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

This experimental study demonstrates that streamwise streaks in underexpanded jets originate from minute geometric perturbations at the nozzle exit, with high-wavenumber artificial roughness significantly amplifying streak growth compared to low-wavenumber or naturally smooth surfaces.

The Gist

Imagine you are blowing a bubble through a straw. If the straw is perfectly smooth, the air comes out in a steady, invisible stream. But if the inside of the straw has tiny, almost invisible scratches or bumps, the air doesn't just flow; it starts to swirl into distinct, ribbon-like patterns as it speeds up.

This paper is about discovering why those swirling ribbons (called "streamwise streaks") appear in high-speed jets of air, like those coming out of rocket engines or supersonic wind tunnels.

Here is the story of the study, broken down into simple concepts:

The Big Mystery: Nature or Nurture?

For 50 years, scientists have argued about what causes these ribbons of air.

• Theory A (Nature): Maybe the air itself is just unstable. Like water in a river that naturally starts to swirl because of how it flows over a curved rock.
• Theory B (Nurture): Maybe the air is just copying the shape of the pipe it came out of. If the pipe has a scratch, the air gets a scratch too.

No one could agree on which one was the boss.

The Experiment: The "Fingerprint" Test

To solve this, the researchers at Peking University built a special vacuum chamber and used two types of nozzles (the "straws"):

1. The "Smooth" Nozzle: A high-quality, polished nozzle that looked perfect to the naked eye.
2. The "Rough" Nozzles: Nozzles that they deliberately scratched with a machine to create specific wave patterns (like ripples on a pond) around the rim.

They shot gas out of these nozzles and used a special high-speed camera (Schlieren imaging) that makes invisible air density changes visible, almost like seeing heat waves on a hot road.

The Discovery: It's All About the "Fingerprint"

Here is what they found, using a simple analogy:

1. The "Smooth" Nozzle wasn't actually smooth.
Even though the "smooth" nozzle looked perfect, the air coming out formed distinct ribbons. When the researchers rotated the nozzle by 60 degrees, the ribbons rotated with it.

• The Analogy: Imagine pressing your thumb into wet clay. Even if you think your thumb is smooth, the clay will take on the exact shape of your fingerprints. The researchers realized that the "smooth" nozzle had microscopic scratches (like tiny fingerprints) left over from the machine that made it. The air was simply amplifying these tiny imperfections. The ribbons were essentially the nozzle's fingerprint blown up to a huge size.

2. The "Rough" Nozzles told a different story.
When they used nozzles with deliberate, large wave patterns:

• Small Waves (Low numbers): The air ignored the big pattern and kept making its own messy ribbons based on the tiny scratches (the "fingerprints").
• Big Waves (High numbers): The air listened! The ribbons lined up perfectly with the big waves they carved into the nozzle.
• The Analogy: Think of a marching band. If the conductor gives a tiny, subtle hand wave, the band might ignore it and march in their own chaotic way. But if the conductor makes a huge, dramatic motion, the whole band follows that big motion immediately.

Why Does This Matter?

You might wonder, "So what? It's just air."

Well, in supersonic wind tunnels (used to test planes and rockets), these ribbons create noise and turbulence. If engineers don't understand that the nozzle itself is creating the noise, they might try to fix the wrong thing.

The Takeaway:
If you want a clean, quiet, and predictable supersonic jet, you can't just make the nozzle "good enough." You have to make it perfectly smooth, because even the tiniest, invisible scratch will leave a giant "fingerprint" on the airflow. The shape of the pipe dictates the shape of the storm.

Technical Summary

1. Problem Statement

The presence of streamwise streaks along the primary Mach cell structures in supersonic underexpanded jets has been observed for decades and is known to be critical for flow mixing and turbulent transition near the jet boundary. However, the origin of these streaks remains a subject of debate with no scientific consensus. Two primary hypotheses exist:

• Intrinsic Hydrodynamic Instability: The streaks arise from the inherent instability of supersonic flow over the concave boundary of the jet (similar to Taylor-Görtler vortices).
• Geometric Perturbations: The streaks are induced by minute roughness or defects at the nozzle exit.

Previous studies have yielded contradictory results; some suggest the flow is insensitive to upstream disturbances, while others indicate that artificial roughness can generate similar structures. This study aims to definitively determine whether hydrodynamic instability or nozzle roughness is the dominant cause.

2. Methodology

The researchers conducted a series of comparative experiments using high-speed schlieren imaging and Planar Laser-Induced Fluorescence (PLIF).

• Experimental Setup:

  • Facility: A vacuum-pumped cylindrical flow chamber (130 mm diameter, 110 mm height) connected to a secondary vacuum system to maintain stable back pressure.
  • Nozzles: Round sonic nozzles with an average radius of 4 mm ($\phi$-4 mm).
  • Working Fluids: Pure nitrogen (Schlieren) and acetone vapor (PLIF).
  • Flow Generation: Underexpanded jets were generated by rapidly opening a slide gate valve, creating a transient flow where back pressure increased from <1 Pa to atmospheric pressure.

• Nozzle Configurations:

  1. "Smooth" Nozzle: Machined and polished by a high-quality commercial lathe.
  2. Perturbed Nozzles: Nozzles with artificially introduced sinusoidal geometric perturbations on the exit contour. These were created using axisymmetric stamping knives with specific wavenumbers ($k$) ranging from 3 to 7.

• Experimental Procedures:

  • Rotation Test: The "smooth" nozzle was rotated azimuthally in 60-degree increments to observe if the streak patterns shifted correspondingly.
  • Modal Analysis: Jets from perturbed nozzles were compared to determine how specific wavenumbers influenced the growth and structure of the streaks.
  • Imaging: Side-view schlieren imaging captured the global flow structure, while PLIF (using a 283 nm laser sheet) attempted to visualize the shear layer at a 45-degree angle.

3. Key Results

A. Origin of Streaks (Smooth Nozzle Case)

• Stability and Reproducibility: Repeated experiments with the "smooth" nozzle revealed a consistent, stable streak pattern near the barrel shock boundary.
• Rotation Correlation: When the nozzle was rotated, the streak patterns rotated by the same angle. This strongly suggests the streaks are not caused by random hydrodynamic instabilities but are "fingerprints" of fixed geometric perturbations.
• Microscopic Evidence: Close inspection of the "smooth" nozzle revealed micron-sized bumps and grooves (machining defects) on the inner exit surface, confirming that even minute roughness is sufficient to trigger streak formation.

B. Effect of Wavenumber (Perturbed Nozzle Case)

The study investigated how the wavenumber ($k$) of the artificial perturbation affected the streaks:

• Low Wavenumbers ($k < 5$): These perturbations exhibited small growth rates. The resulting streak patterns were dominated by residual roughness (similar to the "smooth" case) rather than the intended artificial perturbation. Notably, the number of observed streaks was often higher than the excitation number, indicating that low-wavenumber modes could not suppress the development of higher-order modes.
• High Wavenumbers ($k = 6, 7$): These perturbations exhibited high growth rates. The resulting streak patterns were "clean" and correlated geometrically with the nozzle exit contour. Specifically, for each peak in the sinusoidal disturbance, two homologous streaks were generated, which later merged near the primary Mach disk.

C. Imaging Limitations

While schlieren imaging successfully visualized the global streak patterns, the PLIF technique (intended to resolve shear layer details) yielded insufficient signal strength to extract detailed features of the streaks, though shock cell boundaries were visible.

4. Key Contributions

1. Definitive Attribution: The study provides strong experimental evidence that nozzle roughness (even at the micron scale) is the primary driver of streamwise streaks in underexpanded jets, rather than intrinsic hydrodynamic instability.
2. Modal Sensitivity: It establishes that the wavenumber of the geometric perturbation is critical. High-wavenumber perturbations effectively control streak formation, while low-wavenumber perturbations are easily overwhelmed by background roughness.
3. Rotation Validation: The nozzle rotation experiment serves as a robust control method to distinguish between flow-induced instabilities and geometry-induced patterns.

5. Significance

• Supersonic Wind Tunnel Design: The findings are crucial for the design and operation of supersonic wind tunnels. Since nozzle roughness dictates flow patterns and noise generation, achieving high-precision surface finishes is essential for minimizing unwanted streaks and acoustic noise.
• Noise Prediction: Understanding the link between nozzle geometry and streaks helps in predicting and controlling noise patterns in supersonic flows.
• Future Research: The study highlights the need for improved visualization techniques (e.g., advanced PLIF or Mie scattering) to resolve shear layer details and suggests that increasing the activating wavenumber in future experiments could better match the natural streak patterns observed in standard nozzles.