Optical Density Measurements in Overexpanded Supersonic Jets Using Calibrated Schlieren Imaging

This study presents the use of calibrated Schlieren imaging to reconstruct the mean density field of an overexpanded supersonic jet at multiple nozzle pressure ratios. A Mach 1.75 conical nozzle was tested at nozzle pressure ratios of 3, 4, and 5.32 using a high-speed Schlieren imaging setup. Calibration was performed by imaging the nozzle with the flow off and translating the knife edge across the focal point of the Schlieren setup. These images were used to relate pixel intensity to ray deflection at the focal point which provided information to calculate the gradient of refractive index. The inverse Abel transform was applied to recover the radial profile of the axisymmetric flow and the refractive index gradient was numerically integrated and converted to density through the Gladstone-Dale Relation. The reconstructed density fields revealed periodic shock cell structures consistent with overexpanded jet behavior. The results align well with prior experimental studies which demonstrate the effectiveness of calibrated Schlieren in nonintrusively measuring the density of compressible flows.