Results of numerical simulations of a quasi-one-dimensional unsteady flow in a channel considered as an element of an air-breathing engine are presented. The influence of parameters of energy supplied in the pulsed-periodic mode (power, pulse frequency, and distribution of energy sources along the channel ) on the characteristics of the flow with Mach numbers M 0 = 2.4-4.0 at the channel entrance is determined. A channel configuration that allows the energy supply distribution to be found from the condition of restriction of the maximum value of the gas temperature is proposed.The idea of using an air-breathing engine in flight with hypersonic velocities (flight Mach numbers M ∞ 6) implies fuel burning in a supersonic air flow in the channel. The amount of the fuel being burned should be sufficient to obtain a required thrust (with the air-to-fuel ratio α 1), and the flow has to be supersonic everywhere. Some schemes of fuel injection into the flow are proposed in [1,2], and the structures of the supersonic flows formed thereby are given, though there is no information about implementation of these ideas. It is noted that the processes of mixing and combustion should be considered together. The problem of mixing of supersonic reacting gas flows requires an independent study. It is also necessary to solve the problem of the rational distribution of energy supply along the channel under the condition that the static temperature of the flow does not exceed a certain maximum value. This condition is imposed by the restriction on the degree of dissociation of combustion products, which decreases the gas-flow exergy.The present paper describes the results of numerical simulations of an unsteady flow in a channel considered as an element of an air-breathing engine and consisting of segments with a constant section and an expanding section. The channel configuration is shown in Fig. 1 (x 1 , x 2 , x 3 , and β are the varied parameters). In the classical scheme, energy supply in the combustion chamber is provided by burning the fuel in a certain polytropic process. In the case considered, the energy is supplied to the gas flow in a pulsed-periodic mode. Avoidance of mixing in considerations allows us to determine the direct effect of supplied energy parameters (power, pulse frequency, and distribution of energy sources along the channel) on flow characteristics. The flow Mach number at the channel entrance was varied in the range M 0 = 2.4-4.0 corresponding to flight Mach numbers M ∞ = 6-12. The parameters of the flow with energy supply were calculated by the unsteady quasi-one-dimensional Euler equations ∂U ∂t + ∂F ∂x = G, U = (ρy, ρuy, ey), F = (ρuy, (p + ρu 2 )y, (p + e)uy), G = (0, p dy/dx, qy), p= (γ − 1)(e − ρu 2 /2),
