Experimental investigation of supersonic impinging jets across overexpanded and underexpanded regimes using schlieren and modal analysis

This study examined the effects of nozzle geometry, nozzle pressure ratio (NPR), and nozzle-to-wall distance on the flow structure and unsteady dynamics of supersonic free and impinging jets. Jets issuing from convergent and convergent–divergent nozzles were studied using time-resolved Z-type schlieren visualization and snapshot proper orthogonal decomposition (POD). Free-jet measurements established the shock-cell structure, Mach disk, jet boundary, and shear layers, while impinging jets were examined at L/De=1, 2, and 3. The convergent nozzle remained underexpanded throughout the range, whereas the convergent–divergent nozzle transitioned from overexpanded below its design pressure ratio of approximately 7.9 to underexpanded above it. Decreasing L/De shifted the first normal shock upstream, while its normalized width depended more strongly on nozzle geometry and expansion state. At L/De=1, the wall limits development of a complete shock-cell pattern, resulting in a confined near-wall compression region, whereas at L/De=2 and 3, the first Mach disk and near-wall stand-off shock became increasingly distinct. POD showed that increasing NPR broadened the dominant fluctuation structures from localized shock-intersection and impingement-region motions to structures involving the Mach disk, shock-cell system, extended shear layers, and wall jets. The slightly underexpanded convergent–divergent jet at L/De=3 and NPR=9 exhibited the most pronounced breathing-like motion in the stagnation region. The upstream barrel shock and first Mach disk remained comparatively stable, while the stand-off shock, reflected compression waves, stagnation region, and wall jets underwent strongly coupled motion. These results demonstrate that nozzle geometry, expansion regime, and nozzle-to-wall spacing govern the shock organization and coherent dynamics of supersonic impinging jets.