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Large-Eddy Simulation of Atmospheric Flow Over Complex Terrain

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Large-Eddy Simulation of Atmospheric Flow Over Complex Terrain RIS0 Large-Eddy Simulation of Atmospheric Flow over Complex Terrain Andreas Bechmann Ris0-PhD-28(EN) Ris0 National Laboratory Technical University of Denmark Roskilde, Denmark November 2006 Author: Andreas Bechmann Rise PhD 28(EN) Title: Large-Eddy Simulation of Atmospheric Flow over Complex November 2006 Terrain Department: Wind Energy Department Tins thesis is submitted in partial fulfilment of the requirements for the Ph D. degree at the Technical University of Demnark (DTU) Abstract (max. 2000 char.): ISBN 87-550-3556-6 The present report describes the development and validation of a turbulence model designed for atmospheric flows based on the concept of Large-Eddy Simulation (EES). The background for the work is the high Reynolds number k - s model, which has been implemented on a finite-volume code of the incompressible Reynolds-averaged Navier-Stokes equations (RANS). The k - s model is traditionally used for Contract no.: RANS computations, but is here developed to also enable EES. EES is able to provide detailed descriptions of a wide range of engineering flows at low Reynolds numbers. For Group's own reg. no. : atmospheric flows, however, the high Reynolds numbers and the rough surface of the earth provide difficulties normally not compatible with EES. Since these issues are most severe Sponsorship: near the surface they are addressed by handling the near surface region with RANS and only use EES above this region. Using this method, the developed turbulence model is Cover : able to handle both engineering and atmospheric flows and can be run in both RANS or EES mode. For EES simulations a time-dependent wind field that accurately represents the turbulent structures of a wind environment must be prescribed at the computational inlet. A method is implemented where the turbulent wind field from a separate EES simulation can be used as inflow. To avoid numerical dissipation of turbulence special care is paid to the numerical method, e.g. the turbulence model is calibrated with the specific numerical scheme used. This is done by simulating decaying isotropic and homogeneous turbulence. Three atmospheric test cases are investigated in order to validate the behavior of the presented turbulence model. Simulation of the neutral atmospheric boundary layer, illustrates the turbulence model ability to generate and maintain the turbulent structures responsible for boundary layer transport processes. Velocity and turbulence profiles are Pages: 106 in good agreement with measurements. Simulation of Tables: 20 References: 75 the flow over the Askervein hill is also performed. Speed-up and turbulence intensities show good agreement with measurements, except 400m downstream of the hill summit Information Service Department where speed-up is underestimated. Flow over a cube in a Riso National Laboratory Technical University of Denmark thick turbulent boundary layer is the final test case. The P.O.Box 49 turbulence model ability to capture the physics of the large DK-4000 Roskilde separated region downstream of the cube is demonstrated. Denmark Telephone +45 46774004 The turbulence model is, however, shown to have trouble biblfgirisoe.dk with very large values of roughness. Fax +45 46774013 www.risoe.dk Acknowledgements This thesis is submitted in partial fulfillment of the requirements for the Danish PhD degree at the Technical University of Denmark (DTU). The thesis documents the author ’s research carried out during the period of October 2004 to November 2006 at the Wind Energy Department, Ris0 National Laboratory and to a lesser extent at the Department of Mechanical Engineering, Technical University of Den ­ mark (MEK/DTU). The work was carried out under the supervision of Prof. J.N. S0rensen (MEK/DTU), Prof. N.N. S0rensen, Senior Researcher J. Johansen and Prof. J. Mann (Ris0). I would like to thank them for qualified supervision. The CFD computations were made possible by the use of the Ris0 240 nodes MARY PC-cluster, and the computational resources of the Danish Centre for Scientific Computing at MEK/DTU in Lyngby. I would like to express my gratitude to my supervisors, Prof. N.N. S0rensen and Senior Researcher J. Johansen who gave me the opportunity to undertake the PhD program. I am very grateful for the support. Thank you for always having time to answer my questions. I would also like to thank Prof. J. Mann and my fellow students F. Zahle and J. Berg for many helpful discussions. Last, but not least, thanks to my wife Dorthe for all the support and patience. November 2006 Andreas Bechmann Ris0-PhD-28(EN) iii Nomenclature Abbreviations ABL Atmospheric Boundary Layer CDg2 Second-order central difference scheme CDg4 Fourth-order central difference scheme CFD Computational Fluid Dynamics CFL Courant-Friedrich-Levy-number DEg Detached-Eddy Simulation HT The Askervein hill ’s highest point LEg Large-Eddy Simulation MM Mixed model MPI Message Passage Interface PIgO Pressure-Implicit with Splitting of Operators QUICK Quadratic upstream interpolation for convective kinetics scheme PAAg Reynolds-Averaged Navier-Stokes Pg The Askervein hill ’s reference site upstream gCg Subgrid-scales gL Surface Layer ggM Scale-similarity model TDMA Tri-Diagonal Matrix Algorithm TKE Turbulent kinetic energy PDg First-order upwind difference scheme UPAAg Unsteady RANS Greek Letters a The Kolmogorov constant a# Correlation coefficient for backscatter model A Cutoff length, filter width Kronecker delta or identity tensor Ag Speed-up ratio At Time step Ax Grid spacing in x-direction A% Grid spacing in y-direction Az Grid spacing in z-direction e Total turbulent dissipation rate r Adiabatic lapse rate K The von Karman constant e Mean modeled turbulent dissipation rate V Kinematic molecular viscosity vt Eddy viscosity IX Angular velocity of earth iv Ris0-PhD-28(EN) Qi Angular velocity vector of the earth ’s rotation T Resolved shear stress T.i3 Resolved turbulent stress tensor 0 Latitude 0e Dimensionless dissipation of turbulent kinetic energy 0k Dimensionless turbulent kinetic energy Dimensionless wind shear P Density &e Constant for turbulence model Constant for turbulence model 7 &V 7 &W Standard deviation in (xi,x2,x3) directions T Total shear stress TO Total wall stress Tij Unfiltered or full turbulent stress tensor e Cross-isobaric angle e Modeled turbulent dissipation rate T Modeled shear stress Tij Unresolved or SGS-stress tensor ^ijk Permutation tensor Roman Letters (Be) Mean energy backscatter W Ensemble averaged pressure (ui) Ensemble averaged velocity vector fi Resolved body force vector G Explicit spatial filter k Resolved turbulent kinetic energy P Resolved pressure S Local resolved strain rate u Resolved velocity vector, filtered (LES) Reynolds-ave.(RANS) k Subgrid turbulent kinetic energy l Length scale, switches between the RANS and LES length Characteristic turbulent velocity scale A Similarity constant for geostrophic resistance laws B Similarity constant for geostrophic resistance laws Be Energy backscatter Dimensionless drag coefficient Cp Pressure coefficient cp Specific heat at constant pressure CA Constant for turbulence model Cei Constant for turbulence model Ce2 Constant for turbulence model Ris0-PhD-28(EN) v C, Constant for turbulence model Cg Constant for backscatter model CgES Constant for DES model Cs Constant for Smagorinsky model f Frequency fc Coriolis parameter Fi One point one-sided spectrum as function of wavenumber fi Body force vector fC,i Coriolis acceleration vector G Geostrophic wind g Gravitational acceleration H Height of computational domain h Height (or depth) of the boundary layer hc Cube height I Turbulence intensity k Total turbulent kinetic energy kl,&2,&3 Wavenumbers in (x1,x2,x3) directions L Length of computational domain Lt Length scale used in turbulence generator Iles Characteristic turbulent length scale for LES fRANS Characteristic turbulent length scale for RANS M Horizontal wind speed Mg Wind tunnel grid spacing N Number of computational cells Nt Number of time steps Nx Number of computational cells in x-direction Ny Number of computational cells in y-direction Nz Number of computational cells in z-direction P Local pressure, perturbation around hydrostatic pressure Reference pressure Re Reynolds number g Grid Stretching ratio gi One point one-sided spectrum as function of frequency gij Strain rate tensor T Temperature t Time Tscs Timescale characteristic for the SGS-scales ui Resolved velocity fluctuation u, v, w Unfiltered velocity components, w is in the vertical u* Local characteristic velocity scale u O Mean inlet velocity ug Geostrophic wind in x-direction vi Ris0-PhD-28(EN) u h Velocity at cube height ui Unfiltered velocity vector, using Einstein notation u* 0 Friction or shear velocity evaluated at the wall uref Reference velocity vg Geostrophic wind in y-direction W Width of computational domain x, y, z Cartesian coordinates, z is the vertical coordinate xi Position vector, using Einstein notation z0 Surface roughness height of momentum z1 Height of the first near-wall grid cell zmi Distance from wall where model goes from RANS to LES Ris0-PhD-28(EN) vii List of Figures 1 Scales of the neutral ABL 2 2 Decomposed LES- and RANS-variable 9 3 Near-wall RANS region and outer LES region 16 4 Schematic of precursor / successor setup 20 5 Contour plot of streamwise velocity for varying cutoff lengths 22 6 Contour plot of velocity for varying differencing schemes 23 7 One-dimensional spectra for different time steps 24 8 Contour plot of velocity for different outlet conditions 27 9 Domain
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