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Finite element analysis of the flow around a 155mm caliber projectile in

transonic regime.

Peter ŠKORVAGA

pskorvaga@gmail.com

January 2012

Abstract

This article analyzes velocity, pressure and Mach number distribution of a projectile with 155 mm

caliber in transonic regime. Results of this short study will be used in further research together with

the next study of tubular projectile flow analysis for the development of the new semitubular

projectile.

Keywords: finite element method (FEM), computational fluid dynamics (CFD), projectile, velocity,

pressure, Mach number, Drag Coefficient, ANSYS Workbench CFX.

Introduction

For this kind of analysis the projectile M549 was chosen. The M549 is a standard 155 mm caliber

artillery shell. The M549A1 Rocket Assisted Projectile was developed to provide extended range for

standard and developmental howitzers. The projectile has two distinctive preassembled

components--the high explosive warhead and the rocket motor. The warhead is fabricated from high

fragmentation steel for increased effectiveness and contains a bulk-filled explosive. Currently there

are two models. The M549 contains 16 pounds of Composition B and is restricted from use with the

new top Zone 8S M203 Propelling Charge. To assure compliance with safety requirements in newer

weapon systems, which are capable of using the M203 Propelling Charge, a conversion to TNT fill in

lieu of Composition B was introduced in September 1977 with Type Classification of the M549A1. The

M549A1 contains about 15 pounds of TNT [1]. Geometrical parameters of this 155 mm caliber

projectile are displayed in Figure 1 [2].

FE model

In this analysis the model is divided in two identical parts. The whole solution is performed as a

symmetric problem. The projectile was modeled in Catia V5R16 using dimensions from Figure 1 and

subtracted from the ambient fluid model with Boolean’s operation (Figure 2 and 3). This 3D solid

model represents the ambient fluid volume around the projectile. In order to use the Catia model in

ANSYS Workbench, it was converted to Parasolid .x_t file. Parameters of the meshed model are given

in Table 1 and generated mesh is shown in Figure 4.

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Sizing

Use Advanced Size Function On: Curvature

Relevance Center Medium

Smoothing Medium

Span Angle Center Fine

Curvature Normal Angle 10°

Min Size 2.0 mm

Max Face Size 150 mm

Max Size 150 mm

Growth Rate 1.20

Minimum Edge length 13.640 mm

Inflation

Inflation Option Smooth Transition

Transition Ratio 0.77

Maximum Layers 5

Growth rate 1.20

Statistics

Nodes 39059

Elements 212394

Table 1. Mesh Parameters

Figure 1. Geometrical parameters of the M549 Projectile [2]

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Figure 4. Generated Mesh in ANSYS Workbench CFX

Figure 2. Simplified 3D Model in Catia V5R16

Figure 3. Final fluid volume model for symmetry condition

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Analysis set-up

The simulation is arranged in following domains:

Default Domain – Basic Settings: Fluid Domain, Material is set to Air Ideal Gas, Reference Pressure is

1 atm, Buoyancy Model is set to Non Buoyant. Fluid Models: Heat Transfer Option is set to Total

Energy, Viscous Work Term is enabled, Turbulence Option is set to Shear Stress Transport.

Inlet – Basic Settings: The front plane of the volume model is selected as the Location, Boundary Type

is set to Inlet. Boundary Details: Flow regime is set to subsonic/supersonic (depending on velocity),

Mass And Momentum Option is set to Cartesian Velocity or Cartesian velocity & Pressure (depending

on velocity) and V-velocity vector is set to represent the correct projectile velocity (0.9 – 1.4 Mach) in

y-direction, Relative Static Pressure is set to 0 Pa (in Supersonic option), Turbulence Option is set to

Medium, Heat Transfer Option is set to Static Temperature and value of the Temperature is set to

293 K.

Outlet – Basic Settings: The rear plane of the volume model is selected as the Location, Boundary

Type is set to Outlet. Boundary Details are set as the same as on Inlet Domain.

Projectile – Basic Settings: The 7 surfaces representing the projectile boundaries are selected.

Boundary Type is set to Wall. Boundary Details: Mass And Momentum Option is set to No Slip Wall,

Wall Roughness Option is set to Smooth Wall.

Symmetry – Basic Settings: The symmetry plane is selected as the Location, Boundary Type is set to

Symmetry.

Wall – Basic Settings: The outer cylindrical surface of the volume model is selected as Location,

Boundary Type is set to Wall, Boundary Details are set as the same as on the projectile.

The Solver:

Solver Control – Basic Settings: Convergence Control is set from 1 to 100 Iterations. Fluid Timescale

Control is set to Auto time Scale and Length Scale Option is set to Conservative, Time Scale Factor is

set to 1.0, Convergence Criteria Residual Type is set to RMS and Residual Target is set to 1e-4.

Expert Parameters – Convergence Control: High Speed Models max continuity loop option is enabled

and value is set to 1.

For better illustration Figure 5 shows the domain setup with Inlet, Outlet domains (black arrows) and

the Symmetry plane (red triangle symbols).

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Results

After the successful completion of the solution process, following results are displayed in set of

figures below. Figures 6 – 13 are showing the Mach Number Contours at different velocities from

Mach 0.9 to Mach 1.4.

Figure 6. Mach Nubmer contours at Mach 0.90

Figure 5. Domain setup in ANSYS Workbench CFX

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Figure 9. Mach Nubmer contours at Mach 1.05

Figure 8. Mach Nubmer contours at Mach 1.00

Figure 7. Mach Nubmer contours at Mach 0.95

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Figure 12. Mach Nubmer contours at Mach 1.30

Figure 11. Mach Nubmer contours at Mach 1.20

Figure 10. Mach Nubmer contours at Mach 1.10

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Next set of Figures shows the Pressure Contours (Reference Pressure is set to 0 Pa).

Figure 15. Pressure contours at Mach 0.95

Figure 14. Pressure contours at Mach 0.90

Figure 13. Mach Nubmer contours at Mach 1.40

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Figure 18. Pressure contours at Mach 1.10

Figure 17. Pressure contours at Mach 1.05

Figure 16. Pressure contours at Mach 1.00

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Figure 21. Pressure contours at Mach 1.40

Figure 20. Pressure contours at Mach 1.30

Figure 19. Pressure contours at Mach 1.20

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Finally the velocity vectors are presented in following Figures.

Figure 24. Velocity vectors at Mach 1.00

Figure 23. Velocity vectors at Mach 0.95

Figure 22. Velocity vectors at Mach 0.90

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Figure 27. Velocity vectors at Mach 1.20

Figure 26. Velocity vectors at Mach 1.10

Figure 25. Velocity vectors at Mach 1.05

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The resulting drag forces calculated in ANSYS CFX Postprocessor were converted to the drag

coefficients for each computed velocity. Total Drag Coefficient depending on Mach Number is shown

in Figure 30. Compared to the results presented in Figure 31 [2], there is a difference of 16% at Mach

0.9, at Mach 1.0 the results are almost identical, at Mach 1.2 is the difference about 3% and at Mach

1.4 the values are almost identical.

Figure 29. Velocity vectors at Mach 1.40

Figure 28. Velocity vectors at Mach 1.30

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Conclusion

The main objective of this study, which was the drag computation and flow analysis, was

accomplished. Results of this work, together with other studies data, will be used in further research

in order to provide the comparison to the developed semitubular and tubular projectile design.

References

[1] http://www.globalsecurity.org/military/systems/munitions/m549a1.htm

[2] Sahu, J., Drag predictions for projectiles at transonic and supersonic speeds, US Army Ballistics

Research Laboratory, Aberdeen Proving Ground, MD, BRL-MR-3523, 1986.

[3] ANSYS, Inc., ANSYS CFX Introduction Release 12.1, 2009.

[4] ANSYS, Inc., ANSYS CFX Tutorials Release 13.0, 2010.

Figure 31. Total Drag Coefficient dependence on Mach Number [2]

Figure 30. Total Drag Coefficient dependence on Mach Number