Numerical modeling and simulation of PEM fuel cells: Progress and perspective

This paper provides a comprehensive review on the research and development in multi-scale numerical modeling and simulation of PEM fuel cells. An overview of recent progress in PEM fuel cell modeling has been provided. Fundamental transport phenomena in PEM fuel cells and the corresponding mathematical formulation of macroscale models are analyzed. Various important issues in PEM fuel cell modeling and simulation are examined in detail, including fluid flow and species transport, electron and proton transport, heat transfer and thermal management, liquid water transport and water management, transient response behaviors, and cold-start processes. Key areas for further improvements have also been discussed.

Numerical simulation of slurry jets using mixture model

Slurry jets in a static uniform environment were simulated with a two-phase mixture model in which flow-particle interactions were considered. A standard k-e turbulence model was chosen to close the governing equations. The computational results were in agreement with previous laboratory measurements. The characteristics of the two-phase flow field and the influences of hydraulic and geometric parameters on the distribution of the slurry jets were analyzed on the basis of the computational results. The calculated results reveal that if the initial velocity of the slurry jet is high, the jet spreads less in the radial direction. When the slurry jet is less influenced by the ambient fluid （when the Stokes number St is relatively large）, the turbulent kinetic energy k and turbulent dissipation rate e, which are relatively concentrated around the jet axis, decrease more rapidly after the slurry jet passes through the nozzle. For different values of St, the radial distributions of streamwise velocity and particle volume fraction are both self-similar and fit a Gaussian profile after the slurry jet fully develops. The decay rate of the particle velocity is lower than that of water velocity along the jet axis, and the axial distributions of the centerline particle streamwise velocity are self-similar along the jet axis. The pattern of particle dispersion depends on the Stokes number St. When St = 0.39, the panicle dispersion along the radial direction is considerable, and the relative velocity is very low due to the low dynamic response time. When St = 3.08, the dispersion of particles along the radial direction is very little, and most of the particles have high relative velocities along the streamwise direction.

The numerical simulation of Pacific Ocean circulation with five-level model

A five-level oceanic primitive equation model has been developed. This model is integrated numerically with annual mean wind stress and heat flux at sea surface for 30 a. The ocean circulations tend to quasi-stability. The simulated results show that the computed annual mean currents and sea surface temperature agree well with the observations.

Temperature Distributions in Single Cell of Polymer Electrolyte Fuel Cell Simulated by an 1D Multi-plate Heat-Transfer Model and a 3D Numerical Simulation Model

The purpose of this study is to verify an 1D multi-plate heat-transfer model estimating the temperature distribution on the interface between polymer electrolyte membrane and catalyst layer at cathode in single cell of polymer electrolyte fuel cell, which is named as reaction surface in this study, with a 3D numerical simulation model solving many governing equations on the coupling phenomena in the cell. The results from both models/simulations agreed well. The effects of initial operation temperature, flow rate, and relative humidity of supply gas on temperature distribution on the reaction surface were also investigated. It was found in both 1D and 3D simulations that, the temperature rise （i.e., Treact-Tini） of the reaction surface from initial operation temperature at 70℃ was higher than that at 80℃ irrespective of flow rate of supply gas. The effect of relative humidity of supply gas on Treact- Tini near the inlet of the cell was small. Compared to the previous studies conducted under the similar operation conditions, the Treact - Tini calculated by 1D multi-plate heat-transfer model in this study as well as numerical simulation using 3D model was reasonable.

Numerical simulation study of the failure evolution process and failure mode of surrounding rock in deep soft rock roadways

Based on the safety coefficient method,which assigns rock failure criteria to calculate the rock mass unit,the safety coefficient contour of surrounding rock is plotted to judge the distribution form of the fractured zone in the roadway.This will provide the basis numerical simulation to calculate the surrounding rock fractured zone in a roadway.Using the single factor and multi-factor orthogonal test method,the evolution law of roadway surrounding rock displacements,plastic zone and stress distribution under different conditions is studied.It reveals the roadway surrounding rock burst evolution process,and obtains five kinds of failure modes in deep soft rock roadway.Using the fuzzy mathematics clustering analysis method,the deep soft surrounding rock failure model in Zhujixi mine can be classified and patterns recognized.Compared to the identification results and the results detected by geological radar of surrounding rock loose circle,the reliability of the results of the pattern recognition is verified and lays the foundations for the support design of deep soft rock roadways.

3D numerical simulation of boreholes for gas drainage based on the pore–fracture dual media

A gas migration controlling equation was formulated based on the characteristics of the dual pore–fracture media of coal mass and in consideration of the matrix exchange between pores and fractures.A model of permeability dynamic evolution was established by analyzing the variation in effective stress during gas drainage and the action mechanism of the effect of coal matrix desorption on porosity and fracture in the coal body.A coupling model can then be obtained to characterize gas compressibility and coal deformability under the gas–solid coupling of loading coal.In addition,a 3D model of boreholes was established and solved for gas drainage based on the relevant physical parameters of real mines.The comparison and analysis results for the law of gas migration and the evolution of coal body permeability around the boreholes before and after gas extraction between the dual media and the single-seepage field models can provide a theoretical basis for further research on the action mechanism of gas drainage.

Numerical Simulation for Evolutionary History of Three-Dimensional Basin

Numerical simulation or evolutionary history of an oil and gas-bearing basin is to repeat geological and thermodyanomic history of basin evolution on a computer and then to quantitate petroleum generation,accumulation and migration.The mathemat-ical model describing geological and thermodynamic history of the basin evolution ischaracterised by an initial-boundary value problem of a system of nonlinear partial dif-ferential equations. In the present paper, a numerical method for three-dimensionalproblem and the analysis of its stability are established and a numerical result for apractical model is given, which shows that the abnormal pressure and paleo-temperat-ure computed are reasonable and display physical characteristics clearly as well.

Numerical simulation of avascular tumor growth based on p27 gene regulation

A multi-scale continuous-discrete model based on the effects of the p27 gene control is built to simulate the avascular tumor growth. At the tissue level, the continuous Eulerian model is adopted to determine the distribution of the concentration of oxygen, the extracellular matrix （ECM）, and the matrix-degradative enzyme （MDE）. At the cellular level, the discrete Lagrangien model is adopted to determine the movement, the proliferation, and the death of single tumor cells （TCs）. At the genetic level, whether a cell is committed to mitosis is determined by solving a set of equations modeling the effects of the p27 gene control. The avascular morphological evolution of the solid tumor growth is simulated, including the radius the oxygen distribution over time, and the expression. of the solid tumor, the number of the TCs, inhibiting effect＇ of the up-regulating p27 gene

Mathematical model and numerical method for spontaneous potential log in heterogeneous formations

This paper introduces a new spontaneous potential log model for the case in which formation resistivity is not piecewise constant. The spontaneous potential satisfies an elliptic boundary value problem with jump conditions on the interfaces. It has beer/ shown that the elliptic interface problem has a unique weak solution. Furthermore, a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic problems. Numerical results show validity and effectiveness of the proposed method.

Numerical simulation of flocculation and settling behavior of whole-tailings particles in deep-cone thickener

Rapid dewatering and thickening of whole-tailings with ultrafine particles is one of the most important processes for the whole-tailings paste preparation. Deep-cone thickener, a kind of such process for the flocculation and settling of whole-tailings, is particularly necessary to study. However, there exist many problems in observing the flocculation and settling process of whole-tailings, as well as the particle size distribution(PSD) of whole-tailings floccules in deep-cone thickener. Population balance model(PBM) is applied to predict the PSD in deep-cone thickener, and LUO model and GHADIRI model are employed to study the aggregation and fragmentation mechanism of the whole-tailings particles, respectively. Through three-dimensional numerical simulation on the whole-tailings flocculation and settling in deep-cone thickener using computational fluid dynamics(CFD)-PBM, the distribution of density and turbulent kinetic energy in deep-cone thickener were obtained, at the same time the spatio-temporal changes of whole-tailings floccules particle size distribution are analyzed. Finally, the major flocculation position in deep-cone thickener is found and the flocculation settling rules of whole-tailings are achieved.

Numerical Modeling of a Spherical Buoy Moored by a Cable in Three Dimensions

Floating facilities have been studied based on the static analysis of mooring cables over the past decades. To analyze the floating system of a spherical buoy moored by a cable with a higher accuracy than before, the dynamics of the cables are considered in the construction of the numerical modeling. The cable modeling is established based on a new element frame through which the hydrodynamic loads are expressed efficiently. The accuracy of the cable modeling is verified with an experiment that is conducted by a catenary chain moving in a water tank. In addition, the modeling of a spherical buoy is established with respect to a spherical coordinate in three dimensions, which can suffers the gravity, the variable buoyancy and Froude-Krylov loads. Finally, the numerical modeling for the system of a spherical buoy moored by a cable is established, and a virtual simulation is proceeded with the X- and Y-directional linear waves and the X-directional current. The comparison with the commercial simulation code Proteus DS indicates that the system is accurately analyzed by the numerical modeling. The tensions within the cable, the motions of the system, and the relationship between the motions and waves are illustrated according to the defined sea state. The dynamics of the cables should be considered in analyzing the floating system of a spherical buoy moored by a cable.

Numerical simulation and experimental verification of bubble size distribution in an air dense medium fluidized bed

Bubble size distribution is the basic apparent performance and obvious characteristics in the air dense medium fluidized bed (ADMFB). The approaches of numerical simulation and experimental verification were combined to conduct the further research on the bubble generation and movement behavior. The results show that ADMFB could display favorable expanded characteristics after steady fluidization. With different particle size distributions of magnetite powder as medium solids, we selected an appropriate prediction model for the mean bubble diameter in ADMFB. The comparison results indicate that the mean bubble diameters along the bed heights are 35 mm < D b < 66 mm and 40 mm < D b < 69 mm with the magnetite powder of 0.3 mm+0.15mm and 0.15mm+0.074mm, respectively. The prediction model provides good agreements with the experimental and simulation data. Based on the optimal operating gas velocity distribution, the mixture of magnetite powder and <1mm fine coal as medium solids were utilized to carry out the separation experiment on 6-50mm raw coal. The results show that an optimal separation density d P of 1.73g/cm 3 with a probable error E of 0.07g/cm 3 and a recovery efficiency of 99.97% is achieved, which indicates good separation performance by applying ADMFB.

Dynamic process simulation with a Savage-Hutter type model for the intrusion of landslide into river

Natural damming of rivers by mass movements is a very common and potentially dangerous phenomena which has been documented all over the world. In this paper, a two-layer model of Savage-Hutter type is presented to simulate the dynamic procedure for the intrusion of landslide into rivers. The two-layer shallow water system is derived by depth averaging the incompressible Navier-Stokes equations with the hydrostatic assumption. A high order accuracy scheme based on the finite volume method is proposed to solve the presented model equations. Several numerical tests are performed to verify the realiability and feasibility of the proposed model. The numerical results indicate that the proposed method can be competent for simulating the dynamic process of landslide intrusion into the river. The interaction effect between both layers has a significant impact on the landslide movement, water fluctuation and wave propagation.

2D Coupled 3D:A New Numerical Model for Dual - Structured - Aquifer System

This paper points out that a successful numerical simulation is to construct a correct conceptional model which is very dose to the natural condition. A new model, two dimensional coupled three dimensional model (2D -3D ) is presented in the Present paper,which is the most suitable one for the dual - structured - aquifer system. An example of Wenyinghu area is shown.By using the 2D-3D model, a satisfied result of the simulated area is achieved.

The Corrected Simulation Method of Critical Heat Flux Prediction for Water-Cooled Divertor Based on Euler Homogeneous Model

An accurate critical heat flux（CHF） prediction method is the key factor for realizing the steady-state operation of a water-cooled divertor that works under one-sided high heating flux conditions.An improved CHF prediction method based on Euler＇s homogeneous model for flow boiling combined with realizable k-ε model for single-phase flow is adopted in this paper in which time relaxation coefficients are corrected by the Hertz-Knudsen formula in order to improve the calculation accuracy of vapor-liquid conversion efficiency under high heating flux conditions.Moreover,local large differences of liquid physical properties due to the extreme nonuniform heating flux on cooling wall along the circumference direction are revised by formula IAPWSIF97.Therefore,this method can improve the calculation accuracy of heat and mass transfer between liquid phase and vapor phase in a CHF prediction simulation of water-cooled divertors under the one-sided high heating condition.An experimental example is simulated based on the improved and the uncorrected methods.The simulation results,such as temperature,void fraction and heat transfer coefficient,are analyzed to achieve the CHF prediction.The results show that the maximum error of CHF based on the improved method is 23.7%,while that of CHF based on uncorrected method is up to 188%,as compared with the experiment results of Ref.[12].Finally,this method is verified by comparison with the experimental data obtained by International Thermonuclear Experimental Reactor（ITER）,with a maximum error of 6% only.This method provides an efficient tool for the CHF prediction of water-cooled divertors.

Numerical investigation of hydro-morphodynamic characteristics of a cascading failure of landslide dams

A cascading failure of landslide dams caused by strong earthquakes or torrential rains in mountainous river valleys can pose great threats to people’s lives,properties,and infrastructures.In this study,based on the three-dimensional Reynoldsaveraged Navier-Stokes equations(RANS),the renormalization group(RNG)k-εturbulence model,suspended and bed load transport equations,and the instability discriminant formula of dam breach side slope,and the explicit finite volume method(FVM),a detailed numerical simulation model for calculating the hydro-morphodynamic characteristics of cascading dam breach process has been developed.The developed numerical model can simulate the breach hydrograph and the dam breach morphology evolution during the cascading failure process of landslide dams.A model test of the breaches of two cascading landslide dams has been used as the validation case.The comparison of the calculated and measured results indicates that the breach hydrograph and the breach morphology evolution process of the upstream and downstream dams are generally consistent with each other,and the relative errors of the key breaching parameters,i.e.,the peak breach flow and the time to peak of each dam,are less than±5%.Further,the comparison of the breach hydrographs of the upstream and downstream dams shows that there is an amplification effect of the breach flood on the cascading landslide dam failures.Three key parameters,i.e.,the distance between the upstream and the downstream dams,the river channel slope,and the downstream dam height,have been used to study the flood amplification effect.The parameter sensitivity analyses show that the peak breach flow at the downstream dam decreases with increasing distance between the upstream and the downstream dams,and the downstream dam height.Further,the peak breach flow at the downstream dam first increases and then decreases with steepening of the river channel slope.When the flood caused by the upstream dam failure flows to the downstream dam,it can produce a surge wave that overtops and erodes the dam crest,resulting in a lowering of the dam crest elevation.This has an impact on the failure occurrence time and the peak breach flow of the downstream dam.The influence of the surge wave on the downstream dam failure process is related to the volume of water that overtops the dam crest and the erosion characteristics of dam material.Moreover,the cascading failure case of the Xiaogangjian and Lower Xiaogangjian landslide dams has also been used as the representative case for validating the model.In comparisons of the calculated and measured breach hydrographs and final breach morphologies,the relative errors of the key dam breaching parameters are all within±10%,which verify the rationality of the model is applicable to real-world cases.Overall,the numerical model developed in this study can provide important technical support for the risk assessment and emergency treatment of failures of cascading landslide dams.

Modeling of fiber bridging in fluid flow for well stimulation applications

Accurate acid placement constitutes a major concern in matrix stimulation because the acid tends to penetrate the zones of least resistance while leaving the low-permeability regions of the formation untreated.Degradable materials(fibers and solid particles)have recently shown a good capability as fluid diversion to overcome the issues related to matrix stimulation.Despite the success achieved in the recent acid stimulation jobs stemming from the use of some products that rely on fiber flocculation as the main diverting mechanism,it was observed that the volume of the base fluid and the loading of the particles are not optimized.The current industry lacks a scientific design guideline because the used methodology is based on experience or empirical studies in a particular area with a particular product.It is important then to understand the fundamentals of how acid diversion works in carbonates with different diverting mechanisms and diverters.Mathematical modeling and computer simulations are effective tools to develop this understanding and are efficiently applied to new product development,new applications of existing products or usage optimization.In this work,we develop a numerical model to study fiber dynamics in fluid flow.We employ a discrete element method in which the fibers are represented by multi-rigid-body systems of interconnected spheres.The discrete fiber model is coupled with a fluid flow solver to account for the inherent simultaneous interactions.The focus of the study is on the tendency for fibers to flocculate and bridge when interacting with suspending fluids and encountering restrictions that can be representative of fractures or wormholes in carbonates.The trends of the dynamic fiber behavior under various operating conditions including fiber loading,flow rate and fluid viscosity obtained from the numerical model show consistency with experimental observations.The present numerical investigation reveals that the bridging capability of the fiber–fluid system can be enhanced by increasing the fiber loading,selecting fibers with higher stiffness,reducing the injection flow rate,reducing the suspending fluid viscosity or increasing the attractive cohesive forces among fibers by using sticky fibers.

Mechanism on simulation and experiment of pre-crack seam formation in stope roof

The pre-crack blast technology has been used to control the induction caving area in the roof. The key is to form the pre-crack seam and predict the effect of the seam. The H-J-C blast model was built in the roof. Based on the theories of dynamic strength and failure criterion of dynamic rock, the rock dynamic damage and the evolution of pre-crack seam were simulated by the tensile damage and shear failure of the model. According to the actual situation of No. 92 ore body test stope at Tongkeng Mine, the formation process of the pre-crack blast seam was simulated by Ansys/Ls-dyna software, the pre-crack seam was inspected by a system of digital panoramic borehole camera. The pre-crack seam was inspected by the system of digital panoramic borehole in the roof. The results of the numerical simulation and inspection show that in the line of centers of pre-hole, the minimum of the tensile stress reaches 20 MPa, which is much larger than 13.7 MPa of the dynamic tensile strength of rock. The minimum particle vibration velocity reaches 50 cm/s, which is greater than 30-40 cm/s of the allowable vibration velocity. It is demonstrated that the rock is destroyed near the center line and the pre-crack is successfully formed by the large diameters and large distances pre-crack holes in the roof.

Physical Model of Drying Shrinkage of Recycled Aggregate Concrete

We prepared concretes（RC0, RC30, and RC100） with three different mixes. The poresize distribution parameters of RAC were examined by high-precision mercury intrusion method（MIM） and nuclear magnetic resonance（NMR） imaging. A capillary-bundle physical model with random-distribution pores（improved model, IM） was established according to the parameters, and dry-shrinkage strain values were calculated and verified. Results show that in all pore types, capillary pores, and gel pores have the greatest impacts on concrete shrinkage, especially for pores 2.5-50 and 50-100 nm in size. The median radii are 34.2, 31, and 34 nm for RC0, RC30, and RC100, respectively. Moreover, the internal micropore size distribution of RC0 differs from that of RC30 and RC100, and the pore descriptions of MIM and NMR are consistent both in theory and in practice. Compared with the traditional capillary-bundle model, the calculated results of IM have higher accuracy as demonstrated by experimental verifi cation.