Computation of the Longitudinal and Transverse Dispersion Coefficient in an Adsorbing Porous Medium Using Homogenization

This article compares for the first time, local longitudinal and transverse dispersion coefficients obtained by homogenization with experimental data of dispersion coefficients in porous media, using the correct porosity dependence. It is shown that the longitudinal dispersion coefficient can be reasonably represented by a simple periodic unit cell (PUC), which consists of a single sphere in a cube. We present a slightly modified and simplified approach to derive the homogenized equations, which emphasizes physical aspects of homogenization. Subsequently, we give full dimensional expressions for the dispersion tensor based on a comparison with the convective dispersion equation used for contaminant transport, inclusive the correct dependence on porosity. For the PUC of choice, the dispersion relations are identical to the relations obtained for periodic media. We show that commercial finite element software can be readily used to compute longitudinal and transverse dispersion coefficients in 2D and 3D. The 3D results are for the first time obtained at relevant Peclet numbers. There is good agreement for longitudinal dispersion. The computed transverse dispersion coefficients for a single sphere in a cube are much too low. The effect of adsorption on the dispersion coefficient is also studied. Adsorption does not affect the transverse dispersion coefficient. However, adsorption enhances the longitudinal dispersion coefficient in agreement with an analysis of homogenization applied to Taylor dispersion discussed in the literature.     

The Role of Biofilm Growth in Bacteria-Facilitated Contaminant Transport in Porous Media

Groundwater contaminants adhered to colloid surfaces may migrate to greater distances than predicted by using the conventional advective-dispersive transport equation. Introduction of exogenous bacteria in a bioremediation operation or mobilization of indigenous bacteria in groundwater aquifers can enhance the transport of contaminants in groundwater by reducing the retardation effects. Because of their colloidal size and favorable surface conditions, bacteria can be efficient contaminant carriers. In cases where contaminants have low mobility because of their high partition with aquifer solids, facilitated contaminant transport by mobile bacteria can create high contaminant fluxes. In this paper, we developed a methodology to describe the bacteria-facilitated contaminant transport in a subsurface environment using the biofilm theory. The model is based on mass balance equations for bacteria and contaminant. The contaminant is utilized as a substrate for bacterial growth. Bacteria are attached to solid surfaces as a biofilm. We investigate the role of the contaminant adsorption on both biofilm and mobile bacteria on groundwater contaminant transport. Also, the effect of bacterial injection on the contaminant transport is evaluated in the presence of indigenous bacteria in porous media. The model was solved numerically and validated by experimental data reported in the literature. Sensitivity analyses were conducted to deduce the effect of critical model parameters. Results show that biofilm grows rapidly near the top of the column where the bacteria and contaminant are injected, and is detached by increasing fluid shear stress and re-attach downstream. The adsorption of contaminant on bacterial surfaces reduces contaminant mobility remarkably in the presence of a biofilm. The contaminant concentration decreases significantly along the biofilm when contaminant partition into bacteria. Bacterial injection and migration in subsurface environments can be important in bioremediation operations regardless of the presence of indigenous bacteria.     

Density-driven Transport of Volatile Organic Compounds and its Impact on Contaminated Groundwater Plume Evolution

Density-driven advection of gas phase due to vaporization of chlorinated volatile organic compounds (VOCs) has a significant effect on fate and transport of contaminants. In this study, we investigated the effects of density-driven advection, infiltration, and permeability on contaminant plume evolution and natural attenuation of VOCs in the subsurface system. To analyze these effects, multiphase flow and contaminant transport processes were simulated using a three-dimensional Galerkin-finite-element-based model. Trichloroethylene (TCE) is selected as a target contaminant. Density-driven advection of gas phase elevated the potential of groundwater pollution in the saturated zone by accelerating downward migration of vaporized contaminant in the unsaturated zone. The advection contributed to increased removal rates of non-aqueous phase liquid (NAPL) TCE source and reduced dissolved TCE plume development in the downstream area. Infiltration reduced the velocity of the density-driven advection and its influence zone, but raised TCE transfer from the unsaturated to the saturated zone. The variation in soil permeability showed greater impact on contaminant migration within water phase in the saturated zone than within gas phase in the unsaturated zone. Temporal variations of TCE mass within two-dimensional (2D) and three-dimensional (3D) domains under several modeling conditions were compared. These results are important in evaluation of natural attenuation processes, and should be considered to effectively design monitored natural attenuation as a remedial option.     

Research of air-cushion isolation effects on high arch dam reservoir

A three-dimensional (3D) finite element model of air-cushion isolated arch dam is presented with the nonlinear gas-liquid-solid multi-field dynamic coupling effect taken into account.In this model,the displacement formulation in Lagrange method,pressure formulation in Euler method,nonlinear contact model based on Coulomb friction law are applied to the air-cushion,reservoir and contraction joint domain,respectively.The dynamic response of Jinping I arch dam with a height of 305 m is analyzed using the seismic records of the Wenchuan Earthquake in 2008.Numerical results show that the air-cushion isolation reduces significantly the hydrodynamic pressure as well as the opening width for the contraction joints of high arch dam.     

Static analysis of ultra-thin beams based on a semi-continuum model

A linear semi-continuum model with discrete atomic layers in the thickness direction was developed to investigate the bending behaviors of ultra-thin beams with nanoscale thickness.The theoretical results show that the deflection of an ultra-thin beam may be enhanced or reduced due to different relaxation coefficients.If the relaxation coefficient is greater/less than one,the deflection of micro/nano-scale structures is enhanced/reduced in comparison with macro-scale structures.So,two opposite types of size-dependent behaviors are observed and they are mainly caused by the relaxation coefficients.Comparisons with the classical continuum model,exact nonlocal stress model and finite element model (FEM) verify the validity of the present semi-continuum model.In particular,an explanation is proposed in the debate whether the bending stiffness of a micro/nano-scale beam should be greater or weaker as compared with the macro-scale structures.The characteristics of bending stiffness are proved to be associated with the relaxation coefficients.     

Fluid-solid coupling mathematical model of contaminant transport in unsaturated zone and its asymptotical solution

IntroductionThetransportofcontaminantsinunsaturatedzonehascausedmuchattention .Inearly1960s,contaminationproblemsofsoilandgroundwaterhadbeenstudiedathomeandabroad[1].Andinrecentyears ,thetransformationandtransportationofcontaminantshavebeendeeplystudiedinthefieldsofhydrogeology ,petroleumengineering ,environmentalengineeringandsoon[2 ,3].Somecontaminanttransportmodelshavebeenpresentedsofar.Forexample ,Paker[4 ]etal.presentedaconstitutivemodelgoverningparametersofwater,gasandcontaminantswhenth…     

砂井地基的一个简化计算模型

基于三维有限元方法,提出了一个预测和评价砂井地基的简化计算模型。该计算模型采用块体单元模拟砂井周围的土体,用砂井单元模拟砂井的竖向排水和水平排水过程,并且推导了反映土体单元和砂井单元之间排水过程的连续性方程。克服了以往有限元法计算砂井地基时,需要将砂井和周围土体作均质化等价的缺点,并可用弹塑性模型反映砂井周围土体的非线性变形和强度特性。计算了单个砂井地基固结排水过程。通过和理论解的比较表明,用本文简化计算模型得到的结果和理论解比较接近。同时,还计算了日本某高速公路路基用砂井 堆载预压法处理的过程,通过分析表明,该简化模型能反映砂井地基的固结排水过程,可以应用于实际工程。     

Mathematical analysis of SOFC based on co-ionic conducting electrolyte

In co-ionic conducting solid oxide fuel cell (SOFC), both oxygen ion (O2) and proton (H+) can transport through the electrolyte, generating steam in both the an-ode and cathode. Thus the mass transport phenomenon in the electrodes is quite different from that in conventional SOFC with oxygen ion conducting electrolyte (O-SOFC) or with proton conducting electrolyte (H-SOFC). The generation of steam in both electrodes also affects the concentration over-potential loss and further the SOFC performance. However, no detailed modeling study on SOFCs with co-ionic electrolyte has been reported yet. In this paper, a new mathematical model for SOFC based on co-ionic electrolyte was developed to predict its actual performance considering three major kinds of overpotentials. Ohm’s law and the Butler-Volmer formula were used to model the ion conduction and electrochemical reactions, respectively. The dusty gas model (DGM) was employed to simulate the mass transport processes in the porous electrodes. Parametric simulations were performed to investigate the effects of proton transfer number (tH) and current density (jtotal) on the cell performance. It is interesting to find that the co-ionic conducting SOFC could perform better than O-SOFC and H-SOFC by choosing an appropriate proton transfer number. In addition, the co-ionic SOFC shows smaller difference between the anode and cathode concentration overpotentials than O-SOFC and H-SOFC at certain t H values. The results could help material selection for enhancing SOFC performance.     

Test analysis of detection of damage to a complicated spatial model structure

A two-stage damage detection approach is proposed and experimentally demonstrated on a complicated spatial model structure with a limited number of measurements. In the experiment,five known damage patterns,including 3 brace damage cases and 2 joint damage cases,were simulated by removing braces and weakening beam-column connections in the structure. The limited acceleration response data generated by hammer impact were used for system identification,and modal parameters were extracted by using the eigensystem realization algorithm. In the first stage,the possible damaged locations are determined by using the damage index and the characteristics of the analytical model itself,and the extent of damage for those substructures identified at stage I is estimated in the second stage by using a second-order eigen-sensitivity approximation method. The main contribution of this paper is to test the two-stage method by using the real dynamic data of a complicated spatial model structure with limited sensors. The analysis results indicate that the two-stage approach is ableto detect the location of both damage cases,only the severity of brace damage cases can be assessed,and the reasonable analytical model is critical for successful damage detection.     

A new three-dimensional Hoek-Brown strength criterion

The Hoek-Brown(HB) strength criterion has been widely applied to the estimation of strength of intact rock and rock mass,while evolving ever since.However,negligence of the effect of the intermediate principal stress still remains in the criterion’s latest version.At the same time,several three-dimensional(3D) HB strength,which can takes into account the influence of the intermediate principal stress,have already been proposed,among which the 3D HB criterion proposed by Zhang and Zhu seems to be the most reasonable one.However,the Zhang 3D HB criterion may have problems with some stress path close to triaxial extension state because of the non-convexity characteristic of its failure surface.In this paper,a new 3D HB strength criterion is presented based on a generalized form of the HB criterion,which also considers the effect of the intermediate principal stress and inherits all the merits of the original version of the HB criterion.In addition,this new criterion can remedy to some extent the shortcomings observed in the Zhang 3D HB criterion.Polyaxial tests for five different rocks from published literatures are used for evaluating this new criterion and comparing it with the Zhang 3D HB criterion.The results show that this new criterion may over-predict or underpredict the polyaxial strength of rocks but the errors are relatively small,and similar results are also found for the Zhang 3D HB criterion,which one is better depends on the type of the rock under estimation.     

Precracking and interfacial delamination in a bi-material structure: Static and dynamic loadings

The behavior of a precracked bi-material structure interface under given static and dynamic axial loading is an interest object in the present paper.Firstly,it is shown that the shear-lag model is a proper tool to analyze a delamination process in a precracked bi-material structure undergoing static loading.Secondly,the"shear-lag model"is applied to the structure under dynamic loading.To solve the problem for an interface delamination of the structure and to determine the debond length along the interface,our own 2D boundary element method(BEM)code is proposed in the case of static loading,and the shear-lag model together with the Laplace transforms and half-analytical calculations are used in the case of dynamic loading.The interface layer is assumed as a very thin plate compared with the other two.The parametric(geometric and elastic)analysis of the debond length and interface shear stress is done. The results from the 2D BEM code proved the validity of analytical solutions to the shear-lag model.In the dynamic case,the influence of loading characteristics,i.e.,frequencies and amplitude fluctuations on the shear stress and the value of debond length for an interval of time,is discussed. The analysis of the obtained results is illustrated by an example of the modern ceramic-metal composite,namely cermet, and depicted in figures.     

Effect of induced magnetic field on natural convection in vertical concentric annuli

In the present paper,we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a radial magnetic field.The induced magnetic field produced by the motion of an electrically conducting fluid is taken into account.The transport equations concerned with the considered model are first recast in the non-dimensional form and then unified analytical solutions for the velocity,induced magnetic field and temperature field are obtained for the cases of isothermal and constant heat flux on the inner cylinder of concentric annuli.The effects of the various physical parameters appearing into the model are demonstrated through graphs and tables.It is found that the magnitude of maximum value of the fluid velocity as well as induced magnetic field is greater in the case of isothermal condition compared with the constant heat flux case when the gap between the cylinders is less or equal to 1.70 times the radius of inner cylinder,while reverse trend occurs when the gap between the cylinders is greater than 1.71 times the radius of inner cylinder.These fields are almost the same when the gap between the cylinders is equal to 1.71 times the radius of inner cylinder for both the cases.It is also found that as the Hartmann number increases,there is a flattening tendency for both the velocity and the induced magnetic field.The influence of the induced magnetic field is to increase the velocity profiles.     

Study of modeling unsteady blade row interaction in a transonic compressor stage part 1: code development and deterministic correlation analysis

The average-passage equation system (APES) provides a rigorous mathematical framework for accounting for the unsteady blade row interaction through multistage compressors in steady state environment by introducing deterministic correlations (DC) that need to be modeled to close the equation system.The primary purpose of this study is to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES.In Part 1 of this two-part paper,firstly a 3D viscous unsteady and time-averaging flow CFD solver is developed to investigate the APES technique.Then steady and unsteady simulations are conducted in a transonic compressor stage.The results from both simulations are compared to highlight the significance of the unsteady interactions.Furthermore,the distribution characteristics of DC are studied and the DC at the rotor/stator interface are compared with their spatial correlations (SC).Lastly,steady and time-averaging (employing APES with DC) simulations for the downstream stator alone are conducted employing DC derived from the unsteady results.The results from steady and time-averaging simulations are compared with the time-averaged unsteady results.The comparisons demonstrate that the simulation employing APES with DC can reproduce the time-averaged field and the 3D viscous time-averaging flow solver is validated.     

送风方式对飞机座舱内污染物传播影响研究

采用数值模拟方法研究了波音737-200座舱模型内的气流场以及污染物传播过程,并通过实验数据加以验证;分析了天花板加侧壁送风(混合送风)、侧壁送风以及天花板送风三种送风方式下座舱内的速度场、涡量场、污染物浓度场和空气龄,并且解释了舱内流场结构对污染物传播过程的影响。研究结果表明:不同送风方式下飞机座舱内污染物的传播过程差异明显,这是由流场结构特征的差异造成的,特别是在小尺度范围内,涡结构十分复杂,严重影响污染物的传播规律;在聚集过程中,污染物更容易在漩涡范围内聚集,而变形主导的气流运动会阻碍污染物向更大范围传播;在排除过程中,天花板送风形式下污染物的排除效率最快,混合送风次之,侧壁送风最慢。这对于防控新冠肺炎是有参考价值的。     

Numerical modeling of liquid-waste infiltration from storage facilities into surrounding groundwater and surface-water bodies

This study focuses on the infiltration of saturated brine from liquid-waste storage facilities into the surrounding groundwater and surface-water bodies. The storage facilities are situated at the Verkhnekamsk Potassium and Magnesium Salt Deposit (Perm krai, Russian Federation); they store highly mineralized brine of potassium, sodium, and magnesium chlorides. An analytical solution of a one-dimensional equation of contaminant transport by a homogeneous steady-state groundwater flow is used to estimate the time it takes the contaminant to travel from the storage facilities to the nearest surface water body, as well as to evaluate the formation time of a stationary concentration profile, with contaminant adsorption in the porous matrix either neglected or taken into account. The contaminant concentration at the point of brine entry into the surface water body is calculated. The ANSYS Fluent software package is used for direct 3D simulation of brine infiltration into the surrounding medium. The simulation results revealed different stages of contaminant propagation in the porous medium. The contaminant was found to spread over a wide area with an almost uniform high brine concentration close to the saturation value. The contaminant reaches the nearest riverbed approximately 20 days after the start of infiltration. The estimates of the time required for the contaminant front to reach the surface water body obtained by three-dimensional simulation agree with the analytical estimates derived from a one-dimensional model. The proposed system of physical models adequately describes the hydrodynamic processes accompanying the operation of large storage facilities and can be used to predict contaminant-front propagation in the groundwater near storage facilities.     

Unsteady aerodynamics modeling for flight dynamics application

In view of engineering application, it is practicable to decompose the aerodynamics into three components: the static aerodynamics, the aerodynamic increment due to steady rotations, and the aerodynamic increment due to unsteady separated and vortical flow. The first and the second components can be presented in conventional forms while the third is described using a one-order differential equation and a radial-basis-function (RBF) network. For an aircraft configuration, the mathematical models of 6component aerodynamic coefficients are set up from the wind tunnel test data of pitch, yaw, roll, and coupled yawroll large-amplitude oscillations. The flight dynamics of an aircraft is studied by the bifurcation analysis technique in the case of quasi-steady aerodynamics and unsteady aerodynamics, respectively. The results show that: (1) unsteady aerodynamics has no effect upon the existence of trim points, but affects their stability; (2) unsteady aerodynamics has great effects upon the existence, stability, and amplitudes of periodic solutions; and (3) unsteady aerodynamics changes the stable regions of trim points obviously. Furthermore, the dynamic responses of the aircraft to elevator deflections are inspected It is shown that the unsteady aerodynamics is beneficial to dynamic stability for the present aircraft. Finally, the effects of unsteady aerodynamics on the post-stall maneuverability are analyzed by numerical simulation.     

Comparison of Kinetic and Hybrid-Equilibrium Models Simulating Colloid-Facilitated Contaminant Transport in Porous Media

The presence of colloidal particles in groundwater can enhance contaminant transport by reducing retardation effects and carrying them to distances further than predicted by a conventional advective/dispersive equation with normal retardation values. When colloids exist in porous media and affect contaminant migration, the system can best be simulated as a three-phase medium. Mechanisms of mass transfer from one phase to another by colloids and contaminants can be kinetic or equilibrium-based, depending on the sorption–desorption reaction rate between the aqueous and solid phases. When the rate of sorption between the water phase and the solid phase(s) is not much greater than the rate of change in contaminant concentration in the water phase, kinetic sorption models may better describe the phenomenon. In some cases of modeling one or more mass transfer processes, a useful simplification may be to introduce the local equilibrium assumption. In this study, the local equilibrium assumption for sorption processes on colloidal surfaces (hybrid equilibrium model) was compared with kinetic-based models. Sensitivity analyses were conducted to deduce the effect of major parameters on contaminant transport. The results obtained from the hybrid equilibrium model in predicting the transport of colloid-facilitated groundwater contaminant are very similar to those of the kinetic model, when the point of interest is not at contaminant and colloid source vicinities and the time of interest is sufficiently long for imposed sources.     

Topology optimization of 3D structures with design-dependent loads

Topology optimization of continuum structures with design-dependent loads has long been a challenge. In this paper, the topology optimization of 3D structures subjected to design-dependent loads is investigated. A boundary search scheme is proposed for 3D problems, by means of which the load surface can be identified effectively and efficiently, and the difficulties arising in other approaches can be overcome. The load surfaces are made up of the boundaries of finite elements and the loads can be directly applied to corresponding element nodes, which leads to great convenience in the application of this method. Finally, the effectiveness and efficiency of the proposed method is validated by several numerical examples.     

Numerically gas radiation heat transfer modeling in chemically nonequilibrium reactive flow

A numerical method for calculation of strong radiation for 2D reactive air is developed. Governing equations are taken to be 2D, compressible Reynolds-average Navier–Stokes and species transport equations. Also, radiation heat flux is evaluated using a model of discrete ordinate method. A multiband model is used to construct absorption coefficients. Tangent slab approximation is assumed to determine the characteristic parameters needed in the Discrete Ordinates Method.