Distributed Drag Force Approach for the Numerical Simulation of Urban Flows

摘要

A modified k-epsilon model is proposed for the simulation of the mean wind speed and turbulence for a neutrally- stratified flow through and over a building array, where groups of buildings in the array are aggregated and treated as a porous barrier. This model is based on time averaging the spatially-averaged Navier-Stokes equation, in which the effects of the obstacle- atmosphere interaction are included through the introduction of a volumetric momentum sink (representing drag on the unresolved buildings in the array). In addition, closure of the time-averaged, spatially-averaged Navier-Stokes equations requires two additional prognostic equations, namely one for the time- averaged sub-filter kinetic energy, bar-K, and another for the dissipation rate, epsilon, of bar-K. The transport equation for bar-K can be derived from first principles and explicitly includes additional sources and sinks that arise from time averaging the product of the spatially-averaged velocity fluctuations and the distributed drag force fluctuations. The latter time-averaged product can be approximated systematically to any degree of accuracy using a Taylor series expansion and, to this end, a high-order approximation is derived to represent this sourcelsink term in the transport equation for bar-K which corresponds physically to the work done against pressure (form) and viscous drag in the building array. The dissipation rate (epsilon-) equation is simply obtained as a dimensionally consistent analog of the bar-K - equation.