Thermal versus acoustic response of velocity sensitive premixed flames S. Bomberg a,b , T. Emmert a , W. Polifke a,∗ a Lehrstuhl f¨ ur Thermodynamik, Fakult¨ at f¨ ur Maschinenwesen, Technische Universit¨ at M¨ unchen, Boltzmannstr. 15, D-85748 Garching, Germany b Institute for Advanced Study, Technische Universit¨ at M ¨ unchen, Lichtenbergstr. 2a, D-85748 Garching, Germany Abstract Premixed flames respond to velocity perturbations with fluctuations in heat release rate (“thermal re- sponse”), which in turn generate acoustic perturbations (“acoustic response”). The latter may subsequently in- fluence the velocity field in such a manner that feed- back leads to self-excited thermoacoustic instability. The present paper investigates interrelations between the thermal and the acoustic responses of premix flames. The analysis is formulated such that it properly repre- sents the underlying causality of acoustics–flow–flame– acoustics interactions. A flame-intrinsic feedback loop is revealed, which is quite independent of the acoustic environment of the flame, i.e. the acoustic impedances of plenum and combustor. The eigenmodes of this flame-intrinsic feedback loop coincide with poles of the acoustic scattering matrix of the flame. The correspond- ing frequencies, where the acoustic response is max- imum, are in general quite different from frequencies where the thermal response is strong, i.e. where the flame transfer function exhibits “excess gain”. Even more remarkable, the intrinsic flame modes may result in thermoacoustic instabilities without lock-on to one of the acoustic eigenmodes of the combustor. Experimen- tal results from two combustor test rigs with laminar conical as well as turbulent swirl flames are scrutinized and are found to confirm our analysis. In particular, un- stable modes are identified that are strongly related to flame-intrinsic feedback. Keywords thermoacoustic instability, combustion dynamics, flame transfer function, premixed flame, causality ∗ Corresponding author Email address: polifke@tum.de (W. Polifke) URL: http://www.td.mw.tum.de (W. Polifke) 1. Introduction 1 Thermoacoustic instabilities are a cause for concern 2 in combustion applications ranging from domestic burn- 3 ers to rocket engines. Such instabilities are under- 4 stood to result from flame–acoustic feedback: unsteady 5 combustion generates acoustic perturbations, which are 6 reflected by combustor or plenum such that acoustic 7 waves travel back to the flame, where they modulate 8 the heat release rate. This feedback may lead to self- 9 excited oscillations, possibly causing fatigue or struc- 10 tural damage [1]. In order to avoid thermoacoustic in- 11 stability, careful analysis of the system dynamics should 12 be conducted at every stage of the design process. 13 Thermoacoustic instability is in general conceptual- 14 ized as a non-local phenomenon, which depends on 15 the combined dynamics of the combustion process and 16 the combustor acoustics, possibly including air or fuel 17 supply. A comprehensive thermoacoustic analysis of a 18 combustion system by experiment or simulation is thus 19 difficult and expensive. Simplified, low-order models 20 for the flame dynamics on the one hand, and the system 21 acoustics on the other hand have often proven useful. 22 The present study also makes use of such tools. 23 One may distinguish the “thermal response” from the 24 “acoustic response” of a flame to flow perturbations: 25 the former describes fluctuations in heat release rate, 26 the latter acoustic perturbations generated by unsteady 27 heat release rate. Both thermal and acoustic response 28 are of significant interest in combustion dynamics, and 29 both may exhibit substantial magnitude at favorable fre- 30 quencies. In the present paper, the thermal and acous- 31 tic responses of velocity sensitive premixed flames are 32 compared against each other and their interrelations are 33 investigated. Remarkably, it is shown that a significant 34 amplitude in thermal response does not imply a strong 35 acoustic response, and vice versa. 36 A distinctive feature of the analysis presented in 37 this paper is that the relevant thermoacoustic processes 38 are represented in a manner that properly respects 39 Accepted author’s manuscript (presented at the 35 th Comb. Symp. July 23, 2014