A Distributed Drag Force Approach for the Numerical Simulation of Urban Flows


  1. Yee, E.
  2. Lien, F-S.
Corporate Authors
Defence R&D Canada - Suffield, Ralston ALTA (CAN);Waterloo Univ, Waterloo ONT (CAN)
A modified Kappa-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, Kappa-bar, and another for the dissipation rate, Epsilon, of Kappa-bar. The transport equation for Kappa-bar 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 source/sink term in the transport equation for Kappa-bar 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 dimensionall

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Report Number
DRDC-SUFFIELD-TR-2004-169 — Technical Report
Date of publication
01 Nov 2004
Number of Pages

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