Disturbance energy transport, a tool to analyze backward-facing step combustion instabilities.
Creators: name:  J. KLEIN 
name:   A. GENOT 
name:   A. MURA 
name:   A. VINCENT-RANDONNIER 
Publisher: name: Proceedings of  the 9th European Conference for Aerospace Sciences. Lille, France, 27 June - 1 July, 2022
Year: 2022
Subjects: PROPULSION PHYSICS
LIQUID ROCKET ENGINE
COMBUSTION INSTABILITIES

description: The development of combustion instabilities is relevant to most of propulsion systems and do involve the coupling between several physical phenomena (acoustics, heat release rate oscillations, hydrodynamics ...). It may lead to critical issues such as mechanical and thermal stresses due to high pressure and temperature oscillations, combustion flashback and blow-off, and possible structural damage [1]. In this respect, the geometry of the combustion chamber, as well as the flame anchoring mechanism, are known to be amongst the most important parameters controlling flame dynamics [5]. In the present study, attention is focused on the development of unsteady combustion in the canonical case of a premixed flame stabilized by a backward-facing step. In this geometry the flame usually anchors to the edge of the sudden expansion with combustion stabilization resulting from the recirculation of hot burnt gases at the flame base. However, in some conditions such as the one pictured in Figure 1, an unstable regime featuring periodic flashbacks may arise as previously documented by Brossard et al. [2] or Altay et al. [5]. In this study, large-eddy simulations (LES) of a two-dimensional planar backward-facing step geometry are performed with the multi-physic solver CEDRE [3]. The objective is to analyze the corresponding combustion instabilities [2]. Further and deeper insights into their birth and development are expected to be gained from the disturbance energy balance method [4], which can be used to conduct a posteriori analyses of unsteady LES computational results. For unstable flows, the disturbance energy time derivative will be positive, whereas stable flows are associated to negative time derivatives. Every source term present in the disturbance energy balance is relevant to some couplings between the above-mentioned physical phenomena (thermo-acoustic instabilities, hydrodynamic instabilities, etc.). Thus, analyzing these various terms may allow to discriminate which couplings (and which physical phenomena) are the most destabilizing. The disturbance energy and associated source terms can either be evaluated locally or globally. In the former case, they can be plotted as fields so as to determine in which regions stabilization (or destabilization) occurs whereas, in the latter, these quantities are integrated over the whole volume of the combustion chamber in order to determine if the system is globally unstable (or not) and, if unstable, what are the leading-order contributions that drive the system to instability. A typical example of two local source terms is provided in Figure 2. Following Kalantari et al. [6], combustion chambers with increased wall temperature are prone to boundary layer flashbacks. Therefore, the influence of the wall temperature level deserves to be analyzed in details. The equivalence ratio value also offers a relevant quantity to be analyzed through a parametric study. As previously shown in reference [5], increasing the equivalence ratio may significantly influence the unstable cycle that may switch to a low frequency unstable mode. The corresponding change is studied through a detailed inspection of the disturbance energy source terms. Indeed, the source terms associated to the largest global contributions will highlight the most relevant physical processes. Among these, thermoacoustic instabilities, entropy spot oscillations, and flame/wall interactions source terms are found to be the leading-order phenomena. A detailed parametric study should allow getting a better understanding of this instability, the ultimate objective being to control its development. Two distinct parameters are considered: (a) the inlet mixture equivalence ratio and (b) the combustion chamber wall temperature. The sensitivity of the source terms present in the disturbance energy balance to these two distinct parameters is evaluated.