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

Abstract

The combustion stability of a liquid-propellant rocket engine experiencing a random, finite perturbation from steady-state conditions is examined. The probability is estimated for a nonlinear resonant limit-cycle oscillation to be triggered by a random disturbance. Transverse pressure waves are considered by using a previously published two-dimensional nonlinear pressure wave equation coupled with Euler equations governing the velocity components. The cylindrical combustion chamber is a complex system containing multiple co-axial methane-oxygen injectors; each co-axial jet is analysed for mixing and burning on its own local grid scheme, with the energy release rate coupled to the wave oscillation on the more global grid. Two types of stochastic forcing for the random disturbance are explored: a travelling Gaussian pressure pulse and an oscillating pressure dipole source. The random variables describing the pulse are magnitude, location, duration and orientation of the disturbances. The polynomial chaos expansion (PCE) method is used to determine the long-time behaviour and infer the asymptote of the solution to the governing partial differential equations. Depending on the random disturbance, the asymptote could be the steady-state solution or a limit-cycle oscillation, e.g. a first tangential travelling wave mode. The asymptotic outcome is cast as a stochastic variable which is determined as a function of input random variables. The accuracy of the PCE application is compared with a Monte Carlo calculation and is shown to be significantly less costly for similar accuracy.

Transverse Combustion Instability in a Rectangular Rocket Motor

“…(12)(13)(14) contributes to the good agreement between experiment and simulation: without RDT, the simulated limit-cycle amplitudes are 543, 379, 157, and 66 kPa for the OOXOXOO, OXXOXXO, XOOOOOX, and XOXOXOX cases, respectively. Thus, especially in the cases with a large limit-cycle amplitude, the underprediction of experimental results would be considerably more pronounced without the incorporation of the RDT model.…”

“…These equations, applied previously to a cylindrical chamber [3,12,13], were successful in identifying three domains within the parameter space: unconditional instability, conditional instability, and unconditional stability. Transients and limit cycles were produced for several different instability events.…”

“…The disturbances that trigger combustion instability can result from fluid-mechanical disruptions in the propellant injection process, shedding in the combustion chamber of large rogue vortices that eventually flow through the choked nozzle [11], extraordinary excursions in local burning rates [12,13], an acceleration of the entire LPRE engine [12,14], or a synergism amongst such events.…”

“…Thus, the present study builds on previous analyses [3,12,13]. A particular experimental configuration, the seven-injector rocket engine studied by the Anderson group at Purdue University [15][16][17], is simulated.…”

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].…”