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http://dx.doi.org/10.3744/SNAK.2014.51.5.435

A Numerical Analysis of Gravity and Free Surface Effects on a Two-Dimensional Supercavitating Flow  

Kim, Hyoung-Tae (Department of Naval Architecture & Ocean Engineering, Chungnam National University)
Lee, Hyun-Bae (Department of Naval Architecture & Ocean Engineering, Chungnam National University)
Publication Information
Journal of the Society of Naval Architects of Korea / v.51, no.5, 2014 , pp. 435-449 More about this Journal
Abstract
The effects of the gravity field and the free surface on the cavity shape and the drag are investigated through a numerical analysis for the steady supercavitating flow past a simple two-dimensional body underneath the free surface. The continuity and the RANS equations are numerically solved for an incompressible fluid using a $k-{\epsilon}$ turbulence model and a mixture fluid model has been applied for calculating the multiphase flow of air, water and vapor using the method of volume of fluid and the Schnerr-Sauer cavitation model. Numerical solutions have been obtained for the supercavitating flow about a two-dimensional $30^{\circ}$ wedge in wide range of depths of submergence and inflow velocities. The results are presented for the cavity shape, especially the length and the width, and the drag of the wedge in comparison with those of the case for the infinite fluid flow neglecting the gravity and the free surface. The influences of the gravity field and the free surface on the aforementioned quantities are discussed. The length and the width of the supercavity are reduced and the centerline of the cavity rises toward the free surface due to the effects of the gravity field and the free surface. The drag coefficient of the wedge, however, is about the same except for shallow depths of submergence. As the supercavitating wedge is approaching very close to the free surface, it is found the length and the width of a cavity are shorten even though the cavitation number is reduced. Also the present result suggests that, under the influence of the gravity field and the free surface, the length of the supercavity for a certain cavitation number varies and moreover is proportional to the inverse of the submergence depth Froude number.
Keywords
Supercavitating flows; Free surface effect; Froude No.; Cavity; Drag;
Citations & Related Records
Times Cited By KSCI : 6  (Citation Analysis)
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1 Nesteruk, I., 2008. Hull optimization for high-speed vehicles: supercavitating and unseparated shapes. SuperFAST'2008, St. Petersburg, Russia, July 2-4, 2008, pp.1-15
2 Newman, J.N., 1977. Marine Hydrodynamics. M.I.T: Massachusetts.
3 Plesset, M.S. & Shaffer, Jr.P.A., 1948. Cavity Drag in Two and Three Dimensions. Journal of Applied Physics. 19, pp.934-939.   DOI
4 Passandideh-Farda, M. & Roohi, E., 2008. Transient Simulations of Cavitating Flows using a Modified Volume-of-Fluid (VOF) Technique. International Journal of Computational Fluid Dynamics, 22(1-2), pp.97-114.   DOI   ScienceOn
5 Peng, X. Wang, Z. Pan, S. & Yan, K., 2006. Generation Mechanism of Ventilated Supercavitation in an Axisymmetric Body with Cavitator. 6th Int'l Symposium on Cavitation, CAV2006, Wageningen, Netherlands.
6 Petitpas, F. Saurel, R. Ahn. B.K. & Ko, S., 2011. Modeling Cavitating Flow around Underwater Missiles. International Journal of Naval Architecture and Ocean Engineering, 3(4), pp.263-273.   DOI   ScienceOn
7 Rabiee, A. Alishahi, M.M. Emdad, H. & Saranjam, B., 2011. Part A: Experimental Investigation of Unsteady Supercavitating Flows. IJST, Transactions of Mechanical Engineering, 35(M1), pp.15-29.
8 Rabiee, A. Alishahi, M.M. Emdad, H. & Saranjam, B., 2011. Part B: Numerical Investigation of Unsteady Supercavitating Flows. IJST, Transactions of Mechanical Engineering, 35(M1), pp.31-46.
9 Reichardt, H., 1946. The laws of cavitation bubbles at axially symmetric bodies in a flow. Ministry of Aircraft Production Volkenrode, MAP-VG, Reports and Translations 766. Office of Naval Research.
10 Riabouchinsky, D., 1919. On Steady Fluid Motion with Free Surface. Proceedings London Mathematical Society. 19, pp.206-215.
11 Birkhoff, G. Plesset, M.S. & Simmons, N., 1950. Wall Effects in Cavity Flow. Part. I. Quarterly of Applied Mathematics, 8, pp.151-168.
12 Ahn, B.K. Lee, C.S. & Kim, H.T., 2010. Experimental and Numerical Studies on Super-Cavitating Flow of Axisymmetric Cavitators. International Journal of Naval Architecture and Ocean Engineering, 2(1), pp.39-44.   과학기술학회마을   DOI   ScienceOn
13 Ahn, B.K. Lee, T.K. Kim, H.T. & Lee, C.S., 2012. Experimental Investigation of Supercavitating Flows. International Journal of Naval Architecture and Ocean Engineering, 4(2), pp.123-131.   과학기술학회마을   DOI   ScienceOn
14 Alynak, E. Venkayya, V. Grandhi, R. & Penmesta, R., 2004. Variable shape cavitator design for a supercavitating torpedo. 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, New York, USA, 30 August-1 September 2004, pp.1373-1398.
15 Anderson, R.F., 1953. The correlation of axi-symmetric cavity dat for design use. NAVORD TM No. 1288, July 1953.
16 Armstrong, A. H. 1954 Drag coefficients of wedges and cones in cavity flow. Armament Research Establishment, Report 21/54. Ft. Halstead.
17 Birkhoff, G. Plesset, M.S. & Simmons, N., 1952. Wall effects in cavity flow. Part. II. Quarterly of Applied Mathematics, 9, pp.413-421.   DOI
18 Brennen, C., 1969. A Numerical Solution of Axisymmetric Cavity Flows. Journal of Fluid Mechanics, 37, pp.671-688.   DOI
19 Savchenko, Yu.N. Vlasenko, Yu.D. & Semenenko, V.N., 1998. Experimental Study of High-Speed Cavitation Flows. International Journal of Fluid Mechanics Research, 26(3), 365-374.
20 Savchenko, Yu.N., 2000. Modeling of Supercavitation Processes. Applied Hydromechanics, 2(3), pp.75-86.
21 Savchenko, Yu.N., 2001. Experimental investigation of supercavitating motion of bodies. RTO AVT Lecture Series on "Supercavitating Flows", VKI in Brussels, Begium, 12-16 Feburary 2001.
22 Schaffar, M. Rey, C. & Boeglen, G., 2005. Behavior of supercavitating underwater projectiles fired horizontally in a water tank: Theory and experiments. 35th AIAA Fluid Dynamics Conference and Exhibit, Toronto, 6-9 June 2005.
23 Schot, S.H., 1962. Surface tension and free surface effects in steady two-dimensional cavity flow about slender bodies. DTMB Hydromech Laboratory Research and Development Report 1566.
24 Singhal, A.K. Vaidya, N. & Leonard, A.D., 1997. Multi-dimensional simulation of cavitating flows using a PDF model for phase change. ASME Paper FEDSM97-3272, Proc. ASME Fluids Engineering Division Summer Meeting.
25 Self, M.W. & Ripken, J.F., 1955. Steady-state cavity studies in a free-jet water tunnel. St. Anthony Falls Hydraulic Laboratory, Report No. 47.
26 Singhal, A.K. Athavale, M.M. Li, H. & Jiang, Y., 2002. Mathematical Basis and Validation of the Full Cavitation Model. Trans. ASME, Journal of Fluids Engineering. 124, pp.617-624.   DOI   ScienceOn
27 Silberman, E., 1958. Experimental Studies of Supercavitating Flow about Simple Two-Dimensional Bodies in a Jet. St. Anthony Falls Hydraulic Laboratory, Report No. 59.
28 Eisenberg, P. & Pond, H.L., 1948. Water tunnel investigations of steady state cavities, David Taylor Model Basin Report 668. United States Navy.
29 Choi, J.K & Kim, H.T., 2010. A Study of using Wall Functon for Numerical Analysis of High Reynolds Number Turbulence Flow. Journal of the Society of Naval Architects of Korea, 47(5), pp.647-655.   DOI   ScienceOn
30 Delannoy, Y. & Kueny, J.L., 1990. Cavity flow predictions based on the Euler equations. ASME Cavitation and Multiphase Flow Forum, 109, New York, pp.153-158.
31 Epshtein, L.A. & Laptin, V.M., 1980. Approximate Calculation of Influence of Flow Boundaries on Cavity Length in Two Dimensional Problem and Past the Axisymmetric Body. Trudy Tsagi, 2060, pp.3-24.
32 Fisher, J.W., 1944. The Drag on a Circular Plate Generating a Cavity in Water. Underwater Ballistics Resolution Communication,17.
33 Fluent Theory Guide, 2011. Fluent Theory Guide, Chapter 17. ANSYS Inc.: Pennsylvania.
34 Gadd, G. E. & Grant, S., 1965. Some experiments on cavities behind disks. Journal of Fluid Mechanics, 23, pp.645-656.   DOI
35 Hrubes, J.D. Henoch, C.W. Kirschner, I.N. Curtis, C. M. & Corriveau, P.J., 1998. NUWC supercavitating high-speed bodies test range: description and test results. Proceedings 1998 ITTC Conference.
36 Kirschner, I.N., 1997. Supercavitating Projectile Experiments at Supersonic Speeds. NATO/AGARD Fluid Dynamics Panel Workshop on High Speed Body Motion in Water, AGARD Report 827. Kiev: AGARD.
37 Hrubes, J.D., 2001. High Speed Imaging of Supercavitating Underwater Projectiles. Experiments in Fluids, 30, pp.57-64.   DOI
38 Tulin, M.P., 1964. Supercavitating Flows - Small Perturbation Theory. Journal of Ship Research. 7, pp.16-37.
39 Street, R.L., 1963. Supercavitating Flow about a Slender Wedge in a Transverse Gravity Field. Journal of Ship Research. 7(1), pp.14-23.
40 Street, R.L., 1965. A Note on Gravity Effects in Supercavitating Flow. Journal of Ship Research. 8(4), pp.39-45.
41 Ventikos, Y. & Tzabiras, G., 2000. A Numerical Method for the Simulation of Steady and Unsteady Cavitating Flows. Computer and Fluids, 29(1), pp.63-88.   DOI   ScienceOn
42 Vlasenko, Yu.D., 2000. Supercavitating Rocket Model Experiments. Applied Hydromechanics, 2(3), pp.26-39.
43 Waid, R.L., 1957. Cavity Shapes for Circular Disks at Angles of Attack. California Institute of Technology. Hydrodynamics Laboratory. Report E-73.4.
44 Waid, R.L., 1957. Water tunnel investigation of two-dimensional cavities. California Institute of Technology. Hydrodynamics Laboratory. Report. E-73.6.
45 Wu, T.Y. Whitney, A.K. & Brennen, C., 1971. Cavity-Flow Wall Effects and Correction Rules. Journal of Fluid Mechanics, 49(2), pp.223-256.   DOI
46 Wosnik, M. & Milosevic, I. 2005 Time-Resolved Particle Image Velocimetry (TR-PIV) in ventilated and naturally cavitating flows. Sixth International Symposium on Particle Image Velocity, Pasadena, California, USA, 21-23 September.
47 Wu, T.Y., 1957. A simple method for calculating the drag in the linear theory of cavity flows. Caltech Engineering Division Report. 85-5.
48 Klose, G.J. & Acosta, A.J., 1965. Some New Measurements on the Drag of Cavitating Disks. Journal of Ship Research. 9(2), pp.102-104.
49 Karimi, H. Mohammadi, J. Arabi, H. Fesanghari, R. & Farhadzadeh, F., 2008. Design, production and experiment of small caliber supercavitating projectile. SuperFAST '2008, St. Petersburg, Russia.
50 Kirschner, I.N. Uhlman, J.S. Varghese, A.N. & Kuria, I.M., 1995. Supercavitating Projectiles in Axisymmetric Subsonic Liquid Flows. American Society of Mechanical Engineers, Fluids Engineering Division, 210, pp.75-93.
51 Kunz, R.F. Boger, D.A. Stinebring, D.R. Chyczewski, T.S. Lindau, J.W. & Gibeling, H.J., 2000. A Preconditioned Navier-Stokes Method for Two-Phase Flows with Application to Cavitation. Computers and Fluids, 29(8), pp.849-875.   DOI   ScienceOn
52 Kunz, R.F. Lindau, J.W. Billet, M.L. & Stinebring, D. R., 2001. Multiphase CFD modeling of developed and supercavitating flows. RTO AVT/VKI special course: supercavitating flows. Von Karman Institute for Fluid Dynamics, Rhode-Saint-Genese, Belgium, 12-16 February 2010.
53 Lee, H.B. Choi J.K. & Kim, H.T., 2013. Numerical analysis of supercavitating flows of two-dimensional simple bodies. Journal of the Society of Naval Architects of Korea, 50(6), pp.436-449.   과학기술학회마을   DOI   ScienceOn
54 Logvinovich, G.V., 1969. Hydrodynamics of flows with free boundaries. Kiev (Ukraine), Naukova dumka, p. 208; also 1972 Israel Program for Scientific Translations, Jerusalem, Israel.
55 May, A., 1975. Water entry and the cavity-running behavior of missiles, Naval Sea Systems Command, Hydroballistics Advisory Committee Technical Report 75-2. Hydroballistics Advisory Committee.
56 Wu, J. Wang, G. & Shyy, W., 2005. Time-Dependent Turbulent Cavitating Flow Computations with Interfacial Transport and Filter-based Models. International Journal for Numerical Methods in Fluids, 49(7), pp.739-761.   DOI   ScienceOn
57 Wu, T.Y. & Wang, D.P., 1964. A Wake Model for Free-Streamline Flow Theory. Part 2. Cavity Flows Past Obstacles of Arbitrary Profile. Journal of Fluid Mechanics, 18, pp.65-93.   DOI