Three dimensional numerical simulation of gas-liquid two-phase flow patterns in a polymer-electrolyte membrane fuel cells gas flow channel

Water management in polymer-electrolyte membrane fuel cells (PEMFCs) has a major impact on fuel cell performance and durability. To investigate the two-phase flow patterns in PEMFC gas flow channels, the volume of fluid (VOF) method was employed to simulate the air-water flow in a 3D cuboid channel with a 1.0 mm × 1.0 mm square cross section and a 100 mm in length. The microstructure of gas diffusion layers (GDLs) was simplified by a number of representative opening pores on the 2D GDL surface. Water was injected from those pores to simulate water generation by the electrochemical reaction at the cathode side. Operating conditions and material properties were selected according to realistic fuel cell operating conditions. The water injection rate was also amplified 10 times, 100 times and 1000 times to study the flow pattern formation and transition in the channel. Simulation results show that, as the flow develops, the flow pattern evolves from corner droplet flow to top wall film flow, then annular flow, and finally slug flow. The total pressure drop increases exponentially with the increase in water volume fraction, which suggests that water accumulation should be avoided to reduce parasitic energy loss. The effect of material wettability was also studied by changing the contact angle of the GDL surface and channel walls, separately. It is shown that using a more hydrophobic GDL surface is helpful to expel water from the GDL surface, but increases the pressure drop. Using a more hydrophilic channel wall reduces the pressure drop, but increases the water residence time and water coverage of the GDL surface.     

Impact of channel geometry on two-phase flow in fuel cell microchannels

An important function of the gas delivery channels in PEM fuel cells is the evacuation of water at the cathode. The resulting two-phase flow impedes reactant transport and causes parasitic losses. There is a need for research on two-phase flow in channels in which the phase fraction varies along the flow direction as in operating fuel cells. This work studies two-phase flow in 60 cm long channels with distributed water injection through a porous GDL wall to examine the physics of flows relevant to fuel cells. Flow regime maps based on local gas and liquid flow rates are constructed for experimental conditions corresponding to current densities between 0.5 and 2 A cm⁻² and stoichiometric coefficients from 1 to 4. Flow structures transition along the length of the channel. Stratified flow occurs at high liquid flow rates, while intermittent slug flow occurs at low liquid flow rates. The prevalence of stratified flow in these serpentine channels is discussed in relation to water removal mechanisms in the cathode channels of PEM fuel cells. Corners facilitate formation of liquid films in the channel, but may reduce the water-evacuation capability. This analysis informs design guidelines for gas delivery microchannels for fuel cells.     

An approach to modeling two-phase transport in the gas diffusion layer of a proton exchange membrane fuel cell

A series of analysis methods is proposed to simulate the liquid–gas two-phase and multi-component transport phenomena in the gas diffusion layer (GDL) of a proton exchange membrane fuel cell (PEMFC). These methods involve measuring and predicting the two-phase flow properties of a GDL, and simulating the two-phase multi-component transport in the GDL. The capillary pressure is measured by the porous diaphragm method and predicted by the pore network model. The relative permeability is measured by the steady-state method and predicted by a combination of the single-phase and the two-phase lattice Boltzmann method. And the simulation of the liquid–gas two-phase transport is done using the multi-phase mixture model. The methods are applied to a carbon-fiber paper GDL to identify the two-phase multi-component transport in the GDL.     

Parametric study of the cathode and the role of liquid saturation on the performance of a polymer electrolyte membrane fuel cell—A numerical approach

A two-dimensional two-phase steady state model of the cathode of a polymer electrolyte membrane fuel cell (PEMFC) is developed using unsaturated flow theory (UFT). A gas flow field, a gas diffusion layer (GDL), a microporous layers (MPL), a finite catalyst layer (CL), and a polymer membrane constitute the model domain. The flow of liquid water in the cathode flow channel is assumed to take place in the form of a mist. The CL is modeled using flooded spherical agglomerate characterization. Liquid water is considered in all the porous layers. For liquid water transport in the membrane, electro-osmotic drag and back diffusion are considered to be the dominating mechanisms. The void fraction in the CL is expressed in terms of practically achievable design parameters such as platinum loading, Nafion loading, CL thickness, and fraction of platinum on carbon. A number of sensitivity studies are conducted with the developed model. The optimum operating temperature of the cell is found to be 80-85 °C. The optimum porosity of the GDL for this cell is in the range of 0.7-0.8. A study by varying the design parameters of the CL shows that the cell performs better with 0.3-0.35 mg cm⁻² of platinum and 25-30 wt% of ionomer loading at high current densities. The sensitivity study shows that a multi-variable optimization study can significantly improve the cell performance. Numerical simulations are performed to study the dependence of capillary pressure on liquid saturation using various correlations. The impact of the interface saturation on the cell performance is studied. Under certain operating conditions and for certain combination of materials in the GDL and CL, it is found that the presence of a MPL can deteriorate the performance especially at high current density.     

Two-phase flow pattern in small diameter tubes with the presence of horizontal return bend

This study provides a qualitatively visual observation of the two-phase flow patterns for air-water mixtures inside 6.9, 4.95, and 3 mm smooth diameter tubes with the presence of horizontal return bend. The influence of the return bend on the two-phase flow patterns are investigated. For D=6.9 mm and at a mass flux of 50 kg m⁻² s⁻¹ having a quality less than 0.1, no influence on the flow patterns is seen at a larger curvature ratio of 7.1. However, were the curvature ratio reduced to 3, the flow pattern in the recovery region is temporarily turned from stratified flow into annular flow. The temporary flow pattern transition phenomenon from stratified flow to annular flow is not so pronounced with the decrease of tube diameter. It is likely that this phenomenon is related to the influence of surface tension and the reduction of developing length of the swirl flow. Based on the present flow visualization, three flow pattern maps are proposed to describe the effect of return bend on the transition of two-phase flow pattern.     

Modeling gas flow in PEMFC channels: Part I – Flow pattern transitions and pressure drop in a simulated ex situ channel with uniform water injection through the GDL

The two-phase flow in the gas channels of a proton exchange membrane fuel cell (PEMFC) is studied with an ex situ setup using a gas diffusion layer (GDL) as the sidewall of the channels. Air is supplied at the channel inlet manifold and water is supplied continuously and uniformly through the GDL along the length of the channel. This is different from the simultaneous air and water introduction at the inlet of the channel as studied by previous two-phase flow researchers. The GDL is compressed between the gas channels and the water chambers to simulate PEMFC conditions. The superficial velocity for air and water ranged from 0.25 to 34.5 m/s and 1.54 × 10⁻⁵ to 1.54 × 10⁻⁴ m/s, respectively. The ex situ setup was run in both vertical and horizontal orientations with two GDLs, – Baseline (Mitsubishi Rayon Co. MRC 105 with 5 wt.% PTFE and coated with an in-house MPL by General Motors) and SGL 25 BC – and three channel treatments – hydrophobic, hydrophilic, and untreated Lexan, with contact angles of 116°, 11° and 86°, respectively. No appreciable effect was noted because of the orientation, GDL type or channel coatings. The flow regime is observed at different locations along the channel and is expressed as a function of the superficial air and water velocities. Flow regime criteria are developed and validated against the range of ex situ data observations. A new variable water flow rate pressure drop model is developed in order to account for the variation of water entering the channel at multiple locations along the flow length. Pressure drop models are developed for specific flow regimes and validated against experimental data. The models are able to predict the experimental pressure drop data with a mean error of less than 14%.     

Validity of two-phase polymer electrolyte membrane fuel cell models with respect to the gas diffusion layer

A dynamic two-phase model of a proton exchange membrane fuel cell with respect to the gas diffusion layer (GDL) is presented and compared with chronoamperometric experiments. Very good agreement between experiment and simulation is achieved for potential step voltammetry (PSV) and sine wave testing (SWT). Homogenized two-phase models can be categorized in unsaturated flow theory (UFT) and multiphase mixture (M²) models. Both model approaches use the continuum hypothesis as fundamental assumption. Cyclic voltammetry experiments show that there is a deterministic and a stochastic liquid transport mode depending on the fraction of hydrophilic pores of the GDL. ESEM imaging is used to investigate the morphology of the liquid water accumulation in the pores of two different media (unteflonated Toray-TGP-H-090 and hydrophobic Freudenberg H2315 I3). The morphology of the liquid water accumulation are related with the cell behavior. The results show that UFT and M² two-phase models are a valid approach for diffusion media with large fraction of hydrophilic pores such as unteflonated Toray-TGP-H paper. However, the use of the homgenized UFT and M² models appears to be invalid for GDLs with large fraction of hydrophobic pores that corresponds to a high average contact angle of the GDL.     

Investigation of two-phase flow in the compressed gas diffusion layer microstructures

This study aims to investigate how multiple parameters affect the two-phase flow in compressed gas diffusion layer (GDL). A stochastic model is adopted to reconstruct the GDL microstructures. Solid mechanics simulations on the reconstructed GDL microstructures are performed, based on the finite element method (FEM). Various pore morphologies and distributions of compressed GDLs are observed. Two-phase flow in GDL is simulated using a volume of fluid (VOF) model. Corner droplet (on the GDL surface) and water flow (emerging from GDL bottom) are considered. It is found that two-phase flow in the GDL is highly influenced by compression, fiber diameter, porosity, and GDL thickness. The results indicate that a larger fiber diameter or higher porosity contributes to the water transport due to larger average pore size. Furthermore, water removal from a thicker GDL is more difficult, whereas water transport in the lower part of a compressed thick GDL is easy.     

Experimental analysis for the determination of the convective heat transfer coefficient by measuring pressure drop directly during annular condensation flow of R134a in a vertical smooth tube

This study investigated the direct relationship between the measured condensation pressure drop and convective heat transfer coefficient of R134a flowing downward inside a vertical smooth copper tube having an inner diameter of 8.1 mm and a length of 500 mm during annular flow. R134a and water were used as working fluids on the tube side and annular side of a double tube heat exchanger, respectively. Condensation experiments were performed at mass fluxes of 260, 300, 340, 400, 456 and 515 kg m⁻² s⁻¹ in the high mass flux region of R134a. The condensing temperatures were around 40 and 50 °C; the heat fluxes were between 10.16 and 66.61 kW m⁻². Paliwoda’s analysis, which focused mainly on the determination of the two-phase flow factor and two-phase length of evaporators and condensers, was adapted to the in-tube condensation phenomena in the test section to determine the condensation heat transfer coefficient, heat flux, two-phase length and pressure drop experimentally by means of a large number of data points obtained under various experimental conditions.     

Three-dimensional numerical simulation of water droplet emerging from a gas diffusion layer surface in micro-channels

The dynamic formation of water droplets emerging from a gas diffusion layer (GDL) surface in micro-channels was simulated using the volume of fluid (VOF) method. The influence of GDL surface microstructure was investigated by changing the pore diameter and the number of pore openings on the GDL surface. Simulation results show that the microstructure of the GDL surface has a significant impact on the two-phase flow patterns in gas flow channels. For a non-uniform GDL surface, three stages were identified, namely emergence and merging on the GDL surface, accumulation on the channel sidewalls and detachment from the top wall. It was also found that if the pore size is small enough, the flow pattern in the channel does not change with further reduction in the pore diameter. However, the two-phase flow patterns change significantly with the wettability of the GDL surface and sidewalls, but remain the same when the liquid flow rate is reduced by two orders of magnitude from the reference case.     

Three-dimensional modeling of a PEMFC with serpentine flow field incorporating the impacts of electrode inhomogeneous compression deformation

The effects of compression deformation of gas diffusion layer (GDL) on the performance of a proton exchange membrane fuel cell (PEMFC) with serpentine flow field were numerically investigated by coupling two-dimensional GDL mechanical deformation model based on Finite Element Analysis and three-dimensional two-phase PEMFC model with incorporating the deformation impacts. Emphasis is located on exploring the influences of assembly pressure on the non-uniform geometric deformation and distributions of transport properties in the GDL, flow behaviors and local distributions of oxygen and current density, cell polarization curves and net power densities of the PEMFC. It was indicated that the non-uniform deformation of GDL results in inhomogeneous distributions of porosity and permeability in the GDL due to the presence of rib-channel pattern, and the transport properties in the under-rib region are greatly reduced with increasing the assembly pressure, consequently weakening the gas flow and oxygen transport in the under-rib region and increasing the non-uniformity of local current density distribution. As for the overall cell performance, however, attributed to the tradeoff between the adverse impacts of GDL compression on mass transport loss and positive effects on reducing ohmic loss, the overall cell performance is firstly increased and then decreased with increasing assembly pressure from 0 MPa to 5.0 MPa, and the maximum cell performance can be achieved at the assembly pressure of about 1.0 MPa for all cases studied. As compared with the case for zero assembly pressure, the maximum net power density of the cell can be improved by about 7.7%, 9.9%, 10.5% and 10.7% for the cathode stoichiometry ratios of 2.0, 3.0, 4.0 and 5.0@i_ref = 1 A·cm⁻², respectively. Practically, it is suggested that the assembly pressure is controlled in an appropriate range of 0.5 MPa–1.5 MPa such that the cell net power can be boosted and pressure head requirement for the pump can be maintained in a appropriate level.     

Visualization and quantification of cathode channel flooding in PEM fuel cells

An understanding of two-phase flow mechanisms in micro-channels is critical to water management in fuel cell applications. In this work, an in situ visualization study of cathode flooding in an operating fuel cell is presented. Gas relative humidities of 26%, 42% and 66%, current densities of 0.2, 0.5 and 0.8 A cm⁻²and flow stoichiometries ranging from 2 to 4 are used in this study which represent typical operating conditions for automotive applications. Results are presented in the form of a flow map depicting various two-phase flow patterns. The impact of flooding is also presented in terms of measurable parameters like two-phase pressure drop coefficient and voltage loss. A new parameter called wetted area ratio is introduced to characterize channel flooding and liquid water coverage on a gas diffusion layer, and its repeatability with multiple tests is demonstrated.     

Two-phase flow pressure drop hysteresis in parallel channels of a proton exchange membrane fuel cell

Two-phase flow pressure drop hysteresis was studied in a non-operational PEM fuel cell to understand the effect of stoichiometry, GDL characteristics, operating range, and initial conditions (dry vs. flooded) for flow conditions typical of an operating fuel cell. This hysteresis is noted when the air and water flow rates are increased and then decreased along the same path, exhibiting different pressure drops. When starting from dry conditions, the descending pressure drop tended to be higher than the ascending pressure drop at lower simulated current densities. The hysteresis effect was noted for stoichiometries of 1-4 and was eliminated at a stoichiometry of 5. It was found that the hysteresis was greater when water breakthrough occurred at higher simulated current densities, which is a function of GDL properties. The operating range had to reach a critical simulated current density (800 mA cm⁻² in this case) between the ascending and descending approach to create a pressure drop hysteresis zone. The descending step size does not change the size of the hysteresis effect, but a larger step size leads to lower fluctuations in the pressure drop signal. An initially flooded condition also showed hysteresis, but the ascending approach tended to have a higher pressure drop than the descending approach.     

Quantification and characterization of water coverage in PEMFC gas channels using simultaneous anode and cathode visualization and image processing

A new technique is presented to characterize and quantify the two-phase flow in the anode and cathode flow field channels using simultaneous anode and cathode visualization combined with image processing. In situ visualization experiments were performed at 35 °C with stoichiometric ratios (an/ca) of 1.5/2.5, 1.5/5, 3/8 to elucidate two-phase flow dynamics at lower temperature/low power conditions, when excess liquid water in the cell can be especially prevalent. Video processing algorithms were developed to automatically detect and quantify dynamic and static liquid water present in the flow field channels, as well as discern the distribution of water among different two-phase flow structures. The water coverage ratio was introduced as a parameter to capture the time-averaged flow field water content information through recorded high speed video sequences. The automated processing allows for efficient and robust spatial and temporal averaging of steady state channel water over very large visualization data sets acquired through high speed imaging. The developed algorithm calculates the water coverage ratio using the liquid water in the channels which is contacting the GDL surface, and selectively removes the superficial condensation on the visualization window from the coverage area. The water coverage ratio and distribution metrics techniques were demonstrated by comparing the performance of Freudenberg and Toray gas diffusion layers (GDLs) from a water management perspective, including direct anode to cathode comparisons of simultaneous water coverage data for each GDL sample. The anode water coverage ratio was found to exceed the cathode for both GDL samples at most operating conditions tested in this work. The Freudenberg GDL consistently demonstrated a higher water coverage ratio in the flow field gas channels than the Toray GDL, while the Toray GDL indicated a propensity for greater water retention within the membrane electrode assembly (MEA) based on performance, high frequency resistance (HFR), and water coverage metrics.     

Two-phase flow in GDL and reactant channels of a proton exchange membrane fuel cell

Understanding the effect of two-phase flow in the components of proton exchange membrane fuel cells (PEMFCs) is crucial to water management and subsequently to their performance. The local water saturation in the gas diffusion layer (GDL) and reactant channels influences the hydration of the membrane which has a direct effect on the PEMFC performance. Mass transport resistance includes contributions from both the GDL and reactant channels, as well as the interface between the aforementioned components. Droplet–channel wall interaction, water area coverage ratio on the GDL, oxygen transport resistance at the GDL–channel interface, and two-phase pressure drop in the channels are interlinked. This study explores each factor individually and presents a comprehensive perspective on our current understanding of the two-phase transport characteristics in the PEMFC reactant channels.     

Two-phase flow and maldistribution in gas channels of a polymer electrolyte fuel cell

Liquid water transport in a polymer electrolyte fuel cell (PEFC) is a major issue for automotive applications. Mist flow with tiny droplets suspended in gas has been commonly assumed for channel flow while two-phase flow has been modeled in other cell components. However, experimental studies have found that two-phase flow in the channels has a profound effect on PEFC performance, stability and durability. Therefore, a complete two-phase flow model is developed in this work for PEFC including two-phase flow in both anode and cathode channels. The model is validated against experimental data of the wetted area ratio and pressure drop in the cathode side. Due to the intrusion of soft gas diffusion layer (GDL) material in the channels, flow resistance is higher in some channels than in others. The resulting flow maldistribution among PEFC channels is of great concern because non-uniform distributions of fuel and oxidizer result in non-uniform reaction rates and thus adversely affect PEFC performance and durability. The two-phase flow maldistribution among the parallel channels in an operating PEFC is explored in detail.     

A two-fluid model for two-phase flow in PEMFCs

In this study, a two-fluid (TF) model is developed for two-phase flows in proton exchange membrane fuel cells (PEMFCs). The drag force and lift force between gas and liquid phase are considered in N-S equations. In addition, a simplified model is introduced to obtain the liquid water droplet detachment diameter on the gas diffusion layer (GDL)/channel interface which involves the properties of the GDL/channel interface (contact angle and surface tension). The TF model and the simplified model for the prediction of water droplet detachment diameter on GDL/channel interface are validated by the comparison between the experimental data and the model results, respectively. The effect of the properties of GDL/channel interface (contact angle and surface tension) on two-phase behavior in PEMFCs is investigated, The results show that a high contact angle and a low surface tension are advantageous for liquid water removal in the gas channel and the GDL even though a low surface tension will lead to a low capillary force in the GDL.     

Two-phase flow pressure drop hysteresis in an operating proton exchange membrane fuel cell

Two-phase flow pressure drop hysteresis was studied in an operating PEM fuel cell. The variables studied include air stoichiometry (1.5, 2, 3, 4), temperature (50, 75, 90 °C), and the inclusion of a microporous layer. The cathode channel pressure drops can differ in PEM fuel cells when the current density is increased along a path and then decreased along the same path (pressure drop hysteresis). Generally, the descending pressure drop is greater than the ascending pressure drop at low current densities (<200 mA cm⁻²), and the effect is worse at low stoichiometries and low temperatures. The results show that the hysteresis occurs with or without the inclusion of a microporous layer. Initial results show a modified Lockhart-Martinelli approach seems to be able to predict the two-phase flow pressure drop during the ascending path. The results compare well with photographs taken from the cathode flow field channel of a visualization cell.     

Two-phase friction factor in vertical downward flow in high mass flux region of refrigerant HFC-134a during condensation

The two-phase pressure drop of the pure refrigerant HFC-134a during condensation inside a vertical tube-in-tube heat exchanger was investigated. The double tube test section was 0.5 m long with refrigerant flowing in the inner tube and cooling water flowing in the annulus. The inner tube was constructed from smooth copper tubing of 8.1 mm inner diameter and 9.52 mm outer diameter. The test runs were performed at average condensing temperatures of 40–50 °C. The mass fluxes were between 260 and 515 kg m^− 2 s^− 1 and the heat fluxes between 11.3 and 55.3 kW m^− 2. The quality of the refrigerant in the test section was calculated using the temperature and pressure obtained from the experiment. The pressure drop across the test section was directly measured by a differential pressure transducer. A new correlation for the two-phase friction factor of R134a flow is proposed by means of the equivalent Reynolds number model. The effects of heat flux, mass flux and condensation temperature on the pressure drop are also discussed.