Numerical Methods for Reactive Flow Simulation

A 2D computational fluid dynamics (CFD) solver for simulating reactive flows with coupled fluid dynamics and chemical kinetics.

Overview

This project implements a numerical simulation of a counterflow premixed flame using:

• Incompressible Navier-Stokes solver with fractional step method
• Multi-species reactive chemistry with Arrhenius kinetics
• Operator splitting for advection-diffusion-reaction equations
• Runge-Kutta 4th order (RK4) time integration for species and temperature
• Successive Over-Relaxation (SOR) for pressure correction and enforcing incompressibility with Chorin projection method

Features

• 2D incompressible flow solver with upwind advection / Lax-Wendroff scheme
• Multi-species chemistry manager (CH₄, O₂, CO₂, H₂O, N₂)
• Temperature-dependent reaction rates (Arrhenius law)
• Pressure correction using Successive Over-Relaxation (SOR)
• Automatic time step selection based on CFL and Fourier criteria
• Data export and visualization tools
• Animation generation for temporal evolution
• Use of Numba for performance optimization

Project Structure

nm_method/
├── main.py           # Entry point and simulation setup
├── system.py         # Main system controller
├── fluid.py          # Fluid dynamics solver
├── chemistry.py      # Chemistry manager and species handling
├── constant.py       # Physical constants and parameters
├── plotting.py        # Visualization functions
├── data/             # Simulation output data (*.npy files)
├── .gitignore        # Git ignore rules
└── README.md         # This file
└── LICENSE           # License information

Requirements

• Python 3.8+
• NumPy
• Matplotlib
• SciPy (optional, for advanced features)
• Numba (for performance optimization)

Installation

1. Clone the repository:

git clone https://github.com/EwanBat/combustion_flow.git
cd combustion_flow

2. Install dependencies:

pip install numpy matplotlib

Usage

Run the simulation:

python main.py

The simulation will:

1. Initialize the computational domain and fields
2. Run the time-stepping loop with automatic progress display
3. Save data snapshots at specified intervals to data/ folder
4. Generate visualization plots and animations

Customization

Edit parameters in constant.py to modify:

• Physical properties (density, viscosity, specific heat)
• Reaction kinetics parameters (activation energy, pre-exponential factor)
• Species properties (molecular mass, diffusivity)

Edit main.py to adjust:

• Domain size and grid resolution
• Inlet velocities and boundary conditions
• Total simulation time and data save frequency

Physics

Governing Equations

Momentum (Navier-Stokes):

$$ \frac{\partial \vec{u}}{\partial t} + \vec{u} \cdot \nabla \vec{u} = -\frac{\nabla P}{\rho} + \nu \nabla^2 \vec{u} $$ $$ \nabla \cdot \vec{u} = 0 \quad \text{(incompressibility)} $$

Species transport:

$$ \frac{\partial Y_i}{\partial t} + \vec{u} \cdot \nabla Y_i = D \nabla^2 Y_i + \frac{\omega_i}{\rho} $$

Energy (temperature):

$$ \frac{\partial T}{\partial t} + \vec{u} \cdot \nabla T = \alpha \nabla^2 T + \frac{Q}{\rho c_p} $$

Reaction Model

Simple one-step methane combustion:

$$ \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} $$

With Arrhenius rate:

$$ \omega = A \cdot \exp\left(-\frac{E_a}{RT}\right) \cdot [\text{CH}_4] \cdot [\text{O}_2]^2 $$

Visualization

The code generates:

• Velocity magnitude plots showing flow patterns
• Temperature fields with heated regions
• Species concentration plots for each chemical species
• Animations showing temporal evolution

Example Results

Species concentration profiles showing the distribution of reactants and products in the computational domain.

Output

Simulation data is saved as NumPy arrays (.npy) in the data/ folder:

• simulation_data_t0000_u.npy - x-velocity at timestep 0
• simulation_data_t0000_v.npy - y-velocity at timestep 0
• simulation_data_t0000_T.npy - temperature at timestep 0
• simulation_data_t0000_Y_CH4.npy - CH₄ mass fraction at timestep 0
• ... (and so on for each timestep and species)

License

This project is licensed under the MIT License - see the [LICENSE] file for details.

Authors

• Ewan Bataille

Acknowledgments

Developed as part of a numerical methods course project.