International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) ISSN(P): 2249-6890; ISSN(E): 2249-8001 Vol. 4, Issue 3, Jun 2014, 61-70 TJPRC Pvt. Ltd. NUMERICAL STUDY ON EFFECT OF NOSE ECCENTRICITY ON PENETRATOR PERFORMANCE TUKARAMAPPA P. HADADI 1, GIRISH D. P. 2 & K. PRAHLADA RAOC 3 1 Project Lead-CFD, CSM Software Pvt. Ltd, Bangalore, Karnataka, India 2 Professor, Department of Mechanical Engineering, Government Engineering College,Ramanagara, Karnataka, India 3 Vice Principal & Professor, Department of Mechanical Engineering, JNT University Anantapur, Andhra Pradesh, India ABSTRACT The objective of this work is to study the effect of nose eccentricity on penetrator performance by 3-D Computational Fluid Dynamics (CFD) using commercially available software. The conical nose shaped penetrator was simulated for different eccentricity ranging from 0.3 to 0.9 mm in steps of 0.1mm. The penetrator was meshed with tetrahedral shaped elements with six prism layers of size 0.05 to 1mm spacing. An unstructured hybrid mesh is generated for this analysis. Analysis is carried out with boundary conditions of pressure at one atmosphere; static temperature of 288K, with turbulence model k-omega, and for different velocity ranges (1.2-1.8 Mach number) of air was applied to the penetrator. The results show that location 3 subjected to minimum velocity and maximum pressure due to sudden variation of area irrespective of eccentricity. The increase in eccentricity of the penetrator nose causes more variation in pressure and velocity on penetrator body hence there is instability in the penetrator. The 0.9mm eccentricity shows maximum difference of pressure of 26kPa and difference of velocity of 7m/s throughout the structure which leads to the instability of penetrator during flight condition. KEYWORDS: Computational Fluid Dynamics, Mach Number, Penetrator, Nose Eccentricity 1. INTRODUCTION In the last two decades, the progress made in the optimization of penetrator has completely renewed for their accuracy to reach the target [1]. In these aspects many researchers worked on shape optimization of penetrator using different parameters such as speed of penetrator [2-3], variable geometry [4], different climatic conditions such as air density, temperature, pressure and humidity [5]. Further research works are focused on three-dimensional impactors [6-10], where the problems of shape optimization were investigated. Further research focused on the improvement in aerodynamic stability at higher speed in different environmental impact [11]. More recently, bodies of revolution were considered applying the criterion of the maximum depth of penetration [12-13]. All researchers worked on effect of external parameters on impact performance but as per authors knowledge none of the work is focused on internal parameters i.e. shape eccentricity, manufacturing defects, pits, etc. The defects influence on performance of penetrator. Defects in nose geometry to cause a projectile bending, yawing and break when it strikes target usually at very high velocity [14-15]. www.tjprc.org editor@tjprc.org
62 Tukaramappa P. Hadadi, Girish D. P. & K. Prahlada Raoc The objective of the work was to investigate the effect of nose eccentricity on performance such as speed variation on different location, pressure variation, air density and temperature of penetrator using computational fluid dynamics. A 3D model of a conical penetrator is shown in Figure 1. Figure 1: 3D Model of a Conical Penetrator 2. COMPUTATIONAL METHODOLOGY 2.1 Model Geometry Specifications The geometry model consisting of sharp cone, cylindrical fuselage and fins. The outer diameter (D) of the cylindrical fuselage is 50 mm and its length is of 6D. The length of cone and fins is of 4D and 2D respectively. Commercial CFD software CFX is used for simulation. Figure 2: Domain and Mesh As the free stream flow is supersonic, the inlet and outlet flow domains are taken as 5 times the total length of the projectile from the nose tip and tail end respectively. The upper and lower flow domains are taken 5 times the diameter of the cylindrical fuselage above and below the center of the penetrator. Right and left flow domains are also taken 5 times the diameter of the cylindrical fuselage from the center of the penetrator. Generation of coarse and fine mesh around the body of the conical penetrator specifies the surfaces for which meshing parameters are to be defined. Grids are made very fine in the nose of conical region to capture the complex flow features of the flow field. In the simulation, x- axis is taken along the longitudinal direction from the nose of the conical penetrator. While y-axis is along the normal direction of the penetrator and z axis is along the lateral direction of the penetrator as shown in Figure 2. 2.2 Computational Grid The geometry and unstructured mesh were generated using Ansys ICEM CFD, a geometry and grid preprocessor supplied with the CFX software suite. A full, three-dimensional (3-D) mesh was required to simulate the effect of aerodynamic properties. In generating the meshes, has the capability to produce structured and unstructured tetrahedral Octree Mesh having a total number of elements - 979777, surface mesh setup at the inlet and outlet has minimum and maximum size of 0.1mm and 30mm respectively and total number of elements at inlet and outlet area is 1158 and 1148 respectively. Penetrator eccentricity has a minimum size of 0.05mm, at the defect region having very fine sizes. Impact Factor (JCC): 5.3403 Index Copernicus Value (ICV): 3.0
Numerical Study on Effect of Nose Eccentricity on Penetrator Performance 63 Penetrator which is having a maximum element size 3mm, The unstructured mesh is generated by using Octree method. A hybrid mesh is generated by crating prism layers. Prisms with 0.05mm to 1mm thick layer with 6 numbers are generated around the geometry. Figure 3 shows the section of hybrid mesh. Figure 3: Enlarged View of Mesh Generated Prism Layer on the Body of Conical Penetrator Tetra meshing is not efficient for capturing shear or boundary layer physics. Prism mesh efficiently captures these effects near the surface to determine the aerodynamic properties over the penetrator. This efficiently allows for better resolution of the solution normal to the surface, without increasing the number of elements along the surface. This gives you a quicker and more accurate solution than a very fine tetra mesh. Computational domains of hybrid mesh is import to preprocessor, and create the domain type- fluid domain, material- air ideal gas because of supersonic flow, fluid model has heat transfer- total energy, K-Omega turbulence model. The standard k-omega model results used for determining the aerodynamic properties. The inlet velocity it is of supersonic flow varied from 1.2 to 1.8 Mach number, The problem was setup for the standard atmospheric conditions with static temperature 288 K and solver control has basic setting of advection upwind scheme for forward difference (First-order upwind is available in the pressure-based and density-based solvers), convergence criteria is taken for 1E-6. The output results are extracted after complete convergence of problem. Different Simulations are carried out for eccentricity (a probable defect) from 0.3 to 1mm. Postprocessor visualize of the aero dynamic flow properties. Figure 4: Variation in Eccentricity of 0.5mm 3. RESULTS AND DISCUSSIONS Figure 5 shows effect of aerodynamic velocity on the eccentric penetrator performance at different locations for different speeds of 400, 500, and 600 m/s. www.tjprc.org editor@tjprc.org
64 Tukaramappa P. Hadadi, Girish D. P. & K. Prahlada Raoc Figure 5: Velocity Contours for 400, 500 and 600 m/s In conical eccentric shape penetrator shows almost (linear velocity) equal to wind velocity at the tip of the penetrator and maximum at fillet joining between slope of geometry and cylindrical rod also at presence of defect, like eccentricity, and uniform velocity on cylindrical surface of the domain. Similar ratio can be seen for other velocities of penetrator. Graph-1 shows the result of aerodynamic velocity for 0 (symmetric), 0.3, 0.6 and 0.9 mm eccentricity. The simulation summary of velocity distribution along different location can be classified in two groups a) velocity distribution is almost same from section 1 to section 7. In second region the sudden drop of velocity can be observed. The all graphs show the same trend but speed of air on different location is changes as per velocity of the air. In all cases the velocity of air trend can be seen the same nature. Graph 1: Comparison of Velocity Distribution at Different Locations for 0.0, 0.3, 0.6 and 0.9 mm Eccentricity Impact Factor (JCC): 5.3403 Index Copernicus Value (ICV): 3.0
Numerical Study on Effect of Nose Eccentricity on Penetrator Performance 65 Graph 2: Comparison of Pressure Distribution at Different Locations for Different Eccentricities Graph-2 shows the result of aerodynamic pressure for 0 (symmetric), 0.3, 0.6 and 0.9 mm eccentricity. The simulation outline of pressure distribution at different location can be classified in five groups. a) Sudden increasing in pressure distribution from section 1 to section 2 for the geometry but the maximum variation can be observed in 0.3mm eccentricity for speeds of 400, 500, and 600m/s. In second region the sudden drop of pressure can be observed for eccentric geometry compared to symmetry penetrator for 400m/s and slight increasing in pressure for 500, and 600m/s until at location 4. Sudden increasing in pressure (from cylindrical portion to starting point of fins) from location 4 5 reaches peak value for speeds 500m/s and 600m/s, but a slight increasing in pressure can be observed for a speed 400m/s. There is a linear and sudden decreasing in pressure distribution from extended fins to the back end of penetrator for all the velocities. All graphs show the same trend but aerodynamic pressure on different location is changes as per velocity of the air. In all cases the velocity of air trend can be seen the slight different nature. Graph-3 shows the result of aerodynamic density for 0 (symmetric), 0.3, 0.6 and 0.9 mm eccentricity. The simulation summary of density distribution along different location can be classified in five groups. Graph 3: Comparison of Density Distribution at Different Locations for Different Eccentricities www.tjprc.org editor@tjprc.org
66 Tukaramappa P. Hadadi, Girish D. P. & K. Prahlada Raoc Sudden increasing in density distribution from section 1 to section 2 for the geometry but the maximum variation can be observed in 0.3mm eccentricity for 400, 500, and 600m/s. In second region the sudden drop of density can be observed for eccentric geometry compared to symmetry penetrator for 400m/s and remains unchanged for 500, and 600m/s until at location 4. Sudden increasing in density (from cylindrical portion to starting point of fins) from location 4 5 reaches maximum value for 500m/s and 600m/s, but for 400m/s remains constant density. There is a linear and sudden decreasing in density distribution from extended fins to the back end of penetrator for all the velocities. All graphs show the same trend but aerodynamic density on different location is changes as per velocity of the air. In all cases the velocity of air trend can be seen the slight different nature. Graph 4: Comparison of Temperature Distribution at Different Locations for Different Eccentricities Graph 5: Comparison of Velocity Distribution at Different Locations from Different Eccentricities Graph-4 shows the result of aerodynamic temperature for 0 (symmetric), 0.3, 0.6 and 0.9 mm eccentricity. The simulation review of temperature distribution along different location can be classified in two groups. a) The temperature distribution is almost same from section 1 to section 7. In second region the sudden increasing of temperature can be observed. The all graphs show the same trend but temperature on different location is changes as per velocity of the air. In all cases the velocity of air trend can be seen the same nature. Impact Factor (JCC): 5.3403 Index Copernicus Value (ICV): 3.0
Numerical Study on Effect of Nose Eccentricity on Penetrator Performance 67 At the tip of conical shape of penetrator has temperature less than the atmospheric temperature. In the above simulation it shows not much variation in temperature for symmetric and eccentric geometry penetrator. Graph-5 shows the comparison results of aerodynamic velocity on the eccentric penetrator for 0.0 (symmetric), and 0.3 to 0.9 mm with varying step 0.1mm eccentricity performance at different locations for 400, 500, 600 m/s. In graph-5, at the tip of the symmetrical conical geometry penetrator shows higher velocity of 482m/s, but for defects like eccentricity penetrator shows lower velocity as compare to symmetric geometry locations as 478m/s for 400m/s. As the velocity increase for 500 and 600m/s for symmetric penetrator have aerodynamic velocity at the tip of the penetrator reaches 605m/s and 716m/s respectively, at the same location for the defects shape shows variation like 609m/s and 723m/s respectively. At location 2 its shows not much variation in aerodynamic velocity for defect shape for 400m/s, as the velocity increases for 500m/s and 600m/s it shows difference of 4 and 10m/s for normal and defected one respectively. At location 3 shows a maximum variation due to change in geometry from conical to cylinder with the defect for 500m/s, at location 5 decreasing in velocity due to presence of fins for symmetric but its increase for eccentricity for 400m/s. In graph-6, at the tip of the symmetrical conical geometry penetrator shows aerodynamic pressure of 11428pa, but for defects like eccentricity penetrator shows higher pressure as compare to symmetric geometry location 1 as average of 16200pa for 400m/s. As the velocity increase for 500 & 600m/s for symmetric penetrator have aerodynamic pressure at the tip of the penetrator creates negative pressure at location 1 for 500m/s and at location 1 & 2 for 600m/s respectively, At location 2 its shows much difference (average 7kpa) in aerodynamic pressure for defect shape for 400m/s and 500m/s, as the velocity increases for 600m/s it shows difference (average 4kpa) for normal and defected one respectively. At location 3 shows a maximum variation of average 12kpa due to change in geometry from conical to cylinder with the defect for 500m/s, no change in pressure at location 5 for all the geometry for 400, 500, & 600m/s. at the end of the fin sudden decreasing in pressure found difference in pressure at location 7 for 500m/s and 600m/s. In location 8 at the back end of penetrator is vacuum is created for all the geometry and for all velocities. Graph 6: Comparison of Pressure Distribution at Different Locations from 0, 0.3 to 0.9mm Eccentricity www.tjprc.org editor@tjprc.org
68 Tukaramappa P. Hadadi, Girish D. P. & K. Prahlada Raoc In graph-7 at the front end of the symmetrical conical geometry penetrator shows aerodynamic density of 1.558kg/m3, but for defects like eccentricity penetrator shows higher density as compare to symmetric geometry location 1 as average of 1.61kg/m3 for 400m/s. As the velocity increase for 500 and 600m/s for symmetric penetrator have aerodynamic density difference of 0.02 and 0.05kg/m3 at the tip of the penetrator at location 1 for 500m/s and 600m/s respectively. Graph 7: Comparison of Density distribution at Different Locations from 0, 0.3 to 0.9 mm Eccentricity. At location 2 its shows much difference (average 0.11kg/m3) in aerodynamic density for defect shape for 400m/s and 500m/s, as the velocity increases for 600m/s it shows difference (average 0.07kg/m3) for normal and defected one respectively. At location 3 shows a maximum variation of average 0.135kg/m3 due to change in geometry from conical to cylinder with the defect for 500m/s, no change in density at location 5 for all the geometry for 400, 500, and 600m/s. at the end of the fin sudden decreasing in density found difference in pressure at location 7 for 500m/s and 600m/s. In location 8 at the back end of penetrator is vacuum is created for all the geometry and for all velocities. Graph 8: Comparison of Temperature Distribution at Different Locations from 0, 0.3 to 0.9 mm Eccentricity Impact Factor (JCC): 5.3403 Index Copernicus Value (ICV): 3.0
Numerical Study on Effect of Nose Eccentricity on Penetrator Performance 69 At the tip of conical shape of penetrator has temperature less than the atmospheric temperature ice formation at the tip of the penetrator as it goes above 340m/s. In the above simulation summary it shows not much variation in temperature except location 3, 5 and 7 for symmetric and eccentric geometry penetrator. 4. CONCLUSIONS The CFD analysis is carried out to study the effect of nose eccentricity on the penetrator performance. The simulation results show the effect of aerodynamic velocity, pressure, density and temperature on the eccentric penetrator at different locations for 400, 500, 600 m/s. The results show that location 3 subjected to minimum velocity, maximum pressure and increase in temperature for velocity 500 and 600m/s, also at location 2 as maximum pressure and density for 400m/s, due to sudden variation of area irrespective of eccentricity. The 0.4 and 0.9mm eccentricity shows maximum difference of pressure of 22kPa and 26kPa difference of velocity of 5m/s and 7m/s respectively throughout structure which leads to instability of penetrator during flight condition. The increase in eccentricity of the penetrator nose causes more variation in pressure and velocity on penetrator body hence there is instability in penetrator. Defects in nose geometry cause a penetrator to bend, to yaw, or may not be able to reach the target. A penetrator may break due to this defect before it reaches the target. 5. REFERENCES 1. Ben-Dor G, Dubinsky A, Elperin T. Shape optimization of penetrator nose. Theor Appl Fract Mech; 35:261-70, 2001. 2. Bunimovich AI, Yakunina GE. The shapes of three dimensional minimum-resistance bodies moving in compressible plastic and elastic media. Moscow Univ Mech Bull; 42:59 62, 1987. 3. Yankilevsky DZ. The optimal shape of an earth penetrating projectile. Int J Solids Struct; 19:25 31,1983; 4. Hiroaki Kobayash and Yasuke Maru, study on variable-shape supersonic inlets and missiles with MRD device science direct, 2007. 5. Ostapenko NA, Yakunina GE. Least-drag bodies moving in media subject to locality hypothesis. Fluid Dyn 27: 71 80, 1992;. 6. Din[6] Vedernikov YA, Shchepanovsly VA. Optimization of real gas dynamic systems. Novosibirsk: Nauka; 1995. 7. Ostapenko NA, Romanchenko VL, Yakunina GE. Optimum forms of three-dimensional bodies for penetration of dense media. J Appl Mech Tech Phys; 4:515 21, 1994. 8. Ostapenko NA, Yakunina GE. The shape of slender threedimensional bodies with maximum depth of penetration into dense media. J Appl Math Mech; 63:953 67, 1999. 9. Yakunina GE. The construction of three-dimensional shapes within the framework of a model of local interaction. J Appl Math Mech; 64:289 98, 2000. 10. Yakunina GE. On body shapes providing maximum penetration depth in dense media. Doklady Phys; 46:140 3, 2001. www.tjprc.org editor@tjprc.org
70 Tukaramappa P. Hadadi, Girish D. P. & K. Prahlada Raoc 11. Hiroaki Kobayash and Yasuke Maru, Motoyuki Hongoh, Shinsuke Takeuchi, keiichi okai,, study on variable-shape supersonic inlets and missiles with MRD device science direct, 2007. 12. Jones SJ, Rule WK, Jerome DM, Klug RT. On the optimal nose geometry for a rigid penetrator. Computat Mech; 22:413 7, 1998. 13. Jones SJ, Rule WK. On the optimal nose geometry for a rigid penetrator, including the effects of pressure-dependent friction. Int J Impact Eng; 24:403 15.2000. 14. Bunimovich AI, Yakunina GE. On the shape of minimumresistance solids of revolution moving in plastically compressible and elastic plastic media. J Appl Math Mech; 51:386 92, 1987. 15. Bunimovich AI, Yakunina GE. On the shape of a minimum resistance solid of rotation penetrating into plastically compressible media without detachment. J Appl Math Mech; 53:380 6831989 Impact Factor (JCC): 5.3403 Index Copernicus Value (ICV): 3.0