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Modelling evaporation fronts with reactive Riemann solvers. (English) Zbl 1088.76051
This work deals with the modelling of permeable fronts and the building of a numerical method describing a multi-dimensional propagation of such fronts. Particular attention is paid to evaporation waves which appear in cavitating systems. Such systems leave their metastable liquid state with temperature above the saturated temperature (caused by rarefaction wave excitation) and produce a liquid-vapor mixture at thermodynamic equilibrium, which flows with high velocity (e.g. of about 100 m/s). During such transformations, occuring at finite rate, a subsonic phase transition front propagates through the superheated liquid (with velocity of e.g. 1 m/s). The fronts are considered as discontinuities separating the liquid phase from the liquid-vapor mixture.
In the present paper, no structure of the discontinuity is taken into account. In order to determine the kinetics, the evaporation front is assumed to propagate at maximum admissible speed corresponding to the Chapman-Jouguet deflagration point [J. R. Simões-Moreira, J. E. Shepherd, J. Fluid. Mech. 382, 63–86 (1999; Zbl 0953.76508)]. The Rankine-Hugoniot relations for the equations of state of the liquid and the liquid-vapor mixture are derived to express the mass, momentum and energy conservation across the front. Then the liquid-vapor phase transition is described. Therefore the associated reactive Riemann problem has to be solved. But, in the case of multi-dimensional propagation of permeable fronts which are subsonic, the conventional averaging scheme (such as the Godunov scheme) is inappropriate. To overcome this difficulty, the reactive Riemann problem solution is embedded into the discrete equations method (DEM) [R. Abgrall, R. Saurel, J. Comput. Phys. 186, No. 2, 361–396 (2003; Zbl 1072.76594); R. Saurel, S. Gavrilyuk, F. Renaud, J. Fluid Mech. 495, 283–321 (2003; Zbl 1080.76062)]. Thus, the DEM method is here extended to interfaces and multiphase mixtures and then applied to several two-dimensional examples.
The numerical results are presented and validated over experimental data. Some examples show that the same method may be also applied to the propagation of detonation fronts. The authors believe that the new approach can also be used to propagating flame fronts and ablation fronts such as those encountered in inertial confinement fusion. In the present work, the fluid dynamics has been restricted to the “stiffened gas” equation of state because it was sufficient accurate for the applications. When dealing with other detonation applications, more sophisticated equations of state may be necessary. The building of the reactive Riemann solver seems to be possible in such context, too.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76V05 Reaction effects in flows
76T10 Liquid-gas two-phase flows, bubbly flows
80A32 Chemically reacting flows
Software:
HE-E1GODF
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