The ideal thermodynamic cycle of a detonation engine is substantiated and a method of computing the engine parameters is presented. In the ideal cycle the processes of gas compression and expansion are adiabatic. It is shown that low thermodynamic effectiveness of the detonation engine can be explained by significant wave losses of the total pressure in the shock wave and the entropy increase. The advantage of the engine in comparison with other thermal machines is the capability of obtaining a high value of absolute energy of the gas flow to do the work of gas expansion. While analyzing the thermodynamic cycle it is assumed, like in the gas turbine engine theory, that the characteristics of gas condition are determined by the parameters of stagnation subsonic flow in the sections corresponding to the beginning and the end of the processes making up the cycle. Heat supply downstream of the shock wave takes place in the subsonic flow in a constant-pressure process. Consideration of the cycle with stagnation parameters significantly simplifies its analysis and gives a fuller picture of its energy. A formula for calculating the coefficient of thermal efficiency of the ideal cycle of a detonation engine is presented as a function of the specific speed of propagation of the stabilized shock wave. It is shown that the ideal thermodynamic cycle of a detonation engine is described by two adiabatic curves, an isothermal curve determining huge wave losses, and two isobaric curves. The work of gas expansion in a detonation engine can be implemented both for obtaining the moving force of a vehicle and in industry, e. g., for metal hardening and cutting, production of high-hardness artificial diamonds, geophysical investigation.

Formulas of gas dynamic calculation of detonation parameters in variable cross-section ducts are presented and a design detonation diagram is given. The diagram shows the detonation characteristics of super-compressed detonation and under-compressed detonation as the function of shock wave specific speed depending on the intensity of temperature of the ideal gas in a subsonic one-dimensional flow behind the shock wave propagating in a chemically active air-fuel mixture and on the ratio of geometrical expansion (convergence) of the duct. The propagation of a stationary shock-wave the static pressure of which in the output cross-section of the expanded duct is equal to atmospheric pressure is referred to as design detonation. This means that all the energy of the shock wave at the output of the duct can be converted into polytropic work function of gas expansion in a detonation engine. Otherwise, if the flow takes place in the mode of overexpansion due to the separation of the compressive shock wave inside the duct or in the case of insufficient expansion part of the shock wave energy will be lost. The total impulse equation for a geometrically expanding duct is solved by replacing the integral describing the thrust force with the average integral value of the curve of the static pressure acting on the side wall of the expanding duct. The frictional force is neglected due to its insignificant value. It is shown that the presence of an insufficiently compressed shock wave is not possible as the shock wave moving at the supersonic speed in the convergent duct will be decelerated to the sonic speed. To stabilize it additional heat should be supplied to transform the convergent duct behind the compressive shock wave into a semi-permanent cross-section duct wherein thermal crisis stabilizing the shock wave can be achieved. The minimum value of the detonation pipe diameter of 50 mm is substantiated. Below that value sharp reduction of combustion efficiency takes place. The results of the work can be used for the computation of detonation engine thermodynamic cycle parameters.

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