Engineering Analysis with Boundary Elements 97 (2018) 94–113 Contents lists available at ScienceDirect Engineering Analysis with Boundary Elements journal homepage: www.elsevier.com/locate/enganabound Application of scaled boundary ﬁnite element analysis for sloshing characteristics in an annular cylindrical container with porous structures Wenbin Ye a,b , Jun Liu a,b,c,∗ , Gao Lin a,b , Bin Xu a,b , Long Yu a,b a State Key Laboratory of Coastal and Oﬀshore Engineering, Dalian University of Technology, Dalian 116024, China b School of Hydraulic Engineering, Faculty of Infrastructure Engineering, Dalian University of Technology, China c Centre for Oﬀshore Foundation Systems, School of Civil Environmental and Mining Engineering, the University of Western Australia, Perth 6009, Australia a r t i c l e i n f o Keywords: Scaled boundary ﬁnite element method Liquid sloshing Annular cylindrical tank Porous structure Variational principle a b s t r a c t The scaled boundary ﬁnite element method (SBFEM) is introduced for the investigation of the liquid sloshing in an annular cylindrical container with the coaxial porous structures. The main advantages of the SBFEM for this problem is that only the outer wall of the annular tank is discretized while the inner wall and the porous structures need not be treated, which is not only convenient for the generation of mesh, but also reduces the spatial dimension by one. Meanwhile, the solutions of the velocity potential are analytical in the radical direction of the scaled boundary coordinate system. In this paper, two types of the porous structures, that are, the circular and the arc-shaped porous structures, are taken into account. For the arc-shaped system, a virtual circular by extending the arc-shaped structure porous is introduced and one can set the porous-eﬀect parameter of the virtual section to inﬁnity, so that the whole ﬂow domain can be divided into two sub-domains by the porous structure as the same approach with the circular system. By the assumption of the incompressible, inviscid, and irrotational ﬂow and using the variational principle, the SBFEM governing equations with respect to the radical coordinate of the velocity potential in each sub-domain are obtained. Then, the governing equations can be solved analytically by introducing the Bessel functions and the modiﬁed Bessel functions as the base solutions. The excellent eﬃciency and accuracy of the proposed formulations are demonstrated by comparing the SBFEM numerical results with the analytical solutions. In addition, the eﬀects of the diﬀerent parameters for sloshing characteristics, such as the porous-eﬀect parameter, radius of porous structure, standing wave number, opening degree and location of the arc-shaped porous structure are further studied. 1. Introduction In many practical engineering, such as transportation, aerospace, civil and nuclear industries, the sloshing of liquid in the cylindrical or annular cylindrical tank is a very important problem of research. In re- cent years, a considerable amount of works on liquid sloshing in the cylindrical or annular cylindrical tanks have been studied. For example, Sawada et al. [1] explored the magnetic ﬂuid sloshing in a cylindrical tank with a vertical magnetic ﬁeld under the lateral excitation experi- mentally. Papaspyrou et al. [2] presented a mathematical model to in- vestigate the sloshing responses of liquid in a horizontal cylindrical tank subjected to a longitudinal external excitation. Based upon the assump- tion of ideal ﬂow, Tetsuya et al. [3,4] studied analytically the sloshing motions of liquid in a cylindrical storage container with a elastic ﬂoating roof subjected to a seismic excitation. Wang et al. [5] applied the ﬁnite element technique to investigate the small amplitude liquid sloshing in a rigid cylindrical tank with the diﬀerent contact boundary conditions. He et al. [6] introduced the variational principle and multiple-scales method for the investigation of the non-linear sloshing behaviors of low- ∗ Corresponding author at: State Key Laboratory of Coastal and Oﬀshore Engineering, Dalian University of Technology, Dalian 116024, China. E-mail address: liujun8128@126.com (J. Liu). gravity liquid in the cylindrical container subjected to the pitch excita- tion. Sciortino et al. [7] carried out both a novel Hamiltonian model and some experiments to analyze the sloshing of the layered ﬂow in a cylin- drical container under an arbitrary rigid motion. Firouz-Abadi et al. [8], based on the assumption of incompressible potential ﬂow, developed a boundary element model to study the dynamic sloshing characteristics of liquid in the three-dimensional tanks subjected to a rocking motion. By employing the variational principle, Takahara et al. [9] analyzed the nonlinear sloshing responses of liquid in an annular cylindrical con- tainer with a pitching excitation, and then they conducted a laboratory experiment to verify the eﬀectiveness of the nonlinear formulations. By comparing with the theoretical solutions and experimental results, they found that the nonlinear eﬀects played an important role in the analysis of the sloshing responses. Similarly, with the experimental approach, Keita et al. [10] studied the sloshing phenomena of water in a cylindri- cal container with a rotating bottom. Yoshiaki [11] presented a FLU- ENT computational model to investigate the stable self-induced rotary liquid sloshing characteristics in a cylindrical storage tank under a peri- odic jet. Using the linear potential ﬂow theory, Hasheminejad et al. [12] https://doi.org/10.1016/j.enganabound.2018.09.013 Received 3 May 2018; Received in revised form 2 August 2018; Accepted 26 September 2018 0955-7997/© 2018 Elsevier Ltd. All rights reserved.