Wind Flow Modeling The Basis for Resource Assessment and Wind Power Forecasting

Transcription

1 Wind Flow Modeling The Basis for Resource Assessment and Wind Power Forecasting Detlev Heinemann ForWind Center for Wind Energy Research Energy Meteorology Unit, Oldenburg University

2 Contents Model Physics Planetary Boundary Layer Model Overview for Wind Flow Simulation

3 Subject of Modeling: The Planetary Boundary Layer The PBL is: turbulent layer lowest ~km on the Earth surface directly affected by surface heating, moisture, pollution, surface drag -> turbulent exchange diurnal cycle over land convective and stable PBLs Source: Brutsaert

4 PBL: Effects of Terrain and Stability Source: Beljaars

5 PBL: Diurnal Cycle of Boundary Layer Height Source: Beljaars

6 PBL: Diurnal Cycle of Profiles Source: Beljaars

7 Basic ( Primitive ) Equations Based on conservation principles for momentum, mass & energy: Momentum Equation Continuity Equation Thermodynamic Equation (1st Law) Balance equation for water vapour Gas Law Wind Speed Density Air Temperature Humidity, Clouds Pressure

8 Equation of Motion (Navier Stokes) in vectorised notion: in x, y, z components:

9 Averaged Equations Equations as used in a model represent the evolution of a space-time average of the true solution Equations become empirical once averaged, no longer fundamental Full form of exact equations not necessary to represent an averaged flow E.g.: hydrostatic approximation is o.k. for large enough averaging scales in the horizontal Sub-grid model represents effect of unresolved scales on the averaged flow expressed in terms of the input data (representing an averaged state!) Average of the exact solution may *not* look like what we expect, e.g. since vertical motions over land may contain averages of very large local values.

10 Numerical Models A large variety of numerical models is available, ranging from simple linear solvers through to direct numerical solutions. Their use for ABL flows varies in quality: linear models being easy to put into practice albeit with limited accuracy more complex models being much more difficult to compute, though producing much more precise solutions. Turbulence models use different methods to model fluctuations inherent in the full Navier-Stokes equations. They are used because the use of the full Navier-Stokes equations is normally computationally impractical

11 Numerical Models Numerical methods of studying (turbulent) motion: Linearized flow models Reynolds-average modeling (RANS) Modeling ensemble statistics Direct numerical simulation (DNS) Resolving all eddies Large eddy simulation (LES) Intermediate approach

12 I. Linear Models Famous example: WAsP (Wind Atlas Analysis and Application Program) from RISØ based on the concept of linearised flow models (Jackson and Hunt, 1975) Developed initially for neutrally stable flow over hilly terrain Contains simple models for turbulence and surface roughness Best suited to more simple geometries Quick and accurate for mean wind flows Poorly predict flow separation and recirculation Limitations in more complex terrain regions due to the linearity of the equation set

13 II. Direct Numerical Models Direct numerical simulation of the Navier-Stokes equations for a full range of turbulent motions for all scales Only approximations which are necessary numerically to minimise discretisation errors Clear definition of all conditions (initial, boundary and forcing) and the production of data for every single variable Only simple geometries and low Reynolds numbers will be modelled Very large computational requirements No practical engineering tool Basic computations using DNS provide very valuable information for verifying and revising turbulence models

14 III. Large Eddy Simulation Separation of scales: Large scales: contain most of the energy and fluxes, significantly affected by the flow configuration, are explicitly calculated Smaller scales: more universal in nature & with little energy are pameterized (SFS model) LES solution supposed to be insensitive to SFS model turbulent flow Energy-containing eddies (important eddies) Subfilter scale eddies (not so important)

15 III. Large Eddy Simulation Equations: Apply filter G SFS

16 III. Large Eddy Simulation Example Convective Updraft (Moeng, NCAR)

17 III. Large Eddy Simulation A typical setup of PBL-LES 100 x 100 x 100 points grid sizes < tens of meters time step < seconds higher-order schemes, not too diffusive spin-up time ~ 30 min, no use simulation time ~ hours massive parallel computers

18 LES: Challenges (I) Realistic surface complex terrain, land use, waves Inflow boundary condition SFS effect near irregular surfaces Proper scaling; representations of ensemble mean Computational challenge resolve turbulent ~ 1000 x 1000 x 100 grid points Massive parallel computing

19 LES: Challenges (II) Using for Understand turbulence behavior & diffusion property Develop/calibrate PBL models, i.e. Reynolds average models Case studies of wind flow in technical environments Future Goals Understand PBL in complex environment and improve its parameterization (turbulent fluxes, clouds,...) Application of LES for real-world wind flow modeling e.g. in large wind farms

20 IV. Reynolds-averaged Navier Stokes (RANS) Modeling time-averaged equations of motion f Apply ensemble average non-turbulent

21 IV. Reynolds-averaged Navier Stokes (RANS) Modeling time-averaged equations of motion f Apply ensemble average non-turbulent

22 IV. Reynolds-averaged Navier Stokes (RANS) Modeling unknown Reynolds stress terms -> problem of closure from four unknowns with four equations we have ten unknowns with still four equations Navier-Stokes equations are no longer solvable directly --> RANS Turbulence models must be introduced to solve the flow problem inherently difficult to develop reliable Reynolds stress models RANS based CFD codes remain the most practical tools Hybrid model incorporating LES: Detached Eddy Simulation (DES)

23 Mesoscale Modeling: Weather Research and Forecast Model (WRF) Characteristics of Mesoscale Models: Complete meteorological models (--> forecasting) Resolving mesoscale atmospheric features typical length scale km more detailed turbulence parametrization depending on boundary conditions Advantages WRF: Available input data: Terrain, land properties, meteorol. conditions Higher-order numerical schemes Terrain-following coordinate Design for massive parallel computing

24 Mesoscale Modeling: Weather Research and Forecast Model (WRF) Fully compressible non-hydrostatic (with hydrostatic option) Mass-based, terrain following coordinate η: with π hydrostatic pressure, μ column mass Arakawa C grid staggering v u T u v

25 Nesting of PBL-LES with the WRF model Moeng, NCAR

26 Nesting of PBL-LES with the WRF model mesoscale model domain 500 km 50 km LES domain Moeng, NCAR

27 Wind Farm Wakes

28 Wind Farm Wakes LES Approach Examine idealized far wake evolution in high resolution (10 m) LES Periodic boundary conditions (non-periodic boundary in development) Wakes evolution in the planetary boundary layer Validate with on site measurements WRF - LES Examine far wake evolution in real weather conditions Nested domains Model wind turbine (MYJ- TKE scheme): - sink of kinetic energy - source of Turbulent Kinetic Energy Investigate wind farm wakes

29 Wind Farm Wakes Coherent Structures in Offshore Wakes understanding decay of vortex sheets - formation and stability of coherent structures in the boundary layer - their influence on the wind farm downstream impact of additional turbulent kinetic energy on transport of scalars and on the local weather (tourists!) Picture: Dong Energy

30 Thank you very much!

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