A new semi-empirical model for estimating the drag coefficient of the vertical random staggered arrays using LES

Sheltering of buildings has a significant impact on the total drag of an urban surface. This study performs large eddy simulations (LESs) of flows over vertical random arrays (comprised of buildings with height variability) in staggered layout to estimate the drag coefficient, CD. The vertical random arrays are configured in several frontal area densities, λF (ratio of buildings' frontal area to total surface area) ranging from 0.09 to 0.81. The sheltering effect is parameterized using the individual building's wind pressure coefficient, Cp(t) normalized with that of the isolated building, Cp(iso). The ratio Cp(t)/Cp(iso) is well correlated with the target building's frontal area density, λf(t). Subsequently, the relationship between Cp(t) and λf(t) is expressed using power law equations for three building categories based on the height-to-width ratio, αp(t): tall (2.64 ≤ αp(t) ≤ 3.76), medium-rise (1.32 ≤ αp(t) ≤ 2.00), and low-rise (0.36 ≤ αp(t) ≤ 0.84). Based on the Cp(t), an equation of the CD is formulated, yielding the following outcomes. Firstly, the predicted CD values are mostly within 10% of the previous experimental results. Secondly, a semi-empirical model is derived, whereby the predicted CD values are generally consistent for various vertical random arrays.