Numerical Parametric Analysis of Combustion Instability in Axial-Injected Hybrid Rocket Motors

A computational model of a hybrid rocket motor has been developed for the purpose of simulation of internal ballistics and transient behavior such as combustion instabilities. The numerical model consists of four subcomponents: 1) a quasi-one-dimensional gas dynamics model using Euler equations for flowfield simulation, 2) a chemical model using CEA, 3) an analytical heat-feedback model for transfer of heat from flame to the solid fuel surface, and 4) a one-dimensional thermal conduction model inside the solid fuel. In the unsteady time-dependent simulation, it is seen that upon the application of a temporal boundary layer delay of the wall heat flux to the changes in the regression rate an unstable region ensues. At first, an oscillating periodic increase in the regression rate and chamber pressure is observed (linear regime), which then proceeds into a nonlinear limit cycle. A positive DC shift in the chamber pressure is also observed. The possible reason for the DC shift is explained with an analogy to a simple nonlinear oscillating system. The frequencies of different natural modes (including the intrinsic hybrid oscillation mode) predicted by the model are found to be in good agreement with theoretical prediction. The effect of finite time needed for the unburnt fuel to move from the regressing surface to the flame region is also additionally modeled using a time delay to the heat of combustion. This results in an increased amplitude of oscillations and a higher DC shift. Parametric analyses have been carried out with different boundary layer delays. The effect of the magnitude of boundary layer delay on the values of DC shift and RMS amplitude is also explained.