A NURBS-based isogeometric boundary element method for analysis of liquid sloshing in axisymmetric tanks with various porous baffles.

*(English)*Zbl 07198448Summary: An isogeometric boundary element method (IGA-BEM) based on the non-uniform rational B-splines (NURBS) is firstly performed to investigate the liquid sloshing in axisymmetric tanks with the porous baffles. The proposed method can completely maintain the advantages of the BEM that only the boundary of a domain requires discretization. By applying the NURBS basis functions it can exactly describe the geometry of the boundary. Meanwhile, it can also be obtained better solution field approximation at the domain boundary. Furthermore, as to the axisymmetric geometries of the containers considered in this paper, the 3-D liquid sloshing problems can be effectively reduced to 2-D ones on half of the cross-sections of the containers, which can significantly increase the computational efficiency. Meanwhile, the zoning method is employed in this paper to treat the arbitrary mounted porous baffles, and the Laplace equation is utilized as the governing equation of the potential flow model by assuming the fluid motion to be inviscid, irrotational and incompressible. Additionally, the weighted residual method together with the Green’s theorem is applied to develop the BEM integral equation. The natural sloshing frequencies and dynamic sloshing forces solved by the proposed method are compared with the available literatures and the traditional boundary element method (BEM). Good agreements are observed in the comparisons between numerical results and those of the existing literatures. And higher accuracy and convergence can be achieved by the proposed IGA-BEM method with significantly fewer nodes than the traditional BEM. Moreover, spherical tanks with the coaxial hemispherical, wall-mounted conical or surface-piercing cylindrical porous baffle, ellipsoidal tanks with spheroidal or surface-piercing cylindrical porous baffle, and the toroidal tank with tubular porous baffle are considered to investigate the effects of the porous-effect parameter, radius, length, height, horizontal and vertical semi-axes of the porous baffle on the sloshing characteristics (i.e. dynamic sloshing forces and surface elevations). The results show that the surface-piercing cylindrical porous baffle offers more noticeable suppression on sloshing response than the hemispherical and spheroidal porous baffles. Changing the radius of the tubular porous baffle has almost negligible effect on the sloshing force acting on the toroidal tank. The excitation frequency corresponding to the maximal value of sloshing force can be altered evidently by changing the porous-effect parameter of the porous baffle. In addition, choosing reasonable porous-effect parameter, radius, horizontal semi-axes and relatively larger length, height as well as vertical semi-axes for the porous baffles yields considerable suppression on the sloshing response.

##### MSC:

76-XX | Fluid mechanics |

Full Text:
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##### References:

[1] | Abramson, H. N., The dynamic behavior of liquids in moving containers with applications to space vehicle technology, (NASA SP (1966)), 106 |

[2] | McIver, P., Sloshing frequencies for cylindrical and spherical containers filled to an arbitrary depth, J. Fluid Mech., 201, 243 (1989) |

[3] | Miao, G., Analytical solutions for the sloshing loading on circular cylindrical liquid tanks with interior semi-porous barriers, J. Hydrodyn., 2, 32-39 (2001) |

[4] | Faltinsen, O. M.; Firoozkoohi, R.; Timokha, A. N., Analytical modeling of liquid sloshing in a two-dimensional rectangular tank with a slat screen, J. Eng. Math., 70, 93-109 (2011) |

[5] | Wang, J. D.; Zhou, D.; Liu, W. Q., Response of liquid in cylindrical tank with rigid annual baffle considering damping effect, Adv. Mater. Res., 3687, 255-260-3691 (2011) |

[6] | Wang, J. D.; Lo, S. H.; Zhou, D., Liquid sloshing in rigid cylindrical container with multiple rigid annular baffles: Free vibration, J. Fluids Struct., 34, 138-156 (2012) |

[7] | Wang, J.; Wang, C.; Liu, J., Sloshing reduction in a pitching circular cylindrical container by multiple rigid annular baffles, Ocean Eng., 171, 241-249 (2019) |

[8] | Hasheminejad, S. M.; Aghabeigi, M., Sloshing characteristics in half-full horizontal elliptical tanks with vertical baffles, Appl. Math. Model., 36, 57-71 (2012) |

[9] | Crowley, S.; Porter, R., An analysis of screen arrangements for a tuned liquid damper, J. Fluids Struct., 34, 291-309 (2012) |

[10] | Molin, B.; Remy, F., Experimental and numerical study of the sloshing motion in a rectangular tank with a perforated screen, J. Fluids Struct., 43, 463-480 (2013) |

[11] | Cho, I. H.; Kim, M. H., Effect of dual vertical porous baffles on sloshing reduction in a swaying rectangular tank, Ocean Eng., 126, 364-373 (2016) |

[12] | Cho, I. H.; Choi, J.; Kim, M. H., Sloshing reduction in a swaying rectangular tank by an horizontal porous baffle, Ocean Eng., 138, 23-34 (2017) |

[13] | Xue, M.; Zheng, J.; Lin, P.; Yuan, X., Experimental study on vertical baffles of different configurations in suppressing sloshing pressure, Ocean Eng., 136, 178-189 (2017) |

[14] | Cho, J. R.; Lee, H. W., Numerical study on liquid sloshing in baffled tank by nonlinear finite element method, Comput. Methods Appl. Mech. Engrg., 193, 2581-2598 (2004) |

[15] | Cho, J. R.; Lee, H. W.; Ha, S. Y., Finite element analysis of resonant sloshing response in 2-D baffled tank, J. Sound Vib., 288, 829-845 (2005) |

[16] | Arafa, M., Finite element analysis of sloshing in liquid-filled containers, Prod. Eng. Des. Dev., 79, 3-803 (2006) |

[17] | Love, J. S.; Tait, M. J., Linearized sloshing model for 2D tuned liquid dampers with modified bottom geometries, Can. J. Civil Eng., 41, 106-117 (2014) |

[18] | Celebi, M. S.; Akyildiz, H., Nonlinear modeling of liquid sloshing in a moving rectangular tank, Ocean Eng., 29, 1527-1553 (2002) |

[19] | Saoudi, Z.; Hafsia, Z.; Maalel, K., Dumping effects of submerged vertical baffles and slat screen on forced sloshing motion, J. Water Resour. Hydraul. Eng., 2, 51-60 (2013) |

[20] | Chu, C. R.; Wu, Y. R.; Wu, T. R.; Wang, C. Y.; Abdalla, M. M., Slosh-induced hydrodynamic force in a water tank with multiple baffles, Ocean Eng., 167, 282-292 (2018) |

[21] | Sahin, G.; Bayraktar, S., Flow visualization of sloshing in an accelerated two-dimensional rectangular tank, Int. J. Eng. Technol., 3, 1, 106-112 (2015) |

[22] | Teng, B.; Zhao, M.; He, G. H., Scaled boundary finite element analysis of the water sloshing in 2D containers, Int. J. Numer. Methods Fluid, 52, 659-678 (2006) |

[23] | Wang, W.; Peng, Y.; Zhou, Y.; Zhang, Q., Liquid sloshing in partly-filled laterally-excited cylindrical tanks equipped with multi baffles, Appl. Ocean Res., 59, 543-563 (2016) |

[24] | Wang, W.; Peng, Y.; Zhang, Q.; Ren, L.; Jiang, Y., Sloshing of liquid in partially liquid filled toroidal tank with various baffles under lateral excitation, Ocean Eng., 146, 434-456 (2017) |

[25] | Wang, W.; Zhang, Q.; Ma, Q., Sloshing effects under longitudinal excitation in horizontal elliptical cylindrical containers with complex baffles, Ocean Eng., 144, 2 (2018) |

[26] | Ye, W.; Liu, J.; Lin, G.; Xu, B.; Yu, L., Application of scaled boundary finite element analysis for sloshing characteristics in an annular cylindrical container with porous structures, Eng. Anal. Bound. Elem., 97, 94-113 (2018) |

[27] | Wang, C. Y.; Teng, J. T.; Huang, G. P.G., Numerical simulation of sloshing motion inside a two-dimensional rectangular tank with a baffle or baffles, J. Aeronaut. Astronaut. Aviat. Ser. A, 42, 207-215 (2010) |

[28] | Pal, P.; Bhattacharyya, S. K., Sloshing in partially filled liquid containers—Numerical and experimental study for 2-D problems, J. Sound Vib., 329, 4466-4485 (2010) |

[29] | Dutta, S.; Laha, M. K., Analysis of the small amplitude sloshing of a liquid in a rigid container of arbitrary shape using a low-order boundary element method, Internat. J. Numer. Methods Engrg., 47, 1633-1648 (2000) |

[30] | Gedikli, A.; Ergüven, M. E., Evaluation of sloshing problem by variational boundary element method, Eng. Anal. Bound. Elem., 27, 935-943 (2003) |

[31] | Chen, Y.; Hwang, W.; Ko, C., Sloshing behaviours of rectangular and cylindrical liquid tanks subjected to harmonic and seismic excitations, Earthq. Eng. Struct. Dyn., 36, 1701-1717 (2007) |

[32] | Firouz-Abadi, R. D.; Haddadpour, H.; Noorian, M. A.; Ghasemi, M., A 3D BEM model for liquid sloshing in baffled tanks, Internat. J. Numer. Methods Engrg., 76, 1419-1433 (2008) |

[33] | Sygulski, R., Boundary element analysis of liquid sloshing in baffled tanks, Eng. Anal. Bound. Elem., 35, 978-983 (2011) |

[34] | Gedikli, A.; Ergüven, M. E., Seismic analysis of a liquid storage tank with a baffle, J. Sound Vib., 223, 141-155 (1999) |

[35] | Ebrahimian, M.; Noorian, M. A.; Haddadpour, H., A successive boundary element model for investigation of sloshing frequencies in axisymmetric multi baffled containers, Eng. Anal. Bound. Elem., 37, 383-392 (2013) |

[36] | Ebrahimian, M.; Noorian, M. A.; Haddadpour, H., Equivalent mechanical model of liquid sloshing in multi-baffled containers, Eng. Anal. Bound. Elem., 47, 82-95 (2014) |

[37] | Kolaei, A.; Rakheja, S.; Richard, M. J., A coupled multimodal and boundary-element method for analysis of anti-slosh effectiveness of partial baffles in a partly-filled container, Comput. & Fluids, 107, 43-58 (2015) |

[38] | Degtyarev, K.; Gnitko, V.; Naumenko, V.; Strelnikova, E., Reduced boundary element method for liquid sloshing analysis of cylindrical and conical tanks with baffles, Electron. Eng. Comput. Sci., 1, 14-27 (2016) |

[39] | Gnitko, V.; Naumemko, Y.; Strelnikova, E., Low frequency sloshing analysis of cylindrical containers with flat and conical baffles, Int. J. Appl. Mech. Eng., 22, 867-881 (2017) |

[40] | Hu, Z.; Zhang, X.; Li, X.; Li, Y., On natural frequencies of liquid sloshing in 2-D tanks using Boundary Element Method, Ocean Eng., 153, 88-103 (2018) |

[41] | Hughes, T. J.; Cottrell, J. A.; Bazilevs, Y., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194, 39-41, 4135-4195 (2005) |

[42] | Simpson, R. N.; Bordas, S. P.A.; Trevelyan, J.; Rabczuk, T., A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis, Comput. Methods Appl. Mech. Eng., 209-212, 87-100 (2012) |

[43] | Simpson, R. N.; Bordas, S. P.A.; Lian, H.; Trevelyan, J., An isogeometric boundary element method for elastostatic analysis: 2D implementation aspects, Comput. Struct., 118, 2-12 (2013) |

[44] | Falini, A.; Giannelli, C.; Kanduč, T.; Sampoli, M. L.; Sestini, A., An adaptive IgA-BEM with hierarchical B-splines based on quasi-interpolation quadrature schemes, Internat. J. Numer. Methods Engrg., 117, 1038-1058 (2018) |

[45] | Belibassakis, K. A.; Gerostathis, T. P., A BEM-isogeometric method for the ship wave-resistance problem, Ocean Eng., 60, 53-67 (2013) |

[46] | Peake, M. J.; Trevelyan, J.; Coates, G., Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems, Comput. Methods Appl. Mech. Engrg., 259, 93-102 (2013) |

[47] | Simpson, R. N.; Scott, M. A.; Taus, M.; Thomas, D. C.; Lian, H., Acoustic isogeometric boundary element analysis, Comput. Methods Appl. Mech. Engrg., 269, 265-290 (2014) |

[48] | Coox, L.; Atak, O.; Vandepitte, D.; Desmet, W., An isogeometric indirect boundary element method for solving acoustic problems in open-boundary domains, Comput. Methods Appl. Mech. Engrg., 316, 186-208 (2017) |

[49] | Marussig, B.; Beer, G.; Duenser, C., Isogeometric boundary element method for the simulation in tunneling, Appl. Mech. Mater., 553, 495-500 (2014) |

[50] | Heltai, L.; Arroyo, M.; DeSimone, A., Nonsingular isogeometric boundary element method for Stokes flows in 3D, Comput. Methods Appl. Mech. Engrg., 268, 514-539 (2014) |

[51] | Beer, G.; Duenser, C., Isogeometric boundary element analysis of problems in potential flow, Comput. Methods Appl. Mech. Engrg., 347, 517-532 (2019) |

[52] | Peake, M. J.; Trevelyan, J.; Coates, G., Extended isogeometric boundary element method (XIBEM) for three-dimensional medium-wave acoustic scattering problems, Comput. Methods Appl. Mech. Engrg., 284, 762-780 (2015) |

[53] | Nguyen, B. H.; Tran, H. D.; Anitescu, C.; Zhuang, X.; Rabczuk, T., An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems, Comput. Methods Appl. Mech. Engrg., 306, 252-275 (2016) |

[54] | Gong, Y. P.; Dong, C. Y., An isogeometric boundary element method using adaptive integral method for 3D potential problems, J. Comput. Appl. Math., 319, 141-158 (2017) |

[55] | Liu, C.; Chen, L.; Zhao, W.; Chen, H., Shape optimization of sound barrier using an isogeometric fast multipole boundary element method in two dimensions, Eng. Anal. Bound. Elem., 85, 142-157 (2017) |

[56] | An, Z.; Yu, T.; Bui, T. Q.; Wang, C.; Trinh, N. A., Implementation of isogeometric boundary element method for 2-D steady heat transfer analysis, Adv. Eng. Softw., 116, 36-49 (2018) |

[57] | Qu, X. Y.; Dong, C. Y.; Bai, Y.; Gong, Y. P., Isogeometric boundary element method for calculating effective property of steady state thermal conduction in 2D heterogeneities with a homogeneous interphase, J. Comput. Appl. Math., 343, 124-138 (2018) |

[58] | Gong, Y. P.; Dong, C. Y.; Qu, X. Y., An adaptive isogeometric boundary element method for predicting the effective thermal conductivity of steady state heterogeneity, Adv. Eng. Softw., 119, 103-115 (2018) |

[59] | Brebbia, C. A.; Telles, J. C.F.; Wrobel, L. C., Boundary Element Techniques (1984), Springer-Verlag: Springer-Verlag Berlin and New York |

[60] | Stroud, A. H.; Secrest, D., Gaussian Quadrature Formulas (1966), Prentice-Hall |

[61] | Guiggiani, M.; Casalini, P., Direct computation of Cauchy principal value integrals in advanced boundary elements, Internat. J. Numer. Methods Engrg., 24, 1711-1720 (1987) |

[62] | Piegl, L.; Tiller, W., The NURBS Book (1997), Springer-Verlag New York, Inc. |

[63] | Greville, T., Numerical procedures for interpolation by spline functions, J. Soc. Ind. Appl. Math. Ser. B Numer. Anal., 1964 (1964) |

[64] | Gao, X. W.; Davies, T. G., 3D multi-region BEM with corners and edges, Int. J. Solids Struct., 37, 11, 1549-1560 (2000) |

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