Inertial particle acceleration statistics in turbulence: Effects of filtering, biased sampling, and flow topology

Abstract

In this study, we investigate the effect of “biased sampling,” i.e., the clustering of inertial particles in regions of the flow with low vorticity, and “filtering,” i.e., the tendency of inertial particles to attenuate the fluid velocity fluctuations, on the probability density function of inertial particle accelerations. In particular, we find that the concept of “biased filtering” introduced by Ayyalasomayajula et al. [“Modeling inertial particle acceleration statistics in isotropic turbulence,” Phys. Fluids 20, 0945104 (2008)10.1063/1.2976174], in which particles filter stronger acceleration events more than weaker ones, is relevant to the higher order moments of acceleration. Flow topology and its connection to acceleration is explored through invariants of the velocity-gradient, strain-rate, and rotation-rate tensors. A semi-quantitative analysis is performed where we assess the contribution of specific flow topologies to acceleration moments. Our findings show that the contributions of regions of high vorticity and low strain decrease significantly with Stokes number, a non-dimensional measure of particle inertia. The contribution from regions of low vorticity and high strain exhibits a peak at a Stokes number of approximately 0.2. Following the methodology of Ooi et al. [“A study of the evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence,” J. Fluid Mech. 381, 141 (1999)10.1017/S0022112098003681], we compute mean conditional trajectories in planes formed by pairs of tensor invariants in time. Among the interesting findings is the existence of a stable focus in the plane formed by the second invariants of the strain-rate and rotation-rate tensors. Contradicting the results of Ooi et al., we find a stable focus in the plane formed by the second and third invariants of the strain-rate tensor for fluid tracers. We confirm, at an even higher Reynolds number, the conjecture of Collins and Keswani [“Reynolds number scaling of particle clustering in turbulent aerosols,” New J. Phys. 6, 119 (2004)10.1088/1367-2630/6/1/119] that inertial particle clustering saturates at large Reynolds numbers. The result is supported by the theory presented in Chun et al. [“Clustering of aerosol particles in isotropic turbulence,” J. Fluid Mech. 536, 219 (2005)10.1017/S0022112005004568].