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Abstract
A third order theory is developed to predict the nonlinear behavior of unstable liquid-propellant rocket engines. The stability of a cylindrical combustor with a distributed steady state combustion process and a multi-orifice quasi-steady nozzle is considered. The full system of unsteady conservation equations is analyzed and Crocco×s time-lag hypothesis is used to describe the unsteady combustion response. It is assumed that the spatial dependence of the solutions can be approximated by a single acoustic mode and the Galerkin method is used to obtain a set of ordinary differential equations that describe the time dependence of the unknown variables. Numerical solutions of these equations are used to determine (1) the final behavior of the instability in a linearly unstable engine, (2) “triggering” limits of linearly stable engines, and (3) the relative importance of various non-linearities of the problem.
