Simulated Focused Laser Differential Interferometry of Mixed First- and Second-Mode Instabilities in Hypersonic Flow

This paper presents a computational study of double focused laser differential interferometry (D-FLDI) measurements related to mixed first and second (Mack) mode instabilities. High-fidelity direct numerical simulation (DNS) density fields of multiple first- and second-mode waves were computed and utilized in conjunction with a ray-tracing FLDI simulation to better determine the accuracy of FLDI measurements through a complex realistic flow field. The results are compared to actual DNS density fluctuations, and various FLDI data processing techniques are applied to evaluate their effectiveness in recovering true DNS density fluctuations from the FLDI simulation. Additionally, the convection velocity of the overall instabilities is estimated and compared to the corresponding velocity obtained from the DNS data. The study found that the FLDI diagnostic tends to emphasize the planar second-mode fluctuations while suppressing the oblique first-mode waves. This outcome is attributed to two factors. First, the second-mode wavelengths more closely matched the optimal wavelength for FLDI sensitivity, which is defined as twice the beam separation. Second, the integration of the signal along the optical axis naturally suppressed the oblique first-mode waves and amplified the planar second-mode waves.