Disperse two-phase flows, with applications to geophysical problems

• Published in: arXiv.org 2014-03
• Main Authors: Berselli, Luigi Carlo, Cerminara, Matteo, Iliescu, Traian
• Format: Article
• Language: English
• Subjects: Boussinesq equations; Compressibility; Computational fluid dynamics; Computer simulation; Dilution; Exchanging; Fluid flow; Geophysics; Incompressible flow; Incompressible fluids; Large eddy simulation; Mach number; Mathematical models; Meteorology; Oceanography; Particle inertia; Particle interactions; Simulation; Stokes number; Tracers; Two phase flow; Vortices
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1403.5448

In this paper we study the motion of a fluid with several dispersed particles whose concentration is very small (smaller than \(10^{-3}\)), with possible applications to problems coming from geophysics, meteorology, and oceanography. We consider a very dilute suspension of heavy particles in a quasi-incompressible fluid (low Mach number). In our case the Stokes number is small and --as pointed out in the theory of multiphase turbulence-- we can use an Eulerian model instead of a Lagrangian one. The assumption of low concentration allows us to disregard particle--particle interactions, but we take into account the effect of particles on the fluid (two-way coupling). In this way we can study the physical effect of particle inertia (and not only passive tracers), with a model similar to the Boussinesq equations. The resulting model is used in both direct numerical simulations and large eddy simulations of a dam-break (lock-exchange) problem, which is a well-known academic test case. Keywords: Dilute suspensions, Eulerian models, direct and large eddy simulations, slightly compressible flows, dam-break (lock-exchange) problem.