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

Published online by Cambridge University Press:  17 March 2014

Pavel P. Popov ,
Athanasios Sideris  and
William A. Sirignano
Pavel P. Popov
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA
Athanasios Sideris
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA
William A. Sirignano*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Reacting Flows: Combustion Mathematical Foundations: Computational methods Instability: Nonlinear instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 745 , 25 April 2014 , pp. 62 - 91
Copyright
© 2014 Cambridge University Press 

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