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Hyperelastic materials, which have strong nonlinear mechanical properties, are commonly used in the engineering field. The application of hyperelastic materials to the water entry problem is a new interdisciplinary research topic. Unlike the water entering into a traditional rigid sphere, the hyperelastic sphere is very easy to deform during water entry. In order to explore the fluid-structure coupling problem with large deformations during water entry, a high-speed camera is used to study the problem of vertical water entering into hyperelastic sphere in this paper. Based on the experimental results, the effects of the material properties and impacting conditions on the cavity flow and sphere deformation behaviors during water entry are compared and analyzed. The experimental results show that the formation of the nested cavity after impacting a free surface of the hyperelastic sphere needs large enough impact conditions and small material shear modulus. The time for the nested cavity to be formed and retained during water entry is related to the material shear modulus and sphere diameter. The sphere displacement and length of cavity formed by the hyperelastic sphere increase with the increase of the impact velocity and material shear modulus, but decrease with the increase of the diameter of the sphere. The increase of the impacting velocity can only aggravate the deformation behaviors of the hyperelastic sphere, but does not affect the formation moment of the nested cavity. In addition, the characteristics for the deformation behaviors of the hyperelastic sphere to vary with the Froude number and the dimensionless ratio of material shear modulus to impacting hydrodynamic pressure are described and studied.
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Keywords:
- hyperelastic spheres /
- water entry /
- nested cavity /
- deformation
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图 2 参数测试图
Figure 2. Schematic diagram of test parameters.
图 4 超弹性球入水空泡
Figure 4. Water-entry cavity formed by hyperelastic spheres.
图 5 不同剪切模量球体入水空泡形态对比 (a) G = 6.1 kPa; (b) G = 10.2 kPa; (c) G = 47.0 kPa
Figure 5. Comparison of cavity shapes formed by hyperelastic spheres with different shear moduli: (a) G = 6.1 kPa; (b) G = 10.2 kPa; (c) G = 47.0 kPa.
图 6 不同剪切模量球体的入水位移
Figure 6. Displacement of spheres with different shear moduli.
图 7 不同冲击速度下球体入水空泡形态对比 (a)V = 1.1 m/s; (b) V = 2.5 m/s; (c) V = 3.3 m/s
Figure 7. Comparison of cavity shapes formed by hyperelastic spheres with different impact velocities: (a)V = 1.1 m/s; (b) V = 2.5 m/s; (c) V = 3.3 m/s.
图 8 不同入水冲击速度下的入水位移
Figure 8. Displacement of sphere with different impact velocities
图 9 不同冲击速度下嵌套空泡形态对比 (a) V = 3.3 m/s; (b) V = 4.4 m/s; (c) V = 4.8 m/s
Figure 9. Comparison of nested cavities with different impact velocities: (a) V = 3.3 m/s; (b) V = 4.4 m/s; (c) V = 4.8 m/s.
图 10 不同直径球体入水空泡形态对比 (a) D = 80 mm; (b) D = 61 mm; (c) D = 56 mm
Figure 10. Comparison of cavity shapes formed by hyperelastic spheres with different diameters: (a) D = 80 mm; (b) D = 61 mm; (c) D = 56 mm.
图 11 不同直径球体入水位移
Figure 11. Displacement of sphere with different diameters.
图 12 超弹性球体入水变形量系数的时间历程
Figure 12. Time history of sphere deformation coefficient during water entry.
图 13 超弹性球体(G = 10.2 kPa)第一、二变形周期内λN随Fr的变化
Figure 13. Change of λN in the first and second deformation cycles (G = 10.2 kPa) with Fr
图 14 超弹性球体(D = 61 mm)第一、二变形周期内λN随η的变化
Figure 14. Change of λN in the first and second deformation cycles (D = 61 mm) with η.
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[1] Kubota Y, Mochizuki O 2015 WJM 5 129
Google Scholar
[2] Epps B P, Techet A H 2007 Exp. Fluids. 43 691
Google Scholar
[3] Sun T, Wang H, Zou L, Zong Z, Li H 2019 Ocean. Eng. 194 106597
Google Scholar
[4] Xia W, Cong W, Wei Y, Li C 2020 Appl. Ocean. Res. 103 102322
Google Scholar
[5] Xia W X, Wang C, Wei Y J, Li J C, Yang L 2020 Exp. Fluids. 61 57
Google Scholar
[6] Worthington A M, Cole R S 1897 Philos. Trans. R. Soc. London 189 137
Google Scholar
[7] Worthington A M 1881 P. Roy. Soc. A. Math Phy. 33 347
[8] Wood R W 1909 Science 29 464
Google Scholar
[9] Duclaux V, Caillé F, Duez C, Ybert C, Bocquet L, Clanet C 2007 J. Fluid Mech. 591 1
Google Scholar
[10] Seddon C M, Moatamedi M 2006 Int. J. Impact. Eng. 32 1045
Google Scholar
[11] May A 1952 J. Appl. Phys. 23 1362
Google Scholar
[12] Yang L, Wei Y, Wang C, Xia W, Li J 2020 J. Appl. Phys. 127 064901
Google Scholar
[13] Truscott T T, Epps B P, Techet A H 2012 J. Fluid Mech. 704 173
Google Scholar
[14] Aristoff J M, Truscott T T, Techet A H, Bush J W M 2010 Phys. Fluids 22 70
[15] Aristoff J M, Bush J W M 2009 J. Fluid Mech. 619 45
Google Scholar
[16] 何春涛, 王聪, 何乾坤, 仇洋 2012 物理学报 61 134701
Google Scholar
He C T, Wang C, He Q K, Qiu Y 2012 Acta Phys. Sin. 61 134701
Google Scholar
[17] 施红辉, 周浩磊, 吴岩, 贾会霞, 张晓萍, 周素云, 章利特, 董若凌 2012 力学学报 44 49
Google Scholar
Shi H H, Zhou H L, Wu Y, Jia H X, Zhang X P, Zhou S Y, Zhang L T, Dong R L 2012 J. Mech. Phys. Solids. 44 49
Google Scholar
[18] 李佳川, 魏英杰, 王聪, 邓环宇 2016 物理学报 65 204703
Google Scholar
Li J C, Wei Y J, Wang C, Deng H Y 2016 Acta Phys. Sin. 65 204703
Google Scholar
[19] 李佳川, 魏英杰, 王聪 2019 兵工学报 40 124
Google Scholar
Li J C, Wei Y J, Wang C 2019 Acta. Armamentarii. 40 124
Google Scholar
[20] 卢佳兴, 魏英杰, 王聪, 路丽睿, 许昊 2019 力学学报 51 150
Lu J X, Wei Y J, Wang C, Lu L R, Xu H 2019 J. Mech. Phys. Solids. 51 150
[21] Yun H, Lyu X, Wei Z 2020 Ocean. Eng. 201 107143
Google Scholar
[22] Yun H, Lyu X, Wei Z 2020 J. Visual. Japan. 23 49
Google Scholar
[23] Truscott T T, Epps B P, Belden J 2014 Annu. Rev. Fluid Mech. 46 355
Google Scholar
[24] Truscott T T, Techet A H 2006 Phys. Fluids 18 4173
[25] Speirs N B, Mansoor M M, Belden J, Truscott T T 2019 J. Fluid Mech. 862 R3
Google Scholar
[26] Russo S, Biscarini C, Facci A L, Falcucci G, Jannelli E 2017 J. Mar Sci Tech. Japan. 23 67
[27] Facci A L, Falcucci G, Agresta A, Biscarini C 2019 Water 11 1048
Google Scholar
[28] Russo S, Falcucci G 2018 ICNAAM. Greece 1987 25
[29] Panciroli R, Falcucci G, Erme G, Santis E D, Jannelli E 2015 Aip. Conference, AIP Publishing LLC, April 1, 1648 570011
[30] 孙士丽 2011 博士学位论文 (哈尔滨: 哈尔滨工程大学)
Sun S L 2011 Ph. D. Dissertation (Harbin: Harbin Engineering University) (in Chinese)
[31] Hurd R C, Belden J, Jandron M A, Fanning D T, Bower A F, Truscott T T 2017 J. Fluid Mech. 824 912
Google Scholar
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