Conformal Mapping

Description

This project provides a Python-based implementation of the Joukowsky conformal mapping. The primary goal is to facilitate the transformation of complex shapes, particularly for use in Computational Fluid Dynamics (CFD) simulations. Conformal mapping is a powerful technique in both theoretical and applied mathematics, and this project focuses on its practical applications—such as the optimization of wing designs for wind farming and aerodynamics.

Key Features

• Joukowsky Transformation: Simplifies the analysis of flow around airfoils by mapping a circular region into an airfoil shape.
• Customization Parameters: Offers flexible control over shape and curvature using various parameters.
• Practical Applications: Ideal for use in CFD to simulate airflow and optimize wing design.

Parameters

This project uses several key parameters to control the Joukowsky transformation and shape generation:

• a: Horizontal shift of the circle. Positive values shift the circle to the left. This parameter also affects the vertical scaling of the wing. A larger absolute value (up to the radius) makes the shape more circular.
• b: Vertical shift of the circle. Positive values shift the circle upwards. This parameter controls the cambering of the wing, with larger values resulting in a more curved shape.
• r: Radius of the circle to be transformed.
• r_max: Maximum radius of the grid to represent.
• rad_steps: Number of divisions in the radial direction for the grid.
• phi_steps: Number of divisions in the angular direction for the grid.

Insights

• a Parameter (Vertical Scaling): The value of a determines how much the resulting wing deviates from a perfect circle. Larger values (up to the circle’s radius) make the wing shape rounder, while smaller values stretch it more vertically.

• b Parameter (Cambering): The value of b controls the curvature or camber of the wing. Higher values increase the curvature, allowing for the design of wings with more pronounced aerodynamic profiles.

These parameters allow fine-tuning of wing shapes, offering flexibility to adapt designs for specific applications such as energy-efficient wind turbine blades or optimized aircraft wings.

Installation

1. Clone the repository:

   git clone https://github.com/Zhdanko-Gleb/Conformal-mapping.git

2. Navigate into the project directory:

   cd Conformal-mapping

3. (Optional) Create and activate a virtual environment:

   python3 -m venv env
   source env/bin/activate  # On Windows use `env\Scripts\activate`

4. Install the required dependencies:

   pip install -r requirements.txt

Usage

After installing the project, you can apply the conformal mapping transformation by importing the module and using the functions in your Python code. Here's a basic example of how to use it:

from conformal_mapping import joukowsky_map

# Define parameters
a = 0.1
b = 0.05
r = 1.0
r_max = 5.0
rad_steps = 100
phi_steps = 200

# Apply Joukowsky conformal mapping
wing_shape = joukowsky_map(a, b, r, r_max, rad_steps, phi_steps)

# Output the mapped shape
print(wing_shape)

To visualize the results, you can use the accompanying Jupyter Notebooks or integrate this into your CFD pipeline for further analysis.

Contributing

Contributions are welcome! If you have ideas for improvements or new features, please follow these steps:

1. Fork the repository.
2. Create a feature branch (git checkout -b feature/AmazingFeature).
3. Commit your changes (git commit -m 'Add some amazing feature').
4. Push to the branch (git push origin feature/AmazingFeature).
5. Open a pull request.

For detailed guidelines, check the CONTRIBUTING.md file.

License

This project is licensed under the MIT License. See the LICENSE file for more details.

Credits

• Zhdanko Gleb: Author and main contributor of the project.