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 co-axial 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 ten-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 develops also and the nonlinear resonance creates a sub-harmonic mode with a frequency equal to the difference between the two tangential-mode frequencies. Modification of the characteristic times leads to a triggered instability where the first-tangential mode transfers energy to its harmonics without the appearance of the second-tangential mode or the sub-harmonic mode. Local pulses of pressure and velocity can also trigger instabilities with strong sensitivity to the direction of the pulse.
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