Two-Dimensional Model for Liquid-Rocket Transverse Combustion Instability

Abstract

Nonlinear, transverse-mode, liquid-propellant-rocket-motor combustion instability is examined with a twodimensional 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.

Stochastic modelling of transverse wave instability in a liquid-propellant rocket engine

“…Pressure is sufficiently high and there is sufficient preheating of the propellants to consider propellants and products as compressible fluids. The deviation from steady-state operation will be governed by a system of equations involving the nonlinear wave equation for chamber pressure coupled with Euler equations for the velocity components (Sirignano & Popov 2013). A multiscale approach will be followed where effects of viscosity, turbulence and thermal and mass diffusion are neglected on the scale of the oscillation wavelength or chamber diameter but are considered in the jet flame region surrounding the exit flow from each injector.…”

“…There are advantages in applying a stochastic analysis to this problem. To this end, the deterministic simulations of Sirignano & Popov (2013) are extended to a more general problem, in which the perturbation from the steady-state operational conditions, and therefore the entire solution, is a random variable. This allows for modelling of the uncertainty about key features of the perturbation, such as its location, duration, orientation and amplitude.…”

“…We therefore focus on transverse waves because they are more destructive in general. A simplified two-dimensional model will be used; it was introduced by Sirignano & Popov (2013) and applied to a deterministic set of disturbances that have been found to trigger instabilities when their magnitude is sufficiently large.…”

“…The high energy release by combustion can, in certain conditions, reinforce acoustic oscillations which grow to destructive amplitudes. LPRE combustion instability provides a very interesting nonlinear dynamics problem as shown by both theory and experiment (Harrje & Reardon 1972;Oefelein & Yang 1993;Sirignano & Popov 2013).…”

Dynamics of a transcritical coaxial flame under a high-frequency transverse acoustic forcing: Influence of the modulation frequency on the flame response

“…They showed a reduction of the jet length, indicating altered destabilization and mixing processes, a growth of the expansion angle and a flame oscillation following the acoustic field. Observations provided useful clues on the coupling mechanisms and enabled considerable progress in the modeling of combustion instabilities [1,[41][42][43][44][45][46].…”