The direct simulation Monte Carlo method
Computers in Physics
A new droplet collision algorithm
Journal of Computational Physics
A geometrical area-preserving volume-of-fluid advection method
Journal of Computational Physics
Journal of Computational Physics
A Eulerian level set/vortex sheet method for two-phase interface dynamics
Journal of Computational Physics
A quadrature-based moment method for dilute fluid-particle flows
Journal of Computational Physics
A quadrature-based third-order moment method for dilute gas-particle flows
Journal of Computational Physics
Higher-order quadrature-based moment methods for kinetic equations
Journal of Computational Physics
A parallel Eulerian interface tracking/Lagrangian point particle multi-scale coupling procedure
Journal of Computational Physics
A level set approach for dilute non-collisional fluid-particle flows
Journal of Computational Physics
Conditional quadrature method of moments for kinetic equations
Journal of Computational Physics
A high order moment method simulating evaporation and advection of a polydisperse liquid spray
Journal of Computational Physics
Journal of Computational Physics
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The scope of the present study is Eulerian modeling and simulation of polydisperse liquid sprays undergoing droplet coalescence and evaporation. The fundamental mathematical description is the Williams spray equation governing the joint number density function f(v,u;x,t) of droplet volume and velocity. Eulerian multi-fluid models have already been rigorously derived from this equation in Laurent et al. [F. Laurent, M. Massot, P. Villedieu, Eulerian multi-fluid modeling for the numerical simulation of coalescence in polydisperse dense liquid sprays, J. Comput. Phys. 194 (2004) 505-543]. The first key feature of the paper is the application of direct quadrature method of moments (DQMOM) introduced by Marchisio and Fox [D.L. Marchisio, R.O. Fox, Solution of population balance equations using the direct quadrature method of moments, J. Aerosol Sci. 36 (2005) 43-73] to the Williams spray equation. Both the multi-fluid method and DQMOM yield systems of Eulerian conservation equations with complicated interaction terms representing coalescence. In order to focus on the difficulties associated with treating size-dependent coalescence and to avoid numerical uncertainty issues associated with two-way coupling, only one-way coupling between the droplets and a given gas velocity field is considered. In order to validate and compare these approaches, the chosen configuration is a self-similar 2D axisymmetrical decelerating nozzle with sprays having various size distributions, ranging from smooth ones up to Dirac delta functions. The second key feature of the paper is a thorough comparison of the two approaches for various test-cases to a reference solution obtained through a classical stochastic Lagrangian solver. Both Eulerian models prove to describe adequately spray coalescence and yield a very interesting alternative to the Lagrangian solver. The third key point of the study is a detailed description of the limitations associated with each method, thus giving criteria for their use as well as for their respective efficiency.