Coupled Feed-System and Chamber Modelling of a Gaseous-Oxygen/Kerosene Liquid Rocket Engine

Abstract

Propellant feed systems for small liquid rocket engines are commonly modelled as hydraulic networks discharging into a prescribed chamber pressure. Such models cannot represent the feedback between delivered mass flow and chamber pressure, and therefore they cannot predict injector stiffness, startup coupling, or feed-coupled instability—the quantities the model is usually built to inform. We replace the prescribed boundary condition in a Simscape Fluids model of a gaseous-oxygen/kerosene feed system with a lumped-volume combustion chamber whose pressure is a state, closed through a choked throat and thermochemistry interpolated on instantaneous mixture ratio. The coupled model reproduces the analytical steady state pc=m˙c*/At to better than 10−3%, and it predicts an operating point far from the design point at a chamber pressure the open-loop model reports as nominal by construction. A linear analysis of the coupled system retaining the mixture-ratio dependence of c* yields a closed-form low-frequency stability criterion, Δpinj/pc>[2(1+O/F)]−1+12dlnc*/dln(O/F), of which the classical twenty-percent injector-stiffness rule is the frozen-thermochemistry limit; the second term roughly doubles the critical stiffness at the design mixture ratio. A mechanism-separation procedure identifies which loops sustain an oscillation, and a pump-pressure sweep across the boundary shows the engine oscillating only where the criterion places it.