Numerical simulation of viscous liquid sloshing by moving-particle semi-implicit method

A meshless numerical simulation method, the moving-particle semi-implicit method （MPS） is presented in this paper to study the sloshing phenomenon in ocean and naval engineering. As a meshless method, MPS uses particles to replace the mesh in traditional methods, the governing equations are discretized by virtue of the relationship of particles, and the Poisson equation of pressure is solved by incomplete Cholesky conjugate gradient method （ICCG）, the free surface is tracked by the change of numerical density. A numerical experiment of viscous liquid sloshing tank was presented and compared with the result got by the difference method with the VOF, and an additional modification step was added to make the simulation more stable. The results show that the MPS method is suitable for the simulation of viscous liquid sloshing, with the advantage in arranging the particles easily, especially on some complex curved surface.

Moving-Particle Semi-Implicit Method for Vortex Patterns and Roll Damping of 2D Ship Sections

A meshless method, Moving-Particle Semi-hnplicit Method （MPS） is presented in this paper to simulate the rolling of different 2D ship sections. Sections S. S. 0.5, S.S. 5.0 and S. S. 7.0 of series 60 with CB = 0.6 are chosen for the simulation. It shows that the result of MPS is very close to results of experiments or mesh-numerical simulations. In the simulation of MPS, vortices are found periodically in bilges of ship sections. In section S. S. 5.0 and section S. S. 7.0, which are close to the middle ship, two little vortices are found at different bilges of the section, in section S. S. 0.5, which is close to the bow, only one big vortex is found at the bottom of the section, these vortices patterns are consistent with the theory of Ikeda. The distribution of shear stress and pressure on the rolling hull of ship section is calculated. When vortices are in bilges of the section, the sign clmnge of pressure can be found, but in section S. S. 0.5, there is no sign change of pressure because only one vortex in the bottom of the section. With shear stress distribution, it can be found the shear stress in bilges is bigger than that at other part of the ship section. As the free surface is considered, the shear stress of both sides near the free surface is close to zero and even sign changed.

Numerical Simulation of Sloshing with Large Deforming Free Surface by MPS-LES Method

Moving particle semi-implicit （MPS） method is a fully Lagrangian particle method which can easily solve problems with violent free surface. Although it has demonstrated its advantage in ocean engineering applications, it still has some defects to be improved. In this paper, MPS method is extended to the large eddy simulation （LES） by coupling with a sub-particle-scale （SPS） turbulence model. The SPS turbulence model turns into the Reynolds stress terms in the filtered momentum equation, and the Smagorinsky model is introduced to describe the Reynolds stress terms. Although MPS method has the advantage in the simulation of the free surface flow, a lot of non-free surface particles are treated as free surface particles in the original MPS model. In this paper, we use a new free surface tracing method and the key point is ＂neighbor particle＂. In this new method, the zone around each particle is divided into eight parts, and the particle will be treated as a free surface particle as long as there are no ＂neighbor particles＂ in any two parts of the zone. As the number density parameter judging method has a high efficiency for the free surface particles tracing, we combine it with the neighbor detected method. First, we select out the particles which may be mistreated with high probabilities by using the number density parameter judging method. And then we deal with these particles with the neighbor detected method. By doing this, the new mixed free surface tracing method can reduce the mistreatment problem efficiently. The serious pressure fluctuation is an obvious defect in MPS method, and therefore an area-time average technique is used in this paper to remove the pressure fluctuation with a quite good result. With these improvements, the modified MPS-LES method is applied to simulate liquid sloshing problems with large deforming free surface. Results show that the modified MPS-LES method can simulate the large deforming free surface easily. It can not only capture the large impact pressure accurately on rolling tank wall but also can generate all physical phenomena successfully. The good agreement between numerical and experimental results proves that the modified MPS-LES method is a good CFD methodology in free surface flow simulations.

Large deformation simulations of geomaterials using moving particle semi-implicit method

Numerical simulation tools are required to describe large deformations of geomaterials for evaluating the risk of geo-disasters. This study focused on moving particle semi-implicit(MPS) method, which is a Lagrangian gridless particle method, and investigated its performance and stability to simulate large deformation of geomaterials. A calculation method was developed using geomaterials modeled as Bingham fluids to improve the original MPS method and enhance its stability. Two numerical tests showed that results from the improved MPS method was in good agreement with the theoretical value.Furthermore, numerical simulations were calibrated by laboratory experiments. It showed that the simulation results matched well with the experimentally observed free-surface configurations for flowing sand. In addition, the model could generally predict the time-history of the impact force. The MPS method could be a useful tool to evaluate large deformation of geomaterials.

Numerical Simulation of Sloshing Using the MPS-FSI Method with Large Eddy Simulation

A numerical model has been developed to study sloshing of turbulent flow in a tank with elastic baffles. The Moving-Particle Semi-implicit method(MPS) is a kind of meshless Lagrangian calculation method. The large eddy simulation(LES) approach is employed to model the turbulence by using the Smagorinsky Sub-Particle Scale(SPS)closure model. This paper uses MPS-FSI method with LES to simulate the interaction between free surface flow and a thin elastic baffle in sloshing. Then, the numerical model is validated, and the numerical solution has good agreement with experimental data for sloshing in a tank with elastic baffles. Furthermore, under external excitations,the MPS is applied to viscous laminar flow and turbulent flow, with both the deformation of elastic baffles and the wave height of the free surface are compared with each other. Besides, the impact pressure with/without baffles and wave height of free surface are investigated and discussed in detail. Finally, preliminary simulations are carried out in the damage problem of elastic baffles, taking the advantage of the MPS-FSI method in computations of the fluid–structure interaction with large deformation.

Numerical simulation of liquid sloshing in a spherical tank by MPS method

This paper investigates the sloshing phenomena in a spherical liquid tank using the moving particle semi-implicit(MPS)method,a crucial study in fluid dynamics.Distinct from previous research focused on rectangular or LNG tanks,this work explores the unique motion patterns inherent to spherical geometries.The accuracy of our in-house MPS solver MLParticle-SJTU is validated against experimental data and finite volume method(FVM).And the MPS method reveals a closer alignment with experimental outcomes,which suggests that MPS method is particularly effective for modeling complex,non-linear fluid behaviors.Then the fluid’s response to excitation at its natural frequency is simulated,showcasing vigorous sloshing and rotational motion.Detailed analyses of the fluid motion are conducted by drawing streamline diagrams,velocity vector diagrams,and vorticity maps.The fluid’s motion response is explored using both time-domain and frequency-domain curves of the fluid centroid,as well as the sloshing force.

Research on Numerical Wave Tank Based on the Improved Moving-Particle Semi-Implicit Method with Large Eddy Simulation

Moving-particle semi-implicit(MPS) method is a new mesh-free numerical method based on Lagrangian particle. In this paper, MPS method is applied to the study on numerical wave tank. For the purpose of simulating numerical wave, we combine the MPS method with large eddy simulation(LES) which can simulate the turbulence in the flow. The intense pressure fluctuation is a significant shortcoming in MPS method. So, we improve the original MPS method by using a new pressure Poisson equation to ease the pressure fluctuation. Divergencefree condition representing fluid incompressible is used to calculate pressure smoothly. Then, area-time average technique is used to deal with the calculation. With these improvements, the modified MPS-LES method is applied to the simulation of numerical wave. As a contrast, we also use the original MPS-LES method to simulate the wave in a numerical wave tank. The result shows that the new method is better than the original MPS-LES method.

Numerical simulations of faraday waves in cylindrical and hexagonal tanks based on MPS method

When a partially loaded liquid container vibrates along the vertical direction,the liquid inside will oscillate regularly,which is called Faraday wave.In some cases,the wave form of the Faraday wave is stable and smooth,and sometimes there is violent wave breaking and liquid splashing.In this paper,the Faraday waves inside the cylindrical tank and the hexagonal tanks are simulated by the in-house solver MLParticle-SJTU base on the moving particle semi-implicit(MPS)method.The surface tension model is used to better model the free surfaces with large deformations.Phenomena such as wave breaking and liquid splashing are well captured and simulated.The results show that the waveforms are significantly different at different excitation frequencies.And the tank shape also has an obvious effect on the waveform.

Comparative study of MPS method and level-set method for sloshing flows

This paper presents a comparative study of a meshless level-set method in the simulation of sloshing flows. The numerical moving particle semi-implicit （MPS） method and a grid based schemes of the MPS and level-set methods are outlined and two violent sloshing cases are considered. The computed results are compared with the corresponding experimental data for validation. The impact pressure and the deformations of free surface induced by sloshing are comparatively analyzed, and are in good agreement with experimental ones. Results show that both the MPS and level-set methods are good tools for simulation of violent sloshing flows. However, the second pressure peaks as well as breaking and splashing of free surface by the MPS method are captured better than by the level-set method.

Numerical study of the wave-induced slamming force on the elastic plate based on MPS-FEM coupled method

Slamming is the phenomenon of structure impacting the water surface. It always results in the extremely high load on the structure. This paper is mainly concerned with the slamming force caused by the wave-plate interaction. In this paper, the process of solitary wave impacting onto the horizontal plate is simulated with the help of the moving particle semi-implicit and finite element coupled method（MPS-FEM）. The MPS method is adopted to calculate the fluid domain while the structural domain is solved by FEM method. In the first series of simulations, the profiles of the solitary waves with various amplitudes, which are generated in the numerical wave tank, are compared with the theoretical results. Thereafter the interaction between the solitary waves and a rigid plate is simulated. The effects of wave amplitude, as well as the elevation of the plate above the initial water level, on the slamming force are numerically investigated. The calculated results are compared with the available experimental data. Finally, the interactions between the solitary waves and the elastic plate are also simulated. The effects of the structural flexibility on the wave-induced force are analyzed by the comparison between the cases with elastic and the rigid plate.

Numerical simulations of sloshing waves in vertically excited square tank by improved MPS method

Faraday wave is a phenomenon of sloshing due to a heave motion of a partially filled tank,which is also called parametric instability or parametric resonance.In the present paper,the phenomenon of faraday wave in a pure heave excited square tank is numerically simulated through the moving particle semi-implicit(MPS)method.The surface tension effect and a new Dirichlet boundary condition for the pressure Poisson equation are considered to avert unphysical fragmentation and clustering of particles in splash simulation.In the numerical simulation,the evolution of wave motion,and the non-linearity together with breaking phenomenon of faraday wave can be observed.The agreement is good in general,both amplitude and phase.Besides,the parameter studies including the excitation frequency and the forcing amplitude are carried out to analyses the mechanism of resonances response.

Implementation of the moving particle semi-implicit method on GPU

The Moving Particle Semi-implicit (MPS) method performs well in simulating violent free surface flow and hence becomes popular in the area of fluid flow simulation. However, the implementations of searching neighbouring particles and solving the large sparse matrix equations (Poisson-type equation) are very time-consuming. In order to utilize the tremendous power of parallel computation of Graphics Processing Units (GPU), this study has developed a GPU-based MPS model employing the Compute Unified Device Architecture (CUDA) on NVIDIA GTX 280. The efficient neighbourhood particle searching is done through an indirect method and the Poisson-type pressure equation is solved by the Bi-Conjugate Gradient (BiCG) method. Four different optimization levels for the present general parallel GPU-based MPS model are demonstrated. In addition, the elaborate optimization of GPU code is also discussed. A benchmark problem of dam-breaking flow is simulated using both codes of the present GPU-based MPS and the original CPU-based MPS. The comparisons between them show that the GPU-based MPS model outperforms 26 times the traditional CPU model.

Improvement of solidification model and analysis of 3D channel blockage with MPS method

In a severe accident of a nuclear power reactor,coolant channel blockage by solidified molten core debris may significantly influence the core degradations that follow.The moving particle semi-implicit(MPS)method is one of the Lagrangian-based particle methods for analyzing incompressible flows.In the study described in this paper,a novel solidification model for analyzing melt flowing channel blockage with the MPS method has been developed,which is suitable to attain a sufficient numerical accuracy with a reasonable calculation cost.The prompt velocity diffusion by viscosity is prioritized over the prompt velocity correction by the pressure term(for assuring incompressibility)within each time step over the“mushy zone”(between the solidus and liquidus temperature)for accurate modeling of solidification before fixing the coordinates of the completely solidified particles.To sustain the numerical accuracy and stability,the corrective matrix and particle shifting techniques have been applied to correct the discretization errors from irregular particle arrangements and to recover the regular particle arrangements,respectively.To validate the newly developed algorithm,2-D benchmark analyses are conducted for steady-state freezing of the water in a laminar flow between two parallel plates.Furthermore,3-D channel blockage analyses of a boiling water reactor(BWR)fuel support piece have been performed.The results show that a partial channel blockage develops from the vicinity of the speed limiter,which does not fully develop into a complete channel blockage,but still diverts the incoming melt flow that follows to the orifice region.

CFD simulations of three-dimensional violent sloshing flows in tanks based on MPS and GPU

For violent sloshing,the flow field becomes complicated and 3-D effect is non-negligible.In addition to the excitation direction,the wave can also propagate perpendicular to the excitation direction.Due to the superposition of waves from different directions,the impact pressure imposed on the wall of the tank may increase.In this paper,our in-house solver MPSGPU-SJTU based on moving particle semi-implicit(MPS)method coupled with GPU techniques is employed for the liquid sloshing simulation,to study the factors leading to the 3-D effect.Firstly,a series of sloshing simulations are carried out to validate the reliability of present solver.Then,the sensitivity of 3-D effect against some parameters,such as excitation frequency,dimensions of the tank and filling ratio,is checked through numerical simulations.Time histories of pressure obtained by 2-D and 3-D simulations are compared to judge the occurrence of 3-D effect.It concludes that effects of those parameters are all significant.

Towards development of enhanced fully-Lagrangian mesh-free computational methods for fluid-structure interaction

Simulation of incompressible fluid flow-elastic structure interactions is targeted by using fully-Lagrangian mesh-free computational methods. A projection-based fluid model（moving particle semi-implicit（MPS）） is coupled with either a Newtonian or a Hamiltonian Lagrangian structure model（MPS or HMPS） in a mathematically-physically consistent manner. The fluid model is founded on the solution of Navier-Stokes and continuity equations. The structure models are configured either in the framework of Newtonian mechanics on the basis of conservation of linear and angular momenta, or Hamiltonian mechanics on the basis of variational principle for incompressible elastodynamics. A set of enhanced schemes are incorporated for projection-based fluid model（Enhanced MPS）, thus, the developed coupled solvers for fluid structure interaction（FSI） are referred to as Enhanced MPS-MPS and Enhanced MPS-HMPS. Besides, two smoothed particle hydrodynamics（SPH）-based FSI solvers, being developed by the authors, are considered and their potential applicability and comparable performance are briefly discussed in comparison with MPS-based FSI solvers. The SPH-based FSI solvers are established through coupling of projection-based incompressible SPH（ISPH） fluid model and SPH-based Newtonian/Hamiltonian structure models, leading to Enhanced ISPH-SPH and Enhanced ISPH-HSPH. A comparative study is carried out on the performances of the FSI solvers through a set of benchmark tests, including hydrostatic water column on an elastic plate,high speed impact of an elastic aluminum beam, hydroelastic slamming of a marine panel and dam break with elastic gate.

Investigations on lubrication characteristics of high-speed electric multiple unit gearbox by oil volume adjusting device

In this paper,a numerical simulation model of the flow field in a gearbox with an oil volume adjusting device is established for the first time to study its influence on the lubrication characteristics of a high-speed electric multiple unit(EMU)gearbox.The moving particle semi-implicit(MPS)method is used to numerically simulate the internal flow field of the gearbox of the high-speed EMU under working conditions.The effects of the velocity of the high-speed EMU,the immersion depth,and the oil sump temperature on the power loss of the gears and the lubricant quantity of each bearing are studied and provide an effective tool for the quantitative evaluation of the lubrication characteristics of the gearbox.The lubrication characteristics of the gearbox under different working conditions are studied when the oil volume adjusting device is closed and opened.The results show that the oil volume adjusting device mainly changes the amount of lubricant stirred by the output gear by changing the flow rate of lubricant from the cavity pinion(Cavity P)to the cavity gear(Cavity G),and thus affects the power loss of gears and the lubricant quantity of each bearing.