This paper presents a novel sequential combustor experiment for the study of reheat flame responses to high-frequency, transversal thermoacoustic oscillations. The reheat combustion chamber is of flat, quasi two-dimensional design to distinctly separate combustion areas dominated by auto-ignition and aerodynamic flame stabilization. This specific combustor setup furthermore promotes the occurrence of pressure pulsations at the first transverse resonance frequency, often referred to as screech. For investigation of combustion and acoustic properties, the reheat stage is equipped with pulsation probes at the face plate, and the entire combustion zone is optically accessible from all lateral sides to allow for (laser-) optical flame and flow diagnostics. In order to validate the qualification of the experimental setup for investigations of high-frequency flame dynamics, the reheat combustion regime and resulting transverse pressure dynamics are investigated. The desired flame shape with distinct auto-ignition and aerodynamic flame stabilization zones is achieved and can be sensibly controlled. Analyzing the frequency spectrum of the dynamic pressure measurements at the combustor face plate reveals the first transverse resonance at approximately 1600 Hz, which satisfies a key goal of the specific design. Overall, the setup qualifies for studying flame-acoustics interaction in reheat combustors and provides an experimental benchmark for modeling efforts and their validation. This will eventually contribute to design countermeasures to thermoacoustic pulsations for improved future generations of gas turbine combustors.

High-frequency (HF) thermoacoustic instabilities in stationary gas turbine combustors are receiving increased attention as they reduce the operational flexibility and increase the emissions of such machines. This paper deals with the numerical work regarding the acoustic and flow design needed to commission a reheat combustor test rig with the aim of revealing the physics behind high frequency flame-acoustics interactions. Methods and workflow that allow for the design of such a reheat test rig are presented. The ultimate objective of the testbed is to give insight into the response of non-compact flames to the first transverse (T1) resonant mode of the combustion chamber. Therefore, the acoustic design promotes a thermoacoustically unstable T1 mode. Furthermore, the combustor is of a flat quasi two-dimensional geometry, which allows to clearly distinguish between flame zones stabilized by auto-ignition and by aerodynamics, respectively. Details on the experimental setup and operation of the test rig are provided in a joint publication. In the paper at hand, first the acoustic design is presented. Second, the isothermal flow design to optimize the combustion regime is outlined. Third, the acoustic characterization of the test rig is performed. To do so, the Helmholtz equation for the whole test rig, including the first stage, is solved via FEM. The simulated T1 mode appears at about 1600 Hz, which matches the experimental observations. Finally, an a priori assessment of linear acoustic damping and driving for the T1 mode is carried out. For the damping part, the two main effects are taken into account: damping due to the acoustic boundary layer and damping due to mean flow-acoustic coupling i.e. acoustic energy dissipated in the shear layers. The linear acoustic driving is estimated by means of source terms of deformation and displacement. The required heat release fields are artificially created and later validated with experimental OH* chemiluminiscence images. Driving and damping together define the linear stability behavior of the test rig.

The linearized Euler equations (LEE) provide an accurate — yet computationally efficient — description of propagation and damping of acoustic waves in geometrically complex, non-uniform reactive mean flows like those found in gas turbine combustion chambers. However, direct application of the LEE to perfectly premixed combustors with highly turbulent flows overestimates entropy waves as the LEE solution inherently contains coupled acoustic, vortical and entropy modes. In the present work, the LEE are decomposed into isentropic and non-isentropic parts ultimately obtaining a simplified set of isentropic LEE, in which only acoustic and vortical modes propagate. In the isentropic LEE, only continuity and momentum equations need to be solved. The energy equation is replaced by the isentropic relation between acoustic pressure and density. From the decomposition, the unsteady heat release term, which acts as a source in the energy equation, naturally arises as a source in the continuity equation. This way, the thermoacoustic coupling is still preserved in the isentropic formulation. The derived isentropic set of equations is first tested with a one-dimensional benchmark configuration consisting of a mean flow temperature jump, non-uniform mean flow velocity and unsteady heat release sources. Solutions of the non-isentropic and isentropic set of LEE are compared and the avoidance of entropy waves proved. Finally, isentropic LEE are used for reproducing the frequency of the self-excited first transversal mode of a lab-scale swirl-stabilized premixed combustor. Furthermore, isentropic and non-isentropic LEE solutions are compared. The non-isentropic LEE yield too high levels of entropy at the combustor exit that may explain the increased damping rate of the non-isentropic LEE solution compared to the isentropic LEE solution. This shows the relevance of isentropic LEE for correctly predicting thermoacoustic stability limits at high frequencies in relevant industrial applications.

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, vortical 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.

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, vortical 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.