  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. (2004). The first key feature of the paper is the
application of direct quadrature method of moments (DQMOM) introduced by
Marchisio and Fox (2005) 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 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.
