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2nd IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems Timisoara, Romania October 24 - 26, 2007

Scientific Bulletin of the “Politehnica” University of Timisoara Transactions on Mechanics Tom 52(66), Fascicola 6, 2007

NUMERICAL MODELLING COMPARISON BETWEEN AIRFLOW AND WATER FLOW WITHIN THE ACHARD-TYPE TURBINE Andrei-Mugur GEORGESCU *

Sanda-Carmen GEORGESCU

Hydraulic and Environmental Protection Department, Technical Civil Engineering University Bucharest

Hydraulics and Hydraulic Machinery Department, University “Politehnica” of Bucharest

Mircea DEGERATU

Sandor BERNAD

Hydraulic and Environmental Protection Department, Centre of Advanced Research in Engineering Sciences, Technical Civil Engineering University Bucharest Romanian Academy – Timişoara Branch

Costin Ioan COŞOIU 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

1. INTRODUCTION

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 the Achard 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 accurately 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 performed 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 approximate knowledge about the values of forces that will act upon it during the experiments; such values can be obtained conveniently through numerical simulations. 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 experimental model.

In 2001, the Geophysical and Industrial Fluid Flows Laboratory (LEGI) of Grenoble, France, launched the HARVEST Project (Hydroliennes à Axe de Rotation VErtical STabilisé), to develop a suitable technology for marine and river hydro-power farms using cross-flow current energy converters piled up in towers [1−3]. In 2006, the Technical Civil Engineering University Bucharest, in collaboration with the University “Politehnica” of Bucharest and the Romanian Academy - Timisoara Branch, started the THARVEST Project, within the CEEX Program sustained by the Romanian Ministry of Education and Research [4]. The THARVEST Project aims to study experimentally and numerically the hydrodynamics of this new concept of water-current turbine, called Achard turbine, in collaboration with the LEGI partners involved in the HARVEST Project. 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 the Achard 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 NACA 4518 airfoils [5]. The turbine main geometric dimensions are: the runner radius R = 0.5 m, the runner height H = 1 m, and the shaft radius of 0.05 m.

KEYWORDS Achard turbine, cross-flow water turbine, airfoil, pressure coefficient, force coefficient

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

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of the 2D numerical simulations of the three blades runner model from Fig. 2 turning in water and air, as well as the results obtained for a twin unsteady test case, namely a single blade runner model, are compared to similar experimental data available in the literature [7]. 2. HYDRAULIC SIMILITUDE

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 c0 = 0.18 m (the maximum value of c0 along the delta wing), and the chord length c = 0.179 m. The values of the azimuthal angle of the blades are θ = 0o ; 120o ; 240o , in counter clockwise direction.

{

}

criteria specific to this application: Rec = U ∞ c ν ,

0.5 o

θ=0

0.4

the chord based Reynolds number (where ν = µ ρ

0.3

is the kinematic viscosity of the fluid); ω c U ∞ , a

0.2

criteria related to the velocity; R c , 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 second and third criteria, we get λ = ωR U ∞ , which is known as the tip speed ratio. From the tip speed ratio and the chord based Reynolds number, we get Reb = ωRc ν , which is the blade Reynolds number. Combining the last two non-dimensional criteria, we get σ = cB R , which is known as the solidity. 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 the scales of physical quantities that influence the phenomenon. The values of these scales are presented in Table 1.

0.1

y [m]

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 following 7 dominant physical quantities were identified: c , chord length of the blade; U ∞ , velocity of the fluid upstream of the turbine module; ρ , density of the fluid; µ , dynamic viscosity of the fluid; ω , angular velocity of the turbine; R , radius of the turbine (of the runner); B , number of blades. Applying the principles of Dimensional Analysis, by choosing three of these quantities as fundamental, namely: c , U ∞ and ρ , we obtain 4 non-dimensional

0 −0.1 −0.2 −0.3

θ = 120o o

θ = 240

−0.4 −0.5

−0.6

−0.4

−0.2

0 x [m]

0.2

0.4

0.6

Figure 2. Computational runner cross-section In this paper we focus on the 2D numerical modelling of the unsteady flow inside the Achard turbine. A complete 360° turn of the blades is analysed. The simulations are performed with COMSOL Multiphysics 3.3a software [6]. A test case of the steady flow around a cylinder is performed in order to tune up the input parameters for the unsteady computations. The results


291

Starting from the characteristics of the Achard turbine module, i.e. radius RN = 0.5 m, number of blades

large rivers) the velocity of the fluid can be considered in the range U ∞ N = 0.3 …1.0 m/s, we can

BN = 3 , kinematic viscosity ν N = 10 −6 m2/s, tip speed

compute the values of the angular velocity and rotational speed for the experimental model (Table 2).

ratio λN = 2 , and solidity σ N = 1 , and by taking into account that in the area where it will work (sea,

derived

imposed

Type

Scale length (radius) scale

Table 1. Scales definition Symbol SR = SL

Relationship –

Value 1

SB

–

1

viscosity scale

Sν = ν air ν water

–

15

density scale

S ρ = ρ air ρ water

–

0.0012

chord scale

Sc

S R S B−1

angular velocity scale

Sω

Sω = Sν S R−1S c−1 = Sν S B−1

15

rotational speed scale

Sn

S n = Sω = Sν S B−1

15

number of blades scale

Sc =

SU = Sω S R =

= SL

Sν S B−1S L

1

fluid velocity scale

SU

aerodynamic force scale

SF

S F = S ρ S L2 SU2 = S ρ S L4 Sν2 S B−2

0.27

pressure scale

Sp

S p = S ρ SU2 = S ρ S L2 Sν2 S B−2

0.27

15

Table 2. Angular velocity and rotational speed in nature, and for the experimental model Nature (N) Model (M) U∞N U∞M ωN nN nN ωM nM nM [rad/s] [rot/s] [rot/min] [rad/s] [rot/s] [rot/min] [m/s] [m/s] 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 CASE

In 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 pressure distribution on the cylinder surface, at different Reynolds numbers, for several values of the parameters 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 the dimensions of the computational domain on the pressure coefficients c p , for the minimum and maximum

values of the Reynolds number that are supposed to appear in the unsteady numerical simulations. For the flow around a cylinder of diameter D, the pressure coefficient is defines as:

cp =

p − p∞ , ρU ∞2 2

(1)

where p is the pressure on the cylinder, p∞ is the upstream uniform pressure, and U ∞ is the upstream velocity. The associated Reynolds number is: Re = U ∞ D ν . The turbulence model that was used is the k − ε one, implemented within the finite element scheme with unstructured mesh. Numerical results were com-

292


pared to the well known experimental data presented in Batchelor [8]. The turbulent intensity and the turbulence 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 corresponding 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 Re = 106 and Re = 3 ⋅106 , the minimum and maximum values of the Reynolds number, which are supposed to appear in the unsteady numerical simulations, during a complete rotation. Our results are compared to available experimental data [8], for Re = 6.7 ⋅ 105 and Re = 8.4 ⋅106 ; the irrotational case is also plotted (Fig. 3). Thus, the pressure coefficient variation upon the azimuthal angle θ , with respect to the turbulent intensity, as c p = c p (θ , Re, it ) , for it = {0.005; 0.05; 0.5} , is presented in Fig. 3.a. The pressure coefficient variation upon θ , with respect to the turbulence length scale, as c p = c p (θ , Re, Lt ) , for Lt = {0.005; 0.05; 0.25; 0.5} , is presented in Fig. 3.b. In figure 3.c, we present the variation c p = c p (θ , Re ) with respect to the rectangular computational domain limits, as multiple of the cylinder diameter D, namely: (20 D × 40 D ) and (10 D × 25D ) . 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 constants with 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: it = 0.2 for the turbulent intensity, and Lt = 0.1 for the turbulence length scale. We add that for wind flow in the atmospheric boundary layer, the measured turbulent intensity values range, at 30 m above ground, from it = 0.01 for open sea, to it = 0.2 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 c p versus azimuthal angle θ , with respect to the Reynolds number Re and to the variation of the: (a) turbulent intensity it ; (b) turbulence length scale Lt ; (c) numerical domain limits


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 model from Fig. 2, where the three NACA 4518 airfoils, with a chord length c = 0.179 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 λ = 2 (as prescribed for the Achard turbine) and the approximate value of the solidity was σ = 1 . In order to 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 (σ = 1) , as well as for a tip speed ratio of 2.5 and a solidity of 0.36 (the value σ = 0.36 corresponds to a single rotating blade of our model, termed further as single 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 moderated values). The investigated domain consists of an unstructured mesh having 6549 triangular elements, 397 boundary elements and 142 vertex elements for the three blades model (see Fig. 4.a), and 3240 triangular elements, 243 boundary elements and 54 vertex elements for the single blade model (see Fig. 4.b).

293

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 rotation of the turbine. The boundary conditions used were the following: inflow with a specified velocity, turbulent intensity 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 h / 2 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 investigated. 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 used to 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 azimuthal 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 results corresponding to the single blade model (see Fig. 5), at θ = 105 , 140 , 191 , 242 . Then, in Fig. 6, we present the results corresponding to the three blades model, at θ = 8 , 35 , 62 , 98 .

{

}

{

}

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

294


(a)

(b)

(c)

(d) Figure 5. Flow structure for the single blade model − velocity field (left hand side frames), and base 10 logarithm of the vorticity (right hand side frames), at different azimuthal angles: (a) θ = 105 ; (b) θ = 140 ; (c) θ = 191 ; (d) θ = 242


(a)

(b)

(c)

(d) Figure 6. Flow structure for the three blades model − velocity field (left hand side frames), and base 10 logarithm of the vorticity (right hand side frames), at different azimuthal angles: (a) θ = 8 ; (b) θ = 35 ; (c) θ = 62 ; (d) θ = 98

295


For the single blade model, we only presented results for azimuth angles in the range 100° to 250°, where the main dynamic-stall region is located. For the three blades model, we presented results for azimuth angles in the range 0° to 100°, but taking into account that the blades are shifted by 120°, and that the results were recorded for the second rotation, by observing all the three blades, and not only the one for which the azimuth angle was calculated, we cover a complete rotation. For the 2D modelling, the dynamic forces are computed per unit length. The corresponding normal force coefficient is defined as: C Fn =

Fn . ρ c U ∞2 2

(2)

The variations of the normal force coefficients versus the azimuthal angle θ , obtained for the numerical models running in water, are presented in Fig. 7, with respect to the tip speed ratio values ( λ = 2 and λ = 2.5 ). water, tsr = 2

20

water, tsr = 2.5, single blade

15

water, tsr = 2.5 experimental (strain method)

10

CFn [-]

experimental (pressure meth.) 5 0

-5 -10 -15 -20 0

45

90

135

180

θ [deg]

225

270

315

360

Figure 7. Normal force coefficient C Fn versus the azimuthal angle θ , with respect to the tip speed ratio λ (denoted as tsr in the legend): computed values (solid lines) and experimental data [10] (discrete marks)

4 3 2

CFt [-]

296

(3)

are presented in Fig. 8. The numerical results of the three blades model, and of the single blade model, are compared to the experimental data presented in Oler et al. [10]. The experimental blade forces were measured for a tip speed ratio of 2.5 and solidity σ = 0.25 , with two different methods, which are both presented as there are some differences between the data sets. One set was obtained from integrated pressure measurements, and the other one from strain gage measurements.

water, tsr = 2 water, tsr = 2.5, single blade water, tsr = 2.5 experimental (strain method) experimental (pressure meth.)

-2 -3 -4 0

45

90

135

180

θ [deg]

225

270

315

360

Figure 8. Tangential force coefficient C Ft versus the azimuthal angle θ , with respect to the tip speed ratio λ (denoted as tsr in the legend): computed values (solid lines) and experimental data [10] (discrete marks) From the presented results, one can see that numerical data obtained for the single blade model, which represents a solidity of 0.36 (the closest value to the experimental one, σ = 0.25 ) and a tip speed ratio of 2.5 match well with the experiments. We have to bear in mind that our numerical simulations were performed on a curved airfoil, while the experiments were performed on straight airfoils. The influence of the solidity (i.e. number of blades in our case) can be also determined from the differences between the curves for the single blade model and the three blades model, with a tip speed ratio of 2.5. Computed normal force coefficients C Fn (θ , λ ) , obtained for the three blades model running in water and in air, are presented in Fig. 9, while the tangential force coefficients, C Ft (θ , λ ) , obtained for the same models, are presented in Fig. 10, for both 2.5 and 2 tip speed ratios. 15 10 5

CFn [-]

Ft , ρ c U ∞2 2

0

-1

Similarly, the tangential force coefficients, computed for the models running in water, C Ft =

1

0 water, tsr = 2

-5

water, tsr = 2.5 air, tsr = 2

-10

air, tsr = 2.5

-15 0

45

90

135

180

θ [deg]

225

270

315

360

Figure 9. Normal force coefficient vs the azimuthal angle θ , with respect to the tip speed ratio λ (denoted as tsr in the legend), for the three blades model running in water (solid line) and in air (discrete marks)

Proceedings of the 2nd IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems 3 2

CFt [-]

1 0 water, tsr = 2

-1

water, tsr = 2.5 air, tsr = 2

-2

air, tsr = 2.5

-3 0

45

90

135

180

θ [deg]

225

270

315

360

Figure 10. Tangential force coefficient vs θ , with respect to the tip speed ratio λ (denoted as tsr in the legend), for the three blades model running in water (solid line) and in air (discrete marks) As shown by the graphs from figures 9 and 10, there are practically no differences between the airflow and water flow for the values of the velocities in the limits of the current experimental model, although the values of the forces in air are approximately 10 times smaller than the corresponding ones in water. This was to be expected as long as the similitude criteria are respected. In figure 11 we present the variation of the force coefficients C F (θ ) with respect to the Ox axis (parallel to the flow direction), and to the Oy axis (perpendicular to the flow), corresponding to the whole three blades model, for a complete 360° turn of the model. 0.5 0

CF [-]

-0.5 -1

flow direction cross flow direction

-1.5 -2 -2.5 -3 0

45

90

135

180

θ [deg]

225

270

315

360

Figure 11. Force coefficients C F versus the azimuthal angle θ , 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 − ε

297

turbulence model, for both water and air. The turbulent 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 a single blade model), show clearly 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 dynamicstall duration is shorter. The generation of leading vortices, as described in Oler et al. [10] and in Paraschivoiu [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 forces acting on the turbine model that we have to test in the wind tunnel. ACKNOWLEDGMENTS

Authors gratefully acknowledge the CEEX Programme 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 [−] C F [−] H [m] R [m] Rec [−]

number of blades force coefficient turbine height turbine radius chord based Reynolds number

U ∞ [m/s] c [m] c p [−]

upstream velocity airfoil chord length pressure coefficient

c0 [m]

airfoil mean camber line length

λ ν ω ρ σ θ

[−] [m2/s] [rad/s] [kg/m3]

tip speed ratio kinematic viscosity angular velocity fluid density

[−] [grd]

solidity azimuthal angle

Subscripts and Superscripts n normal direction t tangential direction ∞ upstream

298


REFERENCES [1] Achard, J.-L., and Maître, T., 2004, “Turbomachine hydraulique”, Brevet déposé, Code FR 04 50209, Titulaire: Institut National Polytechnique de Grenoble, France. [2] Achard, J.-L., Imbault, D., and Maître, T., 2005, “Dispositif de maintien d’une turbomachine hydraulique”, Brevet déposé, Code FR 05 50420, Institut National Polytechnique de Grenoble. [3] Maître, T., Achard, J-L., Guittet, L., and Ploeşteanu, C., 2005, “Marine turbine development: Numerical and experimental investigations”. Sci. Bull. Politehnica University of Timişoara, 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 Politehnica, Bucharest, http://hidraulica.utcb.ro/tharvest/ [5] Georgescu, A.-M., Georgescu, S.-C., Bernad, S., and Coşoiu, C. I., 2007, “COMSOL Multiphysics versus

Fluent: 2D numerical simulation of the stationary flow around a blade of the Achard turbine”, Sci. Bull. Politehnica Univ. of Timişoara, Trans. Mechanics, Special Issue, eds. S. Bernad, S. Muntean, R. Resiga, 52(66), pp 13-22. [6] *** 2006, COMSOL Multiphysics 3.3. User’s Guide, COMSOL AB., Stockholm. [7] Paraschivoiu, I., 2002, Wind turbine design with emphasis on Darrieus concept, Polytechnic International Press, Montréal, Chap. 5. [8] Batchelor, G.K., 1994, An Introduction to Fluid Dynamics, 16th edition, Cambridge University Press, Cambridge, Chap. 5. [9] Georgescu, A.-M., 1999, “Contribuţii în ingineria vântului” (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 turbine”, Technical Report No. [11]SAND83-7029, Sandia National Laboratories, Albuquerque, USA.