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Disturbance energy transport and sound production in gaseous combustion

Published online by Cambridge University Press:  12 July 2012

Michael J. Brear*
Department of Mechanical Engineering, University of Melbourne, Parkville 3010, Australia
Frank Nicoud
Université Montpellier II, I3M, Place E. Bataillon, 34095 Montpellier, France Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS), 42 Avenue Gaspard Coriolis, 31057 Toulouse CEDEX 01, France
Mohsen Talei
Department of Mechanical Engineering, University of Melbourne, Parkville 3010, Australia
Alexis Giauque
Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS), 42 Avenue Gaspard Coriolis, 31057 Toulouse CEDEX 01, France Office National d’Etudes et de Recherches Aerospatiales (ONERA), 29 av. de la Div. Leclerc, F-92322 Châtillon, France
Evatt R. Hawkes
School of Photovoltaic and Renewable Energy Engineering / School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney 2052, Australia
Email address for correspondence:


This paper presents an analysis of the energy transported by disturbances in gaseous combustion. It extends the previous work of Myers (J. Fluid Mech., vol. 226, 1991, 383–400) and so includes non-zero mean-flow quantities, large-amplitude disturbances, varying specific heats and chemical non-equilibrium. This extended form of Myers’ ‘disturbance energy’ then enables complete identification of the conditions under which the famous Rayleigh source term can be derived from the equations governing combusting gas motion. These are: small disturbances in an irrotational, homentropic, non-diffusive (in terms of species, momentum and energy) and stationary mean flow at chemical equilibrium. Under these assumptions, the Rayleigh source term becomes the sole source term in a conservation equation for the classical acoustic energy. It is also argued that the exact disturbance energy flux should become an acoustic energy flux in the far-field surrounding a (reacting or non-reacting) jet. In this case, the volume integral of the disturbance energy source terms are then directly related to the area-averaged far-field sound produced by the jet. This is demonstrated by closing the disturbance energy budget over a set of aeroacoustic, direct numerical simulations of a forced, low-Mach-number, laminar, premixed flame. These budgets show that several source terms are significant, including those involving the mean-flow and entropy fields. This demonstrates that the energetics of sound generation cannot be examined by considering the Rayleigh source term alone.

Copyright © Cambridge University Press 2012

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