Elliptical liquid jets in a supersonic cross-flow: Influence of J on atomization mechanism and unsteadiness

TL;DR

This study quantifies how the momentum flux ratio $J$ influences atomization, shock structures, and unsteadiness for elliptical jets injected into a supersonic cross-flow at $M_ty=2.5$, across $AR=0.3$, $1$, and $3.3$. Using PL shadowgraphy, PLMS, PIV, and injection-line pressure measurements, the authors show that $J$ modulates windward Rayleigh–Taylor waves and the dominance of KHI versus RTI depending on $AR$, with a theoretical RT-wavelength scaling $oldsymbol{oldsymbol{oldsymbol{rac{oldsymbol{oldsymbol{}}{}}}}}$ validated against measurements. Higher $J$ yields smaller RT wavelengths, faster breakup times, and smoother upstream shocks, while larger $AR$ amplifies unsteadiness due to greater jet–boundary-layer interaction; SWBLI induces a persistent low-frequency oscillation in injection-line pressure at $St oughly 0.007$, linking upstream boundary-layer dynamics to spray formation. Overall, the work clarifies how $J$ and $AR$ jointly govern near-field instabilities, jet penetration, and spray morphology in high-speed cross-flows, informing design of efficient, predictable injectors in propulsion applications.

Abstract

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.

Figures (21)

• Figure 1: Schematic illustrating the main flow features of liquid jet injection into a supersonic cross-flow in the (i) transverse ($x$-$y$) and (ii) spanwise planes ($x$-$z$).
• Figure 2: Schematic of the supersonic blowdown wind tunnel facility and the liquid injection system. (b) Schematic of the sharp-edged injector that is flush-mounted with respect to the tunnel bottom wall. The length and diameter of the nozzle are represented as $L$ and $D$, respectively. The direction of water flow inside the nozzle is indicated in blue.
• Figure 3: Schematic of the optical diagnostics used for the present study. The imaging plane is indicated in green.
• Figure 4: High-resolution instantaneous images of a water jet in a supersonic cross-flow of $M_\infty$ = 2.5, captured using pulsed laser shadowgraphy, highlighting the differences in the development of the surface waves in the windward side of the jet. These are shown for (i) $J$ = 3.7, and (ii) $J$ = 9.7, and for (a) $AR$ = 0.3, (b) $AR$ = 1 and $AR$ = 3.3, respectively. Insets on the left side of each image indicate the zoomed-in visualizations near the jet exit. The surface wavelength and the mean boundary layer thickness are represented as $\lambda$ and $\delta$, respectively. The column breakup location is indicated with a red colored dot, and its instantaneous streamwise and transverse locations from the orifice center are denoted as $x_b$ and $y_b$, respectively.
• Figure 5: Influence of $J$ on the time-averaged planar laser Mie scattering images of the spray plume cross-section when a liquid jet is injected into a supersonic cross-flow. These are captured at $x/D$ = 60 and for $AR$ = 1. The outer edge of the spray plume cross-section is shown in orange. $\overline{W}$ indicates the mean spray width in the spanwise direction.