Relative velocity between a particle and turbulence

Abstract

The relative velocity between a particle and the surrounding fluid is a key quantity that determines the various phenomena of particle-laden turbulence, such as particle clustering and turbulence modulation due to particles. We theoretically derive the expression for the relative velocity of a particle laden in turbulence by extending the argument of Balachandar (2009). This derivation provides a simplified form of the analytical model of Berk and Coletti (2024), and it makes the underlying physical assumptions explicit. Using direct numerical simulation data of turbulence in a periodic cube and turbulent channel flow, we demonstrate the validity of the derived expression, and show that it also holds for non-spherical particles and droplets.