Liquid sloshing is a key function of propellant tanks in spacecrafts. Moving particle Semi-Implicit (MPS) method is a meshless particle method based on Lagrangian representation, particularly adept at handling strong nonlinear phenomena like free surface breaking and liquid droplet splashing which is commonly observed in liquid sloshing. In this paper, the in-house MPS solver MLPartile-SJTU is used to simulate the liquid sloshing within a three-dimensional spherical tank. The sphere is prescribed to an oscillating motion with different motion amplitudes, frequencies and liquid filling ratio. The simulated results, including forces and free surfaces at specific time snapshots, are compared with experimental data.
Moving particle Semi-Implicit (MPS) method is a meshless particle method developed on the basis of Smoothed particle Hydrodynamics(SPH) method. It was first proposed by Koshizuka (1996) to solve the problem of incompressible flow. Then MPS method was used to study the breaking wave problem and analyze different breaking wave forms by Koshizuka(1998).Yoon et al. (2001) combined MPS and ALE (Arbitrary Lagrange Euler) methods to propose an MPS method that could simulate gas-liquid two-phase flow. Nomura et al. (2001) proposed a surface tension calculation model suitable for MPS method, and studied the falling and breaking process of two-dimensional droplets on this basis. Sueyoshi et al. (2004) studied the large motion of floating body in waves based on MPS method and analyzed the two-dimensional tank damage problem. Liu et al. (2005) proposed a method combining MPS and grid method to study two-phase flow, in which MPS method was used to calculate the solution of the liquid part and grid method was used to calculate the gas part. Shao et al. (2005) tried to introduce SPS (Sub-particle Scale) turbulence model into MPS to study two-dimensional dam break and wave break problems. Pan et al. (2008) applied MPS based on SPS turbulence simulation to the problem of tank sloshing and analyzed the influence of different kernel functions in the calculation of tank sloshing. Kouh et al. (2009) simulated the motion of a two-dimensional floating body in waves, and analyzed the influence of the liquid loaded in the floating body cabin on the motion. Shakibaeinia et al. (2012) proposed a weakly compressible MPS and applied it to multiphase flows. Khayyer et al. (2013)adopted an extended density smoothing method to improve the stability of MPS methods. In addition, an improved gradient model was proposed to improve the stability and accuracy. Shibata et al. (2015)proposed a new free liquid surface boundary condition to improve the MPS method, and the results showed that the pressure oscillation phenomenon was effectively improved. Wen et al.(2018) improved the SPH method by adding the diffusion term to the continuity equation and introducing the corrective smoothed particle method (CSPM). Khayyer et al. (2019)adopted the optimized particle drift improved MPS method to maintain the regularity of particles at the phase interface and free surface, and qualitatively and quantitatively verified the accuracy, energy conservation characteristics and convergence of the method. Xiao et al.(2021) adopted the weakly compressible MPS method to modify the differential operator model by coordinate transformation and smoothing algorithm. The modification of differential operator significantly improves the particle aggregation, smooths the pressure distribution and reduces the pressure oscillation.
