Moving Particle Semi-implicit Method Research Articles

A volume-conservation particle shifting scheme for moving particle method simulating free-surface flow

AbstractIn this study, a novel particle shifting scheme for the moving particle method simulating free surface flow is developed. The overall method is based on the framework of least square moving particle semi-implicit (LSMPS) method, enabling accurate and stable treatment of wall boundary without configuration of dummy or virtual wall particles. To avoid volume expansion, a volume-conservation particle shifting (VCPS) model is developed. An additional term considering the variation of particle numerical density is incorporated into the VCPS model to avoid volume expansion. Several numerical simulations are calculated to validate the effectiveness of the VCPS. It is demonstrated that LSMPS incorporating with VCPS shows satisfactory accuracy and superior capability to conserve volume.

Two‐ and three‐dimensional multiphase mesh‐free particle modeling of transitional landslide with μ(I) rheology

AbstractLandslides, which are the sources of most catastrophic natural disasters, can be subaerial (dry), submerged (underwater), or semi‐submerged (transitional). Semi‐submerged or transitional landslides occur when a subaerial landslide enters water and turns to submerged condition. Predicting the behavior of such a highly dynamic multi‐phase granular flow system is challenging, mainly due to the water entry effects, such as wave impact and partial saturation (and resulted cohesion). The mesh‐free particle methods, such as the moving particle semi‐implicit (MPS) method, have proven their capabilities for the simulation of the highly dynamic multiphase systems. This study develops and evaluates a numerical model, based on the MPS particle method in combination with the μ(I) rheological model, to simulate the morphodynamic of the granular mass in semi‐submerged landslides in two and three dimensions. An algorithm is developed to consider partial saturation (and resulting cohesion) during the water entry. Comparing the numerical results with the experimental measurements shows the ability of the proposed model to accurately reproduce the morphological evolution of the granular mass, especially at the moment of water entry.

Lubrication Reliability and Oil Churning Loss of Differential Gear Trains in a Mechanical-Hydraulic Coupling Mechanism

A differential gear train (DGT) is a crucial component of a mechanical-hydraulic coupling mechanism. The transmission process generates oil churning losses, which significantly impact the overall transmission efficiency. Due to the complexity of DGTs and the unpredictability of lubrication reliability, traditional analysis of churning characteristics is inadequate. In this study, the moving particle semi-implicit (MPS) method is employed to analyze the effects of steady-state rotation speeds, dynamic rotation speeds, and oil filling heights on the oil churning characteristics of DGTs. The accuracy of the MPS method in predicting churning loss is illustrated by the average absolute percentage error of 6.4% obtained experimentally. It is concluded that: increasing the oil filling height improves lubrication reliability by 20.9%, but results in greater power loss. The lubrication reliability and power loss of DGTs with different output forms are mutually advantageous under different influencing factors. This paper helps to improve the lubrication reliability of DGTs.

A novel numerical analysis method for predicting non-Newtonian lubricant (grease) distribution in ball bearings

Grease is a visco-elastic fluid and the most common lubricant for rolling bearings. During the churning phase (initial phase) of bearing operation, most of the grease is collected at various locations in the bearing, e.g. by the seal, at the bottom cage bar, in the cage pockets, which are then called grease reservoirs. These are formed based on bearing operating conditions, grease type, bearing geometry, bearing type. The grease reservoirs supply lubricant to the bearing contacts via bleeding: during operation the oil bleeds out of the reservoirs and lubricates the contacts. Since the distribution of grease is crucial to the bearing lubrication, the design of bearing components e.g., the cage, shall aim at an optimal grease reservoir creation during the churning phase. It is difficult to observe the effect of component design on the grease distribution through real life experiments, so CFD simulations with MPS (Moving Particle Semi-implicit) method are performed here. Flow Simulations with MPS method can help determine the factors influencing the grease distribution inside the bearing after churning, with the final aim of enhancing lubrication. For the current simulations, a CAE software based on MPS, namely Particleworks, was used. Grease consists of a base oil, a thickener, and additives. Since it is a non-Newtonian fluid, it has a nonlinear relation shear stress vs shear rate. It is a visco-elastic material, so it does not flow in the absence of a threshold force. For current simulations, the grease rheology has been modelled using the Herschel-Bulkley model. The model was fitted on in-house rheometer test data and was reduced to a single cage-ball segment. All critical kinematic properties were preserved, that is the speeds of both the inner ring and ball surfaces and the oscillation of the ball position within the pocket as it travels through the loaded and unloaded zones of the bearing. The location and the duration of grease injections resulted in different grease distributions in the model. For demonstration purposes, this document only focuses on the results obtained injecting a grease layer on the inner ring surface in front of the contact. This realistically predicted grease reservoirs to be located at the cage bottom, on the top of cage and in the cage pockets. Sensitivity study on particle size, time step, surface tension and the parametric variation of the bearing speed were also performed. This is an important milestone, as we are able for the first time to virtually simulate the onset of grease reservoirs at locations corresponding to evidence from real bearing operations. The distribution of grease observed at the cage pockets is very important for oil film replenishment. This outcome gives us confidence that the MPS method can be used to support the design of bearing components contributing to enhanced lubrication.

Applicability of Numerical Simulation by Particle Method to Unconfined Compression Tests on Geomaterials

This study emphasizes the importance of accurate input parameters for ensuring the precision and reliability of simulations by conducting a sensitivity analysis to determine the calculation and material parameters. The aim is to determine the exact material parameters, for two different soil samples in a rigid state, by comparing the results of a sensitivity analysis with the unconfined compression test benchmark data for each sample. The moving particle semi-implicit (MPS) method, one of the particle methods, was chosen to reproduce the unconfined compression test simulation. The soil particles were assumed to be in the rigid state of the Bingham fluid bi-viscosity model. The first part of the study focuses on a sensitivity analysis of the basic simulation parameter values inputted during the simulation setup for the calculation procedure and the selection of the criteria for the calculation method, and then recommends the optimum values for a higher degree of accuracy based on the results. The second part of the study uses the results to analyze the sensitivity of each influencing parameter of the bi-viscosity Bingham fluid. In the final section, this study will provide a general guideline for selecting the optimum values for the MPS parameters and will recommend approximate values for other soil samples in future research with properties similar to those used in this study. Doi: 10.28991/CEJ-2024-010-01-01 Full Text: PDF

Research on Splash Lubrication Characteristics of a Spiral Bevel Gearbox Based on the MPS Method

In order to accurately and efficiently analyze the distribution law and motion status of lubricating oil in the spiral bevel gearbox of the electric multiple unit (EMU), a high-fidelity 3D CFD model of the spiral bevel gearbox of the EMU was established for the first time. The moving particle semi-implicit method was used to visualize the lubricating-oil flow field distribution characteristics of the gearbox. The distribution characteristics of lubricating oil in the gearbox with varying gear rotation speeds, initial lubricating-oil volume levels and oil temperatures were analyzed. It was found that the initial lubricating-oil volume is the factor with the largest influence, while the influences of gear rotation speed and oil temperature are relatively small. By analyzing the churning loss under various simulation conditions, it was found that the churning loss is positively correlated with the gear rotation speed and initial oil volume, and is more affected by the initial oil volume. The churning loss is negatively correlated with the oil temperature, and both are nonlinear relationships. The proportion of churning loss related to the driven gear is higher compared to that of the driving gear. These results can provide a theoretical basis for the subsequent optimization of the gearbox.

Study on bubble dynamics in sodium using three-dimensional MPS method

Sodium-cooled fast reactor (SFR) is one of the most promising Generation IV reactors. Design and safety evaluation of a SFR requires sufficient knowledge about gas bubble behavior in sodium pool. It is challenging to perform numerical study on bubble dynamics in sodium pool due to the discontinuity caused by the differences of physical properties. In this study, a three-dimensional (3D) Moving Particle Semi-implicit (MPS) method is presented featuring high-order accurate scheme and Riemann-based stable multiphase model. Numerical discontinuity caused by large density, large viscosity ratio and surface tension can be handled by the proposed method. To verify the proposed method, two cases from the bubble diagram of Grace (1973) is simulated and rising velocities and shapes of rising gas bubbles are compared, both are agreeing very well. Then co-axial coalescence of gas bubbles are calculated and compared with existing experimental and numerical results. Finally bubble rising behavior in sodium is analyzed using the developed 3D MPS method.

Numerical simulation of melt penetration in debris beds using MPS method

During a severe accident of light water reactors (LWR), melt penetration in a debris bed (also called infiltration) may occur due to the failure of a crust which accommodates a molten pool over the debris bed, or due to earlier re-melting of metallic components (i.e., Zr and Fe) which has lower melting points than oxidic ones (i.e., UO2 and ZrO2) of corium debris. Although understanding and modeling of melt infiltration plays a significant role in the prediction of severe accident progression, little work has been done in this respect due to its complexity. To fill this knowledge gap, the present study develops a Moving Particle Semi-implicit (MPS) code with various models representing key physics in melt infiltration. REMCOD experiment, recently carried out at KTH, has been simulated to validate the updated MPS code. The comparative results show that the melt infiltration in the tests can be reproduced by the MPS code. For a debris bed of cylindrical particles, the melt infiltration process in the experiment can be predicted by using Sauter mean diameter of the particles in the simulation. The code is also applied to investigate the influences of important parameters on the melt infiltration, and it is found that contact angle has little impact on melt penetration process in the case of debris beds with large pore sizes.

Improved MPS models for simulating free surface flows

Two improved Laplacian models are introduced in this study for more accurate simulation of free surface flows in the context of the moving particle semi-implicit (MPS) method, a well-known mesh-less approach. The Euler equations are the governing equations of these flows without considering viscous forces which are solved in the Lagrangian frame by the MPS and two-step projection methods for spatial and temporal discretization, respectively. Considering the similarity between the MPS and SPH (smoothed particle hydrodynamics) methods, one of the introduced Laplacian models is formulated by a corrective matrix firstly proposed in an improved SPH method [28]. The other modified Laplacian model is also derived from the divergence of a newly developed MPS gradient model proposed for solving elasticity problems [33]. The higher accuracy of these methods compared to the classic SPH, MPS and even three modified SPH and MPS Laplacian models [7, 34, 44] is verified by solving 2D Poisson equations. Moreover, the excellent performance of the Laplacian models and the improved gradient model in obtaining smooth pressure field is validated by solving three benchmark free surface flows. Furthermore, the problem of wave damping in the original MPS computations can be resolved by using the applied models.

Investigation of hydraulic jump by using the Moving Particle Semi-Implicit method

Investigation of hydraulic jump is necessary to provide the required data in hydraulic structures. Simulations are an alternative to experiments for providing data. The objective of this modeling is to examine the impact of the reservoir level on the height after the jump and the distance of the jump from the front of the exhaust hole. The simulation was performed by using the Moving Particle Semi-Implicit method. The reservoir level was set to 10 m, 18 m, and 32 m with 18174, 23934, and 33942 particles of simulation, respectively. The obtained results indicate that the height of the reservoir after the jump is between 2.68 m and 3.60 m for an initial reservoir level of 10 m. For an initial reservoir level of 18 m, the height of the jump is between 2.90 and 5.18 m. The final height after the jump ranges from 2.98 m to 8.28 meters for an initial reservoir level of 32 m. Consistent with the findings of other researchers, the simulation outcomes are extremely favorable. The higher the reservoir level, the higher the height after the jump, according to the obtained results of this study. In addition, the distance of the jump from the front of the exhaust hole increases as the reservoir fills. Regarding the expansion of this study, additional research must be conducted to investigate this phenomenon in greater depth, particularly with regard to particle velocity during the hydraulic jump process.

Numerical study of debris bed formation behavior for severe accident in sodium-cooled fast reactor by using least square MPS-DEM method

During a Core Disruptive Accident (CDA) in a Sodium-cooled Fast Reactor (SFR), debris beds may form in the lower plenum of the reactor vessel as a result of the accumulation of discharged debris, which is formed from the solidification and fragmentation of core molten materials during their release due to interactions with the sodium coolant. Since the configuration of debris beds plays a vital role in their long-term coolability and neutronic subcriticality for achieving in-vessel retention, it is essential to understand and assess the Debris Bed Formation Behavior (DBFB). In this study, an advanced Moving Particle Semi-implicit (MPS) method, called least square MPS (LSMPS), is utilized and coupled with the Discrete Element Method (DEM) for the numerical investigations of DBFB characteristics in a two-dimensional liquid pool. The applicability and reliability of the proposed LSMPS-DEM method are validated by comparing simulation results with experiments using simulant materials. The LSMPS-DEM method is then employed to study DBFB in sodium. It is observed that debris properties significantly impact the sedimentation and accumulation processes of DBFB, leading to variations in the characteristics of the formed debris beds. The present study is expected to be useful for further investigations of DBFB under more realistic conditions and for the design improvement of safety devices to mitigate the consequences of CDA in SFR.

Arbitrary slip length for fluid-solid interface of arbitrary geometry in smoothed particle dynamics

We model a slip boundary condition at fluid-solid interface of an arbitrary geometry in smoothed particle hydrodynamics and smoothed dissipative particle dynamics simulations. Under an assumption of linear profile of the tangential velocity at quasi-steady state near the interface, an arbitrary slip length b can be specified and correspondingly, an artificial velocity for every boundary particle can be calculated. Therefore, b as an input parameter affects the calculation of dissipative and random forces near the interface. For b→0, the no-slip is recovered while for b→∞, the free-slip is achieved. Technically, we devise two different approaches to calculate the artificial velocity of any boundary particle. The first has a succinct principle and is competent for simple geometries, while the second is subtle and affordable for complex geometries. Slip lengths in simulations for both steady and transient flows coincide with the expected ones. As demonstration, we apply the two approaches extensively to simulate curvy channel flows, dynamics of an ellipsoid in pipe flow and flows within complex microvessels, where desired slip lengths at fluid-solid interfaces are prescribed. The proposed methodology may apply equally well to other particle methods such as dissipative particle dynamics and moving particle semi-implicit methods.

Application of an improved MPS method in simulation of dam break

For the engineering problem of dam break, in order to solve the pressure oscillation caused by the original kernel function and source term in Moving Particle Semi-implicit Method (MPS), the paper presents a new kernel function based on trigonometric functions and a hybrid source term based on Taylor expansion. Furthermore, an improved virtual light-source method (IVLS) is proposed to determine whether the particles are on the free surface. Through the test cases of static water, the improved MPS method can significantly suppress the oscillation of hydrostatic pressure. Moreover, compared with the data of dam-breaking experiments, the improved MPS method can also accurately simulate the change of free surface, and can effectively reduce the oscillation of impact pressure at monitoring points. In addition, the feasibility of the improved MPS method has been validated and meanwhile its limitation is also mainly discussed.

Inflow and outflow numerical simulation using least-square moving particle semi-implicit method on GPU

Inflow and outflow numerical simulation using least-square moving particle semi-implicit method on GPU

An enhanced moving particle semi-implicit method for simulation of incompressible fluid flow and fluid-structure interaction

An enhanced moving particle semi-implicit method for simulation of incompressible fluid flow and fluid-structure interaction

Numerical study of wave-ice floe interactions and overwash by a meshfree particle method

The interaction between regular waves and ice floes under certain wave conditions involves overwash which is characterized by waves running up over the surface of an ice floe with large deformed free surfaces. An in-house moving particle semi-implicit (IMPS) method is employed to simulate the wave-ice floe interaction, especially for the specific behavior namely overwash due to a small freeboard of sea ice and a large body motion. In this work, a series of regular waves are generated using the Lagrangian particle method based on the Stokes wave theory. Models of the floating sea ice are simplified as circular disks without and with an edge barrier and a circular disk with a central hole, which can be used to study the influences of overwash. Hydrodynamic responses of the ice floe in regular wave conditions with different wave lengths and a constant wave height are analyzed. Compared with the mesh-based methods, the Lagrangian particle-based methods have advantages in treating highly deformed free surfaces during wave overwash processes. A piston-type wave maker and a sponge layer are applied for generating waves and avoiding the wave reflection from wall boundaries, respectively. Validations are presented including the circular ice floe with a diameter of 400 mm and a thickness of 15 mm interacting with regular waves with the wave length λ/D from 1.5 to 3.5. RAOs of the original circular disk are compared with those of the circular disks with an edge barrier and with a central hole. Overwash on the ice floe can be prevented by using an edge barrier. A new type of overwash which waves flow over the upper surface and then into the hole was proposed and simulated. The present results of numerical predictions are in good agreement with the experimental data and the published numerical results using the CFD code Flow-3D.

Using a Lagrangian-Lagrangian approach for studying flow behavior inside a bubble column

Bubble columns are widely encountered in several industries, especially in the field of nuclear safety. The Eulerian-Eulerian and the Eulerian-Lagrangian methods are commonly used to investigate bubble columns. Eulerian approaches require additional tasks such as strict volume conservation at the interface and a predefined well-structured grid. In contrast, the Lagrangian approach can be easily implemented. Hence, we introduce a fully Lagrangian approach for the simulation of bubble columns using the discrete bubble model (DBM) and moving particle semi-implicit (MPS) methods. Additionally, we propose a rigorous method to estimate the volume fraction accurately, and verified it through experimental data and analytical results. The MPS method was compared with the experimental data of Dambreak. The DBM was verified by analyzing the terminal velocity of a single bubble for each bubble size. It agreed with the analytical results for each of the four drag correlations. Additionally, the improved method for calculating the volume fraction showed agreement with the Ergun equation for the pressure drop in a packed bed. The implemented MPS-DBM was used to simulate the bubble column, and the results were compared with the experimental results. We demonstrated that the MPS-DBM was in quantitative agreement with the experimental data.

Numerical simulations of the flows past two parallel square columns by MPS method

The hydrodynamic interactions between an offshore platform and surrounding water mainly occurs in way of the pile legs, and the flow past the pile legs can be simplified to the flow past the columns. This is the reason why it is of great significance to simulate the flow around multiple columns with accuracy. In this paper, based on a mesh-less method, Moving Particle Semi-implicit (MPS) method, the MLParticle-SJTU solver is used to simulate the flow past two parallel square columns. Firstly, the reliability and accuracy of the solver is verified by simulating the Poiseuille flow, in which the no-slip boundary condition is applied. Then, the flow past two parallel square columns with different spacing between the two columns is simulated when the Reynold number is 40. The influence of spacing on flow pattern, force on columns and the vortex shedding frequency is analyzed. It is found that when the spacing is relatively small, small vortices will be attached to the surface of the columns. As the spacing ratio increases, periodic shedding of vortices will occur.

Numerical study of green water loads on a fixed structure with elastic sidewalls by MPS-FEM coupled method

In rough seas, large masses of water will exceed the freeboard and cause violent slamming on the deck, known as green water. Due to its high destructive power, many scientists have devoted themselves to the study of green water. Given the complexity, various simplified methods have been used to study the mechanism and stresses of green water. In this paper, the loads and patterns of green water events on a fixed structure with rigid or flexible sidewalls were investigated using the solver MPSFSI-SJTU based on the Moving Particle Semi-Implicit (MPS) method coupled with the Finite Element Method (FEM). The rapid flow-structure interaction is generated by the wet dam-break method. Firstly, the numerical simulation of the water shipping events with the rigid structure was carried out, which was in good agreement with the existing numerical simulation results. Secondly, numerical simulations were carried out for different cases of fixed structures with elastic side wall and elastic upper wall. The influence of elastic modulus on wave loads and waveform was analyzed.

Numerical simulation of violent interactions between dam break flow and a floating box using a modified MPS method

The Moving particle semi-implicit (MPS) method is a widely used approach to simulate the violent interactions between dam break flow and downstream structures. However, most of these simulations involved fixed downstream structures and rarely considered floating objects. In this study, a modified MPS method, named MPS-SP-MG-PS method, is proposed to simulate violent interactions between dam break flow and a floating box. The proposed method includes below modifications: (1) the MPS-SP scheme with a split-pressure Poisson equation; (2) a modified space potential particle (SPP) scheme; and (3) a mixed pressure gradient and a novel particle shifting (PS) technique. Two cases are simulated, one considers heave motion only, and another considers both heave and pitch. Slamming, wave-on-deck and severe motions are involved in the cases. In order to evaluate the effect of these modifications, several numerical models with different combinations of the modifications are tested as well. Numerical results demonstrate the enhancement on stability and accuracy by these modifications: the MPS-SP scheme ensures the stability of heave motion at the initial stage; the modified SPP scheme maintains reasonable distance between free surface particles; and the combination of the mixed pressure gradient and the novel PS technique shows its accuracy in estimating box motions. Furthermore, the numerical results from the MPS-SP-MG-PS method are well consistent with experimental and existing numerical results in terms of box motions, surface elevations, fluid profiles, and slamming pressure. This indicates that the MPS-SP-MG-PS method is suitable for simulating violent interactions between dam break flow and floating structures.