Disturbance energy transport and sound production in gaseous combustion

Abstract

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.

Entropy noise: A review of theory, progress and challenges

“…Both may result in acoustic waves returning to further perturb the flame, giving the potential for thermoacoustic instability. 21,29,67,68 Many of the early tools for predicting thermoacoustic combustor modes accounted only for the direct acoustic waves, neglecting acoustic waves generated by entropy wave acceleration. This is justifiable for many of the laboratory-scale combustors, such as Rijke tubes, which have open ends and so do not exhibit entropy wave acceleration.…”

A nonlinear model for indirect combustion noise through a compact nozzle

“…Since they have moreover been shown recently to be a key ingredient in the onset or sustainability of some combustion instabilities (Giauque 2007;Brear et al 2012;Motheau et al 2013), it is legitimate to consider that their amplitude might be large enough to lie in the nonlinear domain (typically above 100 K for a 1000 K averaged background temperature in the combustion chamber).…”

“…In practical applications, nonlinear acoustic fluctuations are rarely observed because they correspond to very high pressure fluctuations that are seldom generated even in the case of combustion instabilities (Paschereit et al 2002;Boudier et al 2009;Candel et al 2012;Wolf et al 2012). However, recent studies have evidenced the role of coherent entropy waves in the onset or sustainability of combustion instabilities (Giauque 2007;Brear et al 2012;Motheau et al 2013) and it appears reasonable to consider the possibility that this kind of perturbation also has amplitudes lying in the nonlinear domain. The rest of the paper therefore focuses on detailed analyses corresponding to entropy forcings.…”

“…Although obviously affected by the turbulent mixing cascade, no significant damping from the flame to the combustion chamber outlet is in 270 M. Huet and A. Giauque this case expected during the convection process. Recent studies have shown both numerically and experimentally the influence of coherent entropy waves on the onset or sustainability of combustion instabilities (Giauque 2007;Brear et al 2012;Goh & Morgans 2013;Hochgreb et al 2013;Motheau et al 2013) and their role in acoustic mode scattering (Atassi & Gilson 2010). As such, it appears reasonable to consider the possibility that this kind of entropy perturbation also has amplitudes lying in the nonlinear domain (typically above 100 K for a 1000 K averaged background temperature).…”

Flame Quenching at Walls: A Source of Sound Generation

“…Obviously, the perturbation of flame surface plays a significant role in the description of the sound gene ration [18][19][20][21][22]. Starting from the work of Lighthill [23] and its reformulation by Dowling (Chapter 13 in [24]), it was shown by Talei et al [17] that far-field pressure fluctuations for one-dimensional, completely annihilated flames can be expressed by:…”