Linearizing a reacting turbulent jet flow: How to do it, and how not to.

In the last years, linearized methods, such as the resolvent analysis, have helped significantly to enhance comprehension of coherent structures in turbulent flows and how they emit acoustic fluctuations/noise. One specific type of such flows and their acoustic emissions is of significant importance for gas turbine combustion chamber engineers: A turbulent reacting flow, i.e. a turbulent flame. Including the reaction chemistry in the linearized framework would allow to investigate the coherent structures in turbulent reacting flows and the resulting noise emissions by using the resolvent analysis. Furthermore, it could constitute a novel method to tackle the seemingly everlasting problem of thermoacoustic instabilities, a phenomenon with potentially catastrophic consequences in gas turbine combustors.

Driven by this motivation, we investigate the question if and how the strongly non-linear system of a turbulent flame can be treated in a linearized framework. To achieve this goal, we analyze the generic configuration of a perfectly premixed turbulent jet flame. Large Eddy Simulations (LES), which use a progress variable and tabulated chemistry, provide the temporal means. These serve as input to the linear analysis. We demonstrate why a straightforward linearization of the LES reaction model cannot be a valid approach. Instead, we linearize the eddy break up model, a standard RANS reaction model, and superimpose it on the LES mean flow. The linearized reacting flow equations are derived and solved in frequency domain for incomming acoustic perturbations. The resulting flame responses are compared to acoustically forced LES, showing very good agreement. Finally, a perspective on the next necessary steps towards a fully holistic approach to investigate thermoacoustic fluctuations and an appication of the resolvent analysis on the configuration are given.