Combined thermographic measurement and heat-flux compensation methods for aerodynamic heating evaluation in hypersonic flight

This paper presents a novel approach combining high-speed thermographic measurements with heat-flux compensation methods to evaluate aerodynamic heating on a hypersonic projectile, demonstrating that the experimentally derived stagnation Stanton number aligns with both computational fluid dynamics simulations and empirical correlations.

The Gist

Imagine you are trying to take a photo of a hummingbird flying at lightning speed. If you use a standard camera with a slow shutter speed, the bird won't look like a bird; it will look like a blurry streak of feathers. You can't tell where its head is, how fast its wings are beating, or what color it really is.

This is exactly the problem scientists face when studying hypersonic flight (flying faster than Mach 5, or five times the speed of sound). When a vehicle flies this fast, the air in front of it gets incredibly hot due to friction and compression. To design safe spacecraft, engineers need to know exactly how hot the surface gets. But if they try to measure this heat while the vehicle is zooming by, the "blur" of the motion makes the data useless.

This paper from Tohoku University is about inventing a new "smart camera trick" to fix that blur and measure the heat accurately.

The Problem: The "Motion Blur" of Heat

The researchers used a ballistic range (a giant, high-tech cannon) to shoot an 8mm aluminum ball (about the size of a large marble) into the air at roughly Mach 5.

• The Challenge: To capture the heat, they used a high-speed infrared (IR) camera. However, because the ball was moving so fast, the camera's "shutter" had to stay open for a tiny fraction of a second to catch enough light. Even that tiny fraction was too long!
• The Result: In the raw video, the ball didn't look like a sphere. It looked like a long, glowing egg or a streak of light. The heat data was smeared out because the camera was "seeing" the ball in multiple places at once. It was like trying to measure the temperature of a car by looking at a long, blurry smear of it on a highway.

The Solution: The "Mathematical Time Machine"

Instead of trying to build a faster camera (which is hard and expensive), the team invented a clever mathematical compensation method. Think of it as a "de-blurring" algorithm, but for heat.

Here is how they did it, using a simple analogy:

1. Understanding the Camera's "Reaction Time":
   Imagine the camera sensor is like a person who is slow to react. When a hot object passes by, the person doesn't instantly say "It's hot!" They take a split second to realize it, and then their reaction slowly builds up to the full intensity.
   The researchers knew exactly how fast their camera sensor "reacted" (its rise time). They realized the blurry streak wasn't random; it was a predictable pattern caused by the camera's slow reaction combined with the ball's speed.

2. The "Unsmearing" Process:
   They took the blurry, streaky image and ran it through a mathematical model.

   • Analogy: Imagine you have a muddy footprint that has been dragged across the floor, leaving a long smear. If you know exactly how fast the person was walking and how sticky the mud is, you can mathematically reverse the drag to figure out exactly where the original footprint was and how deep it was.
   • They did this with the heat data. They stripped away the "motion blur" and the camera's slow reaction time to reconstruct what the temperature actually was at every single point on the ball's surface.

3. The "Heat Map" Reconstruction:
   Once they fixed the blur, they could see the true picture:

   • The front of the ball (the nose) was the hottest spot.
   • The heat dropped off smoothly as you moved toward the sides.
   • The maximum temperature rise was about 24 degrees Celsius above the surrounding air. (This might sound low, but remember, the ball is aluminum, which conducts heat very well, so it doesn't get as hot as a ceramic tile would).

Why This Matters

The researchers didn't just guess; they checked their work in two other ways:

• Supercomputer Simulation (CFD): They ran a digital simulation of the same flight on a supercomputer. The "de-blurred" camera data matched the supercomputer's prediction almost perfectly.
• Old-School Math: They compared their results to established formulas used by engineers for decades. Again, the numbers matched.

The Big Picture

This study is a breakthrough because it allows scientists to measure heat on fast-moving objects without needing to attach sensors to them (which would change the airflow) or build impossible, ultra-fast cameras.

The Takeaway:
Just as a photo editor can fix a blurry picture, these scientists developed a way to "fix" blurry heat data. This means we can now study how spacecraft heat up during re-entry or how hypersonic jets handle the heat, even if the camera isn't fast enough to freeze the motion perfectly. It opens the door to safer, more efficient designs for the space vehicles of the future.

Technical Summary

1. Problem Statement

Accurate prediction of aerodynamic heating is critical for the design of thermal protection systems (TPS) for hypersonic vehicles. While wind tunnel testing is conventional, it suffers from limitations such as:

• Flow Disturbances: Inherent turbulence from tunnel walls.
• Sting Effects: The mounting sting alters the flow field and shock geometry.
• Dynamic Instability: Fixed models cannot replicate the pitching moment fluctuations and angle-of-attack variations seen in free flight.

Ballistic ranges offer a solution by launching projectiles in quiescent air without a sting. However, existing thermographic methods in ballistic ranges face a trade-off:

• High-Speed Requirement: To avoid motion blur, cameras require extremely short integration times.
• Temperature Limitation: Short integration times require high surface temperatures (high radiant intensity) for detection. This forces the use of low-conductivity materials or high velocities (Mach >10), which limits the ability to test materials and conditions relevant to lower Mach numbers (e.g., Mach 5) or standard re-entry scenarios.
• Motion Blur: At lower velocities or with standard materials, the projectile moves significantly during the camera's integration time, causing severe motion blur that distorts temperature and heat-flux data.

The Core Challenge: How to accurately reconstruct surface temperature and heat-flux distributions from thermographic data acquired under conditions of significant motion blur and finite photodetector response times.

2. Methodology

The study employed a combination of experimental ballistic range testing, advanced image processing/compensation algorithms, and Computational Fluid Dynamics (CFD).

Experimental Setup

• Facility: Ballistic range at the Institute of Fluid Science, Tohoku University.
• Projectile: An 8 mm diameter aluminum sphere (mass 0.72 g) launched at approximately Mach 5 (1.64–1.69 km/s).
• Imaging:
  • Shadowgraph: High-speed digital camera (Phantom v2011) at 22 kHz to visualize shock waves and trajectory.
  • Thermography: Mid-wave high-speed IR camera (FLIR X6981) operating at 2.03 kHz with a long integration time of 0.479 ms. This integration time caused the projectile to travel ~785 mm (approx. 98 diameters) during a single frame, resulting in severe motion blur.

Compensation Framework (Key Innovation)

To recover accurate data from the blurred images, the authors developed a two-step compensation method:

1. Geometric & Temporal Reconstruction:
   • The raw thermographic image showed an elongated ellipsoidal structure due to motion blur.
   • The authors modeled the photodetector's dynamic response using a first-order exponential rise function: $I = I_0 [1 - \exp(-t/\tau)]$.
   • By analyzing the temperature rise from the ambient background to the peak at the stagnation point, they fitted the rise time ($\tau$) and reconstructed the true temporal temperature profile $T(t)$ from the spatially blurred data $T(x)$.
2. Heat-Flux Calculation:
   • Assuming one-dimensional transient heat conduction in a semi-infinite solid (valid as the thermal penetration depth was much smaller than the projectile radius), they used an analytical solution to relate the surface temperature history to the heat transfer coefficient ($h$).
   • The Stanton number ($St$) was then calculated using the derived $h$, ambient density, specific heat, and freestream velocity.

Numerical Validation

• A laminar CFD simulation (using OpenFOAM) was performed with identical boundary conditions (Mach 4.76, Reynolds number $8.45 \times 10^5$) to validate the experimental shock geometry and heat-flux distributions.

3. Key Contributions

• Novel Compensation Algorithm: Developed a systematic method to reconstruct surface temperature and heat-flux distributions from thermographic data heavily affected by motion blur. This eliminates the need for ultra-short integration times that previously limited ballistic experiments to very high temperatures.
• Free-Flight Aerodynamic Heating Data: Successfully acquired high-fidelity heat-flux data for a hypersonic projectile at Mach 5 in a free-flight environment, eliminating sting interference and tunnel wall disturbances.
• Generalizable Framework: Proposed a reproducible correction procedure that relies on physical models (photodetector response and heat conduction) rather than case-specific tuning, making it applicable to various facilities and projectile geometries.

4. Key Results

• Shock Layer Visualization: Shadowgraph images and CFD confirmed the formation of a detached shock wave and a high-temperature shock layer consistent with hypersonic flow theory.
• Temperature Reconstruction:
  • The maximum surface temperature rise due to aerodynamic heating was 24.4 K above the ambient temperature.
  • The temperature distribution decreased monotonically from the stagnation point as the radial distance increased.
  • The reconstructed temperature profile matched the CFD results closely.
• Stanton Number Distribution:
  • The stagnation Stanton number ($St_s$) was calculated to be 0.00366.
  • This value showed excellent agreement with the CFD result (0.00363) and was within the experimental uncertainty of an empirical correlation by Zhou et al. (2023), which yielded 0.00458 (a ~25% difference attributed to the empirical correlation's derivation conditions vs. the laminar flow in this study).
• Uncertainty Analysis:
  • Temperature uncertainty at the stagnation point: ±5.32 K (21.8%).
  • Stanton number uncertainty: ±0.00116 (31.8%).
  • Despite these uncertainties, the consistency across thermography, CFD, and empirical correlations validated the method.

5. Significance

This research represents a significant advancement in hypersonic experimental aerodynamics:

1. Overcoming Motion Blur: It demonstrates that accurate heat-flux measurements are possible even when motion blur is severe, provided a rigorous compensation model is applied. This expands the operational envelope of ballistic ranges to lower Mach numbers and standard materials (like aluminum) that were previously difficult to measure.
2. Validation of Free-Flight Data: It provides a robust dataset for validating CFD codes and empirical correlations in a "clean" flow environment (no sting), which is crucial for refining thermal protection system designs for re-entry vehicles and scramjets.
3. Methodological Standard: The proposed compensation framework offers a generic, reproducible approach that can be adopted by other research facilities to enhance the accuracy of non-intrusive thermographic measurements in high-speed flows.