Linearized Reactive Flows

The objective of projects centred around the Linearised Reactive Flow Equations is to leverage the vast toolbox of linear analysis methods known from incompressible hydrodynamics to study thermoacoustic instabilities in compressible reactive flows.  Using the LRF equations, we aim to gain understanding of thermoacoustic problems from an operator based perspective, i.e., by analysis of the properties of the linear operator that governs the dynamics of small perturbations of the flow, rather than post-processing of data gathered from experiments or high-fidelity simulations.

Input-output analysis of the linearised system of equations is a computationally efficient way to compute flame transfer functions that act as low-order models for flame dynamics [1]. Due to the monolithic character of the LRF equations, flame movement is inherently accounted for in the approach, and spurious perturbations that would result from common frozen flame assumptions are avoided [2].  The global eigenvalue problem provides not only the linear growth rates and frequencies of thermoacoustic instabilities, but also sensitivities based on the adjoint modes to identify driving regions of thermoacoustic instabilities [3]. The appropriate definition of markers for driving regions of self-sustained thermoacoustic instabilities is an ongoing work in the group. Since hydrodynamics are completely resolved in the LRF framework, these equations are a dedicated tool to study the impact of shear induced non-normality on the global transfer behaviour of the flame [4]. For studying the effect of non-normality, as well as, identification of optimal perturbation mechanisms, we are relying on resolvent analysis. The same set of tools is used to characterise swirl perturbations in flow configurations relevant for swirl stabilised combustion systems [5, 6]. Adjoint-based shape optimisation of burners to suppress thermoacoustic instabilities is another ongoing research effort. Due to the monolithic approach, shape modifications that impact the dynamics of the flame can directly be included in the optimisation framework [7]. Apart from applying the LRF equations to study thermoacoustic instabilities, recent efforts focus on investigations of flame-front intrinsic instabilities, i.e., thermo-diffusive or Darrieus-Landau instabilities, to provide a computationally efficient access to dispersion relations of planar hydrogen flames at a variety of load points. These dispersion relations can then contribute to the development of turbulent combustion models for hydrogen..  

With the successful demonstration of the potential of the LRF approach for laminar flames, ongoing research focuses on the linearisation of turbulent reactive flows. This is a challenging task that needs answers to fundamental modelling questions such as, how to account for turbulence-flame interaction and counter gradient diffusion of species in the linearised models? Challenges were recently described in [8]. Since turbulent flows have no steady base flow anymore, fundamental questions on the linearisation of the governing equations about time averaged mean flow fields arise. We are extending the operator driven approach of the LRF equations to the weakly non-linear regime to assess the validity of mean flow analysis [9]. The same framework will offer the possibility to study weakly nonlinear interaction between global modes, e.g., synchronisation, in an operator driven approach, something not possible in the purely linear world.