Investigation of Aeroacoustics and In-flight Particle Transport in Thermal Spray Supersonic Jets

This study develops and validates a combined analytical and numerical framework linking thermal spray nozzle operating conditions to far-field aeroacoustic signatures and in-flight particle transport, demonstrating that acoustic monitoring can serve as a non-intrusive method for controlling and optimizing the thermal spray process.

The Gist

Imagine you are a master chef. You know that when a pot of soup is boiling perfectly, it makes a specific "hiss." If the heat is too low, the sound changes to a gentle bubble; if it's too high, it turns into a violent roar. You don't need to look inside the pot to know the soup is ready; you just listen.

This paper is about doing the exact same thing, but with thermal spray machines. These are industrial "guns" that shoot super-hot, high-speed gas and tiny metal or ceramic particles to coat surfaces (like making airplane engines more heat-resistant).

The researchers wanted to prove that by listening to the machine, we can figure out exactly how the tiny particles are flying inside the invisible jet, without having to stop the machine or put a camera in the way.

Here is the breakdown of their work using simple analogies:

1. The "Ear" and the "Brain" (The Two Approaches)

The team used two different tools to solve the mystery:

• The "Rule of Thumb" (Analytical Model): First, they built a simple math formula. Think of this like a recipe card. It says, "If you turn the pressure knob up by 10%, the noise goes up by this much." It's a quick, easy way to guess what's happening, but it's a bit like guessing the weather by looking at the sky—it misses the tiny details like sudden gusts of wind (turbulence).
• The "Super-Simulation" (CFD & DDES): To get the real details, they built a massive, virtual wind tunnel on a supercomputer. They didn't just guess; they simulated the physics of the gas and the particles moving at supersonic speeds (faster than a bullet).
  • The Trick: They used a "hybrid" approach. Imagine watching a movie. For the background scenery (the calm parts of the room), they used a low-resolution sketch (fast and cheap). But for the main action (the swirling, chaotic gas right where the noise is made), they used 4K high-definition video. This saved them time while keeping the important details sharp.

2. The "Firehose" and the "Confetti" (The Jet and Particles)

Imagine a firehose blasting water at a wall. Now, imagine that instead of water, it's a jet of super-hot gas, and instead of water droplets, it's millions of tiny specks of confetti (the coating particles).

• The Gas: The gas moves so fast it creates shockwaves, like the "crack" of a whip. These shockwaves are what make the loud noise.
• The Particles: The gas grabs the confetti and shoots it forward. The researchers tracked every single piece of confetti in their simulation to see:
  • How fast is it going?
  • Is it flying straight, or is it wobbling around?
  • Does it spread out like a fan, or stay in a tight beam?

3. The "Volume Knob" vs. The "Thermostat" (Pressure vs. Temperature)

The researchers tested two main ways to control the machine: turning up the Pressure and turning up the Temperature.

• Turning up Pressure (The Volume Knob):
  • Effect: It makes the jet "louder" and more chaotic.
  • Result: The particles spread out more. It's like turning up the volume on a speaker; the sound gets louder, but the music gets a bit messy. The particles fly fast but scatter in different directions, making the coating less uniform.
• Turning up Temperature (The Thermostat):
  • Effect: It makes the gas move faster and smoother.
  • Result: The particles fly faster, but they stay in a tight, straight line. It's like turning up the heat in a room; the air moves faster, but the flow is smoother. This is great for hitting a target precisely.

The Big Discovery: If you want your particles to hit a target hard and fast, heat them up. If you want to change how wide the spray is, change the pressure.

4. The "Sound Signature" (The Conclusion)

The most exciting part of the paper is the conclusion. They found a direct link between the sound the machine makes and the behavior of the particles.

• The Analogy: Think of the machine's sound as a "voice."
  • If the voice is deep and rumbling, the particles are likely spreading out too much (bad for precision).
  • If the voice is a sharp, high-pitched whine, the particles are likely flying fast and straight (good for coating).

Why Does This Matter?

Right now, if a factory wants to check if their thermal spray machine is working perfectly, they have to stop, take a sample, and measure it. It's slow and expensive.

This research suggests that in the future, we could just put a microphone next to the machine. By listening to the "voice" of the jet, a computer could instantly tell the operator: "Hey, the particles are wobbling too much, turn up the heat!" or "The spray is too wide, turn down the pressure!"

It turns the machine into a self-aware system that can "hear" its own health and fix itself, ensuring better coatings for everything from jet engines to medical implants.

Technical Summary

Here is a detailed technical summary of the paper "Investigation of Aeroacoustics and In-flight Particle Transport in Thermal Spray Supersonic Jets."

1. Problem Statement

Thermal spray processes rely heavily on operating conditions (chamber pressure and temperature) to determine coating quality. A known empirical indicator of process health is the acoustic signature of the torch; skilled operators can diagnose coating quality based on sound. However, there is a lack of quantitative models linking nozzle operating parameters to far-field acoustic levels and in-flight particle behavior (velocity and distribution).

The study addresses two primary challenges:

1. Predicting Aeroacoustics: Developing a method to predict the sound pressure level (SPL) and spectral content of supersonic thermal spray jets based on nozzle geometry and operating conditions.
2. Particle Transport: Understanding how chamber pressure and temperature affect the velocity, radial spreading, and flux distribution of particles injected into the supersonic jet.

2. Methodology

The research employs a hybrid approach combining an analytical model and high-fidelity numerical simulations using OpenFOAM.

A. Analytical Model

• Derivation: A theoretical model was derived based on gas dynamics and acoustic power conservation. It assumes spherical wave propagation and links nozzle exit parameters (pressure $P_e$, temperature $T_e$, diameter $D_e$) and ambient conditions to the far-field Sound Pressure Level (SPL).
• Calibration: The initial analytical model showed systematic errors due to neglected turbulence effects. A power-law calibration function ($P'_{rms} = A \times P_{rms}^B + C$) was developed using experimental data to correct the discrepancy, significantly improving agreement with measurements.

B. Numerical Framework (CFD)

• Solver: The study utilized a modified version of the sonicDPMFoam solver in OpenFOAM, coupled with the libAcoustics library.
• Turbulence Modeling:
  • URANS (Unsteady Reynolds-Averaged Navier-Stokes): Used for initial flow development on a coarse mesh.
  • DDES (Delayed Detached Eddy Simulation): A hybrid RANS/LES approach used on a finer mesh to resolve unsteady turbulent structures and shock-boundary layer interactions critical for noise generation. The $k-\omega$ SST model served as the RANS closure.
• Particle Tracking: A Lagrangian approach tracked individual particles. Forces included aerodynamic drag, gravity, pressure gradient, and virtual mass. Particle-wall and particle-particle collisions were modeled using rebound and Hertzian contact models.
• Acoustic Prediction: The Ffowcs Williams–Hawkings (FW-H) acoustic analogy was applied to near-field CFD data to predict far-field noise without resolving the entire acoustic field on the flow mesh.
• Validation: The model was validated against:
  • Arkhipov et al.: Microphone spectra for cold spray jets (VRC Nozzle 58/70).
  • Allofs et al.: Shadowgraphy measurements of particle mass flux at the nozzle exit.

3. Key Contributions

1. Hybrid Analytical-Numerical Workflow: The paper presents a streamlined workflow where URANS simulations initialize the flow, which is then mapped to a DDES mesh for high-fidelity resolution. This significantly reduces computational time compared to starting DDES from scratch.
2. Calibrated Analytical Model: The development of a calibrated analytical equation that accurately predicts SPL based on nozzle geometry and operating conditions, offering a low-cost alternative to full CFD for preliminary design.
3. Comprehensive Parametric Study: A detailed investigation into the distinct effects of Chamber Pressure vs. Chamber Temperature on both the acoustic field and particle transport.
4. Open-Source Implementation: Demonstrated the capability of OpenFOAM and libAcoustics to handle complex, high-speed, multiphase thermal spray simulations with accuracy comparable to commercial solvers.

4. Key Results

A. Flow Field and Turbulence

• URANS vs. DDES: URANS predicted a smoother flow with a higher exit Mach number (3.0) compared to DDES (2.7). DDES captured unsteady shock motions, shock-vortex interactions, and delayed turbulent mixing, resulting in a more realistic representation of the jet's potential core and shear layer.
• Shock Structure: The jets exhibited characteristic diamond shock cells. DDES revealed more frequent and sharper oscillations in Mach number and pressure compared to the damped URANS results.

B. Acoustic Predictions

• Pressure vs. Temperature: Increasing chamber pressure increased the amplitude and sharpness of pressure fluctuations (higher RMS and OASPL). Increasing temperature primarily shifted the phase characteristics of the signal and stabilized the acoustic behavior (reducing high-amplitude excursions).
• Model Accuracy: The calibrated analytical model showed the best agreement with experimental data (errors within 6–8%), outperforming the raw numerical model at higher pressures where the CFD slightly underpredicted SPL.
• Doppler Effect: Visualizations confirmed that forward-traveling waves were stronger than backward-traveling waves due to the Doppler effect from the high-speed jet.

C. Particle Transport

• Effect of Pressure: Higher chamber pressures led to wider radial dispersion of particles and faster velocity decay at larger standoff distances. While the core particle population remained focused, the outer percentiles (99%) spread significantly more at 65 bar compared to 45 bar.
• Effect of Temperature: Higher temperatures resulted in higher particle velocities (up to ~1000 m/s at 807 K) and more uniform velocity distributions. Temperature had minimal impact on radial spreading compared to pressure.
• Velocity-Diameter Correlation: Smaller particles accelerated faster but lost velocity more quickly due to drag. Larger particles maintained momentum over longer distances.
• Standoff Distance: As distance increased, the particle cloud expanded radially. At 200 mm, the 99th percentile spread was significantly larger for high-pressure cases (up to 66.9 mm) compared to high-temperature cases (21.1 mm).

5. Significance and Implications

• Non-Intrusive Monitoring: The study validates the hypothesis that aeroacoustic signatures can serve as a non-intrusive pathway to monitor and potentially control thermal spray operating conditions in real-time.
• Process Optimization:
  • Temperature is identified as the primary control parameter for maximizing particle impact velocity (crucial for bonding).
  • Pressure is the primary control parameter for managing particle distribution width and jet structure.
• Coating Quality: Understanding the trade-off between velocity uniformity (favored by high temperature) and spatial uniformity (affected by pressure-driven turbulence) allows for better selection of operating parameters for specific coating applications.
• Future Work: The authors suggest extending the model to include heat transfer for particles, adding a substrate to simulate flow redirection, and testing various nozzle geometries to refine the calibration dataset.

In conclusion, this work successfully bridges the gap between theoretical acoustics, high-fidelity CFD, and particle dynamics in thermal spray, providing a robust framework for optimizing supersonic jet processes.