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Solid-fuel scramjet engines (SFScRE) are considered to be promising propulsion systems of unmanned aerial vehicles. It was established experimentally that the steady combustion of solid fuel in SFScRE is possible only at a certain shape and size of the flame holder, but the detailed mechanism of stabilization of combustion is not completely clear. In this study, we consider the model of PMMA combustion and show that PMMA combustion can occur in different modes. The multicomponent gas mixture is described by the Reynolds-averaged Navier-Stokes equations (RANS) in the fully compressible formulation. Five mixture components are considered: , , , , . Turbulence is described by the standard model, the gas-phase combustion rate is described by the Eddy Break-up (EBU). The heat flux from the gas phase onto the fuel surface required for calculation of the solid fuel gasification mass rate was determined from wall functions for the temperature. The governing equations are solved in the axisymmetric framework by an explicit finite-volume high-resolution scheme on a uniform Cartesian grid. Numerical simulations were carried out for the geometry which resembles closely the well-known experiments. The results of numerical simulations obtained for different initial conditions and different geometries on the combustor are discussed. We show that the model under consideration allows describing the instability of SFScRE operation and we investigate the range of the parameters of SFScRE which correspond to stability of solid fuel combustion in such a combustor.