experimental characterization of the near-wake of a cross...

17th International Symposium on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2014

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Experimental characterization of the near-wake of a cross flow water

turbine with LDV measurements

Guillaume Mercier1,3*, Christian Pellone2, Thierry Maitre1

1: LEGI Laboratory, Grenoble INP, Grenoble, France

2: LEGI, CRNS, Grenoble, France 3: Agency of Energy and Environment ADEME, Angers, France * Correspondent author: [email protected]

Abstract Recent developments in tidal energy converter technology and turbine array projects require fast and robust simulation tools. The simple actuator disc model shows discrepancies as far as the wake and speed recovery is concerned. Blade tip vortices as well as wake rotation provide a strong contribution to turbulence production that is not reproduced in basic actuator disc model. An effective modification of k-ε conservation equation has been proposed to account for non-linear scale interaction behind an axial-flow turbine. The aim of this study is to provide reference data to understand the near-wake dynamic in the case of a cross-flow turbine and build an actuator disc model ad-hoc. Near-wake of a Darrieus turbine is investigated with LDV measurements up to 3 diameters behind the rotor.

1. Introduction

Reliable technologies for Tidal Energy Converters (TEC) are achieving their maturation as prototype. Different technological locks as anchorage or submarine cable are being over-passed. Research on TEC has been developed during the ten last years, following and taking advantage of wind turbine advances. Therefore, designs for standard TEC tend to be established and well optimized. Fair knowledge of machine hydrodynamics leads scientific community to look forward to the next step for marine renewable energies. The idea of an isolated TEC inside current is no longer close to reality. The concept of array to maximize power extraction is prevailing nowadays [4]. Development of turbine arrays project requires fast and robust simulation tools. Such simplified models are mainly based on actuator disc theory. Hydrodynamic performance of turbines are well known therefore main difficulties for these models rely on blocking effect (lateral or free-surface) and wake recovery. Behavior of turbines wake is a key factor for grid design and placement optimization, in marine and river configurations, when several rows of machine can be installed. Manganga et. al. demonstrated the overwhelming influence of turbulence intensity over wake recovery length [7]. Hence accurate and sufficient attention should be focused on turbulence modeling. Near-wake and far-wake of both wind and water axial flow turbines have been widely studied experimentally. Vermeer proposed a complete review of wind turbine wake [14]. Recently Zhang et. al. studied the near-wake of a wind turbine in atmospheric boundary layer condition with PIV measurements [15]. They highlighted a quick dislocation of coherent vortices after a few diameters and their strong impact over turbulence production. This transition determines the end of the near wake around, toward far wake with isotropic turbulence. The simple actuator disc model shows discrepancies as far as the wake description is concern. Blade tip vortices as well as wake rotation provide a strong contribution to turbulence that is not reproduce in basic actuator disc model. An effective modification of k-ε conservation equation has been proposed to account for non-linear scale interaction behind an axial water turbine [5] [10]. It is based on the addition of source terms in conservation equations of k and ε to account for energy transfer from large scale turbulence to low scale turbulence proposed by Sanz to deal with canopy induced turbulence [13]. In the field of hydrokinetic convertors, the work of El Kasmi [5] for axial flow wind turbines and Roc et. al. [11] for marine axial turbine, both successfully adapted the modification to improve actuator disc model.


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The present study focuses on cross-flow water turbine (vertical axis) of Darrieus type. Brochier et. al. produced a reference experimental work for understanding the dynamic stall along the rotation of the blades the wake features [6]. The counter rotating vortices visualized by Brochier are essentially two-dimensional. This property justifies the 2D analysis carried out in the study. Several numerical models using RANS turbulence models coupled with sliding mesh methods demonstrated the ability to simulate the Darrieus turbine in 2D and 3D configurations. The comparison with experimental data showed a good precision for the flow dynamic in the rotor, as well as for the torque estimation [8, 9,3]. Nevertheless these studies did not aim the description of the wake discredited with a coarse mesh. The figure 1 presents the vertical component of the vorticity field, obtained within the present study, with a mesh refinement behind the turbine. The figure shows the highly sheared region behind the rotor due to the positive and negative vortices shed in the wake. The mixing process between velocity deficit zone and the bypass flow is mainly due to these coherent structures. The wake dynamic is therefore different from axial turbine one in which a swirling tube is observed and diffusion process dominates. The elaboration of a reliable actuator disc approach for cross-flow turbine requires for a better description of the turbulent structures in the near wake as well as reference data for model adaptation.

Fig. 1 Instantaneous vorticity map around the rotor of the Darrieus turbine. 2D calculation with

RANS model.

2. Experimental setup

The hydrodynamic tunnel of the LEGI consists in a rectangular section of 0.25x0.7m and a length of 1m stream-wise, inserted in a closed hydraulic loop of 30m. Small scale model of a cross-flow water turbine of Darrieus type is tested in it. Flow velocity varies between 1 to 2.3 m/s. It corresponds to a blade Reynolds number between 1.7x105 and 5x105. Rotational speed is imposed by a synchronous generator connected to the turbine shaft. Turbine has 3 straight blades with NACA0018 foil, link at mid shaft by arms with symmetric profile. The height H and the diameter D of the turbine are equal, H=D=175mm and blade chord c=32mm (figure 2). It represents a lateral blockage ratio ((tunnel width)/(turbine width)) of 4, and a vertical blockage ratio of 1.43. The analysis presented here corresponds to a two-dimensional configuration. The flow can be constrained by adding vertical channeling. In this case distance between blade tips and horizontal walls is reduce to 2.5mm and vertical blockage ration is 1.03. This feature helps to impose a rather two dimensional flow, both inside the rotor and in the wake. Consequently, we have restricted the study on the horizontal plane equidistant to arms and blade tips (at the quarter of the total span). A two-component LDV system with back scattering is placed on a 3-axis traverse (see on figure 3). It allows measurements of stream-wise and transverse velocity in horizontal planes up to a distance of 3D behind the machine. The flow is seeded with 10 μm slivered hollow glass particles, for a sampling frequency up to 5 kHz. The probes volume is around 0.2mmx0.2mm in the XY plan and 2 mm in the vertical direction. Velocity and velocity gradient quantities are mapped at mid-blade plane behind the turbine. The origin reference for the XY coordinates is taken at the axis position. In the region [0.5D < X < 2D][-D < Y < D]. A constant step of ΔX = ΔY = D/40 = C/8 is used, X stands for the stream wise direction and Y for the


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transverse direction. Double space step is used in other zones. Notice that the length scale of vortices is related to blade length rather than turbine diameter.

H = D = 175 mm

H

D

Fig. 2. Schematic representation of the 3-blade

Darrieus turbine.

Fig. 3. Hydrodynamic tunnel in LEGI and LDV

system.

3. Numerical methods

The first approach, corresponding to the actual reference modeling for cross-flow turbine, uses description of the blades and shaft full geometry. The rotor interaction with the flow is simulated with the general CFD solver Code_Saturne [1] using a sliding mesh interface. The chosen turbulence models are the classical k-ε model or the k-Ω−SST models, well adapted for flows with strong adverse pressure gradient and flow reversal as those involved in vertical axis water turbines. A particular attention was taken as building the mesh, especially near the blades (dimensionless wall distance y+ ~ 2). Rotor mesh is composed of about 7.5x104 cells. For the unsteady rotor modeling, a second order time implicit scheme is used with a time step corresponding to a rotation angle of 1°. For the space discretization, a second order upwind scheme is used, the velocity – pressure coupling being SIMPLE method. Further characteristics of these simulations can be found in the work of Maitre et. al. [8] or [12]. Wathever the software, the results in terms of torque and flow dynamics in the turbine are validated with a good agreement against experimental measurements obtained at LEGI. The results obtained with these calculation tools are used as reference data for simpler model elaboration. Yet, it suffers a lack of validation as far as the wake is concerned. The second approach, aimed for turbine array calculation, uses RANS simulation of the flow coupled with momentum sources terms representing the turbine. Force value is calculated through inner flow velocity. In order to adapt this method to cross flow turbines, we have chosen to use a complex and realistic spatial distribution of the forces. Along its rotation, the blades undergo two main phases of drag. The first one is situated in the upstream part of the rotor, and second one in the downstream part. The model presented here imposes two Gaussian-shaped sources terms on these locations. The power of the method lies in the fact that the intensity of the source terms are determined using the forces data base obtained by the full rotor stator calculation presented above. The turbine is represented over roughly 100 cells. This corresponds to a very small number of cells compared to the full rotor-stator calculation but high enough to allow the calculation of power generated by a turbine in a given situation with a good precision.


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Following mention of numerical modeling will refer to these two approaches, in which the turbine is simulated in 2D, with the blockage ratio of the experimental facilities.

4. Results and comparison

The (X,Y) field of the mean quantities (averaged over one revolution) are examined in detail in order to estimate the full CFD simulations results. The methodology applied here looks at the validity of the reference calculation (full CFD) in the near wake. As explained before, the flow dynamics and efforts inside the rotor are fully validated against torque and PIV measurements. On the contrary, turbulence models capacity in the wake suffers a lack of experimental comparison. In this part, LDV measurements are compared with both modeling strategies to estimate the discrepancies and try to extrapolate the behavior in the far wake.

Fig.4. Mean stream-wise velocity U downstream

the Darrieus rotor . Top: measured with LDV, bottom: full CFD calculation.

Fig.5. Mean vertical vorticity ω downstream the

Darrieus rotor . Top: measured with LDV, bottom: full CFD calculation.

Figure 4 represents the time average stream-wise velocity U downstream the Darrieus rotor: the top figure concerns the measured data and the bottom the full CFD calculation. Both figures show a great velocity deficit behind the machine. The CFD wake remains constant at the distance plotted here, whereas the mixing process between the high and low speed regions seems to begin a recovery of the velocity after 2 diameters. For both measurement and calculation, the wake velocity presents a shear layer region. The difference between the two results is small. Figure 5 represents the time average vorticity. We recognize the two alleys of shed contra-rotating vortices. The intensity of the vorticity is under estimated in the CFD calculation compared to the experimental one. Alternatively, these high shear regions widen more quickly in the experience. We can conjecture that vorticity produced by the simulated rotor are less strong but seems to be transported with less attenuation. Notice that the vorticity behaviors are similar under the two configurations. In addition, the two alleys obtained by the experience are more diffuse than those obtain by CFD calculation (the measured shear layer thickness is larger than the calculated one).


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Figure 6 shows 4 non-dimensional time average stream-wise velocity profiles in the near wake (Uref stands for the upstream inlet velocity). These profiles are plotted in the Y direction, respectively at a distance X from the turbine axis respectively of 1D, 1.5D, 2D and 2.5D. Velocity deficit can be compared for both numerical models and measurements. As expected from the field maps, the present rotor-stator CFD simulation shows a very good agreement with LDV data up to 2.5 diameters. The simplified model presents slight discrepancy that let conjecture a quicker recovery in the further wake. Deficit peak is a first (X=1D) sharper and more intense than measured, but then widen and seem to recover energy from the bypass flow faster than the two others.

Fig.6. Mean velocity profiles in the wake of a Darrieus turbine. Comparison between numerical results and

LDV measurements The study of the turbulent kinetic energy levels is helpful to understand mixing speed differences. The problem of comparing experimental data and URANS simulation is subjected to discussion. URANS simulation is based on Reynolds averaging which decomposes the velocity u quantities into two parts: the averaged value U, and the fluctuating part u’ of null average. Notice that the averaged value X is also time dependent. Depending on the grid size, mean fluctuations of u are calculated, and turbulent properties of the mean flow are modeled with transport equations on the turbulent kinetic energy k and an other quantity relative to its dissipation. The instability of the mean flow or big perturbations creates large scale structures. They transport energy which participate to the mixing process, as well as shear flow. We define here to turbulence quantity for the

U-RANS analysis : elcfdk mod is defined as the turbulent kinetic energy from the k-ε model. meanflow

cfdk is the

standart deviation of the mean flow.

)''(2

1 22cfdcfd

meanflowcfd VUk +=

Therefore, turbulent kinetic energy is evaluated form LDV data with the following formula:

)''(2

1 22LDVLDVLDV vuk +=

It is of interest to note that the contribution of both terms is of the same magnitude in the full modeling; whereas the fluctuating velocity energy is 4 times higher with the model. The profile comparison is to be


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seen in figure 7. LDV data and CFD simulation assume a similar shape after 1.5 diameters although the turbulence level is around 4 times higher in the simple modeling. On the contrary, the chosen model presented here over-estimates greatly the production of turbulence, mainly because of the flapping of the wake. This large scale phenomenon mixes quickly the deficit part of the wake with the by-pass flow. This effect produces a quick recovery of the velocity along the symmetry axis as shown in the Figure 8. The instability of the wake is also seen with the full geometry simulation in the low turbulence intensity situation. The recovery of the wake occurs from 6 diameters behind the turbine, when the shedding of big structures start as it represents the best mixing process.

Fig.7. Mean turbulent kinetic energy profiles in the wake of a Darrieus turbine. Comparison of numerical

results and LDV measurements

5. Discussion

The presented results for actuator disc model do not show the same tendency as literature reference [2]. Previous work had established the strong velocity deficit obtained with actuator disc models. Many authors [5] [10] [11] proposed to add turbulence source terms as long as the classical momentum sink, in order to deal with the turbulence production that occurs in the rotor, because of strong gradients, and vortices. The adaptation of the classical actuator disc model presented here uses a realistic distribution of the momentum. This is possible thanks to middle scale of our approach looking for turbine array optimization and power calculation. This distribution creates high shear inside the turbine area that brings an over production of turbulent kinetic energy. This behavior is clearly illustrated in the turbulent kinetic energy profile comparison. In terms of velocity deficit, the distance the area behind the turbine studied here is too short to get a clear idea on the error made in the far wake. As the full CFD comparison seems to give good results after 2.5D, the numerical study is extended 15 diameters after the turbine. The simple actuator disc model imposing a uniform spatial distribution of the drag force on the equivalent turbine disc is also tested. The results over the wake recovery can be seen on figure 8. Although both new model and CFD meet after 8 diameters, the classical uniform approach still shows a deficit of 40% after 15 diameters. The full CFD calculation shows a highly sheared flow with no diffusion of the momentum from the bypass flow. An


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instability of this jet like situation appears after 6 diameter. The large structures created then are responsible for the very quick mixing seen on the figure 8. This behavior is unlikely to represent the physical situation as the shear region seems to widen on the LDV maps after only 2D.

Fig. 8 Mean dimensionless velocity along the symmetry axis

6. Conclusion

This study establishes useful data in the near-wake of a Darrieus (vertical axis) turbine. Its aim is to understand processes in the wake of a cross-flow turbine in order to validate full geometry CFD simulations and build an adapted and simplified model. The velocity deficit produced by the full CFD simulation in the near wake shows a strong agreement with the 2D LDV measurement. Nevertheless the difference in turbulence levels and spreading of the sheared regions found here is likely to generate further differences. The transport of coherent structure within RANS model might be considered as a reason of the discrepancies. This analysis claims for an extension of the present study in the far wake to determine the validity of the RANS modeling approach, in the complex case of cross-flow turbines. As the simple modeling is concerned, the classical actuator disc model is not adapted directly to cross flow turbines. The study shows a direct effect of the momentum source distribution. The complex distribution used by the authors seems to produce an over estimated level of turbulence. On the contrary, a simple uniform distribution predicts a too long length of recovery. The LDV data gather presented here will help to build a adjusted model with a good source terms distribution and/or turbulent sources of k and ε.

Acknowledgment

The authors want to thank the French Agency for Environnement and Energy (ADEME) and EDF Research and Development, for their support and funding.


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References

[1] Archambeau F. et al (2004) Code_Saturne : a Finite Volume Code for the Computation of Turbulent Incompressible Flows - Industrial Applications, International Journal on Finite Volumes, Vol. 1,. [2] Batten, W. M., Harrison, M. E., & Bahaj, A. S. (2013). Accuracy of the actuator disc-RANS approach for predicting the performance and wake of tidal turbines. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371(1985), 20120293. [3] Bossard J. « Caractérisation de l’écoulement dans les turbines à flux transverse par la méthode d’images de particules (PIV) » PhD Thesis, Grenoble-INP, 27 septembre 2012 [4] Bryden IG, Couch SJ, Owen A, and Melville G. (2007) Tidal current resource assessment. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 221(2):125-135. [5] El Kasmi A, and Masson C. (2008) An extended k-ε model for turbulent flow through horizontal-axis wind turbines. Journal of Wind Engineering and Industrial Aerodynamics, 96(1):103-12 122. [6] Fraunie P, Beguier C, Paraschivoiu I, and Brochier G. (1986) Water channel experiments of dynamic stall on darrieus wind turbine blades. Journal of Propulsion and Power, 2(5):445-449. [7] Maganga, F., Germain, G., King, J., Pinon, G., & Rivoalen, E. (2010). Experimental characterisation of flow effects on marine current turbine behaviour and on its wake properties. Renewable Power Generation, IET, 4(6), 498-509. [8] Maitre T, Amet E, and Pellone C. (2013) Modeling of the flow in a Darrieus water turbine: wall grid refinement analysis and comparison with experiments. Journal of Renewable Energy. [9] Pellone C, Maitre T, Amet E. (2012) 3D RANS modelling of a cross flow water turbine, SimHydro 2012: New trends in simulation – Hydro-informatics and 3D modeling, 12-14 September 2012, Sophia Antipolis [10] Rethore P.E.M., et . al. (2009) Study of the atmospheric wake turbulence of a cfd actuator disc model. [11] Roc T, Conley D.C, and Greaves D. (2013) Methodology for tidal turbine representation in ocean circulation model. Renewable Energy, 51:448-464. [12] Sansone E, Pellone C, Maitre T (2010) Modelling the unsteady cavitating flow in a cross-flow water turbin, Journal of Fluids Engineering Vol.132, Iss.07, pp 071302-1-13 [13] Sanz C. (2003) A note on k-ε modeling of vegetation canopy air-flows. Boundary-Layer Meteorology, 108(1):191-197 [14] Vermeer LJ, Sorensen J.N, and Crespo A. Wind turbine wake aerodynamics. Progress in aerospace sciences, 39(6):467-510, 2003.

[15] Zhang W, Markfort C.D, and Fernando P. (2012) Near-wake flow structure downwind of a

wind turbine in a turbulent boundary layer. Experiments in fluids, 52(5):1219-1235.

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