Wind turbine wake interactions at field scale: An LES study of the SWiFT facility

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1 Journal of Physics: Conference Series OPEN ACCESS Wind turbine wake interactions at field scale: An LES study of the SWiFT facility To cite this article: Xiaolei Yang et al 2014 J. Phys.: Conf. Ser View the article online for updates and enhancements. This content was downloaded from IP address on 13/10/2018 at 15:35

2 Wind turbine wake interactions at field scale: An LES study of the SWiFT facility 1 Xiaolei Yang a, Aaron Boomsma a, Matthew Barone b, and Fotis Sotiropoulos a, a St. Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, 2 Third Avenue SE, Minneapolis, MN 55414, USA b Sandia National Laboratories, Albuquerque, NM and Livermore, CA 94550, USA Corresponding author: fotis@umn.edu Abstract. The University of Minnesota Virtual Wind Simulator (VWiS) code is employed to simulate turbine/atmosphere interactions in the Scaled Wind Farm Technology (SWiFT) facility developed by Sandia National Laboratories in Lubbock, TX, USA. The facility presently consists of three turbines and the simulations consider the case of wind blowing from South such that two turbines are in the free stream and the third turbine in the direct wake of one upstream turbine with separation of 5 rotor diameters. Large-eddy simulation (LES) on two successively finer grids is carried out to examine the sensitivity of the computed solutions to grid refinement. It is found that the details of the break-up of the tip vortices into small-scale turbulence structures can only be resolved on the finer grid. It is also shown that the power coefficient C P of the downwind turbine predicted on the coarse grid is somewhat higher than that obtained on the fine mesh. On the other hand, the rms (root-mean-square) of the C P fluctuations are nearly the same on both grids, although more small-scale turbulence structures are resolved upwind of the downwind turbine on the finer grid. 1. Introduction Turbine wake interaction is a key factor affecting wind farm performance and wind turbine lifespan. The Scaled Wind Farm Technology (SWiFT) facility [1, 2], which is located at the Reese Technology Center near Lubbock, TX, USA, is specifically designed to enable investigating turbine wake effects at field scale. Three turbines (rotor diameter D = 27 m, hub height 31.5 m) have been installed with the first two turbines spaced 3D apart, perpendicular to the oncoming wind, and the third turbine 5D downwind forming a 3D-, 5D-, and 6D-length triangle (as shown in Figure 1). Field scale experiments at the SWiFT site will be integrated with highresolution large-eddy simulation (LES), which can resolve the unsteady turbulent fluctuations responsible for intermittent fluctuations of power output and dynamic loadings on wind turbines, to systematically investigate the stability of the tip vortices for each of the three turbines under real-life atmospheric turbulence and quantify wake effects on turbine performance for various wind directions. 1 Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energys National Nuclear Security Administration under contract DE-AC04-94AL Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by Ltd 1

3 LES with the turbines parametrized as actuator lines have been employed extensively in the literature [3, 4, 5, 6, 7, 8, 9]. Grid resolution requirement is a critical issue for actuator line simulation of wind turbines and wind farms. Grids with 33 and 50 nodes per rotor diameter were employed in [6] and [9], respectively, for turbine-array simulations. A grid with 60 nodes per rotor diameter was employed in [5] to investigate the wake interactions between two turbines for various inflow conditions, which were generated using a synthetic turbulence technique. In [7], a grid with 70 nodes per rotor diameter was employed to analyse the stability of tip vortices. In order to lower the computational cost, meshes with coarse resolution are usually employed in the region away from the turbine, e.g. meshes are stretched in the downwind direction for the far wake region. Such low resolution, however, could cause the small-scale turbulence structures in the far wake to be under-resolved. Low resolution in the far wake is often necessitated by computational expedience but raises a number of important questions about the ability of such simulations to accurately resolve turbine wake interactions. In this paper we employ LES to start answering such questions in the context of the SWiFT facility. We employ the University of Minnesota Virtual Wind Simulator (VWiS) [10, 11] to carry out LES to study wake interactions of the SWiFT turbines with the aim to investigate the effects of streamwise resolution on the wake characteristics and the predictions of the downwind turbine performance. Two different grids with stretched and refined streamwise meshes from 1D to 4.5D downstream of the two upstream turbines are employed, respectively. The resolutions for the other two directions, on the other hand, are the same. In both grids 100 nodes per diameters are employed in the near-turbine region. The numerical methods are described in Section 2. In Section 3 the results are presented. A summary is given in Section Numerical methods: The VWiS code The VWiS code solves the 3D, unsteady, spatially-filtered (as required for LES) continuity and Navier-Stokes equations. The curvilinear immersed boundary (CURVIB) method [12] is used to solve these equations in order to simulate topography effects. The governing equations are first written in Cartesian coordinates x i and then transformed fully (both the velocity vector and spatial coordinates are expressed in curvilinear coordinates) in non-orthogonal, generalized, curvilinear coordinates ξ i. The transformed equations read in compact tensor notation (repeated indices imply summation) as follows (i, j = 1, 2, 3), 1 U i J t = ξi l J J U j ξ j = 0, (1) ( ξ j (U j u l ) + µ ρ 1 ρ ξ j (ξj l p J ) 1 ρ ( g jk ξ j J ) τ lj ξ j + f l ) u l ξ k, (2) where ξl i = ξ i / x l are the transformation metrics, J is the Jacobian of the geometric transformation, u i is the i th component of the velocity vector in Cartesian coordinates, U i =(ξm/j)u i m is the contravariant volume flux, g jk = ξ j l ξk l are the components of the contravariant metric tensor, ρ is the density, µ is the dynamic viscosity, p is the pressure, f l (l = 1, 2, 3) are the body forces introduced by the wind turbines and τ ij represents the anisotropic part of the subgrid scale stress tensor, which is modelled by the dynamic Smagorinsky subgrid scale model [13]. The actuator line model [3] is employed for turbine parametrization. The actuator line model accounts for the blades as separate rotating lines. The forces distributed on each line (blade) are calculated based on a blade element approach, in which the blade is 2

4 The Science of Making Torque from Wind 2014 (TORQUE 2014) Figure 1: Field view of the three SWiFT turbines (a) and schematic of the turbine locations (b). divided into elements in the radial direction and tabulated as 2D foil data. The forces fl in the momentum equations (Eq.(2)) is calculated by distributing the forces from the actuator lines to the background grid using the discrete delta function approach of [14]. The governing equations are discretized using a second-order accurate, three-point central finite-differencing scheme for all spatial derivatives. The discrete equations are integrated in time using a secondorder accurate fractional step method. For more details of the VWiS code and the associated numerical schemes, please refer to the papers [10, 15, 11]. 3. Numerical results We simulate the case with the wind is blowing from South to North (as shown in Figure 1). The atmospheric stability is neutral. The Reynolds number based on the inlet streamwise velocity at hub height (Uh ) and turbine rotor diameter (D) is about 2 105, which is within the range where Reynolds number independence can be achieved [16, 10]. A fully developed turbulent boundary layer flow, which is computed from a precursor simulation of a fully developed turbulent channel flow at the same Reynolds number, is fed at the inlet. A wall model is employed to simulate the effects of the ground [10]. Free-slip boundary condition is applied at the top boundary and the spanwise direction. The tip-speed ratio of the turbines is 5. The length of the computational domain is 7D and 5D in the crosswind (y) and vertical (z) directions, respectively. Two sizes in the wind direction (x), 10D and 15D, are employed for the two grids, respectively. The grid numbers are (grid I) and (grid II) for the two grids, in x, y and z directions, respectively. The meshes on the y-z plane are exactly the same for both grids. In the near-turbine locations, the mesh is uniformly distributed with 101 nodes per rotor diameter. The major difference appears from 1D to 4.5D downwind of the upstream turbine, where 101 points and 301 points were distributed for grid I and grid II, respectively. The time step is Uh /D for both grids. The computations were first carried out until the total kinetic energy of the computational domain reached a quasi-steady state, and subsequently the flow fields were averaged for approximately 80 rotor-revolution periods. The vertical profiles of the inflow from the precursor simulation of a fully developed turbulence channel flow are shown in Figure 2. The vertical profiles in Figure 2 are averaged in both time 3

5 Figure 2: energy. Vertical profiles of the inflow for (a) mean streamwise velocity (b) turbulence kinetic Figure 3: Time-averaged flow fields from grid II. (a) streamwise velocity (b) turbulence kinetic energy. and horizontal directions. The time-averaged flow fields are shown in Figure 3. It is noted that only the time-averaged flow fields from grid II are shown in Figure 3 because they are almost the same for the two grids (which can be observed from Figure 7). It is seen that the turbine T2 exhibits a much longer and persistent wake than the upwind turbine T1, underscoring the effect of upwind turbine wakes. Regions of high turbulence kinetic energy (TKE) are found in the shear layers from top and bottom tips of the rotor for both turbines. However, the TKE intensity from the downwind turbine is significantly higher and is distributed within a much wider region especially for that from the top shear layer. The structure of the tip vortices from the two grids are shown in Figures 4 and 5. It is seen that well-defined, helical tip vortices are generated in the wake of the two upwind turbines, which lose coherence and break up 1D-2D downwind from the turbines. For the downwind turbine, on the other hand, the tip vortices are not well defined and break up immediately downwind from the turbine for both grids I and II. Small-scale turbulence structures are generated at further downwind locations on grid II, which are significantly weaker for grid I. It is also seen that small-scale turbulence structures are regenerated further downwind for grid I where the grid is refined. The contours of the instantaneous streamwise velocity from the two grids are compared in Figure 6. It is also observed that much finer flow structures are resolved on grid II from 1D to 4.5D downwind locations from the upstream turbines. 4

6 The Science of Making Torque from Wind 2014 (TORQUE 2014) Figure 4: Comparison of the tip vortices from turbines T1 and T2. The tip vortices are identified by vorticity magnitude ω = 10. Figure 5: Comparison of the tip vortices from turbines T3. The tip vortices are identified by vorticity magnitude ω = 10. Figure 6: Comparison of the instantaneous flow fields from the two grids at x-y plane. 5

7 Figure 7: Inflow characteristics (point A in Figure 6 (b)) for the turbine T2. Red solid lines: grid II; Green dashed lines: grid I. (a) time-averaged streamwise velocity; (b) turbulence kinetic energy; (c) Power spectra density (PSD) of the streamwise velocity fluctuations. Figure 8: Power coefficient C P for the downwind turbine T2. The profiles of the time-averaged streamwise velocity and turbulence kinetic energy (k) are shown in Figure 7(a) and (b), respectively. It is seen that differences of the profiles from grids I and II are minor. The spectrum of the incoming wind (point A shown in Figure 6 (b)) is shown in Figure 8(c). A wider inertial region is observed on the Power of spectra density (PSD) from grid II because of the increased resolution of that grid, which enables more of the energy in the inertial range to be resolved. We have observed that the time-averaged inflow for the downwind turbine are nearly the same in terms of time-averaged streamwise velocity and turbulence kinetic energy (Figure 7(a) and (b)) for the two grids. On the other hand, we have also seen significant differences between these two grids as far as the structures in far wake (Figures 4 and 5), the instantaneous flow field (Figure 6) and the spectra (Figure 7(c)). It is interesting to examine, however, the extent to which how these differences in the inflow are affecting the downwind turbine performance. Figure 8 depicts the power coefficient C P calculated as follows C P = T Ω 1 2 ρau 3 h, (3) where T is the aerodynamic torque on the wind turbine, Ω the turbine rotating velocity, A the rotor-swept area and U h the free incoming velocity at turbine hub height. As seen nearly the same temporal variation of C P is observed on both grids. The time-averaged C P values are and for grids I and II, respectively. The rms (root-mean-square) of the C P fluctuations, on the other hand, are nearly the same, which are and for grids I and II, respectively. 6

8 4. Summary LES results of the SWiFT turbines on two grids were presented. We found that (1) differences of the time-averaged quantities from the two grids are minor; (2) tip vortices break up at 1D to 2D turbine downstream and immediately for upwind and downwind turbines, respectively; (3) break up of the tip vortices into much finer turbulence structures are well resolved on the finer grid; and (4) about 6% difference is observed for the C P from the two grids. This latter finding suggests that accurate prediction of the power output of wind farms will require carefully refined grids in the region between adjacent turbines. Acknowledgments This work was supported by Department of Energy DOE (DE-EE , DE-EE and DE-AC04-94AL85000). Computational resources were provided by Sandia National Laboratories and the University of Minnesota Supercomputing Institute. References [1] Barone M and White J 2011 DOE/SNL TTU scaled wind farm technology facility: Research opportunities for study of turbine-turbine interaction SANDIA REPORT, SAND [2] Berg J, Bryant J, LeBlanc B, Maniaci D, Naughton B, Paquette J, Resor B, White J and Kroeker D 2014 Scaled wind farm technology facility overview AIAA SciTech, January 2014, National Harbor, Maryland, 32nd ASME Wind Energy Symposium, AIAA [3] Sørensen J N and Shen W Z 2002 J. Fluid Eng. Trans. ASME [4] Shen W Z, Zhu W J and Sørensen J N 2012 Wind Energy [5] Troldborg N, Larsen G C, Madsen H A, Hansen K S, Sørensen J N and Mikkelsen R 2011 Wind Energy [6] Lu H and Porté-Agel F 2011 Physics of Fluids [7] Ivanell S, Mikkelsen R, Sørensen J N and Henningson D 2010 Wind Energy [8] Porté-Agel F, Wu Y T, Lu H and Conzemius R J 2011 J. Wind Eng. Ind. Aerodyn [9] Churchfield M J, Lee S, Michalakes J and Moriarty P J 2012 Journal of Turbulence [10] Yang X, Kang S and Sotiropoulos F 2012 Physics of Fluids (pages 28) [11] Yang X, Sotiropoulos F, Conzemius R J, Wachtler J N and Strong M B Wind Energy Under consideration [12] Ge L and Sotiropoulos F 2007 J. Comput. Phys [13] Germano M, Piomelli U, Moin P and Cabot W H 1991 Phys. Fluids A [14] Yang X, Zhang X, Li Z and He G W 2009 Journal of Computational Physics [15] Yang X and Sotiropoulos F 2013 On the predictive capabilities of les-actuator disk model in simulating turbulence past wind turbines and farms American Control Conference (ACC), 2013 (IEEE) pp [16] Chamorro L P, Arndt R and Sotiropoulos F 2012 Wind Energy