Elliptical liquid jets in a supersonic cross-flow: Influence of J on atomization mechanism and unsteadiness
In our previous study [Medipati \textit{et al}., (2025) \textit{J. Fluid Mech}. \textbf{1014}, A34] \cite{medipati2025elliptic}, a detailed experimental investigation is performed on the elliptical liquid jets in a supersonic cross-flow ($M_{\infty}$ = 2.5), focusing on the effect of orifice aspect ratio ($AR$ = spanwise dimension/streamwise dimension) on the atomization mechanism for a fixed momentum flux ratio ($J$). In this paper, we present experimental studies that show the influence of $J$ on the jet breakup mechanism, shock structures, and unsteady interactions for each $AR$. A wide range of $J$ values (1.5 to 9.7) and three $AR$ cases (0.3, 1, and 3.3) are chosen for the study. We find that in the case of lower $J$, the jet exhibits large unsteadiness, with larger wavelength Rayleigh-Taylor (RT) waves on the windward surface. In contrast, as the $J$ increases, the unsteadiness decreases, smaller and more regular RT wavelength is formed due to the enhanced drag resulting from the reduced jet deflection. However, irrespective of $J$, in the case of $AR$ = 0.3 and 1, the primary atomization mechanism is due to the formation of Kelvin-Helmholtz instabilities (KHI) on the lateral surfaces. Furthermore, in the case of lower $J$, the shock waves formed upstream of the jet are highly corrugated with significant variations in time. The intense interaction of the liquid jet with the oncoming boundary layer streaks, in the case of lower $J$, is the primary source of large-scale unsteadiness. These findings highlight the significance of $J$ on the atomization mechanism in supersonic cross-flow.