36_georgescu

7/29/2019 36_Georgescu

1/10

Scientific Bulletin of thePolitehnica University of Timisoara

Transactions on MechanicsTom 52(66), Fascicola 6, 2007

2nd

IAHR International Meeting of the Workgroupon Cavitation and Dynamic Problemsin Hydraulic Machinery and Systems

Timisoara, RomaniaOctober 24 - 26, 2007

NUMERICAL MODELLING COMPARISON BETWEEN AIRFLOWAND WATER FLOW WITHIN THE ACHARD-TYPE TURBINE

Andrei-Mugur GEORGESCU *

Hydraulic and Environmental Protection Department,Technical Civil Engineering University Bucharest

Sanda-Carmen GEORGESCU

Hydraulics and Hydraulic Machinery Department,University Politehnica of Bucharest

Mircea DEGERATU

Hydraulic and Environmental Protection Department,

Technical Civil Engineering University Bucharest

Sandor BERNAD

Centre of Advanced Research in Engineering Sciences,

Romanian Academy Timioara BranchCostin Ioan COOIU

Hydraulic and Environmental Protection Department,Technical Civil Engineering University Bucharest

*Corresponding author: 124 Bd Lacul Tei, Sector 2, Bucharest, 020396, Romania

Tel.: +40212433660, Fax: +40212433660, E-mail: [email protected]

ABSTRACT

The purpose of the present numerical study is to

assess a relatively rough, but quick way, to estimate

the forces acting on an experimental model of theAchard cross-flow turbine that is to be tested in an

aerodynamic wind tunnel. Under normal conditions,

the Achard turbine runs in water, but in order to ac-

curately investigate the flow field inside the turbine,

an experimental set-up of a 1:1 geometric scale model

has to be built, and measurements have to be per-

formed in a wind tunnel (at such a scale, the model

would require a huge channel if tested in water).

Building the model in itself requires at least an ap-

proximate knowledge about the values of forces that

will act upon it during the experiments; such values

can be obtained conveniently through numericalsimulations. Using COMSOL Multiphysics 3.3a

software, a 2D numerical study of the unsteady flow

inside the Achard turbine has been performed, both for

water and air (the latter based on criteria derived for

such a case of similitude). The computed dynamic

forces for a horizontal cross-section of the turbine

agree well with experimental data available for twin

cases, and could be used, in the sequel, to compute

roughly the forces acting on the turbine experimen-

tal model.

KEYWORDS

Achard turbine, cross-flow water turbine, airfoil,

pressure coefficient, force coefficient

1. INTRODUCTION

In 2001, the Geophysical and Industrial Fluid

Flows Laboratory (LEGI) of Grenoble, France,

launched theHARVESTProject (Hydroliennes Axede Rotation VErtical STabilis), to develop a suitable

technology for marine and river hydro-power farms

using cross-flow current energy converters piled up

in towers [13]. In 2006, the Technical Civil Engi-

neering University Bucharest, in collaboration with

the University Politehnica of Bucharest and the

Romanian Academy - Timisoara Branch, started the

THARVESTProject, within the CEEXProgram sus-

tained by the Romanian Ministry of Education and

Research [4]. The THARVESTProject aims to study

experimentally and numerically the hydrodynamics

of this new concept of water-current turbine, calledAchard turbine, in collaboration with the LEGI part-

ners involved in the HARVESTProject. The Achard

turbine, a cross-flow marine or river turbine with

vertical axis and delta blades is suitable to produce

the desired power by summing elementary power

provided by small turbine modules.

In Figure 1 we present theAchard turbine module.

It consists of a runner with three vertical delta blades,

sustained by radial supports at mid-height of the

turbine, and stiffened with circular rims at the upper

and lower part. The blades are shaped with NACA4518 airfoils [5]. The turbine main geometric dimen-

sions are: the runner radius 5.0=R m, the runner

height 1=H m, and the shaft radius of 0.05 m.


2/10

Proceedings of the 2nd IAHR International Meeting of the Workgroupon Cavitation and Dynamic Problems in Hydraulic Machinery and Systems290

Figure 1. The Achard turbine [LEGI courtesy]

Within this paper, the 2D computations correspond

to the horizontal cross-plane placed at mid-height of

the turbine, without radial supports (Fig. 2), where

the three blade profiles have the mean camber line

length 18.00 =c m (the maximum value of 0c along

the delta wing), and the chord length 179.0=c m.The values of the azimuthal angle of the blades are

{ }ooo 240;120;0= , in counter clockwise direction.

0.6 0.4 0.2 0 0.2 0.4 0.60.5

0.4

0.3

0.2

0.1

0

0.1

0.2

0.3

0.4

0.5

x [m]

y[m]

= 0o

= 120o

= 240o

Figure 2. Computational runner cross-section

In this paper we focus on the 2D numerical mod-

elling of the unsteady flow inside the Achard turbine.

A complete 360 turn of the blades is analysed. The

simulations are performed with COMSOL Multiphysics3.3a software [6]. A test case of the steady flow around

a cylinderis performed in order to tune up the input

parameters for the unsteady computations. The results

of the 2D numerical simulations of the three blades

runner modelfrom Fig. 2 turning in water and air, as

well as the results obtained fora twin unsteady test

case, namely asingle blade runner model, are com-

pared to similar experimental data available in the

literature [7].

2. HYDRAULIC SIMILITUDE

In order to accurately design the experimental

model of the Achard turbine module that is to be

tested in the wind tunnel, and particularly, to design

the system that will ensure its rotation, together with

the supports that will hold the model inside the wind

tunnel, certain similitude criteria must be ascertained

between the hydraulic phenomena that occur in nature

(N) and on the model (M). These similitude criteria

will impose values of the different physical quantities

that are to be realized on the experimental model,

in order to preserve the similarities with the natural

phenomenon.

For the phenomenon we are studying, the follow-

ing 7 dominant physical quantities were identified:

c, chord length of the blade;

U , velocity of the

fluid upstream of the turbine module; , density of

the fluid; , dynamic viscosity of the fluid; , angu-

lar velocity of the turbine; R , radius of the turbine

(of the runner); B , number of blades.Applying the principles ofDimensional Analysis,

by choosing three of these quantities as fundamental,

namely: c ,

U and , we obtain 4 non-dimensional

criteria specific to this application: cURec = ,

the chord based Reynolds number (where =

is the kinematic viscosity of the fluid);

Uc , a

criteria related to the velocity; cR , a criteria related

to the geometry of the runner, and B , a criteria that

equals the number of blades (it has to be identical on

the model, to the one in nature). Combining the sec-ond and third criteria, we get

= UR , which

is known as the tip speed ratio. From the tip speed

ratio and the chord based Reynolds number, we get

RcReb = , which is the blade Reynolds number.

Combining the last two non-dimensional criteria, we

get RcB= , which is known as thesolidity.

For the case of modelling a water phenomenon in

air with the length scale of 1:1, and by considering the

above mentioned similitude criteria, we can compute

values of thescales of physical quantities that influ-ence the phenomenon. The values of these scales are

presented in Table 1.


3/10

Proceedings of the 2nd IAHR International Meeting of the Workgroupon Cavitation and Dynamic Problems in Hydraulic Machinery and Systems 291

Starting from the characteristics of the Achard tur-

bine module, i.e. radius 5.0=NR m, number of blades

3=NB , kinematic viscosity6

10

=N m2/s, tip speed

ratio 2=N , and solidity 1=N , and by taking

into account that in the area where it will work (sea,

large rivers) the velocity of the fluid can be consid-

ered in the range 0.13.0 =N

U m/s, we can

compute the values of the angular velocity and rota-

tional speed for the experimental model (Table 2).

Table 1. Scales definition

Type Scale Symbol Relationship Value

length (radius) scale LR SS = 1

number of blades scale BS 1

viscosity scale waterairS = 15imposed

density scale waterairS = 0.0012

chord scale cS LBRc SSSS ==1

1

angular velocity scale S 111

== BcR SSSSSS 15rotational speed scale nS

1== Bn SSSS 15

fluid velocity scale US LBRU SSSSSS1

== 15

aerodynamic force scale FS 22422

== BLULF SSSSSSSS 0.27

derived

pressure scale pS 2222

== BLUp SSSSSSS 0.27

Table 2. Angular velocity and rotational speed in nature, and for the experimental model

Nature (N) Model (M)

NU

[m/s]

N

[rad/s]

Nn

[rot/s]

Nn

[rot/min]

MU

[m/s]

M

[rad/s]

Mn

[rot/s]

Mn

[rot/min]0.3 1.2 0.191 11.46 4.5 18 2.86 172

0.4 1.6 0.254 15.28 6.0 24 3.81 229

0.5 2.0 0.318 19.08 7.5 30 4.77 286

0.6 2.4 0.382 22.92 9.0 36 5.73 344

0.7 2.8 0.445 26.70 10.5 42 6.67 400

0.8 3.2 0.509 30.54 12.0 48 7.63 458

0.9 3.6 0.573 34.38 13.5 54 8.59 515

1.0 4.0 0.637 38.19 15.0 60 9.55 573

3. STEADY FLOW AROUND A

CYLINDER TEST CASEIn the effort to predict the forces acting on the

Achard turbine module during experimental work,

preliminary tests of the code used in the numerical

simulations were performed on a benchmark case of

steady flow around a cylinder. The cylinder test case

focused on the differences that appear in the pres-

sure distribution on the cylinder surface, at different

Reynolds numbers, for several values of the parame-

ters that can be set in the computer code, namely

the turbulent intensity it, and the turbulence length

scale Lt. We also investigated the influence of thedimensions of the computational domain on the pres-

sure coefficients pc , for the minimum and maximum

values of the Reynolds number that are supposed to

appear in the unsteady numerical simulations. Forthe flow around a cylinder of diameterD, the pres-

sure coefficientis defines as:

22

=

U

ppcp

, (1)

where is the pressure on the cylinder,

p is the

upstream uniform pressure, and

U is the upstream

velocity. The associated Reynolds number is:

DURe

= .

The turbulence modelthat was used is the k one, implemented within the finite element scheme

with unstructured mesh. Numerical results were com-


4/10


pared to the well known experimental data presented

in Batchelor [8]. The turbulent intensity and the tur-

bulence length scale are requested by the code to

compute the turbulent kinetic energy and dissipation

rate that are used by the turbulence model. We must

mention that, although we looked up the values cor-responding to marine currents or river flow of those

parameters in the literature, we could not find any

information. Firstly, we started with the values of it

and Lt available by default within the numerical

code, then made tests for some values in the range

recommended by the software manufacturer [6], for

finally trying up values outside of that range, in order

to make the pressure coefficients distributions fit as

well as possible the experimental data.

The computed pressure coefficients variations are

presented in Fig. 3, for

6

10=

Re and

6

103=

Re , theminimum and maximum values of the Reynolds num-ber, which are supposed to appear in the unsteady

numerical simulations, during a complete rotation.

Our results are compared to available experimen-

tal data [8], for 5107.6 =Re and 6104.8 =Re ; the

irrotational case is also plotted (Fig. 3). Thus, the

pressure coefficient variation upon the azimuthal

angle , with respect to the turbulent intensity, as

( )itRecc pp ,,= , for { }5.0;05.0;005.0=it , is pre-

sented in Fig. 3.a. The pressure coefficient variation

upon , with respect to the turbulence length scale, as( )LtRecc pp ,,= , for { ;005.0=Lt }5.0;25.0;05.0 ,

is presented in Fig. 3.b. In figure 3.c, we present the

variation ( )Recc pp ,= with respect to the rectan-

gular computational domain limits, as multiple of

the cylinder diameterD, namely: ( )DD 4020 and( )DD 2510 .

From the presented results, it is straight forward

to notice that the influence of the domain extent is

not that important for the pressure coefficients (if

the domain limits are selected big enough to avoid

blockage effects). As long as the turbulent intensity

and turbulence length scale are concerned, we can

see that none of the tested values assures a very good

mach of the numerical results on the experimental

curves. As a consequence, in the sequel, we will

consider the values of those parameters just as some

tuning constantswith no other physical meaning, and

choose the values that match best the experimental

results. The values that we used in the unsteady flow

inside the Achard turbine are: 2.0=it for the turbu-

lent intensity, and 1.0=Lt for the turbulence length

scale. We add that for wind flow in the atmosphericboundary layer, the measured turbulent intensity val-

ues range, at 30 m above ground, from 01.0=it for

open sea, to 2.0=it for city areas [9].

(a)

(b)

(c)

Figure 3. Test case of steady flow around a cylinder

experimental data [8] and computed results for the

pressure coefficient pc versus azimuthal angle ,

with respect to the Reynolds number Re and to the

variation of the: (a) turbulent intensity it ; (b) turbu-lence length scale Lt ; (c) numerical domain limits


5/10


4. NUMERICAL SET-UP

The numerical set-up aimed at the simulation of

the turbulent flow inside a horizontal cross-section

of the Achard turbine module. We considered first

the three blades modelfrom Fig. 2, where the three

NACA 4518 airfoils, with a chord length 179.0=c

m, are positioned on a circle of 0.5 m radius, with

120 span, rotating counter clockwise; the radius of

the turbine shaft is of 5 cm. The blade geometry was

generated in MATLAB, from 42 points on each blade

cross-section (the points were unevenly distributed

on the airfoil, to better describe the leading and the

trailing edges). Then, it was imported into COMSOL

Multiphysics and converted to boundaries by spline

interpolation. The tip speed ratio value was taken

2= (as prescribed for the Achard turbine) and the

approximate value of the solidity was 1= . In orderto be able to compare the computed results with

experimental data [7], we also performed numerical

simulations for a tip speed ratio of 2.5 and the same

solidity ( )1= , as well as for a tip speed ratio of 2.5and a solidity of 0.36 (the value 36.0= corresponds

to a single rotating blade of our model, termed fur-

ther assingle blade model).

All tests were performed for both water flow and

airflow (air being considered an incompressible fluid,

as the velocities in the numerical set-up have mod-

erated values).

The investigated domain consists of an unstruc-

tured mesh having 6549 triangular elements, 397

boundary elements and 142 vertex elements for the

three blades model(see Fig. 4.a), and 3240 triangu-

lar elements, 243 boundary elements and 54 vertex

elements for the single blade model (see Fig. 4.b).

For both types of models, we used two sub domains:

a rotating one (a circular area of 0.6 m radius that

incorporates the blades), and a fixed one (outside the

former). The rotating sub domain modelled the rota-

tion of the turbine.

The boundary conditions used were the follow-ing: inflow with a specified velocity, turbulent in-

tensity and turbulence length scale on the left hand

side of the domain; zero pressure on the right hand

side of the domain; slip symmetry on the upper and

lower boundaries; logarithmic wall function with the

offset of 2/h on the blades and on the turbine shaft;

neutral identity pair on the boundaries between the

fixed and rotating sub domains.

A complete 360o

turn of the blades was investi-

gated. In order to achieve more accurate results, we

simulated two complete turns of the turbine. No data

was recorded for the first turn of the turbine, and only

the second complete turn was usedto yield results.

5. NUMERICAL RESULTS

To illustrate the flow structure obtained in the

numerical simulations, the evolution of the flow is

presented in figures 5 and 6. Each of those figures

contains 8 frames of the flow at four different azi-

muthal angles. On the 4 frames from the left hand

side of each figure, we present the velocity field, and

on the 4 frames from the right hand side, the base 10

logarithm of the vorticity. We present firstly the resultscorresponding to thesingle blade model(see Fig. 5),

at { } 242,191,140,105= . Then, in Fig. 6, wepresent the results corresponding to the three blades

model, at } 89,26,53,8= .

Figure 4. Computational mesh for the three blades model (left), and single blade model (right)


6/10


(a)

(b)

(c)

(d)

Figure 5. Flow structure for the single blade modelvelocity field (left hand side frames),

and base 10 logarithm of the vorticity (right hand side frames), at different azimuthal angles:

(a) 105= ; (b) 140= ; (c) 191= ; (d) 242=


7/10


(a)

(b)

(c)

(d)

Figure 6. Flow structure for the three blades modelvelocity field (left hand side frames),

and base 10 logarithm of the vorticity (right hand side frames), at different azimuthal angles:

(a) 8= ; (b) 35= ; (c) 62= ; (d) 98=


8/10


For the single blade model, we only presentedresults for azimuth angles in the range 100 to 250,where the main dynamic-stall region is located. Forthe three blades model, we presented results forazimuth angles in the range 0 to 100, but taking

into account that the blades are shifted by 120, andthat the results were recorded for the second rotation,

by observing all the three blades, and not only theone for which the azimuth angle was calculated, wecover a complete rotation.

For the 2D modelling, the dynamic forces are com-puted per unit length. The corresponding normalforce coefficientis defined as:

22

=

Uc

FC nFn

. (2)

The variations of the normal force coefficients

versus the azimuthal angle , obtained for the nu-merical models running in water, are presented inFig. 7, with respect to the tip speed ratio values( 2= and 5.2= ).

-20

-15

-10

-5

0

5

10

15

20

0 45 90 135 180 225 270 315 360

[deg]

CFn

[-]

water, tsr = 2

water, tsr = 2.5, single blade

water, tsr = 2.5

experimental (strain method)

experimental (pressure meth.)

Figure 7. Normal force coefficient FnC versus the

azimuthal angle , with respect to the tip speed

ratio (denoted as tsr in the legend): computed

values (solid lines) and experimental data [10](discrete marks)

Similarly, the tangential force coefficients, com-puted for the models running in water,

22

=

Uc

FC tFt

, (3)

are presented in Fig. 8.The numerical results of the three blades model,

and of the single blade model, are compared to theexperimental data presented in Oleret al. [10]. Theexperimental blade forces were measured for a tip speedratio of 2.5 and solidity 25.0= , with two different

methods, which are both presented as there are somedifferences between the data sets. One set was ob-tained from integrated pressure measurements, andthe other one from strain gage measurements.

-4

-3

-2

-1

0

1

2

3

4

0 45 90 135 180 225 270 315 360

[deg]

CFt

[-

]

water, tsr = 2

water, tsr = 2.5, single blade

water, tsr = 2.5

experimental (strain method)

experimental (pressure meth.)

Figure 8. Tangential force coefficient FtC versus

the azimuthal angle , with respect to the tip speed

ratio (denoted as tsr in the legend): computedvalues (solid lines) and experimental data [10](discrete marks)

From the presented results, one can see that nu-merical data obtained for the single blade model,which represents a solidity of 0.36 (the closest valueto the experimental one, 25.0= ) and a tip speed

ratio of 2.5 match well with the experiments. We haveto bear in mind that our numerical simulations were

performed on a curved airfoil, while the experimentswere performed onstraight airfoils. The influenceof the solidity (i.e. number of blades in our case) can

be also determined from the differences between thecurves for thesingle blade modeland the three bladesmodel, with a tip speed ratio of 2.5.

Computed normal force coefficients ( ),FnC ,obtained for the three blades modelrunning in waterand in air, are presented in Fig. 9, while the tangential

force coefficients, ( ),FtC , obtained for the samemodels, are presented in Fig. 10, for both 2.5 and 2tip speed ratios.

-15

-10

-5

0

5

10

15

0 45 90 135 180 225 270 315 360

[deg]

CFn

[-]

water, tsr = 2

water, tsr = 2.5

air, tsr = 2

air, tsr = 2.5

Figure 9. Normal force coefficient vs the azimuthalangle , with respect to the tip speed ratio (denoted

as tsr in the legend), for the three blades model runningin water (solid line) and in air (discrete marks)


9/10


-3

-2

-1

0

1

2

3

0 45 90 135 180 225 270 315 360

[deg]

CFt

[-

]

water, tsr = 2

water, tsr = 2.5

air, tsr = 2

air, tsr = 2.5

Figure 10. Tangential force coefficient vs , with

respect to the tip speed ratio (denoted as tsr in

the legend), for the three blades model running inwater (solid line) and in air (discrete marks)

As shown by the graphs from figures 9 and 10,there are practically no differences between the air-

flow and water flow for the values of the velocities inthe limits of the current experimental model, althoughthe values of the forces in air are approximately 10times smaller than the corresponding ones in water.This was to be expected as long as the similitudecriteria are respected.

In figure 11 we present the variation of the force

coefficients ( )FC with respect to the Ox axis (paral-

lel to the flow direction), and to the Oy axis (perpen-dicular to the flow), corresponding to the whole threeblades model, for a complete 360 turn of the model.

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

0 45 90 135 180 225 270 315 360

[deg]

CF[-] flow direction

cross flow direction

Figure 11. Force coefficients FC versus the azimuthal

angle , for the three blade model, with respect to

the Ox axis (flow direction), and to the Oy axis(cross flow direction)

6. CONCLUSIONS

The 2D numerical modelling of the unsteady flow

inside the Achard turbine has been performed using

COMSOL Multiphysics 3.3a software, with a k

turbulence model, for both water and air. The turbu-

lent intensity and the turbulence length scale values,

used within the unsteady simulations, were selected

through a test case related to the steady flow around

a cylinder. Results obtained for the tested models (a

three blades model, and asingle blade model), showclearly the distinct features of the Achard cross-flow

turbine. In the first half rotation, a large dynamic-stall

is generated, while in the second half, the dynamic-

stall duration is shorter. The generation of leading

vortices, as described in Oleret al. [10] and in Para-

schivoiu [7], is not clearly observed. The similitude

criteria derived for the modelling of the airflow in the

turbine are accurately chosen. The dynamic forces,

computed for a horizontal cross-section of the turbine,

agree well with the experimental ones, and will be

used, in the sequel, to determine roughly the forcesacting on the turbine model that we have to test in

the wind tunnel.

ACKNOWLEDGMENTS

Authors gratefully acknowledge the CEEX Pro-

gramme from the Romanian Ministry of Education

and Research, for its financial support under the

THARVEST Project no. 192/2006. Special thanks

are addressed to Dr Jean-Luc Achard, CNRS Research

Director, and to PhD student Ervin Amet from LEGI

Grenoble, for consultancy on the Achard turbine.

NOMENCLATURE

B [] number of blades

FC [] force coefficient

H [m] turbine height

R [m] turbine radius

cRe [] chord based Reynolds number

U [m/s] upstream velocity

c [m] airfoil chord length

pc [] pressure coefficient

0c [m] airfoil mean camber line length

[] tip speed ratio

[m2/s] kinematic viscosity

[rad/s] angular velocity

[kg/m3] fluid density

[] solidity

[grd] azimuthal angle

Subscripts and Superscripts

n normal direction

t tangential direction

upstream


10/10


REFERENCES

[1]Achard, J.-L., and Matre, T., 2004, Turbomachinehydraulique, Brevet dpos, Code FR 04 50209,

Titulaire: Institut National Polytechnique de Greno-

ble, France.

[2]Achard, J.-L., Imbault, D., and Matre, T., 2005, Dis-positif de maintien dune turbomachine hydraulique,

Brevet dpos, Code FR 05 50420, Institut National

Polytechnique de Grenoble.

[3]Matre, T., Achard, J-L., Guittet, L., and Ploeteanu,C., 2005, Marine turbine development: Numerical and

experimental investigations. Sci. Bull. Politehnica

University of Timioara, Trans. Mechanics, 50(64),

pp. 59-66.

[4]Georgescu, A.-M., Georgescu, S.-C., and Bernad, S.,2007, Interinfluence of the vertical axis, stabilised,

Achard type hydraulic turbines (THARVEST), Report

No. 2_192/2006, CEEX Programme, AMCSIT Poli-tehnica, Bucharest, http://hidraulica.utcb.ro/tharvest/

[5]Georgescu, A.-M., Georgescu, S.-C., Bernad, S., andCooiu, C. I., 2007, COMSOL Multiphysics versus

Fluent: 2D numerical simulation of the stationaryflow around a blade of the Achard turbine, Sci. Bull.Politehnica Univ. of Timioara, Trans. Mechanics,

Special Issue, eds. S. Bernad, S. Muntean, R. Resiga,52(66), pp 13-22.

[6]*** 2006, COMSOL Multiphysics 3.3. Users Guide,COMSOL AB., Stockholm.

[7]Paraschivoiu, I., 2002, Wind turbine design with em-phasis on Darrieus concept, Polytechnic InternationalPress, Montral, Chap. 5.

[8]Batchelor, G.K., 1994, An Introduction to Fluid Dy-namics, 16th edition, Cambridge University Press,Cambridge, Chap. 5.

[9]Georgescu, A.-M., 1999, Contribuii n ingineriavntului (Contributions in Wind Engineering),

Ph.D. thesis, Technical Civil Engineering University,Bucharest (in Romanian).

[10]Oler, J.W., Strickland, J.H., Im, B.J., and Graham, G.H.,

1983, Dynamic-stall regulation of the Darrieus tur-bine, Technical Report No.[11]SAND83-7029, Sandia National Laboratories, Albu-

querque, USA.

36_georgescu

Documents