Towards Simulating the Atmospheric Boundary Layer and Wind Farm Flows

Transcription

1 Towards Simulating the Atmospheric Boundary Layer and Wind Farm Flows 6 th OpenFOAM Workshop Matthew J. Churchfield Patrick J. Moriarty June 15, 2011 NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

2 Description Aerodynamics simulations to study wind farm physics Wake-turbine interaction Wake-atmospheric boundary layer interaction Wake-wake interaction + = atmospheric boundary layer simulation wind turbine model wind farm aerodynamics simulation 2

3 Motivation Currently used engineering wake models developed in 1980s/1990s Examples (OpenWind, Wasp,etc.) Now turbines are larger than in 1980s/1990s Turbines taller than many meteorological masts Velocity and direction shears across rotor become significant Atmospheric stability is important Wind profile and turbulence differ greatly from unstable to stable Need for improved engineering farm-level wake models CFD can help to understand modern wind farm physics 3

4 Motivation How atmospheric stability affects the Horns Rev wind farm [1] Stability Array Efficiency unstable 74% neutral 71% stable 66% Horns Rev Wind Farm in North Sea off Danish Coast source: UniFly A/S [1] L. E. Jensen. Array Efficiency at Horns Rev and the Effect of Atmospheric Stability, Dong Energy Presentation,

5 Methodology: ABL Flow 5 Large-eddy Simulation Based on buoyantboussinesqpisofoam We use linear spatial interpolation and Crank-Nicholson time integration (SGS and buoyant term explicit, though) i i i b D ij j i D k j ijk i j j i f x p g R x x p u u u x t u 1 ~ 2 0 j j j j R x u x t buoyancy Coriolis driving pressure gradient b

6 Methodology: ABL Flow capping inversion controls boundary layer height geostrophic wind simulation time: s periodic periodic 1 km 3 km Boussinesq approximation for buoyancy effects Coriolis forces included 3 km rough lower surface with temperature flux 6

7 Methodology: ABL Flow SGS Model Standard Smagorinsky Adequate for neutral and unstable stability conditions Implementing a dynamic Smagorinsky for stable conditions Surface Stress Model First layer of grid cells between 5-10 m tall Large eddies not resolved to wall Total (viscous + SGS) surface stress modeled using Moeng s model [1] Wei and Brasseur corrected Moeng s model [2] [1] C.-H. Moeng. A Large-Eddy Simulation Model for the Study of Planetary Boundary Layer Turbulence. Journal of the Atmospheric Sciences, Vol. 41, No. 13, 1984, pp [2] T. Wei and J. G. Brasseur. The Surface Stress Boundary Condition in Large Eddy Simulations of High Reynolds Number Turbulent Boundary Layer Flows. To be submitted to Boundary Layer Meteorology,

8 Methodology: Turbine Model Actuator Line Method [1] Blades represented as lines along which there are discrete sections For each element, we know local flow velocity and angle, rotor-induced speed, chord, twist, and airfoil Use a look-up table to get lift and drag at each section Equal and opposite of lift and drag at each actuator element projected back onto CFD flow field as a body force using a spherical Gaussian. [1] Sørensen, J. N. and Shen, W. Z., Numerical Modeling of Wind Turbine Wakes, Journal of Fluids Engineering 124, 2002, pp

9 Methodology: Wind Farm Simulation Perform horizontally periodic precursor ABL simulation Apply an array of actuator line models to wind farm domain Intialize wind farm domain with precursor volume field Once precursor ABL is developed, use surface functionobject to save boundary planes of data every N time steps Use saved precursor boundary data with timevaryingmappedfixedvalue BC to feed turbulent data into wind farm domain 9

10 Results: ABL Flow Neutral Unstable U (m/s) at hub height of 90 m 8 from from 270 z 0 (m) Q s (K-m/s) Neutral Unstable z i (m) z i /L u* (m/s) w* (m/s) See [1] Re LES Script R [1] J. Brasseur and T. Wei. Designing Large-Eddy Simulation of the Turbulent Boundary Layer to Capture Law-of-the-Wall Scaling, Physics of Fluids, Vol. 22, No. 2,

11 Results: ABL Flow Neutral: -z i /L = 0 Unstable: -z i /L = 2.14 turbine disk vertical sweep 11

12 Results: ABL Flow Neutral: -z i /L = 0 Unstable: -z i /L = 2.14 Increasing height 2-dimensional velocity spectra (black first grid level) (magenta top of boundary layer) 12

13 Results: ABL Flow Neutral: -z i /L = 0 Unstable: -z i /L = 2.14 Streamwise velocity fluctuations at 90 m above surface Vertical velocity fluctuations at 90 m above surface 13

14 Results: ABL with Wind Turbines flow 2.5 m turbine rotor 5 m 10 m Horizontal slice through wind farm mesh at 90 m 14

15 Results: ABL with Wind Turbines Red are positive isosurfaces of second invariant of velocitygradient tensor (Q) Bound and tip vortices of 3-bladed 5MW turbine visible 15

16 Results: ABL with Wind Turbines Neutral: -z i /L = 0 Smaller scales resolved on finer mesh 16

17 Results: ABL with Wind Turbines Unstable: -z i /L = 2.14 Half the turbine in low speed streamwise flow of an updraft 17

18 Results: ABL with Wind Turbines Unstable: -z i /L = 2.14 Half the turbine in low speed streamwise flow in updraft 18

19 Results: ABL with Wind Turbines Neutral: -z i /L = 0 Unstable: -z i /L = 2.14 Horizontal time-averaged wake profiles at hub height Vertical timeaveraged wake profiles 19

20 Problems Encountered blockmesh, refinemesh, mapfields, decomposepar require large amounts of memory for larger meshes Need a better method Coarse mesh with blockmesh Run decomposepar Run refinemesh and mapfields on each processor directory Need to try OF-1.6-ext new generation solvers for pressure 20

21 Questions For You Buoyancy formulation Solve ( UEqn == fvc::reconstruct ( - fvc::sngrad(pd)*mesh.magsf() +(fvc::interpolate(rhok - 1.0)*(g & mesh.sf())) ) ); fvvectormatrix UEqn ( fvm::ddt(u) + fvm::div(phi,u) + divdevr + gradpd //- ((rhok - 1.0)*g) - fcoriolis ); Why is buoyant term interpolated and reconstructed instead of being taken straight from cell center? 21

22 Questions For You Pressure gradient formulation ABL solver (from buoyantboussinesqpisofoam) pisofoam Solve ( UEqn == fvc::reconstruct ( - fvc::sngrad(pd)*mesh.magsf() +(fvc::interpolate(rhok - 1.0)*(g & mesh.sf())) ) ); U += rua*fvc::reconstruct((phi - phiu)/ruaf); solve(ueqn == -fvc::grad(p)); U -= rua*fvc::grad(p); Why is pressure gradient term interpolated and reconstructed unlike in pisofoam? Why is U completed differently than in pisofoam? 22

23 Future Work Validation IEA Task 31 WAKEBENCH - Benchmarking Wind Farm Flow Models Better law-of-the wall scaling in ABL simulations Improve turbine model Coupling with NREL s FAST aeroelastic turbine model (Sang Lee) Implications of local mesh refinement on SGS stresses and turbulence cascade More sophisticated SGS modeling 23

24 Acknowledgements Penn State Jim Brasseur, Ganesh Vijayakumar, Eric Patterson, Adam Lavely, Mike Kinzel NREL Sang Lee, Pat Moriarty, Avi Purkayastha, Mike Sprague, John Michalakes, Julie Lundquist, Kenny Gruchalla RedRock and RedMesa HPC systems University of Puerto Rico, Mayagüez Tony Martínez, Stefano Leonardi Funding U.S. Department of Energy NREL Laboratory-Directed Research and Development Program 24