A second-order multi-fluid model for evaporating sprays

¹ Laboratoire MIP, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex, France. dufour@mip.ups-tlse.fr
² DMAE/Onera - 2, Avenue E. Belin, B.P 4025, 31055 Toulouse Cedex, France. Philippe.Villedieu@onera.fr

Received: 14 October 2004
Revised: 8 April 2005

Abstract

The aim of this paper is to present a method using both the ideas of sectional approach and moment methods in order to accurately simulate evaporation phenomena in gas-droplets flows. Using the underlying kinetic interpretation of the sectional method [Y. Tambour, Combust. Flame 60 (1985) 15–28] exposed in [F. Laurent and M. Massot, Combust. Theory Model. 5 (2001) 537–572], we propose an extension of this approach based on a more accurate representation of the droplet size number density in each section ensuring the exact conservation of two moments (as opposed to only one moment used in the classical approach). A corresponding second-order numerical scheme, with respect to space and droplet size variables, is also introduced and can be proved to be positive and to satisfy a maximum principle on the velocity and the mean droplet mass under a suitable CFL-like condition. Numerical simulations have been performed and the results confirm the accuracy of this new method even when a very coarse mesh for the droplet size variable (i.e.: a low number of sections) is used.