MPS Method Research Articles

An improved MPS-DEM numerical model for fluid–solid coupling problem in nuclear reactor

Compared with the grid method, the moving particle semi-implicit method (MPS) has prominent advantages in capturing the phase interface and avoiding grid distortion at the interface. However, MPS method is not particularly effective in dealing with the fluid–solid coupling problems including the interaction between discrete solid elements. Therefore, the PArticle method software for Nuclear reactor thermal hyDraulic Analysis (PANDA) is developed based on the MPS method and coupled Discrete Element Method (DEM) by introducing the idea of multiphase flow into the MPS-DEM coupling method. In this paper, the model is validated by reappearing the phenomena of DKT(drafting, kissing, and tumbling), and the problems of the slide of dry granular material and the underwater landslide are simulated as well. The numerical results are in good agreement with the experimental results, and the relative error of the leading edge distance is less than 6.12%. Finally, numerical simulation is carried out by taking molten pool accumulation in sereve accident of nuclear reactor as an example, which further confirms the good application prospects of PANDA in engineering problems.

A new potential interface tension model for MPS method avoiding unphysical particle cohesion

Improvement of the capability to accurately track the interface between immiscible phases/components is of great importance to the numerical analysis with complex multi-component and multi-phase flow dynamics, which might be involved in severe accidents of light water reactors, such as Molten Core-Concrete Interaction (MCCI). In order to model the interface tension between immiscible phases/components, Zhu et, al., precedingly developed a potential interface tension model in MPS method based on Kondo et al.‘s earlier model for surface tension and succeeded to stably model the interface tension qualitatively by introducing different attractive forces for different pairs of particle types. However, it has been known that pressure is overestimated in Zhu et, al.‘s potential interface tension model. Moreover, this study has shown that the fluid flow can be numerically hindered with Zhu et al.‘s potential interface tension model. These issues of Zhu et al.‘s potential interface tension model is caused by unphysical particle cohesion due to the inter-particle attractive forces determined by the surface tension coefficients, which are required even when the free surface is not considered. Meanwhile, in the framework of SPH method, Zhou et, al., proposed to model interface tension by introducing the repulsive force between different phases. Hence, this study aimed to develop a new potential interface tension model for MPS method which can overcome the conventional drawbacks of pressure overestimation or unphysical flow hindrance, by incorporating the repulsive force between immiscible fluid phases referring to Zhou et, al.‘s idea within SPH method.The interface tension in the present method is modeled as the repulsive force derived from the “repulsive potential” and is considered only near the interface to avoid the unphysical particle cohesion due to the inter-particle attractive forces. The amplitude coefficient in the repulsive potential is determined by the methodology similar to that proposed by Kondo, et, al.With the newly developed interface tension model, the common issue of numerical flow hindrance that occurred in the previous interface tension models in MPS method has been resolved. The validation of the newly developed interface tension model shows good agreement with theoretical evaluations of Laplace pressure and the droplet deformation ratio in a shear flow. Moreover, the new interface tension model has been validated against a 3-dimensional immiscible fluid stratification test, in which the new interface tension model shows good agreement with the test results and improvement of the pressure profile evaluations compared to that by Zhu et al.‘s model. Further extension of the present model so as to incorporate surface tension and wall wetting is one of the most important issues which require future development.

Experimental and Numerical Studies on Flowing Properties of Grouting Mortar Based on the Modified MPS Method

Grouting mortar has widespread application in engineering because of the advantages of good durability, low cost, and environmental friendliness. To study the flowing properties of grouting mortar, laboratory minislump tests taking different rheological parameters of grouting mortar into consideration were conducted to obtain the flow time and flow pattern of grouting mortar. A modified MPS method (moving-particle semi-implicit method) introduced two sections of Bingham rheological, and segregation was proposed. The effects of the plastic viscosity on the flow state of mortar were studied, and the relationship between the plastic viscosity and the flowing time was established. The numerical results show that the modified MPS method can be used to predict the flow time and flow pattern of mortar in the template, and plastic viscosity has a great influence on the flow time of concrete, and with the increase of plastic viscosity, the time to flow to the specified area also increases. Moreover, the analysis of the rheological parameters can provide the basis for the design of mix ratio in the construction practice.

An axisymmetric multiphase moving particle semi-implicit method for simulation of 3D axisymmetric flow

Axisymmetric flows are widespread problems in the engineering field, but doing complete 3D simulations for them is very time-consuming. This study aims to develop an axisymmetric multiphase MPS method based on the Cartesian coordinate to transform the 3D problems onto 2D planes without losing important flow characteristics. To meet the calculation requirements of the MPS discretization, the virtual rotating particles were imaged within the effective radius of the real particles on the 2D plane, and particle number densities of the real particles were calculated by considering the contributions of the virtual rotating particles. The pressure Poisson equation, gradient, divergence, and Laplace operators were modified correspondingly to consider the interactions of the real particles with the virtual rotating particles. The method was validated by simulating 3D axisymmetric problems, namely, the capillary jet breakup, rising gas bubble, and droplet formation. The accuracy and stability of the developed method were demonstrated by comparing the numerical results with the reference data.

Reducer lubrication optimization with an optimization spiking neural P system

It is very difficult to improve the efficiency and accuracy of reducer lubrication due to the limitation of the traditional simulation method. In this paper, an optimization model with multiple parameters is first established to reflect the relationship between the churning loss and the optimized parameters of the zero-backlash high-precision roller developing reducer (ZHPRER). Then, an optimization spiking neural P system (OSNPS) is applied to optimize the multiparameter model. Finally, a simulation analysis (the semi-implicit moving particle method, MPS) is used to verify the correctness of the optimization results. The experimental results show that the multiparameter optimization model and OSNPS are effective and accurate for solving the multiparameter optimization problem of ZHPRER by MPS method.

Simulation on the fragmentation characteristics of molten core materials in SFRs using modified MPS method

Fragmentation characteristics of molten metallic materials interacted with liquid sodium during core disruptive accidents (CDAs) in SFRs is essential to the evaluation of the severe accident development tendency. In this paper, a modified MPS method is proposed to simulate the fragmentation process of molten core structure material (316 stainless steel) under different dropping modes. The simulated fragments size distribution for the single droplet is consistent with the experimental results under relative low thermal condition, with the solidification and deformation effect being the dominant factors. With increasing thermal and hydrodynamic conditions, the fragments sizes decrease rapidly. For continuous droplets, the fragmentation is accelerated and enhanced under high thermal conditions due to the collision between the droplets if the time interval is short. For the jets, the sodium is observed to be entrained in the melt as well as the continuous cone structure, which are consistent with the experiments and mechanism analysis.

Numerical simulation of jet breakup phenomenon during severe accident of sodium-cooled fast reactor using MPS method

During a core disruptive accident of Sodium-cooled Fast Reactors (SFR), discharged corium may contact with coolant in form of jet, which can be an imminent threat to the integrity of reactor vessel if the jet does not sufficiently break up and cooldown. It is significant to ascertain the morphologies, penetration depth and breakup mechanism of discharged corium jet to evaluate its potential impact on reactor vessel. In this study, numerical simulations are carried out to investigate the characteristics of jet breakup. An advanced moving particle semi-implicit method (MPS), the least square MPS (LSMPS) is applied to study the two-dimensional hydrodynamic corium jet breakup in sodium. Firstly, the applicability and reliability of the method are validated by the comparison between the simulation results and reference experiments. Then, the method is applied to simulate molten corium jet breakup in sodium. It is found that the breakup mechanism is related to Rayleigh–Taylor instability (RT), Kelvin–Helmholtz instability (KH) and Plateau–Rayleigh instability (PR). Under the influence of RT and KH, eddies are formed around the jet and thus the downward velocity of the jet vibrates in a relatively regular pattern. The local velocity difference of the jet narrows the jet and the jet eventually breaks up under the influence of PR. The parameters including diameter and initial velocity of the jet were scrutinized for their influences on jet penetration depth and jet breakup length, which can be useful for the improved design of the SFR reactor vessel.

Development of a numerical model for metal vapor dynamics in low pressure arcs based on moving particle semi‐implicit method and influence of shield wall radius on vapor behavior

AbstractNumerical simulation was conducted for dynamic behavior of copper vapor in arcs under reduced pressure condition using the developed model. The developed model uses MPS method for atoms and ions, while it uses finite volume method for electron energy and electro‐magnetic fields. In this paper, the influence of shield wall inner radius for vapor dynamics was studied on the heavy particle temperature, electron temperature and ionization degree. The particle in MPS method was assumed to be neutralized and mirror‐reflected on the shield wall. As a result, the shield wall with a larger radius causes lower density of metal vapor, lower ionization degree between the electrodes.

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

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

Symmetric boundary condition for the MPS method with surface tension model

In order to supplement the investigation of boundary conditions for the MPS method, a general computational algorithm of symmetric boundary condition for MPS is presented to simulate the symmetric problems. By the MPS method with the symmetric boundary condition (the SBC-MPS method), only half or quarter of the full computational domain needs to be set up, thus, the computational cost is able to be slashed dramatically. In the SBC-MPS method, mirror particles are introduced, which will be arranged symmetrically according to the positions of real liquid particles near to the symmetric plane, but not involved in the solution of physical properties. The function of these mirror particles is to compensate the values for the calculation of real liquid particles. As numerical tests, various of problems including two-dimensional Poiseuille Flow, three-dimensional dam-break, and some surface tension dominant problems, such as droplet wetting / impinging to a solid surface and binary droplets collision have been systematically studied by the SBC-MPS method. As a result, the algorithm shows good robustness, stability and accuracy, which demonstrates a great potential to improve the computational efficiency for dealing with symmetric problems.

An improved moving particle semi-implicit method for interfacial flows

In this paper, the improved moving particle semi-implicit (IMPS) method is further developed into a multiphase method by introducing various multiphase models. Then, the developed multiphase MPS method is applied to a variety of 2-D/3-D simulations of interfacial flows, including Rayleigh-Taylor instability, bubble rising, dam-break flow, and internal solitary waves. The fair agreements between the results of MPS and other reference results demonstrate that the present multiphase MPS method is stable and accurate enough to capture the interface with a large deformation in different flow problems. The phenomenon of air entrapment induced by the dam-break flow is well reproduced in the multiphase simulation and its influence on impact pressure is discussed in detail. The internal solitary waves with different amplitudes are numerically generated and the wave heights show a good agreement with experimental data even after a long-distance propagation, indicating that the numerical diffusion of the present multiphase MPS method is relatively low and the energy conservation can be ensured.

Analysis of the localized metallic phase solidification in VULCANO VF-U1 with MPS method

• MCCI analysis with MPS method has been developed with improved numerical accuracy. • The VULCANO VF-U1 experiment has been analyzed with the developed method. • Molten concrete generated by sidewall ablation dragged the metallic phase upward. • Liquid metallic phases were trapped in oxidic crust films during the cooling phase. • The final metallic phase distribution qualitatively agreed with the experiment.

The molten wood’s metal initial velocity variations effect on breaching simulation by MPS method

Series of MPS simulations have been conducted using two-dimensional geometry. The simulation was based on Sudha’s experiment (2018) about initial velocity variations on molten Wood’s Metal (WM). The molten WM would be flowed through nozzle with the diameter was 6 mm. It would impinge to the Woods Metal Plate (WMP) which 270 mm below the nozzle. The WMP diameter was 470 mm. The temperature of molten WM and WMP were set at 573 K and 300 K, respectively. The initial velocity of molten WM was varied at 0.327 m/s, 0.397 m/s, 0.498 m/s in the y-negative direction. The simulation was calculated by using 2D MPS with additional procedures such as heat transfer calculation and defining a new type of wall particle. The results showed some different spread patterns, leading edge and phase fraction change for each initial velocity. It can be concluded that with varying the initial velocity will affect on the radial spread pattern but not so much effect occurs on the phase volume fraction change.

Numerical simulations of multi-layer-liquid sloshing by multiphase MPS method

Numerical simulations of multi-layer-liquid sloshing by multiphase MPS method

Numerical method for predicting flow and segregation behaviors of fresh concrete

Current meshless particle methods are able to simulate the flow of fresh concrete, but fail to predict the segregation since fresh concrete is regarded as homogeneous fluid. This study aims to develop a numerical approach to predict the segregation of coarse aggregate (CA) in fresh concrete together with the flow behavior. A double-phase & multi-particle (DPMP) model was proposed to describe fresh concrete, which treats fresh concrete as a double-phase fluid composed of matrix mortar and the CA particles that had random shapes, size distribution, and different density from matrix mortar. Each CA particle was formed by the element particles, of which number was dependent on the size and shape of described CA particle. Three types of inter-particle interaction, including CA-CA particles, CA-mortar particles, and two mortar particles, were investigated, respectively. Then, based on the complete implicit MPS (I-MPS) method and the DPMP model, the L-box flow of two series of high fluidity concrete were simulated. The ability of the proposed numerical approach to simultaneously simulate the flow and segregation behaviors of fresh concrete was confirmed. Moreover, this numerical method can analyze the changes of localized rheological parameters of segregated concrete.

STUDY ON THE RHEOLOGICAL CONSTANTS ESTIMATION METHOD OF CEMENT PASTE BY FLOW TEST

With the improvement of earthquake resistance and large scale of buildings, the number of cases where it is difficult to fill the form work with conventional slump-managed concrete is increasing. In addition, slump flows 45 cm, 50 cm, 55 cm, and 60 cm have been added due to the JIS (Japanese industrial standard) revision made in March 2019. In the future, it is estimated that the use of slump flow managed concrete will increase. Furthermore, in recent years, new admixtures have been actively developed, and it is necessary to correctly grasp the flow characteristics of concrete using these admixtures from a rheological point of view. It is the cement paste in concrete that is most affected by the flow properties of the admixture. Therefore, it is useful to be able to grasp the flow characteristics of cement paste. We have already examined the relationship between the rheology constants obtained from the rheology test and the flow characteristics obtained from the paste flow test, and we proposed a rheology constant estimation method. In this study, we reexamined the rheological constant estimation method based on the correlation analysis findings using the visco-plastic finite element method (FEM). First, flow analysis was performed by FEM using any combination of rheological constant and paste density (yield stress: 10 patterns, plastic viscosity: 7 patterns, paste density: 3 patterns, total 210 patterns) as input values. Next, based on the analysis results, the relationship between the paste flow characteristics (flow value, each flow arrival time, flow stop time) and the rheology constant and paste density was examined by correlation analysis. As a result, it was found that the yield stress can be estimated by the flow value, and the plastic viscosity can be estimated by the multiple regression equation of the paste density and the 150 mm flow arrival time. Furthermore, we proposed a new rheological constant estimation equation using the actual test results of the cement paste for the relationship obtained from the correlation analysis. After that, the rheology constant was estimated from the actual paste flow test results using the rheology constant estimation equation. Finally, a paste flow simulation was performed using the MPS method, which can consider the influence of the flow cone, and it was compared and examined: the actual paste flow test results and MPS analysis results. As a result, the actual paste flow test results could be reproduced by MPS analysis, and the validity of the rheological constant equation was confirmed.

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

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

Application of improved multiresolution technique for the MPS method to fluid lubrication

Application of improved multiresolution technique for the MPS method to fluid lubrication

Numerical investigation of oxidation and dissolution behavior in the fuel cladding using MPS-CV method

The Moving Particle Semi-implicit-Controlled Volume (MPS-CV) method, based on the MPS method and Finite Volume Method (FVM), is a particle-grid coupling method. In this method, the particle interaction models in the MPS method are used to discretize and solve the momentum equation. For the eutectic reaction model, the FVM is used to solve the mass transfer equation if the particle locates at the boundary or the interface between different substances. In contrast, the particle interaction models are still used to discretize and solve the remaining particles' mass transfer equations. Therefore, it has advantages in describing fluid interfaces with large deformation and phase transition problems. Simultaneously, the MPS-CV method avoids the apparent error in calculating the mass transfer equation of boundary and interface between different substances due to the truncation of support domain in that area particles while using particle interaction models in the MPS method. In this study, the simulation of one-dimensional mass transfer and phase transition was used to verify the MPS-CV method, and the results were compared with those obtained by the MPS method. It showed that the MPS-CV method could get more accurate results in the calculation than the MPS method. Then the cladding oxidation mechanism at 1300 ~ 1800 K and the dissolution behavior between ZrO2 and molten zirconium at 2373 ~ 2573 K were analyzed using the MPS-CV method. The results indicated that the change of oxygen content obeyed parabolic laws. So did the oxide and α-Zr(O) layers' growth rates in cladding oxidation. And compared with the fixed parabolic relations used in commercial codes, the MPS-CV method can obtain the corresponding relationships according to different reaction conditions. The dissolution between ZrO2 and molten zirconium at high temperatures showed a parabolic pattern in the early stage. In the later stage of the reaction, the oxygen in the melt gradually reached saturation, and the solid ZrO2 did not continue to melt. The simulation results of the molten zirconium with the same volume but different contact areas with ZrO2 crucible showed that the larger the contact area was, the higher the growth rate of oxygen content in the melting the early stage of the reaction was. And it also showed that the larger the contact area was, the less dissolution volume of the ZrO2 crucible was.

Enhanced weakly-compressible MPS method for immersed granular flows

We develop and validate a three-dimensional particle method based on an Enhanced Weakly-Compressible MPS approach for modeling immersed dense granular flows. For this purpose, we adopt a generalized rheological model, using a regularized visco-inertial rheology, for all regimes of multiphase granular flow. Moreover, we propose a new consistent formulation to estimate the effective pressure of the solid skeleton based on the continuity equation of the pore-water. To improve the accuracy of the multiphase particle methods, especially near boundaries and interfaces, we introduce a modified high-order diffusive term by employing the convergent form of the Laplacian operator. The effectiveness of the new diffusive term is particularly demonstrated by modeling the hydrostatic pressure of two fluid phases. Further, coupling the generalized rheology model with the flow equations, we investigate the gravity-driven granular flows in the immersed granular collapse and slide in three dimensions. As a part of this study, we represent the experiment on the immersed granular collapse to validate the model. The evolution and runout length of the granular bulk are compared with those from experiments confirming good compatibility. Overall, the qualitative and quantitative results justify the proposed developments shown to be essential for predicting different states of the immersed granular flows.