A Momentum Potential Theory-Based Framework for Analyzing Experimental Pressure-Sensitive Paint Data

A physics-based decomposition technique, based on Momentum Potential Theory (MPT), is developed to extract insights from experimental time-resolved Pressure-Sensitive Paint (PSP) measurements. In the general case where the complete spatio-temporal flowfield is available, MPT provides insights into the flow dynamics by separating the “momentum-density” fluctuation vector (��u)′ into its acoustic, hydrodynamic (vertical), and thermal (entropic) components. The potential function associated with the acoustic component is derived by solving a Poisson equation, with the source term consisting of spatially varying time derivatives of pressure fluctuations. Spatio-temporally resolved PSP data is found to be adequate for this purpose, providing insights into the near-surface flowfield, augmenting insights from direct analysis of the data. The method is implemented on PSP measurements of supersonic flow past 3D swept (single fin) and compound-swept (double-fin) shock-wave/boundary-layer interactions (SBLI). The MPT-filtered field reveals acoustic waves as larger-scale coherent structures compared to the raw pressure data. These are interpreted as imprints of structures in the outer parts of the separated flows. Since the MPT-filtered acoustic output is a vector, the streamwise and spanwise components of the acoustic component provide insights into directional information encapsulated in the scalar pressure field. These acoustic components are further analyzed with data-driven methods to expose the underlying dynamics. Application of Spectral Proper Orthogonal Decomposition (SPOD) and wavenumber-frequency transformation clarify some of the signal-propagation directions. Standing waves and upstream-propagating acoustic waves are observed in the compound interaction but are absent in the simple-swept interaction. Additionally, the dispersion relation revealed by two-dimensional space-time Fourier transforms in different regions in the flow facilitate the identification of regions where upstream traveling acoustics are more prominent. This MPT-based methodology for experimental PSP data thus enhances insights into near-surface dynamics, while offering broad applicability across different flow conditions and configurations.