A Modeling of Compressible Droplets in a Fluid

Abstract

In this work, we are interested in a complex fluid-kinetic model that aims to take into account the compressibility of the droplets of the spray. The ambient fluid is described by Euler-like equations, in which the transfer of momentum and energy from the droplets is taken into account, while the spray is represented by a probability density function satisfying a Vlasov-like equation. Implicit terms crop up because of the compressibility of the droplets. After having derived the model, we prove that global conservations are satisfied. Then we present two numerical tests. The first one enables us to validate the numerical code, while the second one is performed in a physically realistic situation.

Local Smooth Solutions of a Thin Spray Model With Collisions

“…4). The density g , the velocity u g and the internal energy e g characterize the behavior of the gas (considered as a perfect gas for the sake of simplicity).…”

Finite-time blow-up phenomena of Vlasov/Navier–Stokes equations and related systems

“…Consider the thick sprays which can be governed by For the system (4.10) with internal energy equations, global conservations, such as total energy, momentum, and mass are provided in [7], and the formal derivation of multiphase flows models including the volume fraction from (4.10) with the inelastic collision operator is studied in [22]. We also refer to [5] for numerical study for the system (4.10).…”

Some aspects of the modeling at different scales of multiphase flows

“…Here are also some more specific difficulties of the simulations of the sprays that we have investigated with the CEA-DAM: the gas as well as the droplets can be compressible (cf. [4]); the pressure and energy laws are given by tables and can be quite complex, the collisions between droplets do not conserve the kinetic energy and lead to an exchange of temperature (cf. [12]), and finally (and maybe most significantly) the volume fraction of droplets can be quite large in some regions (in time/space) of the domain of computation.…”