Supersonic Underexpanded Jet Features Extracted from Modal Analyses of High-Speed Optical Diagnostics

Abstract

An experimental study concerning an underexpanded, screeching, Mach 1.5 jet operating at a stagnation-to-ambient pressure ratio of 4.4 is presented. Experimental data were acquired from high-speed schlieren imaging (100,000 frames per second) as well as pulse-burst particle image velocimetry (PIV) at 50 kHz. Spectral analyses of these data are presented and compared, as are the results from modal analyses using both proper orthogonal decomposition (POD) and spectral POD (SPOD). Comparisons revealed that both schlieren images and pulse-burst PIV vector fields could be decomposed to capture the same oscillatory phenomenon in the jet (screech) at $St=0.22$ ( $f=17\mathrm{kHz}$ ). Both techniques captured strong periodic behavior in the shear layer where the influence of screech is observed to be significant and in the turbulent breakdown region of the jet where the shock cells are unsteady. Excellent qualitative and quantitative agreement was found between the spectral and modal analyses of these data, despite the fundamental differences between schlieren and PIV. Challenges associated with the pulse-burst PIV experiment are discussed, and detailed uncertainty analyses of these data are presented, showing excellent convergence of the data with low statistical uncertainties. The comparisons between these diagnostics help to demonstrate the capabilities of pulse-burst PIV, which is still a relatively new diagnostic technique for studying high-speed flows.