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arxiv: 2604.08830 · v1 · submitted 2026-04-10 · ⚛️ physics.flu-dyn

Effects of Nozzle Roughness on the Streamwise Streaks in Underexpanded Jets -- An Experimental Study

Haohan Gong , Shengkai Wang This is my paper

Pith reviewed 2026-05-10 18:06 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords underexpanded jetsstreamwise streaksnozzle roughnessgeometric perturbationsschlieren imagingPLIFsupersonic flownozzle exit
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The pith

Streamwise streaks in underexpanded jets arise from minute geometric roughness at the nozzle exit.

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

The paper demonstrates that streamwise streaks observed in underexpanded jets from round sonic nozzles are caused by small geometric imperfections at the nozzle exit rather than intrinsic flow instabilities. Experiments with a polished nozzle show that rotating it by 60 degrees rotates the streak patterns accordingly. Tests with nozzles bearing added sinusoidal perturbations of various wavenumbers reveal that only higher-wavenumber cases (k=6 and 7) produce strong streaks whose patterns match the exit contour, while lower-wavenumber cases behave like the smooth nozzle. This identification of a geometric origin matters for explaining and potentially controlling flow structures that contribute to noise in supersonic wind tunnel tests.

Core claim

The streamwise streaks most likely originated from geometric perturbations caused by the minute roughness at the nozzle exit. Rotation of the smooth nozzle rotates the streaks with it. Artificial high-wavenumber perturbations at the exit produce streaks that correlate directly with the imposed contour, whereas low-wavenumber perturbations exhibit smaller growth rates dominated by residual roughness.

What carries the argument

Rotation of the nozzle along its axis combined with controlled introduction of sinusoidal perturbations of specific wavenumbers on the circular exit contour.

If this is right

  • Streak patterns in nominally smooth nozzles can be traced to residual manufacturing roughness at the exit.
  • Higher-wavenumber exit perturbations produce faster-growing streaks whose azimuthal positions align with the imposed geometry.
  • Lower-wavenumber perturbations do not drive significant additional streak growth beyond residual roughness effects.
  • Nozzle surface finish becomes a design variable that can influence streamwise flow structure and associated noise in supersonic jets.

Where Pith is reading between the lines

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

  • Precise control of nozzle manufacturing tolerances could be used to suppress or steer streamwise streaks in practical supersonic jet devices.
  • Numerical simulations of underexpanded jets would need to include realistic exit contour details to capture observed streak formation.
  • Similar geometric sensitivity may explain variability in streak observations across different experimental facilities using nominally round nozzles.

Load-bearing premise

Rotating the nozzle or adding artificial perturbations affects only the angular position or shape of the exit geometry without altering other flow conditions or creating imaging artifacts.

What would settle it

Streak patterns that remain fixed in laboratory coordinates and do not rotate when the nozzle is turned by 60 degrees would contradict the geometric-origin claim.

Figures

Figures reproduced from arXiv: 2604.08830 by Haohan Gong, Shengkai Wang.

Figure 1
Figure 1. Figure 1: The current experimental setup. Based on the smooth nozzle, the nozzle exit was modified using axisymmetric stamping knives with different wavenumbers to create nozzles featuring geomet￾ric disturbances of the corresponding modes. These modifications were intended to excite streamwise streak structures in the jet with the respective wavenum￾bers, allowing observation of the streamwise evolution of differen… view at source ↗
Figure 2
Figure 2. Figure 2: Sonic nozzles and the stamping knives used in the current study [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: shows images from three repeated experiments of jets generated by the smooth nozzle. To better visualize the position, morphology, and strength of the streamwise structures, the image contrast was enhanced through digital im￾age processing. A distinctive streak pattern was observed near the boundary of the barrel shock. This pattern was found to be relatively stable and consistent across repeated experimen… view at source ↗
Figure 4
Figure 4. Figure 4: A consistent shift in the streak patterns was observed following each [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Schlieren images of different activating wavenumber jets under unified condi￾tions of L/D0=2.4 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Schlieren images of different activating wavenumber jets under unified condi￾tions of L/D0=4 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Schematic diagram of the streamline at the peak of the disturbance, k=6 As a path-integrated imaging method, schlieren did not provide spatially￾resolved measurement of the detailed features of these streamwise streaks. To address this, we attempted to use high-temperature acetone vapor and a laser light sheet at a wavelength of 283 nm to observe a 45-degree slice of the flow field, aiming for clearer imag… view at source ↗
Figure 8
Figure 8. Figure 8: Schematic diagram of the laser light sheet, and a representative PLIF image 4 Conclusions In summary, this study has demonstrated that the formation of streamwise streaks in underexpanded jets from round sonic nozzles is strongly influenced by geometric perturbations at the nozzle exit. Through systematic experiments using both smooth and intentionally perturbed nozzles, it was found that even minute surfa… view at source ↗
read the original abstract

The present study investigated the formation of streamwise streaks in underexpanded jets from round sonic nozzles, based on direct experimental observation using high-speed schlieren imaging and PLIF methods. The effect of geometric perturbations of the nozzle exit on the streamwise flow structure was examined through a series of comparative experiments. Underexpanded jets were generated in a vacuum chamber using phi-4 mm nozzles of two different configurations: (a) a "smooth" nozzle, shaped and polished by a high-quality commercial lathe machine; and (b) nozzles with artificially introduced sinusoidal perturbation of various wavenumbers on the circular contour of the exit. In the case of the "smooth" nozzle, experiments were repeated following a 60-degree rotation of the nozzle along its axis, and a similar rotation in the streak patterns was observed. This suggests that the streamwise streaks most likely originated from geometric perturbations caused by the minute roughness at the nozzle exit. In the latter case, the effects of modal distribution of geometric perturbation on the streaks were further investigated. The results showed that the low-wavenumber (k < 5) perturbations exhibited much smaller growth rates of streamwise streaks - likely dominated by residual roughness similar to the "smooth" case - compared to higher-wavenumber (k = 6 and 7) perturbations, where the streak patterns were observed to correlate geometrically with the perturbed nozzle exit contour. Results from the present study should prove useful in enhancing the current understanding of noise patterns in supersonic wind tunnel tests, where nozzles are critical components.

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

2 major / 2 minor

Summary. The manuscript presents an experimental study of streamwise streaks in underexpanded jets from round sonic nozzles using high-speed schlieren imaging and PLIF. It compares a polished 'smooth' nozzle with nozzles featuring artificial sinusoidal perturbations of varying wavenumbers at the exit contour. For the smooth nozzle, a 60° axial rotation produces a matching rotation in the observed streak pattern, from which the authors conclude that the streaks originate from minute geometric roughness at the nozzle exit. For the perturbed nozzles, low-wavenumber (k < 5) cases show smaller streak growth rates similar to the smooth nozzle, while k = 6 and 7 cases exhibit streak patterns that correlate geometrically with the imposed exit perturbations and larger growth rates.

Significance. If the central claim holds, the work supplies direct experimental evidence that small exit-plane geometric perturbations can seed streamwise streaks in underexpanded jets. The comparative design—smooth versus artificially perturbed nozzles plus the rotation test—offers a causal link between exit geometry and streak formation that is relevant to noise generation in supersonic wind-tunnel testing. The artificial-perturbation results in particular provide a controlled demonstration that exit-contour features can dominate streak development.

major comments (2)
  1. [smooth nozzle rotation experiments (abstract)] The 60° rotation experiment rotates the entire nozzle assembly and therefore rotates every fixed azimuthal feature along the full nozzle length (internal bore, throat, mounting flange, and seal interfaces) equally. While the artificial-perturbation runs modify only the exit contour, the inference that streaks in the smooth nozzle arise specifically from exit roughness rests on the rotation observation alone. No profilometry, exit-only masking, or differential-rotation test is described that would isolate the exit plane from other nozzle-fixed imperfections.
  2. [perturbed-nozzle results (abstract)] The abstract states that low-wavenumber perturbations exhibit 'much smaller growth rates' than k = 6 and 7 cases, yet no quantitative growth-rate values, measurement methods, error bars, or statistical comparison are supplied. Without these data it is difficult to judge whether the difference is significant or whether residual roughness truly dominates the k < 5 regime.
minor comments (2)
  1. The nozzle diameter is written as 'phi-4 mm'; standard notation (φ = 4 mm or D = 4 mm) would improve clarity.
  2. The abstract mentions that results 'should prove useful' for supersonic wind-tunnel noise but does not indicate which specific noise mechanisms or metrics are expected to be affected.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and constructive feedback on our manuscript. We address each major comment below with point-by-point responses and indicate revisions where the manuscript will be updated.

read point-by-point responses

  1. Referee: The 60° rotation experiment rotates the entire nozzle assembly and therefore rotates every fixed azimuthal feature along the full nozzle length (internal bore, throat, mounting flange, and seal interfaces) equally. While the artificial-perturbation runs modify only the exit contour, the inference that streaks in the smooth nozzle arise specifically from exit roughness rests on the rotation observation alone. No profilometry, exit-only masking, or differential-rotation test is described that would isolate the exit plane from other nozzle-fixed imperfections.

    Authors: We agree that the 60° rotation test rotates the entire nozzle assembly and therefore does not isolate the exit plane from other fixed geometric features such as the internal bore or throat. The test primarily demonstrates that the streak pattern is locked to the nozzle's azimuthal orientation rather than arising from random or external sources. In the revised manuscript we will clarify this point explicitly, noting that the rotation rules out non-nozzle-fixed origins while acknowledging that upstream features could in principle contribute. We will also strengthen the link to the exit by emphasizing that the controlled artificial-perturbation experiments (which modify only the exit contour) produce streak patterns and growth behaviors that closely match those observed in the rotated smooth nozzle. A brief discussion of this limitation and the supporting role of the perturbation data will be added to the relevant section. revision: partial

  2. Referee: The abstract states that low-wavenumber perturbations exhibit 'much smaller growth rates' than k = 6 and 7 cases, yet no quantitative growth-rate values, measurement methods, error bars, or statistical comparison are supplied. Without these data it is difficult to judge whether the difference is significant or whether residual roughness truly dominates the k < 5 regime.

    Authors: We accept that the abstract's qualitative phrasing requires quantitative backing for clarity. Growth rates in the manuscript are derived from streamwise evolution of streak amplitude extracted from both high-speed schlieren and PLIF images. In the revised version we will expand the abstract to include brief quantitative statements and, more importantly, add a dedicated subsection in the results that reports the specific growth-rate values, the extraction method (Fourier-mode amplitude tracking along the jet axis), uncertainty estimates, and direct statistical comparisons between the k < 5 and k = 6,7 cases. This will allow readers to evaluate the significance of the observed differences and the dominance of residual roughness in the low-wavenumber regime. revision: yes

Circularity Check

0 steps flagged

No circularity: purely observational experimental study

full rationale

The paper reports direct high-speed schlieren and PLIF imaging of underexpanded jets from smooth and artificially perturbed nozzles, plus a 60° nozzle rotation test. All claims rest on visual pattern correlation between exit geometry and streak locations; no equations, fitted parameters, models, or derivations are present. The central inference (streaks originate from exit roughness) is an empirical suggestion drawn from the rotation experiment, not a reduction to any input by construction. No self-citations, uniqueness theorems, or ansatzes appear in the provided text. The work is self-contained observational evidence with no load-bearing logical loop.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The study is experimental and introduces no new mathematical parameters, axioms beyond standard compressible flow assumptions, or postulated entities. The claim rests on the validity of the imaging methods and the assumption that nozzle exit geometry is the dominant source of the observed streaks.

axioms (1)
  • domain assumption The underexpanded jet flow structure is sensitive to small geometric perturbations at the nozzle lip.
    This is the hypothesis being tested through the rotation and perturbation experiments.

pith-pipeline@v0.9.0 · 5586 in / 1156 out tokens · 37809 ms · 2026-05-10T18:06:49.094982+00:00 · methodology

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Reference graph

Works this paper leans on

5 extracted references · 5 canonical work pages

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  2. [2]

    Franquet, V

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    work page 2015

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    Krothapalli, G

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    work page 1991

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    S. A. Arnette, M. Samimy, G. S. Elliott. On streamwise vortices in high Reynolds number supersonic axisymmetric jets. Physics of Fluids A: Fluid Dynamics, 1993, 5(1): 187-202

    work page 1993

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    V. I. Zapryagaev, N. P. Kiselev, A. A. Pavlov. Effect of streamline curvature on intensity of streamwise vortices in the mixing layer of supersonic jets. Journal of Applied Mechanics and Technical Physics, 2004, 45: 335-343

    work page 2004