A perturbation analysis of turbulent flow through a porous barrier

Abstract

AbstractEarlier attempts to calculate the mean velocity field in flow about a thin, finite porous barrier (wall‐mounted or otherwise) are reviewed. By simplifying the governing mean vorticity equation and expanding the flow variables in powers of the pressure‐loss coefficient of the barrier (k,) we derive an analytical solution for the mean velocity field in unbounded and homogeneous turbulent flow through a finite barrier. This solution is compared with the earlier solution of Kaiser (1959) and with numerical solutions for windbreak flow (bounded, inhomogeneous turbulence), and it is shown that all these solutions demonstrate a rate of recovery of the mean velocity field which is slower than is observed. It is suggested that the weakness of all the solutions lies in the treatment of the Reynolds stresses. A further point of interest is that a useful approximation to the pressure field may be obtained by dropping the Reynolds stress terms and solving a simplified equation expressing a balance between streamwise advection, pressure gradient, and localized momentum removal at the barrier; this might prove useful for the solution of more general porous barrier flows.