A Novel Decomposition Approach Preventing Spurious Entropy Generation in Hybrid Thermoacoustic Stability Computations

Prominent approaches for the computation of thermoacoustic stability are hybrid methods like the linearized Navier–Stokes equations (LNSE) or the linearized Euler equations (LEE). The transient fluctuations around a precomputed steady-state mean flow field solved with these sets of equations naturally include the energy transition between acoustic, vertical, and entropic modes. It is common practice to account for flame-acoustic interactions by applying measured or computed flame transfer functions (FTF) as a volumetric source term proportional to the mean heat release rate in the energy equation. However, the underlying assumption of a static flame is the root cause of spurious entropy production, which may ultimately falsify the thermoacoustic stability predictions. In the present paper, a methodology to include arbitrary flame movement in the governing set of equations is presented. The procedure makes use of an arbitrary Lagrangian-Eulerian (ALE) description of conservation equations and is demonstrated for the Euler equations. The resulting set of linear perturbation equations is then applied to two test cases. First, the frequency response of a one-dimensional premixed air-methane flame is evaluated. Secondly, the frequency response of the first longitudinal eigenmode of an experimental premixed, swirl-stabilized combustor is computed. To demonstrate the reduction of spurious entropy waves, the results are compared to those of the classic LEE.