Computing Two-fluid Models of Compressible Water-vapour Flows with Mass Transfer

Abstract

This paper is devoted to the simulation of water-vapour flows with mass transfer, using the two-fluid approach proposed in 8, 11,12,17,22,23,27 . The two-fluid model contains stiff source terms associated with pressure-velocity-temperature-Gibbs potential relaxation terms, and the convective part of the model is highly non linear and has no conservative form. Thus the computation of the whole model is rather difficult, and it requires the development of specific algorithms. Actually, a rather slow rate of convergence of schemes with respect to the mesh size is expected for convection-dominated flow computations (more precisely h -respectively hfor so-called first-order -respectively second-orderschemes) , due to the occurence of several contact discontinuities, and the reader is refered to references 7, 9, 13,25,26,28,30,31 for instance, which examine in detail the behaviour of several Riemann solvers and relaxation techniques in order to cope with the convective part of the two-fluid model. Moreover, small time scales in relaxation source terms render the computation even more tricky, and some attempts to deal with pressure-velocity-temperature relaxation effects have been recently reported in . One difficulty is connected with the computation of pressure relaxation effects, since it requires a tight coupling of source terms in energy and statistical void fraction equations. The accurate computation of gas-liquid flows with no mass transfer is not easy, but water-vapour flow simulations that account for mass transfer are clearly even more difficult, and emphasis is given here on this topic.