Criteria for the existence of helical instabilities in subsonic impinging jets

Understanding instability modes in impinging jets is important for the design of advanced vertical takeoff and landing aircraft. Our initial experimental observations of helical modes in subsonic impinging jets were contrary to expectations based on published stability theory results. This paper focuses on the curious phenomenon of the occurrence of these, hitherto unexpected, helical modes in subsonic impinging jets and provides, both experimental and analytical proof for their existence. Past results, based on linear stability analysis, that call for an absence of helical modes in cold, subsonic impinging jets have been re-examined to reconcile new experimental data. Based on this re-examination, a new threshold Mach number has been proposed, above which helical modes are permissible. The revised theory put forth in this paper indicates that the threshold Mach number for the existence of the helical mode depends on the jet temperature and that this threshold decreases as the jet temperature increases. This threshold Mach number has been experimentally verified for unheated jets. Additionally, the experimental results reveal that the threshold Mach number also depends on the stand-off distance. Finally, it has been shown that the experimentally obtained mean Strouhal numbers for the helical mode show excellent agreement with the Strouhal number of the least dispersive wave of the same mode calculated at various Mach numbers. The results presented here offer hope for better understanding of impinging jet instability modes.