A Method to Evaluate Forchheimer Resistance Coefficients for Permeable Screens and Air Louvers Modelled as a Porous Medium

Abstract

Porous medium models are commonly used in Computational Fluid Dynamics (CFD) to simulate flow through permeable screens of various types. However, the setup of these models is often limited to replicating a pressure drop in cases where fluid inflow is orthogonal to the screen. In this work, a porous medium formulation that employs a non-diagonal Forchheimer tensor is presented. This formulation is capable of reproducing both the pressure drop and flow deflection under varying inflow angles for complex screen geometries. A general method to determine the porous model coefficients valid for both diagonal and non-diagonal Forchheimer tensors is proposed. The coefficients are calculated using a nonlinear least-squares optimisation based on an analytical solution of a special case of the Navier–Stokes equations. The applicability of the proposed method is evaluated in four different scenarios supplemented by local CFD simulations of permeable screens: wire mesh, perforated screens, air louvers, and expanded mesh panels. The practical application of this method is demonstrated in the modelling of windbreaks and permeable double-skin facades, which typically employ the aforementioned types of porous screens.