1. Indian Institute of Space Science and Technology STUDY OF EFFECT OF GAS INJECTION OVER A TORPEDO ON FLOW-FIELD USING CFD

2. Study effects of gas injection over axisymmetric body representing a torpedo Mainly to reduce the viscous drag, increase performance Gas chosen was helium Computational results compared to experimental data of [1] Effects of free stream velocity an gas injection is studied Viscous drag reduced to 32% of original drag Aim

3. Torpedoes are under water missiles, axisymmetric bodies propelled by propeller, gas, jet or rocket fuel; based on requirements Drag on torpedo comprises of pressure drag and viscous drag Viscosity of air = 1.78X10 -5, Viscosity of water = 1.003X10 -3, water offers a very high viscous drag. Injecting air over surface of torpedo to remove water and reduce lower viscous drag thus improve performance in terms of payload ratio and reduction of drag. Limited experimental study done, no numerical studies performed till date. Introduction

4. 2D axisymmetric problem without gas injection 3D problem over a axisymmetric body without gas injection Gas injection over a flat plate including unsteadiness and buoyancy. Gas injection over a 3D axisymmetric body with gas injection (including unsteadiness and buoyancy) i.Effects of free stream velocity ii.Effects of flow rate of gas Methodology

5. A Spheroid is chosen for problem whose experimental data was available Reynolds number=1.3X10 6 based on the length of body (1.58 m) with water as fluid The Reynolds number is in transition, hence wall function effects on numerical scheme is also studied. Standard k-ε turbulent model used, wall functions were changed Axisymmetric body without gas injection Image taken form [5 ]

6. Standard wall functions: 11<y + <300, grid points=26341 Enhanced wall treatment: y + <5, grid points=32093 Axisymmetric body without gas injection y + >11.0 at wall, standard wall functions used y + =5.0, Enhanced wall treatment used, grid was made fine using adaptation in Fluent

7. Axisymmetric body without gas injection

8. Axisymmetric body without gas injection-Results C P distribution comparison Variation of skin friction co-efficient with length

9. Air injection over a flat plate Taken from [3] showing air captured in boundary layer

10. Viscous Layer needs to be resolved Enhanced wall treatment used with y + near the wall to be 5. Air injection over a flat plate- Numerical Study Domain used for numerical calculation, air injected normal to free stream Ratio of skin friction drag at free stream velocity-4.2m/s Ratio of skin friction drag at free stream velocity- 3.0 m/s

11. Injection method modified to in-stream, for better realization of problem Results close to theoretical values Air injection over a flat plate- Modified injection method Introduction of step near plate for air inlet, step height=0.004m Ratio of skin friction drags at 4.2 m/s with air injection with introduction of step at leading edge of plate Ratio of skin friction drag at free stream velocity- 4.2m/s

12.  Results compared with experimental data of [1].  Results available for 4.6, 7.6, 10.7 and 16.8 m/s with flow rate varying from 0.001 m 3 /s to 0.009 m 3 /s.  Numerical study done for 10.7 and 16.8 m/s with same flow rates of gas; further study was extended to 30 and 40 m/s.  High Reynolds number, above 10 7 bases on length of body, so standard k-ε with standard wall functions used. 3D axisymmetric body with gas injection Schematic of body taken in experiment[1] and numerical simulation Axisymmetric view of the 3D mesh made

13. y + >11, Number of grid points = 18,60,000 – 38,46,000

14. 3D axisymmetric body with gas injection Effect of flow rate Free stream velocity=10.7 m/s, flow rate of gas=0.006 m 3 /s Free stream velocity=16.8 m/s, flow rate of gas=0.006 m 3 /s 0.004 m 3 /s 0.006 m 3 /s0.008 m 3 /s 0.005 m 3 /s 16.8 m/s

15. Effects of free stream velocity Buoyancy effects will be predominant at lower free stream velocity, hence flow will be highly unsymmetrical Higher free stream velocities flow will be more towards symmetrical, less gas shall escape, hence more drag reduction. Results within error bars with experiment for flow rate of gas above 0.004 m 3 /s. 3D axisymmetric body with gas injection

16. Contours of volume fraction of gas (Helium), free stream velocity =10.7 m/s, flow rate of gas=0.006m 3 /s Contours of volume fraction of gas (Helium), free stream velocity=40 m/s, flow rate of gas=0.006m 3 /s Contours of volume fraction of gas (Helium), free stream velocity=30 m/s, flow rate of gas=0.006m 3 /s Contour of volume fraction of gas (Helium), free stream velocity=16.8 m/s, flow rate of gas=0.006m 3 /s 10.7 m/s 16.8 m/s 30 m/s40 m/s Flow rates (m 3 /s) Skin friction drag ratio 10.710.7 –Exp.[1]16.816.8 Exp. [1]3040 0.0020.4140.60.440.8-- 0.0040.3430.40.3370.5-- 0.0050.35 0.3270.35-- 0.0060.3370.325 0.340.32 0.0080.3350.3250.3230.3-- Variation of skin friction drag ratio with free stream velocity

17. Contours of volume fraction of gas (Helium), free stream velocity =10.7 m/s, flow rate of gas=0.006m 3 /s Pathlines of gas (Helium), free stream velocity=10.7 m/s, flow rate of gas=0.006m 3 /s Contours of volume fraction of gas (Helium), free stream velocity=40 m/s, flow rate of gas=0.006m 3 /s Pathlines of gas (Helium), free stream velocity=40 m/s, flow rate of gas=0.006m 3 /s 10.7 m/s 40 m/s

18. Free stream velocity-10.7 m/s, flow rate=0.006 m 3 /s

19. Free stream velocity-30 m/s, flow rate=0.006 m 3 /s

20. Yu-7 torpedo (China) ET-52 (China) APR-3E (Russia, China, India) A244-S (India) Length (m)2.6 3.6852.8 Diameter (m)0.324 0.3500.324 Range (km)>7.36>36 Top speed (m/s)25.72162220 Fuel typeOtto fuel IIElectricSolid propellant- Warhead (kg)453474- Total weight (kg) 235 525244 3D axisymmetric body with gas injection Applicability and Advantage

21. 3D axisymmetric body with gas injection

22. Applicability and advantage- Energy The energy can be used to increase the mass of payload (for torpedo it is explosives). If the torpedo is driven by consumable fuel (liquid fuels, solid propellant); then energy needed is directly proportional to mass of fuel. 3D axisymmetric body with gas injection Quantities Without Helium injection With Helium injection (flow rate -0.006m 3 /s) % Reduction Pressure drag (N)197.60167.7815 Skin friction drag (N)224. 3272.867.5 Total drag (N)421.92240.5843 Power required (kW)12.6577.217 + 0.8473236 Energy Required (kJ)21141205 +14036

23. Applicability and Advantage- Velocity Velocity obtained is more in the case of injection of gas, for same power required 3D axisymmetric body with gas injection

24. Multiphase flows that flow pattern depends strongly on gravity and free stream velocity. Flow patterns were unsymmetrical for lower free-stream velocities (10.7 m/s) and turned more likely towards symmetrical ones for higher free stream velocities (30 m/s and 40 m/s) Viscous drag reduction becomes a weak function of flow rate of gas i.e. after 0.0045 m 3 Marginal reduction in drag was observed with increase in free stream velocity Power reduction (total drag and power required for pumping helium considered ) becomes effective after velocity = 20 m/s Conclusions

25. Take more realistic problem of torpedo (Range, geometric Dimensions, fuels) and then study the effects of gas injection Extend the study towards more higher speeds 60-100 m/s Future Scope

26. 1.Deutsch, S and Castano, J, “Microbubble Skin Friction Reduction on Axisymmetric Body”, Physics of Fluids, 29,3590, 1986 2.Jerome, S P and Raymond E G, “Shaping of Axisymmetric Bodies for Minimum Drag in Incompressible Flow” Journal of Hydronautics, 8, 3, pp.100-107, 1974 3.Jing-Fa Tsai and Chi-Chuan Chen, “Boundary Layer Mixture Model for a Microbubble Drag Reduction Technique”, International Scholarly Research Network, Mechanical Engineering, 405701, 2011 4.Madavan, N K, Deutsch, S and Castano, J “Reduction of turbulent skin friction by microbubbles”, Physics of Fluids, 27,356, 1984 5.Patel, V C, Nakayama, A and Damian, R, “Measurements in the thick axisymmetric turbulent boundary layer”, J. Fluid Mech., 63, 2 pp. 345-367, 1974 6.Sinnarwalla, A M and Sundaram, T R, “Lift and Drag Effects Due to Polymer Injections on a Symmetric Hydrofoil”, Journal of Hydronautics, 12, pp. 71-77, 1978. References

27. Thank you…

28. Back up-Residuals Constant drag after some iteration, obtained for multiphase flow over flat plate Oscillating drag component, obtained for multiphase flow over axisymmetric body, the drag change is also less Residuals became constant after some iteration, obtained from multiphase flow over axisymmetric body

29. Back up-Original drag

30. y+y+ Grid pointsPressure drag % Difference Viscous drag % Difference ~25190875111.443215.9138 ~15210857411.403670.34555.85231.04 ~11229737511.374580.2555.836070.277 Back up-grid convergence 10.7 m/s, 0.004 m 3 /s

31.  Vapour pressure of water at 25 0 C = 3200 Pa Back up-Cavitation