Numerical Studies of Flow through a Windbreak
"Despite an enormous number of measurements of the wind behind full scale and model fences and shelterbelts, there are not even any useful empirical formulae describing the sheltering effects of these obstructions," (Counihan, Hunt & Jackson; 1974).
Using standard turbulence closure schemes, and a standard numerical procedure (Patankar's "SIMPLE"), the work below showed that in the case of a neutrally-stratified flow at perpendicular incidence to an infinitely long windbreak, good predictions (as verified by comparison with experiment) of the fractional velocity reduction can be obtained upon specification of only two (dimensionless) properties of the system: the ratio H/z0 of the fence height to the surface roughness length, and the "resistance coefficient" (or "pressure-loss coefficient") kr of the barrier.
Abstract of Wilson (1985; J. Wind Eng. Indust. Aero., Vol. 21)
The pattern of flow through a porous windbreak has been investigated numerically, using several well-known closure schemes (turbulence models). The shelter is included as a momentum extraction term in the streamwise momentum equation, for a fence having the value
kr U2 d(x,0) s(z,H)
where U(x,z) is the mean velocity, a function of alongwind (x) and vertical (z) coordinates. The Dirac delta function d(x,0) and the unit step function s(z,H) localise momentum extraction to the barrier at (x=0, z<=H; H is the fence height). For a natural windbreak, the momentum sink is instead Cd A(x,z) U2, where A(x,z) is the "plant area density" function (area of leaf per unit volume of space), and Cd is the drag coefficient of plant parts.
Previous experiments on neutrally-stratified surface-layer flow through a porous fence were numerically simulated.
- Modelled versus Observed Windspeed (normalised by approach windspeed at height z=4m above ground) versus downwind distance from the windbreak x/H, at two heights: z/H=0.4 , 1.4. Model curves are shown for the three closure schemes identified below. Observations from field experiments (H/z0=600, kr=2.0) by E.F. Bradley and P. Mulhearn, CSIRO, Australia.
Very good agreement with the observed velocity deficit in the near wake ( x <= 15 H) was obtained using a Reynolds-stress closure scheme. Almost equally good predictions were obtained using the "k-epsilon" scheme (which includes turbulent kinetic energy and energy dissipation rate equations to estimate the eddy viscosity), and even the simplest scheme tested, eddy viscosity K=Ko=kv u*0 z (eddy viscosity at all downwind distances equal to its value far upstream kv u*0 z, where kv=von Karman's constant, and u*0 is the upstream friction velocity). Satisfactory estimates of the pattern of turbulent kinetic energy behind the fence were also obtained.
Design aids for isolated windbreaks have been generated, giving the maximum value of the fractional velocity reduction to be expected near ground (z < H/2) in the near lee,
DU / Uo = - kr / ( 1 + 2 kr )0.8
where DU is the change in mean windspeed, and Uo is the approach value at the same height. Note: the formula given above re-expresses the original findings so as to uphold the correct limiting value as kr --> 0 .
Subsequent experimental work has confirmed the usefulness of this formula: see for example
- Wilson, J.D. and T.K. Flesch, ``Wind measurements in a square plot enclosed by a shelter
fence.'' In press, Boundary-Layer Meteorology. This paper gives measurements of wind reduction using cup anemometers inside a square plastic fence of height h=1.25 m, sidelength 16h, and resistance coefficient kr=0.4. When the mean wind was nearly perpendicular to a side of the fence, anemometers downwind from that side gave a wind reduction close to that indicated by the above formula
- Windbreak experiment at Ellerslie (Alberta), May 2003. Here both cup and sonic anemometers were disposed around a long (120 m) straight section of the same fence. Again, the formula for maximum wind reduction agreed well with observations for the case of neutral, perpendicular flow.
Follow-up Work (see Publications List for references)
- Perturbation analysis of the very porous case (Analytical Solution).
- Comparison of model predictions with experiment, in the case of height-variable porosity of the barrier.
- Measurements of the mean pressure field about a windbreak, and comparison with simulations
- Wilson, J.D., and T.K. Flesch, 1999: ``Wind and tree sway in forest cutblocks, III: a windflow model to diagnose spatial variation.'' Agric. Forest Meteo. 93, 259-282. Measurements and modelling of mean winds in a periodic array of clearings and wide forest blocks (windbreaks) spanning X=2h, 12h
- Comparative study of the above model and a nearly-identical later treatment by H.Wang & E.Takle
- Wilson, J.D., and E. Yee, 2003: ``Calculation of Winds Disturbed by an Array of
Fences.'' Agric. For. Meteorol., 115, 31-50. Shows RANS models do a poor job of imulation of winds about multiple parallel porous fences.
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Last Modified: 29 May 2003
