influence of pipe flow on bacteria level in water sander ... · the production of domestic hot...

Sander Coppens

Influence of pipe flow on bacteria level in water

Academic year 2017-2018Faculty of Engineering and Architecture

Chair: Prof. dr. ir. Jan VierendeelsDepartment of Flow, Heat and Combustion Mechanics

Chair: Prof. dr. ir. Arnold JanssensDepartment of Architecture and Urban Planning

Master of Science in de industriële wetenschappen: bouwkundeMaster's dissertation submitted in order to obtain the academic degree of

Counsellors: Ir.-arch. Elisa Van Kenhove, Lien De Backer, Asal Sharif, Zaaquib AhmedSupervisors: Prof. Jelle Laverge, Prof. dr. ir. Michel De Paepe

i

The author gives permission to make this master dissertation

available for consultation and to copy parts of this master

dissertation for personal use.

In the case of any other use, the copyright terms have to be

respected, in particular with regard to the obligation to state

expressly the source when quoting results from this master

dissertation.

Ghent, June 1st 2018

Sander Coppens

ii

Foreword

This master’s dissertation has been written and submitted in order to obtain the academic degree of

Master of Science in Civil Engineering Technology (NL: Master of Science in de industriële

wetenschappen: bouwkunde). It was beyond doubt the icing on the cake of my engineering study, but

hasn’t been possible without the help and support of certain people. Therefore, I would like to express

my deepest thank in those who have contributed to this work.

Prof. dr. Ir.-Arch. Jelle Laverge, for the guidance and feedback during the mid-term

presentations.

Prof. dr. Ir. Michel De Paepe, for the guidance and feedback during the mid-term presentations.

Ir.-Arch. Elisa Van Kenhove, for the challenging, but interesting subject and the theoretical

information about the Legionella problemacy and issues in the (macro-) simulation model.

Dr. Ing. Lien De Backer, for her continued help in understanding the CFD software and the

numerous errors I encountered during this work.

Ir. Asal Sharif, and Ir. Zaaquib Ahmed, for their help in the CFD simulations and theoretical

information about the different models and turbulence parameters.

Prof. Dr. Ir. Joris Degroote, for teaching me the numerical basics of Computational Fluid

Dynamics software FLUENT in the introduction course.

Yves Maenhout, for granting me access to the calculation server of the department of flow, heat

and combustion mechanics.

My parents and family, and specially Lenny, for the unconditional love, continued

understanding and feigned interest in the many technical subjects.

iii

Influence of pipe flow on bacteria level in water Sander Coppens Supervisors: Prof. dr. Ir.-Arch. Jelle Laverge, Prof. dr. Ir. Michel De Paepe Counsellors: Ir.-Arch. Elisa Van Kenhove, dr. Ing. Lien De Backer, Ir. Asal Sharif, Ir. Zaaquib Ahmed

Master’s dissertation submitted in order to obtain the academic degree of Master of Science in de industriële wetenschappen: bouwkunde (Civil Engineering Technology)

Department of Architecture and Urban Planning Chair: Prof. dr. ir. Arnold Janssens

Department of Flow, Heat and Combustion Mechanics Chair: Prof. dr. ir. Jan Vierendeels

Faculty of Engineering and Architecture Academic year 2017-2018

Abstract The production of Domestic Hot Water (DHW) dominates the total energy demand of well insulated

and airtight buildings. One of the main reasons for this high demand is that DHW is produced, stored

and distributed at temperatures above 55-60°C to mitigate the risk of infecting the DHW system with

Legionella pneumophila (L. pneum.), a bacterium that, upon exposure, causes acute respiratory disease

(Pontiac Fever) or severe pneumonia (Legionnaires disease) (Van Kenhove, et al., 2016).

A simulation model is developed by Van Kenhove et al. (2015) that allows assessing the L. pneum

infection risk under dynamic conditions, making it possible for HVAC designers to thoroughly assess

the Legionella infection risk associated with their design. In order to improve the parameters of this

simulation model, a micro-scale model is built in this work using Computational Fluid Dynamics (CFD).

Focusing on simplifications made in the macro-model, two different research questions are determined.

Firstly, L. pneum. adhesion is modeled for different Reynolds numbers (Re). It is observed that for Re <

25 000, L. pneum. adhesion is proportional to the second power of Re and that adhesion is higher in

turns than in a straight section. For Re > 25 000, L. pneum. adhesion in straight pipe and turn section

follow a linear trend with increasing Re.

Secondly, temperature patterns in the biofilm are studied for various inlet temperatures , insulation

thicknesses and biofilm viscosity . For ≥ 100 ∙ , temperatures in the

biofilm followed a linear pattern. Furthermore, an asymptotic value is seen for temperature differences

above 30mm insulation, indicating that a further increase in insulation thickness does not result in lower

heat losses to the environment. The model is, however, not capable of predicting temperature patterns

for ≤ 10 ∙ , since in that case flow occurs in the biofilm, causing non-realistic results.

Keywords: Legionella pneumophila (L. pneum.) - Domestic Hot Water (DHW) - Computational Fluid

Dynamics (CFD) – adhesion coefficient – biofilm temperature

Influence of pipe flow on bacteria level in water

Sander Coppens1

Supervisors: Prof. dr. Ir.-Arch. Jelle Laverge, Prof. dr. Ir. Michel De Paepe

Counsellors: Ir.-Arch. Elisa Van Kenhove, dr. Ing. Lien De Backer, Ir. Asal Sharif, Ir. Zaaquib Ahmed

Abstract: A simulation model is developed by Van Kenhove

(2017) that allows assessing the infection risk of Legionella

pneumophila (L. pneum.) under dynamic conditions, making it

possible for HVAC designers to thoroughly assess the Legionella

infection risk associated with their design. In order to improve the

parameters of this simulation model, a micro-scale model is built

in this master’s dissertation using Computational Fluid Dynamics

(CFD). Focusing on simplifications made in the macro-model, two

different research questions are determined. Firstly, L. pneum.

adhesion is studied for different Reynolds numbers (Re). It is

observed that for Re < 25 000, L. pneum. adhesion is proportional

to the second power of Re and that adhesion is higher in turns than

in a straight section. For Re > 25 000, L. pneum. adhesion in

straight and turn pipe sections follows a linear trend with Re.

Secondly, temperature patterns in the biofilm are studied for

various inlet temperatures 𝑻𝒊, insulation thicknesses 𝒅𝒊𝒏𝒔𝒖𝒍𝒂𝒕𝒊𝒐𝒏

and biofilm viscosity 𝝁𝒃𝒊𝒐𝒇𝒊𝒍𝒎. For 𝝁𝒃𝒊𝒐𝒇𝒊𝒍𝒎 ≥ 𝟏𝟎𝟎 ∙ 𝝁𝒘𝒂𝒕𝒆𝒓,

temperatures in the biofilm follow a linear pattern. Furthermore,

an asymptotic value is seen for temperature differences above

30mm insulation, indicating that a further increase in insulation

thickness does not result in lower heat losses to the environment.

The model is, however, not capable of predicting temperature

patterns for 𝝁𝒃𝒊𝒐𝒇𝒊𝒍𝒎 ≤ 𝟏𝟎 ∙ 𝝁𝒘𝒂𝒕𝒆𝒓, since in that case flow occurs

in the biofilm, causing non-realistic results.

Keywords: Legionella pneumophila (L. pneum.) – Domestic

Hot Water (DHW) – Computational Fluid Dynamics (CFD) –

adhesion coefficient – biofilm temperature

I INTRODUCTION

The production of Domestic Hot Water (DHW) dominates

the total energy demand of well insulated and airtight buildings.

One of the main reasons for this high demand is that DHW is

produced, stored and distributed at temperatures above 55°C to

mitigate the risk of infecting the DHW system with Legionella

pneumophila (L. pneum.), a bacterium that, upon exposure,

causes acute respiratory disease (Pontiac Fever) or severe

pneumonia (Legionnaires disease) (Van Kenhove, et al., 2016).

A simulation model is developed by Van Kenhove (2017)

that allows assessing the L. pneum. infection risk in dynamic

conditions. By this mean, HVAC designers will be able firstly to thoroughly assess the Legionella infection risk associated

with their design and secondly to optimize the temperature

regimes, to choose better hydronic controls and to reduce the

energy demand for DHW production, storage and distribution

(Van Kenhove, et al., 2015).

Several parameters in the macro-scale model are simplified

because they are still unknown and further research is needed

in order to improve the simulation model. To do so, a micro-

1 Corresponding author. Tel.: +32 477 05 32 40

E-mail: [email protected]

scale model is built, using Computational Fluid Dynamics

(CFD), representing critical pipe sections of a DHW system.

II PROBLEM CONTEXT AND OBJECTIVE

Focusing on the simplifications made in the macro-scale

model, two research questions are put forward, respectively

focusing on adhesion of L. pneum. bacteria from the liquid flow

to the biofilm, and on the variation of temperature in the biofilm

compared to water.

A L. pneum. adhesion to biofilm

In the macro-scale model, every pipe section of the DHW

system has the same bacterial exchange coefficient between the

liquid flow and stagnant biofilm. However, due to different

flow patterns, a higher exchange (in comparison with a straight

pipe) is expected in critical sections, such as turns and T-

sections.

Several authors already have detailed models in which

different parameters affecting biofilm detachment and adhesion

were simulated. Picioreanu et al. (2000) used CFD to determine

velocity profiles of the moving liquid and then calculated the propagation of stresses imposed on the biofilm structure. Shen

et al. (2015) performed particle tracing simulation in CFD for

flow across biofilms, in which the velocity distribution and

particle movement above the biofilm surface was studied.

These models, however, have the disadvantage of being very

detailed and are thus computationally expensive. The need

arises for a simulation model in which bacterial adhesion and

detachment can be simulated, but still maintains its numerical

efficiency. Moreover, in these simulations (Shen, et al., 2015;

Picioreanu, et al., 2000) only laminar and low Reynolds

turbulent flows were simulated. In DHW systems, however,

flows can be fully turbulent with Re higher than 30 000 in pipes with small diameters, such as DN32. Since L. pneum. bacteria

are dispersed into the fluid flow, turbulence is expected to play

a major role in the bacteria adhesion and detachment rates.

In this master’s dissertation, the bacterial exchange

coefficient is determined in critical sections by assessing L.

pneum. adhesion for different Re in both a straight pipe and a

90 degree turn with equivalent length. The goal of the model is

to investigate the adhesion in both DHW pipe sections and

show the proportionality of the bacteria adhesion in the turn

section to the adhesion in a straight pipe section, with a factor

N. To conclude, the aim is to determine this factor N.

B Biofilm temperature

Bacterial growth is mainly dependent of temperature (Brundrett, 1992), with maximum growth at about 35°C. In a

DHW system, 72% of the cultivable bacteria are found to be

surface-associated (in the biofilm) (Bagh, et al., 2004), making

the temperature in the biofilm an important factor when

modeling L. pneum. infection risk in DHW systems. In the

macro-scale model, bacteria growth in the biofilm is calculated

based on the temperature in the fluid flow, and not with the

biofilm temperature, which can assumed to be lower in certain

cases, favoring bacterial growth. In this master’s dissertation,

temperature patterns in the biofilm are therefore studied for

various inlet temperatures 𝑇𝑖, insulation thicknesses 𝑑𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑖𝑜𝑛

and biofilm viscosity 𝜇𝑏𝑖𝑜𝑓𝑖𝑙𝑚. The aim is to check whether the

simplification made in the macro-scale model of modeling

bacterial growth in the biofilm with the liquid flow

temperature, is correct and for which cases this should be

updated.

III METHODOLOGY

According to the two mentioned research questions, two

simulation models are built in Ansys Fluent (v18.2),

respectively focusing on L. pneum. adhesion, and biofilm

temperature.


In literature, different possible methods are found to model

bacteria transport in Ansys Fluent. The Discrete Phase Model

(DPM) is selected, since as the dispersed phase volume

fractions (L. pneum. particles) are less than 10%, the DPM is

more appropriate (FLUENT Inc., 2001). In DPM simulations,

transport of L. pneum. bacteria is modeled as spherical particle

movement in the flow field based on Newtonian’s law of

motion, drag force, and Brownian motion. The simulation is

conducted in the fluid phase and the flow is at steady state.

Turbulent dispersion is modeled with the Discrete Random

Walk (DRW) model and random eddy lifetime. Infinite particle

adhesion is assumed by setting the DPM boundary condition trapped at the wall. Finally, the adhesion of particles is

represented by deposition probability, which is calculated by

dividing the final number of adhered (trapped) particles with

the total number of released particles.


To make the model in compliance with the assumptions made

in previous work (Xavier, et al., 2005; Cogan, 2008), the

biofilm is modeled as a fluid, of which the viscosity (𝜇𝑏𝑖𝑜𝑓𝑖𝑙𝑚)

is assumed to be in the range of 1 to 1000 times the viscosity of

water (𝜇𝑤𝑎𝑡𝑒𝑟). By doing so, the simulation with 𝜇𝑏𝑖𝑜𝑓𝑖𝑙𝑚 =

𝜇𝑤𝑎𝑡𝑒𝑟 can serve as reference for the macro-scale model, in

which the biofilm is assumed to have the same medium as the

fluid flow. The biofilm temperature research question is divided into three different simulation setups, in which

subsequently the effect of inlet flow temperature 𝑇𝑖 , insulation

thickness 𝑑𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑖𝑜𝑛 , and biofilm viscosity 𝜇𝑏𝑖𝑜𝑓𝑖𝑙𝑚 is studied.

IV RESULTS


L. pneum. adhesion to biofilm simulations are conducted in

the 3D CFD environment for both a straight pipe (Figure 1,

black) and a 90 degree turn section (Figure 1, red) with an

equivalent length of 1m. For Re < 25 000, deposition

probability (and thus adhesion of L. pneum.) is proportional to

the second power of Re. For Re > 25 000, deposition probability

follows a linear trend with increasing Re. In Figure 1

simulation results are represented by filled dots. Parabolic (Re

< 25 000) and linear (Re > 25 000) trendlines are added to

simulation results and represented in dashed lines.

Figure 1. Deposition probability in straight pipe (black) and 90 degree turn (red) with equivalent length of 1m. Simulation results are represented by filled dots. Parabolic (Re<25000) and linear trendlines

(Re>25000) are added to simulation results in dashed lines.

To obtain the proportional factor (N), which has to be determined, trendline function for the turn section is reduced

with the trendline function of the straight pipe, which resulted

in:

𝑁 = −1𝑒−8 ∙ 𝑅𝑒2 + 2.7𝑒−4 ∙ 𝑅𝑒 + 0.1839 (𝑅𝑒 < 25 000)

𝑁 = −0.0001 ∙ 𝑅𝑒 + 1.629 (𝑅𝑒 > 25 000)

In Figure 2, the obtained proportional factor N is represented

for different Re.

Figure 2. Proportional factor N in L. pneum. adhesion of turn section to a straight pipe (as function of Re).

As visualized in Figure 3, immediately after the turn, a low and high shear zone are observed on respectively the inner (Figure 3, red

line) and outer side of the turn (Figure 3, blue line). These high and low shear zones can be explained by studying the fluid flow stream (Figure 4). In the turn section the fluid flow scours against the inner wall of the turn, leading to a maximum peak in wall shear stress at the inner wall and a minimum peak on the outer wall (Figure 3, 0.5m). The flow stream then gets separated from the inner wall causing the minimum peak (Figure 3, red line, 0.5m-0.6m), followed by a low shear stress zone (Figure 3, red line, 0.6m-1.1m). Subsequently, the flow impinges the outer wall, leading to the maximum peak (Figure 3,

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Reynolds number (Re) [-]

Deposition probability [%]

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Proportional factor N [-]

blue line, 0.6m), followed by a high shear stress zone (Figure 3, blue line, 0.7m-1.1m).

Figure 3. Shear stress at biofilm wall boundary in turn section in XY plane for inner wall of turn section (red line) and outer wall of turn section (blue line) with Re = 39 808.

With increasing Re, the mean variation in low and high shear

stress zone also increases, as can be seen in Figure 5. To come

to this mean standardized variation, first the mean value of both

low and high shear stress zone are calculated between 0.7m and

0.9m (Figure 3). These values are then divided by the mean

shear stress in the straight section before the turn between 0.2m

and 0.4m (Figure 3).

Figure 5. Standardized mean variation in Wall Shear Stress for both inner biofilm wall of turn section (red) and outer biofilm wall of turn section (blue).

For Re < 25 000, absolute variation between straight section (before turn) and low shear zone (after turn) is up to 5 times

higher than standardized variation in high shear zone. For Re >

25 000, both standardized variations are, approximately, equal

and could thus possibly explain the trends in deposition

probability.


Biofilm temperature simulations are performed in the CFD

3D environment. The biofilm is modeled as a fluid, of which

the viscosity (𝜇𝑏𝑖𝑜𝑓𝑖𝑙𝑚) is assumed to be in the range of 1 to

1000 times the viscosity of water (𝜇𝑤𝑎𝑡𝑒𝑟). In simulations with

𝜇𝑏𝑖𝑜𝑓𝑖𝑙𝑚 ≥ 100 ∙ 𝜇𝑤𝑎𝑡𝑒𝑟 , temperature differences between

fluid flow and inner pipe wall (outer biofilm layer) follow a

linear trend with flow temperature (Figure 6). Moreover, a

reciprocal trend (Figure 7) exists between temperature

difference (between fluid flow and inner pipe wall) and

insulation thickness. As was already described by Van Hove

(2018), temperature differences seem to reach an asymptotic

value for insulation thicknesses above 30mm, indicating that

further increase in insulation thickness does not result in lower

heat losses to the environment.

Figure 7. Temperature difference between flow and inner pipe wall (outer biofilm layer) as function of the insulation thickness for different inlet temperatures: 333K (red), 318K (blue), 300K (black).

For high biofilm viscosities (𝜇𝑏𝑖𝑜𝑓𝑖𝑙𝑚 ≥ 100 ∙ 𝜇𝑤𝑎𝑡𝑒𝑟),

temperature patterns in the biofilm showed a linear trend,

where temperatures in the flow domain do not seem to cool

down (Figure 8, blue line). Temperature losses to the

environment thus cause the biofilm to cool down to

temperatures where bacterial growth is favored. For

simulations with 𝜇𝑏𝑖𝑜𝑓𝑖𝑙𝑚 ≤ 10 ∙ 𝜇𝑤𝑎𝑡𝑒𝑟 , flow occurred in the

0

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0 10000 20000 30000 40000

Figure 4. Velocity contour in turn section with Re = 39 808.

Wall Shear Stress [Pa]

Standardized mean variation in Wall Shear Stress [Pa]

0

5

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15

20

25

30

35

40

295 300 305 310 315 320 325 330 335

Figure 6. Temperature difference between fluid flow and inner pipe wall as function inlet flow temperature, for different insulation thickness: 0mm(black), 10mm(red), 20mm(green), 30mm(purple)

Temperature difference [K]

0

5

10

15

20

25

30

35

40

0 10 20 30


Insulation thickness [mm]

Flow temperature [K]


Curve length [m]

biofilm (velocity profile in Figure 9) causing a non-realistic

temperature profile, as can be seen in Figure 8 (red line).

Figure 8. Temperature profile in fluid flow (0-10mm pipe radius)

and biofilm (10-13mm pipe radius) for biofilm viscosity 𝜇𝑏𝑖𝑜𝑓𝑖𝑙𝑚 ≥

100 ∙ 𝜇𝑤𝑎𝑡𝑒𝑟 (blue) and 𝜇𝑏𝑖𝑜𝑓𝑖𝑙𝑚 ≤ 10 ∙ 𝜇𝑤𝑎𝑡𝑒𝑟 (red). Inlet fluid

temperature = 318K, insulation = 0mm.

Figure 9. Velocity profile in liquid flow (0-10mm pipe radius) and biofilm (10-13mm pipe radius) for biofilm viscosity 𝜇𝑏𝑖𝑜𝑓𝑖𝑙𝑚 ≤ 10 ∙

𝜇𝑤𝑎𝑡𝑒𝑟 with flow occurring in the biofilm.

V FUTURE MODEL IMPROVEMENTS

Further research is recommended to confirm the assumptions

made in this work and to extend the capabilities of both models.

Therefore, model improvements are discussed in the next sections for both the L. pneum. adhesion coefficient model and

biofilm temperature simulation model.


Bacterial exchange between biofilm and liquid flow consists

of adhesion and detachment. In this master’s dissertation, only

adhesion of L. pneum. is studied. In further work, adhesion and detachment of L. pneum. should therefore both be accurately

modeled to have a better understanding of the whole bacterial

exchange. To this end, a User Defined Function (UDF) could

be used which serves as the DPM boundary condition for the

particle wall interaction (Shankara, 2010). By implementing

such a UDF, temperature dependence, biofilm roughness and

shear stress can also be taken in account. Moreover, only a

distinction is made between adhesion in a straight pipe and turn

section. In further research, other critical sections such as a T-

section can be studied. In this master’s dissertation, the DPM

was selected for modeling L. pneum. transport since L. pneum. volume fractions in the fluid flow are less than 10%. However,

the Species Transport Model in Fluent can be seen as a worthy

alternative of which the use can be studied.


For simulations with 𝜇𝑏𝑖𝑜𝑓𝑖𝑙𝑚 ≤ 10 ∙ 𝜇𝑤𝑎𝑡𝑒𝑟 , flow occurred

in the biofilm causing a non-realistic temperature profile. The

use of a meshed solid zone as biofilm is therefore proposed as

model improvement. By doing so, the energy equation is solved

in a solid zone, representing the biofilm, and flow will not

occur.

VI CONCLUSION AND DISCUSSION

The simplifications made in the macro-scale model are partly

correct in certain conditions. L. pneum. adhesion for Re < 25

000, is proportional to the second power of Re and for Re > 25

000, a linear trend with increasing Re is observed. The

proportional factors, which had to be determined, are:

𝑁 = −1𝑒−8 ∙ 𝑅𝑒2 + 2.7𝑒−4 ∙ 𝑅𝑒 + 0.1839 (𝑅𝑒 < 25 000)

𝑁 = −0.0001 ∙ 𝑅𝑒 + 1.629 (𝑅𝑒 > 25 000)

For high biofilm viscosities (𝜇𝑏𝑖𝑜𝑓𝑖𝑙𝑚 ≥ 100 ∙ 𝜇𝑤𝑎𝑡𝑒𝑟),

temperature follows a linear pattern in the biofilm, where

temperatures in the flow domain not seem to cool down.

Temperature losses to the environment thus cause the biofilm

to cool down to temperatures where bacterial growth is favored.

Moreover, an increase in insulation thicknesses above 30mm,

does not result in lower heat losses to the environment. Varying

the biofilm viscosity to respectively 1000 and 10 000 times the

viscosity of water did not result in different temperature

patterns. However, for simulations with 𝜇𝑏𝑖𝑜𝑓𝑖𝑙𝑚 ≤ 10 ∙

𝜇𝑤𝑎𝑡𝑒𝑟 , flow occurred in the biofilm, causing a non-realistic

temperature profile and simulations thus could not be compared

with the macro model (where 𝜇𝑏𝑖𝑜𝑓𝑖𝑙𝑚 = 𝜇𝑤𝑎𝑡𝑒𝑟).

REFERENCES

Bagh, L. K., Albrechtsen, H. J., Arvin, E. & Ovesen, K.,

2004. Distribution of bacteria in a domestic hot water system

in a Danish apartment building. Wat Res 38, p. 225-235. Brundrett, G., 1992. L. pneum. and Building Services. Oxford

Cogan, N. G., 2008. Two-fluid Model of biofilm Disinfection,

Tallahassee: s.n. FLUENT Inc. , 2001. Discrete Phase Models , s.l.: s.n.

Picioreanu, C., van Loosdrecht, M. C. & Heijnen, J. J., 2000.

Two-dimensional model of biofilm detachment

Shankara, P. S., 2010. CFD Simulation and Analysis of

Particulate Deposition On Gas Turbine Vanes, s.l.: s.n.

Shen, Y. et al., 2015. Role of Biofilm Roughness and

Hydrodynamic Conditions in L. pneum. Adhesion to and

Detachment from Simulated Drinking Water Biofilms. Environ

Sci Technol, p. 49(7): 4274-4282.

Van Hove, M., 2018. Design and operation of domestic hot

water systems: optimalization using building energy

simulation, s.l.: s.n. Van Kenhove, E., 2017. Comparison of Pipe Models to

Simulate Legionella Concentration in Domestic Hot Water.

Van Kenhove, E., De Vlieger, P., Laverge, J. & Janssens, A.,

2016. Towards energy efficient and healthy buildings: trade-off

between Legionella pneuophila infection risk and energy

efficiency of domestic hot water. Instal2020.

Xavier, J. . d. B., Picioreanu, C. & van Loosdrecht, M. C.,

2005. A general description of detachment for

multidimensional modelling of biofilms. Wiley interscience.

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Temperature [K]

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Pipe radius [mm]

Influence of pipe flow on bacteria level in water Sander Coppens1

Promotoren: Prof. dr. Ir.-Arch. Jelle Laverge, Prof. dr. Ir. Michel De Paepe

Begeleiding: Ir.-Arch. Elisa Van Kenhove, dr. Ing. Lien De Backer, Ir. Asal Sharif, Ir. Zaaquib Ahmed

Abstract: Een simulatiemodel is ontwikkeld door Van Kenhove (2017) dat toelaat om het infectierisico van de Legionella bacterie te beoordelen onder dynamische condities. Ten einde de parameters van dit (macro-)model te verbeteren, is in deze masterproef een numeriek (micro-)simulatiemodel opgesteld dat toelaat de verschillende segmenten van een SWW leiding apart te bekijken. Op basis van de vereenvoudigingen die gemaakt worden in het macro-model, zijn twee onderzoeksvragen opgesteld. Allereerst wordt de adhesie van Legionella pneumophila (L. pneum.) bekeken in zowel een rechte buis als bochtstuk voor verschillende Reynolds getallen (Re). Voor Re < 25 000 is de adhesie van L. pneum. proportioneel tot de tweede macht van Re en voor Re > 25 000 wordt een lineair verloop waargenomen. De tweede onderzoeksvraag focust op het temperatuurverloop in de biofilm, waarbij het effect wordt onderzocht van verschillende watertemperaturen , isolatiediktes en viscositeit van de biofilm . Voor ≥ ∙ volgt het temperatuur in de biofilm een lineair veroop. Daarnaast is aangetoond dat isolatiediktes boven 30mm het temperatuurverschil tussen water in de buis en leidingwand niet meer verder doen dalen. Het opgestelde model is echter niet in staat om het temperatuurverloop te voorspellen wanneer ≤ ∙ . In desbetreffende gevallen ontstaat immers stroming in de biofilm.

Kernwoorden: Legionella pneumophila (L. pneum.) – Sanitair warm water (SWW) – Computational Fluid Dynamics (CFD) – adhesie coëfficiënt – biofilm temperatuur

I INLEIDING De productie van sanitair warm water (SWW) domineert de

totale energievraag van goed geïsoleerde en luchtdichte gebouwen. Eén van de voornaamste redenen voor deze hoge energievraag is dat SWW geproduceerd, opgeslagen en vervoerd wordt aan temperaturen boven 55°C om het risico op een Legionella infectie in SWW installaties te voorkomen.

Legionella pneumophila (L. pneum.) is een aerobe bacterie die van nature aanwezig is in zoutwatervoorzieningen en mits blootstelling, acute luchtaandoeningen (Pontiac Fever) of ernstige longontstekingen (Legionellose) kan veroorzaken. Een simulatiemodel is ontwikkeld door Van Kenhove (2017) dat toelaat het infectierisico van L. pneum. te beoordelen in dynamische condities. Dit maakt het mogelijk om temperatuurregimes te optimaliseren, betere hydraulische regelingen te kiezen en de energievraag voor de productie van SWW te reduceren. Ten einde de parameters van dit model te verbeteren is een numeriek simulatiemodel (CFD-simulaties) opgesteld van verschillende segmenten in een SWW leiding.

1 Verantwoordelijk auteur. Tel.: +32 477 05 32 40 E-mail: [email protected]

II PROBLEEM- EN DOELSTELLING Op basis van vereenvoudigingen die gebruikt worden in het

macro-model, zijn twee onderzoeksvragen opgesteld. Hierbij wordt gekeken naar de adhesie coëfficiënt van L. pneum. tussen water in de buis en biofilm, en naar de variatie van temperatuur in de biofilm.

A L. pneum. adhesie naar de biofilm In het macro-model bezit elk leidingsegment van de SWW

installatie dezelfde bacteriële uitwisselingscoëfficiënt tussen waterstroming en biofilm. Door het verschil in stromingspatroon in de buis wordt echter een verhoogde uitwisseling (in vergelijking met een rechte buis) verwacht in kritische secties van de SWW leiding, zoals bocht- en T-stukken. In literatuur zijn reeds gedetailleerde simulatiemodellen beschreven waarin verschillende aspecten die te maken hebben met de adhesie en segregatie van bacteriën en biofilm werden behandeld. Picioreanu et al. (2000) gebruikte numerieke (CFD) simulaties om het snelheidsprofiel van een bewegende vloeistof te bepalen en berekende vervolgens de voortplanting van spanningen op de biofilm. Shen et al. (2015) voerde numerieke (CFD) simulaties uit waarbij bacteriën werden voorgesteld als inerte partikels en bestudeerde hierbij de snelheidsverdeling en beweging van de partikels boven de biofilm. Deze modellen hebben echter het nadeel enorm gedetailleerd te zijn, wat hen erg rekenintensief maakt. De nood dringt zich bijgevolg aan voor een simulatiemodel waarin de uitwisseling van Legionella bacteriën kan worden beoordeeld, maar tegelijk zijn numerieke efficiëntie behoudt. In de hierboven vermelde simulaties (Shen, et al., 2015; Picioreanu, et al., 2000) wordt bovendien enkel gewerkt met lage Reynolds getallen (Re). In SWW installaties kan de stroming echter volledig turbulent worden met Re hoger dan 30 000 in kleine leidingdiameters zoals DN32. Turbulentie wordt verwacht een belangrijke rol te spelen in de uitwisseling van bacteriën, daar deze worden meegevoerd met de waterstroming.

In deze masterproef wordt de uitwisselingscoëfficiënt van bacteriën bepaald in kritieke leidingsegmenten door de adhesie van L. pneum. te beoordelen in zowel een rechte buis als bochtstuk met equivalente lengte. Het doel is om de proportionaliteit aan te tonen van L. pneum. adhesie in een bochtstuk tot de adhesie in een rechte buis, met een welbepaalde factor N. Het doel van deze masterproef is dus om deze factor N te bepalen.

B Temperatuur in de biofilm Groei van bacteriën is voornamelijk afhankelijk van

temperatuur (Brundrett, 1992), met maximale groei bij ongeveer 35°C. In een SWW installatie bevindt 72% van de cultiveerbare bacteriën zich in de biofilm aan de wand (Bagh, et al., 2004). Bijgevolg zal de temperatuur in de biofilm een belangrijke rol spelen in het simuleren van een L. pneum. infectie in SWW installaties.

In het macro-model wordt de groei van bacteriën in de biofilm bepaald met de temperatuur van de stroming, en niet de temperatuur van die biofilm, die lager verondersteld kan worden, en dus groei van bacteriën stimuleert. In deze masterproef wordt daarom het temperatuurverloop in de biofilm onderzocht bij verschillende stromingstemperaturen , isolatiediktes en viscositeit van de biofilm . Het doel is om te bekijken of de vereenvoudiging in het macro-model van bacteriële groei te berekenen met de stromingstemperatuur, correct is en in welke gevallen dit aangepast moet worden.

III METHODE In overeenstemming met de twee onderzoeksvragen, zijn

twee simulatiemodellen opgesteld in Ansys Fluent (v18.2), waarin respectievelijk de adhesie coëfficiënt en biofilm temperatuur wordt onderzocht.

A L. pneum. adhesie naar de biofilm In literatuur zijn verschillende mogelijke methoden gevonden voor het modelleren van bacterieel transport in Ansys Fluent. Het Discrete Phase Model (DPM) is gekozen, daar de volumefractie van L. pneum. in de waterstroming kleiner is dan 10%, en dus het DPM meer geschikt is (FLUENT Inc., 2001). In DPM simulaties wordt transport van L. pneum. gemodelleerd als de beweging van sferische (inerte) deeltjes in het stromingsveld op basis van de eerste wet van Newton, weerstandskracht en Browniaanse beweging. De simulatie is uitgevoerd in de vloeistoffase en de stroom bevindt zich in stabiele toestand. Turbulente dispersie wordt gemodelleerd met het Discrete Random Walk (DRW) model en willekeurige levensduur van de turbulente eddies. Oneindige adhesie wordt verondersteld door de DPM randvoorwaarde aan de wand als vast (trapped) te zetten. De adhesie van L. pneum. deeltjes wordt weergegeven als depositie waarschijnlijkheid, wat berekend wordt door het totaal aantal vaste deeltjes (trapped) te delen door het aantal initieel verstuurde deeltjes.

B Temperatuur in de biofilm Het simulatiemodel wordt in overeenstemming gebracht met de veronderstellingen uit eerdere studies (Xavier, et al., 2005; Cogan, 2008), door de biofilm te modelleren als een vloeistof waarvan de viscositeit ( ) 1 tot 10 000 keer de viscositeit van water ( ) bedraagt. Op deze manier kan de simulatie waarbij = dienen als referentie voor het macro-model, aangezien daar de biofilm verondersteld is hetzelfde medium te hebben als de waterstroming.De biofilm temperatuur onderzoeksvraag is onderverdeeld in drie verschillende modellen, waarin respectievelijk het effect van de watertemperatuur , isolatiedikte en biofilm viscositeit wordt onderzocht.

IV RESULTATEN

A L. pneum. adhesie naar de biofilm L. pneum. adhesie simulaties zijn uitgevoerd in de 3D CFD omgeving voor zowel een rechte buis (Figuur 1, zwart) als voor een bochtstuk van 90 graden (Figuur1, rood). Simulaties zijn uitgevoerd in DN32 tot watersnelheid van 2.00m/s, resulterend in Re 39808. Extrapolatie is verondersteld voor hogere Re. Voor Re < 25 0000 is de adhesie van L. pneum. proportioneel tot de tweede mach van Re. Voor Re > 25 000 volgt de adhesie in zowel een rechte buis als bochtstuk een lineair verloop met Re. In Figuur 1 zijn de simulatieresultaten (volle cirkels), aangevuld met respectievelijk parabolische trendlijnen (Re < 25 000) en lineaire trendlijnen (Re > 25 000) in stippellijn.

Figuur 1. Depositie waarschijnlijkheid in rechte buis (zwart) en bochtstuk (rood). Simulatieresultaten worden voorgesteld door gevulde bollen, trendlijnen door stippellijnen.

De proportionaliteitsfactor N wordt bepaald door de trendlijn functie van het bochtstuk te verminderen met de trendlijn functie van de rechte buis. Dit resulteert in onderstaande functies voor N:

= −1 ∙ + 2.7 ∙ + 0.1839 ( < 25 000)

= −0.0001 ∙ + 1.629 ( > 25 000) In Figuur 2 worden de hierboven verkregen functies van N

uitgezet voor de verschillende waarden van Re.

Figuur 2. Proportionaliteitsfactor N van L. pneum. adhesie in bochtstuk tot rechte buis met equivalente lengte bij verschillende Re

Zoals kan gezien worden in Figuur 3, bevinden zich onmiddellijk na de bocht zones met respectievelijk lage en hoge schuifspanning op binnen- (rode lijn) en buitenbocht (blauwe lijn). Deze waarden kunnen verklaard worden door het snelheidsprofiel (Figuur 4) te bestuderen. In de bocht schuurt de stroming tegen de binnenbocht, wat de maximumpiek op de binnenbocht en minimumpiek in schuifspanning op de

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buitenbocht verklaart (L=0.5m). Vervolgens komt de stroming los van de binnenbocht, wat aanleiding geeft tot de minimumpiek (rode lijn, L=0.5m-0.6m), gevolgd door een zone met lage schuifspanning op de binnenbocht (rode lijn, L=0.6m-1.1m). Na het loskomen, raakt de stroming de buitenbocht wat daar een maximumpiek in schuifspanning veroorzaakt (blauwe lijn, L=0.6m), gevolgd door een zone met hoge schuifspanning (blauwe lijn, L=0.6m-1.1m).

Figuur 3. Schuifspanning op biofilm in bocht bij Re = 39 808, voor binnenbocht (rode lijn) en buitenbocht (blauwe lijn) (XY-vlak).

Zoals te zien in Figuur 5, stijgt de gemiddelde variatie in schuifspanning op binnen- (rood) en buitenbocht (blauw) met stijgende Re. Deze gemiddelde variatie werd bekomen door eerst de gemiddelde schuifspanning op binnen- en buitenbocht te bepalen tussen 0.7m en 0.9m. Deze waarden werden vervolgens gedeeld door de gemiddelde schuifspanning in het gedeelte voor de bocht tussen 0.2m en 0.4m (Figuur 3).

Figuur 5. Gemiddelde variatie in schuifspanning op biofilm in binnenbocht (rood) en buitenbocht (blauw).

Voor Re < 25 000 is de absolute variatie in schuifspanning tussen recht gedeelte (L=0.2m-0.4m) en binnenbocht (lage schuifspanning) tot 5 keer groter dan de gestandaardiseerde variantie op buitenbocht (hoge schuifspanning). Voor Re > 25 000 zijn beide gestandaardiseerde variaties bij benadering gelijk.

B Temperatuur in de biofilm Biofilm temperatuursimulaties zijn uitgevoerd in de 3D CFD

omgeving. De biofilm wordt gemodelleerd als een vloeistof waarvan de viscositeit ( ) verondersteld wordt in het bereik te liggen tussen 1 en 1000 keer de viscositeit van water ( ). In simulaties waarbij ≥ 100 ∙ volgt het temperatuurverschil tussen water in de buis en binnenwand leiding (buitenste laag biofilm) een lineair verloop met stijgende stromingstemperatuur (Figuur 6). Daarnaast wordt een inverse trend waargenomen tussen hetzelfde temperatuurverschil en isolatiedikte (Figuur 7). Zoals reeds werd beschreven door Van Hove (2018), bereikt het temperatuurverschil tussen waterstroming en leidingwand een asymptotische waarde bij isolatiediktes vanaf 30mm, wat erop wijst dat een verdere verhoging van isolatiedikte niet leidt tot een kleiner temperatuurverschil.

Voor hoge viscositeitswaarden van de biofilm ( ≥100 ∙ ), verloopt het temperatuurverloop in de biofilm lineair, terwijl de waterstroming niet lijkt af te koelen (Figuur 8, blauwe lijn).

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Figuur 4. Snelheidsprofiel in bocht bij Re = 39 808.

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Figuur 6. Temperatuurverschil tussen waterstroming en leidingwand (buitenste laag biofilm) in functie van stromingstemperatuur voor verschillende isolatiediktes: 0mm (zwart), 10mm (rood), 20mm (groen), 30mm (paars).

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Figuur 7. Temperatuurverschil tussen waterstroming en leidingwand (buitenste laag biofilm) in functie van isolatiedikte, voor verschillendestromingstemperaturen: 300K (rood), 318K (groen), 333K( zwart-.

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Temperatuurverliezen naar de omgeving zorgen dus voor afkoeling van de biofilm tot temperaturen waarbij bacteriële groei wordt gestimuleerd. In simulaties waarbij ≤ 10 ∙

, ontstaat stroming in de biofilm (snelheidsprofiel in Figuur 9), wat aanleiding geeft tot een onrealistisch temperatuurverloop (Figuur 8, rode lijn).

Figuur 8. Temperatuurverloop in buis; waterstroming (0-10mm buisradius) en biofilm (10-13mm buisradius) bij ≥ 100 ∙

(blauwe lijn) en ≤ 10 ∙ (rode lijn). Stromingstemperatuur = 318K ; isolatiedikte = 0mm

Figuur 9. Snelheidsprofiel in buis; waterstroming (0-10mm buisradius) en biofilm (10-13mm buisradius); ≤ 10 ∙ .

V VERDER ONDERZOEK Verder onderzoek is aangewezen om de assumpties te

bevestigen die in dit werk zijn gemaakt, en om de mogelijkheden van het model uit te breiden. In deze paragraaf worden daarom mogelijke model verbeteringen aangehaald.

A L. pneum. adhesie naar de biofilm Uitwisseling van bacteriën tussen biofilm en waterstroming

bestaat uit adhesie en segregatie. In deze masterproef wordt enkel adhesie bestudeerd. In verder onderzoek is het daarom aangewezen om zowel adhesie als segregatie te modelleren. Hiertoe kan een User Defined Function (UDF) gebruikt worden die dienst doet als DPM randvoorwaarde voor de biofilm wand (i.p.v. vast of trapped in de simulaties van dit werk). Op deze manier kan ook de afhankelijkheid van temperatuur, ruwheid en schuifspanning in rekening worden gebracht. In deze masterproef is enkel een onderscheid gemaakt tussen bochtstuk en rechte buis. In verder onderzoek kan dit uitgebreid worden naar andere kritische secties, zoals T-stukken. Daarnaast werd in deze masterproef het DPM geselecteerd om transport van L.

pneum. te modelleren. Het Species Transport Model kan echter worden gezien als een goed alternatief, waarvan het gebruik onderzocht kan worden.

B Temperatuur in de biofilm In simulaties waarbij ≤ 10 ∙ werd stroming

waargenomen in de biofilm, wat voor een onrealistisch temperatuurverloop zorgde. Een mogelijke oplossing is het gebruik van een vast materiaal (i.p.v. vloeistof) voor de biofilm.

VI CONCLUSIE EN DISCUSSIE De vereenvoudigingen in het macro-model zijn gedeeltelijk

correct in bepaalde omstandigheden. Adhesie van L. pneum. voor Re < 25 000 is proportioneel tot de tweede macht van Re, en voor Re > 25 000 wordt een lineaire trend waargenomen met stijgende Re. De proportionaliteitsfactor N, die bepaald diende te worden, kan geschreven worden als:

= −1 ∙ + 2.7 ∙ + 0.1839 ( < 25 000)

= −0.0001 ∙ + 1.629 ( > 25 000)

Voor hoge viscositeitswaarden van de biofilm ( ≥100 ∙ ), verloopt het temperatuurverloop in de biofilm lineair, terwijl de waterstroming niet lijkt af te koelen. Temperatuurverliezen naar de omgeving zorgen dus voor afkoeling van de biofilm tot temperaturen waarbij bacteriële groei wordt gestimuleerd. Daarnaast is waargenomen dat een verdere verhoging van de isolatiedikte boven 30mm, geen bijkomend effect heeft op verlaging van temperatuurverschil tussen waterstroming en leidingwand. Verhoging van biofilm viscositeit naar respectievelijk 1000 en 10 000 keer de viscositeit van water heeft geen bijkomend effect. Echter, bij

≤ 10 ∙ , wordt stroming waargenomen in de biofilm, wat voor een onrealistisch temperatuurverloop zorgt. Hierdoor was vergelijken met het macro-model (waar

= ) niet mogelijk.

REFERENTIES Bagh, L. K., Albrechtsen, H. J., Arvin, E. & Ovesen, K.,

2004. Distribution of bacteria in a domestic hot water system in a Danish apartment building. Wat Res 38, p. 225-235.

Brundrett, G., 1992. L. pneum. and Building Services. Oxford Cogan, N. G., 2008. Two-fluid Model of biofilm Disinfection,

Tallahassee: s.n. FLUENT Inc. , 2001. Discrete Phase Models , s.l.: s.n. Picioreanu, C., van Loosdrecht, M. C. & Heijnen, J. J., 2000.

Two-dimensional model of biofilm detachment Shankara, P. S., 2010. CFD Simulation and Analysis of

Particulate Deposition On Gas Turbine Vanes, s.l.: s.n. Shen, Y. et al., 2015. Role of Biofilm Roughness and

Hydrodynamic Conditions in Legionella pneumophila Adhesion to and Detachment from Simulated Drinking Water Biofilms. Environ Sci Technol, p. 49(7): 4274-4282.

Van Hove, M., 2018. Design and operation of DHW systems: optimalization using building energy simulation, s.l.: s.n.

Van Kenhove, E., 2017. Comparison of Pipe Models to Simulate Legionella Concentration in Domestic Hot Water.

Van Kenhove, E., De Vlieger, P., Laverge, J. & Janssens, A., 2016. Towards energy efficient and healthy buildings: trade-off between L. pneum. infection risk and energy efficiency of domestic hot water. Instal2020.

Xavier, J. . d. B., Picioreanu, C. & van Loosdrecht, M. C., 2005. A general description of detachment for multidimensional modelling of biofilms. Wiley interscience.

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Content

Foreword ........................................................................................................................................... ii

Abstract ............................................................................................................................................ iii

Extended Abstract (EN) .................................................................................................................... iv

Extended Abstract (NL) .................................................................................................................. viii

List of Figures .................................................................................................................................. xv

List of Tables ..................................................................................................................................xvii

NOMENCLATURE ..................................................................................................................... xviii

1. INTRODUCTION .....................................................................................................................1

1.1. BACKGROUND .................................................................................................................1

1.2. RESEARCH QUESTIONS ..................................................................................................2

1.2.1. L. pneum. adhesion coefficient .....................................................................................2

1.2.2. Biofilm temperature .....................................................................................................3

1.3. OUTLINE ...........................................................................................................................4

2. LITERATURE REVIEW ...........................................................................................................5

2.1. LEGIONELLA PNEUMOPHILA .........................................................................................5

2.1.1. Temperature.................................................................................................................5

2.1.2. Presence of metals .......................................................................................................6

2.1.3. Presence of nutrients ....................................................................................................6

2.2. BIOFILM ............................................................................................................................7

2.2.1. L. pneum. and biofilm ..................................................................................................7

2.2.2. Biofilm formation: adhesion and detachment................................................................7

2.2.3. Mechanical properties ................................................................................................ 10

2.3. MACRO-SCALE SIMULATIONS OF L. PNEUM. IN DHW SYSTEMS ......................... 11

2.4. MICRO-SCALE MODEL (CFD) – NUMERICAL BASICS.............................................. 12

2.4.1. Fundamental equations............................................................................................... 12

2.4.2. Discretization method (Finite Volume)....................................................................... 13

xiii

2.4.3. Turbulence modeling ................................................................................................. 15

2.4.4. Near-wall modeling ................................................................................................... 17

2.5. COUPLING OF MACRO- AND MICRO-SCALE SIMULATION MODEL ..................... 18

2.5.1. Macro-scale simulation model (Modelica) .................................................................. 19

2.5.2. Micro-scale simulation model (CFD) ......................................................................... 20

2.5.3. Strong and weak coupling of micro- and macro-scale simulation models .................... 22

3. SCOPE AND OBJECTIVE...................................................................................................... 24

3.1. L. PNEUM. ADHESION ................................................................................................... 24

3.2. BIOFILM TEMPERATURE ............................................................................................. 25

3.3. MODEL REQUIREMENTS .............................................................................................. 25

4. METHODOLOGY AND MODEL SETUP .............................................................................. 26

4.1. L. PNEUM. ADHESION ................................................................................................... 26

4.1.1. Geometry ................................................................................................................... 27

4.1.2. Energy model............................................................................................................. 29

4.1.3. Turbulence model and mesh generation ...................................................................... 29

4.1.4. Discrete Phase Model................................................................................................. 35


4.2.1. Geometry and mesh generation .................................................................................. 37

4.2.2. Energy model............................................................................................................. 38

4.2.3. Turbulence model ...................................................................................................... 38

5. RESULTS ............................................................................................................................... 39

5.1. L. PNEUM. ADHESION ................................................................................................... 39

5.1.1. 2D simulations ........................................................................................................... 39

5.1.2. 3D simulations ........................................................................................................... 43


5.2.1. Inlet flow temperature ................................................................................................ 52

5.2.2. Insulation thickness .................................................................................................... 53

5.2.3. Biofilm viscosity ........................................................................................................ 53

6. MODEL IMPROVEMENTS ................................................................................................... 55

xiv

6.1. L.PNEUM. ADHESION .................................................................................................... 55


7. CONCLUSION AND DISCUSSION ....................................................................................... 59

7.1. L. PNEUM. ADHESION ................................................................................................... 59


REFERENCES ................................................................................................................................. 62

APPENDIX ...................................................................................................................................... 66

xv

List of Figures

Figure 1. Comparison of ventilation, transmission and domestic hot water heating demand for

buildings before 1984 to passive buildings (Rogatty, 2003) .................................................................1

Figure 2. Bacterial exchange coefficient in a straight (k) and turn section (k x N) ................................3

Figure 3. L. pneum. growth curve as a function of temperature (Brundrett, 1992). Left: multiplication

and death rate of L. pneum. Right: generation time (time to double the number of cells). .....................6

Figure 4. Biofilm formation and development in a drinking water pipe (Moritz, 2011) ........................8

Figure 5. Particle tracing simulation for (a) a rough 4-week biofilm and (b) a smooth 14-week biofilm

at an average flow velocity of 0.007 m/s. (c) Particles accumulated in the peak of one of the asperities

in the rough biofilm. (d) Particles accumulated in the peak and the side facing flow in one asperity in

rough biofilm. Particle size is not drawn to scale. The horizontal length is 1mm. (Shen, et al., 2015) ...9

Figure 6. Surface detachment rate at a point (x) placed at the biofilm interface (Xavier, et al., 2005) . 10

Figure 7. Replacing continuous domain with discrete domain (1D) (Bhaskaran and Collins, sd) ........ 13

Figure 8. Control volume for finite volume method (de la Cruz and Monsivais, 2012) ....................... 14

Figure 9. Difference between laminar and turbulent flow in pipe (CFDsupport, 2016) ....................... 15

Figure 10. Near-wall turbulent flow (Frei, 2017) ............................................................................... 17

Figure 11. Near wall modeling methods for turbulent flow. The red line represents the boundary layer

and yellow dots represent the calculation nodes. On the left, wall functions are used to resolve the

boundary layer (k-ε model), indicating the first cell needs to within the viscous boundary layer. On the

right, the boundary layer is resolved all the way down to the viscous sublayer, demanding

computational grid resolution to be very fine (k-ω model) (Ansys Inc., 2009).................................... 18

Figure 12. Numerical integrated simulation approach using a co-simulation environment (Ljubijankic,

et al., 2011) ....................................................................................................................................... 23

Figure 13. Particle tracing simulations using the DPM in FLUENT. Infinite particle adhesion is

assumed by setting the boundary condition trapped, meaning the trajectory calculations are terminated.

Ni is the initial amount of released particles and Ne the total escaped particles. .................................. 26

Figure 14. Geometry of bacterial adhesion simulation in 2D environment with dimensions and

boundary conditions (velocity inlet, pressure outlet, wall and axis). .................................................. 27

Figure 15. Geometry and boundary conditions of straight pipe in 3D environment for bacterial

adhesion simulations. (a) Longitudinal section of flow domain (blue) with velocity inlet and pressure

outlet. (b) normal section of flow domain. Symmetry is applied in both the XY and XZ plane. .......... 28

Figure 16. Geometry and boundary conditions of turn section in 3D environment for bacterial

adhesion simulations. (a) normal section (b) longitudinal section of flow domain with velocity inlet

and pressure outlet. Inner and outer diameter of turn are set as wall (biofilm). ................................... 28

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Figure 17. Mesh of straight pipe in 2D environment with k-ε turbulence model (face mesh 2.0mm),

representing the inlet face (left). ........................................................................................................ 30

Figure 18. y+ values at (biofilm) wall boundary with constant grid size for different flow velocities

(2D, k-ε turbulence model) ............................................................................................................... 30

Figure 19. Mesh of straight pipe in 2D environment with k-ω turbulence model. Mesh consist of face

mesh 0.2mm and bias factor 10 (cells getting smaller to the biofilm interface). (a) Mesh at the inlet

(on the left). Black rectangle represents detail. (b) Detail: bias factor 10 with cells getting smaller to

the biofilm interface. ......................................................................................................................... 31

Figure 20. Y+ value at (biofilm) wall boundary with Re 39808 (2D, k-ω turbulence model) .............. 33

Figure 21. Mesh of straight pipe section in 3D environment with body mesh 0.5mm and inflation of 10

layers with first cell size 0.02mm. (a) Cross section in YZ plane. (b) Detail of inflation layer. ........... 34

Figure 22: Y+ values on biofilm wall boundary in straight pipe (black) and turn section: inner side of

turn (red) and outer side of turn (blue) (Re = 39808) ......................................................................... 35

Figure 23. Deposition probability in straight pipe section (2D, k-ε turbulence model, L = 1m) ........... 40

Figure 24. Y+ values at pipe wall boundary for varying grid size and constant water velocity 1.5 m/s

(2D, k-ε turbulence model) ............................................................................................................... 41

Figure 25. Deposition probability for constant fluid flow velocity and varying mesh size (surface

injection with 10 tries, straight pipe section, k-E turbulence model) ................................................... 42

Figure 26. Deposition probability for straight section (black) and turn (red) for different Reynolds

numbers (3D, DN32, equivalent length 1m, k-ω SST turbulence model, surface injection with 10

tries). Simulation results are represented by filled dots, trendlines by dashed lines. ............................ 44

Figure 27. Factor of proportionality in L. pneum. adhesion between straight and turn pipe section(N)

for different Re. ................................................................................................................................ 45

Figure 28. Velocity contours in turn section (uniform inlet velocity of 2.00 m/s, Re 39808). (a)

Velocity contour of whole turn section in XY plane. (b) Detail of velocity contour in the turn section

(XY plane). (c) Detail of velocity contour before turn (XZ plane). (c) Detail of velocity contour after

turn (YZ plane). ................................................................................................................................ 47

Figure 29. Illustration of turn section with inner pipe wall (red line) and outer pipe wall (blue line). .. 48

Figure 30. Shear stress at wall boundary (e.g. contact zone between fluid flow and biofilm) in XY

plane for inner pipe wall (red line) and outer pipe wall (blue line) of turn section with Re 39808 (flow

velocity 2.00 m/s). ............................................................................................................................ 48

Figure 31. Mean wall shear stress for simulation results (CFD, black line), and theoretical values in

which skin friction coefficient was calculated by equation 11 and 12 ( green), and equation 7 (purple).

Mean wall shear in simulation results (black) was calculated in straight section before the turn,

between 0.2m and 0.4m. ................................................................................................................... 50

Figure 32. Standardized mean variation in shear stress for both inner wall of turn section (low shear

zone, red) and outer wall of turn section (high shear zone, blue). ....................................................... 51

xvii

Figure 33. Temperature difference in function of inlet flow temperature for insulation thickness: 0mm

(black), 10mm (red), 20mm (green), 30mm (purple). ( = 10 kg/m.s. -flow velocity 2m/s ) . 52

Figure 34. Temperature difference as a function of insulation thickness for given inlet flow

temperature: 333K (red), 318K (blue), 300K (black). ( 10 kg/m.s - flow velocity 1m/s) ....... 53

Figure 35. Temperature pattern in flow domain at cross section (0.50m) for biofilm viscosity of

≥ 100 ∙ (blue line) and ≤ 10 ∙ (red line). Inlet temperature

318K, with 0mm insulation. Dashed black line represents boundary between fluid flow and biofilm. 54

Figure 36. Velocity profile (solid red line) in flow domain at cross section (0.50m) with ≤

10 ∙ ..................................................................................................................................... 54

Figure 37. Diffusive coefficient method (Species Transport Model) .................................................. 56

Figure 38. Representing the biofilm as a meshed solid zone with coupled wall at interface between

solid biofilm and fluid flow. .............................................................................................................. 58

List of Tables

Table I: Material properties biofilms (Xavier, et al., 2005) ............................................................................... 11

Table II: Heat transfer coefficient with different insulation layer thickness ....................................................... 29

Table III: Grid size (mapped cell size, total number of nodes and total number of elements) for different used

turbulence model in 2D simulations................................................................................................................. 32

Table IV: Grid study of bacterial adhesion simulations in 3D environment for straight pipe section ................. 33

Table V: Grid information (total number of nodes and elements) of both straight pipe and turn in L. pneum.

adhesion simulations in the 3D environment. ................................................................................................... 34

Table VI: Parameters used in the DPM simulations ......................................................................................... 36

Table VII: Biofilm temperature simulations - setup and parameters.................................................................. 38

Table VIII: Grid size (total number of nodes and total number of elements) for biofilm temperature simulation

model in 3D environment. ............................................................................................................................... 38

Table IX: Deposition probability for different fluid flow velocities with constant mesh size (2D, surface injection

with 10 tries, straight pipe section, standard k-ε turbulence model) .................................................................. 40

Table X: Deposition probability for constant fluid flow velocity and varying mesh size (surface injection with 10

tries, straight pipe section, standard k-ε turbulence model) ............................................................................... 42

Table XI: Deposition probability for straight and turn pipe section with different flow velocities (3D, DN32,

equivalent length 1m, k-ω SST turbulence model, DPM surface injection with 10 tries) ................................... 43

Table XII: Coefficients of determination (R²) for parabolic and linear trend in both straight pipe and turn section

(3D, equivalent length 1m, k-ω SST turbulence model) ................................................................................... 45

Table XIII: Temperature difference ∆T [K] for different insulation thickness dinsulation [mm] and inlet flow

temperature Ti [K] .......................................................................................................................................... 52

xviii

NOMENCLATURE

surface area ²

equivalent radius

skin friction coefficient −

concentration

mass diffusion coefficient m² s

thickness

elastic (Young) modulus N m

drag force N

safety factor −

gravity

diffusion flux mol s

Boltzmann constant (1.38064852) m kg s

convective mass transfer coefficient

N molar-mass flux mol m s

pressure

order of convergence −

Reynolds number −

thermal resistance m K

Refinement ratio (grid study) −

turbulent Schmidt number −

temperature °

heat transfer coefficient W m

∗ friction velocity

flow velocity

poisson ratio −

non-dimensional distance to the wall −

xix

Greek symbols

boundary layer thickness mm

turbulent dissipation rate −

relative roughness coefficient −

turbulent kinetic energy −

thermal conductivity

dynamic viscosity

density

cohesion strength N m

shear stress

specific turbulence dissipation rate −

Acronyms

CFD Computational Fluid Dynamics

DHW Domestic Hot Water

DNS Direct Numerical Simulations

DPM Discrete Phase Model

DRW Discrete Random Walk

GCI Grid Convergence Index

HVAC Heating, Ventilation & Air Conditioning

LES Large Eddy Simulations

PDF Probability Density Function

RANS Reynolds Averaged Navier-Stokes equations

SST Shear Stress Transport

UDF User Defined Function

WHO World Health Organization

Other abbreviations

L. pneum. Legionella pneumophila

cfu colony forming units

1

1 INTRODUCTION

1.1 BACKGROUND

The energy use for Domestic Hot Water (DHW) represents an important part of the total energy use in

residential building typologies such as dwellings, apartments, hotels, retirement homes, as well as in

sports facilities, hospitals, spa’s etc. (Stout & Muder, 2004). With ever improving insulation levels and

air tightness of building envelopes due to the tightening of energy performance requirements for

buildings, the production of DHW, which has seen comparatively little innovation, now easily dominates

the total energy demand. On average, about 800kWh per occupant per year is needed for DHW

production. For the average dwelling with a floor area of 170m² and 3.5 occupants (Delfruyt, et al.,

2013), this amounts to 15kWh/m² per year. As illustrated in Figure 1, this demand remained unchanged,

while projected energy performance requirements for 2020 state to reduce the total energy demand for

heating, cooling and DHW production to 1/3 of what they were in 2006 (Van Kenhove, et al., 2016).

Figure 1. Comparison of ventilation, transmission and domestic hot water heating demand for buildings

before 1984 to passive buildings (Rogatty, 2003).

As can be noted in Figure 1, the production of Domestic Hot Water (DHW) dominates the total energy

demand in well insulated and airtight buildings. One of the main reasons for this high energy demand is

that DHW is produced, stored and distributed at temperatures above 55-60 °C to mitigate the risk of

infecting the DHW system with Legionella pneumophila (L. pneum.), an aerobic gram-negative

2

bacterium that, upon exposure, causes acute respiratory disease (Pontiac Fever) or severe pneumonia

(Legionnaires disease) (Van Kenhove, et al., 2016).

For most of the applications of DHW, such as showering or doing the dishes, temperatures of only 30-

40°C are required. This disparity between 55-60°C and 30-40°C doubles the temperature difference

between the DHW system and environment along with the associated heat loss and has a detrimental

effect on the efficiency of DHW production units. The 55-60°C temperature limit has been established

by investigating the growth dynamics of L. pneum. bacteria in lab conditions and studying infected cases

(Brundrett, 1992). At these temperatures, 90% of the L. pneum. bacteria are effectively killed in half an

hour and the DHW system is considered safe (Van Kenhove, et al., 2016).

A simulation model is developed by Van Kenhove et al. (2015) that allows assessing the L. pneum.

infection risk under dynamic conditions. This simulation model, which in this master’s dissertation is

referred to as the macro-model, allows to simulate the whole hydraulic DHW system (pipes, pumps,

boiler,…). By this mean, HVAC designers will be able firstly to thoroughly assess the Legionella

infection risk associated with their design and secondly to optimize temperature regimes, to choose

better hydronic controls and to reduce the energy demand for DHW production, storage and distribution

(Van Kenhove, et al., 2015).

1.2 RESEARCH QUESTIONS

Several parameters in the macro-scale model are simplified because they are still unknown and further

research is needed in order to improve the simulation model. To do so, a micro-scale model is built in

this master’s dissertation using Computational Fluid Dynamics (CFD), representing different sections

of a DHW pipe. Focusing on simplifications made in the macro-model, two different research questions

are determined, respectively focusing on adhesion of L. pneum. bacteria from the liquid flow to the

biofilm, and on the variation of temperature in the biofilm compared to water.

1.2.1 L. pneum. adhesion coefficient

L. pneum. appears both in water and biofilm. Moreover, according to Flemming et al. (2002), 95% of

overall bacterial biomass in DHW systems can be located in biofilms on surfaces, while only 5% occur

in the water volume. This biofilm structure is composed of a consortium of microbial cells that are

attached to the pipe surface and forms a protective layer for the bacteria which allows them to grow and

multiply in the biofilm. A transport of bacteria between the biofilm and water volume thus exists; in

which L. pneum. adhere from the water volume to the biofilm and vica versa, L. pneum. detach from the

biofilm to the water volume.

3

One of the simplifications in the macro-scale simulations is that every pipe section of the DHW system

has the same bacterial exchange coefficient between liquid flow and stagnant biofilm. However, due to

different flow patterns in the pipe, a higher exchange coefficient (in comparison with a straight pipe) is

expected in critical sections of the DHW system, such as T-sections and turns.

As explained above, bacterial exchange consists both of adhesion and detachment. In this master’s

dissertation, the focus will be on the adhesion of L. pneum. to the biofilm in both a straight pipe and 90

degrees turn section. The goal of the model is to investigate the adhesion in both DHW pipe sections

and show the proportionality of the bacteria adhesion in the turn section to the adhesion in a straight

pipe (referred to as k in Figure 2), with a factor N. To conclude, the aim is to determine the factor N.

Figure 2. Bacterial exchange coefficient in a straight (k) and turn section (k x N)

1.2.2 Biofilm temperature

Bacterial growth is mainly dependent of temperature (Brundrett, 1992), with maximum growth at about

35°C. In a DHW system, 72% of the cultivable bacteria are found to be surface-associated (in the

biofilm) (Bagh, et al., 2004), making the temperature in the biofilm an important factor when modeling

L. pneum. infection risk in DHW systems. In the macro-scale model, bacterial growth in the biofilm is

calculated based on temperature in the liquid fluid flow, and not with biofilm temperature, which can

assumed to be lower in certain cases, and consequently favoring bacterial growth.

The biofilm temperature research question of this master’s dissertation therefore checks whether the

simplification in the macro-scale model of calculating bacterial growth in the biofilm with liquid flow

temperature, is correct and for which cases this should be updated.

4

1.3 OUTLINE

Before focusing on the two research questions, firstly a thorough literature review is performed in

Chapter 2. The first and second part of this literature review describe L. pneum. growth in water and in

biofilm. The third and fourth part respectively focus on the macro- (section 2.3) and micro-scale

simulation model (section 2.4). After the literature review, the scope and objective of this master’s

dissertation are described more into detail in Chapter 3.

Secondly, the methodology and model set-up of the used micro simulation models are discussed in

Chapter 4, followed by an extensive description of the results obtained from these simulations (Chapter

5) and recommendations for further work (Chapter 6). Finally, to conclude, results are summarized and

discussed in Chapter 7.

5

2 LITERATURE REVIEW

In the framework of this master’s dissertation, L. pneum. adhesion coefficient and biofilm temperature

are studied. To this end, in the following literature review, more information is given of this L. pneum.

bacterium and its growth parameters (section 2.1), followed by an extensive description of the biofilm

(section 2.2). Since in this work, the aim is to improve the parameters of the simulation model developed

by Van Kenhove (2017), the macro-scale model is described briefly in section 2.3. In order to improve

these parameters, a micro-scale model is built using CFD of which the numerical basics are explained

in section 2.4.

2.1 LEGIONELLA PNEUMOPHILA

L. pneum. is a gram-negative, rod-shaped, heterotrophic bacterium, which accounts for 90% of the

reported Legionellosis cases, comprising a severe and possibly fatal pneumonia called Legionnaires’

disease and a milder, flu-like disease referred to as Pontiac Fever (Moritz, 2011). Outbreaks of

Legionnaires’ disease occurred in offices, hotels, hospitals, cruise ships, … Infection occurs

predominantly by the inhalation of contaminated aerosols which can be produced by shower heads,

whirlpools, air conditioning, etc. (Van Kenhove, et al., 2016).

Since the health significance is high, several guidelines and target values for the prevention, detection,

control and elimination of L. pneum. exist. The maximum limit of measured L. pneum. bacteria in water

(i.e. threshold), is 100 colony forming units (cfu) per 100 mL. For health facilities at high risk a target

value of 0 cfu/100 mL is set (WHO, 2008). The growth of L. pneum. is influenced by lukewarm water

between 20 and 45°C, stagnation, an acid environment, the presence of nutrients and the presence of

metals like Iron (Fe) and Zinc (Zn).

2.1.1 Temperature

Legionella species exists as part of the natural microbial flora of many aquatic ecosystems and appear

in most natural water supplies like lakes, ponds and rivers. This is harmless, but very low concentrations

of Legionella from natural habitats can increase markedly in man-made hot water systems where the

temperature is optimal for their growth and reach a dangerous concentration (Katz & Hammel, 1987).

Figure 3 shows an estimation of the mean generation time (time to double the number of cells) of L.

pneum. as a function of the tap water temperature. At temperatures below 20°C the bacteria become

dormant, but remain viable for months. The bacteria grow best at temperatures between 20°C and 45°C,

with an optimum at 35°C. Beyond 45°C pasteurization starts and higher temperatures will eventually

kill the organism. At temperatures above 55°C, 90% of the L. pneum. bacteria are effectively killed in

6

half an hour and the DHW system is considered safe. The death rate at any temperature is proportional

to the number of living cells present (Brundrett, 1992).

Figure 3. L. pneum. growth curve as a function of temperature (Brundrett, 1992). Left: multiplication

and death rate of L. pneum. Right: generation time (time to double the number of cells).

2.1.2 Presence of metals

The presence of metals such as Fe or Zn derived from pipelines and fittings are important parameters

for bacterial growth and virulence (Reeves, et al., 1981; States, et al., 1985; Yaradou, et al., 2007). Fe

favors bacterial growth; moreover, L. pneum. species even cannot grow in culture media without Fe.

Logistic analysis showed that the presence of Fe above 0.095 ppm is associated with L. pneum. Authors

such as Rogers et al. (1994) and Borella et al. (2004), stated that Cu inhibits its growth. The risk of L.

pneum. colonization in the circuits significantly decreased with respect to Cu concentration (Serrano-

Suarez, et al., 2013).

2.1.3 Presence of nutrients

Studies showed that there are greater microbial levels in water where L. pneum. was detected, which

indicated that the presence of L. pneum. species was associated with the presence of biofilm on which it

can grow. This biofilm structure is discussed more in detail in section 2.2. The survival and

multiplication of L. pneum. depends on the presence of other microorganisms providing the essential

demand of amino acids and organic carbon. Thus, aquatic multispecies biofilms are ideal ecological

niches for the growth of L. pneum. Access to nutrients is provided either directly by other

microorganisms living in the biofilm or indirectly by decaying organic matter (Temmerman, et al., 2006;

Serrano-Suarez, et al., 2013; Moritz, 2011).

7

Protozoa however do not only supply nutrients, they also provide protection from hostile environmental

conditions, making L. pneum. able to survive high temperatures, disinfection procedures and drying.

Protozoa also play an important role in the distribution of L. pneum. to new environments. Infected

protozoa can actively leave a biofilm when conditions become unfavorable and have also been shown

to release vesicles of respirable size containing L. pneum. cells (Moritz, 2011).

Although several investigations found that L. pneum. only persisted in biofilm communities and did not

multiply in the absence of amoebae (Murga, et al., 2001; Declerck, et al., 2009), the discussion whether

biofilm associated L. pneum. really require protozoan hosts for their multiplication or whether they are

able to replicate independently in the community is still ongoing (Moritz, 2011).

2.2 BIOFILM

2.2.1 L. pneum. and biofilm

L. pneum. appears in water and in biofilm. According to Flemming et al. (2002), 95% of overall bacterial

biomass in drinking water systems can be located in biofilms on surfaces, while only 5% occur in the

water phase. In a DHW system 72% of the cultivable bacteria were found to be surface-associated (Bagh,

et al., 2004). Biofilms have the ability to function as an environmental reservoir for pathogenic

microorganisms and thus are potential sources of contamination (Moritz, 2011).

A biofilm is composed of a consortium of microbial cells that are attached to the surface and associated

together in an extracellular anionic polymer matrix (Donlan, 2002). The matrix is extremely hydrated

(97% water) and consists mainly of exopolysaccharides, biological macromolecules, nutrients,

metabolites, and inorganic compounds and particles (Farhat, et al., 2012). The bacteria attach to the

biofilm because it consists of micro-organisms which allow cells to adhere and forms a protective layer

for the bacteria which allows them to grow and multiply in the biofilm. Biofilms adjust to their

surroundings and can resist antimicrobial agents (Moritz, 2011).

2.2.2 Biofilm formation: adhesion and detachment

The formation of biofilm is shown in Figure 4 and can be divided into several distinct stages even though

the particular development processes may vary depending on the microbial species involved and the

prevailing environmental conditions. Steps in biofilm formation include the initial attachment of cells

to a surface, subsequent multiplication of the cells resulting in micro-colonies, followed by the

continuous proliferation of attached bacteria leading to the establishment of a mature biofilm, and

passive detachment or active release of single cells or aggregates of cells into the surrounding

environment (Moritz, 2011).

8

Moreira (2014) gives an overview of several studies assessing the effect of surface properties on cell

adhesion – and thus on the initial formation of biofilm – performed in the last 35 years. Biofilm

formation is favored at low flow rates and is being controlled by shear stress which promotes biofilm

erosion or sloughing. Therefore, high flow rates should be used during cleaning and disinfection cycles

because shear stress increase will promote biofilm detachment (Moreira, et al., 2014).

Figure 4. Biofilm formation and development in a drinking water pipe (Moritz, 2011)

Shen et al. (2015) identified that L. pneum. adhesion was enhanced by biofilm roughness because of the

increased interception between the flowing particles and the surface on rough biofilms. After L. pneum.

adheres to the biofilm, subsequent cell detachment is facilitated by high average flow velocity. Biofilm

roughness could protect L. pneum. from detachment by creating larger low shear stress zones.

L. pneum. adhesion on biofilms with different biofilm roughness was experimentally measured for

solutions containing from 3 to 300 mM ionic strength to determine whether electrostatic double layer

compression or biofilm surface roughness controls the adhesion. While the adhesion of L. pneum. on

older biofilms was independent of ionic strength, adhesion measured at both 3 and 100 mM correlated

positively with the relative roughness coefficient (η). The observed higher adhesion on rougher biofilm

surfaces could be explained by an enlarged surface area due to the surface roughness. However, the

surface enlargement parameter was not directly proportional to L. pneum. adhesion, indicating that other

factors besides the enlarged surface contributed to the higher adhesion on rough biofilm surfaces (Shen,

et al., 2015). Kemps & Bhattacharjee (2009) reported that local hydrodynamics make the roughness

asperities act as attractive locations allowing the particles getting closer to the substrate surface. In these

zones, particles could slowly move along the asperities, allowing enhanced interception between

particles and roughness asperities (Shen, et al., 2015).

In addition to the detachment trend with flow velocity (Moreira, et al., 2014), detachment of L. pneum.

also depends on biofilm roughness. Experimental research by Shen et al. (2015) under average flow

velocities of 0.1 and 0.3 m/s, showed higher detachment rates from smooth biofilm surface compared

9

to rough biofilm surface. However, under an average flow velocity of 0.7 m/s similar detachment of L.

pneum. was observed from both smooth and rough biofilms. These findings can be easily explained by

shear stress; under the average flow of 0.3 m/s, on the rough surface, the highest shear stress is formed

near the peak of each asperity, while large low shear stress zones were formed underneath the peak.

Cells adhered in these zones are subjected to less shear stress penetration and therefore have a lower

probability of detachment. On a smooth biofilm surface, the shear stress is distributed more uniformly,

thus most of the biofilm is exposed to shear stress and consequently more cells are expected to detach

from the smooth biofilm surface. However, under an average flow velocity of 0.7 m/s, high shear stress

exerted on the biofilm may penetrate the biofilm causing detachment of biofilm surface layer and not

just the preadhered cells. High shear stress therefore caused equally high detachment of L. pneum. from

both smooth and rough biofilm surfaces. In Figure 5 simulation results are visually represented for flow

velocity distribution and particle tracing above selected rough (4-week) and smooth (14-week) biofilm

contours exposed to an average flow velocity of 0.007 m/s (Shen, et al., 2015).

Figure 5. Particle tracing simulation for (a) a rough 4-week biofilm and (b) a smooth 14-week biofilm

at an average flow velocity of 0.007 m/s. (c) Particles accumulated in the peak of one of the asperities

in the rough biofilm. (d) Particles accumulated in the peak and the side facing flow in one asperity in

rough biofilm. Particle size is not drawn to scale. The horizontal length is 1mm. (Shen, et al., 2015).

An extensive description of biomass detachment was based on the mechanistic representation of

hydrodynamic stress on the biofilm structure (Picioreanu, et al., 2000). Moreover, a framework for

multidimensional modelling of activity and structure of multispecies biofilms was given by Xavier, et

al., (2005). As was explained above, detachment is caused by diverse aspects, such as flow velocity and

10

biofilm roughness. However, for modeling purposes a simple description using overall detachment rates

should be sufficient. A general method for describing biomass detachment was introduced later on

(Xavier, et al., 2005). Biomass losses from processes acting on the entire surface of the biofilm, such as

erosion, were modeled using a continuous detachment speed function( ), defined as the speed of

biofilm front retreat (i.e. mass detachment) resulting from detachment mechanisms that act on the entire

biofilm surface (e.g. erosion). ( ), where x is a point located on the biofilm/liquid interface (here

called surface Γ), is a speed in the direction normal to the surface of the biofilm/liquid interface at that

point, which is expressed by

= − F (1)

In Equation 1, is the vector normal to the surface at point x, which is illustrated in Figure 6. The

method is flexible to allow to take several forms, including expressions dependent on any state

variables such as the local biofilm density.

Figure 6. Surface detachment rate at a point (x) placed at the biofilm interface (Xavier, et al., 2005)

2.2.3 Mechanical properties

There is only very scarce information in literature about the mechanical properties of biofilms. In

previous work (Xavier, et al., 2005), the following assumptions have been made:

i The biofilm body is as an elastic material (Ohashi, et al., 1999)

ii The biofilm is homogeneous and isotropic. There is no variation in elastic coefficient E,

Poisson ratio and tensile strength .

iii The biofilm is considered a ductile material, which exhibits yielding followed by some

plastic deformation prior to fracture. This was shown by experiments of Ohashi and

Harada (1994).

11

In Table I an overview is given of the material properties for biofilms used in the work of Xavier et al.,

(2005).

Table I. Material properties biofilms (Xavier, et al., 2005)

Parameter Symbol Parameter value Units

Biomass properties

Maximum biofilm biomass density 30 kg m

Biofilm mechanical properties

Elastic (Young) modulus E 64 N m

Poisson ratio 0.3 -

Cohesion strength 0.4 – 1 N m

2.3 MACRO-SCALE SIMULATIONS OF L. PNEUM. IN DHW

SYSTEMS

As explained in section 2.1, the health significance of L. pneum. in DHW systems is high, since the

bacteria can compromise both a severe and possibly fatal pneumonia called Legionnaires’ disease and

a milder, flu-like disease referred to as Pontiac Fever. Therefore, a simulation model is developed by

Van Kenhove (2017) that allows to investigate the infection risk for L. pneum. in the design phase of

a DHW system.

Dynamical biological growth models and DHW models usually operate on a different scale. To come

to a manageable model in term of computational resources while designing a full DHW system, a multi-

scale (thermodynamic and biological) macro-scale model is developed by.

To compile the macro-scale simulation model, the Modelica environment is used. This equation based

programming language is non-proprietary and object oriented, making it extremely appropriate for the

development of multi-scale models such as required in the case of Van Kenhove et al. (2015). Extensive

libraries for the simulation of buildings and their services have recently been developed in IEA EBC

annex 60. The work within the research of Van Kenhove et al. (2015) will be added to the capabilities

of the Modelica simulation environment by providing a biological growth library, that is not available

today. Modelica’s open source and modular structure will allow users to use this library to model similar

biological growth problems in all kinds of applications (Van Kenhove, et al., 2015).

12

To assure that the result can be used in as broad a context as possible, the biological growth model is

split into a number of part-models. Each of these part-models can be used independently in Modelica

and therefore has value on its own, reducing the ‘all the eggs in one basket’ risk associated with the

project. The basic split will be between:

i water based proliferation of the bacteria (growth in the water itself and

transport within the water)

ii Legionella growth in the biofilm

iii bacteria transport between the biofilm and water (boundary layer theory)

The first and second sub-model predict the growth and starvation of L. pneum. based on the theory

described in section 2.1. The third sub-model is based on the theory of adhesion and detachment, as

discussed in section 2.2.2. and forms the subject of the first research question as determined in section

1.2.1.

To come to an adequately validated model, a test rig was built, representing a collective DHW system

of an apartment building. The simulation model is validated based on measuring boundary conditions

(temperature, velocity, flow parameters,…) at the test rig. Furthermore, relevant temperature and use

profiles in DHW systems are measured in several buildings (Van Kenhove, et al., 2015).

2.4 MICRO-SCALE MODEL (CFD) – NUMERICAL BASICS

In order to improve the parameters of the macro-scale simulation model, a micro-scale model is built

in this master’s dissertation using CFD, representing different sections of a DHW pipe. Focusing on

simplifications made in the macro-scale model, two research questions are determined, respectively

focusing on the bacteria adhesion coefficient from the liquid fluid flow to the biofilm, and on variation

of temperature in the biofilm compared to water. In this chapter a quick overview is given of the CFD

basics and methods, which will be used in the micro-scale model.

2.4.1 Governing equations

Applying the fundamental laws of mechanics to a fluid gives the governing equations describing the

conservation of mass, momentum and energy. These equations can be written as follows:

Conservation of mass

+ ( ) + ( ) + ( ) = 0 (2)

13

Conservation of momentum

Momentum in x-direction

( ) + ( ) + ( ) + ( ) = − + μ + + (3.1)

Momentum in z-direction

( ) + ( ) + ( ) + ( ) = − + μ + + (3.2)

Momentum in y-direction

( ) + ( ) + ( ) + ( ) = − + μ + + − ρgβ(T − T) (3.3)

Conservation of energy

( ) + ( ) + ( ) + ( ) = k + + + q (4)

In most engineering problems, these equations cannot be solved analytically. To overcome this problem

CFD is used, which solves these governing equations by computer-based solutions (Bhaskaran &

Collins, sd). The main difference between the micro (CFD)- and macro-scale (Modelica) model, is that

in the Modelica simulations, the equations are only computed 1-dimensional. Namely, because the

velocity in the x-direction dominates the flow, the velocity in y- and z-direction are neglected. In

contrast, in CFD the problem is solved in a Cartesian (2D or 3D) coordinate system, where u, v, w

represent the x, y, z components of the velocity vector.

2.4.2 Discretization method (Finite Volume)

Broadly, the strategy of CFD is to replace the continuous problem domain with a discrete domain using

grids, which is illustrated in Figure 7. In the continuous domain, each value of interest is defined at any

point in the domain. In a CFD-solution (discrete domain), one would only determine the value of interest

at discrete or grid points. The values at other locations are then determined by interpolating the values

at the grid points (Bhaskaran and Collins, sd).

Figure 7. Replacing continuous domain with discrete domain (1D) (Bhaskaran and Collins, sd)

14

The differential equations of the continuous domain therefore need to be translated to algebraic

equations. Most commercial CFD codes, such as ANSYS Fluent, use the finite-volume approach in

which the integral form of the conservation equations are applied as starting point. The solution domain

is subdivided into a finite number of contiguous control volumes and the conservation equations are

applied to each control volume. At the centroid of each control volume lies a computational node at

which the variable values are to be calculated. The control volume and computational node are illustrated

in Figure 8. Interpolation is then used to express variable values at the control volume surface in terms

of the nodal center values. In a general situation, the discrete equations are applied to all cells in the

interior of the domain. For cells at or near the boundary, a combination of the discrete equations and

boundary conditions is applied. In the end, a system of simultaneous algebraic equations is obtained

with the number of equations being equal to the number of independent discrete variables. Roache

(1998) suggests a grid convergence index (GCI) to provide a consistent manner in reporting the results

of grid convergence studies and perhaps provide an error band on the grid convergence of the solution.

Figure 8. Control volume for finite volume method (de la Cruz and Monsivais, 2012)

Due to the convective term, the momentum conservation equation for a fluid is nonlinear. Phenomena

such as turbulence and chemical reactions introduce additional non-linearities. The highly nonlinear

nature of the governing equations for a fluid makes it challenging to obtain accurate numerical solutions

for complex flows of practical interest. To deal with these nonlinearities, the equations are linearized

around a guess value and are iterated until the guess value agrees with the solution to a specified

tolerance level. For example, let ugi be the guess value of ui . As ug u , the linearization and matrix

inversion errors tends to zero. The difference between ug and u is called the residual. Scaling with the

average value of u in the domain ensures that the residual is a relative rather than an absolute measure.

15

The iteration process is terminated when the residual falls below a certain point, which is referred to as

the convergence criterion (Bhaskaran and Collins, sd).

2.4.3 Turbulence modeling

In a duct, three different states of flows can be distinguished: laminar flow, turbulent flow and a

transitional regime. As can be seen in Figure 9, laminar flows are characterized by smoothly varying

velocity fields in space and time in which individual “laminae” (sheets) move past one another without

generating cross currents, and occur at low to moderate values of the Reynolds number (Re). In contrast,

turbulent flows occur in the opposite limit of high Reynolds numbers and are characterized by large,

nearly random fluctuations in velocity and pressure, referred to as ‘eddies’. These fluctuations arise from

instabilities that grow until nonlinear interactions cause them to break down into finer and finer eddies

that eventually are dissipated by the action of viscosity (Bhaskaran and Collins, sd). Finally, the

transitional flow regime is a mixture of laminar and turbulent flow, with turbulence in the center of the

pipe, and laminar flow near the pipe walls.

Figure 9. Difference between laminar and turbulent flow in pipe (CFDsupport, 2016)

A flow is fundamentally described by the Navier-Stokes equations. However, a turbulent flow may

contain very small scales, so that resolving all scales in time and space (Direct Numerical Simulation:

DNS) may require extreme computer resources. Even the option to resolve only the largest of the scales

and modelling the small scales (Large Eddy Simulation: LES) is generally not realistic for analysis or

design purposes, again due to the high required computer storage and speed. Moreover, from a practical

point of view, a mean value of the flow is often sufficient for design purposes. This means that if DNS

or LES are used, the result is subsequently averaged statistically. In the Reynolds averaging of the

16

Navier-Stokes equations (RANS), the equations are averaged statistically before solving them. This is

the cheapest option with respect to computer resources. In performing time averaging, six additional

unknowns are obtained, namely the Reynolds Stresses. The main task of turbulence modelling is to

determine these Reynolds Stress and other scalar transport properties (Degroote, 2017).

Common types of turbulence models used in CFD, are two equation turbulence models, such as the k-ε

and k-ω model. By definition, these two equation models include two extra transport equations to

represent the turbulent properties of the flow. This allows a two equation model to account for history

effects like convection and diffusion of turbulent energy. One of the transported variables is the turbulent

kinetic energy, k. The second transported variable varies depending on what type of two equation model

is used. Common choices for the second variable are the turbulent dissipation ε (k-ε model) or the

Specific turbulence dissipation rate ω (the k-ω model). The second variable, ε or ω, can be thought of

as the variable that determines the scale of the turbulence (length-scale or time-scale), whereas the first

variable k, determines the mean kinetic energy per unit mass associated with eddies in turbulent flow

and can be produced by for example fluid shear or friction. (Wilcox, 1998).

Of the two mentioned models, the k-ε model, where ε is the rate at which energy is dissipated to smaller

eddies (Launder and Spalding, 1974), is the simplest turbulence model for which only initial and/or

boundary conditions need to be supplied. It performs particularly well for internal flows which embrace

a wide variety of industrial engineering applications. However, the model shows poor results near wall

boundaries and therefore needs to be combined with additional wall functions to describe near wall

effects. The use of wall functions will be dealt with later in section 2.4.4 (Casey and Wintergerste, 2000).

The second mentioned two equation model, the k-ω model, performs in contrast to the k-ε model, very

well close to walls in boundary layer flows. However, it is very sensitive to the free stream value of ω.

Unless great care is taken in setting the value of ω, spurious results can be obtained in both boundary

layer flows and free shear flows. To resolve the gap between the two models, Menter (1994) proposed

a model which retains the properties of k-ω close to the wall and gradually blends into the k-ε model

away from the wall. This Shear Stress Transport (SST) formulation thus combines the advantages of

both models, which is why this k-ω STT model is chosen in the current work (Casey and Wintergerste,

2000). The use of a k-ω formulation in the inner parts of the boundary layer makes the model directly

usable all the way down to the wall through the viscous sub-layer. The SST formulation also switches

to a k-ε behavior in the free stream and thereby avoids the common k-ω problem that the model is too

sensitive to the inlet free-stream turbulence properties.

17

2.4.4 Near-wall modeling

As mentioned, the ultimate goal of this master’s thesis is to define the adhesion coefficient of L. pneum.

to the biofilm. It will thus be very important to accurately model the flow field near the biofilm or near

the pipe wall.

As can be seen in Figure 10, turbulent flow near a flat wall can be divided into four regions. At the wall,

the fluid velocity is zero and in a thin layer above this, the velocity is linear with the distance from the

wall. This region is called the viscous sublayer or laminar sublayer. Further away from the wall is a

region called the buffer layer, where turbulence stresses begin to dominate over viscous stresses.

Eventually, the flow becomes fully turbulent and the average flow velocity is related to the log of the

distance to the wall. This region is known as the log-law region. Even further away from the wall, the

flow transitions to the free stream region. A typical property to assess the mesh quality in regards to

near-wall modeling in turbulent simulations is the y+ value, which is defined as the non-dimensional

distance to the wall and is used to measure the distance of the first node away from the wall. A y+ value

of 1 corresponds to the upper limit of the viscous sublayer.

Figure 10. Near-wall turbulent flow (Frei, 2017)

The relationship between the y+ value and the first cell height y, is represented by equation (5), whereas,

∗ is the friction velocity (equation 6), the wall shear stress (equation 7) and the skin friction

coefficient (equation 8).

= ∗ ∗ ∗

(5)

∗ = (6)

= ∗ ∗ ∗ (7)

18

= [2 ( ) − 0.65] . , < 10 (8)

There are two ways of modeling the physics of near-wall flow, which is illustrated by Figure 11. In the

full-resolution approach (Figure 11, right), the boundary layer is resolved all the way down to the

viscous sublayer. This requires the first cell to be placed in the viscous sublayer, where y+ ≤ 1. This

procedure demands computational grid resolution to be very fine and is commonly used with the k-ω

model. Another option is the use of wall functions to model the near wall region (Figure 11, left), which

is mainly used in combination with the k-ε model. In this approach, the first cell needs to be within the

log-layer, which means 30 ≤ y+ ≤ 300 (Bradshaw, 1971). If y+ is too high, the first node is outside the

boundary layer and wall functions will be imposed too far into the domain. If y+ is too low, the first node

will lie in the laminar (viscous) part of the boundary layer, where wall functions are not valid.

Figure 11. Near wall modeling methods for turbulent flow. The red line represents the boundary layer

and yellow dots represent the calculation nodes. On the left, wall functions are used to resolve the

boundary layer (k-ε model), indicating the first cell needs to within the viscous boundary layer. On the

right, the boundary layer is resolved all the way down to the viscous sublayer, demanding computational

grid resolution to be very fine (k-ω model) (Ansys Inc., 2009).

2.5 COUPLING OF MACRO- AND MICRO-SCALE

SIMULATION MODEL

As mentioned before, the first research question in this master’s dissertation will focus on the third part-

model of the (macro-scale) simulation model, namely on the adhesion of L. pneum. from the water

volume to the biofilm in DHW systems. Therefore, this paragraph explains how the exchange rate of

bacteria between these two regions is calculated and/or modeled. In the macro-scale model of Van

Kenhove (2017) the boundary layer theory is applied, whereas in a CFD simulation different possible

methods exist to model bacterial transport, such as the discrete phase and species transport model.

y+{

19

2.5.1 Macro-scale simulation model (Modelica)

In the macro-scale model, bacterial transport of L. pneum. between the biofilm and water volume is

modeled based on the boundary layer theory. This boundary layer is the thin region of flow adjacent to

a surface, where the flow is retarded by the influence of friction between the solid surface and the fluid.

The bacterial exchange between biofilm (boundary layer) and water volume can be expressed with the

rate equation for convective mass transfer. Generalized in a manner analogous to Newton’s law of

cooling, this gives (equation 9):

= ∆ (9)

where the mass flux is the molar-mass flux of the species A measured relative to fixed spatial

coordinates, ∆ is the concentration difference between the boundary surface concentration and the

average concentration of the diffusing species in the moving fluid stream, and is the convective mass-

transfer coefficient (Welty, et al., 1995).

The Reynolds analogy states that the mechanisms for transfer of momentum and energy are identical.

In Welty et al. (1995) this postulation was extended with the transfer of mass in a case were the Schmidt

(Sc) number is unity. This Schmidt number (Sc) plays a role in convective mass transfer analogous to

that of the Prandtl number (Pr) in convective heat transfer. It can be expressed as the ratio of the

molecular diffusivity of momentum to the molecular diffusivity of mass.

In the Reynolds analogy, the convective mass transfer coefficient kc can be obtained from the skin

friction coefficient of the boundary layer (equation 10):

= (10)

For a laminar boundary layer, the skin friction coefficient was determined by Blasius (equation 11):

= .√

(11)

For a turbulent boundary layer, an empirical solution is often used (equation 12):

= .( ) . (12)

This was experimentally verified by von Karman (1934a) for a fully turbulent flow with a Schmidt

number (Sc) of 1.

20

2.5.2 Micro-scale simulation model (CFD)

Mixing and transport of multiple species, which is the case with bacteria transport, as is studied in this

master’s dissertation, can be simulated in CFD software, Ansys Fluent, by various models, such as the

mixture model (liquid-liquid flow) and discrete phase model (liquid-solid flow). In this chapter, the

discrete phase and species mixture model are discussed more in detail.

2.5.2.1 Discrete Phase Model

For flows in which the dispersed phase volume fractions (particles) are less than or equal to 10%, the

Discrete Phase Model (DPM) is the most appropriate and will thus be used in this master’s thesis

(FLUENT Inc., 2001). In DPM simulations L. pneum. bacteria are simulated as inert particles in the

fluid flow. The dispersion of these particles due to turbulence in the fluid phase can be predicted using

the stochastic tracking model or the particle cloud model. By computing the trajectory in this manner

for a sufficient number of representative particles (termed the ‘number of tries'’), the random effects of

turbulence on the particle dispersion can be included. The particle cloud model tracks the statistical

evolution of a cloud of particles about a mean trajectory. The concentration of particles within the cloud

is represented by a Gaussian Probability Density Function (PDF) about the mean trajectory. In both

models, the particles have no direct impact on the generation or dissipation of turbulence in the

continuous phase (FLUENT Inc., 2001). Since this master’s thesis will look closely at the particle

adhesion, it is important to know exactly where the particles attach to the wall surface (biofilm) and thus

the stochastic tracking model will be used.

Trajectories are calculated by integrating the particle force balance equation (equation13), in which the

first and second term respectively represent the drag force and gravity force. The last term represents

additional forces which can be added to the model, such as Brownian motion and pressure gradient

force. An overview of the stochastic trajectory calculations and additional forces is given in the Fluent

manual (FLUENT Inc., 2001).

= − + + (13)

Shen et al. (2015) simulated spherical particle movement for flow across biofilms based on Newtonian’s

law of motion, drag force, and Brownian motion. Drag force was calculated from Stokes equation and

flow velocity. Brownian motion was determined by particle size, dynamic viscosity and a random

number generator factor for particle diffusion. The particles were dispersed in the flow by the drag force

and Brownian motion.

ANSYS Fluent software has built-in conditions and offers the following standard boundary conditions

when a particle strikes a boundary face (FLUENT Inc., 2001):

21

i The particle may be reflected via an elastic or inelastic collision.

ii The particle may escape through the boundary. The particle is lost from the calculation at the

point where it impacts the boundary.

iii The particle may be trapped at the wall. Nonvolatile material is lost from the calculation at the

point of impact with the boundary; volatile material present in the particle or droplet is released

to the vapor phase at this point.

iv The particle may pass through an internal boundary zone, such as radiator or porous jump.

v The particle may slide along the wall, depending on particle properties and impact angle.

Due to the fact that the bacterial microfilm is basically non-removable, Jelenikova et al. (2013), assumed

infinite reference particle adhesion in their simulations by using the DPM boundary condition trap.

However, this is not fully correct since the detachment of biofilm and bacteria cells plays an important

factor in the total (measured) concentration of L. pneum. in DHW systems

Since none of these boundary conditions accurately represents the particle-wall interaction, Shankara

(2010) implemented a deposition model in his simulation using User Defined Functions (UDF), serving

as the boundary condition for the particle wall interactions.

2.5.2.2 Species Transport Model

Similar to the particle trajectory calculations in the DPM, ANSYS Fluent software can also model the

mixing and transport of species by solving conservation equations describing convection, diffusion and

reaction sources for each component species. Multiple simultaneous chemical reactions can be modeled

with reactions occurring in the bulk phase and/or on wall or particle surfaces (Fluent Inc., 2001).

Theoretically, it is thus possible to integrate a biochemical multi-species model of a drinking water

distribution system, as was derived in Arminski et al. (2013). From a practical point of view, integration

of such as a detailed model will however be numerically inefficient since it will make the model too

computational expensive.

When solving the conservation equations, the CFD software predicts the local mass fraction of all

species, , through the solution of a convection-diffusion equation. This conservation equation takes

the following general form (equation 14):

( ) + ∇ ∗ ( )= −∇ ∗ + + (14)

where is the net rate of mass production by a certain chemical reaction and is the rate of mass

creation by addition of mass from the dispersed phase and any other user-defined sources (Fluent Inc.,

22

2001). In the conservation equation above, is the diffusion flux of species i, which arises due to

gradients of concentration and temperature. By default, ANSYS Fluent software uses the dilute

approximation (also called Fick’s law) to model mass diffusion due to concentration gradients. In

laminar flows this diffusion flux can be written as (equation 15.1):

= − ∗ , ∗ ∇ ∗ (15.1)

Here , is the mass diffusion coefficient for specie i in the mixture. In turbulent flows, ANSYS

Fluent software computes the mass diffusion in the following form (equation 15.2):

= − , + ∗ ∇ ∗ (15.2)

= (16)

Where in equation 16 is the turbulent Schmidt number (Sc) with a default value of 0.7, the

turbulent viscosity and the turbulent diffusivity. In general, turbulent diffusion overwhelms laminar

diffusion, making the specification of detailed laminar diffusion properties in turbulent flows not

necessary.

2.5.3 Strong and weak coupling of micro- and macro-scale simulation

models

In order to improve the simulation model of Van Kenhove (2017), a micro-scale CFD model is built in

this work in which the bacterial adhesion coefficient and biofilm temperature will be studied. The CFD

simulations of this work will be coupled with the macro-scale simulations of Van Kenhove (2017), in

such order that the results of the CFD simulations will provide a better estimate of the mentioned

parameters. Coupling a system level simulator, such as the Modelica environment used in the macro-

scale model, with a CFD code can be performed through different approaches, namely weak and strong

coupling (Neyrat & Viel, 2010).

Weak coupling is well suited in case of hydraulic models (or a part of it) which can be reduced to a static

relationship between a small number of lumped variables. This relationship is usually characterized by

performing batch runs in the CFD code and gathering the results in lookup tables.

Strong coupling with a CFD software is usually suited to the coupled transient simulation of an hydraulic

component with its surrounding environment. Due to the nature of the solvers used by CFD code, co-

simulation is generally the only way to couple a Modelica system level simulator and a transient CFD

solver (Marcer, et al., 2010). Viel (2011) describes a methodology and the associated technology for

23

establishing a co-simulation between Modelica system level models with detailed CFD models for

transient simulations. In Ljubijankic et al. (2011), the feasibility of the strong coupling approach is

demonstrated by a use case of a solar thermal system. The numerical coupling and integration of both

submodels (Modelica and CFD) is realized by the use of the co-simulation environment TISC, as

visualized in Figure 12. A detailed CFD submodel allows analysis for detailed questions with full

consideration of the surrounding system model. However, one must keep in mind that strong coupling

requires large computational resources and is very time intensive. Therefore strong coupling has to been

avoided when possible.

Figure 12. Numerical integrated simulation approach using a co-simulation environment (Ljubijankic,

et al., 2011)

Since computational time and numerical efficiency are one of the main requirements of the simulation

model, and no transient simulations are performed, weak coupling will be used between the micro-scale

CFD model, which is built in this master’s dissertation, and the macro-scale simulation model of Van

Kenhove (2017).

24

3 SCOPE AND OBJECTIVE

The aim of this study is gaining knowledge on the effect of pipe flow on different aspects of L. pneum.

infection in DHW systems. To do so, a micro-scale model is built using CFD software, ANSYS Fluent

18.2, representing sections of a DHW pipe. The goal is to investigate several unknown parameters and

use the results of this CFD study as inputs in the existing macro-scale Modelica simulation model by

Van Kenhove (2017). This approach will lead to a better understanding of L. pneum. system infection,

hereby making it possible to optimize temperature regimes, to choose better hydronic controls and to

reduce the energy demand for DHW production, storage and distribution.

In this master’s dissertation a micro-scale model is proposed and results of simulations are analyzed.

The focus mainly lies on two different unknow parameters, namely the bacterial adhesion of L. pneum.

from the liquid fluid flow to the stagnant biofilm, and the variation of temperature in the biofilm

compared to water.

3.1 L. PNEUM. ADHESION

L. pneum. appears both in water and biofilm. Moreover, according to Flemming et al. (2002), 95% of

overall bacterial biomass in DHW systems can be located in biofilms on surfaces, while only 5% occur

in the water volume. A transport of bacteria between the biofilm and water volume exists; in which L.

pneum. adhere from the water volume to the biofilm and vica versa, L. pneum. detach from the biofilm

to the water stream.

One of the simplifications in the macro-scale simulations is that every pipe section of the DHW system

has the same bacterial exchange coefficient. However, due to different flow patterns, a higher exchange

coefficient is expected in critical sections of the DHW system, such as T-sections and turns. By building

a micro-scale simulation model, representing these critical sections of the DHW system, a more detailed

exchange coefficient can be obtained and possibly, a distinction can be made in bacterial exchange

between a straight pipe and those critical sections.

Several authors already have detailed models in which different parameters affecting biofilm detachment

and adhesion were simulated. Picioreanu et al. (2000) used CFD to determine velocity profiles of the

moving liquid and then calculated the propagation of stresses imposed on the biofilm structure. Shen et

al. (2015) performed particle tracing simulation in CFD for flow across biofilms, in which the velocity

distribution and particle movement above the biofilm surface were studied. These models, however,

have the disadvantage of being very detailed and thus computationally expensive. The need thus arises

for a simulation model in which bacterial adhesion and detachment can both be simulated, but still

maintains its numerical efficiency (model requirements are discussed in section 3.3). Moreover, in these

25

simulations (Shen, et al., 2015; Picioreanu, et al., 2000) only laminar and low Reynolds turbulent flows

were simulated. In DHW systems, however, flows can be fully turbulent with Re higher than 30 000 in

small pipe diameters, such as DN32. Since L. pneum. bacteria are dispersed into the fluid flow,

turbulence is expected to play a major role in the adhesion and detachment rates.

In this master’s dissertation, adhesion of L. pneum. from the liquid flow to the biofilm is studied for

different Reynolds numbers (Re) in both a straight pipe and turn section. To do so, a micro-scale model

is built using CFD, representing both sections. The goal of the model is to show the proportionality of

the bacteria adhesion in a turn section to the adhesion in a straight section, with a factor N. To conclude,

the aim is to determine this factor N.

3.2 BIOFILM TEMPERATURE

Bacterial growth is mainly dependent of temperature (Brundrett, 1992), with maximum growth at about

35°C. In a DHW system, 72% of the cultivable bacteria are found to be surface associated in the biofilm

(Bagh, et al., 2004), making the temperature in the biofilm an important factor when modeling L. pneum.

infection risk in DHW systems. In the macro-scale model, bacterial growth in the biofilm is calculated

based on the liquid flow temperature, and not with the temperature in the biofilm, which can assumed

to be lower in certain cases and consequently favoring bacterial growth.

The second research question of this master’s dissertation therefore focuses on the variation of

temperature in the biofilm compared to water. The aim is to check whether the simplification in the

macro-scale model of calculating bacterial growth in the biofilm with the liquid flow temperature in the

is correct, and for which cases this should be updated. To this end, temperature patterns in the biofilm

are studied for various inlet temperatures , insulation thicknesses and biofilm viscosity

.

3.3 MODEL REQUIREMENTS

In the scope of this work, following criteria were considered:

i The model will contain only small pipe sections of the DHW system (e.g. straight pipe

or critical sections) with equivalent length of maximum 1m. Other components of the

DHW system will not be modeled.

ii The simulation tool has to be fast; total calculation should be performed in maximum

24 hours.

iii It should be possible to perform the calculations on a ‘standard’ laptop (8GB RAM -

CPU 2 cores - 2.67 GHz).

26

4 METHODOLOGY AND MODEL

SETUP CFD simulations are performed in order to provide a better estimate of the parameters used in the macro-

scale simulation model of Van Kenhove (2017). In this master’s dissertation, adhesion of L. pneum.

from water volume to the biofilm, and biofilm temperature is studied. In the following sections, an

overview is given of the different aspects and parameters of the simulation setup in ANSYS Fluent,

version 18.2. Subsequently, the geometry and mesh are described, followed by different add-in models,

such as energy and turbulence. Two main simulation models were built in this work, namely a model

for bacterial adhesion and one including the biofilm for studying the temperature in this biofilm.


As discussed in section 2.5.2, different possible approaches in CFD were found in literature to model

bacteria transport. Two possible models are the Discrete Phase Model (DPM) and species mixture

model. In this work, the DPM is used, which was also applied in the particle tracing simulations of Shen

et al. (2015). Although both approaches are possible, for flows in which the dispersed phase volume

fractions (particles) are less than or equal to 10%, the DPM is more appropriate (FLUENT Inc., 2001).

At the end of this work, the parameters for applying the species transport model will also be described

as an alternative approach which can be used in further research.

In particle tracing simulations (using DPM in ANSYS Fluent), L. pneum. bacteria are modeled as

individual inert particles within the water volume. The biofilm region is not modeled because infinite

particle adhesion is assumed by setting the boundary condition for the contact region as “trapped”. As

output, the amount of trapped particles at the wall gives an indication of the amount of bacteria that will

adhere to the biofilm. In Figure 13 the particle tracing simulation approach is illustrated.

Figure 13. Particle tracing simulations using the DPM in FLUENT. Infinite particle adhesion is assumed

by setting the boundary condition trapped, meaning the trajectory calculations are terminated. Ni is the

initial amount of released particles and Ne the total escaped particles.

27

4.1.1 Geometry

Bacteria adhesion simulations are both conducted in the 2D and 3D environment. In the 2D environment,

the feasibility of the DPM is tested for a straight pipe. These 2D simulations, and the applied parameter

values, will then provide an indication for further simulations in the 3D environment.

Since the goal of this master’s dissertation is to show the proportionality of L. pneum. adhesion in a

turn section (90 degrees) to adhesion in a straight section, both sections are modeled in the 3D

environment. Similar to the test rig (section 2.3), these sections are PE-x DN32 with 20mm insulation.

The wall thickness is 3mm and the biofilm region is assumed to have a constant thickness of 3mm, but,

as explained, the biofilm is not modeled.

4.1.1.1 2D simulations

The applied geometry and basic boundary conditions of the 2D model are illustrated in Figure 14. The

flow domain is simplified to a rectangle with a length of 1000mm. By setting the problem setup as

axisymmetric, the height of the flow domain is reduced to 10mm (corresponding to the inner pipe

diameter of 20mm).

Figure 14. Geometry of bacterial adhesion simulation in 2D environment with dimensions and boundary

conditions (velocity inlet, pressure outlet, wall and axis). The blue rectangle represents the flow domain.

4.1.1.2 3D-simulations

In the 3D environment, two different pipe sections are modeled, namely a straight pipe section and a 90

degrees turn. The geometry in the 3D environment is similar to the one in the 2D environment as

explained above in section 4.1.1.1. To reduce the amount of cells in the flow domain, and thus the

computational time, symmetry is applied in both the XY- and XZ-planes.

The turn section is composed of a quarter torus with two cylinders of 500mm on both inlet (X-direction)

and outlet face (Y-direction). Symmetry is applied in the XY-plane. The total pipe length of the turn

section is thus about 1m, which makes it possible to compare with the straight section. The mesh of both

28

sections is composed of a body mesh. Grid convergence is studied to determine the ordered

discretization error. By this mean, the error band for the engineering quantities obtained from the finest

grid solution are determined.

Figure 15. Geometry and boundary conditions of straight pipe in 3D environment for bacterial adhesion

simulations. (a) Longitudinal section of flow domain (blue) with velocity inlet and pressure outlet. (b)

normal section of flow domain. Symmetry is applied in both the XY and XZ plane.

Figure 16. Geometry and boundary conditions of turn section in 3D environment for bacterial adhesion

simulations. (a) normal section (b) longitudinal section of flow domain with velocity inlet and pressure

outlet. Inner and outer diameter of turn are set as wall (biofilm).

(a) longitudinal cross section (XY-plane) (b) normal cross section(YZ-plane)

(b) Normal section (YZ plane)

(a) Longitudinal section (XY plane)

29

4.1.2 Energy model

As mentioned in section 2.1.1, at temperatures above 55°C L. pneum. bacteria are effectively killed and

the DHW system is considered safe. However, in this master’s thesis, a fixed inlet flow temperature

condition of 45°C (318K) is applied in the adhesion simulations. At the pipe wall surface, the heat

transfer coefficient is calculated by equations 17 and 18, in which R is the thermal resistance and

the thermal conductivity. The fluid-side heat transfer coefficient is computed based on the local flow

field conditions (e.g., turbulence level, temperature, and velocity profiles). In the adhesion simulations,

a constant insulation thickness ( ) of 20mm is assumed. The corresponding heat transfer

coefficients for different insulation thicknesses are given in Table II.

= + = + (17)

= [ ] (18)

Table II. Heat transfer coefficient with different insulation layer thickness.

[ ] [ / . ]

0 133.333

10 4.166

20 2.116

30 1.418

4.1.3 Turbulence model and mesh generation


In the 2D environment, the effect of turbulence modeling on particle dispersion is tested by running both

simulations with the standard k-ε turbulence model, as well as with the k-ω STT model. As was

explained in section 2.4.4, both turbulence models require a different y+ value, which is why a different

mesh was made for both models. It can be remarked that the y+ value is dependent on flow velocity, as

can be seen in equation 7. This includes that when there is strived for a constant y+ value in all the

simulations, the mesh should be adapted whenever the inlet velocity is changed. However, in the

simulations of this work, the mesh and grid size are kept constant for the all the flow velocities with one

turbulence model, while y+ is kept between the prescribed boundary conditions.

30

k-ε model

When using the standard k-ε model, the first cell needs to lay within the log-layer, which implies the y+

needs to lay within the range of 30 to 300. This is necessary for the wall functions to model the near

wall region (as was explained in section 2.4.4). To do so, a mapped face mesh was maintained of

2.00mm. The resulting mesh is visualized at the inlet in Figure 17 and obtained y+ values in Figure 18.

Figure 18. y+ values at (biofilm) wall boundary with constant grid size for different flow velocities

(2D, k-ε turbulence model).

0

10

20

30

40

50

60

70

80

90

100

110

0 0,2 0,4 0,6 0,8 1 1,2

Length [m]

0.25 m/s

2.00 m/s

1.75 m/s

1.50 m/s

1.25 m/s

1.00 m/s

0.75 m/s

0.50 m/s

Figure 17. Mesh of straight pipe in 2D environment with k-ε turbulence model (face mesh 2.0mm),

representing the inlet face (left).

Y+ value [-]

31

The corresponding y+ values for the used flow velocities were given in Figure 18. The obtained y+

values are all in the range of 30 to 300. In these simulations, the mesh and grid size are kept constant

for all flow velocities, which explains the higher y+ values for increasing flow velocity. The increase in

y+ at about 0.05m can be explained since a uniform inlet water velocity is set and the fluid flow needs

some length, referred to as the entrance length , to fully develop the (turbulent) velocity profile. The

entrance length is approximated to be ten times the inner pipe diameter (0.02m) which in this case is

0.20m and corresponds to what can be seen in Figure 18.

k-ω model

In the full resolution approach with the k-ω model, the boundary layer is explicitly modeled all the way

down to the viscous sublayer. This requires the first cell to be placed in the viscous sublayer and thus ≤ 1. However, unlike in a 3D environment as will be discussed in section 4.1.1.2, the use of an

inflation layer for setting the first cell height in the 2D environment is not possible. Therefore, to obtain

the right y+ at the wall, a mapped face mesh can be used for the whole domain (as was also done for the

mesh with the k-ε model), with cell face size corresponding to the first cell height as can be calculated

by equation 7. Although the use of such a mapped face mesh is the only method in the 2D environment

which is able to explicitly set the first cell height correctly, this would result in a large amount of cells

and thus a computationally too expensive model. Another method, is the usage of a more coarse mapped

face mesh, plus an edge sizing with bias factor at the in- and outlet of the flow domain. To obtain the

right y+ , a cell size of 0.1mm was chosen with bias factor 25. The mesh is visualized in Figure 19 and

grid information for both simulations with k-ε and k-ω turbulence model is given in Table III. As can

be seen in Figure 18, y+ ≤ 1 for simulation with k-ω turbulence model and highest Re 39808, indicating

that for all applied velocities, the y+ values will be lower than 1.

Figure 19. Mesh of straight pipe in 2D environment with k-ω turbulence model. Mesh consist of face

mesh 0.2mm and bias factor 10 (cells getting smaller to the biofilm interface). (a) Mesh at the inlet

(on the left). Black rectangle represents detail. (b) Detail: bias factor 10 with cells getting smaller to

the biofilm interface.

(a) Mesh at inlet (XY plane) (b) Detail of bias factor (black rectangle)

32

Table III. Grid size (mapped cell size, total number of nodes and total number of elements) for

different used turbulence model in 2D simulations.

Turbulence model Cell size [mm] Bias Nodes [#] Elements [#]

Standard k-ε 2.00 - 3 006 2 500

k-ω SST 0.10 25 1 010 101 100 000


Bacterial adhesion simulations were conducted in the 3D environment for both a straight pipe and turn

section. As was explained in section 4.1.1.2, both geometries have an equivalent pipe length (Leq) of 1m

and can thus be compared. In the 3D environment, the k-ω STT model is used since it is both accurate

for the free stream and near wall performance. The mesh is generated using a body mesh over the whole

flow domain. To obtain ≤ 1 at the wall boundaries, an inflation of 10 layers was added with first cell

height 0.02mm. By doing so, the turbulent layer will be fully captured for all applied velocities. Grid

convergence is studied for the body mesh in the straight pipe section to determine the ordered

discretization error and error band for further results.

Grid convergence study

Shen, et al. (2015) determined that shear stress was the determining factor for bacterial adhesion and

detachment. Therefore, the volume averaged wall shear stress was set as value of interest in this grid

study. To assess the quality of the grid, Roache (1998) suggests a grid convergence index GCI, which

can be calculated as (equation19 and 20):

= ∗|∆|) ∗ 100% (19)

= ∗|∆|∗ ∗ 100% (20)

Where = 3.00, is a factor of safety for comparison over two grids, is the order of convergence (here

= 2) and the refinement ratio, which can be calculated as in equation 21 for a 3D flow domain.

and are respectively the total number of grid points (nodes) of the fine and coarse grid.

= ( ) (21)

The GCI is a measure of the percentage the computed value is away from the value of the asymptotic

numerical value. A small value of GCI thus indicates that the computation is within the asymptotic

range. The table below shows the grid information and the resulting volume averaged shear stress

computed from the solutions. Each solution was properly converged with respect to iterations. Table IV

gives an overview of grid convergence study for the straight pipe section.

33

Table IV. Grid study of bacterial adhesion simulations in 3D environment for straight pipe section

with 1m length.

Grid

Body mesh size

[mm]

Nodes

[#]

Elements

[#]

Av. Shear stress

[Pa]

r

[-]

GCI

[%]

3 1.00 320 528 1 000 089 0.040926476 1.49

1.2417

2 0.75 613 707 2 112 105 0.042668667 0.96

1.05

1.3964

1 0.50 1 671 149 6 439 352 0.044372176 0.54

0,0

0,2

0,4

0,6

0,8

1,0

1,2

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

Length [m]

Figure 20. Y+ value at (biofilm) wall boundary with Re 39808 (2D, k-ω turbulence model)

Y+ value [-]

34

Grid convergence study started with body mesh face size of 1.0mm, which was then refined to 0.75 mm.

This resulted in refinement ratio of 1.2417 and GCI 0.96 % and 1.49 % for respectively the finer (2) and

coarser (3) grid. Since the aim was to have GCI < 1%, the grid was further refined to 0.50 mm, which

resulted in refinement ratio of 1.3964 and GCI 0.54% for the finest (1) grid; which will thus be used in

further calculations and is visualized in Figure 21. Grid information (i.e. number of nodes and elements)

of both straight pipe geometry and turn geometry is given in Table V.

Table V. Grid information (total number of nodes and elements) of both straight pipe and turn in L.

pneum. adhesion simulations in the 3D environment.

Pipe section Nodes [#] Elements [#]

Straight 1 671 149 6 439 352

Turn 3 573 064 14 021 068

In Figure 22, y+ values are shown for both geometries with the above mentioned grid size. The straight

pipe is represented by the black line, where the inner and outer biofilm wall of the turn section are

respectively represented by the red and blue line. Similar to Figure 18, high y+ at the beginning in both

straight pipe and turn section are caused by the entrance length. After the entrance length, ≈ 1 for

the whole straight pipe (black line), and straight section (0.0m-0.5m) in the turn geometry. Fluctuations

in velocity cause the spurious results in y+ after the turn. The velocity profile in the turn section is

therefore dealt with later on in this master’s dissertation (section 5.1.2.2). Although, one could argue

that the y+ is too high after the turn section, further refining the mesh would make the simulation model

unnecessary more computationally expensive. Moreover, Figure 22 represents the y+ values obtained in

simulations with the highest applied inlet velocity of 2.00 m/s (Re = 39808) and thus the highest y+. In

Figure 21. Mesh of straight pipe section in 3D environment with body mesh 0.5mm and inflation

of 10 layers with first cell size 0.02mm. (a) Cross section in YZ plane. (b) Detail of inflation layer.

(a) Cross section of mesh in YZ plane (b) Detail: Inflation layer

Detail (b)

35

other simulations, the inlet velocity is lower, leading to a y+ ≤ 1 on the whole biofilm wall boundary of

the turn.

Figure 22: Y+ values on biofilm wall boundary in straight pipe (black) and turn section: inner side of

turn (red) and outer side of turn (blue) (Re = 39808).

4.1.4 Discrete Phase Model

DPM is used in the particle trajectory approach, in which L. pneum. bacteria are simulated as spherical

particle movement in the flow field based on Newtonian’s law of motion, drag force, and Brownian

motion. Drag force is calculated from Stokes equation and flow velocity. Brownian motion is determined

by particle size, dynamic viscosity, and a random number generator factor for particle diffusion. Finally,

the adhesion of particles is represented by deposition probability, which is calculated by dividing the

final number of adhered particles by the number of total released particles. The simulation is conducted

in the fluid phase and the flow is at steady state.

The threshold of 100cfu/100mL is set as the actual amount of living bacteria in the fluid. Since L. pneum.

bacteria are rod-shaped (0.3 to 0.9μm in width and approximately 2μm in length), their volume is

simplified to a cylinder with an average width of 0.6μm. The volume (V) of one bacteria (one cfu) and

further, the equivalent radius (a) of the spherical particles is thus (equation 22 and 23):

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

2

0 0,2 0,4 0,6 0,8 1

Length [m]

Y+ value [-]

36

= ∙ . ∙ 2 μm = 0.5652 μm (22)

= ∙ ∙ = 0.5652μm ⇒ = 0.5129μm (23)

The particles are injected using a surface injection from the inlet. Turbulent dispersion is modeled with

the Discrete Random Walk (DRW) model and random eddy lifetime. Infinite particle adhesion is

assumed by setting the DPM boundary condition trapped at the wall. The adhesion of particles is

represented by deposition probability, which is calculated by dividing the final number of adhered

(trapped) particles with the total number of released particles.

In the circulation loop (DN32) of the test rig, the fluid flow rate (Qf) is maintained at 2 , thus the

flow rate of the L. pneum. bacteria ( . .) in the flow field can be calculated as in equation 24.

Similar to the simulations of Shen, et al. (2015) particle density ( . .) is set to 1050 kg/m³. Table

VI gives an overview of the parameters used in DPM simulations.

. . = 1000 ∙ 0.5652 ∙ 1050 ∙ 2 = 1.978 ∙ 10 (24)

Table VI. Parameters used in the DPM simulations.


The second research question focuses on biofilm temperature, and checks whether the simplification

made in the macro-scale model of modeling bacterial growth with the liquid flow temperature, is correct.

To make the model in compliance with the assumptions made in previous work (see section 2.2.3), the

biofilm is modeled as a fluid with a substantial higher viscosity compared to the viscosity of the flow

domain. This was also done in the simulations of Cogan (2008), in which the biofilm was assumed to

have a viscosity in the range of 1 to 1000 times the viscosity of water. By running different simulations

with various viscosities, the aim is to develop more insight on the effect of the biofilm’s viscosity on its

Parameter Parameter value Units

Shape Sphere -

Radius 0.51 μm

Density 1050 kg/m³

Flow rate 1.978 ∙ 10 kg/s

Wall boundary condition Trapped -

Number of tries 10 -

37

temperature pattern. Simulation results will be expressed as temperature differences ∆ (equation 25),

where is the liquid flow temperature, and is the temperature at the inner pipe wall (outer biofilm

layer).

∆ = − (25)

Since insulation thickness, inlet temperature and biofilm viscosity are varied, three different simulation

setups are modeled. Firstly, in simulation setup A, inlet flow temperatures are varied between 300K,

318K and 333K for insulation thickness in the range of 0 to 30mm. As can be seen in Figure 3, these

temperatures were identified as critical since bacterial growth is favored between 300K and 318, and

pasteurization starts at temperatures above 333K (Brundrett, 1992). Insulation thicknesses above 30mm

are not modeled since Van Hove (2018) showed that an increase in insulation thickness does not have

an impact anymore on temperature in the DHW pipe.

Secondly, in addition to the results of setup A, the effect of insulation thickness is studied. Finally, In

simulation setup C, the biofilm’s viscosity is varied between 10, 1.0, 1, 0.1 and 0.01 kg/m.s, which

respectively correspond to 10 000, 1000, 100, 10 and 1 times the viscosity of water (i.e. medium in the

fluid flow) for the critical temperature regime of 318K. Table VII gives an overview of the parameters

in the three simulation setups.

Since no particle trajectories will be simulated, only the energy and turbulence model will be enabled in

the ANSYS Fluent Setup.

4.2.1 Geometry and mesh generation

Similar to the bacterial adhesion simulations, a straight DN32 pipe section is modeled with 750mm pipe

length in the 3D environment. The geometry is composed of a circular flow domain with 20mm inner

diameter and an outer biofilm layer of 3mm. The flow domain’s mesh is generated using a body mesh

of 0.5mm with an inflation of 10 layers at the contact zone between biofilm and flow domain. The cell

zone conditions (material properties) are set to water-liquid, which are selected from the Fluent Material

Database.

The mesh of the biofilm region is generated using a body mesh of 0.25mm and an inflation of 10 layers

at the contact zone between biofilm and flow domain with first cell height 0.02mm. The material

properties are set similar to those of water-liquid, except of the biofilm’s viscosity. The total number of

nodes and elements is given in Table VIII.

.

38

Table VII. Biofilm temperature simulations - setup and parameters.

Parameter Symbol Parameter value Units

Simulation A

Dynamic viscosity 10 kg/m ∙ s

Insulation thickness 0 - 30 mm

Inlet temperature 300 – 318 – 333 K

Fluid velocity v 1.0 m/

Simulation B

Dynamic viscosity 10 kg/m ∙ s

Insulation thickness 0 – 10 – 20 – 30 mm

Inlet temperature 318-333 K

Fluid velocity v 1.0 m/s

Simulation C

Dynamic viscosity 10 – 1.0 – 0.1 – 0.01 kg/m ∙ s

Insulation thickness 0 mm

Inlet temperature 318 K

Fluid velocity v 1.0 m/s

Table VIII. Grid size (total number of nodes and total number of elements) for biofilm temperature

simulation model in 3D environment.

Number of nodes Number of elements

9350714 37992798

4.2.2 Energy model

As explained above, in these simulations different insulation thicknesses will be modeled at critical inlet

flow temperatures to develop more insight in the temperature profile in the biofilm region. In Table II,

the different insulation thicknesses and their corresponding heat transfer coefficients, , were given.

In all three simulation setups, a fixed inlet flow condition is set in the flow domain and system coupling

is used at the interface between biofilm and fluid flow domain. At the inlet and outlet zone of the biofilm

region, an adiabatic wall boundary is set (zero heat flux).

4.2.3 Turbulence model

In all three simulation setups, the k-ω SST model is used with an ≤ 1.

39

5 RESULTS

In this section the results of the simulation study, of which the model setup was given in Chapter 4, are

discussed. In analogy to the research questions described in section 1.2, first the bacteria adhesion

simulation results are presented (section 5.1), followed by the results of the biofilm temperature

simulation study (section 5.2). .


In order to determine L. pneum. adhesion in both straight and turn section of a DHW pipe, simulations

are conducted in the 2D and 3D environment. The simulations results obtained in the 2D environment

(section 5.1.1) will give a first indication of the adhesion rates and will then be compared with the results

obtained from simulations in the 3D environment (section 5.1.2).

5.1.1 2D simulations

Simulations in the 2D environment for determining L. pneum. adhesion are only performed for a straight

pipe section to check whether the DPM is applicable in this situation. Firstly, the k-ε turbulence model

was applied (section 5.1.1.1), since this model can be used with a more coarse mesh and thus low

computational time. Afterwards, the use of the k-ω turbulence model is also tested (section 5.1.1.2).

5.1.1.1 k-ε turbulence model

Before discussing the results, the y+ values were checked for the used flow velocities. The obtained y+

values were given in Figure 18 and were all in the range of 30 to 300, which was necessary for the wall

functions to model the near wall region correctly (as was explained in section 2.4.4). Table IX, gives an

overview of the simulation results for deposition probability with different flow velocities in a constant

mesh. The results are also visually represented in Figure 23.

The obtained results are all in the same range, with a mean deposition probability of 66.5%. This

constant deposition can be explained by the homogenous turbulent dispersion in a straight pipe section.

However, the obtained deposition probability is higher than expected. This raises the question if

turbulent dispersion of the particles is accurately modeled.

40

Table IX. Deposition probability for different fluid flow velocities with constant mesh size (2D,

surface injection with 10 tries, straight pipe section, standard k-ε turbulence model).

flow velocity

[m/s]

Reynolds

number

[-]

released

particles

[#]

trapped

particles

[#]

mesh face

size

[mm]

deposition

probability

[%]

0.5 9952 50 33 2.0 66

0.75 14928 50 37 2.0 74

1.00 19904 50 34 2.0 68

1.25 24880 50 27 2.0 54

1.50 29856 50 35 2.0 70

1.75 34832 50 32 2.0 64

2.00 39808 50 35 2.0 70

Mean value 66.5 %

Figure 23. Deposition probability in straight pipe section (2D, k-ε turbulence model, L = 1m).

A first point of discussion can be the use of the k-ε turbulence model, which allows a more coarse mesh

at the wall, since wall functions can be used to model the near wall (turbulent) region. In these

simulations the grid size is kept constant at 2mm, so that the y+ value for all the tested velocities is in

the range of 30 < y+ <300 (Figure 18). However, no data or literature was found on how these wall

0

10

20

30

40

50

60

70

80

0 5000 10000 15000 20000 25000 30000 35000 40000 45000



41

functions affect the turbulent dispersion of particles and deposition probability. This can be a source of

incorrectness.

Another consequences of the coarser grid, is that since surface injection is used, one injection is created

from each face and thus the amount of released particles is low and not fully representable for bacteria

transport. Another type of injection, for example group injection (line) and/or user defined injections,

or increasing the number of tries (i.e. representable particles per face), are a potential solution to this

problem (FLUENT Inc. , 2001)

A first indication of the effect of mesh size on deposition probability was tested by simulating L. pneum.

deposition with varying grid size for a constant velocity of 1.5m/s. The corresponding y+ values are

visually represented in Figure 24. The y+ values are proportional to the mesh face size, which can also

be derived from equation 5. The same reasoning as in Figure 18 can be applied for the increased y+ in

the entrance length. Simulation results are given in Table X and are visually represented in Figure 25.

The results, however, do not show a clear generalized relationship between particle deposition and mesh

coarseness.

Figure 24. Y+ values at pipe wall boundary for varying grid size and constant water velocity 1.5 m/s

(2D, k-ε turbulence model)

0

10

20

30

40

50

60

70

80

90

100

0 0,2 0,4 0,6 0,8 1 1,2

2.00mm

1.60mm

1.40mm

1.00mm

0.80mm

Y+ value [-]

Length [m]

42

Table X. Deposition probability for constant fluid flow velocity and varying mesh size (surface injection

with 10 tries, straight pipe section, standard k-ε turbulence model)

Flow

velocity

(m/s)

Reynolds

number

(-)

Released

particles

(#)

Trapped

particles

(#)

Mesh face

size

(mm)

Deposition

probability

(%)

1.5 29856

130 66 0.8 50.7

100 57 1.0 57.0

70 33 1.4 47.1

60 26 1.6 43.3

50 35 2.0 70.0

Figure 25. Deposition probability for constant fluid flow velocity and varying mesh size (surface

injection with 10 tries, straight pipe section, k-ε turbulence model).

5.1.1.2 k-ω turbulence model

In L. pneum. adhesion simulations with the k-ω turbulence model no deposition of particles was

observed. The Fluent Theory Guide (FLUENT Inc. , 2001) warns that the DRW model may give

nonphysical results in strongly nonhomogeneous diffusion-dominated flows, where small particles

should become uniformly distributed, but instead DRW can show a tendency for such particles to

concentrate in low-turbulence regions of the flow.

0

10

20

30

40

50

60

70

80

0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 2,2

Wall spacing - Mesh size [mm]


43

5.1.2 3D simulations

Bacterial adhesion simulations were conducted in the 3D environment for both a straight pipe and turn

(90 degree). As was explained in section 4.1.1.2, both geometries have an equivalent pipe length (Leq)

of 1m and can thus be compared. Grid convergence was studied in section 4.1.1.2 for the straight pipe

section to determine the ordered discretization error and error band for further results. In the following

sections, deposition probability results are described (section 5.1.2.1), and shear stress and velocity

contours are studied (section 5.1.2.2) to possibly explain the obtained results. .

5.1.2.1 Deposition probability

Deposition probability simulation results for different Reynolds numbers in both a straight and turn

sections with equivalent length of 1m are given in Table XI and are visually represented by Figure 26.

Table XI. Deposition probability for straight and turn pipe section with different flow velocities (3D,

DN32, equivalent length 1m, k-ω SST turbulence model, DPM surface injection with 10 tries).

flow velocity Reynolds number deposition probability [%]

[m/s] [-] straight section turn section

0.1 1990 0 0.95

0.25 4976 0 1.02

0.50 9952 0.36 2.45

0.75 14928 2.07 4.33

1.00 19904 6.52 7.68

1.25 24880 11.11 11.36

1.50 29856 14.23 13.74

1.75 34832 16.66 16.09

2.00 39808 20.00 19.24

Deposition probabilities are notably lower than in 2D simulations with the k-ε turbulence model (Table

IX and Figure 23). This can possibly be explained by the use of the k-ω (SST) turbulence model, in

which the (turbulent) boundary layer is explicitly modeled all the way down to the viscous sublayer.

Turbulent dispersion of particles will thus be modeled more realistically. In the following paragraphs,

the simulation results for L. pneum. adhesion to the biofilm are described more detailed for both the

straight pipe and turn section. In Figure 26, simulations results for L. pneum. adhesion are visually

represented for respectively the straight pipe (black) and turn section (red).

44

Straight pipe section (L = 1m)

As expected, turbulence plays an important role in the adhesion of particles since at the lowest simulated

flow velocities no particle deposition is observed in the straight pipe section. This can easily be

explained by the laminar flow regime, in which individual laminae (sheets) move past one another

without generating cross currents. When the flow becomes turbulent, cross currents and turbulent

dispersion force the particles to move closer to the wall and finally to adhere to the biofilm surface. In

the straight pipe, adhesion of L. pneum. particles was firstly observed at a flow velocity of 0.50m/s,

corresponding to a Reynolds number (Re) of 9952 (≈10 000).

With increasing Re, higher deposition was observed. From Figure 26, one can conclude that for Re <

25 000, corresponding to a flow velocity lower than1.25m/s, deposition probability (and thus adhesion

of L. pneum.) is directly proportional to the second power of Re. At Re higher than 25 000, deposition

probability follows a linear trend. It thus seems that further increase of the Re would lead to even more

deposition of L. pneum. However, further research is needed to confirm the made assumptions.

Moreover, simulations were only conducted with maximum Re of 39808, and extrapolation is assumed

for higher values of Re.

Figure 26. Deposition probability for straight section (black) and turn (red) for different Reynolds

numbers (3D, DN32, equivalent length 1m, k-ω SST turbulence model, surface injection with 10 tries).

Simulation results are represented by filled dots; trendlines in dashed line (added to simulation results).

0

2

4

6

8

10

12

14

16

18

20

22

0 5000 10000 15000 20000 25000 30000 35000 40000



45

Turn section (Leq = 1m)

Deposition probability in the turn section follows the same trends as in a straight section, namely a

parabolic (second power) fit for Re < 25 000 and a linear fit for Re > 25 000. Simulations are performed

with maximum fluid velocity of 2.00 m/s, corresponding to Re 39808. Extrapolation is then assumed for

higher Re. To show how close the obtained deposition probability results are to the fitted trendline, the

coefficient of determination (R²) is used, where a R² of 1 indicates that the model fits the data 100%

correctly. For both the straight and turn section, the R² values are given in Table XII. It can be concluded

that both the parabolic and linear trend fit the results 99% correct. To obtain the factor of proportionality,

N, which had to be determined, trendline function for turn section was reduced with the trendline

function of the straight pipe. In Figure 27, the factor of proportionality is visualized for different Re.

Table XII. Parabolic and linear trendline in both straight pipe and turn section and corresponding R²

values (3D, equivalent length 1m, k-ω SST turbulence model).

Section Re ≤ 25 000 Re > 25 000

Trendline R² Trendline R²

Straight 3 ∙ − 3 ∙ + 0.6738 0.9958 0.0006 ∙ − 3.415 0.9967

Turn 2 ∙ − 3 ∙ + 0.8577 0.9989 0.0005 ∙ − 1.786 0.9946

N −1 ∙ + 2.7 ∙ + 0.1839 - −0.0001 ∙ + 1.629 -

Figure 27. Factor of proportionality in L. pneum. adhesion between straight and turn pipe section(N)

for different Re.

-3

-2,5

-2

-1,5

-1

-0,5

0

0,5

1

1,5

2

2,5

0 5000 10000 15000 20000 25000 30000 35000 40000


Factor of proportionality N in L. pneum. adhesion

46

For Re < 25 000, deposition probability in the turn section is higher than in the straight section.

Moreover, where adhesion of L. pneum. particles in the straight pipe was firstly observed at Re of 9952

(≈10 000), deposition in the turn section already occurred at the lowest simulated flow speeds where Re

was 1990. This can be explained since at turns the flow is forced to move in a certain direction and thus

separates, leading to an increase in turbulence and deposition of L. pneum. This can be seen Figure 28,

where the flow initially follows its turbulent velocity profile (Figure 28c) before the actual turn and then

is separated in the turn (Figure 28b), with an increased velocity on the inner side of the turn. For Re ≥

25 000, deposition probability in both turn and straight pipe sections follow a linear trend, but deposition

probability is higher in the straight section. However, as was already mentioned, further research and

thus more simulations are needed to confirm the obtained results and made conclusions.

Since Shen et al. (2015) determined that shear stress mainly controls bacterial adhesion and detachment,

the shear stress at the wall boundaries of the flow domain (e.g. contact zone with biofilm) in the turn

section is studied in the next section to possibly explain the observed trends in deposition probability.

47

Figure 28. Velocity contours in turn section (uniform inlet velocity of 2.00 m/s, Re 39808). (a) Velocity

contour of whole turn section in XY plane. (b) Detail of velocity contour in the turn section (XY plane).

(c) Detail of velocity contour before turn (XZ plane). (c) Detail of velocity contour after turn (YZ plane).

(c) Detail 2: Velocity contour before turn (d) Detail 3: Velocity contour after turn

(a) Velocity contour of turn section

(b) Detail 1: Velocity contour in turn section

Detail 1

48

5.1.2.2 Shear Stress

Wall shear stress is observed for all applied flow velocities on the inner (Figure 29, red line) and outer

wall (Figure 29, blue line) in the XY plane of the turn section. In Figure 30, shear stress on both walls

is visually represented for Re 39808, corresponding to the highest simulated flow velocity of 2.00 m/s.

In Appendix I; similar charts are given for the other simulated flow velocities.

Figure 29. Illustration of turn section with inner pipe wall (red line) and outer pipe wall (blue line).

Figure 30. Shear stress at wall boundary (e.g. contact zone between fluid flow and biofilm) in XY plane

for inner pipe wall (red line) and outer pipe wall (blue line) of turn section with Re 39808 (flow velocity

2.00 m/s).

0

2

4

6

8

10

12

14

16

18

20

22

24

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

Length L [m]

Wall Shear Stress [Pa]

49

Similar to the increase in y+, as was explained in section 4.1.3.1 and can be seen in Figure 18, the high

wall shear stress at the start is caused by the entrance length Lh, in which the fluid flow develops its

turbulent velocity profile. The entrance length was approximated to be ten times the inner pipe diameter

(Lh = 0.20m). As seen in Figure 16 and described in section 4.1.1.2, the turn section is consecutively

composed of a straight section (0m-0.5m), a 90 degree turn (0.5m-0.6m) and straight section (0.6m-

1.1m). In the first straight section (0m-0.5m), the shear stress on both inner and outer pipe wall are

equally high and are approximated to be constant. As was seen in Figure 28, velocity increases at the

inner side of the turn and thus leading to the first peak (red line, L=0.5m) in shear stress. After this

maximum, consecutively a minimum peak (red line, L=0.5m-0.6m) and low shear zone (red line,

L=0.6m-1.1m) are observed at the inner wall of the turn. In contrast, on the outer side of turn, firstly a

minimum in shear stress is observed (blue line, L=0.5m) followed by the maximum shear stress (blue

line, L=0.6m) and high shear stress zone blue line (L=0.6m-1.1m). These high and low shear zones can

be explained with the fluid flow stream. In the turn, the fluid flow scours against the inner wall of the

turn and thus leading to the maximum peak in wall shear stress at the inner wall and minimum peak for

the outer wall (L=0.5m). The flow stream then gets separated from the inner wall; causing the minimum

peak, and impinges the outer wall, which there leads to the maximum peak (L=0.6m) After the turn, a

high shear zone is observed at the outer side of the turn, and similarly, a low shear zone exists on the

inner side of the turn (L=0.6m-1.1m). Since shear stress controls bacterial adhesion and detachment

(Shen, et al., 2015), the increased shear stress and velocity could thus explain the higher deposition

probabilities in the turn section, as was described in section 5.1.2.1.

Equation 7 determines that shear stress is proportional to the skin friction coefficient and flow velocity,

and thus mainly is dominated by turbulence in the pipe. This trend can also be seen in Appendix I: Wall

Shear Stress on biofilm of turn for different Re where shear stress charts, similar to Figure 30, were

given for all simulated inlet velocities. To check whether the shear stress observed in the simulations of

this work corresponds to the theoretical wall shear, Figure 31 shows the mean wall shear stress observed

in the simulations (black line) for all applied velocities versus theoretical determined values of the wall

shear stress. In green, wall shear stress is calculated with skin friction coefficient as determined in the

boundary layer theory of section 2.5.1 by equation 11 and 12. Purple results show wall shear stress

which is calculated with skin friction coefficient as determined by equation 8. Mean wall shear stress

was calculated for the straight section before the turn, between 0.2m and 0.4m. The first 0.2m were

neglected due to the entrance length. Mean wall shear stress from simulation results is lower than

theoretical determined values for the same Re. The obtained results, however, do show the same

parabolic trend and can thus be assumed correct.

50

Figure 31. Mean wall shear stress for simulation results (CFD, black line), and theoretical values in

which skin friction coefficient was calculated by equation 11 and 12 ( green), and equation 7 (purple).

Mean wall shear in simulation results (black) was calculated in straight section before the turn, between

0.2m and 0.4m.

To possibly explain the parabolic and linear trend with increasing Re for deposition probability, as was

seen in Figure 26 and described in section 5.1.2.1, the mean standardized variation in wall shear stress

is studied for both the low shear stress zone after the turn on the inner wall, and high shear stress zone

on the outer wall after the turn. Results are visually represented by

Figure 32, in which red line represents the inner pipe wall (low shear zone), and blue line the outer pipe

wall (high shear zone). To come to the mean standardized variation, first the mean value of both the low

and high shear stress zone were calculated between 0.7m and 0.9m. These values were then divided by

the mean shear stress in the straight section before the turn between 0.2m and 0.4m.

With increasing Re, mean variation in low and high shear stress zone also increases. For Re < 25 000,

absolute variation between straight section and low shear zone (red) is up to 5 times higher than

standardized variation in high shear zone (blue). For Re > 25 000, both standardized variations are,

approximately, equal.

0

2

4

6

8

10

12

0 5000 10000 15000 20000 25000 30000 35000


Mean Wall Shear Stress [Pa]

CFD

Eq. 7

Eq. 11+12

51

Figure 32. Standardized mean variation in shear stress for both inner wall of turn section (low shear

zone, red) and outer wall of turn section (high shear zone, blue).


The second research question focuses on biofilm temperature and checks whether the simplification

made in the macro-scale model of modeling bacterial growth in the biofilm with the liquid flow

temperature is correct. In these simulations, the biofilm is assumed to have a substantial higher viscosity

compared to the viscosity of water ( ≥ 100 ∙ ). In the macro-scale model, however, the

biofilm has the same material properties as the flow stream. Therefore, simulations are both performed

with ≥ 100 ∙ , as well as with low biofilm viscosity ( ≤ 10 ∙ ). The

simulations with = could then serve as a reference for the macro-scale model.

As described in section 4.2 and summarized in Table VII, the problem is divided into three different

simulation setups. Subsequently, the effect of inlet flow temperature, insulation thickness and biofilm

viscosity is studied.

-3,5

-3

-2,5

-2

-1,5

-1

-0,5

0

0,5

1

1,5

2

2,5

3

3,5

0 5000 10000 15000 20000 25000 30000 35000 40000


Standardized mean variation in Wall Shear Stress [Pa]

52

5.2.1 Inlet flow temperature

In the first simulation setup, inlet fluid temperatures are varied between 300K, 3178K and 333K for

different insulation thickness. The obtained results are given in Table XIII and are visually represented

in Figure 33, where insulation thicknesses 0mm, 10mm, 20mm and 30mm, respectively are represented

by the black, red, green and purple line. A linear trend is observed between temperature difference for

a certain insulation thickness and inlet flow temperature. At inlet flow temperatures of 318K and 333K,

temperature differences pipes with no insulation (0mm) are markedly higher than for pipes with

insulation (10mm, 20mm and 30mm). This can easily be explained by the combination of high heat

transfer coefficient Uh (Table II) with high temperature difference between flow (318K – 333K) and

environment (295K).

Figure 33. Temperature difference in function of inlet flow temperature for given insulation thickness:

0mm (black), 10mm (red), 20mm (green), 30mm (purple), with assumed ≥ 100 ∙ .

Table XIII. Temperature difference ∆T [K] for different insulation thickness dinsulation [mm] and inlet

flow temperature Ti [K].

Insulation thickness Temperature difference ∆T [K]

dinsulation [mm] Ti = 300K Ti =318K Ti =333K

0 4.733 21.773 35.973

10 1.785 8.210 13.566

20 1.785 5.063 8.365

30 0.796 3.660 6.048

0

5

10

15

20

25

30

35

40

300 318 333

10mm

20mm

30mm

Inlet flow temperature [K]


0mm

53

5.2.2 Insulation thickness

In order to provide a better overview of the relation between temperature difference and insulation

thickness, the temperature differences from Figure 33 were plotted in function of the insulation

thickness for given flow temperatures in Figure 34. Logically, the same trends are observed as in Figure

33; with increasing insulation thickness, temperature difference between liquid flow and inner pipe wall

decreases. Moreover, as was already described by Van Hove (2018), temperature differences seem to

reach an asymptotic value for insulation thicknesses above 30mm.

Figure 34. Temperature difference as a function of insulation thickness for given inlet flow temperature:

333K (red), 318K (blue), 300K (black) with assumed ≥ 100 ∙ .

5.2.3 Biofilm viscosity

In the third simulation setup, is varied between 10, 1.0, 1, 0.1 and 0.01 kg/m.s for the critical

temperature regime of 318k. These viscosities are respectively 10 000, 1000, 100, 10 and 1 times .

For ≥ 100 ∙ , the obtained temperature patterns are, approximately, equal and follow a

linear trend in the biofilm. The temperature pattern for ≥ 100 ∙ is represented by the

solid blue line in Figure 35. The red line in Figure 35 represents the temperature profile for simulation

with ≤ 10 ∙ . It thus seems that for ≤ 10 ∙ , temperature in the biofilm

does not cool down. The obtained temperature profile can however not be correct, since this would

imply that a temperature difference of 20K exists over the pipe wall.

0

5

10

15

20

25

30

35

40

0 10 20 30

333K318K300K

Insulation thickness [mm]


54

Figure 35. Temperature pattern in flow domain (0-10mm radius) and biofilm (10-13mm radius) at cross

section (0.50m) for biofilm viscosity of ≥ 100 ∙ (blue line) and ≤ 10 ∙

(red line). Inlet temperature 318K, with 0mm insulation. Dashed black line represents boundary between

fluid flow and biofilm.

In the simulations with ≤ 10 ∙ flow occurred in the biofilm, as shown in Figure 36,

which could possibly cause the incorrect temperature profile in the biofilm.

Figure 36. Velocity profile (solid red line) in flow domain (0-10mm radius) and biofilm (10-13mm

radius) at cross section (0.50m) with ≤ 10 ∙ .

295

300

305

310

315

320

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0

0,2

0,4

0,6

0,8

1

1,2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Pipe radius [mm]

Temperature [K]

Pipe radius [mm]

Fluid flow velocity [m/s]

55

6 MODEL IMPROVEMENTS

6.1 L.PNEUM. ADHESION

Bacterial transport between biofilm and water volume consists both of adhesion and detachment.

However, in this master’s dissertation, only adhesion of L. pneum. from the water volume to the biofilm

is studied in both a straight pipe and turn section. Moreover, as mentioned in the previous sections, more

simulations are needed both to provide more data, and to confirm the made assumptions.

As discussed in section 2.5.2, different possible approaches in CFD were found in literature to model

bacteria transport. In this work, the DPM is used, but the Species Transport Mixture Model can be used

as a worthy alternative in further research. In the following sections, therefore, model improvements are

discussed for the DPM (section 6.1.1.1) and parameters for applying the species transport mixture are

described (section 6.1.1.2).

6.1.1.1 Discrete Phase Model

Infinite particle adhesion was assumed by setting the boundary condition for the wall as trapped.

Deposition probability was then calculated by dividing the final number of adhered (trapped) particles

with the total number of released particles. The trapped DPM boundary condition implies that whenever

a particle hits the wall, regardless of its velocity or angle, the trajectory calculations are terminated. By

doing so, only adhesion is simulated and particle detachment is neglected. However, as was written in

section 2.2 BIOFILM, biofilm and cell detachment play an important role in the total L. pneum.

concentration and thus in the bacterial exchange coefficient. Moreover, the higher wall shear stress

observed in the turn section will cause more detachment (Moreira, et al., 2014; Shen, et al., 2015).

Therefore, in further work adhesion and detachment of L. pneum. bacteria should both be accurately

modeled. This can be done by implementing a deposition model using a UDF, serving as the boundary

condition for particle wall interaction. The deposition model of Shankara (2010) can hereby serve as a

starting point. With equation 1, Xavier et al. (2005) proposed a general method for describing biomass

detachment using a continuous detachment speed function in which could take several forms,

including expressions dependent on any state variable. When improving the model with such a UDF,

the following points should be taken in mind:

Temperature dependence

In the DPM-simulations of the current work a constant inlet water temperature of 45°C is used. This

temperature regime is assumed to be the most critical, since temperature losses to the environment will

cause the biofilm region to cool down to temperatures where bacterial growth is favored. Other

56

temperature regimes should also be studied since the main objective of the macro-scale simulation is to

reduce the energy demand for DHW production by optimizing temperature regimes.

In this work, the particles are injected using a surface injection from the inlet, by which the amount of

released particles is determined by the number of cell faces at the inlet. The particles are then given an

amount of mass, corresponding to the flow rate. In further work, the amount of released particles can be

determined by a bacterial growth function which is dependent on the inlet flow temperature. The same

reasoning can be applied to the interface between biofilm and fluid flow.

Biofilm roughness and shear stress

Shen, et al., (2015) identified that L. pneum. adhesion was enhanced by biofilm roughness because of

the increased interception between the flowing particles and the surface on rough biofilms. After the L.

pneum. particles adhered to the biofilm, subsequent cell detachment was facilitated by high average flow

velocity. Biofilm roughness could protect L. pneum. from detachment by creating larger low shear stress

zones. On the other hand, high shear stress zones caused the equally high detachment of L. pneum. from

both smooth and rough biofilm surfaces.

6.1.1.2 Species Transport Model

As an alternative approach, the potential of the Species Transport Model should be studied. In this

approach, L. pneum. bacteria can be modeled as an inlet concentration within a mixture with the bulk

water phase, using a mixture template of the species transport model. The method is visually represented

in Figure 37, where Ci and Ce are respectively the inlet and outlet concentration of L. pneum. in the

mixture. In this section the parameters for modeling bacterial adhesion with the Species Transport Model

will be further discussed.

Figure 37. Diffusive coefficient method (Species Transport Model)

57

As the starting point, the mixture should only contain the liquid water phase, which can be easily added

from the Fluent Material Database, and the L. pneum. bacteria. Later on, nutrients and their interaction

with L. pneum. could be added.

For the pressure based solver in ANSYS Fluent, the net transport of species at inlets consists of both

convection and diffusion components. The convection component is fixed by the specified inlet species

mass, whereas the diffusion component depends on the gradient of the computed species concentration

field (which is not known a priori). The L. pneum. mass fraction at the inlet Ϻ . , (e.g. kg of L.

pneum. in 1 kg of the mixture), can be calculated based on equation 26, in which the same

simplifications, regarding the threshold of 1000cfu/L and L. pneum. density were made as with DPM.

Ϻ . , = 1000 ∙ 0.5652 ∙ 1050 = 5.935 ∙ 10 (26)

As was explained in section 2.5.2.2, ANSYS Fluent uses the dilute approximation (also called Fick’s

law) to model mass diffusion, in which the mass-diffusivity coefficient , [m²/s] needs to be specified.

In Shen et al. (2015) the diffusion coefficient was calculated from the Stokes-Einstein equation

(equation 27) (Clark, 2012) and was then used to calculate the dimensionless Sherwood number (Sh),

which represented the ratio between mass transfer by convection and mass transfer by diffusion.

D , = ∙ ∙ ∙

(27)

In the above equation, K is Boltzmann constant, T temperature, the viscosity of the fluid and a is the

equivalent radius of L. pneum. cells [m], as was determined by equation 16. The mass diffusion

coefficient can also be defined as a polynomial function of temperature (equation 28), which brings

possibilities in modeling bacterial growth.

, = + + + ⋯ (28)


Biofilm temperature simulations are performed to evaluate whether the simplification made in the

macro-scale model of modeling bacterial growth in the biofilm as a function of free stream temperature,

is correct. To make the model in compliance with the assumptions made in previous work (see section

2.2.3), the biofilm was modeled as a fluid with ≥ 100 ∙ . In the macro-scale model,

however, the biofilm has the same material properties as the flow stream (e.g. water). Therefore, the

idea was to both conduct simulations with ≥ 100 ∗ , as well as with low biofilm

viscosity ( ≤ 10 ∙ ) The simulations with = could then serve as a

reference for the macro-scale model.

58

However, for ≤ 10 ∙ , flow occurred in the biofilm causing a non-realistic temperature

profile (Figure 35 and Figure 36). A possible approach to prevent flow occurring in the biofilm, is the

use of a meshed solid zone as biofilm, as is illustrated in Figure 38. By doing so, the energy equation is

solved in a solid zone representing the biofilm. Similar to the fluid-fluid interface when the biofilm is

modeled as fluid with substantial higher viscosity than water, a coupled thermal boundary condition

should be used at the fluid-solid interface (Ansys Inc., 2006).

Figure 38. Representing the biofilm as a meshed solid zone with coupled wall at interface between solid

biofilm and fluid flow.

59

7 CONCLUSION AND DISCUSSION

A simulation model is developed by Van Kenhove et al. (2015) that allows assessing the L. pneum.

infection risk under dynamic conditions. In order to improve the parameters of this macro-scale

simulation model, a micro-scale model is built in this work using CFD, representing different sections

of a DHW pipe. This (weak) coupling approach will lead to a better understanding of L. pneum. system

infection, hereby making it possible to optimize temperature regimes, to choose better hydronic controls

and to reduce the energy demand for DHW production, storage and distribution.

Focusing on the simplifications made in the macro-scale model, two research questions were

determined. Firstly, the adhesion of L. pneum. from the liquid flow to the biofilm was studied, since in

the macro-scale model every DHW pipe section has the bacterial exchange coefficient between biofilm

and water volume. The goal was to investigate the adhesion in both straight pipe and turn section, and

show the proportionality of adhesion in a turn section to the adhesion of a straight section, with a factor

N. All in one, the aim was thus to determine this factor N.

The second research question focused on biofilm temperature and checks whether the simplification

made in the macro-scale model of calculating L. pneum. growth in the biofilm as a function of

temperature in liquid fluid flow, is correct. The problem was divided into three different simulation

setups, in which subsequently the effect of inlet flow temperature , insulation thickness ,

and biofilm viscosity was studied.


In order to determine L. pneum. adhesion in both straight and turn section of a DHW pipe, simulations

were conducted in the 2D and 3D environment. Different possible approaches in CFD were found in

literature to model bacteria transport, of which the DPM was chosen over the Species Transport Model.

In DPM simulations, L. pneum. are modeled as individual inert particles within the water volume and

infinite particle adhesion is assumed by setting the boundary condition at the interface between biofilm

and fluid flow as trapped. Deposition probability was then calculated by dividing the total number of

trapped particles with the number of released particles at the inlet.

In the 2D environment, L. pneum. adhesion simulations were only performed for a straight pipe section

to assess the feasibility of the DPM. Firstly, the k-ε turbulence model was applied since this model can

use wall functions to model the near wall region, which requires a more coarse mesh and thus low

computational time. Afterwards, the k-ω turbulence model was also applied. However, the 2D

environment did not show proper results since in simulations with the k-ε turbulence model, an

60

unrealistic high mean deposition probability of 66.5% was observed. Moreover, when applying the k-ω

turbulence model, no deposition of L. pneum. was seen at all.

The high deposition probability in k-ε turbulence simulations can be caused since the k-ε model shows

poor results near wall boundaries and needs to be combined with wall functions. However, no data is

available on how these wall functions affect the deposition of particles. Moreover, DPM surface

injection of particles was used, which implies that an amount of particles, corresponding to the number

of tries (i.e. representable particles) is released from each inlet face. With a coarse grid, as in the k-ε

turbulence simulations, surface injection thus results in a low amount of released particles, making the

observed deposition probability less accurate. No clear explanation exists why no deposition was seen

in simulations with the k-ω turbulence model. Possibly, the use of the Discrete random Walk (DRW) in

DPM, affects the solution as was also mentioned in the Fluent Theory Guide (FLUENT Inc., 2001).

In the 3D environment, L. pneum. adhesion simulations were performed for both a straight pipe and

turn. Grid convergence was studied for the straight pipe, which resulted in a GCI of 0.54% and thus is

accurate. As expected, turbulence plays an important role in the adhesion of particles since at the lowest

simulated flow velocities, no particle deposition is observed in the straight pipe section due to the

laminar flow regime. In contrast, in the turn, the flow is forced to move in a certain direction and

separates, leading to an increase in turbulence and deposition of L. pneum.

For Re < 25 000, deposition probability (and thus adhesion of L. pneum.) is proportional to the second

power of the Re. Besides, deposition probability of L. pneum. is higher in the turn section, but increases

less with Re than in the straight pipe. For Re > 25 000, deposition probabilities in straight pipe and turn

section follow a linear trend, but are higher in the straight pipe. Simulations were only performed till

maximum flow velocity of 2.00m/s in DN32 pipe section, corresponding to a Re of 39808. Extrapolation

was then assumed for higher values of Re. The factor of proportionality in L. pneum. adhesion of a turn

section to a straight pipe, which had to be determined, as a function of Re is:

< 25 000 = −1 ∙ + 2.7 ∙ + 0.1839

> 25 000 = −0.0001 ∙ + 1.629

Immediately after the turn, a low and high shear zone are observed on respectively the inner and outer

side of the turn. With increasing Re, mean variation in low and high shear stress zone also increases. For

Re < 25 000, absolute variation between straight section (before turn) and low shear zone (after turn) is

up to 5 times higher than standardized variation in high shear zone. For Re > 25 000, both standardized

variations are, approximately, equal and could thus possibly explain the above trends in deposition

probability.

61

In this master’s dissertation only adhesion of L. pneum. is studied. In further work, adhesion and

detachment of L. pneum. should both be accurately modeled to have a better understanding of the whole

bacterial exchange coefficient. Therefore, a UDF is proposed as possible model improvement, which

could serve as the DPM boundary condition for the particle wall interaction.


Simulations are performed (in the 3D environment) in which the biofilm is assumed to have a substantial

higher viscosity compared to the viscosity of water ( ≥ 100 ∙ ). In the macro-scale

model, however, the biofilm has the same material properties as the flow stream. Therefore, simulations

(in the 3D environment) are both performed with ≥ 100 ∙ , as well as with low biofilm

viscosities ( ≤ 10 ∙ ).

With ≥ 100 ∙ , a linear trend was observed in temperature difference (between fluid

flow and inner pipe wall) for a certain insulation thickness and inlet flow temperature. Logically, a

reciprocal trend was seen between temperature difference (between fluid flow and inner pipe wall) and

insulation thickness for a given inlet flow temperature. As was already described by Van Hove (2018),

temperature differences seem to reach an asymptotic value for insulation thicknesses above 30mm,

indicating that further increase in insulation thickness does not result in lower heat losses to the

environment. For these high viscosities ( ≥ 100 ∙ ), temperature patterns in the biofilm

showed a linear trend, where temperatures in the flow domain not seem to cool down. Temperature

losses to the environment thus cause the biofilm to cool down to temperatures where bacterial growth is

favored.

For simulations with ≤ 10 ∙ , flow occurred in the biofilm causing a non-realistic

temperature profile. The use of a meshed solid zone as biofilm is therefore proposed as model

improvement.

62

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66

APPENDIX

Appendix I: Wall Shear Stress on biofilm of turn for different Re……………………………………64

67

Appendix I: Wall Shear Stress on biofilm of turn for different Re

Figure I - 1: Wall Shear Stress on biofilm of turn section for Re 1990. Inner biofilm wall of turn (red) and outer biofilm wall (blue).

Figure I - 2:Wall Shear Stress on biofilm of turn section for Re 4976. Inner biofilm wall of turn (red) and outer biofilm wall (blue).

0,00

0,05

0,10

0,15

0,20

0,25

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1

Wal

l She

ar S

tres

s [Pa

]

Curve length [m]

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

Wal

l She

ar S

tres

s [Pa

]

Curve length [m]

68



0,0

0,5

1,0

1,5

2,0

2,5

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

Wal

l She

ar S

tres

s [Pa

]

Curve length [m]

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

Wal

l She

ar S

tres

s [Pa

]

Curve length [m]

69



0

1

2

3

4

5

6

7

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

Wal

l She

ar S

tres

s [Pa

]

Curve length [m]

0

2

4

6

8

10

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

Wal

l She

ar S

tres

s [Pa

]

Curve length [m]

70



0

2

4

6

8

10

12

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

Wal

l She

ar S

tres

s [Pa

]

Curve length [m]

0

2

4

6

8

10

12

14

16

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

Wal

l She

ar S

tres

s [Pa

]

Curve length [m]

71


0

4

8

12

16

20

24

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

Wal

l She

ar S

tres

s [Pa

]

Curve length [m]

72

Table I - 1: Mean wall shear stress and standardized mean variation in shear stress for different Re.

Flow velocity

v [m/s]

Reynolds number

Re [-]

Mean Wall Shear Stress

, [Pa]

Standardized mean variation in Shear

Stress ∆ , [Pa]

Straight

(0m-0.5m)

Outer wall turn

(blue)

Inner biofilm

wall turn (red)

Outer wall turn

(blue)

Inner wall turn

(red)

0.10 1990 0.13081 0.12807 0.11102 -0.00274 -0.01979

0.25 4976 0.37592 0.31107 0.28583 -0.06485 -0.09009

0.50 9952 1.03187 1.09096 0.72395 0.05909 -0.30792

0.75 14928 2.03073 2.22015 1.40826 018942 -0.62247

1.00 19904 3.40011 4.18926 2.26743 0.78916 -1.13268

1.25 24880 4.91299 5.71751 3.52590 0.80452 -1.38709

1.5 29856 6.75823 8.37447 5.09598 1.61625 -1.66225

1.75 34833 8.98823 11.03669 6.68797 2.04846 -2.30025

2.00 39808 22.49338 14.59011 8.37020 3.09673 -3.12318

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