An-Optimized-deep-learning-framework-for-turbulance-modelling

🌀 Turbulent Flow Prediction Using MLP & Cascade MLP Neural Networks

Predicting turbulent eddy viscosity (νt) and Reynolds stress (−u′v′) using MLP and Cascade MLP neural networks trained on DNS data — published as a thesis project.

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📌 Overview

This project integrates machine learning with RANS (Reynolds-Averaged Navier–Stokes) turbulence modeling to improve CFD predictions without the cost of full DNS simulations.

Two neural network architectures are implemented:

• MLP Network → predicts turbulent eddy viscosity (νt)
• Cascade MLP Network → uses MLP output + strain-rate tensor to predict Reynolds stress (−u′v′)

Training is performed on DNS data at Reτ = 550, and generalization is tested at Reτ = 180, 390, and 590.

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🔬 Scientific Background

Term	Description
RANS	Reynolds-Averaged Navier–Stokes equations — industry-standard CFD approach
DNS	Direct Numerical Simulation — high-fidelity ground truth data
Eddy Viscosity (νt)	Turbulent transport coefficient in RANS models
Reynolds Stress (−u′v′)	Turbulent momentum flux — key quantity in wall-bounded flows
Reτ	Friction Reynolds number — characterizes flow regime

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🗂️ Project Structure

turbulence-ml-rans/

│

├── Final Python.ipynb # MLP & Cascade MLP — training & evaluation

├── Final Matlab.m # Turbulence data processing & DNS extraction

│

├── requirements.txt # Python dependencies

│

├── results/

│ └── (plots, prediction vs DNS comparisons)

│

└── README.md

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⚙️ Methodology

Step 1 — Feature Engineering (MATLAB)

Raw DNS data is processed in MATLAB to extract 10 flow variables:

Variable	Symbol	Description
Wall Distance	y	Distance from wall (most important feature)
Mean Velocity U	Ū	Streamwise mean velocity
Mean Velocity V	V̄	Wall-normal mean velocity
Mean Velocity W	W̄	Spanwise mean velocity
Turbulent Kinetic Energy	TKE	k = 0.5(u′²+v′²+w′²)
Strain Rate	S	Rate of deformation tensor
Dissipation Rate	ε	Turbulent energy dissipation
Cross Correlation	−u′v′	Reynolds shear stress
Eddy Viscosity	νt	Target variable (MLP)
Reynolds Stress	τ	Target variable (Cascade MLP)

Step 2 — Feature Importance (Python)

A Random Forest Regressor ranks input variables by importance. Wall distance (y) emerged as the most influential feature. Variables are grouped into input categories and each group is evaluated separately.

Step 3 — MLP Training (Python)

• Architecture search via GridSearchCV (layers: 1–6, neurons: 10–50, optimizers: Adam/SGD/RMSprop)
• Final model: 3 hidden layers [75 → 65 → 55 neurons], SELU activation
• Optimizer: Adam (lr = 0.001), Loss: MSE
• Training: 20% split, EarlyStopping (patience=16)
• Validation: 5-fold cross-validation

Step 4 — Cascade MLP (Python)

MLP output (νt) + strain-rate tensor → Cascade MLP → Reynolds stress (−u′v′)

Step 5 — Generalization Test

Model trained at Reτ = 550 is tested at Reτ = 180, 390, 590 to evaluate cross-Reynolds-number generalization.

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📊 Evaluation Metrics

Metric	Formula
MSE	Mean Squared Error
RMSE	Root Mean Squared Error
MAE	Mean Absolute Error
R²	Coefficient of Determination

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🛠️ Installation & Usage

Requirements

pip install -r requirements.txt

requirements.txt:numpy, pandas, scipy, tensorflow>=2.10, scikit-learn, matplotlib

Run

1. Place DNS .mat data files in the project root:

   • data_properties_390.mat
   • data_properties_180.mat
   • data_properties_590.mat

2. Open Final Python.ipynb in Jupyter Notebook or VS Code

3. Run cells sequentially

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📂 Data

The input data consists of high-fidelity DNS (Direct Numerical Simulation) results for turbulent channel flow.

• Training data: Reτ = 550
• Test data: Reτ = 180, 390, 590
• Format: .mat files (MATLAB format), loaded via scipy.io.loadmat()
• Grid size: varies by Reynolds number (e.g., 257×256 for Reτ=390, 129×128 for Reτ=180)

⚠️ Raw data files are not included due to size constraints. DNS data can be obtained from the Johns Hopkins Turbulence Database or equivalent sources.

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📈 Key Results

• Wall distance (y⁺) is the most important input feature
• MLP and Cascade MLP both show strong correlation with DNS ground truth
• The model generalizes well across different Reynolds numbers
• Cascade MLP improves Reynolds stress prediction by leveraging νt as intermediate output

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📄 Reference

This project is the implementation of:

Prediction of Turbulent Eddy Viscosity and Reynolds Stress Using MLP and Cascade MLP Neural Networks
Master's Thesis -Iran university of science and technology (IUST)

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👤 Behnam Pourpooneh

M.Sc. in Aerospace engineering Iran university of science and technology (IUST)