Supersonic Flow Analysis of a Bullet

Overview

This project is part of my Mechanical Engineering studies at Çukurova University, analyzing supersonic flow over a bullet to compute drag coefficient (Cd) and drag forces. It combines computational fluid dynamics (CFD) simulations using ANSYS Fluent with analytical calculations in MATLAB, validating theoretical models against industry-standard numerical results. The project was conducted in 2025 to study shock wave formation and aerodynamic performance at Mach 1.5 and Mach 2.

Methodology

• Geometry: 2D bullet model (8 mm length, 2 mm diameter) due to ANSYS Student version limitations.
• CFD Simulations:
  • Software: ANSYS Fluent with k-epsilon turbulence model.
  • Conditions: Mach 1.5 and Mach 2, ideal gas model, steady-state solver.
  • Mesh: Quad-dominant meshes (50k, 100k, 300k elements) for convergence study.
  • Outputs: Pressure, velocity, Mach number contours; drag force and Cd.
• Analytical Calculations: MATLAB code to compute Cd using oblique shock relations, Prandtl-Meyer expansion, and modified Newtonian theory.
• Tools: CAD for geometry, ANSYS Fluent for CFD, MATLAB for post-processing and validation.

Key Features

• Bullet Geometry:
  
  2D bullet model used in simulations.
• Mesh Diagram:
  
  100k quad-dominant mesh for balanced accuracy and computational cost.
• Pressure Contour (Mach 1.5):
  
  Shock wave formation at Mach 1.5, 100k mesh.
• Velocity Contour (Mach 2):
  
  Flow behavior at Mach 2, 100k mesh.

Results

• CFD Findings:
  • Mach 1.5: Cd ≈ 0.42, drag force ≈ 270 N (300k mesh).
  • Mach 2: Cd ≈ 0.46, drag force ≈ 310 N (300k mesh).
  • Higher mesh density improves accuracy, but 100k mesh balances cost and precision.
• MATLAB vs. CFD:
  • Mach 1.5: MATLAB (Cd = 0.4167, drag = 265.98 N) closely matches CFD (Cd = 0.42, drag = 270 N).
  • Mach 2: MATLAB (Cd = 0.30, drag = 340.45 N) deviates from CFD (Cd = 0.46, drag = 310 N), indicating limitations in analytical assumptions.
• Conclusion: MATLAB is reliable for lower Mach numbers; higher Mach requires refined models or denser meshes.

Code

• code/mach_number_1.5_calculation.m: MATLAB script for computing drag coefficient and drag force at Mach 1.5.
• code/mach_number_2_calculation.m: MATLAB script for computing drag coefficient and drag force at Mach 2.

Report

• Full Report
  Detailed methodology, results, and comparisons.