) ll this space.

reduced for the raised panels in unfavourable position at z/H < 1.1, for theraised panels and 10 (both in advantageous position) at z/H < 1.14, and atthe rest of the cases at z/H < 1.28, reaching a reduction rate of 14% for 30

in advantageous position. Additionally, the raised panels in advantageousposition show slightly higher values of k at 1.14 < z/H < 1.35, and also theraised panels in unfavourable position at 1.1 < z/H < 1.28.


0.00 0.05 0.10 0.15 0.20 0.25k/Uref

2

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H


(a) V1

0.00 0.05 0.10 0.15 0.20 0.25k/Uref

2

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H

(b) V2

0.00 0.05 0.10 0.15 0.20 0.25k/Uref

2

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H

(c) V3

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16k/Uref

2

1.00

1.05

1.10

1.15

1.20

1.25

1.30

z/H

(d) V4

Figure 3.9: Comparison of turbulent kinetic energy at the vertical sectionat the center of the domain, for the full-scale model.

The most signicant aspects for the qualitative analysis are the winddirection and the recirculations on the roof. Figure 3.10 shows the recircu-lation vortices generated on the roof at the raised panels cases. In all othercases, recirculation vortices appear between all the arrays as in gure 3.10a,in agreement with the experiment of Pratt and Kopp (2013). For the raisedpanels in unfavourable position, a massive recirculation that involves thewhole roof length is observed (see gure 3.10b). This massive recirculationis not identied in the experiment of Pratt and Kopp (2013) due to a scaling


issue related to the Reynolds number similarity constraints that is explainedin detail below. In all the cases, a recirculation vortex appears between theupstream edge of the roof and the rst array of solar panels, also observedin the experiment of Pratt and Kopp (2013).

(a) Advantageous position raised (b) Unfavourable position raised

Figure 3.10: Streamlines that show the recirculation vortices on the roof forthe 30 raised panels, at the full-scale model.

3.4.1 Reynolds number similarity constraints

Possible scaling issues were briey commented in previous sections. In orderto verify these issues, we have simulated all the previous cases using a 1:250reduced-scale model. Specically, we have used the wind-tunnel buildingused for the validation of the main ow (gure 2.13 in Chapter 2). Themain objective is to analyse the scaling issues involved in wind-tunnel ex-periments for the present application. The number of mesh cells used are9.8M and 10.1M for the cases of close (both 10 and 30) and raised panels,respectively.

Figures 3.11 and 3.12 show a comparison of vertical proles of U and k,respectively, at the dierent roof positions for all the situations describedin gure 3.7. It is observed that, in general, the behaviour of both U andk for the reduced-scale model are in accordance with the behaviour for thefull-scale model: decrease of k due to the presence of the solar panels, recir-culation of the ow between each solar array and between the rst array andthe upstream edge. The exception is for the case of the raised panels in un-favourable position, that for the reduced-scale model behaves as in the restof the cases, and the massive recirculation does not appear, as is shown ingures 3.11c and 3.13. Additionally, the results for the reduced-scale modelshow a more moderate behaviour than the full-scale models (the variations


are lower and they take place at a lower height).

0.2 0.4 0.6 0.8 1.0 1.2U/Uref

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H


(a) V1

−0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2U/Uref

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H

(b) V2

−0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2U/Uref

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H

(c) V3

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4U/Uref

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H

(d) V4

Figure 3.11: Comparison of the velocity at the vertical section at the centerof the domain, for the reduced-scale model.

The behaviour of the ow at the reduced-scale model is in agreementwith the experimental results obtained by Pratt and Kopp (2013). Thisis because the Reynolds number (based on the building height H and thereference velocity Uref ) has the same order of magnitude in both cases:Re = 4.7 × 104 for the reduced-scale CFD simulations and Re = 1.9 ×105 for the wind-tunnel experiment of Pratt and Kopp (2013). However,typical Reynolds numbers of full scale high-rise buildings are two orders of


0.00 0.05 0.10 0.15 0.20 0.25 0.30k/Uref

2

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H

(a) V1

0.00 0.05 0.10 0.15 0.20 0.25k/Uref

2

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H

(b) V2

0.00 0.05 0.10 0.15 0.20k/Uref

2

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H

(c) V3

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14k/Uref

2

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H


(d) V4

Figure 3.12: Comparison of turbulent kinetic energy at the vertical sectionat the center of the domain, for the reduced-scale model.

magnitude higher than the wind tunnel reduced-scale models. The Reynoldsnumber corresponding to the full-scale building considered in this chapter(where the scaling issues have been observed) is Re = 1.2 × 107. Prattand Kopp (2013) recognize that the Reynolds number of the wind-tunnelexperiment is 2 orders of magnitude too low for being compared with realcases. For the case of raised panels in unfavourable position, the separationbetween solar panels and the roof surface becomes more important with the


Figure 3.13: Streamlines that show the recirculation vortices on the roof forraised panels in unfavourable position, at the reduced-scale model.

increase of the Reynolds number. The interaction between the neighbouringvortices is promoted by the negative-velocity ow between the solar panelsand the roof. Since the ow is more turbulent in the full-scale building, therecirculation vortices between the solar arrays interact with the neighbouringones, causing a massive recirculation of the ow that involves the whole rooflength (see gure 3.10b). A solution verication (presented below) is carriedout in order to determine if these eects are real.

Therefore, the necessity of further experiments with higher Reynoldsnumbers is conrmed in the present investigation, in order to experimen-tally validate the results obtained with the numerical simulations for full-scale buildings. These future experiments can be carried out by means ofmeasurements on real-scale buildings, or in wind tunnels using water as amedium.

3.4.2 Solution verication

The independence of the nal results from the grid resolution must bedemonstrated. Since the cases where the recirculation vortices appear be-tween each solar array were tested for dierent meshes and even for dierentscales, this solution verication is going to focus on the case of the raisedpanels in unfavourable position, where a massive recirculation of the ow isobserved.

In order to check the independence of the results from the mesh reso-


lution, the simulation case of the raised panels in unfavourable position iscarried out by varying the mesh renement on the roof (with the same back-ground mesh), resulting in 3 dierent meshes: coarse (3.6M cells), medium-size (4.2M cells) and ne (7.1M cells) mesh.

Figure 3.14 shows the comparison of U between the 3 mesh resolutionsand the empty roof at the dierent positions described in gure 3.7. It isobserved that the behaviour of U is analogous for the 3 mesh resolutions,regarding the result on the empty roof. The most important point is thatthe massive recirculation of the ow is clearly conrmed for the 3 cases (seegure 3.14c).

Figure 3.15 shows the comparison of k between the 3 mesh resolutionsand the empty roof at the dierent positions described in gure 3.7. It isobserved that the behaviour of k is also analogous for the 3 mesh resolu-tions, regarding the result on the empty roof, showing a clear decrease ofk in comparison with the empty roof. Therefore, the nal solution can beconsidered veried.

3.4.3 Wind energy exploitation and wind turbine position-

ing

According to the European Wind Turbine Standards II (Pierik et al. (1999)),for a turbulence intensity higher than TI = 0.15 the fatigue loads of VAWThave to be re-evaluated based on the real wind conditions. Therefore,TI = 0.15 is used as a maximum admissible value for HAWT. Figure 3.16shows a plot of the vertical proles of TI up and downstream for the case ofthe raised panels (the most turbulent case) in comparison with the emptyroof and with the wind-tunnel experimental results of Meng and Hibi (1998).Five incident wind directions have been simulated in order to get a generalconclusion about wind turbines positioning: 0 (advantageous position), 45

(oblique-advantageous), 90 (lateral), 135 (oblique-unfavourable) and 180

(unfavourable position). From the incident wind directions tested, the ad-vantageous position (0) reaches the threshold TI = 0.15 at a higher heightboth up and downstream, at z/H = 1.2 and z/H = 1.29, respectively, whereH = 40 m is the height of the building. The oblique incident directions (45

and 135) reach the threshold at the lower heights in all cases, at z/H = 1.11and z/H = 1.2 up and downstream, respectively. For the rest of the incidentwind directions tested, the threshold TI = 0.15 is reached at z/H = 1.19and z/H = 1.28 up and downstream, respectively. This threshold is reachedfor the wind-tunnel experiment of Meng and Hibi (1998) at z/H = 1.19 andz/H = 1.31 up and downstream, respectively. An additional scaling issueis reported here, because the threshold at the reduced-scale case is reachedabove than at the full-scale building. This is expected because the higher isthe Reynolds number (2 orders of magnitude in this case) the thinner it is


0.0 0.2 0.4 0.6 0.8 1.0 1.2U/Uref

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H

Empty roofCoarse meshMedium-size meshFine mesh

(a) V1

−0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2U/Uref

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H

(b) V2

−0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2U/Uref

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H

(c) V3

−0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2U/Uref

1.00

1.05

1.10

1.15

1.20

z/H

(d) V4

Figure 3.14: Comparison of velocity at the vertical section at the center ofthe domain using 3 dierent meshes. Case of raised panels in unfavourableposition.

the boundary layer width.Figure 3.17a shows the turbulence intensity eld around the raised pan-

els in unfavourable position, and the isosurface corresponding to TI = 0.15throughout the roof. The grey line represents the limit (TI = 0.15) betweenthe most adequate areas for a HAWT and a VAWT. The most adequate areato install a HAWT is above TT = 0.15. Below this threshold a VAWT ismore appropriate because it is more resistant to velocity uctuations (Carp-man (2011)). It is important to mention that such velocity uctuations are


0.00 0.05 0.10 0.15 0.20 0.25k/Uref

2

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H

Empty roofCoarse meshMedium-size meshFine mesh

(a) V1

0.00 0.05 0.10 0.15 0.20 0.25k/Uref

2 )

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H

(b) V2

0.00 0.05 0.10 0.15 0.20 0.25k/Uref

2 )

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

z/H

(c) V3

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16k/Uref

2 )

1.00

1.05

1.10

1.15

1.20

1.25

1.30

z/H

(d) V4

Figure 3.15: Comparison of turbulence kinetic energy at the vertical sectionat the center of the domain using 3 dierent meshes. Case of raised panelsin unfavourable position.

lower due to the presence of the roof-mounted solar panels, and note thatthe presence of the solar panels does not aect signicantly the wind owbelow the threshold TI = 0.15 in comparison with the empty roof. Fromthe results above, a general rule for the wind turbines positioning on thiskind of building roofs is proposed considering the most conservative values:HAWT must be positioned at z/H > 1.20 upstream and z/H > 1.29 down-stream. Regardless of the incident wind direction, a HAWT can be placed


0.09 0.10 0.11 0.12 0.13 0.14 0.15TI

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

z/H

Exp. Meng and HibiEmpty roof0 - Advantageous4590135180 - Unfavourable

(a) Upstream

0.09 0.10 0.11 0.12 0.13 0.14 0.15TI

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

z/H

(b) Downstream

Figure 3.16: Vertical proles of turbulence intensity up and downstream ofthe roof considering dierent incident wind directions for the raised solarpanels, until the threshold TI = 0.15.

at z/H > 1.29 everywhere on the roof. Below these heights a VAWT mustbe considered.

Additionally, a VAWT can be placed in horizontal positions between theupstream edge of the roof and the rst array of solar panels in order to takethe most of the recirculation of the ow, as is shown in gure 3.17b. Dueto the rotative character of the wind at this region, this wind turbine willnot have opposite forces due to the wind (as in its conventional operation),which can signicantly enhance the eciency of the machine. One importantfactor to mention for this application is that for the advantageous directionsthe wind turbine may cause shadows over the solar panels and, therefore,the unfavourable directions are most adequate. Note that the names ad-vantageous and unfavourable refer to the most/less aerodynamic positionsaccording to the inlet wind although in this case, and also considering theresults for the raised panels, the appropriateness has been found opposite totheir respective names.

3.5 Conclusions

This Chapter presents an investigation of the eects of roof-mounted solarpanels on the wind ow on building roofs, from the point of view of the windenergy exploitation, in order to analyse the compatibility of both systems.CFD simulations of the wind ow around an isolated building were per-

3.5. Conclusions 101

(a) TI eld around the building (b) Detail VAWT in horizontal position up-stream

Figure 3.17: Turbulence intensity eld around the building and detail of aVAWT in horizontal position upstream. The grey line represents the thresh-old TI = 0.15 for the installation of HAWT (above) and VAWT (below),and the vectorial eld is the velocity.

formed with OpenFOAM using a modied Durbin RANS turbulence model.The turbulence model was validated twice: the main ow was validatedusing a wind-tunnel benchmark, and the ow around the solar panels bycomparing CFD results with a wind-tunnel experiment of an innite array.The wind ow on the empty roof is compared with roof-mounted solar pan-els cases. The solar panels are tested with tilt angles of 10 and 30, themost adequate inclination for solar panels in the Mediterranean region. Forthe tilt angle of 30 the solar panels are tested both close and raised fromthe roof surface. Additionally, each inclination is simulated with 2 incidentwind directions: advantageous and unfavourable, according to the aerody-namic position with respect to the incident wind. The analysis is carriedout both quantitatively and qualitatively. The full-scale building resultswere compared with a reduced-scale model and scaling issues are reported.Additionally, the solution is veried in order to check the independence ofthe results from the mesh resolution. Finally, the wind ow on the roof isanalysed and the most adequate wind turbine model for each roof region issuggested.

On the qualitative side, the recirculations on the roof were analysed andthe most appropriate wind turbine model for each roof region was suggested.As it is expected, recirculation vortices appear between the solar-panelsarrays. The rst vortex (between the upstream edge and the rst array) hasthe highest velocities. The installation of a VAWT in horizontal positioninside this vortex shows a very interesting potential. A general value (the


highest value obtained) for the installation of HAWT has been found atz/H > 1.29, regardless of the incident wind direction The installation of aVAWT is recommended below this limit.

The quantitative analysis includes the comparison of vertical proles ofstreamwise velocity and turbulent kinetic energy. No signicant dierencescompared to the empty roof are found above the isoline of TI = 0.15. Belowthe isoline TI = 0.15 the most important dierences appear for k, thatsignicantly decreases due to the presence of the solar panels; such decreaseis more pronounced for higher tilt angles. The decrease of the turbulentkinetic energy may be due to the damping eect of the recirculation vorticesbetween the solar arrays. The results are in agreement with the experimentsreported in the literature.

Scaling issues are reported. A massive recirculation takes place at theraised panels in unfavourable position due to the interaction of the neigh-bouring vortices between the arrays. This solution is veried in order todetermine if it is a real eect. This massive recirculation is not identiedat a reduced-scale model because of a Reynolds number decrease (2 ordersof magnitude lower than full-scale building). These scaling issues show thenecessity of further experimental studies considering full-scale conditions inorder to conrm the simulation results obtained. These further experimentsmust involve higher Reynolds numbers, either by means of measurements onreal (full-scale) buildings or in wind tunnels using water as a medium.

Bibliography notes

The content of this Chapter has been published in Toja-Silva et al. (2015b).

Chapter 4

Optimization of thebuilding-roof shape for thewind energy exploitation

All truths are easy to understand oncethey are discovered; the point is to

discover them.

Galileo Galilei

4.1 Methodology

After the detailed study of the at roof in previous chapters, this chapterfocus in the analysis of dierent roof shapes in order to identify which showsthe highest speed-up and the lower turbulence intensity.

The rst step is to verify the results of previous building-roof shapesstudied at the literature (Section 4.2). The basic shapes that are comparedare: at, pitched, shed, vaulted and spheric. The shed roof shape was studiedby Lu and Ip (2009), the pitched roof was investigated by Ledo et al. (2011)and the curved shapes were analysed by Abohela (2012). The spheric roofshape tested in Section 4.2 is the particular shape proposed by Abohela(2012) (see gure 4.5d). This step is important in order to continue theoptimization process from a rigorous analysis of the state-of-the-art data.

Then, the inuence of the roof-edge shape on the wind ow is analysedin Section 4.3. This task is carried out by comparing the results obtainedfor the conventional edge shape (simple corner) with a railing, a cantileverand a curved edge (see gure 4.6). The base-building is the same used inChapter 3 (gure 3.3), squared-plant (20x20 m) building 40 m high. Theedge-type with the best results will be used for the design of the optimumbuilding roof shape.

103

104 Chapter 4. Building-roof shape optimization

Once the best basic roof and edge shapes are identied, the building-roof shape optimization continues with the analysis of the roof-wall cou-pling (Section 4.4). Since the spherical roof is obtained as the best basicroof shape, dierent variations of a spherical roof on a high-rise building aretested: spherical roof studied in the literature, spherical roof geometricallyintegrated with the walls (squared-plant) and spherical roof with a cylin-drical wall. A comparison of U , k and TI is carried out. Additionally, asensitivity analysis of the roof width is applied to the optimum building-roofshape obtained in Section 4.5. The ow behaviour on the roof according tothe variation of the incident wind direction is commented.

Finally, the issues regarding the environment of the building are treated.The aspect ratio of the building and the eect of the surrounding buildingson the wind ow on the target building roof are analysed in Sections 4.6 and4.7, respectively.

4.2 State-of-the-art roof shapes

Several authors (Ledo et al. (2011); Lu and Ip (2009); Balduzzi et al. (2012))describe the inuence of sharp building-roof shapes on both the wind veloc-ity and turbulence intensity from results obtained using CFD simulations.These kind of studies are essential for determining the most appropriatebuilding shape and the optimal location and wind turbine model (Tabrizi etal. (2014)). In these studies, four types of roof shape were analysed: at,shed, pitched and pyramidal. The results showed that, considering bothvelocity distributions and turbulence intensity, at roofs were more attrac-tive for installing wind turbines (Ledo et al. (2011)). Shed roofs were alsointeresting, and a wind turbine could be installed on the top edge becauseboth high velocities and low turbulence intensities were present (Lu and Ip(2009)).

Abohela (2012) demonstrated the interest of both vaulted and sphericroofs because of the lower turbulence and the speed-up factor. Althoughthey are infrequently used, the curved shapes present a clear advantage forthe wind energy exploitation.

At this Section, the roof shapes previously analysed are tested, and theconclusions obtained at the present investigation are compared with thosefrom the literature commented above. This section is important in order torigorously analyse the advantages and drawbacks of the conventional roofshapes for continuing the optimization process from the state-of-the-art data.

4.2. State-of-the-art roof shapes 105

4.2.1 Description of the cases

As commented above, the state-of-the-art roof shapes are tested in thissection, specically: at, pitched, shed, spheric and vaulted roof shapes.The base-building is the same used in Chapter 3 (gure 3.3), squared-plant(20x20 m) building 40 m high. Figure 4.1 shows a diagram of the dierentroof shapes investigated (note that the vertical section of spheric and vaultedroofs is the same). The shed roof shape is the same studied by Lu and Ip(2009), the pitched roof is the same investigated by Ledo et al. (2011) andthe curved shapes are the same analysed by Abohela (2012). The sphericroof shape tested in this section is the particular shape proposed by Abo-hela (2012), a squared-plant building with a half sphere on the roof (seegure 4.5d).

As in Chapter 3, the background mesh is constructed using the structuredblockMesh application with a grading of 4 in the vertical direction and thebuilding geometry, previously designed with a CAD tool and saved in STLformat, is embedded into this background mesh using the snappyHexMesh

application of OpenFOAM (snappyHexMesh (2013); snappyHexMeshDict(2013)). The mesh around the building is rened and adapted to its shape.The renement distance around the building surfaces is 80 m. Figure 4.2shows a detail of the nal mesh obtained and the number of mesh cells usedat the roof shapes simulated.

The rest of the simulation details (inlet wind proles, boundary con-ditions, domain size, etc.) are the same than in Chapter 3. The turbu-lence model used is the Durbin k − ε (Durbin (1996)) proposed in Chapter2 (Toja-Silva et al. (2015d)) with the coecients of Crespo et al. (1985):Cµ = 0.0333, Cε1 = 1.176, Cε2 = 1.92, σk = 1.0, σε = 1.3 and κ = 0.42. Theturbulence modelling is validated in Chapter 2 (Toja-Silva et al. (2015d,c)).

4.2.2 Simulation results

The quantitative results are analysed by comparing U , k and TI between thedierent cases at the vertical axes shown in gure 4.1. These axes are locatedat the most advantageous position from the wind energy exploitation pointof view (highest speed-up and lowest turbulence intensity) for each case.This is on the upstream edge for the at roof, on the downstream edgefor the shed roof and on the center of the roof for the rest of the shapesinvestigated.

Figure 4.3a shows the comparison of vertical proles of U at the roofpositions described above. The eect of the roof shape on U is appreciableat z/H < 1.50. Both shed and pitched shapes show a similar behaviour, areduction of U , although it increases with respect to the at roof at z/H <1.06. The curved roofs cause a speed-up, with a concentration factor of the


(a) Flat roof. (b) Shed roof.

(c) Pitched roof. (d) Spheric/vaulted roof.

Figure 4.1: Central vertical section detail of the dierent roof shapes inves-tigated. The red AXIS indicates the points where the data is comparedbetween the dierent cases.

wind of around a 30%. The highest value of U is reached at the vaultedroof, although the value of U for the spheric roof studied by Abohela (2012)is only a 2.5% lower.

Figure 4.3b shows the comparison of vertical proles of k at the roofpositions described above. The eect of the edge shape on k is also appre-ciable at z/H < 1.35. All the tested models signicantly reduce the valueof k with respect to the at roof, and the peak value of k is reduced untila 63.8%. The spheric roof shows the global higher reduction, although thelower values at z/H < 1.05 are reached for shed and pitched roofs.


(a) Shed, 6.4M cells. (b) Pitched, 6.5M cells.

(c) Vaulted, 6.6M cells. (d) Spheric, 6.4M cells.

Figure 4.2: Vertical section detail of the rened meshes obtained using snap-pyHexMesh for the state-of-the-art analysis.

As is shown in gure 4.3c, the eect of the dierent roof shapes on thewind ow is clearly appreciated at the height of the turbulence intensity limitfor HAWT of TI < 0.15 (Pierik et al. (1999); Toja-Silva et al. (2015d,b))which, compared with the at roof, moderately increases for pitched andshed roofs (15.2% and 26.6%, respectively), moderately decreases at thevaulted roof (11.4%) and signicantly decreases at the spheric roof (40.5%).The lower TI threshold is reached for the spheric roof, at z/H = 1.12.

Figure 4.3d shows a comparison of the speed-up (U/Uref ) and the TIthreshold height for the state-of-the-art cases at the roof positions describedabove. The most interesting cases from the wind energy exploitation pointof view are at the low-right position in the graphic of gure 4.3d. Thatis, maximum speed-up and minimum turbulence intensity threshold height.


0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4U/Uref

1.0

1.1

1.2

1.3

1.4

1.5

z/H

FlatShedPitchedSphericVaulted

(a) Speed-up (U/Uref )

0.00 0.05 0.10 0.15 0.20 0.25k/Uref

2

1.0

1.1

1.2

1.3

1.4

1.5

z/H


(b) Nondimensional TKE (k/U2ref )

0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15TI

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

z/H


(c) TI below the limit of TI < 0.15

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4Maximum speed-up (U/Uref)

1.10

1.12

1.14

1.16

1.18

1.20

1.22

1.24

1.26

Height of the th

reshold TI=0.15

(z/H)


(d) Comparison of the speed-up (U/Uref ) andthe TI threshold height

Figure 4.3: Comparison of speed-up, nondimensional TKE and TI for thestate-of-the-art roof shapes analysis at the vertical axis on the center of theroof.

Therefore, the most interesting cases that will be investigated afterwardsin order to obtain the optimum shape are both vaulted and spheric. Thevaulted shape reaches a higher speed-up and the spheric a lower TI thresholdheight.


(a) Speed-up eld at roof (b) TI eld at roof

(c) Speed-up eld pitched roof (d) TI eld pitched roof

(e) Speed-up eld shed roof (f) TI eld shed roof

Figure 4.4: Comparison of speed-up (U/Uref ) and TI elds on the roof forthe state-of-the-art cases: sharp roofs.


The qualitative results are analysed by comparing both U and TI eldson the roof at the dierent cases, shown in gures 4.4 and 4.5. Regardingthe U eld, it is appreciated that the curved shapes (vaulted and spheric)generate a higher concentration factor that makes U even higher than thevalue of U several meters above the building. In the sharp cases (at, pitchedand shed) U is not horizontal at the highest speed position. Furthermore, itis appreciated that the curved shapes reduce the TI value, specially in thecase of the spheric shape.

(a) Speed-up eld vaulted roof (b) TI eld vaulted roof

(c) Speed-up eld spheric Abohela (d) TI eld spheric Abohela

Figure 4.5: Comparison of speed-up (U/Uref ) and TI elds on the roof forthe state-of-the-art cases: curved roofs.

4.2.3 Conclusion

Within this Section, the roof shapes previously analysed at the state-of-the-art are tested, and the results obtained at the present investigation are


compared with those obtained at the literature. The roof shapes analysedare: at, pitched, shed, spheric and vaulted roofs. The base-building isthe same used in Chapter 3, squared-plant (20x20 m) building 40 m high.A comparison of U , k and TI between the dierent cases is done with aquantitative approach, and a comparison of the U and TI elds on the roofis yield from a qualitative point of view.

The results show a similar behaviour of the ow at the sharp (pitchedand shed) and at the curved cases (spheric and vaulted), respectively.

In the sharp cases (at, pitched and shed) U is not horizontal at thehighest speed position. The highest speed-up is observed for the pitchedroof with a value close to the speed-up reached for the shed roof, that isaround a 35% higher than for the at roof at z/H < 1.06. This is inagreement with Lu and Ip (2009). However, a higher speed-up is observedfor the at roof at z/H > 1.06, showing there an agreement with Ledo etal. (2011). Therefore, the results of both investigations (higher speed-up forthe shed roof in Lu and Ip (2009) and higher speed-up for the at roof inLedo et al. (2011)) are conrmed by focusing at a dierent height.

Nevertheless, it is appreciated that the curved shapes (spheric and vaulted)generate a concentration factor much higher than the sharp shapes. Thisconcentration factor makes U even higher than the value of U several me-ters above the building. This conclusion is in the line of by Abohela (2012).However, in the present investigation, the speed-up reached for the vaultedroof is only 2.5% lower than for the spherical roof, and the TI thresholdheight for HAWT on the spherical roof is around a 30% lower than on thevaulted roof. Therefore, the results obtained in the present Thesis for thespherical roof are very interesting for the wind energy application. Further-more, it is appreciated that the curved shapes signicantly reduce the TIvalue with respect to the sharp shapes, specially in the case of the sphericshape. The spheric roof has the additional advantage that it will presentthe same behaviour (or very similar) for whichever incident wind direction.

The most important conclusion within the framework of this investiga-tion is that an optimum building-roof shape for the wind energy exploitationnecessarily passes by the use of curved shapes. Specically, the curved roofshapes that present a better performance are spheric and vaulted shapes.The further work recommendation for obtaining an optimum building-roofshape is to investigate the wall-roof coupling of the spheric shape, and tocarry out geometrical sensitivity analyses of both vaulted and spheric shapes.


4.3 Inuence of the roof-edge shape on the wind

ow

The analysis of the inuence of the roof-edge shape on the wind ow arounda conventional building is necessary before investigating the wall-roof cou-pling with more complex building-roof shapes. This task is carried out bycomparing the results obtained for the conventional edge shape (simple cor-ner) with a railing, a cantilever and a curved edge (see gure 4.6).

(a) Simple edge. (b) Curved edge.

(c) Railing. (d) Cantilever.

Figure 4.6: Examples of the dierent roof-edges tested.


The base-building is the same used in Chapter 3 (gure 3.3), squared-plant(20x20 m) building 40 m high. All the simulation details (inlet wind, bound-ary conditions, domain size, etc.) are thus the same. Additionally, the turbu-lence model used is the Durbin k − ε (Durbin (1996)) proposed in Chapter2 (Toja-Silva et al. (2015d)) with the coecients of Crespo et al. (1985).The turbulence modelling is validated at Chapters 2 and 3 (Toja-Silva et al.

4.3. Inuence of the roof-edge shape on the wind ow 113

(2015d,b)).As stated above, the present analysis is carried out by comparing the

results obtained for the conventional edge shape (simple corner) with thoseobtained in CFD simulations for railing, cantilever and curved edges. Fig-ure 4.7 shows a diagram of the dierent options investigated. The regulationUNE-EN ISO 14122-3:2002/A1:2010 (Asociación Española de Normaliza-ción y Certicación (2010); International Organization for Standardization(2001)) stats that the height of a handrail on a building roof must be atleast 1.1 m. Therefore, 1 m is used as a round value for the railing height inthe CFD simulations. The same value is used for both cantilever and curvededge in order to be rigorous and honest in the analysis of the eect of thegeometric shape on the ow, because geometric elements of the same sizeare compared.

(a) Simple edge. (b) Curved edge.

(c) Railing. (d) Cantilever.

Figure 4.7: Central vertical section detail of the dierent roof-edge shapesinvestigated. The red axes V1-V4 indicate the points where the data iscompared between the dierent cases. Note that the axes V1 and V4 startfrom the normal height of the roof also for the curved edge, although bothupstream and downstream edges of the roof are 1 m below in this case.Additionally, note that the axes V1 and V4 start from 1 m above the normalroof height for the railing due to the presence of this element.

As in Chapter 3, the background mesh is constructed using the structuredblockMesh application with a grading of 4 in the vertical direction and thebuilding geometry, previously designed with a CAD tool and saved in STLformat, is embedded into this background mesh using the snappyHexMesh


application of OpenFOAM (snappyHexMesh (2013); snappyHexMeshDict(2013)). The mesh around the building is rened and adapted to its shape.The renement distance around the building surfaces is 80 m. Figure 4.8shows a detail of the nal meshes obtained and the number of mesh cellsused for each case.

(a) Simple edge, 6.7M cells. (b) Curved edge, 6.7M cells.

(c) Railing, 6.9M cells. (d) Cantilever, 6.9M cells.

Figure 4.8: Vertical section detail of the rened meshes obtained using snap-pyHexMesh.


The quantitative results are analysed by comparing U , k and TI betweenthe dierent cases at the vertical axes V1-V4 located at the central plane ofthe domain according to the diagram shown in gure 4.8.

Figure 4.9 shows the comparison of vertical proles of U at the dierentroof positions described in gure 4.8. The eect of the edge shape on U


−0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2U/Uref

1.0

1.1

1.2

1.3

1.4

1.5

z/H

SimpleCantileverRailingCurved

(a) V1

−0.5 0.0 0.5 1.0U/Uref

1.0

1.1

1.2

1.3

1.4

1.5

z/H

(b) V2

−0.4−0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2U/Uref

1.0

1.1

1.2

1.3

1.4

1.5

z/H

(c) V3

0.0 0.2 0.4 0.6 0.8 1.0 1.2U/Uref

1.0

1.1

1.2

1.3

1.4

1.5

z/H

(d) V4

Figure 4.9: Comparison of the speed-up (U/Uref ) at the vertical section onthe center of the domain.

is signicant at z/H < 1.25. Additionally, the railing edge also aect Udownstream at z/H < 1.33. Both the simple edge and the cantilever showa similar behaviour. The railing has a very negative eect on U , reducing itconsiderably. The positive aspect of the railing is that the negative velocity


0.00 0.05 0.10 0.15 0.20 0.25 0.30k/Uref

2

1.0

1.1

1.2

1.3

1.4

1.5

z/H


(a) V1

0.00 0.05 0.10 0.15 0.20 0.25k/Uref

2

1.0

1.1

1.2

1.3

1.4

1.5

z/H

(b) V2

0.00 0.05 0.10 0.15 0.20 0.25k/Uref

2

1.0

1.1

1.2

1.3

1.4

1.5

z/H

(c) V3

0.00 0.05 0.10 0.15 0.20k/Uref

2

1.0

1.1

1.2

1.3

1.4

1.5

z/H

(d) V4

Figure 4.10: Comparison of the nondimensional TKE (k/U2ref ) at the vertical

section on the center of the domain.

at the recirculation ow is very high, reaching values of U/Uref = −0.4 atthe central-upstream region of the roof. The curved edge has a very positiveeect on U at the whole roof, reaching upstream velocities even higher than


the freestream velocity.

0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15TI

1.1

1.2

1.3

1.4

1.5

1.6

1.7

z/H


(a) V1

0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15TI

1.1

1.2

1.3

1.4

1.5

1.6

1.7

z/H

(b) V2

0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15TI

1.1

1.2

1.3

1.4

1.5

1.6

1.7

z/H

(c) V3

0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15TI

1.1

1.2

1.3

1.4

1.5

1.6

1.7

z/H

(d) V4

Figure 4.11: Comparison of TI below the limit of TI < 0.15 at the verticalsection on the center of the domain.

Figure 4.10 shows the comparison of vertical proles of k at the dierentroof positions described in gure 4.8. The eect of the edge shape on k isimportant at z/H < 1.35. Again, the railing aects the value of k also atz/H < 1.45, specially at the center and downstream. Both the simple edgeand the cantilever show almost the same behaviour on the entire roof. The kis increased at the railing case at 1.06 < z/H < 1.45, specially at the centerand downstream. The value of k at the curved edge signicantly decreases


at 1.03 < z/H < 1.35, specially at the center and downstream, reachingdecrease rates close to 30%. Therefore, the curved edge has a very positiveeect also on k.

The eect of the dierent edge types tested is clearly appreciated at theheight of the turbulence intensity threshold for HAWT of TI < 0.15 (Pieriket al. (1999); Toja-Silva et al. (2015d,b)), which remains rather constant atthe cantilever and the simple edge, signicantly increases at the railing anddecreases at the curved edge (see gure 4.11). At the railing, the heightof the turbulence intensity threshold of TI = 0.15 is raised up to a 20%upstream, a 16% at the central region and 10% downstream. At the curvededge, the TI threshold height decrease around a 16% upstream and a 12%at the central region and downstream.

(a) Speed-up eld simple edge (b) TI eld simple edge

(c) Speed-up eld cantilever (d) TI eld cantilever

Figure 4.12: Comparison of speed-up (U/Uref ) and TI elds on the roof.

The qualitative results are analysed by comparing both U and TI eldson the roof at the dierent cases, shown in gures 4.12 and 4.13. As in the


quantitative analysis, a similar behaviour of the ow is appreciated at thesimple edge and the cantilever cases. At the railing, a massive recirculationof the ow that exceeds the roof length is shown (gure 4.13a), and theheight of the TI threshold of TI = 0.15 is raised up. The curved edge showsa clear favourable behaviour. On one hand, it is appreciated a very smallrecirculation of the ow on the roof (XR = 0.08) and U presents a speed-up around the upstream edge, and on other hand the TI threshold heightsubstantially decreases (12-16%).

(a) Speed-up eld railing (b) TI eld railing

(c) Speed-up eld curved edge (d) TI eld curved edge

Figure 4.13: Comparison of speed-up (U/Uref ) and TI elds on the roof.

4.3.3 Conclusion

Within this Section, an analysis of the inuence of the roof-edge shape onthe wind ow on a high-rise building is carried out. A comparison of theCFD results obtained for the conventional edge shape (simple corner) with


a railing, a cantilever and a curved edge is presented. A comparison of U , kand TI between the dierent cases is done with a quantitative approach, anda comparison of the U and TI elds on the roof is yield from a qualitativepoint of view.

The results show a similar behaviour of the ow at the simple edge andthe cantilever cases. At the railing, a massive recirculation of the ow thatexceeds the roof length is appreciated, and the height of the TI threshold ofTI = 0.15 is raised up. At the curved edge there is a very small recirculationof the ow on the roof, U presents a speed-up around the upstream edgeand the TI threshold height substantially decreases.

The most important conclusion within the framework of this investiga-tion is that the coupling between the walls and the roof has a great impor-tance. Another important conclusions is the conrmation that an optimumbuilding-roof shape for the wind energy exploitation necessarily passes bythe use of curved edges and shapes, clearly leading to U speed-up and TIdecrease.

4.4 Wall-roof coupling analysis


In addition to the squared-plant building with a half sphere on the roofanalysed at Abohela (2012), two additional variations of the spheric roof aretested in the present investigation: a spheric roof geometrically integratedwith the walls (squared-plant) and a spheric roof with a cylindrical wall.Figure 4.16 shows a 3D diagram of the three cases, where the dierencesbetween models can be appreciated.

The background mesh is constructed using the structured blockMesh

application with a grading of 4 in the vertical direction and the buildinggeometry, previously designed with a CAD tool and saved in STL format, isembedded into this background mesh using the snappyHexMesh applicationof OpenFOAM (snappyHexMesh (2013); snappyHexMeshDict (2013)). Themesh around the building is rened and adapted to its shape. The renementdistance around the building surfaces is 80 m. Figure 4.14 shows a detailof the nal mesh obtained and the number of cells used at the additionalvariations of the spheric roof simulated in this investigation.

The rest of the simulation details (inlet wind, boundary conditions, do-main size, etc.) are the same than in Chapter 3. The turbulence model usedis the Durbin k − ε (Durbin (1996)) proposed in Toja-Silva et al. (2015d)with the coecients of Crespo et al. (1985). The turbulence modelling isvalidated in Chapters 2 and 3 (Toja-Silva et al. (2015d,b)).

4.4. Wall-roof coupling analysis 121

(a) Spheric roof integrated, 6.0M cells. (b) Spheric roof cylinder, 6.1M cells.

Figure 4.14: Vertical section detail of the rened meshes obtained usingsnappyHexMesh for the additional spheric roofs.


The quantitative results are analysed by comparing U , k and TI between thedierent cases at the vertical axis located at the most advantageous positionfor the wind energy exploitation (highest speed-up and lowest turbulenceintensity), the center of the roof in this case (AXIS in gure 4.1d).

Figure 4.15a shows the comparison of vertical proles of U on the centerof the roof. The eect of the wall-roof coupling on U is signicant at z/H <1.16. The lower value of U is reached for the spheric roof studied by Abohela(2012), intermediate values are reached for the spheric roof integrated andthe highest values are reached for the spheric roof with a cylindrical wall,showing an increase of U by 12% with respect to the worst case (spheric roofof Abohela (2012)).

Figure 4.15b shows the comparison of vertical proles of k on the centerof the roof. The eect on k of the wall-roof coupling between the spheric roofof Abohela (2012) and the rest of the shapes is shown z/H < 1.5. Betweenintegrated and cylindric cases, the dierences at the k prole appear atz/H < 1.2. The lowest values of k are shown in the case of the spheric roofwith a cylindrical wall, yielding a decrease rate of 38% with respect to thesecond best option.

As is shown in gure 4.15c, the wall-roof coupling has a strong inuenceon the turbulence intensity at z/H < 1.75. The height of the turbulenceintensity threshold for HAWT of TI < 0.15 (Pierik et al. (1999); Toja-Silvaet al. (2015d,b)) is lower in the case of the integrated spheric case and, inthe case of the cylindrical wall this threshold is not matched on the roof(TI is always lower than 0.15 on the roof). This is a very important feature,


0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6U/Uref

1.00

1.02

1.04

1.06

1.08

1.10

z/H

Spheric integratedSpheric AbohelaSpheric cylinder


0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10k/Uref

2

1.00

1.05

1.10

1.15

1.20

z/H



0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15TI

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

z/H



1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44Maximum speed-up (U/Uref)

1.00

1.05

1.10

1.15

Heig

ht o

f the

thre

shol

d TI

=0.

15 (z

/H)

VaultedSpheric cylinderSpheric integratedSpheric Abohela


Figure 4.15: Comparison of speed-up, nondimensional TKE and TI for thewall-roof coupling analysis at the vertical axis on the center of the roof.

because a HAWT can be used on a cylindric spheric roof at whichever height,signicantly increasing the eciency and, thus, increasing the power output.Note that HAWT have higher eciency (or power coecient) than VAWT(see Chapter 1).

Figure 4.15d shows a comparison of the speed-up (U/Uref ) and the TIthreshold height for the wall-roof coupling analysis on the center of the roof.The values corresponding to the vaulted roof are also represented. The mostinteresting cases from the wind energy exploitation point of view are at the


low-right position. The most interesting case is clearly the spheric roof witha cylindrical wall. From the gures can be deduced that the spheric roofshapes reduce the turbulence intensity in all cases. Additionally, the softlycoupling (curved edge) of the wall and the roof leads to a speed-up increase.

The qualitative results are analysed by comparing both U and TI eldson the roof at the dierent cases, shown in gure 4.16. It is clearly observedthat the cylindric wall obtains the best results, specially attending to theTI threshold for HAWT, that is not reached and, thus, a HAWT can beinstalled on the center of the roof at whichever height. It is conrmed thata smooth coupling between the walls and the roof has a great importance inorder to obtain a U increase and a TI decrease on the roof.

(a) Speed-up eld spheric roof integrated (b) TI eld spheric roof integrated

(c) Speed-up eld spheric roof cylinder (d) TI eld spheric roof cylinder

Figure 4.16: Comparison of speed-up (U/Uref ) and TI elds for the wall-roofcoupling analysis of the spheric roofs.

An additional advantage of the spheric roof with a cylindrical wall isthat the ow behaviour is the same for all the incident wind angles. If a


(a) Transversal speed-up eld vaulted roof (b) Transversal TI eld vaulted roof

(c) Transversal speed-up eld spheric roofcylinder

(d) External view of the isosurface TI = 0.15around spheric roof-cylinder building

Figure 4.17: Transversal elds of speed-up (U/Uref ) and TI for vaulted andcylindrical wall-spheric roof.

specic site has a clearly identied incident wind angle, a very frequent situ-ation (Jiménez and Dudhia (2013); Whiteman (2000)), the vaulted roof hasan apparent advantage because the whole transversal plane is available forinstalling wind turbines (gure 4.17a). However, also the sides are suitablefor installing wind turbines on the spheric roof with cylindrical wall (seegure 4.17c) being U higher than on vaulted roof; and HAWT can be in-stalled because TI is lower than the threshold on the roof and sides of thebuilding. Figure 4.17d show the isosurface (in grey colour) correspondingto TI = 0.15 for the spheric-cylinder case, where it is observed that thisisosurface does not cover the whole building (in red colour). In the case ofthe vaulted roof, if the wind turbines may be installed close to the buildingsurface, only VAWT can be installed because of the higher TI (higher than


the threshold). Figure 4.17b shows the isoline corresponding to TI = 0.15around the vaulted roof building. A HAWT can only be installed outsidethis isoline. Note that the discussion is from the building aerodynamicspoint of view and structural, manufacturing and installation considerationsare not taken into account.

4.4.3 Solution verication

In order to verify the independence of the results from the mesh resolution,the simulation case of the most advantageous building-roof shape (sphericalroof cylinder) is carried out by varying the mesh renement, resulting in3 dierent meshes: coarse (3.8M cells), medium-size (6.1M cells) and ne(9.8M cells) mesh. Figure 4.18 shows a detail of the 3 dierent meshes tested.

(a) Coarse mesh, 3.8M cells (b) Medium mesh, 6.1M cells (c) Fine mesh, 9.8M cells

Figure 4.18: Detail of the 3 dierent meshes used for the solution verication.

Figure 4.19 shows the comparison of U and k between the 3 mesh reso-lutions on the center of the roof. It is observed that the behaviour of bothU and k is analogous for the 3 mesh resolutions. Due to the lower meshresolution close to the roof surface, the coarse mesh results show a clearunderestimation of U and an overestimation of k at 1 < z/H < 1.025. Theresults for both medium and ne meshes do not show signicant dierences.Therefore, the solution can be considered veried.

4.4.4 Conclusion

Two new variations of the spheric roof are tested in the present investigation:a spheric roof geometrically integrated with the walls (squared-plant) and aspheric roof with a cylindrical wall. A comparison of U , k and TI betweenthe dierent cases is carried out, and the nal results are compared withthose obtained for the spheric roof of Abohela (2012) and for the vaultedroof.

The spheric roof shapes reduce the turbulence intensity in all cases. Ad-ditionally, the softly coupling (curved edge) of the wall and the roof leads to a


speed-up increase. The most interesting case is clearly the spheric roof witha cylindrical wall. The speed-up is higher than for the other cases, but alsospecially attending to the turbulence intensity threshold for HAWT, that isnot reached and, thus, a HAWT can be installed on the roof at whicheverheight. An additional advantage of the spheric roof with a cylindrical wallis that the ow behaviour is the same for all the incident wind angles. Addi-tionally, the roof and wall sides are also suitable for installing wind turbines,under the same conditions than on the top of the roof.

The independence of the results from the mesh resolution was veriedby the simulation of the most advantageous building-roof shape (sphericalroof cylinder) using 3 dierent meshes (coarse, medium-size and ne).

In this investigation is observed that the wall shape has a great impor-tance on the roof wind ow, and that the softly coupling of a cylindrical wallwith a spheric roof is the best conguration for the wind energy exploita-tion on the roof, leading to speed-up maximization and turbulence intensityminimization. Further investigations for obtaining an optimum roof shapemay deal with a sensitivity analysis of the roof width keeping the obtainedconguration.

1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45U/Uref

1.00

1.05

1.10

1.15

1.20

z/H

Coarse meshMedium meshFine mesh


0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055k/Uref

2

1.00

1.05

1.10

1.15

1.20

z/H

Coarse meshMedium meshFine mesh


Figure 4.19: Comparison of speed-up and nondimensional TKE on the centerof the roof using 3 dierent meshes for the solution verication.

4.5. Sensitivity analysis of the roof width 127

4.5 Sensitivity analysis of the roof width


Based on the previous results, the spherical roof coupled with a cylindricalwall is the best shape for the wind energy exploitation. Therefore, dierentroof widths are investigated in order to identify the most adequate designattending to the highest speed-up and the lowest turbulence intensity.

The base-building is the same as above. In addition to the exact spheretested above (r/H = 0.25), four additional roof-shapes with dierent width-to-height ratios are simulated. Figure 4.20 shows a diagram of the four cases,two with higher and two with lower widths, respectively. Note that theseshapes correspond to stretched versions of the spherical shape.

(a) r/H=0.125 (b) r/H=0.2

(c) r/H=0.5 (d) r/H=1

Figure 4.20: Diagram of the dierent roof-shapes investigated for the sensi-tivity analysis of the roof width (r).


All the computational settings (boundary conditions, inlet proles, tur-bulence model, coecients, discretization schemes, meshing methodology,etc.) are the same used above. Figure 4.21 shows a close-up view of thenal meshes obtained.

(a) r/H=0.125, 6.1M cells. (b) r/H=0.2, 6.1M cells.

(c) r/H=0.5, 5.6M cells. (d) r/H=1, 5.5M cells.

Figure 4.21: Vertical section detail of the rened mesh obtained using snap-pyHexMesh for the sensitivity analysis of the roof width.

4.5.2 Results and discussion

The quantitative results are analysed by comparing U , k and TI betweenthe dierent cases at the vertical axis located on the center of the roof.

Figure 4.22a shows a comparison of vertical proles of U on the centerof the roof. The eect of the wider roofs on U is signicant at z/H < 1.75.The thinnest roof (r/H = 0.125) aect U at z/H < 1.2, whereas U is onlyaected at z/H < 1.02 for r/H = 0.2. Velocity decreases in all cases with


respect to the exact spherical shape (r/H = 0.25), specially for r/H = 0.125where the maximum value of U decreases a 9%. The wider roofs show adecrease at the whole U prole, and the thinner roofs show a decrease nearthe roof surface but more signicant attending to the maximum value.

1.0 1.1 1.2 1.3 1.4 1.5U/Uref

1.00

1.05

1.10

1.15

1.20

1.25

1.30

z/H

r/H=0.125r/H=0.2r/H=0.25r/H=0.5r/H=1


0.00 0.02 0.04 0.06 0.08 0.10 0.12k/Uref

2

1.00

1.05

1.10

1.15

1.20

1.25

1.30

z/H

r/H=0.125r/H=0.2r/H=0.25r/H=0.5r/H=1


0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15TI

1.00

1.05

1.10

1.15

1.20

1.25

1.30

z/H

r/H=0.125r/H=0.2r/H=0.25r/H=0.5r/H=1


1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44Maximum speed-up (U/Uref)

1.00

1.02

1.04

1.06

1.08

Height of t

he th

resh

old TI=0.15

(z/H

)

r/H=0.125r/H=0.2r/H=0.25r/H=0.5r/H=1


Figure 4.22: Comparison of speed-up, nondimensional TKE and TI for theroof width analysis at the vertical axis on the center of the roof.

Figure 4.22b shows a comparison of vertical proles of k on the center ofthe roof. A decrease of k is shown at z/H < 1.15 for the thinner roofs. Thethinner the roof the higher the decrease. For the wider roofs k increases upto 120% at z/H < 1.07− 1.09. Both wider cases show a similar behaviour.


Contrary to the expected, the behaviour of k for the wider roofs is moresimilar to the at roof, showing a sudden peak value close to the roof.

Figure 4.22c shows a comparison of TI below the threshold value ofTI = 0.15. The thinner roofs show a decrease of TI with respect to thecase of r/H = 0.25 at z/H < 1.17. The thinner is the roof the higher isthe decrease in TI. The wider roofs reach the threshold of TI = 0.15 atz/H = 1.08 and z/H = 1.06 for the cases of r/H = 0.5 and r/H = 1,respectively.

Figure 4.22d shows a comparison of the speed-up (U/Uref ) and the TIthreshold height for the roof width analysis on the center of the roof. Themost interesting case is clearly the exact spherical roof (r/H = 0.25), fol-lowed by the case with r/H = 0.2. As shown in gure 4.23, the thinnerroofs show a good behaviour from the point of view of TI, but the decreaseof U is higher for lower values of r. The maximum value of U is reached forthe exact sphere (r/H = 0.25). The wider roofs show a moderate decreaseof U but a signicant increase of k, as is clearly appreciated in gure 4.23.

1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44Maximum speed-up (U/Uref)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

r/H

(a) Maximum speed-up)

0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12Maximum turbulent kinetic energy (k/Uref

2 )

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

r/H

(b) Maximum nondimensional TKE

Figure 4.23: Maximum values of speed-up (U/Uref ) and nondimensionalTKE (k/U2

ref ) for the dierent roof widths investigated.

The results are analysed qualitatively by comparing both U and TI eldson the roof for the dierent cases, shown in gures 4.24 and 4.25. It is clearlyobserved that the thinner roofs show the best results with a low TI thresholdfor HAWT. Specially, the case of r/H = 0.125 shows a bigger region on theroof with TI < 0.15 (see gure 4.24b). The maximum values of U are alsospread onto a bigger roof surface for r/H = 0.125 (see gure 4.24a). It is


observed in gures 4.25b and 4.25d that VAWT cannot be installed close tothe wider roof surfaces because TI > 0.15.

(a) Speed-up eld r/H = 0.125 (b) TI eld r/H = 0.125

(c) Speed-up eld r/H = 0.2 (d) TI eld r/H = 0.2

Figure 4.24: Comparison of speed-up (U/Uref ) and TI elds for the roofwidth analysis: thinner width shapes.

4.5.3 Conclusions

A sensitivity analysis of the roof width was applied to the optimum building-roof shape obtained. The most interesting case for the wind energy exploita-tion is the exact sphere (r/H = 0.25), leading to a low TI and to the maxi-mum speed-up between the shapes analysed. The thinner roofs show a lineardecrease of k (and of TI by extension), but they also show a linear decreaseof U (reaching signicant values for low values of r). The wider roofs showa moderate decrease in U but a signicant increase in k (exceeding the TIthreshold for HAWT close to the roof surface).


(a) Speed-up eld r/H = 0.5 (b) TI eld r/H = 0.5

(c) Speed-up eld r/H = 1 (d) TI eld r/H = 1

Figure 4.25: Comparison of speed-up (U/Uref ) and TI elds for the roofwidth analysis: wider width shapes.

4.6 Analysis of the building aspect ratio


Based on the previous results, the exact spherical roof (r/H = 0.25) coupledwith a cylindrical wall is the best shape for the wind energy exploitation.The inuence of the building aspect ratio (AR) on the wind ow on the roofis also investigated in this Section.

In addition to the 1:1:2 aspect ratio building tested thus far, three ad-ditional aspect ratios are simulated, always keeping the exact spherical roofand the height of the building (40 m). Figure 4.26 shows a diagram of thethree cases.

All the computational settings (domain, boundary conditions, inlet pro-

4.6. Analysis of the building aspect ratio 133

(a) AR=1:1:4 (b) AR=1:1:1

(c) AR=2:2:1

Figure 4.26: Diagram of the dierent aspect ratios (AR) investigated.

les, turbulence model, coecients, discretization schemes, meshing method-ology, etc.) are the same used above. Figure 4.27 shows a detail of the nalmeshes obtained. Note that, keeping the same renement conditions, thenumber of cell nodes considerably increases with the aspect ratio. The higherthe aspect ratio (D/H) the larger the surface of the building and, therefore,the higher the number of cell nodes.


The results are qualitatively analysed by comparing U , k and TI betweenthe dierent cases at a vertical axis located on the center of the roof.


(a) AR=1:1:4, 5.2M cells. (b) AR=1:1:1, 7.1M cells. (c) AR=2:2:1, 9.5M cells.

Figure 4.27: Vertical section detail of the rened mesh obtained using snap-pyHexMesh for the dierent aspect ratios tested. The aspect ratio (AR) andthe number of mesh cells are also indicated.

Figure 4.28a shows the comparison of vertical proles of U on the centerof the roof. The cases with a higher aspect ratio (D/H) show a more ho-mogeneous vertical prole for U , but they reach a lower maximum velocityclose to the roof surface. On the other side, the lower aspect ratio leadsto a higher maximum velocity that suddenly increases approaching the roofsurface.

Figure 4.28b shows a comparison of vertical proles of k on the center ofthe roof. The higher the aspect ratio the higher the value of k, and the higherthe height where the inuence on the ow is observed. The case AR=2:2:1(half sphere) shows a dierent behaviour than the case AR=1:1:1 due tothe absence of the cylindrical wall. Although k increases with respect tothe base-case (AR=1:1:2), the half sphere breaks the clearly dened patternfollowed by the other cases. Higher values of k are reached at higher heightswhile reaching a lower maximum close to the roof surface compared to otherhigh aspect ratio cases. Therefore, slender shapes are the most interestingfrom the point of view of k reduction.

Figure 4.28c shows a comparison of TI below the threshold value ofTI = 0.15. The vertical prole of TI shows a similar behaviour for aspectratios of D/H ≤ 0.5. Although TI decreases for lower aspect ratios, themaximum values are on the same order. On the other side, the higher aspectratios lead to higher values of TI, reaching the threshold of TI = 0.15 in thecases of AR=1:1:1 and AR=2:2:1 at z/H < 1.12 and 1.04 < z/H < 1.09,respectively. Due to the absence of the cylindrical wall on k described above,the case AR=2:2:1 show values lower than the TI threshold close to the roofsurface.

Figure 4.28d shows a comparison of the speed-up (U/Uref ) and the TIthreshold height on the center of the roof. It is clearly observed that thelower aspect ratios are the most interesting. As shown in gure 4.29a, U

4.6. Analysis of the building aspect ratio 135

1.0 1.1 1.2 1.3 1.4 1.5U/Uref

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

z/H

AR=1:1:4AR=1:1:2AR=1:1:1AR=2:2:1


0.01 0.02 0.03 0.04 0.05 0.06 0.07k/Uref

2

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

z/H

AR=1:1:4AR=1:1:2AR=1:1:1AR=2:2:1


0.09 0.10 0.11 0.12 0.13 0.14 0.15TI

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

z/H

AR=1:1:4AR=1:1:2AR=1:1:1AR=2:2:1



1.00

1.02

1.04

1.06

1.08

1.10

1.12

Height of the

threshold TI=0.15

(z/H)

AR=1:1:4AR=1:1:2AR=1:1:1AR=2:2:1


Figure 4.28: Comparison of speed-up, nondimensional TKE and TI for theaspect ratio analysis at the vertical axis on the center of the roof.

is higher for the lower aspect ratios, showing the maximum for the case ofAR=1:1:2. Additionally, as shown in gure 4.29b, k increases for higheraspect ratios, reaching the maximum value before removing the wall (half-sphere building).

A qualitative comparison of U and TI on the roof for the dierent casesis shown in gure 4.30. The case AR=1:1:1 exceeds the TI threshold for



0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

D/H

(a) Maximum speed-up

0.045 0.050 0.055 0.060 0.065 0.070Maximum turbulent kinetic energy (k/Uref

2 )

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

D/H



ref ) for the dierent aspect ratios investigated.

HAWT close to the roof. The case AR=2:2:1 also exceeds this threshold, butlower values of TI are observed slightly downstream from the center of theroof (see gure 4.30f). According to this, VAWT may be considered in bothcases. However, since the vertical prole of U is more homogeneous withheight (as commented above), wind turbines can be installed at a higherheight on the roof.

4.6.3 Conclusion

The aspect ratio of the building-roof shape was explored keeping both theheight of the building and the obtained optimum geometry. A comparisonof U , k and TI was carried out for the isolated building.

The results showed that slender shapes (low aspect ratio) are more inter-esting for the wind energy exploitation, leading to a higher speed-up and toa lower TI. The maximum value of U was found for the aspect ratio 1:1:2.The lower the aspect ratio the lower the k. Due to the variations in U andk, similar values of TI were found for D/H < 0.5.

4.7 Inuence of the surrounding buildings


An urban environment is considered in this section. An analysis of the window over the spherical-roof with cylindrical wall building surrounded by

4.7. Inuence of the surrounding buildings 137

(a) Speed-up eld AR=1:1:4 (b) TI eld AR=1:1:4

(c) Speed-up eld AR=1:1:1 (d) TI eld AR=1:1:1

(e) Speed-up eld AR=2:2:1 (f) TI eld AR=2:2:1

Figure 4.30: Comparison of speed-up (U/Uref ) vector eld and TI = 0.15isosurface for the dierent aspect ratios.


neighbouring buildings is presented. According to the classication of Oke(1988) explained in Section 2.4, the surrounding buildings (general patternfor the representation of an urban environment) considered are in wake in-terference or skimming ow depending on their height in each case, avoidingthe case of isolated roughness ow because the isolated building is exten-sively studied in previous sections. The separation between the buildings isset to 20 m in order to consider a conventional street. A regular pattern isfollowed in order to provide this study for a benchmark of the urban windenergy community. Figure 4.31 shows the domain and dimensions of thetarget building surrounded by neighbouring ones (general pattern). As inthe previous cases, the domain is set according to Best Practice Guidelines(Franke et al. (2007)).

Figure 4.31: Diagram of the computational domain for the surrounding-buildings eect analysis. All values are in meters. The conguration showncorresponds to h/H = 0.5, as an example.

Based on the previous results, the aspect ratio 1:1:2 showed the highestspeed-up. A slender building shape (AR=1:1:4) is also investigated in thepresent Section due to its potential for TI reduction, since an increase of kis expected due to the presence of the surrounding buildings. Figure 4.32shows a 3D diagram of the two cases. Additionally, four dierent surroundingheights (h/H) are investigated: 0.25, 0.5, 0.75 and 1.

The background mesh is constructed using the structured blockMesh

application with a grading of 4 in the vertical direction and the buildingsgeometry, previously designed with a CAD tool and saved in STL format, isembedded into this background mesh using the snappyHexMesh applicationof OpenFOAM (snappyHexMesh (2013); snappyHexMeshDict (2013)). Themesh around the buildings is rened and adapted to their shapes. The rene-ment distance around the target building surfaces is 80 m, and 2 m aroundthe surrounding buildings. According to van Hoo and Blocken (2010b), thesurrounding buildings can have a coarser mesh resolution. These settings are


(a) AR=1:1:2 (b) AR=1:1:4

Figure 4.32: Diagram of the dierent aspect ratio buildings. The congura-tion shown corresponds to h/H = 0.5, as an example.

used for all the simulations performed in the present Section. Figures 4.33and 4.34 show a detail of the nal mesh obtained for each case investigated.Note that the dierent height of the surrounding buildings (h) does not havea signicant eect on the total number of cells because of the lower meshrenement around these buildings.

All the computational settings (boundary conditions, inlet proles, tur-bulence model, coecients, discretization schemes, etc.) are the same usedabove.


The quantitative results are analysed by comparing U , k and TI between thedierent cases at the vertical axis located at the center of the roof (AXISin gure 4.31).

Figures 4.35a and 4.35b show a comparison of vertical proles of U onthe center of the roof for the aspect ratios 1:1:2 and 1:1:4, respectively. Bothcases show a similar behaviour. The higher the height of the surroundingbuildings (h) the lower the maximum velocity reached on the roof. The eectof the surrounding buildings on U is negative, and this eect is observed fromvery small heights, specially for the higher aspect ratio (1:1:2). This eectis shown in the decrease of the peak value of U . Although the maximumvalue decreases, the positive aspect is that the U vertical prole is morehomogeneous, specially for AR=1:1:2. For the lower aspect ratio (1:1:4),the sudden peak value of U close to the roof surface is observed regardlessof the surrounding buildings height. Around h/H = 0.75 the vertical proleof U/Uref is rather constant at the whole vertical prole. For higher heights(h/H > 0.75) U drastically decreases (U/Uref < 1 for h/H ≈ 1).

Figures 4.36a and 4.36b show a comparison of vertical proles of k on


(a) h/H = 0.25, AR=1:1:2, 8.1M cells. (b) h/H = 0.25, AR=1:1:4, 7.3M cells.

(c) h/H = 0.5, AR=1:1:2, 8.1M cells. (d) h/H = 0.5, AR=1:1:4, 7.3M cells.

Figure 4.33: Vertical section detail of the rened mesh obtained using snap-pyHexMesh for the surrounding buildings analysis (short surrounding build-ings).

the center of the roof for the aspect ratios 1:1:2 and 1:1:4, respectively. Bothcases show a similar behaviour. The presence of the surrounding buildingsstrongly aects the vertical prole of k on the roof. Short surroundingbuildings (h/H ≤ 0.5) aect the lower region of the k proles, at z/H < 1.25and z/H < 1.2 for AR=1:1:2 and AR=1:1:4, respectively. For h/H ≈ 0.75,the value of k increases at z/H < 1.8. The only dierence between thedierent aspect ratios is that for AR=1:1:2 the maximum value of k decreasesfor h/H > 0.5, but for AR=1:1:4 such a decrease is observed at h/H > 0.75(with a maximum at h/H = 0.75). For h/H ≈ 1, the vertical prole of k ismore homogeneous, with the highest values of k at z/H > 1.15 and z/H >1.1 for AR=1:1:2 and AR=1:1:4, respectively. However, the maximum valueof k for h/H ≈ 1 is the lowest for both aspect ratios.


(a) h/H = 0.75, AR=1:1:2, 8.1M cells. (b) h/H = 0.75, AR=1:1:4, 7.3M cells.

(c) h/H = 1, AR=1:1:2, 8.1M cells. (d) h/H = 1, AR=1:1:4, 7.3M cells.

Figure 4.34: Vertical section detail of the rened mesh obtained using snap-pyHexMesh for the surrounding buildings analysis (tall surrounding build-ings).

Figures 4.37a and 4.37b show a comparison of TI below the thresholdvalue of TI = 0.15 on the center of the roof for the aspect ratios 1:1:2 and1:1:4, respectively. Both cases show a similar behaviour. The inuence ofthe surrounding buildings is very important. In all cases the TI threshold forHAWT is exceeded and, therefore, only VAWT is recommended close to theroof in built environments. Regarding this aspect, the results obtained forthe isolated building considered before this section do not apply for buildingssurrounded by neighbouring ones. The higher the value of h/H the higherthe TI threshold height. In general, lower heights are observed for the slimbuilding (AR=1:1:4). The TI threshold is located around 1.1 < z/H < 1.15and 1.05 < z/H < 1.15 for AR=1:1:2 and AR=1:1:4, respectively. However,this threshold suddenly increases in both cases up to around z/H ≈ 1.4


0.6 0.8 1.0 1.2 1.4U/Uref

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

z/H

h/H=0h/H=0.25h/H=0.5h/H=0.75h/H=1

(a) AR=1:1:2

0.6 0.8 1.0 1.2 1.4U/Uref

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

z/H

h/H=0h/H=0.25h/H=0.5h/H=0.75h/H=1

(b) AR=1:1:4

Figure 4.35: Comparison of the speed-up (U/Uref ) for the surrounding-buildings inuence analysis at the vertical axis on the center of the roof.

0.02 0.04 0.06 0.08 0.10k/Uref

2

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

z/H

h/H=0h/H=0.25h/H=0.5h/H=0.75h/H=1

(a) AR=1:1:2

0.00 0.02 0.04 0.06 0.08 0.10 0.12k/Uref

2

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

z/H

h/H=0h/H=0.25h/H=0.5h/H=0.75h/H=1

(b) AR=1:1:4

Figure 4.36: Comparison of the nondimensional TKE (k/U2ref ) for the

surrounding-buildings inuence analysis at the vertical axis on the centerof the roof.

when h/H ≈ 1 due to the low value of U .


0.09 0.10 0.11 0.12 0.13 0.14 0.15TI

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

z/H

h/H=0h/H=0.25h/H=0.5h/H=0.75h/H=1

(a) AR=1:1:2

0.09 0.10 0.11 0.12 0.13 0.14 0.15TI

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

z/H

h/H=0h/H=0.25h/H=0.5h/H=0.75h/H=1

(b) AR=1:1:4

Figure 4.37: Comparison of TI below the limit of TI < 0.15 for thesurrounding-buildings inuence analysis at the vertical axis on the centerof the roof.

Figure 4.38 shows a comparison of the speed-up (U/Uref ) and the TIthreshold height on the center of the roof. It is clearly observed that theslender building (AR=1:1:4) is the most interesting case, showing alwaysa higher speed-up and a lower TI threshold case. A very interesting issueobserved is that there is a linear relationship between U/Uref and the thresh-old height in all the cases. Regardless the aspect ratio nor the surroundingbuildings height, the point is close to the same line in gure 4.38.

As is shown in gure 4.39a, the highest the height of the surroundingbuildings the lower the speed-up. The concentration factor of the wind iscancelled (U/Uref < 1) around h/H & 0.8. Higher values of U are observedfor the slender building (AR=1:1:4). Additionally, as shown in gure 4.39b,k progressively increases for 0 < h/H < 0.5 with very similar values betweenthe dierent aspect ratios. The value of k progressively decreases for 0.5 <h/H for the case of AR=1:1:2. The slender building shows higher values ofk for h/H > 0.5, and it starts to decrease at 0.75 < h/H.

A qualitative comparison of U and TI on the roof is shown in gures 4.40, 4.41 , 4.42 and 4.43 for both aspect ratios investigated for h/H = 0.25, 0.5,0.75 and 1, respectively. In all cases the TI threshold for HAWT is reachedon the roof. Although the ow pattern is similar between both aspect ratios,the slender building (AR=1:1:4) is more advantageous. Therefore, a VAWTmay be considered close to the roof surface although HAWT can be installedat a higher height.


0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5Maximum speed-up (U/Uref)

1.0

1.1

1.2

1.3

1.4

Heig

ht o

f the

thre

shol

d TI

=0.

15 (z

/H)

AR=1:1:2, h/H=0AR=1:1:2, h/H=0.25AR=1:1:2, h/H=0.5AR=1:1:2, h/H=0.75AR=1:1:2, h/H=1AR=1:1:4, h/H=0AR=1:1:4, h/H=0.25AR=1:1:4, h/H=0.5AR=1:1:4, h/H=0.75AR=1:1:4, h/H=1Linear

Figure 4.38: Comparison of the maximum speed-up (U/Uref ) and the TIthreshold height for the surrounding-buildings inuence analysis at the ver-tical axis on the center of the roof.

4.7.3 Conclusions

The eect of the neighbouring buildings was investigated considering dier-ent heights for the surroundings. A comparison of U , k and TI was carriedout.

Both U and k are strongly aected by the presence of surrounding build-ings. The TI threshold for HAWT is reached close to the roof surface inall the cases with surrounding buildings. Therefore, VAWT may be consid-ered close to the roof surface although HAWT can be installed at a higherheight (z/h > 1.05 − 1.15). Additionally, slender shapes (low aspect ratio)are conrmed as the most adequate building shapes for the wind energyexploitation, leading to a higher speed-up and to a lower TI.

This analysis for considering an urban wind energy environment is clearlya contribution because, as far as the author's knowledge is concerned, similaranalyses were not carried out beyond the work of Abohela (2012).



0.0

0.2

0.4

0.6

0.8

1.0

h/H

AR=1:1:2AR=1:1:4

(a) Maximum speed-up

0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11Maximum turbulent kinetic energy (k/Uref

2 )

0.0

0.2

0.4

0.6

0.8

1.0

h/H

AR=1:1:2AR=1:1:4



ref ) for the surrounding-buildings inuence analysis consideringthe dierent aspect ratios investigated.

4.8 Conclusions

This chapter presents an investigation about the empirical optimization of ahigh-rise building-roof shape for the urban wind energy exploitation. State-of-the-art roof shapes were tested, and the results were compared with thosereported in the literature. An analysis of the inuence of the roof-edge shapeon the wind ow on a high-rise building roof was carried out. An analysisof the roof-wall coupling was performed by modelling dierent variationsof a spherical roof on a high-rise building: spherical roof studied at theliterature, spherical roof geometrically integrated with the walls (squared-plant) and spherical roof with a cylindrical wall. A sensitivity analysis of theroof width was applied to the optimum building-roof shape obtained. Theaspect ratio of the building-roof shape was explored keeping both the heightof the building and the obtained optimum geometry. Finally, the eect ofthe neighbouring buildings was investigated considering dierent heights forthe surroundings. Comparisons of velocity, turbulent kinetic energy andturbulence intensity were carried out.

The results of the state-of-the-art roof shapes analysis show a similar owbehaviour on the sharp (pitched and shed) and on the curved roofs (spher-ical and vaulted), respectively. The curved shapes (spherical and vaulted)generate a higher concentration factor of U . On the sharp roofs (at, pitched


(a) Speed-up eld AR 1:1:2 (b) TI eld AR 1:1:2

(c) Speed-up eld AR 1:1:4 (d) TI eld AR 1:1:4

Figure 4.40: Comparison of speed-up (U/Uref ) and TI elds for h/H = 0.25.

and shed) U is not horizontal at the highest speed position. Furthermore,the curved shapes signicantly reduce the TI value, specially for sphericalshapes. Among the state-of-the-art geometric shapes tested, spherical andvaulted roofs are the best options from the wind energy exploitation pointof view. The results of both Lu and Ip (2009) and Ledo et al. (2011) (higherspeed-up for the shed roof and for the at roof, respectively) are conrmedby focusing at a dierent height. This is also a contribution of the presentthesis because, as far as the author's knowledge, any other work has inves-tigated this apparent contradiction. The results of Abohela (2012) are alsoconrmed (curved roofs lead to higher speed-up). However, in the presentinvestigation, the spherical roof shows more promising values for turbulenceintensity than the vaulted roof. Additionally, the spheric roof has the ad-ditional advantage that it will present the same behaviour for whicheverincident wind direction.





The results of the edge-roof shape analysis show a similar behaviour ofthe ow over a simple edge and a cantilever edge. With a railing edge, amassive recirculation of the ow that exceeds the roof length is observed, andthe height of the TI threshold of TI = 0.15 increases. On the curved edgethere is a very small recirculation of the ow on the roof, a speed-up is ob-served around the upstream edge and the TI threshold height substantiallydecreases.

Spherical roof shapes reduce turbulence intensity in all cases. Addi-tionally, the soft transition (curved edge) between wall and roof leads to aspeed-up increase. The most interesting case is clearly the spherical roofwith a cylindrical wall. The speed-up is higher than for the other casestested, particularly for the turbulence intensity threshold for HAWT, that isnot reached and, thus, a HAWT can be installed on the roof at any height.An additional advantage of the spherical roof with a cylindrical wall is that





the ow behaviour is the same for all the incident wind directions. Addi-tionally, the roof and wall sides are also suitable for installing wind turbines,under the same conditions than on the top of the roof.

An optimum building-roof shape for the wind energy exploitation nec-essarily passes by the use of curved shapes. Specically, the curved roofshape that shows the best performance is the spherical roof shape, leadingto U speed-up and TI decrease. The transition between walls and roof hasa strong inuence on the behaviour of the ow. Additionally, the wall shapeis also very signicant on the roof wind ow.

The sensitivity analysis of the roof width showed that the most interest-ing case for the wind energy exploitation is the exact spherical shape, leadingto a low TI and to the maximum speed-up between the shapes analysed.The thinner roofs show a linear decrease of k (and of TI by extension), butthey also show a linear decrease of U that can be signicant for thin widths.




Figure 4.43: Comparison of speed-up (U/Uref ) and TI elds for h/H = 1.

The wider roofs show a moderate decrease of U but a signicant increase ofk (exceeding the TI threshold for HAWT close to the roof surface).

The results of the aspect ratio investigation for the isolated buildingshowed that slender shapes (low aspect ratio) are more interesting for thewind energy exploitation, leading to a higher speed-up and to a lower TI.The maximum value of U was found for the aspect ratio 1:1:2. The lowerthe aspect ratio the lower the k. Due to the variations in U and k, similarvalues of TI were found for D/H < 0.5.

Both U and k are strongly aected by the presence of surrounding build-ings. The TI threshold for HAWT is reached close to the roof surface inall cases with surrounding buildings. Therefore, VAWT may be consideredclose to the roof surface although HAWT can be installed at a higher height(z/h > 1.05 − 1.15). Additionally, slender shapes (low aspect ratio) areconrmed as the most interesting building shapes for the wind energy ex-


ploitation, leading to a higher speed-up and to a lower TI.Future investigations may include full-scale experimental measurements

of the wind ow around a cylindrical building with an spherical roof sur-rounded by neighbouring buildings, in order to conrm the results of thesimulations performed in the present study. Wind tunnels using water as amedium (in order to preserve similitude constraints) can be considered asan alternative to full-scale measurements. Additionally, the CFD simulationof wind turbines located on the roof of the investigated building is also ofgreat interest. These investigations can start dealing with wind turbinesmodels, such actuator line or disc, and can continue with the real geometryimplementation in an unsteady ow using URANS or LES.

Bibliography notes

The content of Sections 4.2 and 4.3 has been published in Toja-Silva et al.(2015c), and the rest of the contents of this chapter have been submitted forpublication in Toja-Silva et al. (2015a).

Chapter 5

Concluding remarks

First they ignore you, then they laugh atyou, then they ght you, then you win.

Mahatma Gandhi

5.1 Final conclusions

5.1.1 Contributions of this Thesis

The contributions of the present Thesis can be summarized as follows:1. It is demonstrated that RANS turbulence models obtain better results

for the wind ow around buildings using the coecients proposed by Crespoet al. (1985) and those proposed by Bechmann and Sørensen (2010) than byusing the standard ones. The standard coecients may be more appropriatefor industrial conned ows.

2. It is demonstrated that RANS turbulence models can be validated forturbulent kinetic energy focusing on building roofs. This is a clear contribu-tion because it is well known that the k−ε RANS turbulence models do notreproduce well the wind ow behind the building, and the TKE is not repro-duced well around the building. But in the present thesis it is demonstratedthat it is possible to validate TKE focusing only on the building roof. Thiscontribution is complementary to the Contribution 1.

3. A new modication of the Durbin k− ε turbulence model is proposedin order to obtain a better agreement of the recirculation distance betweenCFD simulations and experimental results. This contribution is an stepbeyond the Contributions 1 and 2.

4. A linear relationship between the recirculation distance (XR) and theconstant factor involved in the calculation of the turbulence velocity timescale (TD) is demonstrated. This result can be used to improve the turbu-lence modeling in dierent solvers (OpenFOAM, Fluent, CFX, etc.). This

151

152 Chapter 5. Concluding remarks

contribution is complementary to the Contribution 3, and was discoveredduring the modication of the Durbin k − ε turbulence model.

5. The compatibility of both photovoltaic-solar and wind energies onbuilding roofs is investigated. A decrease of turbulence intensity due to thepresence of the solar panels is demonstrated. Therefore, the installation ofsolar panels on a building roof may have a positive inuence over the windenergy exploitation on the roof.

6. Scaling issues are demonstrated between full-scale buildings and wind-tunnel reduced-scale models. The necessity of respecting the similitude con-straints is demonstrated. Either full-scale measurements or wind-tunnel ex-periments using water as a medium are needed in order to accurately repro-duce the wind ow around buildings, specially when dealing with complexshapes (as solar panels, etc.).

7. The most adequate position (most adequate roof region) for the dif-ferent kinds of wind turbines is highlighted considering both velocity andturbulence intensity. The wind turbine positioning was investigated for themost habitual kind of building-roof shapes (at, pitched, shed, vaulted andspherical).

8. The most habitual roof-edge shapes (simple edge, railing, cantileverand curved) were investigated, and their eect on the wind ow on a high-rise building roof were analysed from the point of view of the wind energyexploitation.

9. The results of both Lu and Ip (2009) and Ledo et al. (2011) (higherspeed-up for the shed roof and for the at roof, respectively) are conrmed byfocusing at a dierent height. This is also a contribution of the present Thesisbecause, as far as the author's knowledge, any other work has investigatedthis apparent contradiction.

10. The results of Abohela (2012) are also conrmed (curved roofs leadto higher speed-up). However, in the present investigation, the sphericalroof shows more promising values (low) for turbulence intensity than thevaulted roof. The Contributions 6, 9 and 10 identify misleading conclusionsfrom previous works.

11. An optimum building-roof shape is proposed for the urban wind en-ergy exploitation. Such optimization includes: state-of-the-art roof shapestest, analysis of the inuence of the roof-edge shape on the wind ow, studyof the roof-wall coupling, sensitivity analysis of the roof width, explorationof the aspect ratio of the building-roof shape and investigation of the eectof the neighbouring buildings (considering dierent surrounding heights) onthe wind ow on the target building roof. The investigations comprise anal-ysis of velocity, turbulent kinetic energy and turbulence intensity for all thecases. The optimum roof shape obtained is an exact spherical roof softlycoupled with a cylindrical wall. Slender aspect ratios show better results.

5.1. Final conclusions 153

This contribution complete the present Thesis, reaching the main objectiveproposed in Chapter 1.

5.1.2 Conclusions from the investigations

5.1.2.1 Main ow validation and at roof analysis

The rst validation carried out consists in CFD simulations of the wind owaround a at-roof isolated building, that were performed with OpenFOAMusing several RANS turbulence models. The results were compared withthe experimental results of a wind-tunnel benchmark case. On the qualita-tive side, the new modied Durbin model (with Crespo coecients) showed aperfect agreement with the experimental data for recirculation distance. Ad-ditionally, Durbin-Tominaga (with Crespo coecients), MMK (with Crespocoecients) and original Durbin (with standard coecients) models showeda reasonable good agreement with the experiment. The SKE model (withBechmann coecients) also matched the same value of the recirculation dis-tance obtained by the experiment, but it is not successfully validated forTKE. All the k− ε models tested show a better agreement with the experi-mental data by using the coecients proposed by Crespo et al. (1985) andby Bechmann and Sørensen (2010) than by using the standard coecients.On the quantitative side, all the models successfully passed the validationfor U but only some of them passed it for k. The new modied Durbin modelwith Crespo coecients gave the best results from a global point of view,both qualitatively and quantitatively. Additionally, the MMK model (withCrespo coecients) gave the best quantitative results and a reasonably goodqualitative (recirculation distance) agreement with the experimental data.

The analysis of the wind turbines positioning for the at roof is based inthe turbulent kinetic energy, limited up to a turbulence intensity TI < 0.15for HAWT. This criteria was set according the European Wind TurbineStandards II (Pierik et al. (1999)) recommendations (see Section for a deeperdiscussion). According to that, the most appropriate areas to install HAWTwere identied and discussed. The results show that HAWT can be placedat z/H > 1.31 everywhere at the investigated case, regardless of the incidentwind direction. Below this height, VAWT may be considered. The installa-tion of a VAWT in horizontal position at the central-upstream region closeto the roof surface was also considered, to make the most of the recircu-lation of the ow. Additionally, the installation of a ducted wind turbineat the upstream corner of the building roof, in order to make the most ofthe pressure dierence between the vertical wall and the roof surface, is alsointeresting.

The k − ε RANS turbulence models successfully validated for the at-roof building with hit rates of HR ≥ 75% were validated twice by comparing


the simulation results with the experimental measurements in a curved-roofbuilding model in an atmospheric boundary layer wind tunnel. All the testedmodels successfully passed the validation procedure for U and k. The MMKmodel (with Crespo coecients) obtained the highest hit rate for U .

From the results obtained for the main ow validation, it can be con-cluded that Yap, Durbin and MMK k− ε turbulence models can be used toaccurately analyse the wind ow on complex-geometry building roofs thatinclude both sharped and curved surfaces. Although the MMK turbulencemodel (with Crespo coecients) shows the best behaviour in both cases,the new modication of the Durbin model presented in Chapter 2 is recom-mended to be used in further simulations because it has been empiricallyfound a higher stability dealing with very complex geometries (for examplewith solar panels in Chapter 3). Additionally, the MMK model (with Cre-spo coecients) tends to slightly underestimate TKE, and the new modiedDurbin tends to slightly overestimate it. Therefore, it is recommended theuse of the new modied Durbin model (with Crespo coecients) in orderto bring more conservative results, what is very important for being used inreal facilities because the real buildings have more roughness elements thanthe considered in the theoretical studies (antennas, ornamental elements,odd edges, birds, etc.).

5.1.2.2 Compatibility of photovoltaic-solar and wind energies

On the qualitative side, the recirculations on the roof were analysed and themost appropriate wind turbine model for each roof region was suggested. Asit is expected, recirculation vortices appear between the solar-panels arrays.The rst vortex (between the upstream edge and the rst array) has thehighest velocities. The installation of a VAWT in horizontal position insidethis vortex shows a very interesting potential. A general value (the highestvalue obtained) for the installation of HAWT has been found at z/H > 1.29,regardless of the incident wind direction. The installation of a VAWT isrecommended below this limit.

The quantitative analysis includes the comparison of vertical proles ofstreamwise velocity and turbulent kinetic energy. No signicant dierencescompared to the empty roof are found above the isoline of TI = 0.15. Belowthe isoline TI = 0.15 the most important dierences appear for k, thatsignicantly decreases due to the presence of the solar panels; such decreaseis more pronounced for higher tilt angles. The decrease of the turbulentkinetic energy may be due to the damping eect of the recirculation vorticesbetween the solar arrays.

Scaling issues are reported. A massive recirculation takes place at theraised panels in unfavourable position due to the interaction of the neigh-bouring vortices between the arrays. This massive recirculation is not ob-

5.1. Final conclusions 155

served for the reduced-scale model because of the Reynolds number decrease(2 orders of magnitude lower than full-scale building).

5.1.2.3 Building-roof shape optimization

The results of the state-of-the-art roof shapes analysis show a similar owbehaviour on the sharp (pitched and shed) and on the curved roofs (spher-ical and vaulted), respectively. The curved shapes (spherical and vaulted)generate a higher concentration factor of U . On the sharp roofs (at, pitchedand shed) U is not horizontal at the highest speed position. Furthermore,the curved shapes signicantly reduce the TI value, specially for sphericalshapes. Among the state-of-the-art geometric shapes tested, spherical andvaulted roofs are the best options from the wind energy exploitation pointof view. The results of both Lu and Ip (2009) and Ledo et al. (2011) (higherspeed-up for the shed roof and for the at roof, respectively) are conrmedby focusing at a dierent height. The results of Abohela (2012) are alsoconrmed (curved roofs lead to higher speed-up). However, in the presentinvestigation, the spherical roof shows more promising values for turbulenceintensity than the vaulted roof. Additionally, the spheric roof has the ad-ditional advantage that it will present the same behaviour for whicheverincident wind direction.

The results of the edge-roof shape analysis show a similar behaviour ofthe ow over a simple edge and a cantilever edge. With a railing edge, amassive recirculation of the ow that exceeds the roof length is observed,and the height of the TI threshold of TI = 0.15 increases. On the curvededge, a speed-up is observed around the upstream edge and the TI thresholdheight substantially decreases.

Spherical roof shapes reduce turbulence intensity in all cases. Addi-tionally, the soft transition (curved edge) between wall and roof leads to aspeed-up increase. The most interesting case is clearly the spherical roofwith a cylindrical wall. The speed-up is higher than for the other casestested, particularly for the turbulence intensity threshold for HAWT, that isnot reached for the isolated building and, thus, a HAWT can be installed onthe roof at any height. An additional advantage of the spherical roof witha cylindrical wall is that the ow behaviour is the same for all the incidentwind directions. Additionally, the roof and wall sides are also suitable forinstalling wind turbines, under the same conditions than on the top of theroof.

An optimum building-roof shape for the wind energy exploitation nec-essarily passes by the use of curved shapes. Specically, the curved roofshape that shows the best performance is the spherical roof shape, leadingto U speed-up and TI decrease. The transition between walls and roof hasa strong inuence on the behaviour of the ow. Additionally, the wall shape


is also very signicant on the roof wind ow.The sensitivity analysis of the roof width showed that the most interest-

ing case for the wind energy exploitation is the exact spherical shape, leadingto a low TI and to the maximum speed-up between the shapes analysed.The thinner roofs show a linear decrease of k (and of TI by extension), butthey also show a linear decrease of U that can be signicant for thin widths.The wider roofs show a moderate decrease of U but a signicant increase ofk (exceeding the TI threshold for HAWT close to the roof surface).

The results of the aspect ratio investigation for the isolated buildingshowed that slender shapes (low aspect ratio) are more interesting for thewind energy exploitation, leading to a higher speed-up and to a lower TI.The maximum value of U was found for the aspect ratio 1:1:2. The lowerthe aspect ratio the lower the k. Due to the variations in U and k, similarvalues of TI were found for D/H < 0.5.

Both U and k are strongly aected by the presence of surrounding build-ings. It causes that the TI threshold for HAWT is reached close to the roofsurface in all the cases with surrounding buildings. Therefore, VAWT maybe considered close to the roof surface in all the cases, although HAWTcan be installed at a higher height (z/h > 1.05 − 1.15). Additionally, slen-der shapes (low aspect ratio) are conrmed as the most interesting buildingshapes for the wind energy exploitation, leading to a higher speed-up andto a lower TI.

5.2 Suggestions for further works

Scaling issues due to similarity constraints are demonstrated in this Thesis.Specically, these similarity constraints refer to a dierence in some orders ofmagnitude between the Reynolds number in wind-tunnel experiments andin full-scale buildings. These scaling issues show the necessity of furtherexperimental studies considering full-scale conditions in order to conrmthe simulation results obtained. These further experiments must involveeither measurements on real (full-scale) buildings or in wind tunnels usingwater as a medium. The specic experiments with interest for the presentinvestigation deal with measurements of:

- A building with solar panels on the roof. Specically, the separatedsolar panels in unfavourable position analysed in Chapter 3 have interest inorder to conrm the scaling issues observed in the CFD simulations.

- A building with the optimum shape obtained (cylindrical wall softlycoupled with an spherical roof). It is preferable to analyse the building inan urban environment (surrounded by neighbouring buildings) in order toconrm the conclusions derived from Chapter 4.

Additionally, the CFD simulation of wind turbines located on the roof

5.2. Suggestions for further works 157

of the investigated building is also of great interest. These investigationscan start dealing with wind turbines models, such actuator line or disc, andthey can continue with the real geometry implementation in an unsteadyow using URANS or LES. An interesting alternative for dealing with mov-ing boundaries in CFD simulations is by using immersed boundary methods.Within the framework of this Thesis, a new interpolation-spreading proce-dure for the immersed boundary method has been developed. This newmethodology uses radial basis functions (RBF). It has not been applied toRANS solvers yet, but it is promising. This procedure has been imple-mented in a DNS solver to impose both Dirichlet and Neumann boundaryconditions. It is presented in Appendix A.

A new concept of wind turbines can be developed for taking the most ofthe recirculation of the wind ow on the roof. This application is commentedin Chapters 2 and 3 as a very interesting application for at roofs, referred asVAWT in horizontal position. Both full-scale experiments in real buildingsand CFD simulations of wind turbines close to a at roof edge would havea great interest. In the personal opinion of the author, this application isreally promising for at roof buildings. It can have a very good economicalresult specially for tall oce buildings.

An extension of the present investigation is the conception and analy-sis of internal wind energy exploitation systems through ducted passagesin buildings. This analysis may include the study of dierent building,walls, passages and inlet/outlet nozzle shapes, including an aerodynamicoptimization of the internal wind energy harvesting system. The successfulalternatives would be validated by reproducing the CFD simulations withwind-tunnel experiments, using water as a medium in order to maintain thesimilitude constraints.

158 Bibliography

Bibliography

All knowledge which ends in words willdie as quickly as it came to life, with theexception of the written word: which is

its mechanical part.

Leonardo da Vinci

Abiola-Ogedengbe, A., Hangan, H. and Siddiqui, K. Experimentalinvestigation of wind eects on a standalone photovoltaic (PV) module.Renewable Energy , vol. 78, pages 657665, 2015.

Abohela, I. Eect of roof shape, wind direction, building height and urbanconguration on the energy yield and positioning of roof mounted windturbines. PhD, Newcastle University, 2012.

Abohela, I., Hamza, N. and Dudek, S. Eect of roof shape, wind di-rection, building height and urban conguration on the energy yield andpositioning of roof mounted wind turbines. Renewable Energy , vol. 50,pages 11061118, 2013.

Ackermann, T., Andersson, G. and Söder, L. Distributed generation:a denition. Electric Power Systems Research, vol. 57, pages 195204,2001.

Aly, A. M. and Bitsuamlak, G. Aerodynamics of ground-mounted so-lar panels: test model scale eects. Journal of Wind Engineering andIndustrial Aerodynamics, vol. 123, pages 250260, 2013.

Amandolese, X., Michelin, S. and Choquel, M. Low speed utterand limit cycle oscillations of a two-degree-of-freedom at plate in a windtunnel. Journal of Fluids and Structures, vol. 43, pages 244255, 2013.

Anderson, J. D. Computational uid dynamics. The basics with applica-tions. McGraw-Hill, 1995.

159

160 Bibliography

ANSYS. ANSYS Fluent. 2015. Available at http://aerojet.engr.

ucdavis.edu/fluenthelp/html/ug/node992.htm (Last access, February,2015).

Aynsley, R. M., Melbourne, W. H. and Vickery, B. J. Architecturalaerodynamics. Applied Science Publishers, 1977.

Aynsley, R. M., Stathopoulos, T., English, E., Aynsley, R. M.and G. A. Kopp, e. a. Urban aerodynamics: wind engineering for urbanplanners and designers. American Society of Civil Engineers, 2011.

Bahaj, A. S., Myers, L. and James, P. A. B. Urban energy genera-tion: inuence of micro-wind turbine output on electricity consumptionin buildings. Energy and Buildings, vol. 39, pages 154165, 2007.

Bakker, A. Applied computational uid dynamics. 2015. Available athttp://www.bakker.org/dartmouth06/engs150/05-solv.pdf (Last ac-cess, February, 2015).

Balduzzi, F., Bianchini, A. and Ferrari, L. Microeolic turbines inthe built environment: inuence of the installation site on the potentialenergy yield. Renewable Energy , vol. 45, pages 163174, 2012.

Balogh, M., Parente, A. and Benocci, C. RANS simulation of ABLow over complex terrains applying an Enhanced k − ε model and wallfunction formulation: implementation and comparison for Fluent andOpenFOAM. Journal of Wind Engineering and Industrial Aerodynamics,vol. 104106, pages 360368, 2012.

Bansal, R. C., Bhatti, T. S. and Kothari, D. P. On some of thedesign aspects of wind energy conversion systems. Energy Conversionand Management , vol. 43, pages 21752187, 2002.

Ajuntament de Barcelona, A. B. Autosuciencia BCN. 2015.Available at http://ajuntament.barcelona.cat/autosuficiencia/es/webapp.php (Last access, June, 2015).

Bartzis, J. G., Vlachogiannis, D. and Sfetsos, A. Thematic Area 5:Best practice advice for environmental ows. The QNET-CFD NetworkNewsletter , vol. 2, pages 3439, 2004.

Bechmann, A. and Sørensen, N. N. Hybrid RANS/LES method forwind ow over complex terrain. Wind Energy , vol. 13, pages 3650, 2010.

Beckert, A. and Wendland, H. Multivariate interpolation for uid-structure-interaction problems using radial basis functions. AerospaceScience and Technology , vol. 5, pages 125134, 2001.

http://aerojet.engr.ucdavis.edu/fluenthelp/html/ug/node992.htm

http://aerojet.engr.ucdavis.edu/fluenthelp/html/ug/node992.htm

http://www.bakker.org/dartmouth06/engs150/05-solv.pdf

http://ajuntament.barcelona.cat/autosuficiencia/es/webapp.php

http://ajuntament.barcelona.cat/autosuficiencia/es/webapp.php

Bibliography 161

Beranek, W. J. and van Koten, H. Beperken van windhinder omgebouwen, deel 1, Stichting Bouwresearch no. 65, Kluwer TechnischeBoeken BV, Deventer (in Dutch). 1979.

Biswas, G. and Eswaran, V. Turbulent ows. Fundamentals, experimentsand modeling . Alpha Science International, 2010.

Blocken, B. 50 years of computational wind engineering: past, presentand future. Journal of Wind Engineering and Industrial Aerodynamics,vol. 129, pages 69102, 2014a.

Blocken, B. Sports and buildings aerodynamics. Massive open onlinecourse, TU/e and Coursera. 2014b. Available at https://www.coursera.org/course/spobuildaerodynamics (Last access, February, 2015).

de Boer, A., van der Schoot, M. and Bijl, H. Mesh deformation basedon radial basis function interpolation. Computers and Structures, vol. 85,pages 784795, 2007a.

de Boer, A., van Zuijlen, A. and Bijl, H. Review of coupling methodsfor non-matching meshes. Computer Methods in Applied Mechanics andEngineering , vol. 196, pages 15151525, 2007b.

Bosch, G. and Rodi, W. Simulation of vortex shedding past a squarecylinder near a wall. International Journal of Heat and Fluid Flow , vol.17, pages 267275, 1996.

Brown, D. L., Cortez, R. andMinion, M. L. Accurate projection meth-ods for the incompressible Navier-Stokes equations. Journal of Computa-tional Physics, vol. 168, pages 464499, 2001.

Campbell, N., Stankovic, S., Graham, M. and P. Parkin, e. a. Windenergy for the built environment (Project WEB). Procs. European WindEnergy Conference and Exhibition, Copenhagen, 2001.

Carpman, N. Turbulence intensity in complex environments and its inu-ence on small wind turbines. PhD, Uppsala University, 2011.

Asociación Española de Normalización y Certificación, A. E.N. O. R. UNE-EN ISO 14122-3:2002/A1:2010. 2010. Avail-able at http://www.aenor.es/aenor/normas/normas/fichanorma.asp?tipo=N&codigo=N0046059#.VdykrrylilM (Last access, August, 2015).

Changnon, S. A. Inadvertent weather modication in urban areas: lessonsfor global climate change. Bulletin of the American Meteorological Society ,vol. 73, pages 619752, 1992.

https://www.coursera.org/course/spobuildaerodynamics

https://www.coursera.org/course/spobuildaerodynamics

http://www.aenor.es/aenor/normas/normas/fichanorma.asp?tipo=N&codigo=N0046059#.VdykrrylilM

http://www.aenor.es/aenor/normas/normas/fichanorma.asp?tipo=N&codigo=N0046059#.VdykrrylilM

162 Bibliography

Cheng, Y., Lien, F. S., Yee, E. and Sinclair, R. A comparison of LargeEddy Simulations with a standard k−εReynolds-AveragedNavier-Stokesmodel for the prediction of a fully developed turbulent ow over a matrixof cubes. Journal of Wind Engineering and Industrial Aerodynamics, vol.91, pages 13011328, 2003.

Cheng, Y. M., Liu, Y. C., Hung, S. C. and Cheng, C. S. Multi-input inverter for grid-connected hybrid PV/wind power system. IEEETransactions on Power Electronics, vol. 22, pages 10701076, 2007.

Chicco, G. andMancarella, P. Distributed multi-generation: a compre-hensive view. Renewable and Sustainable Energy Reviews, vol. 13, pages535551, 2009.

Chong, W. T., Fazlizan, A., Poh, S. C., Pan, K. C. and Ping, H. W.Early development of an innovative building integrated wind, solar andrain water harvester for urban high rise application. Energy and Buildings,vol. 47, pages 201207, 2012.

Chong, W. T., Naghavi, M. S., Poh, S. C.,Mahlia, T. M. I. and Pan,K. C. Techno-economic analysis of a wind-solar hybrid renewable energysystem with rainwater collection feature for urban high-rise application.Applied Energy , vol. 88, pages 40674077, 2011.

Chong, W. T., Pan, K. C., Poh, S. C., Fazlizan, A., Oon, C. S.,Badarudin, A. and Nik-Ghazali, N. Performance investigation of apower augmented vertical axis wind turbine for urban high-rise applica-tion. Renewable Energy , vol. 51, pages 388397, 2013.

Clay Mathematics Institute, C. M. I. Millennium Problems:Navier-Stokes equation. 2015. Available at http://www.claymath.org/millenium-problems/navier%E2%80%93stokes-equation (Last access,February, 2015).

Cochran, L. and Peterka, J. On breached building envelopes and in-creased internal pressures. International Conference on Building EnvelopeSystems and Technologies, Ottawa (Canada. 1999.

Comrie, A. C. Mapping a wind-modied urban heat island in Tucson,Arizona (with comments on integrating research and undergraduate learn-ing). Bulletin of the American Meteorological Society , vol. 81, pages 24172431, 2000.

Comsol. Which turbulence model should I choose for my CFD ap-plication? 2015. Available at http://www.comsol.com/blogs/

which-turbulence-model-should-choose-cfd-application/ (Last ac-cess, February, 2015).

http://www.claymath.org/millenium-problems/navier%E2%80%93stokes-equation

http://www.claymath.org/millenium-problems/navier%E2%80%93stokes-equation

http://www.comsol.com/blogs/which-turbulence-model-should-choose-cfd-application/

http://www.comsol.com/blogs/which-turbulence-model-should-choose-cfd-application/

Bibliography 163

Coutanceau, M. and Bouard, R. Experimental determination of themain features of the viscous ow in the wake of a circular cylinder inuniform translation. Part 1. Steady ow. Journal of Fluid Mechanics,vol. 79, pages 231256, 1977.

Cowan, I. R., Castro, I. P. and Robins, A. G. Numerical considera-tions for simulations of ow and dispersion around buildings. Journal ofWind Engineering and Industrial Aerodynamics, vol. 6768, pages 535545, 1997.

Craighead, G. High-rise cecurity and re life safety (third edition). Chap-ter 1: High-rise building denition, development, and use. Butterworth-Heinemann, 2009.

Crespo, A., Manuel, F., Moreno, D., Fraga, E. and Hernandez, J.Numerical analysis of wind turbine wakes. Proceedings of Delphi Workshopon Wind Energy Applications, Delphi (Greece), pages 1525, 1985.

Dabis, H. S. and Chignell, R. J. Wind turbine electromagnetic scattermodeling using physical optics techniques. Renewable Energy , vol. 16,pages 882887, 1999.

D'Alessandro, V., Montelpare, S., Ricci, R. and Secchiaroli, A.Unsteady aerodynamics of a Savonius wind rotor: a new computationalapproach for the simulation of energy performance. Energy , vol. 35, pages33493363, 2010.

Dayan, E. Wind energy in buildings. Power generation from wind in theurban environment - where it is needed most. Refocus, pages 3338, 2006.

Durbin, P. A. On the k − ε stagnation point anomaly. InternationalJournal of Heat and Fluid Flow , vol. 17, pages 8990, 1996.

Eco-Hi-Solar. 2014. Available at http://www.ecohisolar.co.uk/

case-studies/schuco-10-kwp (Last access, November, 2014).

El-Ela, A. A. A., Allam, S. M. and Shatla, M. M. Maximal optimalbenets of distributed generation using genetic algorithms. Electric PowerSystems Research, vol. 80, pages 869877, 2010.

El-Samanoudy, M., Ghorab, A. A. E. and Youssef, S. Z. Eect ofsome design parameters on the performance of a Giromill vertical axiswind turbine. Ain Shams Engineering Journal , vol. 1, pages 8595, 2010.

Emeis, S. Wind energy meteorology, green energy and technology . Springer,2013.

http://www.ecohisolar.co.uk/case-studies/schuco-10-kwp

http://www.ecohisolar.co.uk/case-studies/schuco-10-kwp

164 Bibliography

Encyclopædia Britannica, E. B. Atmosphere: vertical structure. 2015.Available at http://global.britannica.com/EBchecked/topic/41364/atmosphere/261445/Planetary-boundary-layer (Last access, Febru-ary, 2015).

Instituto para la Diversificación y Ahorro de la Energía, I. D.A. E. Instalaciones de energía solar fotovoltaica, Pliego de CondicionesTécnicas de Instalaciones Conectadas a Red. PCT-C-REV (Spanish reg-ulation), 2011.

Eriksson, S., Bernhoff, H. and Leijon, M. Evaluation of dierent tur-bine concepts for wind power. Renewable and Sustainable Energy Reviews,vol. 12, pages 14191434, 2008a.

Eriksson, S., Bernhoff, H. and Leijon, M. Evaluation of dierent tur-bine concepts for wind power. Renewable and Sustainable Energy Reviews,vol. 12, pages 14191434, 2008b.

European Commission, E. C. Communication from the Commissionof 13 November 2008 - Energy eciency: delivering the 20% target(COM/2008/0772). 2008. Available at http://eur-lex.europa.eu/

legal-content/EN/ALL/?uri=CELEX:52008DC0772 (Last access, Decem-ber, 2014).

European Commission, E. C. Horizon 2020 Programme. 2015. Avail-able at http://ec.europa.eu/programmes/horizon2020/ (Last access,January, 2015).

European Union, E. U. Directive 2010/31/EU of the EuropeanParliament and of the Council of 19 May 2010 on the en-ergy performance of buildings. 2010. Available at http:

//eur-lex.europa.eu/legal-content/EN/ALL/;ELX_SESSIONID=

pYTKJQJVCnsLtvvTQYwvq2mhVggH4bGvfhbnzbBflyJph87tlv7p!

1397879892?uri=CELEX:32010L0031 (Last access, December, 2014).

Fadlun, E. A., Verzicco, R., Orlandi, P. andMohd-Yusof, J. Com-bined immersed-boundary nite-dierence methods for three dimensionalcomplex ow simulations. Journal of Computational Physics, vol. 161,pages 3560, 2000.

Fage, A. and Johansen, F. C. On the ow of air behind an inclined atplate of innite span. Proceedings of the Royal Society of London SeriesA, vol. 116, pages 170197, 1927.

Fang, J., Diebold, M., Higgins, C. and Parlange, M. B. Towardsoscillation-free implementation of the immersed boundary method with

http://global.britannica.com/EBchecked/topic/41364/atmosphere/261445/Planetary-boundary-layer

http://global.britannica.com/EBchecked/topic/41364/atmosphere/261445/Planetary-boundary-layer

http://eur-lex.europa.eu/legal-content/EN/ALL/?uri=CELEX:52008DC0772

http://eur-lex.europa.eu/legal-content/EN/ALL/?uri=CELEX:52008DC0772

http://ec.europa.eu/programmes/horizon2020/

http://eur-lex.europa.eu/legal-content/EN/ALL/;ELX_SESSIONID=pYTKJQJVCnsLtvvTQYwvq2mhVggH4bGvfhbnzbBflyJph87tlv7p!1397879892?uri=CELEX:32010L0031




Bibliography 165

spectral-like methods. Journal of Computational Physics, vol. 230, pages81798191, 2011.

Favier, J., Revell, A. and Pinelli, A. A Lattice Boltzmann-immersedboundary method to simulate the uid interaction with moving and slen-der exible objects. Journal of Computational Physics, vol. 261, pages145161, 2014.

Ferziger, J. and Peric, M. Computational methods for uid dynamics.3rd Ed . Springer, 2002.

Franke, J., Hellsten, A., Schlünzen, H. and Carissimo, B. Bestpractice guideline for the CFD simulation of ows in the urban environ-ment . COST Action 732, COST Oce, 2007.

Frechette, R. E. and Gilchrist, R. Towards zero energy: A casestudy of the Pearl River Tower, Guangzhou, China. CTBUH 8th WorldCongress, Dubai , 2008.

Garratt, J. R. The atmospheric boundary layer . Cambridge UniversityPress, 1994.

Geostationary Operational Environmental Satellites R Series,G. O. E. S. R. Introduction to tropical meteorology, COMET project.2015. Available at http://www.goes-r.gov/users/comet/tropical/

textbook_2nd_edition/navmenu.php_tab_2_page_8.1.0.htm (Last ac-cess, February, 2015).

Gibou, F., Fedkiw, R. P., Cheng, L. T. and Kang, M. A second-order-accurate symmetric discretization of the Poisson equation on irregulardomains. Journal of Computational Physics, vol. 176, pages 205227,2002.

Giles, M. B. and Pierce, N. A. An introduction to the adjoint ap-proach to design. Flow, Turbulence and Combustion, vol. 65, pages 393415, 2000. Available at http://www.piercelab.caltech.edu/assets/

papers/ftc00.pdf (Last access, February, 2015).

Gousseau, P., Blocken, B. and van Heijst, G. J. F. Quality assess-ment of large-eddy simulation of wind ow around a high-rise building:validation and solution verication. Computers and Fluids, vol. 79, pages120133, 2013.

Grant, A., Johnstone, C. andKelly, N. Urban wind energy conversion:the potential of ducted turbines. Renewable Energy , vol. 33, pages 11571163, 2008.

http://www.goes-r.gov/users/comet/tropical/textbook_2nd_edition/navmenu.php_tab_2_page_8.1.0.htm

http://www.goes-r.gov/users/comet/tropical/textbook_2nd_edition/navmenu.php_tab_2_page_8.1.0.htm

http://www.piercelab.caltech.edu/assets/papers/ftc00.pdf

http://www.piercelab.caltech.edu/assets/papers/ftc00.pdf

166 Bibliography

Grauthoff, M. Utilization of wind energy in urban areas. chance orutopian dream? Energy and Buildings, vol. 1516, pages 517523, 19901991.

GreenSpec. Housing retrot: concrete at roof insulation. 2015.Available at http://www.greenspec.co.uk/building-design/

concrete-flat-roof-insulation/ (Last access, August, 2015).

Guilmineau, E. and Queutey, P. A numerical simulation of vortex shed-ding from an oscillating circular cylinder. Journal of Fluids and Struc-tures, vol. 16, pages 773794, 2002.

Hall, R. C. Evaluation of modelling uncertainty. CFD modelling of near-eld atmospheric dispersion. Project EMU nal report, European Com-mission Directorate - General XII Science, Research and DevelopmentContract EV5V-CT94-0531 . WS Atkins Consultants Ltd., 1997.

Hanna, S. R. and Britter, R. E. Wind ow and vapor cloud dispersionat industrial and urban sites. American Institute of Chemical Engineers,2002.

He, J. and Song, C. C. S. A numerical study of wind ow around theTTU building and the roof corner vortex. Journal of Wind Engineeringand Industrial Aerodynamics, vol. 6768, pages 547558, 1997.

Holdsworth, B. Options for microwind generation: Part I. RenewableEnergy Focus, pages 6063, 2009a.

Holdsworth, B. Options for microwind generation: Part II. RenewableEnergy Focus, pages 4245, 2009b.

Holdsworth, B. Options for microwind generation: Part III. RenewableEnergy Focus, pages 3640, 2009c.

Hong, C.-M. and Chen, C.-H. Intelligent control of a grid-connectedwind-photovoltaic hybrid power systems. Electrical Power and EnergySystems, vol. 55, pages 554561, 2014.

van Hooff, T. and Blocken, B. Coupled urban wind ow and indoornatural ventilation modelling on a high-resolution grid: a case study forthe Amsterdam ArenA stadium. Environmental Modelling and Software,vol. 25, pages 5165, 2010a.

van Hooff, T. and Blocken, B. On the eect of wind direction and ur-ban surroundings on natural ventilation of a large semi-enclosed stadium.Computers and Fluids, vol. 39, pages 11461155, 2010b.

http://www.greenspec.co.uk/building-design/concrete-flat-roof-insulation/

http://www.greenspec.co.uk/building-design/concrete-flat-roof-insulation/

Bibliography 167

Howell, R., Qin, N., Edwards, J. and Durrani, N. Wind tunnel andnumerical study of a small vertical axis wind turbine. Renewable Energy ,vol. 35, pages 412422, 2010.

Huang, Q., Shi, Y., Wang, Y., Lu, L. and Cui, Y. Multi-turbine wind-solar hybrid system. Renewable Energy , vol. 76, pages 401407, 2015.

Inanici, M. N. andDemirbilek, F. N. Thermal performance optimizationof building aspect ratio and south window size in ve cities having dierentclimatic characteristics of Turkey. Building and Environment , vol. 35,pages 4152, 2000.

Irwin, P. A simple omni-directional sensor for wind-tunnel studies ofpedestrian-level winds. Journal of Wind Engineering and Industrial Aero-dynamics, vol. 7, pages 219239, 1981.

Architectural Institute of Japan, A. I. J. Guidebook for practi-cal applications of CFD to pedestrian wind environment around build-ings. 2013. Available at http://www.aij.or.jp/jpn/publish/cfdguide/index_e.htm (Last access, November, 2013).

Ji, L., Sreenivas, K., Hyams, D. G. and Wilson, R. V. A paralleluniversal mesh deformation scheme for hydrodynamic applications. 28thSymposium on Naval Hydrodynamics, Pasadena (USA). 2010.

Jiménez, P. A. and Dudhia, J. On the ability of the WRF model toreproduce the surface wind direction over complex terrain. Journal ofApplied Meteorology and Climatology , vol. 52, pages 16101617, 2013.

Johnson, G. An investigation of the dispersive properties of an ur-ban canyon wind ow model. Proc. 15 International Congress ofBiometeorology and International Conference on Urban Climatology,University of Sydney (Australia). 1999.

Joubert, E. C., Harms, T. M. and Venter, G. Computational simu-lation of the turbulent ow around a surface mounted rectangular prism.Journal of Wind Engineering and Industrial Aerodynamics, vol. 142, pages173187, 2015.

Jubayer, C. M. and Hangan, H. Numerical simulation of wind eectson a stand-alone ground mounted photovoltaic (PV) system. Journal ofWind Engineering and Industrial Aerodynamics, vol. 134, pages 5664,2014.

Kaimal, J. C. and Finnigan, J. J. Atmospheric boundary layer ows:their structure and measurement . Oxford University Press, 1994.

http://www.aij.or.jp/jpn/publish/cfdguide/index_e.htm

http://www.aij.or.jp/jpn/publish/cfdguide/index_e.htm

168 Bibliography

Kamoji, M. A., Kedare, S. B. and Prabhu, S. V. Performance tests onhelical Savonius rotors. Renewable Energy , vol. 34, pages 521529, 2009.

Kampolis, I., Papadimitriou, D., Petropoulou, S., Pappou, T.,Koubogiannis, D. and Giannakoglou, K. Adjoint techniques foraerodynamic shape optimization problems: new mathematical formula-tions and software assessment for well-posed problems with acceptable so-lutions. 2015. Available at http://www.ntua.gr/eseve/Vasikh_Ereyna/Thalis/Thalis_projects_English_summaries/Giannakoglou.pdf

(Last access, February, 2015).

van Kan, J. A second-order accurate pressure-correction scheme for viscousincompressible ow. SIAM Journal on Scientic and Statistical Comput-ing , vol. 7, pages 870891, 1986.

Kansa, E. J. Multiquadrics-A scattered data approximation scheme withapplications to computational uid-dynamics-II solutions to parabolic,hyperbolic and elliptic partial dierential equations. Computers & Math-ematics with Applications, vol. 19, pages 147161, 1990.

Kato, M. and Launder, B. E. The modeling of turbulent ow aroundstationary and vibrating square cylinders. 9th Symposium on TurbulentShear Flows, Kyoto, vol. 10, pages 16, 1993.

Kim, J. J. and Baik, J. J. A numerical study of the eects of ambientwind direction on ow and dispersion in urban street canyons using theRNG k − ε turbulence model. Atmospheric Environment , vol. 38, pages30393048, 2004.

Kirke, B. K. and Lazauskas, L. Limitations of xed pitch Darrieus hy-drokinetic turbines and the challenge of variable pitch. Renewable Energy ,vol. 36, pages 893897, 2011.

Kono, T. and Kogaki, T. Numerical investigation of wind conditions overa rectangular prism-shaped building for mounting small wind turbines.Wind Engineering , vol. 36, pages 111122, 2013.

Kooiman, S. J. and Tullis, S. W. Response of a vertical axis wind turbineto time varying wind conditions found within the urban environment.Wind Engineering , vol. 34, pages 389401, 2010.

Kopp, G. A., Farquhar, S. and Morrison, M. J. Aerodynamic mech-anisms for wind loads on tilted, roof-mounted, solar arrays. Journal ofWind Engineering and Industrial Aerodynamics, vol. 111, pages 4052,2012.

http://www.ntua.gr/eseve/Vasikh_Ereyna/Thalis/Thalis_projects_English_summaries/Giannakoglou.pdf

http://www.ntua.gr/eseve/Vasikh_Ereyna/Thalis/Thalis_projects_English_summaries/Giannakoglou.pdf

Bibliography 169

Koppes, W. Design wind loads for building wall elements. U.S. Dept. ofCommerce, National Bureau of Standards, Wind Loads on Buildings andStructures, Building Science Series, vol. 30, pages 918, 1970.

Launder, B. E. and Kato, M. Modeling ow-induced oscillations inturbulent ow around a square cylinder. ASME Fluid Engineering Con-ference, 1993.

Ledo, L., Kosasih, P. B. and Cooper, P. Roof mounting site analysis formicro-wind turbines. Renewable Energy , vol. 36, pages 13791391, 2011.

Lee, J. and You, D. An implicit ghost-cell immersed boundary methodfor simulations of moving body problems with control of spurious forceoscillations. Journal of Computational Physics, vol. 233, pages 295314,2013.

Lee, S. Natural ventilation and medium density house forms in the tropics.PhD, James Cook University, 1998.

Li, Z. and Ito, K. The immersed interface method. Numerical solutions ofPDEs involving interfaces and irregular domains . Society for Industrialand Applied Mathematics, 2006.

Li, Z. and Lai, M. The immersed interface method for the Navier-Stokesequations with singular forces. Journal of Computational Physics, vol.171, pages 822842, 2001.

Lim, H. C., Thomas, T. G. and Castro, I. P. Flow around a cubein a turbulent boundary layer: LES and experiment. Journal of WindEngineering and Industrial Aerodynamics, vol. 97, pages 96109, 2009.

Liu, J., Zhao, N., Hu, O., Goman, M. and Li, X. K. A new immersedboundary method for compressible Navier-Stokes equations. InternationalJournal of Computational Fluid Dynamics, Taylor and Francis, vol. 27,pages 151163, 2013.

q. Liu, L. and x. Wang, Z. The development and application practiceof wind-solar energy hybrid generation systems in China. Renewable andSustainable Energy Reviews, vol. 13, pages 15041512, 2009.

Lu, L. and Ip, K. Y. Investigation on the feasibility and enhancementmethods of wind power utilization in high-rise buildings of hong kong.Renewable and Sustainable Energy Reviews, vol. 13, pages 450461, 2009.

Lu, X. Y. and Dalton, C. Calculation of the timing of vortex formationfrom an oscillating cylinder. Journal of Fluids and Structures, vol. 10,pages 527541, 1996.

170 Bibliography

Mai-Duy, N. and Tran-Cong, T. A Cartesian-grid collocation methodbased on radial-basis-function networks for solving PDEs in irregular do-mains. Numerical Methods for Partial Dierential Equations, Wiley On-line Library , vol. 23, pages 11921210, 2007.

Martinuzzi, R. and Tropea, C. The ow around surface-mounted, pris-matic obstacles placed in a fully developed channel ow. Journal of FluidsEngineering , vol. 115, pages 8592, 1993.

Memon, R. A., Leung, D. Y. C. and Liu, C. H. Eects of building aspectratio and wind speed on air temperatures in urban-like street canyons.Building and Environment , vol. 45, pages 176188, 2010.

Meng, T. and Hibi, K. Turbulent measurements of the ow eld arounda high-rise building. Journal of Wind Engineering (in Japanese), vol. 76,pages 5564, 1998.

Menter, F. R. Two-equation eddy-viscosity turbulence models for engi-neering applications. AIAA Journal , vol. 32, pages 15981605, 1994.

Mertens, S. Wind energy in urban areas. Concentrator eects for windturbines close to buildings. Refocus, pages 2224, 2002.

Mittal, R., Dong, H., Bozkurttas, M., Najjar, F. M., Vargas, A.and von Loebbecke, A. A versatile sharp interface immersed boundarymethod for incompressible ows with complex boundaries. Journal ofComputational Physics, vol. 227, pages 48254852, 2008.

Mittal, R. and Iaccarino, G. Immersed boundary method. AnnualReview of Fluid Mechanics, vol. 37, pages 239261, 2005.

Mohamed, M. H., Janiga, G., Pap, E. and Thévenin, D. Optimiza-tion of Savonius turbines using an obstacle shielding the returning blade.Renewable Energy , vol. 35, pages 26182626, 2010.

Mouzakis, F., Morfiadakis, E. and Dellaportas, P. Fatigue loadingparameter identication of a wind turbine operating in complex terrain.Journal of Wind Engineering and Industrial Aerodynamics, vol. 82, pages6988, 1999.

Müller, G., Jentsch, M. F. and Stoddart, E. Vertical axis resistancetype wind turbines for use in buildings. Renewable Energy , vol. 34, pages14071412, 2009.

Murakami, S. Overview of turbulence models applied in CWE-1997. Jour-nal of Wind Engineering and Industrial Aerodynamics, vol. 7476, pages124, 1998.

Bibliography 171

National Aeronautics & Space Administration, N. A. S. A.Reynolds number. 2015. Available at http://www.grc.nasa.gov/WWW/

BGH/reynolds.html (Last access, February, 2015).

Ntinas, G. K., Zhang, G., Fragos, V. P., Bochtis, D. D. and Nikita-Martzopoulou, C. Airow patterns around obstacles with arched andpitched roofs: wind tunnel measurements and direct simulation. EuropeanJournal of Mechanics B/Fluids, vol. 43, pages 216229, 2014.

Oke, T. R. Street design and urban canopy layer climate. Energy andBuildings, vol. 11, pages 103113, 1988.

Olgyay, V. Design with climate: a bioclimatic approach to architecturalregionalism. Van Nostrand Reinhold, 1992.

OpenFOAM. 2013. Available at http://www.openfoam.com (Last access,November, 2013).

Oppenheim, D. Outside the square. integrating wind into urban environ-ments. Refocus, pages 3235, 2004.

Panofsky, H. and Dutton, J. Atmospheric turbulence. Wiley, 1984.

Pantazopoulou, G. Noise issues and standards for domestic windturbines. Microwind: the complete picture. Warwick Microwind Trialproject (Encraft), 2009. Available at http://www.warwickwindtrials.

org.uk/resources/Giota+Pantazopoulou+-+BRE.pdf (Last access, Jan-uary, 2013).

Parente, A., Gorlé, C., van Beeck, J. and Benocci, C. A compre-hensive modelling approach for the neutral atmospheric boundary layer:consistent inow conditions, wall function and turbulence model. Bound-ary Layer Meteorology , vol. 140, pages 411428, 2011.

Peskin, C. S. Flow patterns around heart valves: a numerical method.Journal of Computational Physics, vol. 10, pages 252271, 1972.

Peskin, C. S. The immersed boundary method. Acta Numerica, vol. 11,pages 479517, 2002.

Peterka, J. A. and Cernak, J. E. Adverse wind loading induced byadjacent buildings. Journal of Structural Engineering , vol. 102, pages533548, 1976.

Pierik, J. T. G., Dekker, J. W. M., Braam, H., Bulder, B. H.,Winkelaar, D. and G. C. Larsen, e. a. European wind turbine stan-dards II (EWTS-II). Wind energy for the next millennium. Proceedings.James and James Science Publishers, 1999.

http://www.grc.nasa.gov/WWW/BGH/reynolds.html

http://www.grc.nasa.gov/WWW/BGH/reynolds.html

http://www.openfoam.com

http://www.warwickwindtrials.org.uk/resources/Giota+Pantazopoulou+-+BRE.pdf

http://www.warwickwindtrials.org.uk/resources/Giota+Pantazopoulou+-+BRE.pdf

172 Bibliography

Pinelli, A., Naqavi, I. Z., Piomelli, U. and Favier, J. Immersed-boundary methods for general nite-dierence and nite-volume Navier-Stokes solvers. Journal of Computational Physics, vol. 229, pages 90739091, 2010.

Plate, E. Engineering meteorology: fundamentals of meteorology and theirapplication to problems in environmental and civil engineering . Elsevier,1982.

Pope, S. Turbulent ows. Cambridge University Press, 2000.

Potangaroa, R. The natural ventilation of high rise buildings in the trop-ics. PhD, James Cook University, 2001.

Pratt, R. N. and Kopp, G. A. Velocity measurements around low-prole,tilted, solar arrays mounted on large at-roofs, for wall normal wind di-rections. Journal of Wind Engineering and Industrial Aerodynamics, vol.123, pages 226238, 2013.

Rákai, A., Kristóf, G. and Franke, J. Sensitivity analysis of microscaleobstacle resolving models for an idealized Central European city center,Michel-Stadt. Quarterly Journal of the Hungarian Meteorological Service,vol. 118, pages 5377, 2014.

Ramponi, R., Blocken, B., de Coo, L. B. and Janssen, W. D. CFDsimulation of outdoor ventilation of generic urban congurations with dif-ferent urban densities and equal and unequal street widths. Building andEnvironment , vol. 92, pages 152166, 2015.

Richards, P. J. and Hoxey, R. P. Appropriate boundary conditions forcomputational wind engineering models using the k−ε turbulence model.Journal of Wind Engineering and Industrial Aerodynamics, vol. 4647,pages 145153, 1993.

Richards, P. J., Hoxey, R. P., Connell, B. D. and Lander, D. P.Wind-tunnel modelling of the Silsoe Cube. Journal of Wind Engineeringand Industrial Aerodynamics, vol. 95, pages 13841399, 2007.

Riegler, H. HAWT versus VAWT. Small VAWTs nd a clear niche.Refocus, pages 4446, 2003.

Roache, P. J. Verication of codes and calculations. AIAA Journal , vol.36, pages 696702, 1998.

Rott, N. Note on the history of the Reynolds number. Annual Reviews ofFluid Mechanics, vol. 22, pages 112, 1990. Available at http://158.110.32.35/download/CERN07/R_ARFM_90.pdf (Last access, February, 2015).

http://158.110.32.35/download/CERN07/R_ARFM_90.pdf

http://158.110.32.35/download/CERN07/R_ARFM_90.pdf

Bibliography 173

Sagaut, P. Large Eddy Simulation for incompressible ows. Springer, thirdedition, 2006.

Saidur, R., Rahim, N. A., Islam, M. R. and Solangi, K. H. En-vironmental impact of wind energy. Renewable and Sustainable EnergyReviews, vol. 15, pages 24232430, 2011.

Saitoh, T. S., Shimada, T. and Hoshi, H. Modeling and simulation ofthe Tokyo urban heat island. Atmospheric Environment , vol. 30, pages34313442, 1996.

Santiago, J. L., Martilli, A. and Martín, F. CFD simulation ofairow over a regular array of cubes. Part I: three-dimensional simulationof the ow and validation with wind-tunnel measurements. Boundary-Layer Meteorology , vol. 122, pages 609634, 2007.

Scaperdas, A. and Gilham, S. Thematic Area 4: Best practice advicefor civil construction and HVAC. The QNET-CFD Network Newsletter ,vol. 2, pages 2833, 2004.

Schlünzen, K. H., Bächlin, W., Brünger, H., Eichhorn, J., Grawe,D., Schenk, R. and Winkler, C. An evaluation guideline for prog-nostic microscale wind eld models. In: 9 th International Conference onHarmonisationWithin Atmospheric DispersionModelling for RegulatoryPurposes, Garmisch-Partenkirchen, June 1-4, Germany. 2004.

setDiscreteFields. Contrib setDiscreteFields, OpenFOAM Wiki.2013. Available at http://openfoamwiki.net/index.php/Contrib_

setDiscreteFields (Last access, November, 2013).

Shademan, M., Balachandar, R. and Barron, R. M. Detached eddysimulation of ow past an isolated inclined solar panel. Journal of Fluidsand Structures, vol. 50, pages 217230, 2014.

Shankar, V., Wright, G. B., Fogelson, A. L. and Kirby, R. M. Aradial basis function (RBF)-nite dierence method for the simulation ofreaction-diusion equations on stationary platelets within the augmentedforcing method. International Journal for Numerical Methods in Fluids,vol. 75, pages 122, 2014.

Shankar, V., Wright, G. B., Kirby, R. M. and Fogelson, A. L.Augmenting the immersed boundary method with radial basis functions(RBFs) for the modeling of platelets in hemodynamic ows. 2013. Avail-able at arXiv:1304.7479 (Last access, October, 2014).

Shao, J., Liu, J. and Zhao, J. Evaluation of various non-linear k−εmodelsfor predicting wind ow around an isolated high-rise building within the

http://openfoamwiki.net/index.php/Contrib_setDiscreteFields

http://openfoamwiki.net/index.php/Contrib_setDiscreteFields

arXiv: 1304.7479

174 Bibliography

surface boundary layer. Building and Environment , vol. 57, pages 145155, 2012.

Sharpe, T. and Proven, G. Crossex: concept and early development ofa true building integrated wind turbine. Energy and Buildings, vol. 42,pages 23652375, 2010.

Shih, T. H., Zhu, J. and Lumley, J. L. A realizable Reynolds stressalgebraic equation model. NASA Tech Memo, vol. 105993, 1993.

snappyHexMesh. SnappyHexMesh, OpenFOAM Wiki. 2013. Availableat http://openfoamwiki.net/index.php/SnappyHexMesh (Last access,November, 2013).

snappyHexMeshDict. SnappyHexMeshDict, snappyWiki. 2013. Avail-able at https://sites.google.com/site/snappywiki/snappyhexmesh/snappyhexmeshdict (Last access, November, 2013).

International Organization for Standardization, I. S. O. ISO14122-3:2001. 2001. Available at https://www.iso.org/obp/ui/#iso:

std:iso:14122:-3:ed-1:v1:en (Last access, August, 2015).

Stankovic, S., Campbell, N. and Harries, A. Urban wind energy .BDSP Partnership Ltd, 2009.

Stathopoulos, T., Chiovitti, D. and Dodaro, L. Wind shielding ef-fects of trees on low buildings. Building and Environment , vol. 29, pages141150, 1994.

Stathopoulos, T., Wu, H. and Bedard, C. Wind environment aroundbuildings: a knowledge-based approach. Journal of Wind Engineering andIndustrial Aerodynamics, vol. 44, pages 23772388, 1992.

Stathopoulos, T., Zisis, I. and Xypnitou, E. Local and overall windpressure and force coecients for solar panels. Journal of Wind Engineer-ing and Industrial Aerodynamics, vol. 125, pages 195206, 2014.

Stull, R. B. An introduction to boundary layer meteorology . Kluwer Aca-demic Publishers, 1988.

Sumner, J. Towards improved RANS k − ε modelling of turbulent incom-pressible ows for wind energy applications. PhD, École de TechnologieSupérieure, Université du Québec, 2012.

Sumner, J., Watters, C. S. and Masson, C. CFD in wind energy: thevirtual, multiscale wind tunnel. Energies, vol. 3, pages 9891013, 2010.

http://openfoamwiki.net/index.php/SnappyHexMesh

https://sites.google.com/site/snappywiki/snappyhexmesh/snappyhexmeshdict

https://sites.google.com/site/snappywiki/snappyhexmesh/snappyhexmeshdict

https://www.iso.org/obp/ui/#iso:std:iso:14122:-3:ed-1:v1:en

https://www.iso.org/obp/ui/#iso:std:iso:14122:-3:ed-1:v1:en

Bibliography 175

Sunpower. Datasheet solar panel X21-345. 2014. Available at http://us.sunpower.com/sites/sunpower/files/media-library/data-sheets/

ds-x21-series-335-345-residential-solar-panels-datasheet.pdf

(Last access, September, 2014).

Sunpower. Datasheet T10 solar roof tile. 2015. Availableat http://www.aadvanced.com/grs/FILES/FIRESTONE%20PV%20system.pdf (Last access, August, 2015).

Syngellakis, K., Carroll, S. and Robinson, P. Small wind power.Refocus, pages 4045, 2006.

Tabrizi, A. B., Whale, J., Lyons, T. and Urmee, T. Performance andsafety of rooftop wind turbines: use of CFD to gain insight into inowconditions. Renewable Energy , vol. 67, pages 242251, 2014.

Taira, K. and Colonius, T. The immersed boundary method: a projec-tion approach. Journal of Computational Physics, vol. 10, pages 252271,2007.

Centro de Investigaciones Energéticas Medioambientales yTecnológicas, C. I. E. M. A. T. Euler supercomputer characteristics.2015. Available at https://intranet.ciemat.es:8444/ICIEMATportal/portal.do?TR=C&IDR=874 (Last access, August, 2015).

Tegral. Tegral at roof decking. 2015. Available at http://www.tegral.com/index.php?page=Flat-Roof-Decking (Last access, August, 2015).

Tennekes, H. and Lumley, J. L. A rst course in turbulence. The MITPress, 1972.

Thai-Quang, N., Mai-Duy, N., Tran, C. D. and Tran-Cong, T. Adirect forcing immersed boundary method employed with compact in-tegrated rbf approximations for heat transfer and uid ow problems.Computer Modeling in Engineering and Sciences, vol. 96, pages 4990,2013.

Thévenin, D. and Janiga, G. Optimization and computational uid dy-namics. Springer, 2008.

Toja-Silva, F., Colmenar-Santos, A. and Castro-Gil, M. Urbanwind energy exploitation systems: behaviour under multidirectional owconditions - opportunities and challenges. Renewable and Sustainable En-ergy Reviews, vol. 24, pages 364378, 2013.

Toja-Silva, F., Favier, J. and Pinelli, A. Radial basis function (RBF)-based interpolation and spreading for the immersed boundary method.Computers and Fluids, vol. 105, pages 6675, 2014.

http://us.sunpower.com/sites/sunpower/files/media-library/data-sheets/ds-x21-series-335-345-residential-solar-panels-datasheet.pdf



http://www.aadvanced.com/grs/FILES/FIRESTONE%20PV%20system.pdf

http://www.aadvanced.com/grs/FILES/FIRESTONE%20PV%20system.pdf

https://intranet.ciemat.es:8444/ICIEMATportal/portal.do?TR=C&IDR=874

https://intranet.ciemat.es:8444/ICIEMATportal/portal.do?TR=C&IDR=874

http://www.tegral.com/index.php?page=Flat-Roof-Decking

http://www.tegral.com/index.php?page=Flat-Roof-Decking

176 Bibliography

Toja-Silva, F., Lopez-Garcia, O., Peralta, C., Navarro, J. andCruz, I. Optimal roof geometry for urban wind energy exploitation inhigh-rise buildings. Applied Energy (under review), 2015a.

Toja-Silva, F., Peralta, C., Lopez-Garcia, O., Navarro, J. andCruz, I. Eect of roof-mounted solar panels on buildings wind energypotential. Journal of Wind Engineering and Industrial Aerodynamics, vol.145, pages 123138, 2015b.

Toja-Silva, F., Peralta, C., Lopez-Garcia, O., Navarro, J. andCruz, I. On the roof geometry for urban wind energy exploitation inhigh-rise buildings. Computation, vol. 3, pages 299325, 2015c.

Toja-Silva, F., Peralta, C., Lopez-Garcia, O., Navarro, J. andCruz, I. Roof region dependent wind potential assessment with dierentRANS turbulence models. Journal of Wind Engineering and IndustrialAerodynamics, vol. 142, pages 258271, 2015d.

Tominaga, Y., Mochida, A., Murakami, S. and Sawaki, S. Compar-ison of various revised k − ε models and LES applied to ow around ahigh-rise building model with 1:1:2 shape placed within the surface bound-ary layer. Journal of Wind Engineering and Industrial Aerodynamics, vol.96, pages 389411, 2008.

Tompitak, M. Rapid diusion. 2015. Avail-able at http://www.rapiddiffusion.com/science/

navier-stokes-millennium-prize-problem-solved/ (Last access,February, 2015).

Tong, N. Y. O. and Leung, D. Y. C. Eects of building aspect ratio,diurnal heating scenario, and wind speed on reactive pollutant dispersionin urban street canyons. Journal of Environmental Sciences, vol. 24, pages20912103, 2012.

Triton, D. J. Experiments on the ow past a circular cylinder at lowReynolds numbers. Journal of Fluid Mechanics, vol. 6, pages 547567,1959.

Tseng, Y. and Ferziger, J. H. A ghost-cell immersed boundary methodfor ow in complex geometry. Journal of Computational Physics, vol. 192,pages 593623, 2003.

Tsuchiya, M., Murakami, S., Mochida, A., Kondo, K. and Ishida,Y. Development of a new k− ε model for ow and pressure elds aroundblu body. Journal of Wind Engineering and Industrial Aerodynamics,vol. 6768, pages 169182, 1997.

http://www.rapiddiffusion.com/science/navier-stokes-millennium-prize-problem-solved/

http://www.rapiddiffusion.com/science/navier-stokes-millennium-prize-problem-solved/

Bibliography 177

TU/e. Bahrain World Trade Center is exactly thewrong way round. 2014. Available at https:

//www.tue.nl/en/university/news-and-press/news/

bahrain-world-trade-center-is-exactly-the-wrong-way-round

(Last access, December, 2014).

Vanella, M. and Balaras, E. A moving-least-squares reconstruction forembedded-boundary formulations. Journal of Computational Physics, vol.228, pages 66176628, 2009.

Vitruvius, P. The ten books on architecture. (Translated by M. H. Mor-gan). Dover, 1960.

Walker, S. L. Building mounted wind turbines and their suitability forthe urban scale - a review of methods of estimating urban wind resource.Energy and Buildings, vol. 43, pages 18521862, 2011.

Wang, F., Bai, L., Fletcher, J., Whiteford, J. and Cullen, D.Development of small domestic wind turbine with scoop and predictionof its annual power output. Renewable Energy , vol. 33, pages 16371651,2008a.

Wang, F., Bai, L., Fletcher, J., Whiteford, J. and Cullen, D. Themethodology for aerodynamic study on a small domestic wind turbinewith scoop. Journal of Wind Engineering and Industrial Aerodynamics,vol. 96, pages 124, 2008b.

Watson, S. J. Predicting the yield of small wind turbines in theroof-top urban environment - an update. Microwind: the complete pic-ture. Warwick Microwind Trial project (Encraft), 2009. Availableat http://www.warwickwindtrials.org.uk/resources/Simon+Watson+-+Loughborough+University.pdf (Last access, February, 2013).

Wendland, H. Scattered data approximation. Cambrigde monographs onapplied and computational mathematics. Cambridge University Press,2005.

Werne, J. Turbulence notes. 2015. Available at http://www.cora.nwra.com/~werne/eos/text/turbulence.html (Last access, February, 2015).

Whiteman, C. D. Mountain meteorology: fundamentals and applications.Oxford University Press, 2000.

WINERCOST. COST Action TU1304, WINd Energy technol-ogy Reconsideration to enhance the COncept of Smart ciTies(WINERCOST). 2015. Available at http://www.cost.eu/domains_

actions/tud/Actions/TU1304 (Last access, January, 2015).

https://www.tue.nl/en/university/news-and-press/news/bahrain-world-trade-center-is-exactly-the-wrong-way-round



http://www.warwickwindtrials.org.uk/resources/Simon+Watson+-+Loughborough+University.pdf

http://www.warwickwindtrials.org.uk/resources/Simon+Watson+-+Loughborough+University.pdf

http://www.cora.nwra.com/~werne/eos/text/turbulence.html

http://www.cora.nwra.com/~werne/eos/text/turbulence.html

http://www.cost.eu/domains_actions/tud/Actions/TU1304

http://www.cost.eu/domains_actions/tud/Actions/TU1304

178 Bibliography

World Meteorological Organization, W. M. O. Technical docu-ment 778. Documentation on RSMC support for environmental emer-gency response. 2015. Available at http://www.wmo.int/pages/prog/

www/DPFSERA/td778-sec3.htm (Last access, February, 2015).

Wright, A. K. and Wood, D. H. The starting and low wind speedbehaviour of a small horizontal axis wind turbine. Journal of Wind Engi-neering and Industrial Aerodynamics, vol. 92, pages 12651279, 2004.

Yakhot, V. and Smith, L. M. The renormalization group, the ε-expansionand derivation of turbulence models. Journal of Scientic Computing , vol.7, pages 3561, 1992.

Yao, L. and Fogelson, A. L. Simulations of chemical transport andreaction in a suspension of cells I: an augmented forcing point methodfor the stationary case. International Journal for Numerical Methods inFluids, vol. 69, pages 17361752, 2012.

Yap, C. J. Turbulent heat and momentum transfer in recirculating andimpinging ows. PhD, Faculty of Technology, University of Manchester,1987.

Zhang, L., Gerstenberger, A., Wang, X. and Liu, W. K. Immersednite element method. Computer Methods in Applied Mechanics and En-gineering , vol. 193, pages 20512067, 2004.

http://www.wmo.int/pages/prog/www/DPFSERA/td778-sec3.htm

http://www.wmo.int/pages/prog/www/DPFSERA/td778-sec3.htm

Appendix A

Radial basis function(RBF)-based interpolation andspreading for the immersedboundary method

The power of mathematics is often tochange one thing into another, to change

geometry into language.

Marcus du Sautoy

A.1 Introduction

When considering complex geometries, immersed boundary (IB) methodsconstitute an ecient alternative to avoid either dicult or even impossiblegrid generation procedures when dealing with body-tted formulations orextra computational costs associated with unstructured grid solvers. Thosediculties associated to classical body tted or unstructured solvers, be-come even more severe for moving or deformable boundary, as is the case inuid-structure interaction problems. Moreover, in those cases, the immersedboundary methods are not restricted to small boundary displacements suchas other techniques based on smooth mesh deformation (Ji et al. (2010)).An alternative to immersed boundary methods is the immersed nite ele-ment method (IFEM) proposed by Zhang et al. (2004). This work extendsthe idea of the discrete Delta functions to unstructured meshes using theidea of Reproducing Kernel Particle Methods (RKPM). Both uid and soliddomains are modeled with nite element methods and the continuity be-tween the uid and solid sub-domains are enforced via the interpolation of

179

180 Appendix A. RBF-based immersed boundary method

the velocities, and the distribution of the forces with the reproducing kernelparticle method (RKPM) Delta function. The immersed boundary methodwas historically introduced by Peskin (1972), in a pioneering work focussedon heart dynamics. Since then it has continuously evolved to tackle nu-merical simulations of new scientic domains, from biomedical to chemicalengineering and aeronautics. The classical approach is to solve the problemequations on a uniform cartesian grid (Eulerian) for both solid and uidphases. The boundary of the solid is described through a set of markers(Lagrangian) which do not coincide with the uid mesh points. The commu-nications between uid and solid is done through volume forces that enforcethe no-slip boundary condition and ensure the conservation at the wall oflinear momentum, force and torque by means of interpolation-spreading op-erators (discrete Delta functions in the case of the classical method). Usingthe same discrete Delta functions for both interpolation and spreading guar-antees conservation of energy, along with conservation of force and torque(Peskin (2002)).

A review of the dierent avours of the method can be found in Mittaland Iaccarino (2005), where they are divided in two groups. The rst groupof techniques, called continuous forcing (Peskin (1972); Li and Lai (2001);Taira and Colonius (2007)), where the derivation of the body forces is car-ried out before the discretisation step, have been widely used when dealingwith sharp boundaries and rigid objects (Mittal and Iaccarino (2005)). Thesecond group termed as discrete forcing methods (Pinelli et al. (2010);Fadlun et al. (2000); Tseng and Ferziger (2003); Mittal et al. (2008); Leeand You (2013); Yao and Fogelson (2012)) is based on a set of singular bodyforces, dened on the Eulerian uid nodes, to enforce the desired bound-ary values. This second group of techniques allows to use larger time-stepsand, certain formulations, can handle sharp boundaries too (Mittal et al.(2008)). The immersed boundary method that is proposed in the presentwork, which makes use of radial basis functions (RBFs), can be classiedwithin the second group.

Traditionally, RBFs have been used for scattered data interpolation andtheir processing, and for function approximation. In the last decades, RBFshave also been employed as basis functions for the solution of PDEs, in-cluding uid dynamics conservation laws (see the seminal paper by Kansa(1990)). Applications that are related with the present contribution, in-clude the interpolation of the displacements of boundary nodes of mov-ing meshes to inner unstructured domains (de Boer et al. (2007a)), datatransfer through interfaces of non-matching meshes (de Boer et al. (2007b)),multivariable interpolation in uid-solid-interaction problems (Beckert andWendland (2001)), etc. More recently, RBFs have been also applied in thecontext of immersed boundary methods. Specic works proposing RBFs forinterpolation in uid-structure interaction applications are briey reviewed

A.1. Introduction 181

hereafter. Mai-Duy and Tran-Cong (2007) introduce one-dimensional in-tegrated RBF networks within a collocation framework to solve PDEs onCartesian grids. In the proposed formulation, Dirichlet boundary conditionsare enforced in a direct way, while Neumann boundary conditions are im-posed by means of integration constraints. Fang et al. (2011) use GaussianRBFs to smooth Gibbs oscillations occurring in velocity derivatives near theimmersed boundary when spectral-like discretization of the Navier-Stokesequations is used in conjunction with the IB method. Shankar et al. (2013)introduce a parametric RBF model to represent the surface of the immersedelastic object. This approach allows for tracking the deformation of the sur-face eciently since just a small set of Lagrangian markers is required tothat end. Surface boundary conditions are imposed via an interpolation-spreading approach using pseudo delta functions dened on a larger set ofimmersed surface nodes. Liu et al. (2013) use local RBFs (also termed asRBF-FD, i.e., RBF-generated nite dierences) to solve the compressibleNavier-Stokes equations. The boundary conditions are kept into account bymoding locally the values of the nodes neighbouring the domain limitingsurface in such a way that the interpolated values are the desired ones at theboundary. The whole boundary value enforcement procedure is carried outat each Runge-Kutta stage of their time stepping algorithm (a three stageRK method). Thai-Quang et al. (2013) present a direct forcing methodbased on compact integrated radial basis functions, using a smoothed ver-sion of the discrete delta functions to transfer the physical quantities be-tween Eulerian and Lagrangian nodes. Shankar et al. (2014) use RBF-basedsymmetric Hermite interpolation to extend the Augmented Direct Forcingmethod (Yao and Fogelson (2012)) to handle objects with concavities orobjects in close proximity. This modied version of the Augmented Di-rect Forcing method was used in conjunction with an RBF-FD method forsolving reaction-diusion equations on object surfaces. Their method onlyrequires the coordinates of the scattered nodes representing the surface andits normal-to-the-surface vectors at those locations.

In the present work an original immersed boundary method based on ra-dial basis functions interpolation is proposed. To the best of the authorknowledge, the method diers from previous literature implementations,proving to be easier to implement and more versatile than existing ones.The most signicant advantages of the present method are: i) it is aplicableto any underlying grid system because based on an interpolation-spreadingprocess dened on a scattered cloud of nodes; ii) the weights of the RBFare calculated independently from the velocity of the nodes (i.e., for staticgeometries they only depend on the geometry); and, iii) both interpolationand spreading (or convolution) are carried out simultaneously in a singlestage.

The presentation of this procedure is organised as follows: rstly, the


formulation of the RBFs used within the IB algorithm is presented; next,the numerical algorithm that we envisaged to impose Dirichlet boundaryconditions is presented and validated in the context of a 2D Navier-Stokessolver. Afterwards, the imposition of Neumann boundary conditions is dis-cussed and applied in the case of a 2D unsteady heat conduction problem.Finally, conclusions and recommendations for further future works are given.

A.2 RBF interpolation from an arbitrarily scat-

tered set of nodes

Following the basic idea behind immersed boundary methods, we dene a setof Lagrangian nodes Xi, i = 1 · · ·m on the immersed surface Γ surroundedby a cloud of neighbouring nodes (Eulerian nodes) xk, k = 1 · · ·n, belongingto the underlying uid grid. The key idea of the IB method is to compute theuid velocity at nodes Xi via interpolation from the xk, and thus nd the setof localised forces (per unit mass, and unit time) on the interface that restorethe desired velocity condition on Γ. Typically, this set of singular forces Fi,dened on Γ, is later on distributed on the uid nodes via a convolution(spreading) operation, obtaining a set of Eulerian forces fk, k = 1 · · ·n. Moredetails on how this procedure has been adapted to the present algorithm willbe illustrated later on. Here, we just highlight that one of the key ingredientsof any IB method is the transfer of a force eld from the Lagrangian to theEulerian nodes and viceversa (Peskin (2002); Favier et al. (2014)). We willwrite the relationship between the force dened on the immersed surfaceand the one acting on the uid as:

F = Wf, with F = (F1, F2, · · · , Fn)T and f = (f1, f2, · · · , fm)T (A.1)

whereW is a transformation matrix with m rows and n columns (in general,n 6= m) which entries depend on the basis functions used for the interpola-tion. The W matrix must obey the constraint of having all its column-sumequal to unity to conserve the total force,

∑mi=1 Fi =

∑nk=1 fk, and to guar-

antee energy conservation (i.e., the work done by the forces in the two gridsystems, see (de Boer et al. (2007b); Beckert and Wendland (2001))). Indeedif∑

iWi,k = 1, we have:∑i

Fi =∑i

∑k

Wi,kfk =∑k

fk∑i

Wi,k =∑k

fk (A.2)

Thus, the column-sum of W must be equal to unity independently of theinterpolatory technique that is used. Next, we assemble matrix W makinguse of RBFs also introducing the inverse operator that transfer the forcedata from the immersed interface to the uid grid. We start by writing one

A.2. RBF interpolation from an arbitrarily scattered set of nodes 183

of the equations of (A.1), that provides the interpolated value on a point Xl

of the immersed surface as a function of the n values on the uid grid:

Fl =

n∑j=1

ωjfj , with Fl = F (Xl) and fj = f(xj) (A.3)

where ωi, i = 1, · · ·n are unknown interpolation weights. To determine thevalues of the weights, we rewrite (A.3) as:

Fl =

n∑j=1

[n∑k=1

λj,kφ(‖Xl − xk‖) + γj

]︸︷︷︸

ωj

fj , (A.4)

Where φj,k = φ(‖xj − xk‖) is a radial basis function: a symmetric functionwhich value just depends on the Euclidean distance ‖xj−xk‖ between nodes.To determine the value of the unknown parameters λj,k and γj (and thus ofωj), for each node xj , j = 1, · · · , n we impose the cardinality conditions:

n∑k=1

λj,kφj,k + γj = δj,k (A.5)

(where δj,k is the usual Kroeneker symbol) together with the constraint thatthe interpolant should exacly represent a constant function

∑nk=1 λj,k = 0.

Thus, for each node of the support xj , we need to solve a linear system ofequations to determine the λj,k, k = 1 · · ·n:

φ1,1 · · · φ1,n 1· · · · · · · · · · · ·φj,1 · · · φj,n 1· · · · · · · · · · · ·φn,1 · · · φn,n 1

1 · · · 1 0

λj,1· · ·λj,j· · ·λj,nγj

=

0· · ·1· · ·00

(A.6)

For the present work we have used the inverse multiquadric radial basisfunctions (IMQ-RBF):

φj,k ≡ φ(rj,k) := 1√1 + (εrj,i)2

: j, k ∈ =l, rj,k = ‖xj − xk‖ (A.7)

where =l denotes the interpolation support of node Xl (that is discussedin detail later), ε > 0 is the shape parameter and rj,k the radial distancebetween the nodes j and k. Note that φi,i = 1. The optimum value ofthe shape parameter ε depends on the noise in the data set, and it hasto be determined according to each application. In summary, by solving


the linear systems formed by Eqs. (A.6) we determine the weights λj,kthat are independent on the location of Xl. Next, we compute the ωj byevaluating the expression ωj =

∑nk=1 λj,kφ(‖Xl − xk‖) + γj to be used in

the interpolatory formula (A.3). By considering all the Lagrangian pointsXl, and thus all the respective Eulerian support =l, we can compute all theweights ωj that correspond to the entries of matrix W appearing in (A.1).

An important feature of this interpolant is that the weights λj,k canbe also used to approximate the value of the derivative (or of any lineardierential operator L(f)) at the Lagrangian node l. Indeed, we have:

L(f)(Xl) =

n∑j=1

n∑k=1

[λj,kL(φ)(‖Xl − xk‖) + γj ] fj (A.8)

where L(φ)(‖Xl−xk‖) is the linear dierential operator applied to the IMQ-RBF evaluated in Xl.

In the particular case of the normal derivative to the immersed boundaryΓ at point Xl where the unit normal vector is ~n and the tangent vector isgiven by ~τ = [τx, τy]

T , one can dene the linear dierential operator viathe projection P = I − ττT (where I is the identity matrix). Using P ,the approximation to the normal derivative of a function f at Xl = (xl, yl)reads:

L(f)(Xl) = ~∇f · ~n =n∑j=1

n∑k=1

P ~∇φ(‖Xl − xk‖)fj (A.9)

with ~∇φ(‖Xl − xk‖) = (∂xφ(‖Xl − xk‖), ∂yφ(‖Xl − xk‖))T and:

∂xφ(‖Xl − xk‖) ≡ −ε2(xl − xk)

(1 + (εrl,k)2)3/2, (A.10)

∂yφ(‖Xl − xk‖) ≡ −ε2(yl − yk)

(1 + (εrl,k)2)3/2, (A.11)

i.e., the partial x and partial y derivatives of (A.7). The convergence orderof the IMQ-RBF depends on both the smoothness of the target functionand the node density of the data sites. For smooth target functions thatlie in its native space, the IMQ-RBF can exhibit spectral convergence. Fora full discussion, see Wendland (2005). In the present case, described in3.1, the interpolation functions have a rst order convergence rate. Theorder that can be achieved is mainly related with the support used for theinterpolation. Figure A.1 shows the norm of the interpolation error ERBFat the immersed surface dened by

ERBF = maxlURBF , (A.12)

A.3. Imposition of Dirichlet boundary conditions 185

where URBF refers to the interpolation error of an arbitrary known eld ateach Lagrangian point l (dierence between the interpolated value and theknown function at the point). The given results correspond to the methodand the support choice described in the next section.

10−2

10−1

10−3

10−2

10−1

100

∆ x

ERBF

Figure A.1: Norm of the interpolation error at the Lagrangian points for thecase described in 3.1. Red squares: interpolation error; solid line: ∆x (1storder); dashed line: ∆x2 (2nd order).

A.3 Imposition of Dirichlet boundary conditions

A common way of dealing with the incompressible Navier Stokes equationsis by employing a continuous projection method (see van Kan (1986) andBrown et al. (2001), for example). In this framework, a popular time ad-vancement procedure (as it is done in Pinelli et al. (2010) for instance) readsas:

u∗ − un

∆t= −Nl(u

n, un−1)−Gφn−1 +1

ReL(u∗, un), (A.13)

for the predicted momentum equation, and

Lφ =1

∆tDu∗, (A.14)


for the value of the projector (i.e., the pseudo pressure) that enforces thedivergence free condition via:

un+1 = u∗ −∆tGφn, (A.15)

In the given, time discretised equations, u∗ is the predicted velocity eld, un

is the velocity eld obtained at the time-step n, ∆t is the time step, Nl, G andD are, respectively, the nite-dierence discrete approximation of the non-linear, the gradient and the divergence operators, L is the discrete Laplacianand φ is a projection variable (related to the pressure eld). Normally, allthose operators are dened on a staggered grid system (Ferziger and Peric(2002)).

To impose assigned Dirichlet boundary values on the immersed boundaryΓ, the above time sequence is modied by carrying out the time advancementof the predicted momentum equations in two stages: Firstly, a fully explicitprediction step is performed without body force (without keeping into ac-count the Dirichlet values on Γ) by advancing Eq. (A.13). The predictedvelocity eld u∗ leads to a predicted force eld u∗/∆t (per unit mass), thatis interpolated on the immersed boundary using the procedure described inthe previous section. Next, we determine the necessary force per unit massrequired to enforce the desired boundary conditions on Γ.

F =Uo

∆t− I(u∗)

∆t, (A.16)

In (A.16), Uo is the desired velocity distribution on the immersed boundary,and I is the interpolator operator (Eulerian mesh to immersed surface).Once the value of the restoring force F on Γ has been determined, we seekcorrections to the momentum equation, discretised on the Eulerian mesh,by introducing a set of singular body forces. In other words, we shoulddetermine the values of f to be assigned to the interpolating Eulerian nodesto recover the values of F on Γ given by (A.16):

f = R(u∗/∆t), (A.17)

where R refers to the interpolation-spreading using a radial basis function.The regularized force f is then added to the right hand side of the momentumequations, and the time advancement of Eq. (A.13) is repeated:

u∗ − un

∆t= −Nl(u

n, un−1)−Gφn−1 +1

ReL(u∗, un) + f. (A.18)

The algorithm completes the time step with the usual solution of the pressurePoisson equation, Eq. (A.14), and the completion of the projection step (i.e.,equation (A.15)).


A.3.1 Methodology

For sake of clarity, we consider Γ to be a circle of radius r, centred at (xc,yc).The Eulerian nodes neighbouring the immersed surface belong to a an anulusof width 2∆r dened along the immersed boundary. The nodes enclosed inthis region will be the ones involved with the interpolation and spreadingoperations (see gure A.2). We start by tagging the inner nodes, adjacent

Figure A.2: Diagram of the interpolation support.

to the embedded surface, using the following condition:

Sr−∆r < (xin, yin) < Sr, (A.19)

Similarly, the outer nodes satisfy:

Sr < (xout, yout) < Sr+∆r. (A.20)

where Sr+α is the circumference of a circle of radius r+α centred at (xc,yc).For more general geometries, to tag the inner and outer nodes, one couldresort to a level set function (Li and Ito (2006)) (in the simple case of acircle given by h(x, y) = (x − xc)2 + (y − yc)2 − r2) and discriminate theposition according to the sign of the function (positive/negative value atpoint (x,y) corresponds to an outer/inner location). The number of innerEulerian nodes will also dene the number of Lagrangian nodes used to dis-cretise Γ. The same number will also dene the size of the linear systemto be solved for the interpolation-spreading process (i.e., n, the size of ma-trix W of equation (A.1)). As explained in the following, if the number of


Lagrangian nodes is equal to the number of inner Eulerian nodes, the re-sulting linear system will have the same number of equations and unknowns(square matrix). Other choices are possible if a least square approximationof the boundary values is seeked. In this case to improve the accuracy ofthe method, one should specify a number of Lagrangian nodes larger thanthe number of Eulerian nodes falling within the internal part of the anulus.The interpolation support is shown in gure A.2. A number of numericalexperiments has been performed considering dierent boundary layer thick-ness (i.e., Reynolds numbers of the ow around the circle) and dierentmesh sizes. Those numerical experiments suggest that a good compromisebetween stability and accuracy is attained for a number of Lagrangian nodestaken to be about three times the number of nodes in the inner region. Theset of all inner points corresponds to the union of the interpolation supportsof each Lagrangian node. The interpolation support for each one of them,is determined using another smaller circle centered on a point belonging toSr and with a radius of ∆r. This circle is thus tangent to both Sr+∆r andSr−∆r (see gure A.2). After a parametric study, the value of ∆r = ∆x hasbeen found to be robust over variations of the Γ geometry (circular, ellipti-cal, with sharp arcs, etc.). Both the inner Eulerian and Lagrangian nodesthat fall within this circle, constitute the inner subset of the support that isused for the interpolation step.

Once the set of all the supports is dened, we proceed to interpolate theuid velocity onto the Lagrangian nodes using a the compact radial basisfunction method described in the previous section. Firstly, we evaluate theweights ωj(Xl) using (A.6) in conjunction with (A.7). Concerning the valueof the parameter ε appearing in (A.7), we have found, via a parametric study,that the value ε = Re/∆x is a robust choice over variations of the Reynoldsnumber Re. This point clearly requires further investigation. However, inthis work, we simply use this empirically-determined value and found thatit performs quite well in the ranger 25 < Re < 250. During our numericalexperiments we have also systematically veried that the column-sum of allweigths in matrix W (i.e., equation (A.1)) is indeed equal to unity.

Having determined the value of the interpolating weights, the uid ve-locity (computed using Eq. (A.13) is estimated on each node Xl by theLagrangian interpolation formula:

ul∆t

= ω1u1

∆t+ ω2

u2

∆t+ ...+ ωn

un∆t

. (A.21)

As previously mentioned, the uid velocity is decomposed into an es-timated velocity u∗ (computed by Eq. A.13), and a regularized force fimposing the desired conditions on Γ. In the specic case of homogeneousDirichlet conditions (no-slip: UXl

= 0 on Γ), the merging of the interpolated


values with the unknown values on the support, leads to :

0 = ωi1(u∗i1∆t

+ fi1) + ...+ ωin(u∗in∆t

+ fin) + ωo1u∗o1∆t

+ ...+ ωonu∗on∆t

. (A.22)

Equation (A.22) is an overdetermined system of linear equations Wf = b,having the values of f at the internal support nodes as unknowns. Thematrix W , and the right-hand-side of the system are given by:

W =

ωi1(l1) 0 0 ωi4(l1) 0

0 ωi2(l2) 0 ωi4(l2) 0...

......

......

ωi1(ln−1) 0 0 0 ωi5(ln−1)

0 0 ωi3(ln) 0 ωi5(ln)

, (A.23)

and

b =

−∑ωi

u∗i∆t |l1 −

∑ωo

u∗o∆t |l1

−∑ωi

u∗i∆t |l2 −

∑ωo

u∗o∆t |l2

...

−∑ωi

u∗i∆t |ln−1 −

∑ωo

u∗o∆t |ln−1

−∑ωi

u∗i∆t |ln −

∑ωo

u∗o∆t |ln

(A.24)

As the matrixW is not necessarily squared, we use a classical least squaremethod to compute the regularized force fi:

W TWf = W T b. (A.25)

Before proceeding further, a word of caution is due. We have found thatwhen one or more external Eulerian nodes, belonging to the support, areexcessively close to the embedded surface (normal distance less than 0.1∆x),the weights can take on very large values leading to numerical instabilities.This numerical issue can be xed by assigning to those nodes the samevelocity as the closest ones laying on Γ. In the case of non-regular grids,this normal distance can be computed as 0.1∆r, being ∆r the thickness ofthe interpolation support, which is dened according to the mean distancebetween the cells close to the embedded surface. Since the boundary isapproximated as piecewise linear, the accuracy is hardly aected by dividinga segment into two parts (Tseng and Ferziger (2003)). According to Gibouet al. (2002), this approach preserve second order accuracy when solving thePoisson equation in irregular domains.

A.3.2 Results and discussion

To validate the proposed methodology, we have considered the case of aow around a circular cylinder of diameter D at two Reynolds numbers,


ReD = 30 and ReD = 185. Following the numerical settings of Pinelli et al.(2010), the dimensions of the domain are Lx = 49D in streamwise directionand Ly = 34D in the normal direction. The center of the cylinder is locatedat (x, y) = (9D, 17D). The mesh spacing is ∆x = ∆y = 0.0576D (Cartesianmesh).

The no-slip boundary condition at the cylinder wall are imposed usingthe proposed algorithm. It is found that the methodology is able to re-produce successfully the characteristics of the ow at both ReD = 30 andReD = 185. Figures A.3 and A.4 show the velocity elds and the vorticitycontours. There is a qualitative agreement with the literature: at ReD = 30the ow remains steady with the presence of a recirculating region in thewake; at ReD = 185, periodic shedding vortices are formed downstream ofthe body (even if this case is nominally a 3D one since an instability in thespanwise direction should already be present, many authors have consideredthe 2D numerical study of the ow).

(a) Streamwise velocity u. (b) Vertical velocity v.

(c) Vorticity contours.

Figure A.3: Mean velocity and vorticity contours at ReD = 30.

A more quantitative analysis is provided in Table A.1 that shows compar-


(a) Streamwise velocity u. (b) Vertical velocity v.

(c) Instantaneous vorticity contours.

Figure A.4: Instantaneous velocity and vorticity contours at ReD = 185.

isons with the literature on the values of the main topological parameters ofthe wake at Re = 30 (see gure A.5). Table A.2 gives quantitative compar-isons for the higher Re, unsteady case considering the values of the Strouhalnumber and the drag mean coecient obtained. A general good agreementis obtained, conrming the correct treatment of the boundary condition atthe wall using the present method.

l/D a/D b/D θ CDPresent 1.71 0.56 0.53 47.93 1.78Pinelli et al. (2010) 1.70 0.56 0.52 48.05 1.80Coutanceau and Bouard (1977) 1.55 0.54 0.54 50.00 -Triton (1959) - - - - 1.74

Table A.1: Comparison of the main parameters of the wake and the dragcoecient at ReD = 30 with other works and experimental data.


St CDPresent 0.195 1.31Pinelli et al. (2010) 0.196 1.43Vanella and Balaras (2009) - 1.38Guilmineau and Queutey (2002) 0.195 1.28Lu and Dalton (1996) 0.195 1.31

Table A.2: Comparison of the Strouhal number and the drag coecient atReD = 185 with other works and experimental data.

Figure A.5: Shape parameters of the wake formed at Re = 30 (Pinelli et al.(2010)).

Figure A.6 shows the norm of the interpolation error El at the immersedsurface dened by

El = maxlUl , (A.26)

where Ul refers to the interpolated velocity computed at each LagrangianpointXl after the advancement of the second corrected momentum equation.From the gure, it clearly appears that the global method is of order one.

A.4 Treatment of Neumann boundary conditions

We have tested the viability of our approach for imposing Neumann condi-tions by considering a simple 2D heat conduction equation around a ther-mically insulated cylinder.

Considering constant physical properties, and an implicit time advancingtreatment, the governing equation of the heat conduction problem reads as:

Tn+1 − Tn

∆t= α∇2Tn+1, (A.27)

A.4. Treatment of Neumann boundary conditions 193

10−2

10−1

10−4

10−3

10−2

10−1

100

∆ x

El

Figure A.6: Norm of the interpolation error at the immersed surface for aDirichlet boundary condition. Red squares: error u; blue asterisks: error v;solid line: ∆x (1st order); dashed line: ∆x2 (2nd order).

where T is the temperature and α the thermal diusivity, set to a valueof α = 110 · 10−6m2/s (which would correspond to copper thin plate). Inwhat follows, we describe the method by which Neumann conditions ∂T

∂~n = 0are imposed at the immersed surface.

A.4.1 Methodology

As for the case of Dirichlet conditions, the internal and the external nodes ofthe Eulerian grid dened by the embedded surface are found using the levelset method. The subsequent selection of the support is also performed in thesame way as previously described. The choice on the number of Lagrangiannodes dening the immersed contour is more demanding for the case ofNeumann conditions. We have found that the minimal number necessary tomantain the accuracy is about the double than the one required for imposingDirichlet values.

As already mentioned, the use of radial basis functions for the inter-polation of the derivative of the variable over the immersed boundary is asimple variation of the technique used for the interpolation of the values ofthe variable, thus rendering the method very friendly.


The rst step is to evaluate the weights ωi of the function, applyingthe following relationship between the Lagrangian node l and each Euleriannode 1 . . . n within the interpolation support:

φ~nl,1 = ω0 + ω1∆φ1,1 + ω2∆φ1,2 + ...+ ωn∆φ1,n

φ~nl,2 = ω0 + ω1∆φ2,1 + ω2∆φ2,2 + ...+ ωn∆φ2,n

...

φ~nl,n = ω0 + ω1∆φn,1 + ω2∆φn,2 + ...+ ωn∆φn,n, (A.28)

where φi,j is the radial basis function between the node i and the nodej, and φ~nl,i is the derivative radial basis function between the l Lagrangiannode and the i Eulerian node projected on the normal surface direction ~n,as previously dened. By adding the extra condition: ω1 +ω2 + ...+ωn = 0,the following linear system of equations is obtained.

1 φ1,2 ... φ1,n 1φ2,1 1 ... φ2,n 1...

.... . .

......

φn,1 φn,2 ... 1 11 1 ... 1 0

ω1

ω2...ωnω0

=

φ~nl,1φ~nl,2...

φ~nl,n0

. (A.29)

By interpolating the value of the temperatune normal derivative at eachLagrangian node as:

∂T

∂~n= ω1T1 + ω2T2 + ...+ ωnTn; (A.30)

and following the same methodology as for the Dirichlet case, we canwrite the equation:

0 = ωi1(T ∗i1 + δi1) + ...+ ωin(T ∗in + δin) + ωo1T∗o1 + ...+ ωonT

∗on, (A.31)

In (A.31), T ∗i is the temperature on the boundary without having imposedany condition of the surface, and δi is the correction term to be applied tothe nodes inside the embedded surface.

Using the same algebraic manipulations as for the Dirichlet case, wenally obtain the linear system W f = b, with

W =

ωi1(l1) 0 0 ωi4(l1) 0

0 ωi2(l2) 0 ωi4(l2) 0...

......

......

ωi1(ln−1) 0 0 0 ωi5(ln−1)

0 0 ωi3(ln) 0 ωi5(ln)

(A.32)


and

b =

−∑ωiT

∗i |l1 −

∑ωoT

∗o |l1

−∑ωiT

∗i |l2 −

∑ωoT

∗o |l2

...−∑ωiT

∗i |ln−1 −

∑ωoT

∗o |ln−1

−∑ωiT

∗i |ln −

∑ωoT

∗o |ln

(A.33)

Again, if W is not a squared matrix, the solution is found by resortingto a least square formulation: W T W δ = W T b. We have found thatthe direct sum of the correction terms δi to the estimated temperatures T ∗iinduce a strong jump close to the immersed body. To avoid this problem, thecorrections δi are included in the governing equation of the problem (A.27)instead. If Ti denotes the nal (i.e., that keeps into account the Neumannconditions) temperature eld, the values T ∗i = Ti − δi are introduced intothe nite dierence-discretized governing equation, obtaining:

aP (Ti,j − δi,j) + aS(Ti,j−1 − δi,j−1) + aN (Ti,j+1 − δi,j+1)+

aE(Ti+1,j − δi+1,j) + aW (Ti−1,j − δi−1,j) = b,(A.34)

where aI and b are the coecients of the nite dierence discretization ofthe governing equation. Separating the unknowns in Eq. (A.34) yields:

aPTi,j + aSTi,j−1 + aNTi,j+1 + aETi+1,j + aWTi−1,j =

b+ aP δi,j + aSδi,j−1 + aNδi,j+1 + aEδi+1,j + aW δi−1,j .(A.35)

which, nally gives the linear system A T = b, where A is the samematrix as the rst linear system that must be solved to obtain the estimatedtemperature eld (i.e., standard nite dierence Laplacian matrix).

A.4.2 Results and discussion

Following the procedure described above, we compute the temperature dis-trihution within a section of an innitely long bar. The boundary on theright (east, E) is a perfectly insulated edge while the other three edges aremaintained at a prescribed temperature value: TN = 100, TS = 25 andTW = 75. Figure A.7a shows the temperature eld obtained for the wholedomain without having introduced any immersed boundary. In the samegure, the location of the immersed boundary that has been considered asa validation experiment has been introduced for illustrative purposes. Fig-ure A.7b shows the temperature eld obtained when the insulated conditionif applied using our immersed boundary method. As expected, the temper-ature isolines approach the embedded surface in an orthogonal fashion (lefthand side of the embedded surface).

To complete the validation, the same problem has been tackled usinga body conforming mesh. Figure A.8 shows a longitudinal section in x


(a) Without immersed boundary. (b) With immersed boundary.

Figure A.7: Final temperature eld T (x, y). External boundary conditions:TN = 100, TS = 25, TW = 75 and the right hand side wall is consideredadiabatic.

direction at the center of the domain, where it can be seen that the resultsof both methodologies, body conformal (blue line) and immersed boundaryusing radial basis function (black line), fully agree.

Figure A.8: Streamwise section of the temperature eld at the center ofthe domain. Red line: without considering the adiabatic embedded surface.Black line: considering the adiabatic embedded surface. Blue line: bodyconformal case.


Furthermore, gure A.9 gives the values of the normal derivative of thetemperature eld just outside the vertical wall, using nite dierences. Thevalues of this parameter approach to zero (black squares) in front of thevalues without considering the adiabatic embedded surface (red circles).

Figure A.9: Normal derivative of the closest temperature eld outside thevertical wall, in front of the height. Red circles: without considering theadiabatic embedded surface. Black squares: considering the adiabatic em-bedded surface.

Figure A.10 shows the norm of the interpolation error Ed at the immersedsurface dened by

Ed = maxlUd, (A.36)

where Ud refers to the interpolated temperature derivative from the externalside computed at each Lagrangian point l. It results a decreasing of order∆x (1st order).

The method was also checked for other geometries as, for example, acircular adiabatic surface (see gure A.11).


10−2

10−4

10−3

10−2

10−1

∆ x

Ed

Figure A.10: Norm of the interpolation error of the derivative at the im-mersed surface. Red squares: derivative error; solid line: ∆x (1st order);dashed line: ∆x2 (2nd order).

(a) Without immersed boundary. (b) With immersed boundary.

Figure A.11: Temperature eld T (x, y). External boundary conditions:TN = 100, TS = 25, TW = 75 and TE = 50.

A.5 Conclusions

In this work, a new interpolation and spreading procedure based on radialbasis functions was implemented. The procedure is easy to implement and


allows the imposition of both Dirichlet and Neumann boundary conditions.Both interpolation and spreading tasks are carried out together within thesame stage, which yields a straightforward implementation. As the radialbasis functions require a scattered cloud of points, another advantage is thatthe method works for any type of mesh, even unstructured.

To validate the method, a Dirichlet boundary condition has been imposedon a 2D cylinder geometry in a Navier-Stokes CFD solver, and a Neumannboundary condition has been imposed in an adiabatic embedded surfacein an unsteady heat conduction problem. The obtained results agree withliterature results.

The convergence rate of this method is one. This value is expectedto be increased by future works on the interpolation support. This newinterpolation support should use more external nodes, since the rst orderaccuracy derives from the order of the interpolation process. The mostimportant challenge is to dene a simple rule to select the appropriatednodes that will be able to deal with any surface shape.

A rst version of the method is presented in this work, showing to berobust over variations of geometry and Reynolds number (staying in laminarows). As deeper improvements of the method, further investigations on thesize and shape of the interpolation support are expected, as well as the useof other kinds of RBFs and other ways to determine the shape parameter.Finding the optimal number of Lagrangian nodes for dierent geometriesis also a remaining issue, which is also encountered in other methods inliterature.

Short-term applications of the work also includes the imposition of Neu-mann boundary conditions on the Poisson equation in a CFD code, andthe use of the present method to implement wind turbine models such asactuator disc and actuator line ones.

Bibliography notes

The content of this appendix was published in Toja-Silva et al. (2014).

Appendix B

Curriculum Vitae

Caminante no hay camino, se hacecamino al andar.

(There is no path travelers, path is madeby walking.)

Antonio Machado

Nationality: Spain-EuropePhone numbers: +34 649 382 293 / +34 91 637 66 27Address: Arenalón street 5. Las Rozas de Madrid 28231, Madrid, SpainDate of birth: May 9th 1979E-mail: [email protected] / [email protected]

B.1 Education

Ph. D. in Aerospace Engineering

- Urban wind energy: empirical optimization of high-rise building roof shapefor the wind energy exploitation.- Madrid. October 2015.- Polytechnic University of Madrid, ETSIA-UPM.

M. Sc. in Industrial Technology Research - Energy Engineering

- Terrassa (Barcelona). October 2011.- National University of Distance Education, UNED.

Industrial Engineer - Thermal-energy

- Terrassa (Barcelona). February 2007.

201

202 Appendix B. Curriculum Vitae

- Polytechnic University of Catalonia, ETSEIAT-UPC BarcelonaTech.

Industrial Technical Engineer - Industrial Chemistry

- Manresa (Barcelona). June 2003.- Polytechnic University of Catalonia, EUPM-UPC BarcelonaTech.

Industrial Management Bachelor

- Coursed simultaneously with the Industrial Technical Engineering.- Manresa (Barcelona). June 2003.- Polytechnic University of Catalonia, EUPM-UPC BarcelonaTech.

B.2 Publications and patents

F. Toja-Silva, A. Z. Dhunny, C. Peralta, M. R. Lollchund, S. D. D. V.Rughooputh. CFD simulation and full-scale experimental validation of thewind ow in an urban area: Campus of University of Mauritius. In develop-ment.

F. Toja-Silva, O. Lopez-Garcia, C. Peralta, J. Navarro, I. Cruz. Optimal roofgeometry for urban wind energy exploitation in high-rise buildings. AppliedEnergy, under review.

F. Toja-Silva, C. Peralta, O. Lopez-Garcia, J. Navarro, I. Cruz. Eect ofroof-mounted solar panels on the wind energy exploitation on high-rise build-ings. Journal of Wind Engineering and Industrial Aerodynamics, Volume145, October 2015, Pages 123-138.

- Audioslides (presentation) of this work: http://www.sciencedirect.com/science/article/pii/S0167610515001488

F. Toja-Silva, C. Peralta, O. Lopez-Garcia, J. Navarro, I. Cruz. Roof re-gion dependent wind potential assessment with dierent RANS turbulencemodels. Journal of Wind Engineering and Industrial Aerodynamics, Volume142, July 2015, Pages 258-271.

- Audioslides (presentation) of this work: http://www.sciencedirect.com/science/article/pii/S016761051500104X

F. Toja-Silva, C. Peralta, O. López, J. Navarro, I. Cruz. On the roof geome-try for urban wind energy exploitation in high-rise buildings. Computation,Special Issue Computational Fluid Dynamics in Civil Engineering, Volume3, June 2015, Pages 299-325.

B.2. Publications and patents 203

F. Toja-Silva, J. Favier, A. Pinelli. Radial basis function (RBF)-based in-terpolation and spreading for the immersed boundary method. Computersand Fluids, Volume 105, December 2014, Pages 66-75.

- Top 24 downloaded articles of the Journal in the last 90 days, January2015.

- Audio Slides (presentation) of this work: http://www.sciencedirect.com/science/article/pii/S0045793014003636

F. Toja-Silva, A. Rovira. A rst and second thermodynamics law analysisof a hydrogen-fueled micro-gas turbine for combined heat and power gen-eration. Journal of Engineering for Gas Turbines and Power, Volume 136,February 2014, Pages 021501-1-8.

Divulgation of this work (in Spanish):

- F. Toja-Silva, A. Rovira. Producción eléctrica y térmica en lugares de fríointenso. Microturbina de cogeneración alimentada con hidrógeno generadoa partir de energía eólica. Eolus, Actualidad de la Energía Eólica. Edition68, March/April 2014, Pages 48-52.

- Radio Nacional de España, RNE-Radio 3. Program Radio UNED. Inter-view 03/04/2014. http://www.rtve.es/alacarta/audios/uned/uned-microturbina-verde-para-combatir-frio-04-03-14/2433166/

- Radio Televisión Pública de Asturias, RTPA. Program La Buena Tarde.Interview 02/14/2014 (18h).

- E. Ocampo. Crean una microturbina ecológica que genera calor y elect-ricidad contra el frío. Faro de Vigo, Newspaper 03/03/2014, Page 18.

- EFE agency. http://www.efeverde.com/blog/noticias/una-microturbina-verde-podria-aprovechar-energia-almacenada-en-zonas-frias/

- Etc.

F. Toja-Silva, A. Colmenar-Santos, M. Castro-Gil. Urban wind energy ex-ploitation systems: Behaviour under multidirectional ow conditions - Op-portunities and challenges. Renewable and Sustainable Energy Reviews,Volume 24, August 2013, Pages 364-378.

F. Toja-Silva. A novel water heater using injected hydrogen combustionexhaust. Energy and Buildings, Volume 43, Issue 9, September 2011, Pages2320-2328.

F. Toja Silva. The diculties of the mini-hydraulic energy integrated intoresidential buildings water pipelines. March 2010. Energias Renovables.com


F. Toja Silva, M. Furió Bruno, C. Laplana Conesa. Machine for the sepa-ration of radiation emission particles (with or without physical stimulation)from geological materials. December 2007. Invention patent ES 2359691.

F. Toja Silva. Chemical energy storage and power plant by means of thehydrogen production. September 2005. Invention patent ES 2285911.

F. Toja Silva. Mortadella-mold extraction machine. August 2005. Inventionpatent ES 2288088.

B.3 Conferences, congresses and seminars

F. Toja Silva. CFD simulation of the wind ow around buildings: Case studyin Soria (Spain) - Computational issues. International Energy Agency (IEA)- Task 27 meeting, University of Applied Sciences Technikum Wien, Vienna(Austria), April 2015. Online presentation.

F. Toja Silva. Validation of RANS turbulence models for wind ow assess-ment on building roofs. International Energy Agency (IEA) - Task 27 meet-ing, National Wind Power Integration Research and Test Center (NWIC),Zhangbei (China), August 2014. Online presentation.

F. Toja Silva. Urban wind energy: wind ow on building roof and windturbines positioning. VI Seminars of Young Researchers, CIEMAT, Madrid(Spain), June 2014.

F. Toja Silva. Urban wind energy: wind ow on building roof and windturbines positioning. International Energy Agency (IEA) - Task 27 meeting,National Renewable Energy Laboratory (NREL), Boulder (CO, USA), May2014. Online presentation.

F. Toja Silva. Urban wind assessment: CFD simulation of wind ow overan isolated building. International Energy Agency (IEA) - Task 27 meet-ing, National Renewable Energy Laboratory (NREL), Boulder (CO, USA),February 2014. Online presentation.

F. Toja Silva. Immersed boundary methods in CFD: new method usingradial basis functions (RBFs). V Seminars of Young Researchers, CIEMAT,Madrid (Spain), July 2013.

B.4 Research experience, fellowships and awards

Energy, Environment and Technology Research Center, CIEMAT

- Madrid. December 2011 - currently.

B.5. Complementary education 205

- Energy Department, Renewable Energy Division, Wind Energy Unit. Ph.D.Fellowship. CFD research, urban wind energy resources.

Fraunhofer IWES

- Oldenburg, Germany. September - December 2013.- Department of Turbine Simulation, Software Development and Aerody-namics. Research stay. CFD research, urban wind energy resources.

Hydrogen and Renewable Energy Association of Catalonia, ACH2ER

- Barcelona. July 2011.- Fellowship - award for the M. Sc. studies. Amount 600e.

Heat and Mass Transfer Technological Center, CTTC-UPC

- Terrassa (Barcelona). August - November 2011.- Training program in CFD and heat transfer.

Static Converters and Operations Technology Innovation Center,

CITCEA-UPC

- Barcelona. September 2006 - June 2007.- Energy Area. Fellowship to develop the nal engineering project and tocollaborate with the research activities in energy eciency, renewable energyand hydrogen and fuel cells technology.

Thermal Machines and Engines Department, UPC BarcelonaTech

- Terrassa (Barcelona). September 2005 - September 2006.- Fellowship to collaborate with the research and academic activities of theThermal Engines and Automobiles Laboratory.

B.5 Complementary education

Sports and building aerodynamics

- April - June 2014. Duration: 36 hours.- Organizer: Eindhoven University of Technology. Netherlands.

Linux operating system orientated to the scientic environment

- May - June 2012. Duration: 20 hours.- Organizer: CIEMAT. Madrid.


Workshop: Simulation of complex ows: large scale DNS and LES

of gaseous and two-phase ows

- April 2012. Duration: 20 hours.- Organizers: UC3, UPM and CIEMAT. Madrid.

Mini-symposium: Analysis and representation of large data sets

- February 2012. Duration: 5 hours.- Organizer: ETSIA-UPM. Madrid.

English - Advanced level B2 (equivalent Cambridge FCE)

- November 2009 - September 2010. Duration: 150 hours (2 credits ECTS).- Organizer: UNED. Barcelona.

Technical conference: Opportunities in energy eciency with LON

technology

- November 2009. Duration: 6 hours.- Organizer: LonMark Spain. Barcelona.

Development of low-voltage power projects

- October 2009. Duration: 16 hours.- Organizer: COEIC. Sabadell (Barcelona).

Electricity market

- October - November 2006. Duration: 20 hours.- Organizers: CITCEA-UPC and Omel. Barcelona.

Technical conference: Energy eciency management

- October 2006. Duration: 6 hours.- Organizers: UPC and Unión Fenosa. Barcelona.

Velocity variation in electric engines

- March 2003. Duration: 4 hours.- Organizers: UPC and Schneider Electric. Manresa (Barcelona).

B.6. Complementary work experience 207

Technical conference: Sustainable water management

- September - October 2001. Duration: 20 hours.- Organizers: UPC and Catalan Institution of Natural History. Manresa(Barcelona).

Radioactivity protection. Radioactive waste management and nu-

clear facilities dismantling

- July 2001. Duration: 30 hours.- Organizers: Rovira and Virgili University and ENRESA. Tarragona.

B.6 Complementary work experience

External Consultant

February 2010 - November 2011.

- Business, Economy and Governments Research Group (BEG),

Autonomous University of Barcelona, Cerdanyola del Vallès (Barcelona).Activities: participation in a technical-economical analysis of the use of pho-tovoltaic solar energy in public buildings, for the autonomic government.

- Catalan Institute of Paleontology, Autonomous University of

Barcelona, Cerdanyola del Vallès (Barcelona). Activities: technical advicein transversal projects; concept and design of a system for fossils separationfrom aggregate mixtures.

- ECO2-System Europe, Barcelona. Activities: technical advice in re-newable energy technology; CO2 emission assessment at industry and trans-portation.

Industrial Engineer

July 2007 - January 2010.

- Renovatium, Santa Perpètua de Mogoda (Barcelona). Activities: initialtechnical development of the company, design and management of photo-voltaic solar energy projects and training of the commercial team.

- Amphos XXI Consulting, Valldoreix (Barcelona). Activities: develop-ment of greenhouse gas emission studies, elaboration of argumentaries forthermal power plants, participation in R+D projects of waste energy val-orization for the cement industry, and development of bio-methane plantstudies.


- ECO 100, Terrassa (Barcelona). Activities: design and management ofphotovoltaic solar energy projects, and participation in the marketing policyof the company.

Teacher

- EIMM School, Council of El Masnou (Barcelona). October - November2006. Activities: teacher in a course of 160 hours about renewable energies,with intensication in photovoltaic solar energy.

- Center of Studies Catalonia, Manresa (Barcelona). February - May2001. Activities: teaching of technology and technical drawing.

B.7 Computational skills

Oce IT and operating systems: Internet, e-mail, Windows, Linux,Oce, LATEX, etc.

CAD, CFD and visualization: AutoCAD, MicroStation, OpenFOAM,ANSYS, Paraview, Tecplot, etc.

Mathematics: Matlab, Python, Maxima, Mapple, Eureka, Polimath, Minitab,etc.

Programming: Languages C, C++, Fortran, etc.

B.8 Languages

Spanish: Native.

Catalan: Native.

English: High.

Airplanes are interesting toys but of no military value.

Ferdinand Foch, 1911

Supreme Commander of Allied forces WWI, 1918

I hear rather the same above about urban wind energy continuously.

It is obvious that Foch was wrong about military aircrafts,

time will talk about urban wind energy.

Francisco Toja Silva, 2015

urban wind energy: empirical optimization of high-rise building roof

Documents