Identification of severe wind conditions using a Reynolds Averaged Navier-Stokes solver

Transcription

1 Journal of Physics: Conference Series Identification of severe wind conditions using a Reynolds Averaged Navier-Stokes solver To cite this article: N N Sørensen et al 2007 J. Phys.: Conf. Ser View the article online for updates and enhancements. Related content - Detached Eddy Simulations of the local Atmospheric Flow Field within a Forested Wind Energy Test Site located in Complex Terrain Patrick Letzgus, Thorsten Lutz and Ewald Krämer - CFD and Experimental Studies on Wind Turbines in Complex Terrain by Improved Actuator Disk Method Xin Liu, Shu Yan, Yanfei Mu et al. - Numerical simulation of the impact of atmospheric turbulence on a wind turbine in complex terrain Christoph Schulz, Patrick Letzgus, Pascal Weihing et al. Recent citations - Predicting wind farm wake interaction with RANS: an investigation of the Coriolis force M P van der Laan et al - Modelling of atmospheric boundary-layer flow in complex terrain with different forest parameterizations R Chávez Arroyo et al This content was downloaded from IP address on 09/01/2019 at 09:57

2 Identification of severe wind conditions using a Reynolds Averaged Navier-Stokes solver N N Sørensen 1, 2, A Bechmann 1, J Johansen 1, L Myllerup 1, P Botha 3, S Vinther 4, B S Nielsen 4 1 Wind Energy Dep., Risø National Lab., Technical University of Denmark, DK-4000 Roskilde, Denmark 2 Department of Civil Engineering, Aalborg University, DK-9000 Aalborg, Denmark 3 Meridian Energy Limited, PO Box 10840, Wellington, New Zealand 4 Siemens Wind Power A/S, DK-7330 Brande, Denmark nns@risoe.dk Abstract. The present paper describes the application of a Navier-Stokes solver to predict the presence of severe flow conditions in complex terrain, capturing conditions that may be critical to the siting of wind turbines in the terrain. First it is documented that the flow solver is capable of predicting the flow in the complex terrain by comparing with measurements from two meteorology masts. Next, it is illustrated how levels of turbulent kinetic energy can be used to easily identify areas with severe flow conditions, relying on a high correlation between high turbulence intensity and severe flow conditions, in the form of high wind shear and directional shear which may seriously lower the lifetime of a wind turbine. 1. Introduction Many of the sites chosen for erecting new wind farms today are located in areas with highly complex terrain. Often, the wind resource at these sites are significant, and the main concern may not be maximizing the production, but to assure that the turbine will not fail prematurely. For this type of complex terrain, the flow will not obey the normal scaling laws used for atmospheric boundary layer flows. Several of these deviations from the normal atmospheric conditions can reduce the lifetime of the turbine, produce velocity profiles with negative vertical shear, wind direction shear of more than 20 degrees over the rotor disc and extremely high turbulence intensity. Classical wind resource estimation techniques were developed for terrain with smooth hills and moderate slopes. In complex or rugged terrain, however, the wind flow may separate where steep slopes occur, thus creating a different wind profile than that predicted by a classical flow model, such as the one used by the industry-standard Wind Atlas Analysis and Application Program (WAsP), Troen [1],[2], Jackson and Hunt [3] and Taylor et al. [4]. Recently, the finite volume Navier-Stokes solver EllipSys3D has been applied successfully to several complex sites, with the aim to identify positions with severe wind conditions that may significantly reduce the lifetime of a wind turbine. The use of Navier-Stokes simulations for complex terrain is not new, see [5][6][7][8] for application in terrain with moderate slopes and [9], [10] and [11] for a more complex site. The main problems of complex flow simulations are the establishment of the correct inflow boundary conditions, and the high number of computational cells needed to resolve a large region properly in all directions. c 2007 Ltd 1

3 In the present work a procedure is illustrated by a case, where a relatively large site ~16 km x 25 km is analyzed. The procedure is based on a series of Reynolds Averaged Navier-Stokes computations, using a computational grid of approximately 25 million cells for each of the six considered wind direction. For each of the wind directions severe wind conditions are identified by extracting vertical profiles of turbulence intensity, velocity, and horizontal and vertical flow inclination at more than 50 possible turbine positions. At three of the possible future turbine positions, measurements from meteorology masts exist. For these positions severe wind events observed for a very narrow flow direction range, can be identified by the flow solver. It is shown how visualizations of iso-surfaces of turbulence intensity can be used to choose the positions where severe flow conditions are absent. Further more; detailed flow visualizations can greatly help to understand the effect of the terrain on the flow, creating severe wind conditions. 2. Method The in-house flow solver EllipSys3D is used in all computations presented in this paper. The code is developed in co-operation between the Department of Mechanical Engineering at DTU and The Department of Wind Energy at Risø National Laboratory, see [12],[13] and [14]. The EllipSys3D code is a multiblock finite volume discretization of the incompressible Reynolds Averaged Navier-Stokes (RANS) equations in general curvilinear coordinates. The code uses a co-located variable arrangement, and Rhie/Chow interpolation [15] is used to avoid odd/even pressure decoupling. As the code solves the incompressible flow equations, no equation of state exists for the pressure, and in the present work the SIMPLE algorithm of [16] is used to enforce the pressure/velocity coupling. The EllipSys3D code is parallelized with MPI for execution on distributed memory machines, using a non-overlapping domain decomposition technique. Both steady state and unsteady computations can be performed. For the unsteady computations the solution is advanced in time using a 2nd order iterative time-stepping (or dual time-stepping) method. In each global time-step the equations are solved in an iterative manner, using under-relaxation. First, the momentum equations are used as a predictor to advance the solution in time. At this point in the computation the flow field will not fulfil the continuity equation. The rewritten continuity equation (the so called pressure correction equation) is used as a corrector making the predicted flow field satisfy the continuity constraint. This two step procedure corresponds to a single sub-iteration, and the process is repeated until a convergent solution is obtained for the time step. When a convergent solution is obtained, the variables are updated, and we continue with the next time step. For steady state computations, the global time-step is set to infinity and dual time stepping is not used, this corresponds to the use of local time stepping. In order to accelerate the overall algorithm, a multi-level grid sequence is used in the steady state computations. The convective terms are discretized using a third order QUICK upwind scheme, implemented using the deferred correction approach first suggested by Khosla and Rubin [17]. Central differences are used for the viscous terms, in each sub-iteration only the normal terms are treated fully implicit, while the terms from nonorthogonally and the variable viscosity terms are treated explicitly. Thus, when the sub-iteration process is finished all terms are evaluated at the new time level. In the present work the turbulence in the boundary layer is modeled by the k-ε eddy viscosity model of [18], with constants calibrated for atmospheric conditions. As described in [14] this can be obtained by using the following expressions: ε1 C 4 2 μ = uτ k, (1) C = C κc σ. (2) ε 2 1/ 2 μ ε The three momentum equations are solved decoupled using a red/black Gauss-Seidel point solver. The solution of the Poisson system arising from the pressure correction equation is accelerated using a 2

4 multi-grid method. In order to accelerate the overall algorithm, a multi-level grid sequence and local time stepping are used Boundary conditions Both the inlet and the wall boundary conditions are based on the logarithmic law-of-the-wall, which can be derived for a boundary-layer flow, where variation in the flow direction is negligible, following [19]. In this special case we have zero stream wise gradients except for the favorable pressure gradient driving the flow, which in fact is a one-dimensional Couette flow. Inflow conditions, using a standard logarithmic equilibrium profile, are assumed at the upstream face of the computational grid and at the lid of the computational domain, which for the velocity, corresponds to the condition (3). In accordance with the logarithmic velocity profile the turbulent kinetic energy profile is specified as constant with a value given by (4), while the equilibrium profile for the dissipation of the turbulent kinetic energy corresponds to (5), resulting in the well known expression for the eddy viscosity of the neutral atmospheric boundary layer (6). = 1 z U ( z) u τ κ ln (3) z0 2 uτ k( z) = (4) C 3 4 μ 3 2 C μ k ε ( z) = κz (5) μ = ρκu z (6) t τ At the outlet fully developed flow is assumed. In the code this is implemented by using a zero gradient assumption in the mesh direction normal to the outlet plane. At the two cross stream planes, symmetry conditions are used. The equilibrium assumptions for the wall bounded flow results in the following treatment of the velocities and turbulent quantities at the walls, see [14] and [20]. The boundary conditions for the velocities are implemented through the skin friction at the wall, as described in [21]. In the EllipSys implementation the first cell is placed on top of the roughness elements, at the height z 0. The advantages of this procedure is that there are no restrictions on the height of the first cell, which in case of large shifts in roughness height from sea to shore may pose unwanted restriction on the computational grid. The skin friction is evaluated at the cell centre where the variables are stored: ρκc μ k U ( z P ) τ w =, (7) Δz ln + 1 z0 where Δz is the distance from the bottom face of the cell to the cell (z p ) centre. The boundary condition for the turbulent kinetic energy equation reduces to a balance between the production and dissipation of the quantity itself. In the code this is implemented by a von Neumann condition on the turbulent kinetic energy, and replacing the production term in the first cell by the equilibrium value. The production of turbulent kinetic energy is obtained from the average value of the 3

5 production in the wall cell by integration over the wall cell, assuming constant wall shear stress: The production term can then be written as: P τ ln(2δzz 1 w 0 = 1 2Δz ln( Δzz0 + 1) U ( z + 1) p ). (8) The equation for the dissipation of turbulent kinetic energy is abandoned in the wall cell; instead the dissipation is specified according to the balance between the production and dissipation obtained for the fully developed flow: C μ k ε = (9) κ Δz + z ) ( Validation of the method The method has previously been validated for flow over terrain, using the Askervein Hill data [14], [22] and using the Hjardemål data [23], and in connection with rotor aerodynamics over the last many years. For flow over complex terrain, only very limited data are available, and the few cases where the solver has been applied previously the results can not be shown as the data are proprietary. At the moment a small scale complex terrain study is being planned near Risø National Laboratory at the Bolund site, where one of the aims is to provide new data for model verification. 3. Considered site The planned turbine park near Wellington in New Zealand will eventually consist of up to 70 turbines. At the moment measurements are available from two masts. One is a 40 meter mast located at ( E; N) and the other is a 60 meter mast located at ( E; N). The wind rose show two dominating wind directions, around 350 degrees from north and 150 degrees from south east, see Figure 1. Figure 1 The measured wind rose from the Wellington site show two dominating wind directions. 4

6 During the measuring campaign, events with high turbulent kinetic energy were measured at the 60 meter mast, for a flow direction of 330 degrees, while similar behavior was not seen for the remaining flow directions. It was decided to investigate whether these conditions could be reproduced by the Navier-Stokes computations, and additionally to check the remaining turbine park for similar events. Based on the very narrow wind rose, it was decided to investigate the following six flow direction [135, 150, 165, 330, 345, 360] degrees, afterwards an additional wind direction of 338 degrees was added to further investigate the directional sensitivity. Figure 2 Overview of the terrain at the Wellington site, clearly showing the complexity of the terrain of the planned site right. The left figure show the location of the three erected measuring masts, the 40 meter reference mast is at the M1 location and the 60 meter mast is placed at the M2 location. For all flow direction, the flow approaches the terrain from the sea, and simple inflow conditions corresponding to equilibrium flow conditions, with a logarithmic velocity profile can be used. For the southern flow directions (150, 135), the south east part of the terrain has been extended to sea level by approximated terrain due to lack of actual information. As several kilometers (~6km) of terrain bridge the region between the approximated terrain and the turbine park, this approximation is believed to be of minor importance. The assumed roughness is meter for the sea surface, and in lack of detailed data for the terrain a uniform roughness length of 0.03 meters was estimated. Based on the turbulence measured at the 40 meter met mast, which seems relatively undisturbed by the terrain, a turbulence intensity of 0.1 was used as inflow conditions, along with a wind speed at hub height in the inlet profile of 11 m/s. To fulfill both the desired velocity profile, and the required turbulence intensity the Cμ constant was adjusted according to (1) giving a value of Computational mesh The computational mesh is a very important part of a CFD simulation, and in the present application the following three step procedure is used. First, based on a map file a gridded file covering 12.8 km times 16.7 km and with a resolution of 25 meter times 32 meter is generated, using the WAsP utility Map2Grid. Secondly, the surface mesh (x, y and z) values of the computational grid are constructed using an in-house 2D surface grid generator. Finally, having generated the surface mesh, the enhanced hyperbolic grid generator HypGrid3D is used to generate the final volume mesh. HypGrid has for many years been developed in connection with the computations of rotor aerodynamics. In the vertical direction 80 cells are used, giving a total 5

7 of 25.6 million cells and a cell height of 0.1 meter at the wall surface for the 5 km high domain, see Figure 3. The grid for each of the six wind directions is aligned with the intended mean flow direction, in order to minimize numerical diffusion and to ease the implementation of the slip conditions at the side borders. The number of grid points is 800 cells in the flow direction and 400 in the cross stream direction. Figure 3 Details of the computational mesh used for the terrain computations showing the rapidly expanding grid away from the surface. 5. Results 5.1. Grid Independence To assure that the flow is sufficiently resolved by the computation, the turbulent kinetic energy at hub height is compared for the three finest grid levels, showing that already grid level two provides sufficient resolution. The coarse grid levels are constructed by simply removing every second point in all directions, so that level-2 has 3.2 million cells and level-3 has 0.4 million cells. The same observation can be made by comparing the vertical velocity profiles at the turbine positions, where a minimum of deviation is seen for the two finest levels Comparison with measured values In the following the measured data used for comparison are all 10 minute averaged values, measured using sonic anemometers. The computed values are all steady state values. To validate the computations, comparison of the measured and computed values at two positions is performed. The reference position is 40 meter above terrain for the 40 meter mast (M1), while the test position is the 60 meter station of the 60 meter mast (M2), see Figure 2. The terrain induced flow distortion near the 40 meter mast is small with respect to the conditions enforced at the inflow boundary, and in the study no iterative adjustment of the inflow direction was pursued to obtain the exact flow direction at the 40 meter mast. The consequence of this can be seen when looking at Figure 5 to Figure 6, where the computed direction at the 40 meter mast shown along the x-axis does not agree fully with the measured values. When comparing the measured and computed data, the fact that the measured data are 10 min averaged data, and thus represents a range of flow direction and velocities around the mean must be considered. In contrast the computed data are for one single flow direction and one wind speed only, and the inherent smoothing present in the measurements are therefore not included in the computations. 6

8 Looking at the flow direction at the 60 meters mast, Figure 4, the agreement is not especially good, showing generally deviations in the range of 2 to 10 degrees. For the 165 degrees flow direction a large deviation of nearly 15 degrees is observed. In the left figure showing the northern direction, the scale has been shifted so that 0 degrees corresponds to flow directly from North while the plus and minus values indicates flow from North East or North West respectively. Figure 4 Comparison of computed and measured flow direction at the 60 meter mast as function of the flow direction at the 40 meter mast, for the seven computed cases. The left figure shows the northern directions and right figure shows the southern directions. Figure 5 Comparison of computed and measured increase in turbulence intensity at the 60 meter mast as function of the flow direction at the 40 meter mast, for the seven computed cases. The left figure shows the northern direction and right figure shows the southern directions. 1 1 I T = σ U = 1.07 ku (10) 7

9 The change in computed turbulence intensity from the 40 meters level at the 40 meter mast to the 60 meter position at the 60 meter mast were compared to measured values, see Figure 5. The turbulence intensity used in these comparisons is defined by (10) using the local velocity for normalization. Comparing the overall trend in the turbulence intensity increase, the computation show the same overall trend as the measurements, with a decreasing value for the northern direction when the flow direction increases from 330 to 360, clearly showing an extreme high turbulence level at the 60 meter mast for the 330 degrees direction. The same behavior is observed for the southern directions when the flow changes from 135 to 165 degrees, where the turbulence level also approaches the 40 meter mast level when the flow direction decreases. Generally, the increase in turbulence level is much over predicted in the computations, and part of this is believed to be due to the fact that the previously mentioned smoothing inherent to the measurements is absent in the computations, where the flow direction is fixed at a single value at the inlet. In order to further investigate this effect, an additional flow direction of 338 degrees was included; showing that even this small change in flow direction results in less than half the turbulence intensity observed at 330 degrees, see Figure 5. This observed over prediction of around 100 % in the increase in turbulence intensity, is directly linked with events where the flow velocity is low at the 60 meter mast position, see Figure 6. As high turbulence is mainly a problem for turbines at high wind, the error is not considered critical for the purpose of identifying severe flow conditions. Finally, the computed and measured speedup is shown in Figure 6. This figure shows the relative increase of the velocity of the 60 meter positions at the 60 meter mast compared to the 40 meter position at the 40 meter mast. From the figure it is clear that the quantitative agreement is far from perfect, but again the general trend predicted by the flow solver shows a reasonably good agreement with the measured values. Figure 6 Comparison of computed and measured speedup at the 60 meter mast as function of flow direction at the 40 meter mast, for the seven computed flow cases. The left figure shows the northern directions and right figure shows the southern directions Identification of severe flow conditions A good impression of the areas with severe flow conditions can be obtained by viewing isosurfaces of high turbulent kinetic energy, see Figure 7. The figure shows the terrain seen directly from above, and the red iso-surfaces correspond to areas with turbulent kinetic energy equal to 9 m 2 /s 2. In 8

10 the plot, all high levels below 40 meters over terrain has been filtered out, in order to remove the effect of strong shear very close to the surface which do not reach typical rotor height. For the flows directly from north, none of the selected turbine positions are predicted to experience high turbulent flow. For the 345 degrees flow direction, some of the turbine positions at the upper left part of the figure are shrouded in high turbulence, generated by the steep upstream ridge. Finally, the 330 degrees flow direction, which was identified as problematic in the measurements, a large production of turbulent Figure 7 Iso-contour of turbulent kinetic energy clearly indicating areas where problems may arise. The wind directions for the six cases are, from top to bottom left row (360, 345, 330) and from top to bottom right row (165, 150, 135) degrees, where the pictures are oriented with north pointing upwards. 9

11 kinetic energy is seen from the upstream ridge covering the turbine positions at the downstream ridge and the position of the measuring mast. In the accompanying paper [24], this phenomenon is studied in more detail using an advanced hybrid RANS/LES method. For the flow direction of 165 degrees from south, no turbines seem to be affected by high turbulence. For the 150 degrees, some of the turbines at the bottom part of the picture may be affected. Finally, for the 135 degrees direction, two turbines seems to be hit by a very high turbulent wake of a far upstream ridge in the lower part of the picture Extended evaluation of sites Besides the direct visual evaluation of the site by plots similar to Figure 7, profiles of velocity, directional shear and turbulence intensity are typically extracted at several positions around the terrain, especially at the planned turbine positions. Below in Figure 8, two locations in the terrain are selected and compared for the three northern directions. The positions are chosen so that one of them is located in the area near mast M2 where the turbulence tongues from an upstream ridge of Figure 7 are influencing the position for given wind directions and one is chosen near mast M3 so that no disturbance from upstream turbulence is present for the investigated flow directions. From the velocity profiles it is clear that the position influenced by the upstream turbulence exhibits a distinct deviation from a standard atmospheric profile, whereas the other profile more resembles the normal logarithmic profile, see Figure 8. Figure 8 Comparison of the velocity profiles at two positions in the terrain for the three northern flow direction, one experiencing normal conditions (left) and one experiencing severe flow conditions (right). The severe conditions correspond to situations where the terrain location is embedded in the turbulence tongues. Looking at the profiles of turbulent kinetic energy at the same two stations, see Figure 9, the tendency is much the same. The profile located in the turbulent wake exhibits an extremely high turbulence level several times the free stream level, and the high levels are occurring far above the terrain level. The profile free of upstream wake effects has much lower turbulence and the high levels are concentrated much closer to the ground, see Figure 9. 10

12 Figure 9 Comparison of the turbulent kinetic energy profiles at two positions in the terrain for the three northern flow directions. Normal conditions (left) and severe conditions (right). Finally, the directional shear, here shown as the deviation of the flow direction from the free stream flow direction, is another clear sign of the high influence of the terrain. In Figure 10 the two positions are compared with respect to directional shear, again it is clear that the position influenced by the wake from the upstream ridge shows an extreme directional shear of more than 40 degrees, while the position free from severe upstream influence do not show a behaviour like this. Figure 10 Comparison of the directional shear at two positions in the terrain for the three northern flow direction. Normal conditions (left) and severe conditions (right). 6. Conclusion A series of CFD computations of flow over complex terrain has been performed. The solution was shown to be relatively grid independent, and the finest mesh featured 16.7 million cells to cover the 13 times 17 km terrain. First it was demonstrated that the solution was capable of capturing the overall behavior of the flow measured by two Sonics, with respect to velocity as well as turbulence and change in flow direction. Following this, it was illustrated how the occurrence of tongues of high turbulence intensity can be used to identify positions with severe flow conditions. Having identified the positions with high turbulence, the difference in flow quality was illustrated by comparing a typical position with and 11

13 without high turbulence intensity. This clearly shows how critical these positions may be for the lifetime of a turbine. Acknowledgement The CFD computations were made possible by the use of the Risø 240 CPU PC-cluster Mary. References [1] Troen, I. and E.L. Petersen (1989). European Wind Atlas. Risø National Laboratory, Roskilde. ISBN pp.a reference [2] Troen, I. (1990). A high resolution spectral model for flow in complex terrain. Ninth Symposium on Turbulence and Diffusion, Roskilde, April 30 - May 3, 1990, [3] Jackson P.S. and Hunt J.C.R. Turbulent Wind Flow Over a Low Hill. Quart. J.R. Met. Soc.,101: [4] Taylor P.A., Walmsley, J.L. and Salmon, J.R., A Simple Model of Neutrally Stratified Boundary-Layer Flow Over Real Terrain Incorporating Wavenumber-Dependent Scaling, Boundary-Layer Meteorol. 26, , [5] Raithby G D, Stubley G D and Taylor P A, The Askervein Hill Project: A Finite Control Volume Prediction of Three-Dimensional Flows Over the Hill. Boundary-Layer Meteorology, 39: , [6] Castro F A, Palma J M L M, Sliva Lopes A. Simulation of the Askervein Flow. Part 1: Reynolds Averaged Navier Stokes Equations (k-ε Turbulence Model) Journal: Boundary- Layer Meteorology Volume 107, Number 3 / June, 2003,Pages [7] Undheim O, Andersson H I and Berge E. Non-Linear, Microscale Modelling of the Flow Over Askervein Hill Journal Boundary-Layer Meteorology Volume 120, Number 3 September, 2006,Pages [8] Prospathopoulos J, Voutsinas S G. Implementation Issues in 3D Wind Flow Prediction Over Complex Terrain, J. Sol. Energy Eng., Volume 128, pp [9] Berge E, Gravdahl A R, Schelling J, Tallhaug L, Undheim O, Wind in complex terrain. A comparison of WAsP and two CFD-models, In Proceedings from EWEC 2006, 27 feb.- 02 march, Athens, Greece. [10] P.Chaviaropoulos, D.Douvikas, Mean Wind Field Prediction over Complex Terrain in the Presence of W/Ts, European Wind Energy Conference and Exhibition, Nice-France [11] P.Chaviaropoulos, D.Douvikas, Mean-Flow-Field Simulations over Complex terrain using a 3- D Reynolds Average Navier Stokes Solver, ECCOMASS 98, Athens 7-11/9/1998. [12] Michelsen, J.A.. Basis3D - a Platform for Development of Multiblock PDE Solvers. Technical Report AFM 92-05, Technical University of Denmark, [13] Michelsen J.A., Block structured Multigrid solution of 2D and 3D elliptic PDE's, Technical Report AFM 94-06, Technical University of Denmark, [14] Sørensen, N.N.. General Purpose Flow Solver Applied to Flow over Hills. Risø-R- 827-(EN), Risø National Laboratory, Roskilde, Denmark, June [15] Rhie C.M. A numerical study of the flow past an isolated airfoil with separation Ph.D. thesis, Univ. of Illinois, Urbane-Champaign, [16] Patankar S.V. and Spalding D.B. A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows. Int. J. Heat Mass Transfer, 15:1787,1972 [17] Khosla P.K. and Rubin S.G., A diagonally dominant second-order accurate implicit scheme, Computers Fluids, 2: , [18] Launder B.E. and Spalding D.B.. The Numerical Compuation of Turbulent Flows. Comput. Meths. Appl. Mech. Eng., 3: ,1974. [19] Tennekes H. and Lumley J.L. A First Course in Turbulence. MIT Press, Cambridge, MA (US), 3 edition,

14 [20] Hackman L.P., A Numerical Study of the Turbulent Flow Over a Backward Facing Step Using a Two Equation Turbulence Model, Ph.D. thesis, Univ Waterloo, Ontario, [21] Peric M. A finit volume method for prediction of three-dimensional fluid flow in complex ducts. Ph.D. thesis, Univ. of London, [22] Bechmann A., Sørensen N.N. and Johansen J. Atmospheric Flow over Terrain using Hybrid RANS/LES, In Scientific proceedings, Ewec 2007 Milan, 7-10 May [23] Jørgensen, B.H.; Hansen, A.D.; Myllerup, L.; Sørensen, N.N.; Mann, J.; Ott, S.; Badger, J., Computational wind power meteorology in complex terrain compared to measurements (poster). In: Proceedings CD-ROM European Wind Energy Conference and Exhibition, London (GB), Nov (European Wind Energy Association, Brussels, 2005) 7 p. [24] A. Bechmann, N.N. Sørensen and J. Johansen, P. Botha, Hybrid RANS/LES Method for High Reynolds Numbers, Applied to Atmospheric Flow over Complex Terrain, In The Science of maing Torque from Wind, August, Lyngby, Denmark. 13