Two dimensional dynamic modeling of a shell-and-tube water-to-gas membrane humidifier for proton exchange membrane fuel cell

Water management is a crucial factor in determining the performance of proton exchange membrane fuel cell (PEMFC) for automotive application. The shell-and-tube water-to-gas membrane humidifier is useful for humidifying the PEMFC due to its good performance. Shell-and-tube water-to-gas membrane humidifiers have liquid water on one side of the tube wall and a dry gas on the other. In order to investigate humidifier performance, a two-dimensional dynamic model of a shell-and-tube water-to-gas membrane humidifier is developed. The model is discretized into three control volumes – shell, tube and membrane – in the cross-sectional direction to resolve the temperature and species concentration of the humidifier. For validation, the dew point temperature of the simulation result is compared with that of experimental data and shows good agreement with only a slight difference. The distribution of humidification characteristics can be captured using the discretization along the air-flow direction. The humidification performance of two different flow configurations, counter and parallel, are compared under various operating conditions and geometric parameters. Finally, the dynamic response of the humidifier at the step-change of various air flow rates is investigated. These results suggest that the model can be used to optimize the inlet flow humidity of a PEMFC.     

Dynamic modeling and analysis of a shell-and-tube type gas-to-gas membrane humidifier for PEM fuel cell applications

A gas-to-gas humidifier using membranes is the preferred technology for external humidification of fuel cell reactant gases in mobile applications because no extra power supply is required and there are no moving parts. In particular, a shell and tube structure is compact, which allows its easier integration in a fuel cell vehicle.

This paper proposes a mathematical model for the humidifier using the principles of thermodynamics, including analysis of heat and mass transfer and of static and dynamic behaviors. Firstly, the heat and mass transfer behavior was simulated and the results compared with the experimental data. Secondly, the model was used to investigate the sensitivity of the geometric parameters and the effects of various operating conditions on performance. Finally, step responses of the humidifier at various flow rates were analyzed.     

A parametric study of the performance of a planar membrane humidifier with a heat and mass exchanger model for design optimization

The performance of a proton exchange membrane fuel cell (PEMFC) is seriously changed by the humidification capability available when equipped with a PTFE® membrane. Typically, the humidification of a fuel cell is carried out by means of an internal or external humidifier. A membrane humidifier is applied to the external humidification of residential power generation fuel cell due to its convenience and high performance. In this study, a static model is constructed to understand the physical phenomena of the membrane humidifier in terms of geometric parameters and operating parameters. The model utilizes the concept of planar type heat exchanger with mass transport through the membrane. The model is constructed with FORTRAN in a Simulink® environment for consistency with other components of the model we previously developed. The results show that the humidity of the wet gas and the channel length, the membrane thickness and wet gas inlet humidity are critical parameters affecting the performance of the humidifier.     

Modeling and experimental validation of H2 gas bubble humidifier for a 50 kW stationary PEMFC system

Ensuring uniform membrane hydration in a PEMFC (Proton Exchange Membrane Fuel Cell) is important for its performance and durability. In this study, a bubble humidifier for humidifying hydrogen in a 50 kW PEMFC pilot plant was designed, built, and modeled. Initial tests, carried out by humidifying air, show that a dew point temperature of higher than 59 °C is attained when operating the PEMFC plant at nominal power at 65 °C. The model simulation results show good agreement with experimental data and the model is used for studying humidifier performance at other conditions. Steady state simulation results suggest that by increasing the heating water flow rate, the humidifier outlet dew point temperature can be increased by several degrees because of improved heat transfer. Finally, dynamic simulation results suggest that the humidity of the hydrogen can be controlled by manipulating the heat supply to the humidifier.     

Dynamic modeling of a proton exchange membrane fuel cell system with a shell-and-tube gas-to-gas membrane humidifier

The proton exchange membrane fuel cell (PEMFC) system with a shell-and-tube gas-to-gas membrane humidifier is considered to be a promising PEMFC system because of its energy-efficient operation. However, because the relative humidity of the dry air flowing into the stack depends on the stack exhaust air, this system can be unstable during transients. To investigate the dynamic behavior of the PEMFC system, a system model composed of a lumped dynamic model of an air blower, a two-dimensional dynamic model of a shell-and-tube gas-to-gas membrane humidifier, and a one-dimensional dynamic model of a PEMFC system is developed. Because the water management during transient of the PEMFC system is one of the key challenges, the system model is simulated at the step change of current. The variations in the PEMFC system characteristics are captured. To confirm the superiority of the system model, it is compared with the PEMFC component model during transients.     

Transient analysis of alkaline anion exchange membrane fuel cell anode

Alkaline anion exchange membrane (AAEM) fuel cell has attracted increasing attention in recent years due to its several outstanding advantages over proton exchange membrane (PEM) fuel cell such as fast electrochemical kinetics and friendly alkaline environment for catalysts. In this study, a three-dimensional (3D) half-cell transient model is developed to study the dynamic characteristics of AAEM fuel cell under different step changes of operating conditions. It is found that the current density has significant effects on the distribution of liquid water, while the anode stoichiometric ratio effect is insignificant. More time is needed to reach a steady state when the current density decreases rather than increases, and the similar phenomenon also occurs when the operating temperature decreases rather than increases, however, this effect within a low temperature range becomes insignificant. Moreover, the overshoot and undershoot of water diffusion through membrane can also be observed with the step change of the anode stoichiometric ratio and anode inlet relative humidity. The model prediction also has reasonable agreement with published experimental data. The dynamic behaviors observed in this study are of significant importance to the development of AAEM fuel cells for portable and automotive applications.     

Modeling the phenomena of dehydration and flooding of a polymer electrolyte membrane fuel cell

A one-dimensional, two-phase, transient PEM fuel cell model including gas diffusion layer, cathode catalyst layer and membrane is developed. The electrode is assumed to consist of a network of dispersed Pt/C forming spherically shaped agglomerated zones that are filled with electrolyte. Water is modeled in all three phases: vapor, liquid and dissolved in the ionomer to capture the effect of dehydration of the ionomer as well as flooding of the porous media. The anode is modeled as a sophisticated spatially reduced interface. Motivated by environmental scanning electron microscope (ESEM) images of contact angles for microscopic water droplets on fibers of the gas diffusion layer, we introduce the feature of immobile saturation. A step change of the saturation between the catalyst layer and the gas diffusion layer is modeled based on the assumption of a continuous capillary pressure at the interface. The model is validated against voltammetry experiments under various humidification conditions which all show hysteresis effects in the mass transport limited region. The transient saturation profiles clearly show that insufficient liquid water removal causes pore flooding, which is responsible for the oxygen mass transport limitation at high current density values. The simulated and measured current responses from chronoamperometry experiments are compared and analyzed.     

Transient behavior of run-around heat and moisture exchanger system. Part IІ: Sensitivity studies for a range of initial conditions

Part І of this paper [17] developed and verified the numerical model for simultaneous heat and moisture transfer in the run-around membrane energy exchanger (RAMEE) system to determine the transient behavior of the system under different initial and operating conditions.This paper presents the transient response of the RAMEE system for step changes in the inlet supply air temperature and humidity ratio. Also the system quasi-steady state operating conditions are predicted as the system approaches its asymptotic operating condition. The transient responses are predicted with changes in various parameters. These include: the number of heat transfer units, thermal capacity ratio, heat loss/gain ratio, storage volume ratio and the normalized initial salt solution concentration. It is shown that the storage volume ratio and the initial salt solution concentration have significant impacts on the transient response of the system and heat transfer between the RAMEE system and the surrounding environment can change the system quasi-steady conditions substantially.     

Experimental verification of a membrane humidifier model based on the effectiveness method

Experiments conducted on a commercial fuel cell humidifier determined that the water recovery ratio is the best performance metric because it considers the water supplied to the humidifier. Data from a porous polymer membrane with a hydrophilic additive were analyzed under a heat and mass transfer model. The membrane showed low water uptake profiles at relative humidities below 80 percent, and a steep increase in water uptake above threshold.The experiments were conducted with samples of the porous membrane in a single cell humidifier at isothermal conditions at temperatures of 25, 50, and 75 °C. The water recovery ratio for the porous membrane decreased with increasing flow rate.The model was verified experimentally and its predictions agreed with the measured data.     

Analysis of the water and thermal management in proton exchange membrane fuel cell systems

Water and thermal management is essential to the performance of proton exchange membrane (PEM) fuel cell system. The key components in water and thermal management system, namely the fuel cell stack, radiator, condenser and membrane humidifier are all modeled analytically in this paper. Combined with a steady-state, one-dimensional, isothermal fuel cell model, a simple channel-groove pressure drop model is included in the stack analysis. Two compact heat exchangers, radiator and condenser are sized and rated to maintain the heat and material balance. The influence of non-condensable gas is also considered in the calculation of the condenser. Based on the proposed methodology, the effects of two important operating parameters, namely the air stoichiometric ratio and the cathode outlet pressure, and three kinds of anode humidification, namely recycling humidification, membrane humidification and recycling combining membrane humidification are analyzed. The methodology in this article is helpful to the design of water and thermal management system in fuel cell systems.     

Dynamic modeling of a high-temperature proton exchange membrane fuel cell with a fuel processor

A dynamic model of a high-temperature proton exchange membrane fuel cell with a fuel processor is developed in this study. In the model, a fuel processing system, a fuel cell stack, and an exhaust gas burner are modeled and integrated. The model can predict the characteristics of the overall system and each component at the steady and transient states. Specifically, a unit fuel cell model is discretized in a simplified quasi-three-dimensional geometry; therefore, the model can rapidly predict the distribution of fuel cell characteristics. Various operating conditions such as the steam-to-carbon ratio, oxygen-to-carbon ratio, and autothermal reforming inlet temperature are varied and investigated in this study. In addition, the dynamic characteristics exhibited during the transient state are investigated, and an efficiency controller is developed and implemented in the model to maintain the electrical efficiency. The simulation results demonstrate that the steam-to-carbon ratio and the oxygen-to-carbon ratio affect the electrical and system efficiency and that controlling the fuel flow rate maintains the electrical efficiency in the transient state. The model may be a useful tool for investigating the characteristics of the overall system as well as for developing optimal control strategies for enhancing the system performance.     

A new dynamic model for predicting transient phenomena in a PEM fuel cell system

In this paper, a mathematical model is developed to simulate the transient phenomena in a polymer electrolyte membrane fuel cell (PEMFC) system. At present many electrochemical models are available to the fuel cell designers to capture steady state behavior by estimating the equilibrium voltage for a particular set of operating conditions, but models capable of describing transient phenomena are scanty. In practical applications such as powertrains of land-based vehicles or submarines, the output power from the fuel cell system undergoes large variations especially during acceleration and deceleration. During such processes, many transient dynamic mechanisms become significant, while simple empirical models are unable to represent the transient dynamics caused by such as diffusion effect and double layer capacitance at the interface between the electrodes and the electrolyte. Hence, a novel dynamic fuel cell model is developed in this paper which incorporates the effects of charge double layer capacitance, the dynamics of flow and pressure in the anode and cathode channels and mass/heat transfer transient features in the fuel cell body. This dynamic model can predict the transient response of cell voltage, temperature of the cell, hydrogen/oxygen out flow rates and cathode and anode channel temperatures/pressures under sudden change in load current. The proposed model is implemented in SIMULINK environment. The simulation results are analyzed and compared to benchmark results. Lab tests are carried out at Connecticut Global Fuel Cell Center and a good agreement is found between tests and simulations. This model will be very useful for the optimal design and real-time control of PEM fuel cell systems.     

Non-isothermal transient modeling of water transport in PEM fuel cells

Dynamic responses of PEM fuel cells are crucial for mobile applications such as in automobiles. There are four main transient processes in a PEM fuel cell, namely, species transport, electric double layer charge/discharge, membrane hydration/dehydration, and heat transfer. In this study, a rigorous transient model has been developed, accounting for all four transient mechanisms. The dynamic characteristics have been analyzed, corresponding to various changes in working conditions, such as relative humidity and/or cell voltage. Moreover, by using three different membrane types, Nafion 112, Nafion 115, and Nafion 117, the effect of membrane thickness on the cell dynamic performance has been investigated, and the importance of heat transfer effects on the cell dynamic responses have been highlighted.     

Steady state and dynamic performance of proton exchange membrane fuel cells (PEMFCs) under various operating conditions and load changes

The steady-state performance and transient response for H₂/air polymer electrolyte membrane (PEM) fuel cells are investigated in both single fuel cell and stack configurations under a variety of loading cycles and operating conditions. Detailed experimental parameters are controlled and measured under widely varying operating conditions. In addition to polarization curves, feed gas flow rates, temperatures, pressure drop, and relative humidity are measured. Performance of fuel cells was studied using steady-state polarization curves, transient I–V response and electrochemical impedance spectroscopy (EIS) techniques. Different feed gas humidity, operating temperature, feed gas stoichiometry, air pressure, fuel cell size and gas flow patterns were found to affect both the steady state and dynamic response of the fuel cells. It was found that the humidity of cathode inlet gas had a significant effect on fuel cell performance. The experimental results showed that a decrease in the cathode humidity has a detrimental effect on fuel cell steady state and dynamic performance. Temperature was also found to have a significant effect on the fuel cell performance through its effect on membrane conductivity and water transport in the gas diffusion layer (GDL) and catalyst layer. The polarization curves of the fuel cell at different operating temperatures showed that fuel cell performance was improved with increasing temperature from 65 to 75 °C. The air stoichiometric flow rate also influenced the performance of the fuel cell directly by supplying oxygen and indirectly by influencing the humidity of the membrane and water flooding in cathode side. The fuel cell steady state and dynamic performance also improved as the operating pressure was increased from 1 to 4 atm. Based on the experimental results, both the steady state and dynamic response of the fuel cells (stack) were analyzed. These experimental data will provide a baseline for validation of fuel cell models.     

Dynamic simulation and experimental verification on absorption refrigeration driven by vehicle waste heat

Waste heat exhausted from vehicle engine has significant influences on the performances of absorption refrigeration driven by vehicle exhaust heat (VARS), especially for the transient response of VARS to the exhaust temperature and flow rate. Moreover, ambient temperature and flow rate of solution pump also affect its performances. Based on these, a dynamic mathematical model of VARS was proposed and established to observe its dynamic performances in this work. Further, the dynamic model was solved, and the simulation results were compared to the experimental data of a prototype in the same operating conditions. Finally, the transient response of VARS to exhaust temperature and flow rate, ambient temperature, and flow rate of solution pump were analyzed. The simulation results showed that the response time is about 2000 seconds when a disturbance was imposed. The research findings can supply some guidance for a reliable design, optimization, and control strategy for the actual application of the VARS.     

Design methodology for membrane-based plate-and-frame fuel cell humidifiers

Currently, polymer electrolyte membrane fuel cells require some method of humidification to operate effectively. External gas-to-gas membrane-based humidifiers can provide an efficient method to recycle exhaust heat and product water from the fuel cell stack. This work describes a design methodology involving a series of design equations for plate-and-frame membrane humidifiers. Humidifiers of different flow channel geometries were created with a rapid prototyping technique. These humidifier units were tested at different operating conditions in an attempt to validate the design equations. The ratio between the residence time of gas in the humidifier over the diffusion time of water from the surface of the membrane into the channel can be used as a design parameter. This ratio was shown to offer a good starting point for humidifier design, and a target range between 2.0 and 4.0 was identified (with a nominal desired value of 3.0). A humidifier design procedure and suggestions are presented based on this parameter and the packaging requirements of the humidifier in a fuel cell system. This algorithm was validated by creating a further prototype humidifier.     

Transient computation fluid dynamics modeling of a single proton exchange membrane fuel cell with serpentine channel

The proton exchange membrane fuel cell (PEMFC) has become a promising candidate for the power source of electrical vehicles because of its low pollution, low noise and especially fast startup and transient responses at low temperatures. A transient, three-dimensional, non-isothermal and single-phase mathematical model based on computation fluid dynamics has been developed to describe the transient process and the dynamic characteristics of a PEMFC with a serpentine fluid channel. The effects of water phase change and heat transfer, as well as electrochemical kinetics and multicomponent transport on the cell performance are taken into account simultaneously in this comprehensive model. The developed model was employed to simulate a single laboratory-scale PEMFC with an electrode area about 20 cm². The dynamic behavior of the characteristic parameters such as reactant concentration, pressure loss, temperature on the membrane surface of cathode side and current density during start-up process were computed and are discussed in detail. Furthermore, transient responses of the fuel cell characteristics during step changes and sinusoidal changes in the stoichiometric flow ratio of the cathode inlet stream, cathode inlet stream humidity and cell voltage are also studied and analyzed and interesting undershoot/overshoot behavior of some variables was found. It was also found that the startup and transient response time of a PEM fuel cell is of the order of a second, which is similar to the simulation results predicted by most models. The result is an important guide for the optimization of PEMFC designs and dynamic operation.     

Mass transfer characteristics of the hydrophilic membrane with the isolation of heat transfer effect by isothermal bath

The efficiency and lifetime of a proton exchange membrane fuel cell (PEMFC) system is critically affected by the humidity of incoming gas which should be maintained properly for normal operating conditions. But the experimental characteristics of the humidifier are rarely reported. Water transport through the hydrophilic membrane is a coupled phenomenon of heat and mass transport. In this study, a laboratory scale test bench is designed to investigate the characteristics of water transport through the hydrophilic membrane. The mass transfer capability of the hydrophilic membrane is evaluated over various flow rates, temperature, pressure, and flow arrangements. In the experiment, the test bench is submerged in a constant temperature bath in order to isolate the effect of temperature variation between dry air and humid air. The results show the water transport of the hydrophilic membrane is significantly affected by operating temperature and operating pressure. Additionally, the flow arrangement demonstrates a minor effect but it should be considered along with the heat transfer effect.     

燃料电池空气系统增湿器建模与仿真

建立气-气增湿器的数学理论模型,并基于Amesim软件建立燃料电池增湿器及空气系统仿真模型,从燃料电池系统层面分析干湿侧不同温度、压力、水含量等输入条件下的干侧出口空气的湿度变化情况,并采用水转移率（water vapor transfer rate,WVTR）对增湿器增湿性能进行评价,结果表明此模型可进行前期验证,能较好地预测汽车运行过程中增湿器的动态响应特性。     

Dynamic modelling and simulation of a polymer membrane fuel cell including mass transport limitation

The direct conversion of hydrogen into electricity by polymer membrane fuel cells (PEFC) is a promising option for future transportation and stationary energy supply systems.A model for heat and water transport in a polymer membrane fuel cell has been developed for evaluation with regard to structure and material. Moreover the dynamic simulation allows simulation of the transient state after changes of electrical load or gas flow rate and humidification.The polymer membrane fuel cell is subdivided into different components: gas distributor, gas diffusion layer, catalytic layer and membrane. Each of these components is described by a mathematical model which accounts for the physical phenomena arising in this structure: i.e. energy and mass transfer and electrochemical kinetics. In the simulation program each component is represented by a separate module. Coupling these modules results in a model describing a single electrode membrane unit or a complete fuel cell stack.Results are presented by current-voltage curves or temperature plots. The influence of model parameters such as thickness and porosity of the diffusion layer, or the structure of the catalytic layer, are shown. Furthermore, results of the dynamic behaviour of a polymer membrane fuel cell are presented.