Dynamic modeling of drainage through three-dimensional porous materials

The interplay of viscous, gravity and capillary forces determines the flow behavior of two or more phases through porous materials. In this study, a rule-based dynamic network model is developed to simulate two-phase flow in three-dimensional porous media. A cubic network analog of porous medium is used with cubic bodies and square cross-section throats. The rules for phase movement and redistribution are devised to honor the imbibition and drainage physics at pore scale. These rules are based on the pressure field within the porous medium that is solved for by applying mass conservation at each node. The pressure field governs the movement and flow rates of the fluids within the porous medium. Film flow has been incorporated in a novel way. A pseudo-percolation model is proposed for low but non-zero capillary number (ratio of viscous to capillary forces). The model is used to study primary drainage with constant inlet flow rate and constant inlet pressure boundary conditions. Non-wetting phase front dynamics, apparent wetting residuals (S_wr), and relative permeability are computed as a function of capillary number (N_ca), viscosity ratio (M), and pore-throat size distribution. The simulation results are compared with experimental results from the literature. Depending upon the flow rate and viscosity ratio, the displacement front shows three distinct flow patterns—stable, viscous fingering and capillary fingering. Capillary desaturation curves (S_wr vs. N_ca) depend on the viscosity ratio. It is shown that at high flow rates (or high N_ca), relative permeability assumes a linear dependence upon saturation. Pseudo-static capillary pressure curve is also estimated (by using an invasion percolation model) and is compared with the dynamic capillary pressure obtained from the model.     

Mathematical Modeling and Simulation of Ozonation Processes in a Downstream Static Mixer with Sieve Plates

New standards for drinking water disinfection require better optimization of the ozonation stage on the basis of the concentration×contact time (CT) concept, and production of ozone from pure oxygen at higher concentrations presumes application of the new type of contactors operating efficiently at lower gas/liquid volumetric ratios. One possible construction to meet these requirements is a downstream static mixer with sieve plates. At higher flow rates of liquid in this mixer, the interfacial area may reach 10,000m²/m³ at energy dissipation 1–5kW/m³. Due to the very intensive hydrodynamic regime the ozone utilization degree in the gas phase reaches 98–100% in natural lake water ozonation. Mathematical simulation of lake water ozonation in this mixer indicated that the process proceeds mostly in the diffusion or kinetic regime depending on the operating parameters. The dominating parameters besides the sieve geometry are the liquid flow rate in the holes of the sieves and the volumetric liquid/gas ratio.     

Analysis of Human Joint Forces in Standing Posture

Using the software Anybody Modeling System, a human static-standing musculoskel etal model based on inverse dynamics is presented, which are defined as segm ents, muscles and joints as elements. Simulation is based on data obtained from experiments using motion capture system VICON and force plate AMTI. In the model AnyBody Modeling System is introduced to help solve the redundancy problem and obtain results of muscle activities, muscle forces and joint forces. From the mo del, hip and knee joint forces cou...     

Modeling of time to corrosion-induced cover cracking in reinforced concrete structures

Service life of the concrete structures depends on the protective action provided by the cover concrete against the susceptibility of the reinforcement to the corrosive environment. Depending on the level of the oxidation of metallic iron, corrosion products may have much greater volume than the original iron that gets consumed by the process of corrosion. This volume expansion is mainly responsible for exerting the expansive radial pressure at the steel-concrete interface and development of hoop tensile stresses in the surrounding concrete resulting ultimately in the through cracking of the cover concrete. This cover cracking would indicate the loss of the service life for the corrosion-affected structures. In the present paper, an attempt has been made to develop analytical models for predicting the time to cover cracking by considering the residual strength of the cracked concrete and the stiffness provided by the combination of the reinforcement and expansive corrosion products. The problem is modeled as a boundary value problem wherein the governing equations are expressed in terms of the radial displacement and the analytical solutions are presented considering a simple 2-zone model for the cover concrete viz. cracked or uncracked. The analytical models are then evaluated through their ability to reproduce available experimental trends and subsequently a sensitivity analysis has also been carried out to show the influence of the various variable parameters of the proposed models with reference to the experimental trends.     

离散零空间算法在机织物仿真中的应用

针对机织物卡尔丹角多体模型维数较高,计算效率不理想的问题,提出采用离散零空间算法降低多体动力学方程维数,减少计算复杂度和约束违约所导致的数值漂移.首先结合离散零空间等效变换消去拉格朗日乘子项,然后进行结点参数化,实现两次系统降维,提高机织物仿真速度.通过KES剪切试验与仿真,验证了上述算法应用的可行性.通过仿真计算复杂度及效率特征指标对比,反映出优化方程的降维优势和计算高效,尤其适用于大型织物仿真.     

Investigation of mass transport in gas diffusion layer at the air cathode of a PEMFC

In a polymer electrolyte membrane fuel cell (PEMFC), slow diffusion in the gas diffusion electrode may induce oxygen depletion when using air at the cathode. This work focuses on the behavior of a single PEMFC built with a Nafion^® based MEA and an E-TEK gas diffusion layer and fed at the cathode with nitrogen containing 5, 10 and 20% of oxygen and working at different cell temperatures and relative humidities. The purpose is to apply the experimental impedance technique to cells wherein transport limitations at the cathode are significant. In parallel, a model is proposed to interpret the polarization curves and the impedance diagrams of a single PEMFC. The model accounts for mass transport through the gas diffusion electrode. It allows us to qualitatively analyze the experimental polarization curves and the corresponding impedance spectra and highlights the intra-electrode processes and the influence of the gas diffusion layer.     

关于数学建模教学及竞赛改革的思考

从笔者学校实际情况出发,阐述数学建模课程的特点,探讨数学建模教学及竞赛存在的问题,从开设《数学建模与实验》公共选修课、编写教材或讲义、教学方法改革、成立数学建模竞赛教学团队及考核形式多样化等五个方面提出数学建模课程改革的思路,并给出数学建模教学及竞赛改革的具体建议。     

Liquid flow and phase holdup—measurement and CFD modeling for two-and three-phase bubble columns

Bubble columns are an important class of contacting devices in chemical industry and biotechnology. Their simple setup makes them ideal reactors for two- and three-phase operations such as fermentations or heterogeneous catalysis. Still, design and operation of these reactors is subject to widely empirical scale-up strategies. With recent advances in the development of measurement techniques, a more detailed approach to the development of optimized reactors for specific operations should become possible. This report is based on detailed measurements of local dispersed phase holdups in a pilot plant-sized bubble column operated at high superficial gas velocities and solid holdups. It deals with the influence of superficial gas velocity, solid loading and sparger geometry on measured and computed liquid flow velocities and holdup distributions. Liquid velocity measurements have been performed using the electrodiffusion method, modeling calculations have been carried out using the computational fluid dynamics (CFD) code CFX-4.3. Measurement results presented here give an insight into the development of liquid circulation and fluctuating velocity distribution depending on superficial gas velocity, solid loading and sparger geometry. CFD results implementing a multi-fluid model with k-ε turbulence and special momentum exchange terms for direct gas-solid interactions show that, even on standard PC workstations, this kind of computations can deliver qualitatively reasonable agreement with measurements.     

Experimental study and numerical simulation on the formation of microstructure in cementitious materials at early age

The formation of microstructure in early age cement paste and concrete was examined with an ultrasonic experimental set-up. Research parameters included the influence of curing temperature (isothermal curing at 20, 30 and 40 °C), water/cement ratio (0.40, 0.45 and 0.55) and amount of aggregate. In parallel with the experiments, the cement hydration model HYMOSTRUC was utilized to simulate the formation of the microstructure. In this study, the cement paste was considered as a four-phase system consisting of water, unhydrated cement, hydration products and that part of the hydration product that causes the contact between the hydrating cement grains (so called “bridge volume”). A correlation has been found between the growth of bridge volume calculated with the model and the changes in the pulse velocity. It is believed that ultrasonic pulse velocity (UPV) measurements can represent a valuable tool to investigate the development of the microstructure at early age.     

Characterization and modeling of diffusion process for mass transport through the Tournemire argillites (Aveyron, France)

Argillites are one of the geological formations studied by IRSN for their confining properties for isolation of radioactive wastes. One of the main objectives is the study of water transport through rocks with very low water content and very low hydraulic conductivity by modeling of natural tracer profiles. This paper presents the protocol developed for and applied to the acquisition of data for chloride content in interstitial water of the Toarcian argillites at the Tournemire site (Southern France). This protocol is based on laboratory diffusion experiments and on modeling. Experimental data obtained during the transient and steady-state parts of diffusion experiments enable, respectively, the assessment of the diffusion coefficient and the determination of Cl concentration in pore water. Using this protocol, profiles with depth for both of these data sets have been acquired along the geological sequence. Taking into account the present knowledge of the geological and hydrogeological history of the Tournemire massif, a conceptual model granting the main role for mass transport to diffusion has been proposed. According to this conceptual model, a one-dimensional numerical model was built for simulating the mass transport of chloride through the sedimentary column, over 53 Ma. The good agreement between experimental data and calculated values for both diffusion coefficients and concentrations of chloride confirms that diffusion is likely the main process for mass transport in the massif. This model was also tested with the deuterium content of interstitial water, applying variable concentrations at the aquifer system boundaries for reflecting the thermal dependency of isotopic composition in precipitation. These simulations also reveal the likely important role of heterogeneities, such as fractures, in the variability of tracer concentrations with regards to a simple diffusion profile.