Resolving entropy waves in an RQL combustion chamber via SPOD-based post-processing

Entropy waves can be measured as temperature gradients with the optical measurement technique, Background-Oriented Schlieren (BOS). This article introduces an alternative way of post-processing BOS data to solve for temperature fluctuations. For this, the modal analysis spectral proper orthogonal decomposition (SPOD) is applied to BOS data. SPOD decomposes temperature gradients of BOS into eigenmodes which oscillate at a single frequency and sorts them by energetic contribution, enabling a separation of different flow dynamics. We propose to solve for the temperature by solving for specific SPOD eigenmodes directly in the frequency domain with numerical methods. Solving the Poisson equation underlying BOS in the frequency domain yields frequency-dependent solutions of the refractive index, which correlate directly to temperature. The benefit of this approach compared to the conventional phase-averaging is noise reduction by a low-rank approximation and the resolution of higher harmonics of the excitation frequency. The combination of BOS with SPOD analysis is shown for entropy waves generated in the dilution zone of an academic RQL combustion chamber. The SPOD eigenmodes of the deflections are shown for the forcing frequency and its higher harmonics, as well as for frequencies related to hydrodynamic instabilities in the shear layers. The resulting solutions of the refractive index and temperature fields from solving the Poisson equation in the frequency domain are presented and discussed.