Nonparallel analysis and measurements of instability waves in a high-speed liquid jet

A multi-scale analysis has been developed to assess the effects of nonparallel mean flows on the spatial stability of a high speed liquid jet. This analysis is complemented with experimental measurements of surface waves and it is compared with results from a parallel stability analysis. The multi-scale analysis consists of a linear stability analysis which accounts for streamwise variations of mean flow, wavenumber and disturbance amplitude. It is found that solutions from this analysis yield corrections to the eigenvalues obtained from a parallel stability analysis solved at every streamwise location of the flow. Furthermore, the solution to this nonparallel analysis is forced at a frequency that corresponds to the most unstable global mode as calculated from the parallel analysis. It is shown that this mode corresponds to the most unstable local mode at an axial location where the flow transitions from an absolute (AU) to a convectively (CU) unstable flow. Where in an AU region, perturbations travel both upstream and downstream, while in a CU region perturbations only travel downstream. A set of experiments using three different nozzles of length-to-diameter ratios of one, five and ten are performed at various flow velocities. These sets of tests allow variations in flow Reynolds number, based on the momentum thickness at the exit of the nozzle, between 150 and 750. Experimental measurements presented in this study provide statistically validated wavelength measurements as a function of the axial coordinate. In addition, preliminary wave velocity and amplitude measurements are presented for one of the nozzles. This study leads to the conclusion that the most important mechanism responsible for the appearance of the instability waves is the pocket of absolute instability present near the exit of the nozzle. This pocket is responsible for amplifying disturbances of a given frequency as well as feeding them upstream into the flow. Of importance is also the momentum thickness of the boundary layer inside the orifice, for it dictates the location and size of these disturbance waves. It is also concluded that the largest nonparallel flow effect is in the prediction of the stretching of the waves. The multi-scale analysis shows a much slower stretching in the near exit region than the parallel analysis and compares better to experimental measurements at these locations.