Coaxial Jet Flame Subject to Long-Wavelength Acoustic Oscillations

Abstract

A linear model is developed to relate the response of energy release rate per unit volume to velocity and pressure oscillations in a liquid-propellant rocket engine. Coaxial injection of fuel (outer flow) and oxygen (inner flow) is considered with chemical reaction in a thin flame and turbulent mixing as the controlling factor in an axisymmetric diffusion flame. The combustion process has a characteristic time for mixing, producing a time lag in the energy release rate relative to pressure. The model applies to an individual injector but can be used to couple the multipoint combustion processes and wave dynamics for a multi-injector chamber. In particular, the impacts of long-wavelength oscillations of pressure and velocity in the surrounding chamber gas on the mixing and burning rates are determined. The results are developed in a way that feedback to the chamber oscillations can be determined for either a computational analysis or a perturbation analysis of the chamber wave dynamics. Both the steady-state behavior and the unsteady linear perturbation for the coaxial jet are studied using an axisymmetric Green’s function. Flame temperature, flame shape, and burning rates are found as a function of mixture ratio and injector size (mixing time). The combustion response factor for oscillatory behavior is also determined.