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Gas dynamic calculation of detonation in constant-cross-section ducts

The paper presents a computational method with the use of gas-dynamic functions of parameters of detonation in a one-dimensional subsonic flow of ideal gas behind the shock wave propagating in chemically active air-and-fuel mixture in a uniform-cross-section duct, where the resultant of normal pressure forces acting on its side surface is equal to zero. Stabilization of the shock wave is provided by the onset of thermal crisis with the air-and-fuel mixture combustion heat supply to the gas behind the wave. In this case the value of the specific speed of the combustion products is equal to the critical one. The solution of the total-impulse equation considering the above mentioned peculiarities of the flow in a uniform-cross-section duct establishes clear correlation of the specific speed of the stabilized shock wave to the rate of rise of the temperature of the gas behind it, which gives an opportunity to determine all detonation parameters. The shock wave can be initiated by the detonation of an explosive substance and carries a huge amount of energy. It is shown that the shock wave can be obtained only if the source of small disturbances itself moves at the supersonic speed. It is shown that total pressure behind the shock wave decreases significantly and the entropy increases due to the wave losses, whereas the static pressure increases significantly. An explanation of this effect is given. A formula for calculating the rate of gas temperature rise was derived as a function of the specific speed of the shock wave, the air-and-fuel mixture heat value and the heat availability factor that designates the dissociation of the combustion products and heat loss through the duct wall under specified initial conditions. The reliability of the method of calculating detonation was experimentally substantiated. The work is currently important for the evaluation of the detonation engine efficiency.