ISSN 1990-7931, Russian Journal of Physical Chemistry B, 2011, Vol. 5, No. 5, pp. 800–812. © Pleiades Publishing, Ltd., 2011. Original Russian Text © V.V. Vlasenko, 2011, published in Khimicheskaya Fizika, 2011, Vol. 30, No. 9, pp. 42–54. 800 1. INTRODUCTION In this work, we studied the effect of the type of mathematical model of flow on the results of numeri- cal simulation of unsteady combustion in a duct with a supersonic flow of viscous gas. We consider a model combustion chamber that was experimentally investi- gated by O.V. Voloshenko, V.N. Ostras’, E.V. Piotrov- ich, V.N. Sermanov, A.A. Nikolaev, and S.A. Zosimov at Zhukovsky Central Institute of Aerohydrodynamics [1, 2]. The combustion chamber was a duct with a ledge, consisting of a narrow section with an angle of expansion of 0.5° (isolator) and a broad section of con- stant cross section (Fig. 1). All cross-sections of the duct had a rectangular shape. In the experiments, the model combustion chamber was studied in a system with an attached air duct. The Mach number at the inlet of the combustion chamber was M ≈ 2.5. A short distance upstream from the stepwise expansion of the duct, on the lower wall, a pylon with four holes was installed, from which liquid hydrocarbon fuel was injected. The airflow entering the nozzle of the wind tunnel was heated by a firing heater and had a temper- ature of ~700 K at the inlet of the combustion cham- ber. Under these conditions, no self-ignition occurred in the combustion chamber. To initiate combustion, the duct was throttled by short-term blowing of air jets from lateral openings at the bottom of the duct near the outlet of the combustion chamber. The experi- ments were aimed at measuring the distribution of static pressure along the upper and lower walls of the duct and cinematographing the outflow from the com- bustion chamber. To complement the experimental data with information on the flow structure and vari- ous processes in the combustion chamber, numerical simulations of the flow in the chamber were per- formed. This article describes some of the results of this work. The flow was simulated using the nonstationary Reynolds equations for a multicomponent compress- ible gas flow with nonequilibrium chemical reactions in the two-dimensional approximation. The system of equations was closed by: (1) The Coakley turbulence model [3], which includes two additional partial differential equations derived for the turbulence parameters; (2) A kinetic scheme of the combustion of fossil fuels similar the kinetic scheme presented in [4]. Although in experiment, a liquid fuel is injected, it was assumed that it very rapidly evaporates in the high temperature flow. Therefore, burning is considered to occur in the homogeneous mode. We consider the reactions in a mixture of ideal gases. The kinetic scheme from [4] includes a one-way (direct) global decomposition reaction of hydrocarbon fuel to CO and H 2 O and eleven reversible reactions between H, O, OH, H 2 O, O 2 , H 2 , CO, CO 2 , with the participation of inert nitrogen. This kinetic scheme requires the solution of nine additional partial differential equa- tions for the mass concentrations of the reaction mix- ture components. We used the second-order approximation method for all variables, including the explicit monotone Godunov–Kolgan–Rodionov scheme for convective flows, modified explicit central difference approxima- q -ω COMBUSTION, EXPLOSION, AND SHOCK WAVES Numerical Simulation of the Unsteady Propagation of Combustion in a Duct with a Supersonic Viscous Gas Flow V. V. Vlasenko Zhukovsky Central Institute of Aerohydrodynamics, Zhukovskii, Moscow oblast, 140160 Russia e-mail: vvvlas@progtech.ru Received April 19, 2010 Abstract—The effect of the type of mathematical model on the results of numerical simulations of combus- tion in a flat model combustion chamber with a supersonic flow is considered. The process of formation of a flow with combustion in a chamber includes the propagation of the combustion wave along the chamber and the emergence of a pseudoshock structure. The results of nonstationary calculations by the explicit scheme using (1) the no-slip boundary condition at the chamber walls and the local time stepping procedure, (2) law- of-the-wall and the local time stepping procedure, and (3) law-of-the-wall and the fractional time stepping procedure are compared. Arguments in favor of the applicability of the latter approach to solving this class of problems are presented. The physical results obtained are analyzed. Keywords: supersonic flow, combustion chamber, pseudoshock, numerical simulation. DOI: 10.1134/S1990793111040105