A review of methods,applications and limitations for incorporating fluid flow in the discrete element method

The past decade has witnessed the substantial growth in research interests and progress on the subject of coupled hydro-mechanical processes in rocks and soils,driven mainly by the surge of research in unconventional hydrocarbon reservoirs and associated hazards.Many coupling techniques have been developed to include the effects of fluid flow in the discrete element method(DEM),and the techniques have been applied to a variety of geomechanical problems.Although these coupling methods have been successfully applied in various engineering fields,no single fluid/DEM coupling method is universal due to the complexity of engineering problems and the limitations of the numerical methods.For researchers and engineers,the key to solve a specific problem is to select the most appropriate fluid/DEM coupling method among these modeling technologies.The purpose of this paper is to give a comprehensive review of fluid flow/DEM coupling methods and relevant research.Given their importance,the availability or unavailability of best practice guidelines is outlined.The theoretical background and current status of DEM are introduced first,and the principles,applications,and advantages and disadvantages of different fluid flow/DEM coupling methods are discussed.Finally,a summary with speculation on future development trends is given.

A multiscale 3D finite element analysis of fluid/solute transport in mechanically loaded bone

The transport of fluid, nutrients, and signaling molecules in the bone lacunar-canalicular system （LCS） is critical for osteocyte survival and function. We have applied the fluorescence recovery after photobleaching （FRAP） approach to quantify load-induced fluid and solute transport in the LCS in situ, but the measurements were limited to cortical regions 30-50 μm underneath the periosteum due to the constrains of laser penetration. With this work, we aimed to expand our understanding of load-induced fluid and solute transport in both trabecular and cortical bone using a multiscaled image-based finite element analysis （FEA） approach. An intact murine tibia was first re-constructed from microCT images into a three-dimensional （3D） linear elastic FEA model, and the matrix deformations at various locations were calculated under axial loading. A segment of the above 3D model was then imported to the biphasic poroelasticity analysis platform （FEBio） to predict load-induced fluid pressure fields, and interstitial solute/fluid flows through LCS in both cortical and trabecular regions. Further, secondary flow effects such as the shear stress and/or drag force acting on osteocytes, the presumed mechano-sensors in bone, were derived using the previously developed ultrastructural model of Brinkman flow in the canaliculi. The material properties assumed in the FEA models were validated against previously obtained strain and FRAP transport data measured on the cortical cortex. Our results demonstrated the feasibility of this computational approach in estimating the fluid flux in the LCS and the cellular stimulation forces （shear and drag forces） for osteocytes in any cortical and trabecular bone locations, allowing further studies of how the activation of osteocytes correlates with in vivo functional bone formation. The study provides a promising platform to reveal potential cellular mechanisms underlying the anabolic power of exercises and physical activities in treating patients with skeletal deficiencies.

Rare earth elements in CO_2-fluid inclusions in mantle Iherzolite

Trace elements including REE (Rare Earth Elements) in fluid inclusions inlherzolite, olivine, orthopyroxene, and clinopyroxene have been determined by heating-decrepitationand ICP-MS (Element Type Inductively Coupled Plasma-Mass Spectrometry) method. Normalized CO_2fluid/chondrite data show that mantle fluids are rich in REEs, especially LREEs (Light Rare EarthElements), several times or dozen times higher than mantle rocks and mantle minerals. There areclose relationships among the REE data of olivine, orthopyroxene, clinopyroxene and lherzolite.Compared to the data of chemical dissolution method, it is believed that REE data obtained fromheating-decrepitation and ICP-MS technique are contributed by CO_2 fluid inclusions. About 60percent (mass fraction) of tiny inclusions are observed not to be decrepitated above 1000 deg C, soREE data obtained are only contributed by decrepitated inclusions. Mantle fluids rich in LREE playan important role in mantle metasomatism, partial melting and mineralization.

Fractional four-step finite element method for analysis of thermally coupled fluid-solid interaction problems

An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal stress in the solid. The fractional four-step finite element method and the streamline upwind Petrov-Galerkin （SUPG） method are used to analyze the viscous thermal flow in the fluid. Analyses of the heat transfer and the thermal stress in the solid axe performed by the Galerkin method. The second-order semi- implicit Crank-Nicolson scheme is used for the time integration. The resulting nonlinear equations are lineaxized to improve the computational efficiency. The integrated analysis method uses a three-node triangular element with equal-order interpolation functions for the fluid velocity components, the pressure, the temperature, and the solid displacements to simplify the overall finite element formulation. The main advantage of the present method is to consistently couple the heat transfer along the fluid-solid interface. Results of several tested problems show effectiveness of the present finite element method, which provides insight into the integrated fluid-thermal-structural interaction phenomena.

GEOCHEMICAL EFFECTS OF MAJOR ELEMENTS DURING FLUID ROCKS INTERAC TION IN MARINWOBO FAULT IN THE SOUTH MARGIN AREAS OF ALTAI MOUNTAINS

There are four types of metamorphic rocks in the Marinwobo fault, i.e, cataclasite, mylonite, mictosite and migmatitic granite, and the formation of these rocks is due to the progressive metamorphism of the pyroclastics. The fluids play a very important role in the metamorphic process of these rocks in the Marinwobo fault, the most important feature is that the fluids not only result in the migration of the major elements of the deformation rocks, but also result in the volume loss of the deformation rocks in the deformation process. Thus the migration laws of the major elements in different stages of the progressive metamorphic process are discussed according to mass balance equations. Finally, the quantitative analysis of the mass loss and volume loss of the different rocks the in Marinwobo fault is discussed in this paper.

INFLUENCE OF SURFACE-ACTIVE ELEMENTS ON FLUID FLOW OF MIG WELDPOOL

A mathematical model describing the behavior of metal inert gas (MIG) welding isformulated in the paper. By means of numerical simulation, the influence of surface-active elements on fluid flow of MIG weldpool is studied. The calculation resultsshow that by adding surface-active elements, the fluid flow behavior is drasticallychanged and the flow fluid flows from lower to upper in vertical direction at the rearof weldpool (w>0). The physical phenomenon is explained from the viewpoint of fluidflow behavior of weldpool that the properties of weld metal is greatly improved andthe content of diffused hydrogen is reduced, thus providing a basis for developing newwelding materials.

A hybrid finite volume/finite element method for incompressible generalized Newtonian fluid flows on unstructured triangular meshes

This paper presents a hybrid finite volume/finite element method for the incompressible generalized Newtonian fluid flow （Power-Law model）. The collocated （i.e. non-staggered） arrangement of variables is used on the unstructured triangular grids, and a fractional step projection method is applied for the velocity-pressure coupling. The cell-centered finite volume method is employed to discretize the momentum equation and the vertex-based finite element for the pressure Poisson equation. The momentum interpolation method is used to suppress unphysical pressure wiggles. Numerical experiments demonstrate that the current hybrid scheme has second order accuracy in both space and time. Results on flows in the lid-driven cavity and between parallel walls for Newtonian and Power-Law models are also in good agreement with the published solutions.

Least-Squares Finite Element Method for the Steady Upper-Convected Maxwell Fluid

In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the linearized version of the viscoelastic UCM model. The L2 least-squares functional involves the residuals of each equation multiplied by proper weights. The corresponding homogeneous functional is equivalent to a natural norm. The error estimates of the finite element solution are analyzed when the conforming piecewise polynomial elements are used for the unknowns.

Trace Elements in Fluid Inclusions in the Carlin-Type Gold Deposits, Southwestern Guizhou Province

Fluid inclusions in quartz from the Lannigou and Yata Carlin\|type gold deposits in southwestern Guizhou were analyzed by inductively coupled plasma\|mass spectrometry for their trace elements (Co, Ni, Cu, Pb, Zn, Pt, etc.). The results show that quartz fluid inclusions entrapped at different ore\|forming stages contain higher Co, Ni, Cu, Pb and Zn. It has been found for the first time that the ore\|forming fluids responsible for the Carlin\|type gold deposits are rich in Pt. From this it can be concluded that basic volcanic rocks seem to be one of the important sources of ore\|forming materials for the Carlin\|type gold deposits.

A BOUNDARY ELEMENT METHOD FOR SMALL-AMPLITUDE VISCOUS FLUID SLOSHING IN COUPLE WITH STRUCTURAL VIBRATION

A boundary element method is presented for the coupled motionanalysis of structural vibration with small-amplitude fluid sloshingin two-dimensional space. The linearized Navier-Stokes equations areconsidered in frequency domain and transformed into boundary integralequations. An appropriate fundamental solution for the Helmholtzequation with pure imaginary constant is found. The condition ofzero-stress is imposed on the free surface, and non-slip condition offluid particles is Imposed on the walls of the container. For rigidmotion models, the expressions for added mass and Added damping tothe structural motion equations are obtained. Some typical numericalexamples are Presented.

Using Prostatic Fluid Levels of Some Trace Elements and Their Combinations in Non-Invasive and Highly Accurate Screening for Prostate Cancer

Objective: Prostate specific antigen (PSA) does not provide the high reliability and precision that is required for an accurate screening for prostate cancer?(PCa). The aim of our study was to search for a simple, rapid, direct, preferably non-invasive, and highly accurate biomarker and procedure for the screening for PCa. Method: The levels of trace elements (TE) Br, Fe, Rb, Sr,?and Zn were prospectively evaluated in expressed prostatic fluid (EPF). Also?Zn/Br, Zn/Fe, Zn/Rb, Zn/Sr concentration ratios as well as ZnRb and (ZnRb)/Fe concentration combinations were calculated for EPF samples, obtained from 38 apparently healthy males and from 33, 51, and 24 patients with chronic prostatitis, benign prostatic hyperplasia, and PCa, respectively. Measurements were performed using an energy dispersive X-ray fluorescent (EDXRF) microanalysis. Results: It was found that in the EPF of cancerous prostates the levels of Rb, Zn, Zn/Br, Zn/Fe, Zn/Sr, ZnRb, and (ZnRb)/Fe were significantly lower in comparison with those in the EPF of normal, inflamed, and hyperplastic prostates. For example, in comparison hyperplastic?with cancerous prostates p values obtained using Student’s t-test and?Wilcoxon-Mann-Whitney U-test were Conclusions: The levels of TE and their combinations in EPF, obtained by EDXRF, is a fast, reliable, andnon-invasive diagnostic tool that can be successfully used by local, non- urologist physicians at the point-of-care to provide a highly effective PCa screening and as an additional confirmatory test before a prostate gland biopsy.

PENALTY FINITE ELEMENT METHOD FOR NONLINEAR DYNAMIC RESPONSE OF VISCOUS FLUID-SATURATED BIPHASE POROUS MEDIA

The governing equations as well as boundary land initial conditions for nonlinear dynamic response problems of viscous fluid-saturated biphase porous medium model, based on mixture theory, are presented. With Galerkin weighted residual method the corresponding nonlinear dynamic penalty finite element equation, in which the dependencies of volume fraction and permeation coefficients an deformation are included, is obtained. The iteration solution method of the nonlinear system equation is also discussed. As a numerical example, the dynamic response of a porous medium column under impulsive loading action is analyzed with the developed finite element program. The numerical results demonstrate the efficiency and correctness of the method.

Method and portable facility for measurement of trace element concentration in prostate fluid samples using radionuclideinduced energy-dispersive X-ray fluorescent analysis

A facility and method for109 Cd radionuclide-induced energy-dispersive X-ray fluorescent(EDXRF) were developed to determine the Fe,Zn,Br,Rb,and Sr concentrations in the specimens of human prostatic fluid.Specimens of expressed prostatic fluid were obtained from 51 men(mean age 51 years,range 18–82 years) with apparently normal prostates using standard rectal massage procedure.Mean values(M ± SEL) for concentration of trace elements(mg L^(-1)) in human prostate fluid were:Fe 9.04 ±1.21,Zn 573 ± 35,Br 3.58 ± 0.59,Rb 1.10 ± 0.08,and Sr B 0.76.It was shown that the results of trace element analysis in the micro-samples(20 l L) are sufficiently representative for assessment of the Fe,Zn,Br,and Rb concentration in the prostate fluid.The facility for109 Cd radionuclide-induced EDXRF is comparatively compact and can be located in close proximity to the site of carrying out the massage procedure.The means of Zn and Rb concentration obtained for prostate fluid agree well with median of reported means.For the first time,the Fe and Br concentrations,as well as the upper limit of the Sr concentration,were determined in the human prostate fluid.

LAPLACE TRANSFORM-BOUNDARY ELEMENT COUPLING METHOD FOR VISCOUS FLUIDSTRUCTURE IMPACT ANALYSIS

Based on linearized 2-D Navier-Stokes equation, a Laplacetransform-boundary element coupling method for viscousfluid-structure impact analysis is proposed. Under assumption ofincompressibility for the fluid, the corresponding equivalentboundary integral equation in terms of the potential function andstream function is first established by Lamb's transform in theLaplace transform domain.

ALE Fractional Step Finite Element Method for Fluid-Structure Nonlinear Interaction Problem

A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction,step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.

FINITE ELEMENT ANALYSIS OF THE FREE EXTRUSION FLOWS OF BOGER FLUIDS

The stream-line finite element method proposed by Luo and Tanner has been improvedand used to simulate the extrudate swell of the so called Boger fluid.The element withdiscontinuous pressure proves to be a successful choice and superior to that with continuous pressureIt is revealed that the visccsity of Newtonian solvent of the Boger fluid has a great influence on thecalculated swelling.The Weissenberg number is suggested to take the place of recoverable shear strainin Tanner′s formula to estimate the swelling of the Boger or Oldroyd-B fluids.

A WEIGHTED PENALTY FINITE ELEMENT METHOD FOR THE ANALYSIS OF POWER-LAW FLUID FLOW PROBLEMS

In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an alternative perturbation, which is weighted by viscosity, of the continuity equation. A numerical example is presented to exhibit the efficiency of the method.

Finite element analysis of fluid-structure interaction in buried liquid-conveying pipeline

Long distance buried liquid-conveying pipeline is inevitable to cross faults and under earthquake action,it is necessary to calculate fluid-structure interaction(FSI) in finite element analysis under pipe-soil interaction.Under multi-action of site,fault movement and earthquake,finite element model of buried liquid-conveying pipeline for the calculation of fluid structure interaction was constructed through combinative application of ADINA-parasolid and ADINA-native modeling methods,and the direct computing method of two-way fluid-structure coupling was introduced.The methods of solid and fluid modeling were analyzed,pipe-soil friction was defined in solid model,and special flow assumption and fluid structure interface condition were defined in fluid model.Earthquake load,gravity and displacement of fault movement were applied,also model preferences.Finite element research on the damage of buried liquid-conveying pipeline was carried out through computing fluid-structure coupling.The influences of pipe-soil friction coefficient,fault-pipe angle,and liquid density on axial stress of pipeline were analyzed,and optimum parameters were proposed for the protection of buried liquid-conveying pipeline.

MIXED COMPATIBLE ELEMENT AND MIXED HYBRID INCOMPATIBLE ELEMENT VARIATIONAL METHODS IN DYNAMICS OF VISCOUS BAROTROPIC FLUIDS

This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.

Simulation of fluid-structure interaction in a microchannel using the lattice Boltzmann method and size-dependent beam element on a graphics processing unit

Fluid-structure interaction （FSI） problems in microchannels play a prominent role in many engineering applications. The present study is an effort toward the simulation of flow in microchannel considering FSI. The bottom boundary of the microchannel is simulated by size-dependent beam elements for the finite element method （FEM） based on a modified cou- ple stress theory. The lattice Boltzmann method （LBM） using the D2Q13 LB model is coupled to the FEM in order to solve the fluid part of the FSI problem. Because of the fact that the LBM generally needs only nearest neighbor information, the algorithm is an ideal candidate for parallel computing. The simulations are carried out on graphics processing units （GPUs） using computed unified device architecture （CUDA）. In the present study, the governing equations are non-dimensionalized and the set of dimensionless groups is exhibited to show their effects on micro-beam displacement. The numerical results show that the displacements of the micro-beam predicted by the size-dependent beam element are smaller than those by the classical beam element.