Supersonic Flow Analysis of a Bullet

2D steady RANS simulation of supersonic flow over a bullet at Mach 1.5 and Mach 2 in ANSYS Fluent, with a mesh-convergence study and comparison against an empirical drag correlation in MATLAB.

Static pressure at Mach 1.5 (100k mesh): bow shock at the nose, expansion over the shoulder, recompression at the base.

• Resolve the shock and expansion structure around a bullet at Mach 1.5 and 2.
• Compute the drag force and drag coefficient, and check their sensitivity to the mesh.
• Compare CFD results against a simple empirical drag estimate.

Geometry	100k mesh

* Planar 2D model, so forces are per unit depth (1 m).

The MATLAB scripts use the free-stream conditions (ISA sea level, $T$ = 288.15 K, $p$ = 101 325 Pa) and the empirical supersonic drag correlation

$$ C_d \approx 0.15 + \frac{0.6}{M^2}, \qquad D = \tfrac{1}{2}\rho V^2 A_{ref} C_d $$

Velocity at Mach 2 (100k)

• Mach 1.5: CFD and the empirical estimate agree within about 1 % in $C_d$.
• Mach 2: The correlation predicts a falling $C_d$ as Mach number increases, while the CFD predicts a rising one. The gap (0.30 vs. 0.46) shows the limits of the simple correlation, and also shows that the Mach 2 CFD needs more work (see below).
• Refining the mesh from 50k to 300k lowers $C_d$ by about 6–7 % at both Mach numbers.

• Residuals at Mach 2 did not converge well on any of the meshes. A density-based coupled solver, shock-adapted mesh refinement and the k-ω SST model would make these results more reliable.
• An axisymmetric model would give 3D-equivalent drag values that can be compared directly with ballistic data.

├── code/
│   ├── mach_number_1.5_calculation.m   # Empirical Cd and drag, Mach 1.5
│   └── mach_number_2_calculation.m     # Empirical Cd and drag, Mach 2
├── docs/
│   └── bullet_analysis_1.pdf           # Full report (30 pages)
└── figures/                            # Geometry, mesh and contour plots

📄 Full report (PDF): theory, all residual, contour and drag histories for the 50k, 100k and 300k meshes.

• Anderson, J. D. (2016). Fundamentals of Aerodynamics, 6th ed. McGraw-Hill.
• Liepmann, H. W., & Roshko, A. (1957). Elements of Gas Dynamics. Wiley.
• Carlucci, D. E., & Jacobson, S. S. (2013). Ballistics: Theory and Design of Guns and Ammunition. CRC Press.

Burak Yörükçü, Mechanical Engineering, Çukurova University · GitHub · burakyorukcu@outlook.com