Consequences of non-normality and nonlinearity in flow / premixed flame / acoustic interactions for combustion instability

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In dynamical systems with non-normal eigenmodes, modal interactions can result in large transient growth even if all modes are linearly stable. Under such circumstances, subcritical transition to instability may occur in the presence of low-amplitude perturbations, and classical linear stability analysis becomes a poor indicator of system behaviour.The non-normal nature of thermo acoustic interactions has been identified only recently; possible consequences for combustion dynamics have until now been explored only in the context of very simple, idealized model problems. The current proposal aims to examine non-normality and nonlinearity in the context of flow / premixed flame / acoustic interactions, and to develop corresponding tools that have the potential to handle with quantitative accuracy also configurations of applied interest, e.g. turbulent premix swirl flames.It is proposed to proceed systematically: Starting from a “monolithic” approach based on a compressible flow formulation, a variety of coupled modelling strategies shall be developed and validated. The monolithic approach, which is in a sense model-free, shall be used primarily to generate reference data, as it is computationally very expensive. Coupled approaches, which make use of an incompressible model for the flow / combustion interaction and subsequent model reduction, are much more efficient. However, their accuracy in particular in regard to non-normal effects, must be validated.Results from these simulations will be used to develop methodologies for system identification that can capture non-normal and nonlinear effects. Of particular interest is the role of the internal dynamics (corresponding to internal degrees of freedom) of the flame in thermo acoustic evolution. This touches the question of the appropriate definition of fluctuation energy (mathematically speaking: the choice of “norm” of the system state vector) as well as the appropriate model structure for identification of reduced models. The following point is also important for the latter: according to asymptotic analysis, acoustic Reynolds stress terms appear in the hydrodynamic flow/combustion sub-model. It has to be investigated, if and how these terms should be considered in the identification of flame model parameters.The application of complementary numerical and experimental tools as well as analytical methods for thermo acoustic stability analysis ensures synergistic benefits.