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Statistics of the relative velocity of particles in turbulent flows : monodisperse particles
- Source :
- Phys. Rev. E 97, 023105 (2018)
- Publication Year :
- 2017
-
Abstract
- We use direct numerical simulations to calculate the joint probability density function of the relative distance $R$ and relative radial velocity component $V_R$ for a pair of heavy inertial particles suspended in homogeneous and isotropic turbulent flows. At small scales the distribution is scale invariant, with a scaling exponent that is related to the particle-particle correlation dimension in phase space, $D_2$. It was argued [1, 2] that the scale invariant part of the distribution has two asymptotic regimes: (1) $|V_R| \ll R$ where the distribution depends solely on $R$; and (2) $|V_R| \gg R$ where the distribution is a function of $|V_R|$ alone. The probability distributions in these two regimes are matched along a straight line $|V_R| = z^\ast R$. Our simulations confirm that this is indeed correct. We further obtain $D_2$ and $z^\ast$ as a function of the Stokes number, ${\rm St}$. The former depends non-monotonically on ${\rm St}$ with a minimum at about ${\rm St} \approx 0.7$ and the latter has only a weak dependence on ${\rm St}$.
- Subjects :
- Physics - Fluid Dynamics
Subjects
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. E 97, 023105 (2018)
- Publication Type :
- Report
- Accession number :
- edsarx.1710.04917
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevE.97.023105