Wall Boundary Model Research Articles

A multi-layer SPH method to simulate water-soil coupling interaction-based on a new wall boundary model

A multi-layer SPH method to simulate water-soil coupling interaction-based on a new wall boundary model

Influence of Frictional Stress Models on Simulation Results of High-Pressure Dense-Phase Pneumatic Conveying in Horizontal Pipe

Based on the two-fluid model, a three-zone drag model was developed, and the kinetic theory of granular flows and the Schneiderbauer solids wall boundary model were modified to establish a new three-dimensional (3D) unsteady mathematical model for high-pressure dense-phase pneumatic conveying in horizontal pipe. With this mathematical model, the influence of the three frictional stress models, namely Dartevelle frictional stress model, Srivastava and Sundaresan frictional stress model, and the modified Berzi frictional stress model, on the simulation result was explored. The simulation results showed that the three frictional stress models accurately predicted the pressure drop and its variations with supplementary gas in the horizontal pipe, with relative errors ranging from −4.91% to +7.60%. Moreover, the predicted solids volume fraction distribution in the cross-section of the horizontal pipe using these frictional stress models exhibited good agreement with the electrical capacitance tomography (ECT) images. Notably, the influence of the three frictional stress models on the simulation results was predominantly observed in the transition region and deposited region. In the deposited region, stronger frictional stress resulting in lower solids volume fraction and a higher pressure drop in the horizontal pipe were observed. Among the three frictional stress models, the simulation results with the modified Berzi frictional stress model aligned better with the experimental data. Therefore, the modified Berzi frictional stress model is deemed more suitable for simulating high-pressure dense-phase pneumatic conveying in horizontal pipe.

Compatible interface wave–structure interaction model for combining mesh-free particle and finite element methods

This study presents a novel wave–structure interaction model, which is a compatible interface wave–structure interaction model that is based on mesh-free particle methods for free-surface flow analysis; the FEM for structural analysis. We adopt the explicitly represented polygon (ERP) wall boundary model, which is a polygon wall boundary model for mesh-free particle methods, to express the fluid–structure interfaces. The fluid–structure interfaces in the proposed model are geometrically compatible because the ERP model has advantages in dealing with complex-shaped and moving boundaries and it enables the direct use of surface meshes and shape functions given by finite element models of structures. This allows the automatic generation of polygons for free-surface flow analysis from finite elements, and therefore, it greatly increases the flexibility of the analysis. Based on the compatible interface between the polygons and finite elements, we propose a strong coupling algorithm based on an iterative partitioned scheme that defines the interacting models between the fluid and the structure. We model the force exerted by fluid particles on structures such that the kinetic boundary condition on the fluid–structure interface is satisfied. We perform the verification and validation tests of the proposed model by solving two benchmark problems.

Grid-Stamping on a Polygon Model for Implementing Arbitrary-Shaped Boundary Conditions in a Moving Particle Semi-Implicit Method

This study proposes a new wall boundary condition for the grid-stamping on a polygon (G-StoP) model, which enables a simpler and more efficient handling of boundary surfaces of arbitrarily complex-shaped bodies represented using polygons (or meshes). For example, computer-aided design surface data can be used to analyze flow using a particle-based fluid-solver moving particle semi-implicit method. For coupling simulations of fluid–multibody dynamics, the Pusan-National-University-modified MPS method is improved, and the coupling analysis is performed using RecurDyn, a commercial software package for multibody (or flexible multibody) dynamics. To confirm the applicability of the developed G-StoP model, hydrostatic pressure simulations are conducted in a rectangular tank at various corner angles. Then, the hydrostatic pressure results are compared with previously proposed polygonal wall boundary model results and theoretical solutions. That is, in the case with a corner angle of 30°, it was confirmed that the relative error to the experiment of the polygon model was 11.3%, while that of the G-StoP model was 1.3%. This demonstrates that the proposed G-StoP model is exceptional for numerical stability and robustness even when it is difficult to secure information on neighboring particles as the corner angle of the object becomes small. In addition, the G-StoP model was applied to dam breaking, subaerial landslide tsunami, and wine sloshing problems, and its accuracy and applicability were tested through comparison with experimental and other simulation results. As a result, it was shown that the present simulation results were much closer to the experiments than other simulations.

Numerical simulation of aerosol permeation through microstructure of face masks coordinating with x-ray computed tomography images

Face masks act as air filters that collect droplets and aerosols, and they are widely used to prevent infectious diseases, such as COVID-19. Herein, we present a numerical simulation model to understand the collection behavior of aerosols containing submicron-sized droplets inside a realistic microstructure of commercially available face masks. Three-dimensional image analysis by x-ray computed tomography is used to obtain the microstructures of two types of commercial face masks, and the aerosol permeation behavior in the obtained microstructures is investigated with a numerical method coupled with computational fluid dynamics and a discrete phase model. To describe the complex geometry of the actual fibers, a wall boundary model is used, in which the immersed boundary method is used for the fluid phase, and the signed distance function is used to determine the contact between the droplet and fiber surface. Six different face-mask domains are prepared, and the pressure drop and droplet collection efficiency are calculated for two different droplet diameters. The face-mask microstructure with the relatively larger pore, penetrating the main flow direction, shows a high quality factor. A few droplets approach the pore accompanied by fluid flow and fibers collect them near the pore. To verify the effect of the pore on the collection behavior, six different model face-mask domains of variable pore sizes were created. Additionally, droplet collection near the pore is observed in the model face-mask domains. Specific pore-sized model masks performed better than those without, suggesting that the large pore may enhance performance.

Comparative study of the single and double specularity coefficients on two-fluid modeling of a pseudo-2D gas–solid fluidized bed

The specularity coefficient is an unmeasurable parameter in the most popular wall boundary model during the two-fluid modeling of dense gas–solid flows. Using multiphaseEulerFoam solver, the influence of different specularity coefficient setting strategies on the gas–solid flow inside a pseudo-2D fluidized bed has been explored. It is found that the single specularity coefficient plays a regulatory role in the quantitative prediction. Increasing the specularity coefficient would cause a fluidization transition from freely bubbling to slugging, and the bed characteristics such as pressure drop and bed expansion present monotonic nonlinear changes. The double specularity coefficients approach is shown to significantly improve the predictive accuracy through verifying with the measured particle velocities, bubble diameter and rise velocity. In addition, the lognormal bubble size distribution and Gaussian bubble rise velocity distribution are observed. The specularity coefficient for walls in thickness direction is crucial and its different effects are unignorable. Overall, the present study provides a practical strategy of double specularity coefficients for the solid wall boundary conditions during two-fluid modeling.

Three‐dimensional weakly compressible moving particle simulation coupled with geometrically nonlinear shell for hydro‐elastic free‐surface flows

AbstractA three‐dimensional fluid–structure interaction solver based on an improved weakly compressible moving particle simulation (WC‐MPS) method and a geometrically nonlinear shell structural model is developed and applied to hydro‐elastic free‐surface flows. The fluid–structure coupling is performed by a polygon wall boundary model that can handle particles and finite elements of distinct sizes. In WC‐MPS, a tuning‐free diffusive term is introduced to the continuity equation to mitigate nonphysical pressure oscillations. Discrete divergence operators are derived and applied to the polygon wall boundary, of which the numerical stability is enhanced by a repulsive Lennard–Jones force. Additionally, an efficient technique to deal with the interaction between fluid particles placed at opposite sides of zero‐thickness walls is proposed. The geometrically nonlinear shell is modeled by an unstructured mesh of six‐node triangular elements. Finite rotations are considered with Rodrigues parameters and a hyperelastic constitutive model is adopted. Benchmark examples involving free‐surface flows and thin‐walled structures demonstrate that the proposed model is robust, numerically stable and offers more efficient computation by allowing mesh size larger than that of fluid particles.

Advanced DEM simulation on powder mixing for ellipsoidal particles in an industrial mixer

Tons of products are facilitated through powder mixing processes. The quality of the final products is highly influenced by the mixing state. Hence, detailed information about the mixing state is necessary to improve the quality. Recent remarkable advancements in computer hardware enable the evaluation of the mixing state via numerical simulation. The Discrete Element Method (DEM) is frequently used in numerical simulations, where computational particle shapes are typically modeled by a spherical body. On the other hand, not all particle shapes in industries are spherical, and the structure of industrial mixers is generally complex. Thus, when the DEM is applied to an industrial mixer, modeling of particle shape and the complex structure of the mixers may be taken into consideration. In the present study, an innovative model is newly developed to simulate the powder mixing of non-spherical particles in an industrial mixer. Here, a non-spherical particle is modeled by the ellipsoidal equation, and an industrial mixer is modeled using the Signed Distance Function (SDF), where the wall boundary shape is flexibly modeled by a scalar field. This approach is referred to as the ellipsoidal DEM/SDF. In the current study, the adequacy and applicability of the ellipsoidal DEM/SDF are demonstrated by the following steps. First, the compatibility of the ellipsoidal DEM with the SDF wall boundary model and the applicability of a soft linear spring in the ellipsoidal DEM/SDF are demonstrated through validation tests. Subsequently, the effect of particle shape on mixing progress in a ribbon mixer is examined. Through computations, the effect of the non-spherical shape is shown to be insignificant on powder mixing progress in the ribbon mixer. Consequently, the ellipsoidal DEM/SDF is shown to be applicable to the industrial powder mixing, and therefore, will contribute to optimization of the mixer design and the operational conditions in chemical, food, and pharmaceutical engineering fields.

壁領域の角を考慮したポリゴン壁境界モデルの開発およびその ISPH 法への適用

壁領域の角を考慮したポリゴン壁境界モデルの開発およびその ISPH 法への適用

Development of a robust Eulerian–Lagrangian model for the simulation of an industrial solid–fluid system

The discrete elements method (DEM) coupled with computational fluid dynamics (CFD) is widely employed in the numerical simulation of a multiphase flow including solid particles. The stable conditions have been examined in the DEM–CFD simulations, where a semi-implicit algorithm is often emplyed in computation of a solid-fluid flow. The stable DEM conditions can easily be derived based on the oscillation period, and the Courant condition provides stable conditions for CFD. Accordingly, the time step should be given to satisfy them simultaneously in the DEM–CFD method. However, when the drag force acting on the solid particles becomes some extent high, the DEM–CFD simulation cannot be stably performed even if the above conditions are satisfied. In this case, the time step should be decided through trial and error. Although several studies regarding the stability of the DEM–CFD method have been conducted, the theoretical time step for the drag force term has not been derived to date. Additionally, no model has been proposed to solve the instability problem regarding the drag force term in the DEM–CFD method. From this background, this paper aims to theoretically derive a stable condition for the drag force term and to develop a new implicit algorithm for the DEM–CFD method. To illustrate the accuracy and stability of the implicit algorithm, verification tests are performed in a fixed bed system. Subsequently, the DEM–CFD simulations are performed in a fluidized bed to show the capability of the implicit algorithm. Finally, the compatibility of the implicit algorithm with the wall boundary model, composed of the signed distance function and the immersed boundary method, is examined through the validation tests.

On artificial density treatment for the pressure Poisson equation in the DEM-CFD simulations

The discrete element method (DEM) coupled with computational fluid dynamics (CFD) is regarded to be a standard approach in a numerical calculation of gas-solid flow. When the DEM-CFD method is applied to the simulation of industrial systems, we cannot shy away from the modeling of arbitrary shape wall boundaries. Very recently, we have developed an innovative wall boundary model in the DEM-CFD simulations, where the signed distance function (SDF) and the immersed boundary method (IBM) are used for the wall boundary in the DEM and CFD. The SDF makes it possible to create an arbitrary shape wall boundary based on the scalar field. The IBM can be used for the wall boundary model by reflecting the number of the SDF points on the local volume fraction in CFD grid. Thus, the arbitrary shape wall boundary can be easily created in the DEM-CFD method by combining the SDF with the IBM. On the other hand, the authors' group has pointed out the necessity of the density scale technique in CFD. In the density scale technique, the density scale coefficient is considered in the calculation of the pressure Poisson equation. When the SDF/IBM is applied to CFD without density scaling technique, an unnatural fluid flow might occur through the wall boundary object. The effect of the density scaling coefficient on a gas-solid flow has not been examined so far. From this background, the influence of the density scale coefficient on a gas-solid flow is investigated in the present study. Through this study, introduction of the density scaling technique is designated to be crucial when the IBM is used for the wall boundary in the DEM-CFD simulation. The density scaling coefficient is shown to be decided not by theory but by experience, and the value should become 100 to 1000 in a typical gas-solid flow system. Besides, it is illustrated that the calculation cost is not influenced by the value of the density scale coefficient in the DEM-CFD simulations.

Coarse graining DEM simulations of a powder die-filling system

Application of numerical simulations are desired to improve the quality of powder products and to optimize the production process in powder die-filling. In the powder die-filling, complex gas-solid interaction should be simulated since the solid particles are significantly influenced by the gas flow under moving wall boundary. The discrete element method (DEM) coupled with computational fluid dynamics (CFD) has been widely utilized in the simulation of gas-solid flows, and the adequacy has been proved through countless studies. On the other hand, the existing DEM-CFD method is extremely difficult to simulate the gas-solid flow where the wall boundary is moving. Besides, in the existing DEM-CFD method, huge number of computational particles cannot be simulated on a single PC. Hence, numerical simulations of the industrial powder die-filling becomes a challenging topic from a viewpoint of evolution of the DEM-CFD method, because modeling of the moving wall boundary as well as modeling of large number of computational particles should be considered simultaneously. Very recently, the authors' group has developed the Integrated DEM-CFD method including the arbitrary shape wall boundary model and the scaling law model. In the Integrated DEM-CFD method, the wall boundary is modeled by the signed distance functions and the immersed boundary method, and besides the coarse graining DEM is employed as the scaling law model. Adequacy of the Integrated DEM-CFD method has been proved through verification tests. In the current study, applicability of the Integrated DEM-CFD method is examined in the powder die-filling. Adequacy of the Integrated DEM-CFD method is shown by agreement between the original particle system and the coarse graining particle system in the powder die-filling. Through the verification tests, macroscopic characteristics of the powder die-filling are shown to be reproduced by the Integrated DEM-CFD method. Consequently, the Integrated DEM-CFD method is illustrated to be effective for the simulation of the industrial powder die-filling systems.

Parallel analysis system for free-surface flow using MPS method with explicitly represented polygon wall boundary model

This study develops a parallel solver of free-surface flow based on a mesh-free particle method, the explicit MPS method, with polygon boundary representation. We adopt the explicitly represented polygon (ERP) wall boundary model, which expresses wall boundaries as arbitrarily shaped triangular polygons. A bucket-based domain decomposition algorithm for dynamic load balancing is expanded to the polygon-based computation of the ERP model. The validity and parallel efficiency of the developed solver are tested by analyzing a dam break problem, and the numerical results are compared with experimental results. Our developed solver can simplify the evaluation of the integrity of coastal structures since it can be easily connected to finite element analyses of the structures.

Interaction Simulations Between Fluids and Complicated Structures Using EMPS-FEM

The interactions between fluids and complicated solid structures are common phenomena in practical engineering applications, e.g., water-tire interaction in the hydroplaning problem. In this work, we advocate the coupled explicit moving particle simulation method and the finite element method (EMPS-FEM) to solve this problem, where the EMPS is used to describe the fluid flow and the FEM is for structural deformation. In the existing EMPS-FEM method, the interface interaction between the fluid and the structure is solved by an explicitly represented polygon (ERP) wall boundary model. For the situations with complicated solid structures, e.g.,angled edges, the ERP model attempts to address the particle leakage problem by adding repulsive forces to the particles. However, numerical inaccuracy and instability may arise in this model, because only the repulsive force contributed by the nearest polygon is considered for each particle undergoing leakage. The purpose of this work is to develop a robust and accurate EMPS-FEM coupling approach based on the ERP wall boundary model. Special attention is paid to the interaction situations with complicated solid structures. Numerical examples are performed to validate the effectiveness of the proposed algorithm.

Coupling methods between finite element–based Boussinesq‐type wave and particle‐based free‐surface flow models

SummaryWe develop one‐way coupling methods between a Boussinesq‐type wave model based on the discontinuous Galerkin finite element method and a free‐surface flow model based on a mesh‐free particle method to strike a balance between accuracy and computational cost. In our proposed model, computation of the wave model in the global domain is conducted first, and the nonconstant velocity profiles in the vertical direction are reproduced by using its results. Computation of the free‐surface flow is performed in a local domain included within the global domain with interface boundaries that move along the reproduced velocity field in a Lagrangian fashion. To represent the moving interfaces, we used a polygon wall boundary model for mesh‐free particle methods. Verification and validation tests of our proposed model are performed, and results obtained by the model are compared with theoretical values and experimental results to show its accuracy and applicability.

Analysis of molten pool behavior by flux-wall guided metal transfer in low-current submerged arc welding process

A three-dimensional numerical heat transfer and fluid flow model is developed to understand the temperature distribution and molten pool behavior in a low-current submerged arc welding process. The model solves the equations of the conservation of mass, momentum, and energy along with the volume of fluid method. The volume of fluid method is used to track the shape of the free surface. Further, this paper suggests a flux wall boundary model to simulate flux-wall guided transfer for a single-wire low-current submerged-arc welding process. This study simulates how porosity can be trapped in the V-groove joint with a flux-wall guided transfer. The computed weld width and fusion-zone shape are in fair agreement with the corresponding experimental results.

Numerical study of the mixing efficiency of a batch mixer using the discrete element method

In this study the simulations of granular flow in a batch mixer with independent double axial mixing are presented. The simulated granular flows were used to analyze the mixing efficiency. Such analysis has not been conducted previously for such a batch mixer, because of the complex mixing conditions. The simulations performed in this study use the discrete element method (DEM) with a wall boundary model based on a signed distance function (SDF). Introduction of the SDF allows for an accurate representation of the boundary, which is important for proper analysis of granular flow in the batch mixer. The adequacy of the DEM/SDF approach was validated quantitatively in experiments. The degree of mixing in the batch mixer was evaluated using a mixing index of a binary mixture. The effects of the powder amount, blade speed, initial loading patterns and secondary mixing on the degree of mixing were investigated numerically. In the batch mixer considered in this work, the change in mixing state in the axial direction was found to be much smaller than that in the perpendicular direction. The increase in the mixing speed not only reduces mixing time but also substantially increases the mixing performance if measured per number of rotations. However, the increase in the powder amount reduces the mixing performance. The additional secondary mixing affects the axial-mixing performance. However, the overall mixing performance does not change. In addition, neither the mixing axis position nor the mixing speed appreciably affects the mixing performance. All the mixing differences can be associated with the differences in the granular behavior, irrespective of different speeds, powder amounts or mixing setups.

Numerical study of the mixing efficiency of a ribbon mixer using the discrete element method

We describe a simulation of granular flow in an industrial ribbon mixer. Such simulations are important to analyze mixing efficiency but they have not been conducted previously in a ribbon mixer, owing to complex boundary conditions. The simulations in this study use the discrete element method (DEM) with a wall boundary model based on a signed distance function (SDF). Introduction of the SDF allows for an accurate representation of the boundary, which is important for proper analysis of granular flow in the ribbon mixer. The adequacy of the DEM/SDF approach was validated qualitatively and quantitatively. The degree of mixing in the ribbon mixer was evaluated using a binary mixture mixing index. The effects of the amount of powder, blade speed and initial loading on the degree of mixing were investigated numerically. In the ribbon mixer, the change of mixing state in the axial direction was found to be much smaller than in the perpendicular direction and an increase in the amount of powder and the blade speed generate better mixing. Only the initial loading and amount of powder were found to be critical for good mixing in the ribbon mixer. The mixing mechanism was investigated by DEM/SDF and an optimal initial loading and amount of powder were suggested for better solid mixing.

Discrete element simulation for the evaluation of solid mixing in an industrial blender

Recent improvements in computer hardware have made it possible to simulate granular flow in an industrial system. There is a desire in industry to apply a numerical technology to design of an actual powder process. In the present study, the discrete element method (DEM) was applied to a twin-screw kneader as an example of an actual industrial blender, and the mixing efficiency was investigated for different operational parameters. The complexly shaped wall boundaries of the paddles and vessel were created using the signed distance function (SDF). Validation tests were first performed to demonstrate the applicability of the DEM employing the SDF-based wall boundary model. In the validation tests, simulations and experiments were shown to be in quantitative agreement in terms of the spatial distribution of solid particles. The mixing efficiency was then investigated for different rotational speeds and amounts of powder, where the degree of mixing was evaluated using Lacey’s mixing index. The numerical simulation could clarify the mixing mechanism behind observed phenomena. The study thus illustrated that the total amount of powder affected the mixing efficiency of the twin-screw kneader.

Explicitly represented polygon wall boundary model for the explicit MPS method

This study presents an accurate and robust boundary model, the explicitly represented polygon (ERP) wall boundary model, to treat arbitrarily shaped wall boundaries in the explicit moving particle simulation (E-MPS) method, which is a mesh-free particle method for strong form partial differential equations. The ERP model expresses wall boundaries as polygons, which are explicitly represented without using the distance function. These are derived so that for viscous fluids, and with less computational cost, they satisfy the Neumann boundary condition for the pressure and the slip/no-slip condition on the wall surface. The proposed model is verified and validated by comparing computed results with the theoretical solution, results obtained by other models, and experimental results. Two simulations with complex boundary movements are conducted to demonstrate the applicability of the E-MPS method to the ERP model.