Large-eddy simulation of flows over idealized urban roughness in unstable thermal stratification

Abstract

Large-eddy simulation (LES) equipped with the one-equation subgrid-scale model is employed to investigate the flows and turbulence over idealized two-dimensional (2D) street canyons in various thermal stratification configurations. The prevailing wind, which is driven by a background pressure gradient above the building roof level, is perpendicular to the street axis representing the worst scenario of pollutant removal. The building-height-to-street-width(aspect) ratio is kept unity so the flows fall into the skimming flow regime. Cyclic boundaries are assigned to the domain inlet and outlet, and the spanwise extent, simulating the infinite horizontally homogenous building structures. The buoyancy force is modeled by Boussinesq approximation so incompressible flows at small Richardson number are assumed. In isothermal conditions over an aerodynamically smooth surface, it is well-known that the mean flows exhibit a logarithmic region(law of the wall).The conceptual model of logarithmic wind profile is also applicable to flows over homogenously rough surfaces, such as the idealized 2D street canyons in this study, in which the parameters, including the aerodynamic roughness height and the displacement height, are determined empirically as functions of the roughness configuration. However, in thermal stratification with the presence of buoyancy force(induced by the temperature difference between the urban fabrics and the prevailing wind),the mean wind profile deviates from its isothermal counterpart in which the extent of the logarithmic region depends on the Richardson number. In slightly unstable stratification, the conventional law of the wall is modified by multiplying an empirical constant to the logarithmic term to account for the contributions from thermal stratification. A range of thermal stratification is tested by LES. The corresponding aerodynamic roughness height, displacement height, and empirical constant are obtained by regression to the LES data. It is found that, with increasing buoyancy force, the aerodynamic roughness height decreases while the displacement height increases. It thus implies that practically buoyancy force tends to shift the logarithmic mean wind profile upwards. Moreover, aerodynamic roughness height is a function of both geometric configuration and thermal stratifications.