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

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

Turbophoresis in forced inhomogeneous turbulence

We show, by direct numerical simulations, that heavy inertial particles (characterized by Stokes number St) in inhomogeneously forced statistically stationary isothermal turbulent flows cluster at the minima of mean-square turbulent velocity. Two turbulent transport processes, turbophoresis and turbulent diffusion together determine the spatial distribution of the particles. If the turbulent diffusivity is assumed to scale with turbulent root-mean-square velocity, as is the case for homogeneous turbulence, the turbophoretic coefficient can be calculated. Indeed, for the above assumption, the non-dimensional product of the turbophoretic coefficient and the rms velocity is shown to increase with St for small St, reach a maxima for St ≈ 10 and decrease as ∼ St - 0. 33 for large St. © 2018, The Author(s).publishedVersio