Imaging of the Conical Kelvin-Helmholtz Instability

Randall Paton Beric William Skews
Flow Research Unit, University of the Witwatersrand

The behavior of a conical shock wave reflecting off of itself was first studied numerically and three reflection regimes defined by the number of Mach reflection lines formed were identified. It was thought that this could not be studied experimentally as the boundary conditions were considered impractical to produce repeatably. Through a shaped focusing of a plane shock wave, an experimental facility has been developed which allows for the study of these flow systems. Based on this apparatus experimental studies were undertaken and a fourth reflection pattern was identified [1]. As in all cases of Mach reflection, there is a shear layer which forms in the flow field behind the triple point where the incident shock wave, reflected shock wave, and Mach stem meet, due to the difference in fluid velocity downstream of the reflected shock wave and Mach stem respectively. In the case of the conical shock wave reflection, this shear layer will itself be conical in form. During the preceding tests examining the shock wave topology it was noted that this shear layer showed possible signs of Kelvin-Helmholtz instability (KHI) but these would need confirmation. The current study confirms the existence of the conical Kelvin-Helmholtz instability by means of time-resolved schlieren imaging. The KHI exists for a broad range of Mach numbers of the incident shock wave, as specified by the shock tube driver pressure. The frequency and amplitude of the instability waveform can be tracked over time, though this is complicated by interaction with the various vortices inherent to the axial reflection of a conical shock wave. It is suggested that an alternative flow visualisation method, such as focusing schlieren, be used to eliminate the obstruction of the flow features of interest by those same features at other azimuthal positions about the reflection axis.









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