Direct numerical simulation of a stationary spherical particle in fluctuating inflows

Fully resolved direct numerical simulations are conducted to study the effects of fluctuating freestream flow on the drag force and wake characteristics of a stationary spherical particle. Sinusoidal fluctuation around a mean value is adopted as the freestream velocity. The interaction between the particle and fluctuating flow is computed by the direct-forcing immersed boundary method. We principally consider the relative difference between the computed mean drag and the drag law of a uniform flow past the particle and the properties of drag fluctuation in different freestream fluctuation directions. For the influence of streamwise fluctuating inflow, the relative mean drag difference increases with the particle Reynolds number. At small or intermediate particle scale ratios, the relative mean drag difference is very close to zero, indicating that the classical drag law can be used in these cases, while a large particle scale ratio can induce a notable increase in the relative mean drag difference at a large particle Reynolds number and high fluctuation intensity. For the transverse fluctuating inflow, generally, there is an evident increase in the mean drag coefficient when the particle scale ratio is small. Compared with the streamwise fluctuation case, the drag fluctuation intensity is a little smaller with the transverse fluctuating inflow. An explicit empirical drag fluctuation law is obtained by fitting the data for streamwise fluctuating inflow. The wake characteristics are also analyzed, and they are found to be strongly dependent on the direction of inflow fluctuation.