2024 Volume 80 Issue 16 Article ID: 23-16079
The influence of the kernel representation of the history force in the Maxey–Riley equation on the particle behavior in isotropic turbulence was investigated under a wide range of the particle-to-fluid mass density ratio (from 0 to 10000). The Basset kernel based on the classical theory and the Mei–Adrian kernel, which adequately represents the effects of finite-Reynolds numbers and long-time delays, are compared. It is revealed that the Basset kernel overestimates the history effect, but the extent is only slightly, at least under the present investigation. While the history force is negligible for quite-heavy particles, it plays an essential role for slightly-heavy or light particles. The importance of the history force is more remarkable for light particles. An examination of the probability density function of each term of the Maxey–Riley equation has shown that (i) it is the pressure-gradient force for light particles and the Stokes drag for heavy particles that yield particle clustering and (ii) the presence of the history force partly cancels the contribution of the pressure-gradient force for light particles and weakens the contribution of the Stokes drag for not-so-heavy particles, and hence relaxes the non-uniformity in the particle distribution.
