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Research Papers

An Immersed Boundary Method for Simulation of Wind Flow Over Complex Terrain

[+] Author and Article Information
S. Jafari

N. Chokani, R. S. Abhari

 Laboratory for Energy Conversion, Department of Mechanical and Process Engineering, ETH Zurich, Zurich, Switzerland

J. Sol. Energy Eng 134(1), 011006 (Nov 01, 2011) (12 pages) doi:10.1115/1.4004899 History: Received January 26, 2011; Accepted August 09, 2011; Published November 01, 2011; Online November 01, 2011

The accurate modeling of the wind resource over complex terrain is required to optimize the micrositing of wind turbines. In this paper, an immersed boundary method that is used in connection with the Reynolds-averaged Navier–Stokes equations with k-ω turbulence model in order to efficiently simulate the wind flow over complex terrain is presented. With the immersed boundary method, only one Cartesian grid is required to simulate the wind flow for all wind directions, with only the rotation of the digital elevation map. Thus, the lengthy procedure of generating multiple grids for conventional rectangular domain is avoided. Wall functions are employed with the immersed boundary method in order to relax the stringent near-wall grid resolution requirements as well as to allow the effects of surface roughness to be accounted for. The immersed boundary method is applied to the complex terrain test case of Bolund Hill. The simulation results of wind speed and turbulent kinetic energy show good agreement with experiments for heights greater than 5 m above ground level.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram of the computational stencil used for the implicit IBM. The immersed surface (shown as a black line) divides the domain into physical, interfacial, and ghost cells (lower plot). Illustration of the implicit boundary condition at the point Xs which is on the immersed boundary (upper plot). The computed flow at the mirror point Xm is used to specify the flow at the ghost point Xg such that the boundary condition is implicitly fulfilled on the immersed surface.

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Figure 2

Definition of the geometry for the 2D hill, L is the upwind half-length of the hill at the one-half height of the hill

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Figure 3

Representative H-grid (upper plot) and nonuniform Cartesian grid (lower plot) of the two-dimensional hill used for the grid-aligned with geometry and immersed boundary method simulations, respectively

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Figure 4

Pressure coefficient distribution over the hill (a) and speed-up at hilltop (b). GA and IBM results are shown in comparison with experiment.

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Figure 5

Comparison of pressure coefficient (a) and axial velocity (b) over the two-dimensional hill in grid-aligned with geometry and immersed boundary method simulations. Note for the immersed boundary method, the flow properties below the surface have no physical meaning.

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Figure 6

Elevation (a) and roughness (b) maps for Bolund Hill

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Figure 7

Side view of the computational grid A at the leading edge of the hill

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Figure 8

Nonuniform Cartesian grid superimposed on digital elevation map of Bolund Hill for simulations with three wind directions, 239 deg, 270 deg, and 301 deg. The same grid is used for all directions and only the rotated digital elevation map is provided as an input to the solver.

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Figure 9

Comparison of normalized wind speed (solid line) over the Bolund Hill for three different wind directions, 239 deg, 270 deg, and 301 deg, 5 m above ground. The elevation of the topography is shown as a dashed-dotted line.

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Figure 10

Digital elevation of Bolund Hill superimposed on nonuniform Cartesian gird generated for westerly wind directions

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Figure 11

Comparison of normalized wind speed over the Bolund Hill for 90 deg wind direction along line B, 2 and 5 m above ground

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Figure 12

Comparison of normalized wind speed for the 270 deg wind direction at 2 and 5 m above the surface along line B

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Figure 13

Vertical profiles of wind speed at four mast locations. M3, M6, M7, and M8 are the meteorological masts along line B described in Bechmann [17] for the 270 deg wind direction

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Figure 14

Comparison of predicted nondimensionalized turbulent kinetic energy to experiments for the 270 deg wind direction case at 2 and 5 m above the surface along line B

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Figure 15

Flowfield of velocity contours over Bolund Hill along line B for the 270 deg wind direction

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Figure 16

Vertical profiles of wind speed at four mast locations. M1, M2, M3, and M4 are the masts along line A described in Bechmann [17] for wind direction 239 deg.

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Figure 17

Vertical profiles of nondimensionalized turbulent kinetic energy at masts M1 and M2 for 239 deg wind direction

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Figure 18

Prediction of inclination angle at four mast locations, M1, M2, M3, and M4 compared to measurement for wind direction 239 deg

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Figure 19

Prediction of turning angle at four mast locations, M1, M2, M3, and M4 compared to measurement for wind direction 239 deg

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