Numerical studies of flow through a windbreak

Abstract 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 k r u | u |δ(x,0)s(z,H) where k r is the pressure-loss coefficient of the fence, ū is the local mean horizontal ( x ) velocity, δ ( x ,0) is the delta function and s ( z , H ) is a unit step function which is zero for heights ( z ) greater than the fence height, H . Previous experiments on neutrally stratified surface-layer flow through a porous fence were numerically simulated. Very good agreement with the observed velocity deficit in the near wake ( x ⩽ 15 H where H = fence height) of the fence was obtained using a Reynolds-stress closure scheme. The predictions of the “k-ϵ” closure scheme (which includes turbulent kinetic energy and energy dissipation rate equations to estimate the eddy viscosity) and the simplest scheme tested, eddy viscosity K = K 0 = ku ∗0 z eddy viscosity at all downwind distances equal to its value far upstream ku ∗0 z where k = von Karman's constant, u ∗o = friction velocity , z = height ) were only slightly less satisfactory. Satisfactory estimates of the pattern of turbulent kinetic energy behind the fence were obtained. All simulations failed to predict the sharp speedup observed over the fence, and consequently yielded a slower rate of recovery towards equilibrium than observed. Attempts to improve prediction of the speed-over and the far wake by including corrections for mean streamline curvature were unsuccessful. Design aids for isolated windbreaks have been generated from the prediction of the second-order closure model. These give the velocity reduction to be expected in the near wake of the fence and the drag on the fence for a range of values of the fence pressure-loss coefficient, k rmr .