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 (Pr_t=0.9)	Calibrated (Pr_t=0.566)	Improvement
Temperature RMSE	0.739	0.286	-61.3%
Turbulent Prandtl Number	0.9 (SA default)	0.566 (optimized)	Data-driven calibration

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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 with two execution modes:

Mode 1 — Single-condition optimization (validated at Mach 14)

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)   │<────│                 │
└─────────────────┘     └──────────────┘     └─────────────────┘

Mode 2 — GP surrogate + active learning (machinery validated; SU2 calibration pending)

Extends Mode 1 to multiple flow conditions using a Gaussian Process (BoTorch) that maps [Mach, Tw/Taw, pressure-gradient angle] → optimal Pr_t, with UCB acquisition to decide where to run new SU2 simulations. The GP/active-learning machinery is validated against a 5-case DNS family (validate_surrogate.py), including per-point observation noise to down-weight lower-fidelity data. The remaining step is replacing the DNS placeholder targets with real RANS-optimal Pr_t from per-case SU2 calibration.

┌──────────────┐     ┌──────────────┐     ┌──────────────┐
│ FlowCondition│────>│  GP Surrogate│────>│  UCB         │
│ (case_config)│     │  (BoTorch)   │     │  Acquisition │
└──────────────┘     └──────────────┘     └──────┬───────┘
                                                  │ high uncertainty
                                                  v
                                          ┌──────────────┐
                                          │ SU2 + Brent  │
                                          │ (inner loop) │
                                          └──────────────┘

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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 (Zhang, Duan & Choudhari, 2018)

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Technologies

• CFD Solver: SU2 (open-source, MPI-parallel)
• Optimization: SciPy (Brent's bounded method)
• Surrogate Model: PyTorch + GPyTorch + BoTorch (GP, active learning)
• Data Processing: Pandas, NumPy
• Visualization: Matplotlib (AIAA publication style)
• Environment: Linux/WSL2, Python 3.9+

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Quick Start

# Install dependencies
pip install -r requirements.txt

# Mode 1: Single-condition optimization (validated)
cd src
python run_optimization.py

# Mode 2: Active learning (scaffold — not yet validated)
python run_active_learning.py --dry-run    # GP logic only, no SU2
python run_active_learning.py --budget 10    # full loop (requires SU2 + MPI)
python run_active_learning.py --resume       # resume from checkpoints/

SU2 must be on PATH. Parallel runs use mpirun -n 4 SU2_CFD.

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Project Structure

├── src/
│   ├── run_optimization.py       # Mode 1: Brent optimization (validated)
│   ├── run_active_learning.py    # Mode 2: GP + active learning orchestrator
│   ├── case_config.py            # FlowCondition dataclass + 5 DNS case factories
│   ├── surrogate.py              # GP surrogate (BoTorch, per-point noise support)
│   ├── active_loop.py            # UCB acquisition loop
│   ├── su2_interface.py          # SU2 wrapper (accepts FlowCondition)
│   ├── extract_dns_profiles.py   # NASA TMR .dat -> normalized T-u profile CSVs
│   ├── validate_surrogate.py     # GP/AL machinery sanity check (placeholder data)
│   └── generate_ramp.py          # Mesh generator (future work)
├── checkpoints/                  # GP model + AL log (runtime, gitignored)
├── config/                       # SU2 configuration files
├── data/
│   └── dns_database/             # 5-case DNS family (Mach 2.5-14): raw + profiles
└── post_processing/              # Visualization scripts

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References

• Zhang, C., Duan, L. & Choudhari, M. M. (2018). Direct Numerical Simulation Database for Supersonic and Hypersonic Turbulent Boundary Layers. AIAA Journal, 56(11). (DNS validation data, via NASA Langley Turbulence Modeling Resource.)
• 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. (RANS turbulence-model reference.)

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Author

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

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License

MIT