The reactive Riemann problem for thermally perfect gases at all combustion regimes

Abstract

In this work we analyze the reactive Riemann problem for thermally perfect gases in the deflagration or detonation regimes. We restrict our attention to the case of one irreversible infinitely fast chemical reaction; we also suppose that, in the initial condition, one state (for instance the left one) is burnt and the other one is unburnt. The indeterminacy of the deflagration regime is removed by imposing a (constant) value for the fundamental flame speed of the reactive shock. An iterative algorithm is proposed for the solution of the reactive Riemann problem. Then the reactive Riemann problem and the proposed algorithm are investigated from a numerical point of view in the case in which the unburnt state consists of a stoichiometric mixture of hydrogen and air at almost atmospheric condition. In particular, we revisit the problem of 1D plane-symmetric steady flames in a semi-infinite domain and we verify that the transition from one combustion regime to another occurs continuously with respect to the fundamental flame speed and the so-called piston velocity. Finally, we use the 'all shock' solution of the reactive Riemann problem to design an approximate ('all shock') Riemann solver. 1D and 2D flows at different combustion regimes are computed, which shows that the approximate Riemann solver, and thus the algorithm we use for the solution of the reactive Riemann problem, is robust in both the deflagration and detonation regimes. Copyright © 2009 John Wiley & Sons, Ltd.