README.md

Rocket Pogo Effect Simulation

Welcome to the Rocket Pogo Effect Simulation repository! 🚀

This project aims to simulate the Pogo effect, also known as Pogo oscillation or Pogo instability, observed in rockets and aerospace vehicles during powered flight. The simulation provides insights into the dynamics of the propulsion system and the structural response of the vehicle to mitigate the Pogo effect.

Index

1. Mathematical Formulation
2. Coupling Equations
3. Overview
4. Usage
5. Analysis and Mitigation
6. License

Mathematical Formulation

The simulation is based on mathematical equations that describe the dynamics of the propulsion system and the structural dynamics of the vehicle. These equations include:

Propulsion System Dynamics

The dynamics of the propulsion system are described by equations that govern the behavior of various components such as the rocket engine, fuel lines, and valves. These equations typically involve fluid dynamics, combustion processes, and mechanical vibrations.

A simplified representation of the propulsion system dynamics can be expressed using a lumped-parameter model. For example:

• Mass flow rate equation:

where:

• (\dot{m}) is the mass flow rate,

• (C_d) is the discharge coefficient,

• (A) is the cross-sectional area of the nozzle,

• (\Delta P) is the pressure drop across the nozzle, and

• (\rho) is the density of the propellant.

• Thrust equation:

where:

• (F) is the thrust force,
• (v_e) is the exhaust velocity,
• (P_e) is the pressure at the exit of the nozzle,
• (P_a) is the ambient pressure, and
• (A_e) is the area of the nozzle exit.

Vehicle Structural Dynamics

The structural dynamics of the vehicle are governed by equations of motion that describe its translational and rotational motion. These equations typically include terms related to mass, stiffness, damping, and external forces.

A simplified model of the vehicle's structural dynamics can be represented by a set of coupled second-order differential equations. For example, considering a one-degree-of-freedom model for longitudinal motion:

where:

• (m) is the mass of the vehicle,
• (x) is the displacement of the vehicle,
• (c) is the damping coefficient,
• (k) is the stiffness coefficient,
• (F_{\text{ext}}) is the external force acting on the vehicle, and
• (F_{\text{Pogo}}) is the Pogo-induced force.

Coupling Equations

To model the interaction between the propulsion system and the vehicle structure, coupling equations are used to relate the forces exerted by the propulsion system to the resulting structural displacements. These equations capture the transfer of energy and momentum between the propulsion system and the vehicle.

The coupling equations typically involve relating the thrust force generated by the propulsion system to the resulting changes in the vehicle's

mass distribution and structural stiffness. These equations are often derived based on the specific configuration and dynamics of the vehicle.

Overview

The Pogo effect refers to the undesirable oscillations experienced by a rocket along its longitudinal axis during powered flight. These oscillations result from the interaction between the propulsion system dynamics and the structural dynamics of the vehicle.

Usage

To run the simulation, follow these steps:

1. Clone this repository to your local machine using Git:

   git clone https://github.com/Rishit-katiyar/Rocket_Pogo_Effect_Simulation.git

2. Navigate to the project directory:

   cd Rocket_Pogo_Effect_Simulation

3. Before running the simulation, ensure you have Python installed on your system. You can download Python from here.

4. Install the required dependencies using pip. It's recommended to create a virtual environment before installing dependencies:

   python -m venv venv         # Create a virtual environment
   source venv/bin/activate    # Activate the virtual environment (for Linux/Mac)
   .\venv\Scripts\activate     # Activate the virtual environment (for Windows)
   pip install -r requirements.txt

   This will install all the necessary packages required to run the simulation.

5. Once the dependencies are installed, you can execute the simulation script by running:

   python rocket_simulation.py

6. This will launch the simulation interface, which provides various options such as:

   • Update simulation parameters: Allows you to modify parameters such as mass flow rate, discharge coefficient, nozzle area, etc.
   • Save the animation: Saves the simulation animation as a video file for further analysis or presentation.
   • Show the default simulation (recommended): Displays the default simulation of the Pogo effect with predefined parameters.
   • Quit: Exits the simulation interface.

7. Select the appropriate option by entering the corresponding number and pressing Enter.

8. If you choose to update simulation parameters, follow the on-screen prompts to input the desired values for each parameter. Press Enter to confirm each input.

9. After selecting the desired options, the simulation will run and display the results in real-time. You can observe the behavior of the rocket and analyze the Pogo effect.

10. Once you're done with the simulation, you can exit the interface by selecting the "Quit" option or closing the simulation window.

These detailed instructions provide a comprehensive guide for running the simulation and interacting with the interface. Feel free to explore different options and parameters to gain insights into the dynamics of the Pogo effect.

The script will display a menu with options to update simulation parameters, save the animation, show the default simulation (recommended), or quit.

Analysis and Mitigation

The simulation allows for the analysis of Pogo-induced oscillations and the assessment of mitigation strategies. Engineers can explore modifications to the propulsion system, structural enhancements, and active control systems to minimize the Pogo effect and ensure mission safety and stability.

License

This project is licensed under the GNU General Public License v3.0. See the LICENSE file for details.