Accounting for convective effects in zero-Mach-number thermoacoustic models

Emmanuel Motheau (1) , Laurent Selle (2) , Franck Nicoud (3)

1 CERFACS - Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique
2 IMFT - Institut de mécanique des fluides de Toulouse
3 I3M - Institut de Mathématiques et de Modélisation de Montpellier

This paper presents a methodology to account for some mean-flow effects on thermo-acoustic instabilities when using the zero-Mach-number assumption. It is shown that when a computational domain is represented under the M=0 assumption, a nonzero-Mach-number element can simply be taken into account by imposing a proper acoustic impedance at the boundaries so as to mimic the mean flow effects in the outer, not computed flow domain. A model that accounts for the coupling between acoustic and entropy waves is presented. It relies on a "delayed entropy coupled boundary condition" (DECBC) for the Helmholtz equation satisfied by the acoustic pressure. The model proves able to capture low-frequency entropic modes even without mean-flow terms in the fluctuating pressure equation.

Mots clés: Thermoacoustics; Combustion instabilities; Mean-flow effects

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Emmanuel Motheau, Laurent Selle, Franck Nicoud. Accounting for convective effects in zero-Mach-number thermoacoustic models. Journal of Sound and Vibration, 2014, 333, pp.246-262. ⟨10.1016/j.jsv.2013.08.046⟩. ⟨hal-00905802⟩