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, C_D. The vertical random arrays are configured in several frontal area densities, λ_F (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, C_p(t) normalized with that of the isolated building, C_p(iso). The ratio C_p(t)/C_p(iso) is well correlated with the target building's frontal area density, λ_f(t). Subsequently, the relationship between C_p(t) and λ_f(t) is expressed using power law equations for three building categories based on the height-to-width ratio, α_p(t): tall (2.64 ≤ α_p(t) ≤ 3.76), medium-rise (1.32 ≤ α_p(t) ≤ 2.00), and low-rise (0.36 ≤ α_p(t) ≤ 0.84). Based on the C_p(t), an equation of the C_D is formulated, yielding the following outcomes. Firstly, the predicted C_D values are mostly within 10% of the previous experimental results. Secondly, a semi-empirical model is derived, whereby the predicted C_D values are generally consistent for various vertical random arrays.