Numerical design of a novel reheat combustor experiment for the analysis of high-frequency flame dynamics

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.