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During the water-entry of the parallel axisymmetric bodies, the water-entry cavities are asymmetrical due to the mutual interference between the cavities. In the current study of the cavity dynamic models, the relatively perfect models of axially symmetric dynamic calculation of low speed single water entry have been established. These models mainly focus on the evolution of cavitation, and thus simplifying the flow pattern. However, due to the particularity of parallel water, the fluid forms a relative flow during the evolution of the cavitation in the inner region of the axisymmetric body axis. As a result, the flow is no longer axisymmetric but develops into a complex three-dimensional flow with strong nonlinearity, making the the theoretical model more difficult to establish. In order to analyze the evolution of the parallel cavities of the parallel axisymmetric body water-entry, the flow of the water-entry cavity interference region is simplified by the existing single water-entry calculation model based on the potential flow theory. The constraint of the relative flow to the cavity is simplified into a constraint potential, and the variation of cavity shape is analyzed. Based on the nonlinear hypothesis, the influence function is introduced to establish the calculation model of three-dimensional cavity and the three-dimensional evolution characteristics of parallel cavities are analyzed. The obtained results show that the velocity potential of the axisymmetric body water-entry can be regarded as the superposition of a point source and a line source located on the axis of the cavity. The expansion of the cavity is affected mainly by the point source, while the shrinkage of the cavity is influenced mainly by the line source. During the parallel water-entry of the axisymmetric body, the evolution of the parallel cavities in space is mirror symmetric and the mutual interference between cavities can be analyzed by introducing the potential wall surface. The potential wall has an inhibitory effect on the evolution of the cavities. The variation of the parallel water-entry cavity radius with the polar angle is related to the depth of the cavity cross section. In the inhibition evolution area near the closed point, the cavity radius decreases gradually with the increase of the polar angle, and the void section radius in the inhibition evolution region far from the closed point increases with the polar angle increasing, and is opposite to the radius law. In the shallower depth of the water-entry, the excessive evolution is formed in the expansion process of the cavity, and the excessive evolution will gradually weaken and disappear in the contraction process of the cavity.
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Keywords:
- potential flow theory /
- parallel water-entry /
- asymmetric water-entry cavity /
- cavity evolution model
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[2] Worthington A M, Cole R S 1990 Phil. Phil. Trans. Roy. Soc. 194 A175
[3] Waugh J G 1968 J. Hydrodyn. 2 87
[4] Birkhoff G, Caywood T E 1949 J. Appl. Phys. 20 646
[5] Glibarg D, Anderson R A 1948 J. Appl. Phys. 19 127
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[7] He C T, Wang C, He Q K, Qiu Y 2012 Acta Phys. Sin. 61 134701 (in Chinese) [何春涛, 王聪, 何乾坤, 仇洋 2012 物理学报 61 134701]
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[9] Tabuteau H, Sikorski D, Simon J, Bruyn J 2011 Phys. Rev. E 84 031403
[10] Logvinovich G V 1969 Hydrodynamics of Flows with Free Boundaries (Naukova Dumka: Kiev) (in Russian)
[11] Lee M, Longoria R G, Wilson D E 1997 Phys. Fluids 9 540
[12] Lee M, Longoria R G, Wilson D E 1997 J. Fluids Struct. 11 819
[13] Truscott T T 2009 Ph. D. Dissertation (Boston: Massachusetts Institute of Technology).
[14] Yan H, Liu Y, Kominiarczuk J, Yue D 2009 J. Fluid Mech. 641 441
[15] Gordillo J M, Sevilla A, Rodriguez J, Martinez C 2005 Phys. Rev. Lett. 95 194501
[16] Aristoff J M, Bush J W M 2009 J. Fluid Mech. 619 45
[17] Ye Q Y 1990 Chin. J. Appl. Mech. 7 17 (in Chinese) [叶取源 1990 应用力学学报 7 17]
[18] Lu Z L 2017 Ph. D. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese) [路中磊 2017 博士学位论文 (哈尔滨: 哈尔滨工业大学].
[19] Ye Y L, Li Y Q, Zhang A M 2014 Acta Phys. Sin. 63 054706 (in Chinese) [叶亚龙, 李艳青, 张阿漫 2014 物理学报 63 054706]
[20] Duclaux V, Caill F, Duez C, Ybert C, Bocquet L, Clanet C 2007 J. Fluid Mech. 59 1
[21] Mann J, Liu Y, Kim Y, Yue D K P 2007 IEEE J. Ocean Engng. 32 21
[22] Lu L R 2018 M. S. Thesis (Harbin: Harbin Institute of Technology) (in Chinese) [路丽睿 2018 硕士学位论文 (哈尔滨: 哈尔滨工业大学)]
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[1] Worthington A M, Cole R S 1897 Phil. Phil. Trans. Roy. Soc. 189 A137
[2] Worthington A M, Cole R S 1990 Phil. Phil. Trans. Roy. Soc. 194 A175
[3] Waugh J G 1968 J. Hydrodyn. 2 87
[4] Birkhoff G, Caywood T E 1949 J. Appl. Phys. 20 646
[5] Glibarg D, Anderson R A 1948 J. Appl. Phys. 19 127
[6] May A, Woodhull J C 1948 J. Appl. Phys. 19 1109
[7] He C T, Wang C, He Q K, Qiu Y 2012 Acta Phys. Sin. 61 134701 (in Chinese) [何春涛, 王聪, 何乾坤, 仇洋 2012 物理学报 61 134701]
[8] Holfeld B, Maier F, Izzo M, Dinardo S 2009 Micr. Sci. Tech. 21 73
[9] Tabuteau H, Sikorski D, Simon J, Bruyn J 2011 Phys. Rev. E 84 031403
[10] Logvinovich G V 1969 Hydrodynamics of Flows with Free Boundaries (Naukova Dumka: Kiev) (in Russian)
[11] Lee M, Longoria R G, Wilson D E 1997 Phys. Fluids 9 540
[12] Lee M, Longoria R G, Wilson D E 1997 J. Fluids Struct. 11 819
[13] Truscott T T 2009 Ph. D. Dissertation (Boston: Massachusetts Institute of Technology).
[14] Yan H, Liu Y, Kominiarczuk J, Yue D 2009 J. Fluid Mech. 641 441
[15] Gordillo J M, Sevilla A, Rodriguez J, Martinez C 2005 Phys. Rev. Lett. 95 194501
[16] Aristoff J M, Bush J W M 2009 J. Fluid Mech. 619 45
[17] Ye Q Y 1990 Chin. J. Appl. Mech. 7 17 (in Chinese) [叶取源 1990 应用力学学报 7 17]
[18] Lu Z L 2017 Ph. D. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese) [路中磊 2017 博士学位论文 (哈尔滨: 哈尔滨工业大学].
[19] Ye Y L, Li Y Q, Zhang A M 2014 Acta Phys. Sin. 63 054706 (in Chinese) [叶亚龙, 李艳青, 张阿漫 2014 物理学报 63 054706]
[20] Duclaux V, Caill F, Duez C, Ybert C, Bocquet L, Clanet C 2007 J. Fluid Mech. 59 1
[21] Mann J, Liu Y, Kim Y, Yue D K P 2007 IEEE J. Ocean Engng. 32 21
[22] Lu L R 2018 M. S. Thesis (Harbin: Harbin Institute of Technology) (in Chinese) [路丽睿 2018 硕士学位论文 (哈尔滨: 哈尔滨工业大学)]
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