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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


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Model Physics Planetary Boundary Layer Model Overview for Wind Flow Simulation

Subject of Modeling: The Planetary Boundary Layer
The PBL is: • turbulent layer

lowest ~km on theEarth surface

• directly affected by surface
heating, moisture, pollution, surface drag -> turbulent exchange

• diurnal cycle over land
convective and stable PBLs

Source: Brutsaert

PBL: Effects of Terrain and Stability

Source: Beljaars

PBL: Diurnal Cycle of Boundary Layer Height

Source: Beljaars

PBL: Diurnal Cycle of Profiles

Source: Beljaars

Basic („Primitive“)Equations
Based on conservation principles for momentum, mass & energy:

Momentum Equation Continuity Equation

Wind Speed Density Air Temperature Humidity, Clouds Pressure

Thermodynamic Equation (1st Law) Balance equation for water vapour Gas Law

Equation of Motion (Navier Stokes)
in vectorised notion:

in x, y, z components:

Averaged Equations
‣ Equations as usedin 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 expressedin 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.

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 inquality: ‣ 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 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

I. Linear Models
‣ Famous example: WAsP (Wind Atlas Analysis and Application Program)
from RISØ based on the concept oflinearised 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

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‣ Limitations in more complex terrain regions due to the linearity of the
equation set II. Direct Numerical Models
‣ Direct numerical simulation of the Navier-Stokes equations for a full range of
turbulent motions for all scales discretisation errors

‣ Only approximations which are necessary numerically to minimise ‣ Clear definition of all conditions (initial, boundary and forcing) and the
production of data for every single variable

‣ Only simple geometries and low Reynoldsnumbers 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

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...
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