Abstract
Cavitating flow is of considerable importance in underwater high-speed applications because of the desirable drag reduction effect. A proper design of submerged bodies should not only produce a stable motion but also maximize the distance travelled underwater. Physical experiment and Computational Fluid Dynamics-CFD simulation can be used to investigate the cavitating flow dynamics and the interaction between the body and the surrounding flow. However, in the previous studies little specific data regarding body design have been documented. This study investigates numerically the behavior of the natural cavitating flow around submerged bodies. The bodies differ in cavitator shape and length. Steady-state simulations are carried out using the CFD approach. A two-phase mixture formulation, the turbulence k-ε model, and the Zwart—Geber—Belamri (ZGB) cavitation modeling are used. Comparisons with the published data are carried out. The behavior of the natural cavitating flow around different bodies is obtained. A modified value of the drag coefficient is proposed.
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References
G. I. Bykovtsev and G. S. Razarenov, “Pulsation of a spherical bubble in an incompressible fluid,” Fluid Dynamics 10(2), 322–324 (1975).
D. V. Georgievskii, “Cavitation bubble collapse in nonlinear viscous and viscoplastic media,” Fluid Dynamics 29(2), 299–302 (1994).
A. L. Gonor, V. I. Zabutnaya, and N. N. Yas’ko, “Existence of an optimal cavitation body,” Fluid Dynamics 26(2), 208–212 (1991).
Y. Murai, H. Fukuda, Y. Oishi, Y. Kodama, and F. Yamamoto, “Skin friction reduction by large air bubbles in a horizontal channel flow,” Int. J. Multiphase Flow 33(2), 147–163 (2007).
S. L. Ceccio, “Friction drag reduction of external flows with bubble and gas injection,” Annu. Rev. Fluid Mech. 42, 183–203 (2010).
A. Karn, R. E. Arndt, and J. Hong, “An experimental investigation into the physics of supercavity closure,” J. Fluid. Mech. 789, 259–284 (2015).
R. I. Nigmatulin, Dynamics of Multiphase Media (Hemisphere, New York, 1989).
K. M. Shyue, “A fluid-mixture type algorithm for compressible multicomponent flow with Van Der Waals equation of state,” J. Comput. Phys. 156(1), 43–88 (1999).
D. Zeidan, “Numerical resolution for a compressible two-phase flow model based on the theory of thermodynamically compatible systems,” Appl. Math. Comput. 217(11), 5023–5040 (2011).
R. Saurel, P. Boivin, and O. Le Métayer, “A general formulation for cavitating, boiling and evaporating Flows,” Comput. Fluids 128, 53–64 (2016).
S. Fechter, C. D. Munz, C. Rohde, and C. Zeiler, “A sharp interface method for compressible liquid—vapor flow with phase transition and surface tension,” J. Comput. Phys. 336, 347–374 (2017).
A. May, Water Entry and the Cavity-Running Behavior of Missiles. SEAHAC Technical Report No. 75-2 (Naval Surface Weapons Center, White Oak Laboratory, Silver Spring, MD, 1975).
J. P. Franc and J. M. Michel, Fundamentals of Cavitation (Springer, 2006).
B. Vanek, Control Methods for High-Speed Supercavitating Vehicles, Ph. D. Thesis, University of Minnesota, 2008.
T. T. Truscott, P. E. Brenden, and Jesse Belden, “Water entry of projectiles,” Annu. Rev. Fluid Mech. 46, 355–378 (2014).
A. N. Varghese, J. S. Uhlman, and I. N. Kirschner, “Numerical analysis of high-speed bodies in partially cavitating axisymmetric flow,” J. Fluids Eng. 127(1), 41–54 (2005).
I. Rashidi, M. Passandideh-Fard, and M. Pasandideh-Fard, “The optimum design of a cavitator for high-speed axisymmetric bodies in partially cavitating flows,” J. Fluids Eng. 135(1), 011301–1–011301–12 (2013).
M. Nouroozi, M. Pasandidehfard, M. H. Djavareshkian, “Simulation of partial and supercavitating flows around axisymmetric and quasi-3D bodies by boundary element method using simple and reentrant jet models at the closure zone of cavity,” Math. Probl. Eng., paper no. 1593849 (2016).
R. F. Kunz, D. A. Boger, D. R. Stinebring, T. S. Chyczewski, J. W. Lindau, H. J. Gibeling, V. Sankaran, and T. R. Govindan, “A preconditioned Navier—Stokes method for two-phase flows with application to cavitation prediction,” Computers Fluids 29(8), 849–875 (2000).
R. F. Kunz, J. W. Lindau, M. L. Billet, and D. R. Stinebring, Multiphase CFD Modeling of Developed and Supercavitating Flows (Pennsylvania State University, University Park Applied Research Lab., 2001)
C. T. Hsiao, J. Ma, and G. L. Chahine, “Multiscale two-phase flow modeling of sheet and cloud cavitation,” Int. J. Multiphase Flow 90, 102–117 (2017).
E. Romenski, A. Resnyansky, and E. F. Toro, “Conservative hyperbolic formulation for compressible two-phase flow with different phase pressures and temperatures,” Quart. Appl. Math. 65(2), 259–279 (2007).
I. Peshkov and E. Romenski, “A hyperbolic model for viscous Newtonian flows,” Continuum Mech. Therm. 28(1–2), 85–104 (2016).
D. H. Kim, W. G. Park, and C. M. Jung, “Numerical simulation of cavitating flow past axisymmetric body,” Int. J. Nav. Arch. Ocean Eng. 4(3), 256–266 (2012).
K. J. Paik, H. G. Park, and J. Seo, “RANS simulation of cavitation and Hull pressure fluctuation for marine propeller operating behind Hull condition,” Int. J. Nav. Arch. Ocean Eng. 5(4), 502–512 (2013).
D. Yang, Y. L Xiong, and X. F. Guo, “Drag reduction of a rapid vehicle in supercavitating flow,” Int. J. Nav. Arch. Ocean Eng. 9(1), 35–44 (2017).
T. T. Nguyen, H. N. Duong, T. Q. Nguyen, and H. Kikura, “CFD simulations of the natural cavitating flow around high-speed Submerged Bodies,” in: Int. Conf. Advances Comput. Mech. 2017, ACOME 2017, Lecture Notes in Mech. Eng., Ed. by H. Nguyen-Xuan, P. Phung-Van, and T. Rabczuk (Springer, Singapore, 2018), 851–873.
T. H. Shih, W. W. Liou, A. Shabbir, Z. Yang, and J. Zhu, “A new eddy-viscosity model for high Reynolds number turbulent flows — model development and validation,” Comput. Fluids 24(3), 227–238 (1995).
P. J. Zwart, A. G. Gerber, and T. Belamri, “A two-phase flow model for predicting cavitation dynamics,” in: Fifth Int. Conf. Multiphase Flow, Yokohama, Japan, Ed. by Y. Matsumoto, K. Hishida, A. Tomiyama, et al. (Tsukuba, Japan, 2004).
H. Rouse and J. S. McNown, “Cavitation and pressure distribution, head forms at zero angle of yaw,” Studies in Engineering Bulletin, State University of Iowa 32 (1948).
T. Sarkar, P. G. Sayer, and S. M. Fraser, “Flow simulation past axisymmetric bodies using four different turbulence models,” Appl. Math. Model. 21(12), 783–792 (1997).
A. Asnaghi, E. Jahanbakhsh, and M. S. Seif, “Unsteady multiphase modeling of cavitation around NACA 0015,” J. Mar. Sci. Tech. Taiwan 18(5), 689–696 (2010).
G. H. Yeoh and J. Tu, Computational Techniques for Multiphase Flows (Butterworth-Heinemann, Elsevier Science and Technology, 2009).
I. Senocak and W. Shyy, “A pressure-based method for turbulent cavitating flow computations,” J. Comput. Phys. 176(2), 363–383 (2002).
S. I. Bernad and R. Susan-Resiga, “Numerical model for cavitational flow in hydraulic poppet valves,” Modelling and Simulation in Engineering 10 (2012).
A. Ducoin, B. Huang, and Y. L. Young, “Numerical modeling of unsteady cavitating flows around a stationary hydrofoil,” Int. J. Rotating Machinery (2012).
M. Coussirat, F. Moll, F. Cappa, and A. Fontanals, “Study of available turbulence and cavitation models to reproduce flow patterns in confined flows,” J. Fluids Eng. 138(9), paper no. 091304 (2016).
K. Saha and X. Li, “Assessment of different cavitation models in mixture and Eulerian framework for two-phase flow in Diesel injectors,” in: ASME 2013 Internal Combustion Engine Division Fall Technical Conference (American Society of Mechanical Engineers, 2013), p. V002T02A011.
H. L. Liu, J. Wang, Y. Wang, H. Zhang, and H. Huang, “Influence of the empirical coefficients of cavitation model on predicting cavitating flow in the centrifugal pump,” Int. J. Nav. Arch. Ocean Eng. 6(1), 119–131 (2014).
S. G. Shereena, S. Vengadesan, V. G. Idichandy, and S. K. Bhattacharyya, “CFD study of drag reduction in axisymmetric underwater vehicles using air jets,” Eng. Appl. Comp. Fluid 7(2), 193–209 (2013).
A. Prosperetti and G. Tryggvason, Computational Methods for Multiphase Flow (Cambridge University Press, 2009).
M. Jain, B. Puranik, and A. Agrawal, “A numerical investigation of effects of cavity and orifice parameters on the characteristics of a synthetic jet flow,” Sens. Actuator A-Phys. 165(2), 351–366 (2011).
M. Manninen, V. Taivassalo, and S. Kallio, On the Mixture Model for Multiphase Flow (Technical Research Centre of Finland-VTT, 1996).
P. R. Garabedian, “Calculation of axially symmetric cavities and jets,” Pac. J. Math. 6(4), 611–684 (1956).
V. N. Semenenko, Artificial Supercavitation. Physics and Calculation, Technical Report (Ukrainian Academy of Sciences, Kiev Institute of Hydromechanics, 2001).
J. K. Choi, B. K. Ahn, and H. T. Kim, “A numerical and experimental study on the drag of a cavitating underwater vehicle in cavitation tunnel,” Int. J. Nav. Arch. Ocean Eng. 7(5), 888–905 (2015).
H. N. Duong, T. T. Nguyen, T. P. Truong, and Q. T. Nguyen, “Some results of the experimental measurements of the cavitating flow after horizontal water entry,” in: 8th Asia Pacific Workshop on Marine Hydrodynamics-APHydro 2016, Ed. by H. N. Duong (Publishing House for Science and Technology, Hanoi, 2016), pp. 341–353.
T. T. Nguyen, H. N. Duong, Q. T. Nguyen, and T. P. Truong, “Experimental measurements of the cavitating flow after horizontal water entry,” Fluid Dyn. Res. 49(5), paper no. 055508 (2017).
D. R. Stinebring, M. L. Billet, J. W. Lindau, and R. F. Kunz, Developed Cavitation-Cavity Dynamics (Pennsylvania State University, University Park Applied Research Lab., 2001).
V. P. Karlikov and G. I. Sholomovich, “Method of approximate account for the wall effect in cavitation flow around Bbodies in water tunnels,” Fluid Dynamics 1(4), 61–64 (1966).
Funding
Partial financial support from the scientific research project NCVCC42.02/19-19 of VAST, whose project manager is Prof. Duong Ngoc Hai-the second author of this paper, is gratefully acknowledged.
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Russian Text © The Author(s), 2019, published in Izvestiya RAN. Mekhanika Zhidkosti i Gaza, 2019, No. 11, pp. 99–113.
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Thang, N.T., Ngoc, D. Numerical Study of the Natural-Cavitating Flow around Underwater Slender Bodies. Fluid Dyn 54, 835–849 (2019). https://doi.org/10.1134/S0015462819060120
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DOI: https://doi.org/10.1134/S0015462819060120