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The scope of the present study is Eulerian modeling and simulation ofpolydisperse liquid sprays undergoing droplet coalescence and evaporation. Thefundamental mathematical description is the Williams spray equation governingthe joint number density function f(v, u; x, t) of droplet volume and velocity.Eulerian multi-fluid models have already been rigorously derived from thisequation in Laurent et al. (2004). The first key feature of the paper is theapplication of direct quadrature method of moments (DQMOM) introduced byMarchisio and Fox (2005) to the Williams spray equation. Both the multi-fluidmethod and DQMOM yield systems of Eulerian conservation equations withcomplicated interaction terms representing coalescence. In order to validateand compare these approaches, the chosen configuration is a self-similar 2Daxisymmetrical decelerating nozzle with sprays having various sizedistributions, ranging from smooth ones up to Dirac delta functions. The secondkey feature of the paper is a thorough comparison of the two approaches forvarious test-cases to a reference solution obtained through a classicalstochastic Lagrangian solver. Both Eulerian models prove to describe adequatelyspray coalescence and yield a very interesting alternative to the Lagrangiansolver.

Numerical simulation of spray coalescence in an eulerian framework : direct quadrature method of moments and multi-fluid method