Modal Analysis of Supersonic Jet Flow Structures via Proper Orthogonal Decomposition Under Temperature and Pressure Variations

This study experimentally investigates supersonic free jets from convergent and convergent-divergent nozzles over a range of nozzle pressure ratios, 3 ≤ NPR ≤ 20, and inlet temperatures, Tin = 288 K (room temperature) down to Tin = 123 K. Instantaneous Schlieren images are recorded with horizontal and vertical knife edges to obtain sensitivity to transverse and streamwise density gradients, $\partial \rho / \partial y$ and $\partial \rho / \partial x$. Proper orthogonal decomposition (POD) is then applied to the Schlieren fields to identify the dominant spatial modes associated with the jet shear layers, the shock-cell system, and the outer plume. For the convergent nozzle at room temperature, the vertical knife edge emphasizes the shock-cell train at higher NPR, while the horizontal knife edge highlights the growth and spreading of the shear layers. The leading POD modes confirm that, as NPR increases, the flow energy shifts from shear-layer wave packets to a more organized streamwise shock pattern. The convergent-divergent nozzle exhibits a clear transition from overexpanded to underexpanded operation between NPR = 7 and NPR = 9, with a longer and more regular shock train than the convergent case at the same NPR. At the same NPR and low Tin, the convergent jet spreads more in the transverse direction downstream, whereas the convergent-divergent jet remains more collimated. Cooling the jet’s inlet temperature to Tin = 203–123 K increases the jet-to-ambient density ratio and strongly modifies the Schlieren response and POD modes. More energy is carried by large-scale structures in the outer plume and by the extended potential core, while near-nozzle mixing is reduced. The combined Schlieren-POD analysis thus provides a clear picture of how nozzle geometry, pressure ratio, and inlet temperature reorganize the dominant flow structures in supersonic jets.