1. 4th Global Engineering, Science and Technology Conference
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet by
Md. Tarique Hasan Khan, Department of Mechanical Engineering
Wayne State University, USA
&
Sudipta Saha, Department of Mechanical Engineering
Bangladesh University of Engineering and Technology, Bangladesh

2. OBJECT OF THE PAPER Numerical Simulation of a Paraboloid-tip Bullet
Aerodynamic characteristic analysis
Closer look on pressure and velocity contour
Stream line across the bullet
Vortex formation along the trailing edge
Static pressure and velocity distribution
Identification and analysis of sonic boom creation
Study on Pressure drag and wake formation
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

3. BULLET Projectile propelled by a firearm Does not contain explosives
Damage is done by indentation or penetration
Generation of Shockwave
Creation of Low Pressure Drag and Sonic Boom
Different types of Bullet

4. PARABOLOID-TIP BULLET
Fired from a .38 super automatic pistol cartridge
Tip is Paraboloid
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

5. PARABOLOID-TIP BULLET – Some Facts and Figures
Designed by Georg Luger and introduced in 1902 by the German weapons manufacturer Deutsche Waffen- und Munitionsfabriken (DWM)
World's most popular and widely used military handgun cartridge
60% of police in the U.S. use this cartridge
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

6. PARABOLOID-TIP BULLET - Specification
9x19mm Paraboloid (abbreviated 9mm, 9x19mm or 9x19)
Also known as The 9×19mm Parabellum
The specifications for the bullet are as follows:
Bullet Diameter, d =9.03 mm
Bullet length, l =10.54 mm.
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

7. PARABOLOID-TIP BULLET - Specification
Our interest lies here only into the leading part of the bullet of which experiences various aerodynamic properties
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

8. Numerical Simulation Model Development: Gambit Simulation: Fluent
Mesh type:
Quadrilateral Structured Mesh along the Straight portion
Curved Structured Mesh along the curved portion
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

9. Meshing of total contour
Meshing of total contour with bullet (closer view)
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

10. Numerical Methodology
Basic Equation: Nutonian Fluid Equations
Bullet Velocity: 1350 ft/s
Mach Number: 1.21
Flow: Steady, Supersonic, Compressible and Inviscid
Inlet Boundary: Pressure 1 atm, Temperature 300k
Since the flow is supersonic compressible, a density-based algorithm was used for numerical solution.
Gravitational Effect is neglected
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

11. Post-processing analysis and Result
Pressure contour of the continuum and bullet
Stagnation Pressure: Pa
Bow Shock wave
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

12. Post-processing analysis and Result
Velocity contour of the continuum and bullet
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

13. Post-processing analysis and Result
Prandtl Mayer Expansion Fan process
In supersonic flows, expansion is achieved through an expansion fan called Prandtl Mayer Expansion Fan
Across the expansion fan, the flow accelerates (velocity increases) and the Mach number increases
Static pressure, Temperature and Density decrease
The leading edge of the object causes a shock and the trailing edge causes an expansion
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

14. Post-processing analysis and Result
Prandtl Mayer Expansion Fan process (Contd.)
Pressure Contour:
The angle through which the flow has turned by expansion fan process
Dramatic reduction in pressure
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

15. Post-processing analysis and Result
Prandtl Mayer Expansion Fan process (Contd.)
Velocity Contour:
The angle through which the flow has turned by expansion fan process
Flow accelerates in the same direction and through the same angle
(velocity increases)
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

16. Post-processing analysis and Result
Prandtl Mayer Expansion Fan process (Contd.)
Static Temperature of flow past the bullet profile
The angle through which the flow has turned by expansion fan process
Decrease in Temperature
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

17. Post-processing analysis and Result
Prandtl Mayer Expansion Fan process (Contd.)
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

18. Post-processing analysis and Result
Vortex:
It is the region in the flow where fluid is spinning about an imaginary axis
Wake:
It is region of disturbed flow at downstream
Pressure Drag:
Type of drag caused by difference in air pressure between the leading and trailing side of an object
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

19. Post-processing analysis and Result
Vortex, Wake and Pressure Drag
Vortex is formed
Small wake area: Due to parabolic geometry
Due to wake formation, pressure decreases to about Pa and velocity rises to about 300 to 380 m/s
Total drag coefficient was found to be , which indicates low-pressure drag due to small wake area
Streamline across the bullet
Vortex formation along the trailing edge of bullet
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

20. Post-processing analysis and Result Graphical Representation
Static pressure distribution on bullet surface
Velocity distribution across the bullet surface
This can be explained from Bernoulli’s Equation
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

21. Conclusion Bow shock wave Low pressure drag Small wake formation
High Stagnation Pressure
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

22. Further Recommendation
No gravitational effect has been considered
As Mach Number>1, it was assumed to be inviscid flow. No matter how fast the airflow is, there is always a viscosity effect. So, the results may be a little deviated from the actual one.
Further research on other types of bullets ( e.i sharp tip bullet, spherical tip bullet etc.) taking gravitational and viscous effect in consideration is recommended.
Numerical Simulation and aerodynamic characteristic analysis of a Paraboloid-tip Bullet

23. Thank You