Relative velocity distribution of inertial particles in turbulence: A numerical study

Relative velocity distribution of inertial particles in turbulence: A numerical study

Perrin, V.E.
Jonker, H.J.J.

Civil Engineering and Geosciences

Geoscience & Remote Sensing

2015-10-30

The distribution of relative velocities between particles provides invaluable information on the rates and characteristics of particle collisions. We show that the theoretical model of Gustavsson and Mehlig [K. Gustavsson and B. Mehlig, J. Turbul. 15, 34 (2014)], within its anticipated limits of validity, can predict the joint probability density function of relative velocities and separations of identical inertial particles in isotropic turbulent flows with remarkable accuracy. We also quantify the validity range of the model. The model matches two limits (or two types) of relative motion between particles: one where pair diffusion dominates (i.e., large coherence between particle motion) and one where caustics dominate (i.e., large velocity differences between particles at small separations). By using direct numerical simulation combined with Lagrangian particle tracking, we assess the model prediction in homogeneous and isotropic turbulence. We demonstrate that, when sufficient caustics are present at a given separation and the particle response time is significantly smaller than the integral time scales of the flow, the distribution exhibits the same universal power-law form dictated by the correlation dimension as predicted by the model of Gustavsson and Mehlig. In agreement with the model, no strong dependency on the Taylor-based Reynolds number is observed.

http://resolver.tudelft.nl/uuid:2faaf207-ee32-4a34-a076-ad0ad517303d

American Physical Society

1539-3755

https://doi.org/10.1103/PhysRevE.92.043022

Physical Review E, 92 (4), 2015

Institutional Repository

journal article

© 2015 American Physical Society