Spatial Variability of Flow Statistics within Regular Building Arrays

Abstract

Turbulence statistics obtained by direct numerical simulations are analysed to investigate spatial heterogeneity within regular arrays of building-like cubical obstacles. Two different array layouts are studied, staggered and square, both at a packing density of $\lambda_p=0.25$ . The flow statistics analysed are mean streamwise velocity ($\overline{u}$), shear stress ($\overline{u^{\prime}w^{\prime}}$), turbulent kinetic energy (k) and dispersive stress fraction ($\tilde{u}\tilde{w}$). The spatial flow patterns and spatial distribution of these statistics in the two arrays are found to be very different. Local regions of high spatial variability are identified. The overall spatial variances of the statistics are shown to be generally very significant in comparison with their spatial averages within the arrays. Above the arrays the spatial variances as well as dispersive stresses decay rapidly to zero. The heterogeneity is explored further by separately considering six different flow regimes identified within the arrays, described here as: channelling region, constricted region, intersection region, building wake region, canyon region and front-recirculation region. It is found that the flow in the first three regions is relatively homogeneous, but that spatial variances in the latter three regions are large, especially in the building wake and canyon regions. The implication is that, in general, the flow immediately behind (and, to a lesser extent, in front of) a building is much more heterogeneous than elsewhere, even in the relatively dense arrays considered here. Most of the dispersive stress is concentrated in these regions. Considering the experimental difficulties of obtaining enough point measurements to form a representative spatial average, the error incurred by degrading the sampling resolution is investigated. It is found that a good estimate for both area and line averages can be obtained using a relatively small number of strategically located sampling points.