Modeling two-phase flow in PEM fuel cell channels

This paper is concerned with the simultaneous flow of liquid water and gaseous reactants in mini-channels of a proton exchange membrane (PEM) fuel cell. Envisaging the mini-channels as structured and ordered porous media, we develop a continuum model of two-phase channel flow based on two-phase Darcy's law and the M² formalism, which allow estimate of the parameters key to fuel cell operation such as overall pressure drop and liquid saturation profiles along the axial flow direction. Analytical solutions of liquid water saturation and species concentrations along the channel are derived to explore the dependences of these physical variables vital to cell performance on operating parameters such as flow stoichiometric ratio and relative humility. The two-phase channel model is further implemented for three-dimensional numerical simulations of two-phase, multi-component transport in a single fuel-cell channel. Three issues critical to optimizing channel design and mitigating channel flooding in PEM fuel cells are fully discussed: liquid water buildup towards the fuel cell outlet, saturation spike in the vicinity of flow cross-sectional heterogeneity, and two-phase pressure drop. Both the two-phase model and analytical solutions presented in this paper may be applicable to more general two-phase flow phenomena through mini- and micro-channels.     

Liquid-solid separation phenomena of two-phase turbulent flow in curved pipes

The present study is to contribute some knowledge of phase separation phenomena of liquid-solid two-phase turbulent flow in curved pipes and provide a basis for the invention and development of a new type of curved pipe separator. Firstly, the solid-liquid two-phase flows in two-dimensional (2D) curved channels were numerically simulated using a two-way coupling Euler-Lagrangian scheme. Phase distribution characteristics of 2D curved channel two-phase flow were examined under conditions of different particle size, liquid flowrate and coil curvature. Based on the numerical results, the dynamic effects and contributions to phase separation of particle-subjected forces, including centrifugal force, drag force, pressure gradient force, gravity force, buoyancy force, virtual mass force and lift force, were exposed by kinematic and dynamic analysis along particle trajectories. Secondly, measurement of particle size and concentration profiles in helically coiled tube two-phase flow was conducted using a nonintrusive Malvern 2600 particle sizer based on laser diffraction. Particle size and concentration distribution characteristics of helically coiled tube two-phase flow and the effect of secondary flow on phase separation were analyzed based on experimental data.     

An improved model for two-phase hydrogen flow dynamics

Two-phase boiling hydrogen pressure drop is studied in the context of high velocity upflow in a constant, high heat flux, steady state, internal pipe flow environment. The approach of this analysis is to reverse-engineer the best available data to determine mass quality, void fraction, and velocity slip. This is accomplished by applying a one-dimensional, five-equation model, with pressure gradient being the one combined equation. The resulting velocity slips are correlated for high and low pressure conditions. Good agreement is achieved between the pressures predicted using the slip correlations and the measured pressures. Results are in general significantly better than those from the homogeneous equilibrium model.     

Interface resolving two-phase flow simulations in gas channels relevant for polymer electrolyte fuel cells using the volume of fluid approach

With the increased concern about energy security, air pollution and global warming, the possibility of using polymer electrolyte fuel cells (PEFCs) in future sustainable and renewable energy systems has achieved considerable momentum. A computational fluid dynamic model describing a straight channel, relevant for water removal inside a PEFC, is devised. A volume of fluid (VOF) approach is employed to investigate the interface resolved two-phase flow behavior inside the gas channel including the gas diffusion layer (GDL) surface. From this study, it is clear that the impact on the two-phase flow pattern for different hydrophobic/hydrophilic characteristics, i.e., contact angles, at the walls and at the GDL surface is significant, compared to a situation where the walls and the interface are neither hydrophobic nor hydrophilic (i.e., 90° contact angle at the walls and also at the GDL surface). A location of the GDL surface liquid inlet in the middle of the gas channel gives droplet formation, while a location at the side of the channel gives corner flow with a convex surface shape (having hydrophilic walls and a hydrophobic GDL interface). Droplet formation only observed when the GDL surface liquid inlet is located in the middle of the channel. The droplet detachment location (along the main flow direction) and the shape of the droplet until detachment are strongly dependent on the size of the liquid inlet at the GDL surface. A smaller liquid inlet at the GDL surface (keeping the mass flow rates constant) gives smaller droplets.     

Gas–liquid two-phase flow distributions in parallel channels for fuel cells

In the present study, gas–liquid two-phase flow in a parallel square minichannel system oriented horizontally and at an incline is studied under operating conditions relevant to fuel cell operations. Flow mal-distribution in parallel channels occurs at low gas and liquid flow rates. In general, high superficial gas velocities are required to ensure even flow distribution, and the minimum gas flow rates required to achieve even distribution depend on the liquid flow rates, channel orientation and experimental procedures. As the inclination angle is increased, a higher gas flow rate is required to ensure even gas–liquid flow distribution while flow channels inclined downward seems to help in improving the even flow distribution. The presence of flow hysteresis phenomena indicate that multiple flow distributions exist at the same given flow conditions when the gas flow rates are varied in ascending and descending manners. Flow mal-distribution and flow hysteresis are directly linked with flow stability. More specifically, the actual gas and liquid distribution in parallel channels is determined by the stability of mathematical solutions of mass and momentum balance equations and also the flow history. For the first time, the present work investigates flow distributions in fuel cell flow fields by accounting for two-phase flow conditions. In addition, a novel approach is introduced to ensure flow distributions and their stability through contour construction of isobars where unstable flow region can be identified, which can be used in the design of parallel channel flow fields, especially for fuel cells.     

Gas–liquid two-phase flow patterns in parallel channels for fuel cells

Two-phase flow in horizontal parallel channels has been experimentally investigated under fuel cell related operating conditions. Pronounced hysteresis is observed in the pressure drop versus flow characteristic curve when starting from either flooded or dry conditions. When gas is introduced into channels initially filled with water (flooded initial condition), both gas and liquid tend to flow predominantly in one channel at low gas or liquid flow velocities. As the gas flow velocity increases, even distribution of gas and liquid flow in both channels is observed, accompanied with a sudden decrease in the pressure drop. On the other hand, even gas and liquid flow distribution between both channels is found at comparatively lower gas flow velocities when starting with dry-gas flow conditions with liquid introduced into channels filled with gas (stratified flow regime). The flow regimes of this system are visualized in plots of the pressure drop against gas and liquid flow velocities. However, this phenomenon tends to vanish at high gas and liquid flow velocities, suggesting that high gas and liquid flow velocities are required to ensure even flow distribution in parallel channels. The hysteresis points appear at the same level of the pressure drop, reflecting intrinsic characteristics of the parallel channels used in this study. These results have important implications for PEM fuel cell operational strategies. In order to avoid reactant mal-distribution in parallel flow channels in the flow field in the two-phase flow regime, fuel cells should be operated at sufficiently high gas flow velocities.     

Experimental and theoretical analysis of annular two-phase flow regimen in direct steam generation for a low-power system

This study aims to quantify and to model the temperature profile around an absorber tube of a parabolic trough concentrator with low fluid flow. This study was specifically developed for the solar power plant of the Engineering Institute, National University of Mexico. This work presents experimental results under saturated conditions and low pressures (1.5–3 bar) using water as the thermal and working fluid for direct steam generation (DSG). The control variable was feed flow. Solar irradiance was used as the restriction variable because all experimental tests should be developed under very specific values of this variable (for example, I > 700 W/m²). The objective of this experiment was to study the thermal behavior of a temperature gradient around the absorber tube under steady-state conditions and with low flow. Additionally, a theoretical analysis was carried out by means of the homogeneous heat conduction equation in the cylindrical coordinate system using only two dimensions (r, ). The finite-difference numerical method was used with the purpose of proposing a solution and obtaining a temperature profile. The objective of this theoretical analysis was to complement the experimental tests carried out for direct steam generation (DSG) with annular two-phase flow patterns for low powers in parabolic trough concentrators with carbon steel receivers.     

Experimental investigation on PEM fuel cell using serpentine with tapered flow channels

The performance comparison of various flow fields for practical application can be better understood when loading the cell at a lower voltage region for an operational duration of more than an hour. In this paper, the performance of serpentine and serpentine with tapered channels are compared by loading the Polymer Electrolyte Membrane (PEM) fuel cell at a constant voltage of 0.5 V for an operational duration of 5 h. Purging with nitrogen at the inlets is done to recover the drop in current over the period of operation and flush out water. The presence of tapered flow fields in a serpentine flow channel shows an improvement of 15% in the current obtained due to better reactant gas transport in the gas diffusion layer. The performance of both flow fields were studied with polarization and power density curve obtained after 5 h of testing. Further, to confirm the performance improvement at lower voltage region, impedance study is done and obtained Nyquist plot confirms the better transport phenomenon of reactant gases to catalyst site and better removal of water in Gas Diffusion Layer (GDL).     

A two-phase flow model for hydrogen evolution in an electrochemical cell

Hydrogen evolution, flow field and current density distribution in an electrochemical cell are investigated with a two-phase flow model. The mathematical model involves solutions of transport equations for the variables of each phase with allowance for inter-phase transfer of mass and momentum. The buoyancy force generated due to density difference between two phases modifies flow profile and increases fluid velocity at the vicinity of the electrode. The current density decreases over the electrode mainly because of the decrease in effective conductivity of electrolyte. It is found that the hydrogen generation significantly increases at higher electrolyte flow by reducing the residence time of bubbles over the electrode. The predicted results satisfactorily agree with data available in the literature.     

A critical review of two-phase flow in gas flow channels of proton exchange membrane fuel cells

Water management in PEM fuel cells has received extensive attention due to its key role in fuel cell performance. The unavoidable water, from humidified gas streams and electrochemical reaction, leads to gas-liquid two-phase flow in the flow channels of fuel cells. The presence of two-phase flow increases the complexity in water management in PEM fuel cells, which remains a challenging hurdle in the commercialization of this technology. Unique water emergence from the gas diffusion layer, which is different from conventional gas-liquid two-phase flow where water is introduced from the inlet together with the gas, leads to different gas-liquid flow behaviors, including pressure drop, flow pattern, and liquid holdup along flow field channels. These parameters are critical in flow field design and fuel cell operation and therefore two-phase flow has received increasing attention in recent years. This review emphasizes gas-liquid two-phase flow in minichannels or microchannels related to PEM fuel cell applications. In situ and ex situ experimental setups have been utilized to visualize and quantify two-phase flow phenomena in terms of flow regime maps, flow maldistribution, and pressure drop measurements. Work should continue to make the results more relevant for operating PEM fuel cells. Numerical simulations have progressed greatly, but conditions relevant to the length scales and time scales experienced by an operating fuel cell have not been realized. Several mitigation strategies exist to deal with two-phase flow, but often at the expense of overall cell performance due to parasitic power losses. Thus, experimentation and simulation must continue to progress in order to develop a full understanding of two-phase flow phenomena so that meaningful mitigation strategies can be implemented.     

Experimental study for the stratified to slug flow regime transition mechanism of gas-oil two-phase flow in horizontal pipe

Theoretical relations that predict the transition from a stratified pattern to a slug pattern, including a one-dimensional wave model that contains less empiricism than the commonly used Taitel-Dukler model, and the ideal model for stratified flow for the gas-liquid flow in horizontal pipes are presented. Superficial velocities of each phase, as the onset of slugging occurs, were predicted, and theoretical analysis was conducted on the stratified to slug flow regime transition. The friction, existing between the fluid and pipe wall, and on the interface of two phases, was especially taken into account. A theoretical model was applied to an experiment about air-oil two-phase flow in a 50 mm horizontal pipe. The effect of pipe diameter on the transition was also studied. The results show that this approach gives a reasonable prediction over the whole range of flow rates, and better agreement has been achieved between predicted and measured critical parameters.     

Experimental study for the stratified to slug flow regime transition mechanism of gas-oil two-phase flow in horizontal pipe

Theoretical relations that predict the transition from a stratified pattern to a slug pattern, including a onedimensional wave model that contains less empiricism than the commonly used Taitel-Dukler model, and the ideal model for stratified flow for the gas-liquid flow in horizontal pipes are presented. Superficial velocities of each phase, as the onset of slugging occurs, were predicted, and theoretical analysis was conducted on the stratified to slug flow regime transition. The friction, existing between the fluid and pipe wall, and on the interface of two phases, was especially taken into account. A theoretical model was applied to an experiment about air-oil two-phase flow in a 50 mm horizontal pipe. The effect of pipe diameter on the transition was also studied. The results show that this approach gives a reasonable prediction over the whole range of flow rates, and better agreement has been achieved between predicted and measured critical parameters. __________ Translated from Journal of Shanghai Jiaotong University, 2006, 40(10): 1782–1785, 1789 [译自: 上海交通大学学报]     

Turbulent mixed convection of a nanofluid in a horizontal curved tube using a two-phase approach

Turbulent mixed convection heat transfer of a nanofluid consisting of water and Al₂O₃ (d_p = 28 nm) throughout a horizontal curved tube has been investigated numerically. Two-phase mixture model has been implemented to study such a flow field. Elliptical governing equations have been solved to investigate the flow behaviors. Simultaneous effects of the buoyancy force, centrifugal force, and nanoparticles concentration have been presented and discussed. The computed results are compared with previously published experimental and numerical data for a base fluid (very low volume fraction, Φ ≈ 0, in the present simulation) and good agreement between the results is observed. It is seen that the nanoparticle volume fraction does not have a direct effect on the secondary flow and the skin friction coefficient. However its effects on the thermal parameters and flow turbulent intensity are significant.     

Experimental and numerical study on the flow characteristics in curved rectangular microchannels

In this paper, the flow characteristics in curved rectangular microchannels with different aspect ratios and curvature ratios for Re numbers ranging from 80 to 876 are investigated. The obtained experimental results are compared with simulated values based on classical Navier–Stokes equations and available correlation in the literature. An empirical equation based on experimental data is proposed to provide a better prediction of the frictional pressure drop in the curved rectangular microchannels.     

A two-phase flow pattern map for annular channels under a DC applied voltage and the application to electrohydrodynamic convective boiling analysis

An experimental study of tube side boiling heat transfer of HFC-134a has been conducted in a single-pass, counter-current flow heat exchanger under an electric field. By applying 0–8 kV to a concentric inner electrode, the mechanics of EHD induced flow and heat transfer augmentation/suppression have been investigated for flow conditions with inlet qualities of 0% to 60%, mass fluxes from 100 kg/m² s to 500 kg/m² s, and heat flux levels between 10 kW/m² and 20 kW/m². A theoretical Steiner type two-phase flow pattern map for flow boiling in the annular channel under applied DC high voltage is also developed. The flow regimes encountered in the convective boiling process have been reconstructed experimentally and compared with the proposed EHD flow regime map. The results show that when the proposed dimensionless criterion M_d Re² is satisfied, EHD interfacial forces have a strong influence on the flow pattern which is considered to be the primary mechanism affecting the increase in pressure drop and the augmentation or even suppression of heat transfer.     

Thermal-hydraulic analysis of the two-phase annular flow under microgravity

The design of the two-phase flow loops applied for thermal control systems of future spacecraft requires knowledge of two-phase flow and heat transfer phenomena under microgravity conditions. This paper deals with a fundamental approach for evaporators or cold plates in two-phase flow loops. A straight evaporator tube was mathematically modeled as a simplified thermal configuration of the cold plate. Simultaneous ordinary differential equations for the two-phase annular flow under microgravity conditions were derived from the separated flow model, and numerical analyses were conducted for the purpose of parametric studies. As a result, properties' distribution of the working fluid along the flow direction, critical limits of the working conditions, and the thermal performance difference owing to the working fluids were clarified. © 1999 Scripta Technica, Heat Trans Asian Res, 29(1): 45–58, 2000     

急流弯道的水力特性试验研究

通过模型试验 ,进一步揭示了急流弯道中 Fr1和 r0 / B对θ及 h2 / h1的影响 ,提出了防止弯道出现干底现象的界限 ,并给出了波角β1的经验公式     

Experimental investigation on inner two-phase flow in counter-flow spray saturator for HAT cycle

An experiment investigation of inner two-phase flow in the counter-flow spray saturator (CFSS) for humid air turbine (HAT) cycle and the simulation of the moving distance of water droplets in counter-flow air are presented here aimed at the understand of two-phase flow in the CFSS in detailed. Dual phase Doppler anemometry (DualPDA) system is applied to obtain the spatial change of the droplet size spectrum in the flow-field to correlate droplet size–velocity correlation. The local measurement profiles of 3D mean velocities and diameters of water droplets are obtained by averaging droplet size classes. Moreover, DualPDA signal processing allows for accurate determination of the volume flux of spherical water droplets. The transient velocity fields are measured by a laser-based particle image velocimetry (PIV) system. The commercial CFD software, FLUENT, is used to simulate the maximum moving distance of water droplets with different diameters and inlet velocities in the counter-flow air with different inlet velocities, then the quantity of water droplet entrainment in the saturator can be estimated.     

弯曲管内的泰勒-迪安流动的数值模拟

流过横截面为正方形的弯曲管内的泰勒-迪安流,除了外墙以外的其它墙壁随着弯曲管中心轴旋转,沿着管的轴向具有压力梯度.数值计算使用光谱分析法.内圆筒旋转的流动和由于压力的流动的综合作用所产生的流动,在较宽的角速度和压力梯度范围内进行了计算.获得了断面二次流动类型的变化的情况.并对得到的解进行了线性稳定性分析.     

燃气轮机回流式燃烧室内两相流动数值模拟及分析

利用流体分析软件STAR—CD对某回流式燃气轮机燃烧室的内部流场进行了三维冷态数值模拟及两相流反应数值模拟。建立了燃烧室的三维计算几何模型及计算网格,计算了燃烧室的单相流场及喷雾两相流场。在计算中气相采用N-S方程求解,采用高雷诺数κ-ε湍流模型及SIMPISO算法;液相采用Lagrange法处理,采用颗粒群轨道模型。根据计算结果进行流动分析,为进一步进行燃烧室内部燃烧过程的数值计算分析及改善燃烧室的结构设计、降低排放奠定了基础。