The detonation capacity of kerosene vapor is numerically studied in supersonic flow around a circular cylinder with an end windward wall. The model of kerosene combustion in the air takes into account 68 reactions for 44 components. Its testing is made by the way of comparison with the available calculated and experimental data on the ignition delay time under adiabatic conditions at a constant density. The mathematical model flow past cylinder is based on twodimensional non-stationary Euler equations for a multi-component reacting gas. The enthalpy and entropy of the initial mixture and combustion products are determined by polynomials from the NASA base. Calculations are performed on the basis of the Godunov finite-difference scheme and its modification of increased accuracy. The results allow justifying the parameters of the nozzle with a central body for a supersonic direct-flow chamber with detonative combustion of kerosene.

The work continues research on stabilization of detonation combustion of hydrogen-air mixtures entering axisymmetric convergent-divergent nozzles with high supersonic speed. The possibility of thrust generation under atmospheric conditions at heights of up to 30 km is numerically studied. Hydrogen-air mixture flow modeling is carried out on the basis of non-stationary twodimensional equations of an inviscid multi-component gas with chemical transformations. Calculations are performed on the basis of S.K. Godunov is of the first order of accuracy, as well as its modification, which increases the approximation order of smooth solutions to the second in spatial variables. It is shown the possibility of stable detonative combustion of hydrogen-air mixtures at altitudes up to 30 km (see figure below) at Mach number of oncoming flow of 7 up to 9. The configuration of suitable axisymmetric convergent-divergent nozzle and a central coaxial body is determined.

The paper verifies the ability of previously proposed modifications of the Godunov's scheme develop physically justified numerical solutions of the inviscid gas dynamics equations. The modifications constructed using the approach proposed by Kolgan to improve the accuracy of solutions on spatial variables are being considered. As test it is being solved the problems of flow around of semi-infinite rectangle and of a circular cylinder by a coaxial supersonic flow. The calculations are performed on a rectangular uniform grid. It is shown that the numerical solution can correspond both to stationary and a pulsating flow around with different shape of the shock waves in front of the end wall (see figure below) depending on the viscosity of the numerical scheme and the initial parameter distribution.