Underexpanded Screeching Jets From Circular, Rectangular, and Elliptic Nozzles

The screech frequency and amplitude, the shock spacing, the hydrodynamic-acoustic standing wave spacing, and the convective velocity of large organized structures are measured in the nominal Mach number range of 1.1 less than or = Mj less that or = l0.9 for supersonic, underexpanded jets exhausting from a circular, a rectangular and an elliptic nozzle. This provides a carefully measured data set useful in comparing the importance of various physical parameters in the screech generation process. The hydrodynamic-acoustic standing wave is formed between the potential pressure field of large turbulent structures and the acoustic pressure field of the screech sound. It has been demonstrated earlier that in the currently available screech frequency prediction models replacement of the shock spacing by the standing wave spacing provides an exact expression. In view of this newly found evidence, a comparison is made between the average standing wavelength and the average shock spacing. It is found that there exists a small, yet important, difference, which is dependent on the azimuthal screech mode. For example, in the flapping modes of circular, rectangular, and elliptic jets, the standing wavelength is slightly longer than the shock spacing, while for the helical screech mode in a circular jet the opposite is true. This difference accounts for the departure of the existing models from predicting the exact screech frequency. Another important parameter, necessary in screech prediction, is the convective velocity of the large organized structures. It is demonstrated that the presence of the hydrodynamic-acoustic standing wave, even inside the jet shear layer, becomes a significant source of error in the convective velocity data obtained using the conventional methods. However, a new relationship, using the standing wavelength and screech frequency is shown to provide more accurate results.