Hypersonic Turbulent Prandtl Number Optimization

Automated calibration of RANS turbulence models for hypersonic cold-wall boundary layers using data-driven inverse modeling.

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Key Results

Metric	Baseline	Optimized	Improvement
Temperature RMSE	0.387	0.286	-26%
Turbulent Prandtl Number	0.9	0.566	Calibrated

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The Problem

Standard RANS turbulence models assume a constant turbulent Prandtl number (Pr_t = 0.9). This assumption breaks down for hypersonic flows with cold walls, leading to significant errors in heat flux prediction - critical for thermal protection system design.

The Solution

This project implements an automated calibration pipeline that:

1. Wraps the SU2 CFD solver in a Python interface
2. Runs parametric simulations automatically
3. Computes loss against DNS ground truth
4. Optimizes Pr_t using Brent's method (SciPy)

┌─────────────────┐     ┌──────────────┐     ┌─────────────────┐
│   SciPy         │────>│  SU2 RANS    │────>│  Loss Function  │
│   Optimizer     │     │  Solver      │     │  (RMSE vs DNS)  │
│  (Brent's)      │<────│  (Mach 14)   │<────│                 │
└─────────────────┘     └──────────────┘     └─────────────────┘

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Test Case

Parameter	Value
Mach Number	13.6
Wall Temperature Ratio (Tw/Taw)	0.186
Reynolds Number	5×10⁶
Turbulence Model	Spalart-Allmaras
Validation Data	DNS (Murphy & Agarwal, 2025)

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Technologies

• CFD Solver: SU2 (open-source, MPI-parallel)
• Optimization: SciPy (Brent's bounded method)
• Data Processing: Pandas, NumPy
• Visualization: Matplotlib (AIAA publication style)
• Environment: Linux/WSL2, Python 3.8+

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Quick Start

# Install dependencies
pip install -r requirements.txt

# Run optimization (requires SU2 with MPI)
cd src
python run_optimization.py

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Project Structure

├── src/
│   ├── run_optimization.py    # Main optimization loop
│   ├── su2_interface.py       # SU2 wrapper class
│   └── generate_ramp.py       # Mesh generator for future work
├── config/                    # SU2 configuration files
├── data/                      # DNS validation dataset
└── post_processing/           # Visualization scripts

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References

• Murphy, A. R. & Agarwal, R. K. (2025). Application and Evaluation of the Wray-Agarwal Turbulence Model with Compressibility Corrections in SU2 for RANS Hypersonic Flow Prediction. AIAA Aviation Forum.

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Author

Matar Hedi
M.Sc. Researcher, Technion | Thermal Engineer, Elbit Systems
LinkedIn

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License

MIT