A two-dimensional two-phase mass transport model for direct methanol fuel cells adopting a modified agglomerate approach

A two-dimensional two-phase mass transport model for liquid-feed direct methanol fuel cells (DMFCs) is presented in this paper. The fluid flow and mass transport across the membrane electrode assembly (MEA) is formulated based on the classical multiphase flow theory in the porous media. The modeling of mass transport in the catalyst layers (CLs) and membrane is given more attentions. The effect of the two-dimensional migration of protons in the electrolyte phase on the liquid flow behavior is considered. Water and methanol crossovers through the membrane are implicitly calculated in the governing equations of momentum and methanol concentration. A modified agglomerate model is developed to characterize the microstructure of the CLs. A self-written computer code is used to solve the inherently coupled differential governing equations. Then this model is applied to investigate the mechanisms of species transport and the distributions of the species concentrations, overpotential and the electrochemical reaction rates in CLs. The effects of radius and overlapping angle of agglomerates on cell performance are also explored in this work.     

汽轮发电机组轴系弯扭耦合振动的数学模型

根据汽轮发电机组轴系各轴段所处位置不同，将轴系分为3类微元轴段，在分析微元轴段力和力矩基础上，分别推导了各类轴段的弯扭耦合振动偏微分方程组。该方程组是基于分布质量模型的耦合振动数学模型，它能综合考虑机组诸多因素，比较接近实际地研究机组动力特性。该方程组是高度非线性的，轴系质量偏心是弯扭耦合的一个前提。利用本文给出的方程组，可以进行弯扭耦合振动的固有频率、振型及瞬态响应计算。     

3d-Transient modeling of heat and mass transfer during heat treatment of wood

In the current work, three-dimensional Navier-Stokes equations along with the energy and concentration equations for the fluid coupled with the energy and mass conservation equations for the solid (wood) are solved to study the transient heat and mass transfer during high thermal treatment of wood. The model for wood is based on Luikov's approach and solves a set of coupled heat and mass transfer equations. The model equations are solved numerically by the commercial package FEMLAB for the temperature and moisture content histories under different treatment conditions. The simulation of the proposed conjugate problem allows the assessment of the effect of the heat and mass transfer within wood on the transfer in the adjacent gas, providing good insight on the complexity of the transfer mechanisms.     

太阳能吸附式制冷吸附床的热力计算方法

建立了吸附式太阳能制冷装置的吸附床热力计算模型。这一模型综合考虑了吸附床内温度、压力及脱附量等因素的相互影响，更全面地反映了吸附床内的传热、传质情况。依据初始条件、边界条件及热力计算模型，给出了数值计算的内点、边界点差分方程，构造了求解方程组。根据太阳辐射强度情况，进行了数值计算，计算结果与实际相吻合。这为进一步分析吸附床内的动态特性，优化系统设计提供了依据。     

On-board hydrogen storage in an adsorbent bed: Development of a multi-scale dynamic “1D-plus-1D” model

Reliable design, analysis and optimization of on-board adsorptive hydrogen storage systems require mathematical models that capture the key physics across multiple scales. Pellets of adsorbent may sometimes be preferred for adsorptive storage in fixed beds, compared to powders. Heat and mass transfer within individual pellets play a significant role in the overall dynamics of a fixed bed filled with adsorbent pellets. However, multiscale dynamical model that captures the effect of pellet behavior on the overall dynamics of adsorbent bed is so far missing. In this study, a combined bed–and–pellet “1D-plus-1D” model is developed and analyzed for hydrogen adsorption in a fixed bed of MOF-5 pellets at cryogenic temperatures. Specifically, a 1D axial bed model with mass, momentum and energy balance equations is coupled with a 1D radial pellet model comprising of mass and heat transfer with adsorption within the pellets present at different locations in the bed. The 1D bed and 1D pellet model equations are coupled through surface fluxes on the pellet. We show that internal diffusional resistances within pellets must be considered for pellets greater than 2 mm diameter, for parameters relevant to MOF-5 pellets. The role of various physical parameters of pellets is analyzed.     

涡流室式LPG柴油双燃料发动机燃烧模型

根据涡流室、主燃室中气体流动过程的质量和能量的交换关系 ,建立了涡流室式 LPG ( liquefiedpetrdeum gas) /柴油双燃料发动机准维燃烧模型的方程 ,提出了如何使两种不同性质燃料的燃烧在同一个燃烧过程中相互联系、相互作用的燃烧模型。根据模型提供的方程 ,对缸内燃烧过程和 NOx 的生成进行了模拟仿真 ,将其同发动机台架试验的结果进行了验证、分析和讨论。     

Zonal thermal model of the ventilation of underground transformer substations: Development and parametric study

An algebraic thermal zonal model of the ventilation of underground transformer substations during a standardised temperature rise test is presented in this paper. The development and adjustment of the proposed model rely on the analysis of the air flow pattern and temperature distributions obtained by a more complex model numerically solved by means of CFD techniques. The flow domain of the model represents a section of the substations divided into several interrelated zones where the mass and the energy conservation equations are formulated and the generated system of nonlinear algebraic equations is solved. The model is validated by comparing its results with the ones obtained by the CFD model and with the experimental results of eight temperature rise tests under different conditions. A parametric analysis was carried out on the model to prove its utility as an efficient tool to improve and optimise the thermal performance of transformer substations during the design process. From the parametric study it has been inferred that the main parameters affecting the ventilation of the substations are the pass area between the LV–MV zone and the transformer zone, the surface area of the ventilation grilles in the substation with horizontal ventilation, and the perimeter of the protruding ventilation vents in the substation with vertical ventilation.     

Modeling and simulation of a proton exchange membrane fuel cell using computational fluid dynamics

An isothermal, three dimensional, single phase model was presented to evaluate a proton exchange membrane fuel cell (PEMFC) with serpentine flow. The mass, momentum and electrochemical equations were solved simultaneously for the steady state condition using computational fluid dynamics (CFD) software based on the finite element method. The model considered reactions as mass source/sink terms, and electron transport in the catalyst layers and GDLs. To validate the model, the numerical results were compared to the experimental data collected from the fabricated membrane electrode assemblies. The exchange current density parameter of the catalysts was fitted by the model to calibrate the results. The model showed good agreement with experimental data and predicted a higher current density for the catalyst with a higher surface area and Pt content. The oxygen, hydrogen and water mass fraction distribution, velocity magnitude and pressure distribution were estimated by the model. Moreover, the effect of pressure and temperature, as two important operating conditions, on the current density was predicted by the validated model.     

火花点火发动机准维湍流卷吸燃烧模型的适用性研究（1）

本文在分析火花点火发动机湍流涡结构及缸内湍流特性参数的基础上，提出了适用于火花点火发动机燃烧计算的准维湍流卷吸模型，通过建立相应的子模型及求解方程，实现了燃烧过程的计算；对压缩比为１０的紧凑型燃烧室，在改变发动机转速、负荷、空燃比以及点火正时的情况下，计算得到的压力示功图、质量燃烧率等与实测值一致，从而证实了该模型的合理性。     

Numerical Simulation of Air-cooling Tower

A mathematic model for packed air-cooling tower thermodynamic calculation is set up in this paper on the basis of fundamental heat and mass transfer equations. Based on the Double Film theory, direct equation-solving method is used to simulate air-cooling tower, and variation of parameters is taken to analyze the data and results of the program.     

Non-Fourier effect in the presence of coupled heat and moisture transfer

The objective of this paper is to study heat and mass transfer coupling under non-Fourier effect. The non-Fourier model is applied on Luikov’s equations. The governed equation is called Luikov’s Corrected (LC) equations and is solved by hybrid analytical–numerical method. Heat and mass propagation in LC field is shown to be wavelike; so, wavefront speed is obtained. Applying non-Fourier model instead of Fourier’s law sensitizes Luikov’s equations to respond in fast transient process. Further, the effect of heat and mass transfer coupling on interpreting non-Fourier affects is investigated. It is seen that the presence of heat and mass transfer coupling reduces wavefront speed with respect to uncoupled non-Fourier heat transfer.     

A numerical model for segmented flow in a microreactor

A numerical model for segmented flow in a microreactor has been developed. The model is based on computational fluid dynamics (CFD) which means that the flow field and mass transfer are described by a set of partial differential equations. A general purpose CFD code was extended in order to predict the internal flow patterns of fluid segments and the transfer of dissolved chemical species within segments and across fluid segment interfaces. The model has been validated by comparing predicted data with experimental microreactor titrations.     

Parametric and transient analysis of non-isothermal, planar solid oxide fuel cells

A multidimensional, model of non-isothermal planar solid oxide fuel cells (SOFCs) including detailed coupled mass and charge transport phenomena, has been developed. The dusty-gas model has been used, in this a comprehensive SOFC model, and has been explicitly written/constructed, for the first time in the COMSOL multiphysics modelling framework to describe mass transport in the porous electrode and detailed charge conservation equations have been taken into account. As we have shown in a recent publication [9] the incorporation of the dusty-gas model results in more accurate predictions of the SOFC behaviour compared to mass transport models based on Fick’s law or Stefan-Maxwell multi-component diffusion. Our model allows prediction of the species composition profiles, temperature profiles, electronic and ionic voltage and current density distributions, and polarisation curves in a single cell. SOFC dynamics have also been considered including responses to step changes in the operating conditions. The model is implemented in two-spatial dimensions, however, the underlying theory is independent of the geometry used. Extensive parametric analysis has been performed and the corresponding SOFC behaviour has been analysed through the resulting polarisation curves. It is shown that SOFCs exhibit higher power outputs at increased operating temperatures and pressures. It was also found that the electrodes’ porosity and tortuosity have a smaller effect on power output. Furthermore, step changes in the inlet temperatures were found to induce slower dynamic behaviours than step changes in the operating voltage.     

A three-fluid model of two-phase dispersed-annular flow

A three-fluid model of the dispersed-annular regime of two-phase flow is suggested. The model is based on the conservation equations of mass, momentum, and energy for the gas phase, the dispersed phase (droplets), and the film. Additionally, this model includes the equation for the number density of particles of the dispersed phase, which is used to determine the mean particle size. Calculations are compared with experimental data on the entrainment coefficient, film and droplet flow rates, film thickness, pressure drop, and droplet size.     

Modelling of heat and mass transfer in a tunnel dryer

This work presents a numerical model for heat and mass transfer of granular products in a fixed-bed tunnel dryer. The drying process is simulated under real operating conditions based on a thin layer model and experimental drying kinetics. A simplified heat and mass transfer numerical model is developed based on the governing equations and the drying rate of a thin layer bed of granular products.The obtained system of non-linear partial differential equations is numerically solved by a finite volume method. The turbulent airflow and granular bed convection coefficient as well as the effective conductivity are estimated using the turbulent airflow over flat-plate correlations. Simulations are compared with experimental data from drying of grapes in a thin layer model.In order to study the effects of the air inlet conditions on the relative moisture content and the drying time and therefore to optimise the tunnel dryer operation, the influences of different parameters essentially the air flow characteristics and the fixed-bed dryer length are examined. The numerical code allows establishing the drying front propagation for several operating conditions.     

预测单个火灾房间内温度场分布的多层区域模型

建立了一种预测单个室内火灾发展的多层区域模型(multi-layer zone model)．整个火灾房间被划分成任意多个水平分布的区域，假设每一层内的物理化学参数分布均匀，通过质量守恒、能量守恒等建立每一层的控制方程．介绍了模型中应用的火灾模型，包括燃烧、流动和传热模型．利用Runge-Kutta积分方法得到每一层内气体温度随火灾发展过程的变化．模型预测结果和Steckler实验对比表明模型具有较好的准确性．     

Comparison of the multicomponent mass transfer models for the prediction of the concentration overpotential for solid oxide fuel cell anodes

In this study, multicomponent mass diffusion models, namely the Stefan-Maxwell model (SMM), the Dusty Gas model (DGM) and the Binary Friction model (BFM) have been compared in terms of their predictive capabilities of the concentration polarization of an anode supported solid oxide fuel cell (SOFC) anode. The results show that other than the pore diameter, current density and concentration of reactants, which have a high importance in concentration polarization predictions, the tortuosity (or porosity/tortuosity) term, has a substantial effect on the model predictions. Contrary to the previous discussions in the literature, for the fitted value of tortuosities, SMM and DGM predictions are similar, even for an average pore radius as small as 2.6e−07 and current density as high as 1.5 A cm⁻². Also it is shown that the BFM predictions are similar to DGM for the case investigated in this study. Moreover, in this study, the effect of the pressure gradient term in the DGM and the BFM has been investigated by including and excluding this term from the model equations. It is shown that for the case investigated and model assumptions used in this study, the terms including the pressure coefficient have an insignificant effect on the predictions of both DGM and BFM and therefore they can be neglected.     

Numerical simulation and experimental validation of Ti0.95Zr0.05Mn0.9Cr0.9V0.2 alloy in a metal hydride tank for high-density hydrogen storage

In order to achieve rapid hydrogen charging and discharging of high-density hydrogen storage alloys in metal hydride (MH) tank, it is key to optimize the design of MH tank by simulation based on a credible numerical model. Herein, a multi-physical field mathematical model coupled with kinetic equations and heat & mass transfer equations for the de-/hydrogenation of Ti_0.95Zr_0.05Mn_0.9Cr_0.9V_0.2 alloy in MH tank is proposed. According to experimental kinetic curves, appropriate kinetic equations dominated by different rate control steps are chosen for simulating gas-solid reactions. With excellent match between experimental and simulated kinetic results under different pressure and temperature operating conditions, a novel numerical model is established to predict the local temperature variation during the de-/hydrogenation of Ti_0.95Zr_0.05Mn_0.9Cr_0.9V_0.2 alloy in a self-designed hydrogen storage tank with high-density hydrogen storage of 55.1 g H₂/L. Interestingly, further calculated results reveal that the temperature evolution can be accurately matched, which proves the reliability of the designed numerical model and favors to predict the de-/hydriding behaviors. This investigation provides an effective means for subsequent structure optimization and energy & mass transfer performance optimization of high-density hydrogen storage devices, and sheds light on the numerical simulation of heat & mass transfer for advanced energy storage applications.     

Effects of Cattaneo–Christov heat flux analysis on heat and mass transport of Casson nanoliquid past an accelerating penetrable plate with thermal radiation and Soret–Dufour mechanism

In this analysis, the effect of Catteneo–Christov model on heat alongside mass transport magnetohydrodynamics of a Casson nanoliquid with thermal radiation and Soret–Dufour mechanism is considered. The fluid flow is considered through porous media as the thermophysical attributes such as viscosity along with thermal conductivity are considered to be constant. Suitable similarity transformations were employed on the governing coupled flow equation to yield total differential equations (ODE). An accurate and newly developed spectral method called spectral homotopy analysis method (SHAM) was employed to provide solution to the simplified equations. The numerical method of homotopy analysis method (HAM) is SHAM. SHAM portrays the division of nonlinear equations into linear as well as nonlinear parts. The findings in this study show that an increment in the Casson parameter is seen to elevate the velocity plot at the wall and lessen the velocity far away from the plate. An increase in the Brownian motion and thermophoresis term is observed to speed up the local skin friction coefficient.     

A mathematical model of variable displacement wobble plate compressor for automotive air conditioning system

Based on the force balance equations, mass and energy conservation equations, a mathematical model of control valve used in the variable displacement wobble plate compressor (VDC) is developed firstly. The dynamic model of the moving components is developed then by analyzing the forces and force moments acting on the piston, piston rod, wobble plate, rotating journal and shaft sleeve. The compression process model is obtained by fitting the data from our experiments. And finally the steady-state mathematical model of VDC is developed by combining the three models above. In order to verify the mathematical model of compressor, a test bench for the control valve and the test system for the VDC have been established, and the simulated results agree well with the experimental data. The simulation results show that there are four operation modes for the VDC, i.e. constant rotary speed and constant piston stroke length (PSL), variable rotary speed and constant PSL, constant rotary speed and variable PSL, variable rotary speed and variable PSL, which have included almost all operation modes of the refrigeration compressor in common use.