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arxiv: 2512.23360 · v1 · submitted 2025-12-29 · ⚛️ physics.flu-dyn

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

Chandrasekhar Medipati , Sivakumar Deivandren , Raghuraman N Govardhan This is my paper

Pith reviewed 2026-05-16 19:44 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords supersonic cross-flowelliptical liquid jetsatomization mechanismKelvin-Helmholtz instabilityRayleigh-Taylor instabilitymomentum flux ratiojet unsteadinessboundary layer interaction
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The pith

For elliptical liquid jets with aspect ratios 0.3 and 1 in Mach 2.5 cross-flow, Kelvin-Helmholtz instabilities on the lateral surfaces drive primary atomization regardless of momentum flux ratio J.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tracks how changes in momentum flux ratio J alter the breakup behavior of elliptical liquid jets injected into supersonic air. At low J the jet deflects more, creating large unsteady Rayleigh-Taylor waves on the windward face, corrugated upstream shocks, and strong interactions with boundary-layer streaks. Raising J reduces deflection, strengthens drag, and produces smaller, steadier waves while the shocks become smoother. Across the full J range examined, however, the dominant breakup for aspect ratios 0.3 and 1 remains Kelvin-Helmholtz instabilities growing on the side surfaces.

Core claim

Lower J produces large unsteadiness with longer-wavelength Rayleigh-Taylor waves on the windward surface and highly time-varying corrugated shocks caused by intense liquid-boundary-layer streak interactions. Higher J reduces jet deflection, increases drag, and yields smaller, more regular Rayleigh-Taylor wavelengths together with steadier shocks. Irrespective of J, the primary atomization mechanism for AR = 0.3 and 1 remains Kelvin-Helmholtz instabilities on the lateral surfaces.

What carries the argument

The momentum flux ratio J, which sets the jet's penetration, deflection angle, and interaction strength with the oncoming boundary layer, thereby controlling wave size, shock steadiness, and the relative importance of lateral surface instabilities.

If this is right

  • Higher J produces visibly steadier upstream shock structures with reduced temporal corrugation.
  • Boundary-layer streak interactions become the dominant source of large-scale unsteadiness only at low J.
  • Atomization mode for AR = 0.3 and 1 stays fixed as KHI even while overall jet behavior changes with J.
  • Shock and surface features become more repeatable as J rises because jet deflection and drag both increase.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Designers of supersonic fuel injectors could favor higher J to obtain more repeatable atomization timing while still relying on lateral KHI for the actual breakup.
  • Selecting low aspect ratios may lock in a consistent breakup route even when operating conditions vary J.
  • Quantitative wave measurements would be a direct next step to confirm the visual instability assignments.

Load-bearing premise

Visual classification of wave types and unsteadiness sources from high-speed movies correctly identifies the dominant physical mechanism without quantitative checks such as measured growth rates or frequency spectra.

What would settle it

Spectral or growth-rate measurements on the lateral surfaces that match Rayleigh-Taylor rather than Kelvin-Helmholtz predictions would contradict the claim that KHI is the primary atomization driver.

Figures

Figures reproduced from arXiv: 2512.23360 by Chandrasekhar Medipati, Raghuraman N Govardhan, Sivakumar Deivandren.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustrating the main flow features of liquid jet injection into a supersonic cross-flow in the (i) transverse ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Schematic of the supersonic blowdown wind tunnel facility and the liquid injection system. (b) Schematic of the sharp-edged injector [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Schematic of the optical diagnostics used for the present study. The imaging plane is indicated in green. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. High-resolution instantaneous images of a water jet in a supersonic cross-flow of [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Influence of [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Variation of measured dimensionless surface wavelength with [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Ensemble-averaged image of the circular jet for [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. (a) Variation of mean streamwise breakup location with [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Instantaneous visualizations captured using high-speed shadowgraphy highlighting the shock structures, the windward spray edge, and [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Instantaneous visualizations captured using high-speed shadowgraphy highlighting the shock structures, the windward spray edge, [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Instantaneous visualizations captured using high-speed shadowgraphy highlighting the shock structures, the windward spray edge, [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Influence of [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Schematic highlighting the instantaneous flow features of the liquid jet in supersonic flow. [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Instantaneous and mean traces of bow shock wave (left) and windward spray edge (right) of liquid jet for (a) [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Instantaneous and mean traces of bow shock wave (left) and windward spray edge (right) of liquid jet for (a) [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Instantaneous and mean traces of bow shock wave (left) and windward spray edge (right) of liquid jet for (a) [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. (a) Scatter plot between instantaneous variation in jet and shock positions at [PITH_FULL_IMAGE:figures/full_fig_p019_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Variation of [PITH_FULL_IMAGE:figures/full_fig_p021_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. Instantaneous velocity fields of the boundary layer in the upstream of the jet exit in the mid span plane to emphasize the fluctuations [PITH_FULL_IMAGE:figures/full_fig_p021_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20. Pressure traces in the liquid injection line corresponding to without and with cross-flow conditions for different [PITH_FULL_IMAGE:figures/full_fig_p022_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21. Premultiplied power spectral density versus Strouhal number corresponding to without and with cross-flow conditions for different [PITH_FULL_IMAGE:figures/full_fig_p023_21.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript experimentally examines the influence of momentum flux ratio J (range 1.5–9.7) on atomization mechanisms, shock structures, and unsteadiness for elliptical liquid jets in a Mach 2.5 cross-flow, using three aspect ratios (AR = 0.3, 1, 3.3). It reports that low J produces large-wavelength RT waves on the windward surface and high unsteadiness from boundary-layer streak interactions and corrugated upstream shocks, while high J yields smaller, more regular RT waves due to reduced jet deflection. The central claim is that, irrespective of J, the primary atomization mechanism for AR = 0.3 and 1 is Kelvin-Helmholtz instabilities on the lateral surfaces, identified via high-speed imaging.

Significance. If the instability classifications hold, the work supplies useful observational trends on how J modulates breakup and unsteadiness in supersonic elliptical-jet injection, extending the authors’ prior fixed-J study. Such data can inform reduced-order models for fuel atomization in high-speed propulsion, particularly where orifice shape and momentum ratio are design variables.

major comments (1)
  1. [Abstract] Abstract: the claim that KHI on lateral surfaces is the primary atomization mechanism for AR = 0.3 and 1 at all tested J rests solely on visual classification of high-speed shadowgraph/schlieren sequences. No quantitative support—such as extracted dominant wavelengths, temporal growth rates, or direct comparison to the appropriate shear-layer dispersion relation—is provided to distinguish KHI from projected RT structures or boundary-layer-induced features.
minor comments (1)
  1. [Abstract] Abstract: the statement that unsteadiness decreases with increasing J due to “enhanced drag resulting from the reduced jet deflection” would benefit from a brief reference to the supporting imaging or deflection-angle data in the results section.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. The single major comment identifies a genuine limitation in the current presentation of the KHI classification, which we address directly below by committing to added quantitative analysis in revision.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that KHI on lateral surfaces is the primary atomization mechanism for AR = 0.3 and 1 at all tested J rests solely on visual classification of high-speed shadowgraph/schlieren sequences. No quantitative support—such as extracted dominant wavelengths, temporal growth rates, or direct comparison to the appropriate shear-layer dispersion relation—is provided to distinguish KHI from projected RT structures or boundary-layer-induced features.

    Authors: We agree that the original manuscript relies on visual identification from high-speed imaging sequences, which is a standard experimental approach for classifying surface instabilities in jet breakup studies. However, the referee correctly notes that this leaves the claim open to alternative interpretations. In the revised manuscript we will add quantitative support by extracting dominant wavelengths from the lateral surfaces in the high-speed sequences for AR = 0.3 and 1 across the J range, estimating temporal growth rates where frame rates permit, and comparing these values to the expected scales from the compressible shear-layer dispersion relation. We will also explicitly discuss why the observed lateral features are inconsistent with projected RT waves or boundary-layer streak signatures. These additions will be placed in the results section and the abstract will be updated to reflect the strengthened evidence. revision: yes

Circularity Check

0 steps flagged

No significant circularity in experimental observations

full rationale

This is a purely experimental study reporting direct observations from high-speed shadowgraph/schlieren imaging of jet breakup, shock structures, and unsteadiness across J values and AR cases. No mathematical derivations, dispersion relations, fitted parameters, or predictions exist that could reduce to inputs by construction. The single self-citation to the authors' prior work (Medipati et al. 2025) supplies only contextual background on fixed-J behavior and does not bear the load of the present claims, which rest on new imaging data for varying J. Visual classification of KHI vs. RT features is an interpretive step but does not constitute a self-referential loop or fitted-input prediction. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The study is empirical and introduces no new free parameters, mathematical axioms, or postulated entities; it relies on standard fluid-mechanics classification of observed surface waves as Rayleigh-Taylor or Kelvin-Helmholtz instabilities.

axioms (1)
  • domain assumption Surface waves on the jet can be reliably classified as Rayleigh-Taylor or Kelvin-Helmholtz instabilities from high-speed shadowgraph or schlieren images alone.
    Invoked when stating primary atomization mechanism and wave characteristics.

pith-pipeline@v0.9.0 · 5675 in / 1348 out tokens · 32487 ms · 2026-05-16T19:44:09.988290+00:00 · methodology

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Reference graph

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