Two-Dimensional Model for Liquid-Rocket Transverse Combustion Instability

Nonlinear, transverse-mode, liquid-propellant-rocket-motor combustion instability is examined with a two-dimensional model. The three-dimensional equations are integrated over the axial direction, for a multi-orifice short nozzle. Nonlinear transverse-wave oscillations in the circular combustion chamber are examined with the primary flow in the axial direction. Turbulent mixing of methane and gaseous oxygen with coaxial injection is analyzed. The combustion has two characteristic times, one for mixing and the other for chemical kinetics, producing a time lag in the energy-release rate relative to pressure. Then, the coupled combustion process and wave dynamics are calculated for a 10-injector chamber with methane and gaseous-oxygen propellants. The linear first tangential mode is imposed initially. Nonlinear triggering occurs; above a critical initial amplitude, the amplitude grows; otherwise, it decays with time. The second tangential mode also develops, and the nonlinear resonance creates a subharmonic mode with a frequency equal to the difference between the two tangential-mode frequencies. A modification of the characteristic times leads to a triggered instability, in which the first tangential mode transfers energy to its harmonics without the appearance of the second tangential mode or the subharmonic mode. Local pulses of pressure and velocity can also trigger instabilities with a strong sensitivity to the direction of the pulse.