Water Entry Problems Simulated by an Axisymmetric SPH Model with VAS Scheme

Abstract

Water entry of marine structures has long been an important problem in ocean engineering. Among the different techniques to predict fluid-structure interactions during water entry, smoothed particle hydrodynamics (SPH) method gradually becomes a promising method that is able to solve the impact pressure and the splashing fluid jets simultaneously. However, for three-dimensional (3D) problems, SPH method is computationally expensive due to the huge number of particles that are needed to resolve the local impact pressure accurately. Therefore, in this work an axisymmetric SPH model is applied to solve different water entry problems with axisymmetric structures including spheres and cones with different deadrise angles. Importantly, the Volume Adaptive Scheme (VAS) is added to guarantee the homogeneousness of particle volumes during the simulation. The axisymmetric SPH model with VAS scheme will be introduced in detail and the numerical results will be sufficiently validated with experimental data to demonstrate the high robustness and accuracy of the SPH model for solving 3D axisymmetric water entry problems in an efficient way.

Keywords

Water entry / Smoothed particle hydrodynamics / Slamming / Ocean engineering

References

[1] Adami S, Hu XY, Adams NA. A generalized wall boundary condition for smoothed particle hydrodynamics. Journal of Computational Physics, 2012, 231(21): 7057-7075

[2] Antuono M, Colagrossi A, Marrone S. 12. Numerical diffusive terms in weakly-compressible SPH schemes. Computer Physics Communications, 2012, 183: 2570-2580

[3] Antuono M, Colagrossi A, Marrone S, Molteni D. Free-surface ows solved by means of SPH schemes with numerical diusive terms. Computer Physics Communications, 2010, 181(3): 532-549

[4] Aristo JM, Truscott TT, Techet AH, Bush JWM. The water entry of decelerating spheres. Physics of Fluids, 2010, 22(3): 032102

[5] Bckmann A, Shipilova O, Skeie G. Incompressible SPH for free surface ows. Computers & Fluids, 2012, 67: 138-151

[6] Brookshaw L (2003) April. Smooth particle hydrodynamics in cylindrical coordinates. In K. Burrage and R. B. Sidje (Eds.), Proc. of 10th Computational Techniques and Applications Conference CTAC-2001, Volume 44: pp. C114–C139

[7] Cheng H, Ming F, Sun P, Sui Y, Zhang AM. Ship hull slamming analysis with smoothed particle hydrodynamics method. Applied Ocean Research, 2020, 101: 102268

[8] Chiron L, Oger G, De Lee M, Touze DL. Analysis and improvements of adaptive particle renement (APR) through cpu time, accuracy and robustness considerations. Journal of Computational Physics, 2018, 354: 552-575

[9] Colagrossi A, Landrini M. Numerical simulation of interfacial ows by smoothed particle hydrodynamics. Journal of Computational Physics, 2003, 191(2): 448-475

[10] De Backer G, Vantorre M, Beels C, De Pre J, Victor S, De Rouck J, Blommaert C, Van Paepegem W. Experimental investigation of water impact on axisymmetric bodies. Applied Ocean Research, 2009, 31(3): 143-156

[11] Dobrovol’skaya ZN. On some problems of similarity ow of uid with a free surface. Journal of Fluid Mechanics, 1969, 36(4): 805-829

[12] Fang XL, Colagrossi A, Wang PP, Zhang AM. An accurate and robust axisymmetric SPH method based on riemann solver with applications in ocean engineering. Ocean Engineering, 2022, 244: 110369

[13] Gong K, Shao S, Liu H, Lin P, Gui Q. Cylindrical smoothed particle hydrodynamics simulations of water entry. Journal of Fluids Engineering, 2019, 141: 7

[14] Gong K, Shao S, Liu H, Wang B, Tan SK. Two-phase SPH simulation of uid-structure interactions. Journal of Fluids and Structures, 2016, 65: 155-179

[15] Grenier N, Antuono M, Colagrossi A, Le Touze D, Alessandrini B. An hamiltonian interface SPH formulation for multiuid and free surface ows. Journal of Computational Physics, 2009, 228(22): 8380-8393

[16] Hammani I, Marrone S, Colagrossi A, Oger G, Le Touze D. Detailed study on the extension of the -SPH model to multi-phase ow. Computer Methods in Applied Mechanics and Engineering, 2020, 368: 113189

[17] He F, Zhang H, Huang C, Liu M. Numerical investigation of the solitary wave breaking over a slope by using the nite particle method. Coastal Engineering, 2020, 156: 103617

[18] He F, Zhang H, Huang C and Liu M (2022) A stable SPH model with large c numbers for multi-phase ows with large density ratios. Journal of Computational Physics: 110944

[19] Huang L, Tavakoli S, Li M, Dolatshah A, Pena B, Ding B, Dashtimanesh A. Cfd analyses on the water entry process of a freefall lifeboat. Ocean Engineering, 2021, 232: 109115

[20] Iafrati A, Grizzi S, Siemann M, Monta∼nes LB. High-speed ditching of a at plate: Experimental data and uncertainty assessment. Journal of Fluids and Structures, 2015, 55: 501-525

[21] Iranmanesh A, Passandideh-Fard M. A three-dimensional numerical approach on water entry of a horizontal circular cylinder using the volume of uid technique. Ocean Engineering, 2017, 130: 557-566

[22] Khayyer A, Gotoh H. A multiphase compressible-incompressible particle method for water slamming. International Journal of Oshore and Polar Engineering, 2016, 26(01): 20-25

[23] Lin MC, Shieh LD. Simultaneous measurements of water impact on a two-dimensional body. Fluid Dynamics Research, 1997, 19(3): 125

[24] Lin P. A xed-grid model for simulation of a moving body in free surface ows. Computers & Fluids, 2007, 36(3): 549-561

[25] Liu M, Zhang Z. Smoothed particle hydrodynamics (SPH) for modeling uid-structure interactions. SCIENCE CHINA Physics, Mechanics & Astronomy, 2019, 62(8): 984701

[26] Long T, Zhang Z, Liu M. Multi-resolution technique integrated with smoothed particle element method (spem) for modeling uid-structure interaction problems with free surfaces. Science China Physics, Mechanics & Astronomy, 2021, 64(8): 1-22

[27] Luo M, Khayyer A, Lin P. Particle methods in ocean and coastal engineering. Applied Ocean Research, 2021, 114: 102734

[28] Lyu HG, Deng R, Sun PN, Miao JM. Study on the wedge penetrating uid interfaces characterized by dierent density-ratios: Numerical investigations with a multi-phase SPH model. Ocean Engineering, 2021, 237: 109538

[29] Lyu HG, Sun PN, Huang XT, Zhong SY, Peng YX, Jiang T, Ji CN. A review of SPH techniques for hydrodynamic simulations of ocean energy devices. Energies, 2022, 15(2): 502

[30] Marrone S, Colagrossi A, Park J, Campana E. Challenges on the numerical prediction of slamming loads on lng tank insulation panels. Ocean Engineering, 2017, 141: 512-530

[31] Ming F, Sun PN, Zhang AM, . Investigation on charge parameters of underwater contact explosion based on axisymmetric SPH method. Applied Mathematics and Mechanics, 2014, 35(4): 453-468

[32] Moghisi M, Squire P. 07. An experimental investigation of the initial force of impact on a sphere striking a liquid surface. Journal of Fluid Mechanics, 1981, 108: 133-146

[33] Nair VV, Bhattacharyya S. Water entry and exit of axisymmetric bodies by cfd approach. Journal of Ocean Engineering and Science, 2018, 3(2): 156-174

[34] Oger G, Doring M, Alessandrini B, Ferrant P. Two-dimensional SPH simulations of wedge water entries. Journal of Computational Physics, 2006, 213(2): 803-822

[35] Omidvar P, Stansby PK, Rogers BD. Wave body interaction in 2d using smoothed particle hydrodynamics (SPH) with variable particle mass. International Journal for Numerical Methods in Fluids, 2012, 68(6): 686-705

[36] Randles P, Libersky LD. Smoothed particle hydrodynamics: some recent improvements and applications. Computer methods in applied mechanics and engineering, 1996, 139(1–4): 375-408

[37] Shao S. Incompressible SPH simulation of water entry of a free-falling object. International Journal for Numerical Methods in Fluids, 2009, 59(1): 91-115

[38] Shao S, Gotoh H. Simulating coupled motion of progressive wave and oating curtain wall by SPH-les model. Coastal Engineering Journal, 2004, 46(2): 171-202

[39] Skillen A, Lind S, Stansby PK, Rogers BD. Incompressible smoothed particle hydrodynamics (SPH) with reduced temporal noise and generalised ckian smoothing applied to body-water slam and ecient wave-body interaction. Computer Methods in Applied Mechanics and Engineering, 2013, 265: 163-173

[40] Skillen A, Lind S, Stansby PK, Rogers BD. Incompressible smoothed particle hydrodynamics (SPH) with reduced temporal noise and generalised ckian smoothing applied to body-water slam and ecient wave-body interaction. Computer Methods in Applied Mechanics and Engineering, 2013, 265: 163-173

[41] Sun P, Colagrossi A, Marrone S, Antuono M, Zhang AM. A consistent approach to particle shifting in the-plus-SPH model. Computer Methods in Applied Mechanics and Engineering, 2019, 348: 912-934

[42] Sun P, Colagrossi A, Marrone S, Zhang A. The plus-SPH model: Simple procedures for a further improvement of the SPH scheme. Computer Methods in Applied Mechanics and Engineering, 2017, 315: 25-49

[43] Sun P, Colagrossi A, Touze DL, Zhang AM. Extension of the-plus-SPH model for simulating vortex-induced-vibration problems. Jour-nal of Fluids and Structures, 2019, 90: 19-42

[44] Sun P, Ming F, Zhang A. Numerical simulation of interactions between free surface and rigid body using a robust SPH method. Ocean Engineering, 2015, 98: 32-49

[45] Sun P, Zhang AM, Marrone S, Ming F. An accurate and e-cient SPH modeling of the water entry of circular cylinders. Applied Ocean Research, 2018, 72: 60-75

[46] Sun PN, Le Touze D, Oger G, Zhang AM. An accurate fsi-SPH modeling of challenging uid-structure interaction problems in two and three dimensions. Ocean Engineering, 2021, 221: 108552

[47] Sun PN, Le Touze D, Oger G, Zhang AM. An accurate SPH volume adaptive scheme for modeling strongly-compressible multiphase ows. part 2: Extension of the scheme to cylindrical coordinates and simulations of 3d axisymmetric problems with experimental validations. Journal of Computational Physics, 2021, 426: 109936

[48] Sun PN, Le Touze D, Oger G, Zhang AM. An accurate SPH volume adaptive scheme for modeling strongly-compressible multiphase ows. part 1: Numerical scheme and validations with basic 1d and 2d benchmarks. Journal of Computational Physics, 2021, 426: 109937

[49] Truscott TT, Techet AH. Water entry of spinning spheres. Journal of Fluid Mechanics, 2009, 625: 135-165

[50] Van Nuel D, Vepa K, De Baere I, Lava P, Kersemans M, Degrieck J, De Rouck J, Van Paepegem W. A comparison between the experimental and theoretical impact pressures acting on a horizontal quasirigid cylinder during vertical water entry. Ocean Engineering, 2014, 77: 42-54

[51] Vandamme J, Zou Q, Reeve DE. Modeling oating object entry and exit using smoothed particle hydrodynamics. Journal of Waterway, Port, Coastal, and Ocean Engineering, 2011, 137(5): 213-224

[52] Von Karman T and Wattendorf F (1929) The impact of sea planes during landing. naca tech. Technical report, Note 321

[53] Wagner H. Phenomena associated with impacts and sliding on liquid surfaces. Journal of Applied Mathematics and Mechanics, 1932, 12(4): 193-215

[54] Wang J, Lugni C, Faltinsen OM. Experimental and numerical investigation of a freefall wedge vertically entering the water surface. Applied Ocean Research, 2015, 51: 181-203

[55] Wang L, Xu F, Yang Y. SPH scheme for simulating the water entry of an elastomer. Ocean Engineering, 2019, 178: 233-245

[56] Wang S, Islam H, Soares CG. Uncertainty due to discretization on the ale algorithm for predicting water slamming loads. Marine Structures, 2021, 80: 103086

[57] Wang S, Soares CG. Numerical study on the water impact of 3d bodies by an explicit nite element method. Ocean Engineering, 2014, 78: 73-88

[58] Wang S, Soares CG. Eects of compressibility, threedimensionality and air cavity on a free-falling wedge cylinder. Ocean Engineering, 2020, 217: 107589

[59] Wang S, Soares CG. Three-dimensional eects on slamming loads on a free-falling bow- are cylinder into calm water. Journal of Oshore Mechanics and Arctic Engineering, 2022, 144(4): 044502

[60] Wang S, Xiang G, Soares CG. Assessment of three-dimensional eects on slamming load predictions using openfoam. Applied Ocean Research, 2021, 112: 102646

[61] Woodgate MA, Barakos GN, Scrase N, Neville T. Simulation of helicopter ditching using smoothed particle hydrodynamics. Aerospace Science and Technology, 2019, 85: 277-292

[62] Xiao T, Qin N, Lu Z, Sun X, Tong M, Wang Z. Development of a smoothed particle hydrodynamics method and its application to aircraft ditching simulations. Aerospace Science and Technology, 2017, 66: 28-43

[63] Yang Q, Qiu W. Numerical simulation of water impact for 2d and 3d bodies. Ocean Engineering, 2012, 43: 82-89

[64] Yang Q, Xu F, Yang Y, Wang L. A multi-phase SPH model based on riemann solvers for simulation of jet breakup. Engineering Analysis with Boundary Elements, 2020, 111: 134-147

[65] Ye T, Pan D, Huang C, Liu M. Smoothed particle hydrodynamics (SPH) for complex uid ows: Recent developments in methodology and applications. Physics of Fluids, 2019, 31(1): 011301

[66] Yettou EM, Desrochers A, Champoux Y. Experimental study on the water impact of a symmetrical wedge. Fluid Dynamics Research, 2006, 38(1): 47

[67] Yu J, Liu Z, Zhang X, Zhang H. CFD numerical simulation of air-liquid two-phase ow in vertical tube of airlift pump. Water Resources and Hydropower Engineering, 2015, 46(9): 144-147

[68] Zhang AM, Sun PN, Ming FR, Colagrossi A. Smoothed particle hydrodynamics and its applications in fluid-structure interactions. Journal of Hydrodynamics, Ser. B, 2017, 29(2): 187-216

[69] Zhao R, Faltinsen O. Water entry of two-dimensional bodies. Journal of uid mechanics, 1993, 246: 593-612