Mache Effect and Combustion Instability in Solid Rocket Motor

Abstract

A theoretical analysis of nonacoustic low-frequency instability ( Linstability) of combustion in solid rocket mo- tors (SRM) is considered. Such an instability takes place when the timescale of thethermal inertia of a combustion wave ?T is comparable with the timescale ?W of pressure relaxation in the motor cavity. An original model is proposed for unsteady combustion process in SRM. This model allows the e ame temperature and temperature distribution in a gas e ow to e uctuate with the chamber pressure (Mache effect (Mache, H., Die Physik der Ver- brennungserscheinungen , Veit and Co., Leipzig, Germany, 1918)). A laminar one-dimensional gas e ow (without dissipation and mixing) is assumed. The propellant unsteady combustion is described using the Zel' dovich phe- nomenological approach and taking into account the variation of the combustion surfacetemperature (Novozhilov model) as well as e ame temperature (Gostintsev and Sukhanov model (Gostintsev, Y. A., Sukhanov, L. A., and Pokhil, P. P., On the Theory of Unsteady Combustion of Solid Propellant. Stability of the Process in Semi-Closed Volume, Journal of Applied Mechanics and Technical Physics , Vol. 12, No. 6, 1971, pp. 65- 73)). Emphasis is on the dependence of the critical conditions of stable combustion on the temperature distribution in gas e ow under variable gas pressure (Mache effect). This problem is considered in detail for SRM having an end-burning charge. The result of the analysis shows that the Mache effect can signie cantly extend the instability region on the plane (k;Â=?W/?T), if  2 are close to the asymptote (at ?W A ? T) that corresponds to the criterion of intrinsic instability of combustion under constant pressure. Application of these results to rocket motors with a common cone guration of the propellant charge is discussed.