In heated supersonic jets, Mach wave radiation and crackle have been identified as dominant noise components that propagate to the downstream region of the jet, in a direction noted as the Mach wave angle. At certain conditions, the Mach waves coalesce in the near field causing steepening of the wavefront, which exceeding a certain level produces a noise feature called "crackle." The skewness and kurtosis of the pressure and its time derivative (dP/dt) have been widely studied as a measurement of crackle. In this paper, we investigate the impact of different test conditions and different nozzle exit diameters on the far-field high-order statistics of the pressure and dP/dt signals of three converging-diverging conical nozzles, with a design Mach number of 1.5 and jet exit diameters of 0.542, 0.813, and 1.085. Results are compared to a smooth contoured nozzle designed by the Method of Characteristics, with the same design Mach number. For all nozzles, cold and heated jets, TR=1.0 to 3.0, are tested at over, design, and under-expanded conditions. Second, third, and fourth order statistics are examined in three far-field arrays positioned at a non-dimensionalized constant radial distance of r=40De. The OASPL, skewness, and kurtosis magnitudes and their propagation angles are proportional to the jet temperature and the NPR, and have peak amplitudes near the Mach wave angle. The pressure skewness and kurtosis plots collapsed for all three scaled nozzles when the pressure signals were not filtered. The dP/dt statistics collapsed when the signals were downsampled proportional to the nozzle exit diameters, applying beforehand a low-pass filter at a proportional cutoff frequency, to avoid aliasing effects.
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