CALCULATION OF SECOND PHASE PARTICLE-GRAIN BOUNDARY INTERACTION RANGE

On the basis of the grain boundary equation by HeUman and corresponding analysis of Worner, this article deals with the interaction range between the second-phase particle （SPP） and grain boundary （GB） as viewed from the applicability of grain boundary equation. Also, a new expression describing the interaction range has been derived, which solves the problem in theory that the interaction range between SPP and GB can only be qualitatively analyzed previously. It is shown that given the interaction position between SPP and GB, the interaction range can be quantitatively determined by use of this expression.

A Corrected Solid Boundary Treatment Method for Smoothed Particle Hydrodynamics

Smoothed Particle Hydrodynamics method （SPFI） has a good adaptability for simulating of free surface flow problems. However, there are some shortcomings of SPH which are still in open discussion. This paper presents a corrected solid boundary handling method for weakly compressible SPH. This improved method is very helpful for numerical stability and pressure distribution. Compared with other solid boundary handling methods, this corrected method is simpler for virtual ghost particle interpolation and the ghost particle evaluation relationship is clearer. Several numerical tests are given, like dam breaking, solitary wave impact and sloshing tank waves. The results show that the corrected solid boundary processing method can recover the spurious oscillations of pressure distribution when simulating the problems with complex geometry boundary.

Convection and correlation of coherent structure in turbulent boundary layer using tomographic particle image velocimetry

The present experimental work focuses on a new model for space-time correlation and the scale-dependencies of convection velocity and sweep velocity in turbulent boundary layer over a flat wail. A turbulent boundary layer flow at Reo = 2460 is measured by tomographic particle image velocimetry （tomographic PIV）. It is demonstrated that arch, cane, and hairpin vortices are dominant in the logarithmic layer. Hairpins and hairpin packets are responsible for the elongated low-momentum zones observed in the instantaneous flow field. The conditionally-averaged coherent structures systemically illustrate the key roles of hairpin vortice in the turbulence dynamic events, such as ejection and sweep events and energy transport. The space-time correlations of instantaneous streamwise fluctuation velocity are calculated and confirm the new elliptic model for the space-time correlation instead of Taylor hypothesis. The convection velocities derived from the space-time correlation and conditionally-averaged method both suggest the scaling with the local mean velocity in the logarithmic layer. Convection velocity result based on Fourier decomposition （FD） shows stronger scale- dependency in the spanwise direction than in streamwise direction. Compared with FD, the proper orthogonal decomposition （POD） has a distinct distribution of convection velocity for the large- and small-scales which are separated in light of their contributions of turbulent kinetic energy.

Effect of Coagulation and Diffusion on Nanoparticle Distribution in a Fully Developed Turbulent Boundary Layer

Nanoparticle distributions in a fully developed turbulent boundary layer are simulated numerically using the moment method.The effects of Schmidt number and Damk(o)hler number on the nanoparticle distribution are studied.It is found that the particle number concentration and total particle mass increase from the wall to the outside.The difference of particle number concentration and total particle mass near the wall and near the outside becomes smaller with the increasing Schmidt number Sc.The particle diameter and geometric standard deviation increase from the wall to the outside at a fixed Damk(o)hler number Da,and grow with the increase of Da at the same lateral position.

Application of Smoothed Particle Hydrodynamics(SPH)for the Simulation of Flow-Like Landslides on 3D Terrains

Flow-type landslide is one type of landslide that generally exhibits characteristics of high flow velocities,long jump distances,and poor predictability.Simulation of its propagation process can provide solutions for risk assessment and mitigation design.The smoothed particle hydrodynamics(SPH)method has been successfully applied to the simulation of two-dimensional(2D)and three-dimensional(3D)flow-like landslides.However,the influence of boundary resistance on the whole process of landslide failure is rarely discussed.In this study,a boundary condition considering friction is proposed and integrated into the SPH method,and its accuracy is verified.Moreover,the Navier-Stokes equation combined with the non-Newtonian fluid rheologymodel was utilized to solve the dynamic behavior of the flow-like landslide.To verify its performance,the Shuicheng landslide event,which occurred in Guizhou,China,was taken as a case study.In the 2D simulation,a sensitivity analysis was conducted,and the results showed that the shearing strength parameters have more influence on the computation accuracy than the coefficient of viscosity.Afterwards,the dynamic characteristics of the landslide,such as the velocity and the impact area,were analyzed in the 3D simulation.The simulation results are in good agreement with the field investigations.The simulation results demonstrate that the SPH method performs well in reproducing the landslide process,and facilitates the analysis of landslide characteristics as well as the affected areas,which provides a scientific basis for conducting the risk assessment and disaster mitigation design.

Transport of particles in an atmospheric turbulent boundary layer

A program incorporating the parallel code of large eddy simulation （LES） and particle transportation model is developed to simulate the motion of particles in an atmospheric turbulent boundary layer （ATBL）. A model of particles of 100-micrometer order coupling with large scale ATBL is proposed. Two typical cases are studied, one focuses on the evolution of particle profile in the ATBL and the landing displacement of particles, whereas the other on the motion of particle stream.

A Parallel Boundary Element Formulation for Tracking Multiple Particle Trajectories in Stoke’s Flow for Microfluidic Applications

A new formulation for tracking multiple particles in slow viscous flow for microfluidic applications is presented.The method employs the manipulation of the boundary element matrices so that finally a system of equations is obtained relating the rigid body velocities of the particle to the forces applied on the particle.The formulation is specially designed for particle trajectory tracking and involves successive matrix multiplications for which SMP(Symmetric multiprocessing)parallelisation is applied.It is observed that present formulation offers an efficient numerical model to be used for particle tracking and can easily be extended for multiphysics simulations in which several physics involved.

Anomalous boundary deformation induced by enclosed active particles

We simulate a two-dimensional model of a round soft boundary enclosed with self-propelled particles. Persistent motion drives these particles to accumulate near the boundary, thereby dramatically deforming the boundary shape through collisions. Quantitative analyses of the boundary shape and the particle distribution show that there are two typical regimes in the variation of the morphology with the increase of self-propulsion of particles. One is under small forces, characterized by the radially inhomogeneous distribution of particles and the suppression of local fluctuations of the almost round boundary, and the other is under large forces, featured by the angularly inhomogeneous distribution of particles and the global shape deformation of the boundary. These two features are strongly cooperative. We also find different mechanisms in the particle relocation at low and high particle concentrations.

RESEARCH ON THE FLOW STABILITY IN A CYLINDRICAL PARTICLE TWO-PHASE BOUNDARY LAYER

Based on the momentum and constitutive equations, the modified Orr_Sommerfeld equation describing the flow stability in a cylindrical particle two_phase flow was derived.For a cylindrical particle two_phase boundary layer, the neutral stability curves and critical Reynolds number were given with numerical simulation. The results show that the cylindrical particles have a suppression effect on the flow instability, the larger the particle volume fraction and the particle aspect_ratio are, the more obvious the suppression effect is.

LAGRANGIAN MODEL ON THE TURBULENT MOTION OF SMALL SOLID PARTICLE IN TURBULENT BOUNDARY LAYER FLOWS

The Lagrangian equations of motion of small particle in turbulent boundary layer flows, taking into account the effects of the drug force caused by the wall presence, the Saffman and the Magus lift forces et al., is studied. Using the spectral method, analytical expression relating to the Lagrangian power spectra of particle velocity to that of the fluid are developed and the results are used to evaluate various responses statistics. In this paper, the results clearly show that the turbulent diffusivity of the particle may be larger than that of the fluid for a period of long-time.

THE DISTRIBUTION OF PARTICLES IN A SHOCK-INDUCED BOUNDARY LAYER OF A DUSTY GAS OVER A SOLID SURFACE

The laminar boundary layer behind a constant-speed shock wave moving through a dusty gas along a solid surface is studied.The Saffman lift force acting on a spherical particle in a gas boundary layer is taken into account.A method for calculating the density profile of dispersed phase near the wall is pro- posed and some numerical results are given.It is shown that behind the shock wave,there exists a curved thin layer where the density of particles is many times higher than the original one.This dust collection effect may be of essential importance to the problem of dust explosion in industry.

THE EFFECT OF PARTICLES ON FLUID TURBULENCE IN A TURBULENT BOUNDARY LAYER OVER A CYLINDER

The turbulent fluid and particle interaction in the turbulent boundary layer for cross how over a cylinder has been experimentally studied. A phase-Doppler anemometer was used to measure the mean and fluctuating velocities of both phases. Two size ranges of particles (30 mu m similar to 60 mu m and 80 mu m similar to 150 mu m) at certain concentrations were used for considering the effects of particle sizes on the mean velocity profiles and on the turbulent intensity levels. The measurements clearly demonstrated that the larger particles damped fluid turbulence. For the smaller particles, this damping effect was less noticeable. The measurements further showed a delay in the separation point for two phase turbulent cross how over a cylinder.

Heterogeneities of grain boundary contact for simulation of laboratoryscale mechanical behavior of granitic rocks

From a practical point of view,grain structure heterogeneities are key parameters that control the rock response and still remains a challenge to incorporate in a quantitative manner.One of the less discussed topics in the context of the grain-based model(GBM)in the particle flow code(PFC)is the contact heterogeneities and the appropriate contact model to mimic the grain boundary behavior.Generally,the smooth joint(SJ)model and linear parallel bond(LPB)model are used to simulate the grain boundary behavior.However,the literature does not document the suitability of different models for specific problems.Another challenge in implementing GBM in PFC is that only a single bonding parameter is used at the grain boundaries.The aim of this study is to investigate the responses of a laboratory-scale specimen with SJ and LPB models,considering grain boundary heterogeneous and homogeneous contact parameters.Uniaxial and biaxial compression tests are performed to calibrate the response of Creighton granite.The stressestrain curves,volumetric dilation,inter-crack(crack in the grain boundary),and intra-crack(crack within the grain)development,and failure patterns associated with different contact models are examined.It was found that both the SJ and LPB models can reproduce the pre-peak behavior observed for a granitic rock type.However,the LPB model is unable to reproduce the post-peak behavior.Due to the large interlocking effect originating from the balls in contact and the ball size in the LPB model,local dilation is induced at the grain boundaries.This overestimates the volumetric dilation and residual shear strength.The LPB model tends to result in discontinuous inter-cracks and stress localization in the rock specimen,resulting in fine fragments at the rock surface during failure.

A Simplified Approach of Open Boundary Conditions for the Smoothed Particle Hydrodynamics Method

In this paper,we propose a simplified approach of open boundary conditions for particle-based fluid simulations using the weakly compressible smoothed-particle hydrodynamics(SPH)method.In this scheme,the values of the inflow/outflow particles are calculated as fluid particles or imposed desired values to ensure the appropriate evolution of the flow field instead of using a renormalization process involving the fluid particles.We concentrate on handling the generation of new inflow particles using several simple approaches that contribute to the flow field stability.The advantages of theδ^(+).-SPH scheme,specifically the particle shifting technique,were successfully applied to correct the position,velocity,and pressure terms of the particles.Therefore,unexpected errors were removed and tensile instabilities of the particles were prevented.The proposed technique is validated for several benchmark test cases,and the tests show that the results match the reference solutions well.A viscous open-channel flow is used to demonstrate the stability of the flow field during the computational time.Based on this stability,we compress the computational domain to a lower resolution in a second test case while preserving the accuracy of the simulation.Flow over a backward-facing step is used to highlight the challenges of inflow boundary conditions with prescribed or non-prescribed values.The developed technique is well suited to the wall boundaries and the evolution of the flow field.The results demonstrate the robustness and versatility of the proposed technique for a variety of simulations.

Boundary Estimation in Annular Two-Phase Flow Using Electrical Impedance Tomography with Particle Swarm Optimization

In this study we consider the boundary estimation of annular two-phase flow in a pipe with the potential distribution on the electrodes mounted on the outer boundary of the pipe, by taking use of electrical impedance tomography (EIT) technique with the numerical solution obtained from an improved boundary distributed source (IBDS) method. The particle swarm optimization (PSO) is used to iteratively seek the boundary configuration. The simulation results showed that PSO and EIT technique with numerical solution obtained from IBDS has been successfully applied to the monitoring of an annular two-phase flow.

Smoothed particle hydrodynamics modeling and simulation of foundry filling process

A numerical model of foundry filling process was established based on the smoothed particle hydrodynamics（SPH）method.To mimic the constraints that the solid mold prescribes on the filling fluid,a composite treatment to the solid boundaries is elaborately designed.On solid boundary surfaces,boundary particles were set,which exert Lennard-Jones force on approaching fluid particles;inside the solid mold,ghost particles were arranged to complete the compact domain of near-boundary fluid particles.Water analog experiments were conducted in parallel with the model simulations.Very good agreement between experimental and simulation results demonstrates the success of model development.

Heat transfer analysis in particle-laden flows using the immersed boundary method

This paper investigates an efficient immersed boundary method(IBM)for multiple-core CPU machines with local grid refinement for the calculation of heat transfer between fluids and finite-sized particles.The fluid momentum equations are solved by using the fractional step method,while the energy equation is solved by employing the second-order Adams-Bashforth method.For efficient load balancing between the CPU cores,the coupling between particles and fluid is obtained by applying the body force in the fluid equations,which depends on the solid volume fraction of particles contained in each grid cell,and then by linearly interpolating the particle temperature and velocity on the fluid grid cell(in place of the delta function commonly used in literature).Several test cases from the literature are studied,and good agreement is observed between the simulation results and the literature.Finally,a scaling study on multiple core machines is performed,demonstrating the proposed IBM's capabilities for a significant reduction in processing time.

Numerical Simulation of Viscous Flow Through Spherical Particle Assemblage with the Modified Cell Model

The cell model developed since 1950s is a useful tool forexploring the behavior of particle assemblages, but it demandsfurther careful development of the outer boundary conditions so thatinteraction in a particle swarm is better represented. In this paper,the cell model and its development were reviewed, and themodifications of outer cell boundary conditions were suggested. Atthe cell outer boundary, the restriction of uniform liquid flow wasremoved in our simulation conducted in the reference frame fixed withthe particle.

Application of particle splitting method for both hydrostatic and hydrodynamic cases in SPH

Smoothed particle hydrodynamics（SPH） method with numerical diffusive terms shows satisfactory stability and accuracy in some violent fluid–solid interaction problems. However, in most simulations, uniform particle distributions are used and the multi-resolution, which can obviously improve the local accuracy and the overall computational efficiency, has seldom been applied. In this paper, a dynamic particle splitting method is applied and it allows for the simulation of both hydrostatic and hydrodynamic problems. The splitting algorithm is that, when a coarse（mother） particle enters the splitting region, it will be split into four daughter particles, which inherit the physical parameters of the mother particle. In the particle splitting process,conservations of mass, momentum and energy are ensured. Based on the error analysis, the splitting technique is designed to allow the optimal accuracy at the interface between the coarse and refined particles and this is particularly important in the simulation of hydrostatic cases. Finally, the scheme is validated by five basic cases, which demonstrate that the present SPH model with a particle splitting technique is of high accuracy and efficiency and is capable for the simulation of a wide range of hydrodynamic problems.Smoothed particle hydrodynamics（SPH）method with numerical diffusive terms shows satisfactory stability and accuracy in some violent fluid–solid interaction problems.However,in most simulations,uniform particle distributions are used and the multi-resolution,which can obviously improve the local accuracy and the overall computational efficiency,has seldom been applied.In this paper,a dynamic particle splitting method is applied and it allows for the simulation of both hydrostatic and hydrodynamic problems.The splitting algorithm is that,when a coarse（mother）particle enters the splitting region,it will be split into four daughter particles,which inherit the physical parameters of the mother particle.In the particle splitting process,conservations of mass,momentum and energy are ensured.Based on the error analysis,the splitting technique is designed to allow the optimal accuracy at the interface between the coarse and refined particles and this is particularly important in the simulation of hydrostatic cases.Finally,the scheme is validated by five basic cases,which demonstrate that the present SPH model with a particle splitting technique is of high accuracy and efficiency and is capable for the simulation of a wide range of hydrodynamic problems.

Reducing the anisotropy of a Brazilian disc generated in a bonded-particle model

The Brazilian test is a widely used method for determining the tensile strength of rocks and for calibrating parameters in bondedparticle models（BPMs）. In previous studies, the Brazilian disc has typically been trimmed from a compacted rectangular specimen. The present study shows that different tensile strength values are obtained depending on the compressive loading direction. Several measures are proposed to reduce the anisotropy of the disc. The results reveal that the anisotropy of the disc is significantly influenced by the compactibility of the specimen from which it is trimmed. A new method is proposed in which the Brazilian disc is directly generated with a particle boundary, effectively reducing the anisotropy. The stiffness（particle and bond） and strength（bond） of the boundary are set at less than and greater than those of the disc assembly, respectively,which significantly decreases the stress concentration at the boundary contacts and prevents breakage of the boundary particle bonds. This leads to a significant reduction in the anisotropy of the disc and the discreteness of the tensile strength. This method is more suitable for carrying out a realistic Brazilian test for homogeneous rock-like material in the BPM.