**Fluid Flow in Polymer Electrolyte Membrane Fuel Cells**

Alfredo Iranzo, Antonio Salva and Felipe Rosa *Thermal Engineering Group, Energy Engineering Department School of Engineering, University of Seville Spain* 

#### **1. Introduction**

Polymer Electrolyte Membrane Fuel Cells (PEMFC) have attracted significant interest during the last few decades, as they are considered to be one of the most promising alternative clean power generation devices for portable, mobile and stationary applications. However, different technological barriers such as cost, durability, or heat and water management, are limiting the implementation of fuel cell systems into the global energy markets, and therefore significant research efforts and investments are being carried out.

Fuel cells are devices where electrochemical reactions transform chemical energy available in fuels into electrical energy. Fuel cells are not limited by the thermodynamic restrictions of conventional power generation systems, such as the Carnot efficiency, meaning that fuel cells can be operated with higher efficiency for energy conversion. Additionally, the environmental impact is low as no combustion processes occurs and no pollutants are generated (U.S. Department of Energy [DOE], 2004).

A typical fuel cell power system consists of different components:


Single or unit cells are the core of a fuel cell. They convert the chemical energy contained in a fuel into electrical energy, via electrochemical reactions. The basic configuration of a fuel cell consists of an electrolyte layer or membrane in contact with an anode and a cathode on either side.

In a PEM fuel cell, hydrogen is continuously supplied to the anode or negative electrode, and an oxidant, often oxygen or air, is also continuously supplied to the cathode or positive electrode. Electrochemical reactions occur at the electrodes, generating an electric current through the electrolyte thus driving the corresponding electric current that performs the electric work on the load.

At the anode, hydrogen is fed to the cell and a reaction takes place at the catalyst layer:

$$2H\_2 \to 4H^+ + 4e^- \tag{1}$$

Fluid Flow in Polymer Electrolyte Membrane Fuel Cells 267

the gases over the entire surface. In order to provide a better uniformity of the reactants over the electrode, a Gas Diffusion Layer (GDL) is placed between Bipolar Plate and electrode.

Hydrogen Oxygen (air)

e- ee- e-

H+ H+

H+ H+

GDLan CLan Membrane Clcat GDL cat

e- e-

ee-

e-

e-

Heat

80 ºC LTPEMFC 120-160 ºC HTPEMFC

Electric circuit

The main components of a cell are depicted in Figure 1.

Fig. 1. Main components of a single fuel cell


back diffusion.

diffusion layers.

The following processes take place inside the fuel cell:


convection to reactant gases and cooling medium.





The design of the cell components must comprise a trade-off of these processes with minimum losses. A typical example is the porosity of the GDL: while high porosity would help the gas diffusion, this would hinder the electric conductivity and thus the cell performance. In general, the processes depicted above are tightly coupled in the cell. For

A schematic diagram of the main transport mechanisms is depicted in Figure 2.

The protons migrate through the polymeric membrane and react with the oxygen and the electrons at the cathode catalyst layer:

$$2O\_2 + 4H^+ + 4e^- \rightarrow 2H\_2O\tag{2}$$

Therefore, the overall reaction taking place in the cell is:

$$2H\_2 + O\_2 \rightarrow 2H\_2O\tag{3}$$

Fuel cells are modular, so that unit cells can be combined into a stack to achieve the voltage and power required for the specific application. This involves connecting multiple unit cells in series via electrically conductive materials. The connection is achieved via the bipolar plate (BP), that also provides a gas barrier that separates the fuel and oxidant of adjacent cells (DOE, 2004), (Larminie & Dicks, 2003), (Barbir, 2005). The channels that distribute the gas to the electrode surface are usually imprinted in the plate.

The design of a fuel cell must therefore comprise a number of physical and chemical phenomena, such as electrochemical reactions, heat transfer and thermal management, material selection, fluid dynamics for laminar flow and flow in porous media, flow distribution of the reactants in the stack manifolds, and others. These phenomena are tightly coupled, making the design and optimization of a fuel cell a complicated task usually aided by numerical models and simulations, as well as by experimental techniques. A considerable effort and intense developments are being made by governments, public institutions, universities, research institutes and private companies in the field of fuel cell research.

In this chapter, the fluid flow within single cells and fuel cell stacks is analysed.

#### **2. Fluid flow in PEM fuel cells**

The fluid flow characteristics within the Fuel Cell are of major importance for the final performance of the system. This chapter deals with the main fluid flow mechanisms occurring within a Fuel Cell at two different levels: single cells and stacks.

The flow inside a single cell comprises a number of different transport mechanisms, namely laminar flow in channels, flow in porous media, multiphase flow with phase change, and diffusion mechanisms. This will be addressed in section 3. On the other hand, the flow in a Fuel Cell stack is mainly concern about the flow in the inlet/outlet stack manifolds, and the reactant distribution over the different cells. This will be addressed in section 4.

#### **3. Fluid flow in a single cell**

#### **3.1 Description of a single cell: Main components and processes**

The core of a single cell is a polymer membrane acting as an electrolyte. The membrane is a proton-conductive material, with porous electrodes on both sides of the membrane. The electrodes are porous materials to allow both reactant gases to reach the catalyst sites and products to leave the electrode. Electrochemical reactions occur at the catalyst surface on the electrodes. This multilayer assembly is called Membrane Electrode Assembly (MEA). The MEA is located between collector or separator plates called bipolar plates. Bipolar plates connect the cathode of one cell to the anode of the adjacent cell both physically and electrically. Reactant gases are fed to the Bipolar Plates, where imprinted channels distribute

The protons migrate through the polymeric membrane and react with the oxygen and the

Fuel cells are modular, so that unit cells can be combined into a stack to achieve the voltage and power required for the specific application. This involves connecting multiple unit cells in series via electrically conductive materials. The connection is achieved via the bipolar plate (BP), that also provides a gas barrier that separates the fuel and oxidant of adjacent cells (DOE, 2004), (Larminie & Dicks, 2003), (Barbir, 2005). The channels that distribute the

The design of a fuel cell must therefore comprise a number of physical and chemical phenomena, such as electrochemical reactions, heat transfer and thermal management, material selection, fluid dynamics for laminar flow and flow in porous media, flow distribution of the reactants in the stack manifolds, and others. These phenomena are tightly coupled, making the design and optimization of a fuel cell a complicated task usually aided by numerical models and simulations, as well as by experimental techniques. A considerable effort and intense developments are being made by governments, public institutions, universities, research institutes and private companies

The fluid flow characteristics within the Fuel Cell are of major importance for the final performance of the system. This chapter deals with the main fluid flow mechanisms

The flow inside a single cell comprises a number of different transport mechanisms, namely laminar flow in channels, flow in porous media, multiphase flow with phase change, and diffusion mechanisms. This will be addressed in section 3. On the other hand, the flow in a Fuel Cell stack is mainly concern about the flow in the inlet/outlet stack manifolds, and the

The core of a single cell is a polymer membrane acting as an electrolyte. The membrane is a proton-conductive material, with porous electrodes on both sides of the membrane. The electrodes are porous materials to allow both reactant gases to reach the catalyst sites and products to leave the electrode. Electrochemical reactions occur at the catalyst surface on the electrodes. This multilayer assembly is called Membrane Electrode Assembly (MEA). The MEA is located between collector or separator plates called bipolar plates. Bipolar plates connect the cathode of one cell to the anode of the adjacent cell both physically and electrically. Reactant gases are fed to the Bipolar Plates, where imprinted channels distribute

In this chapter, the fluid flow within single cells and fuel cell stacks is analysed.

occurring within a Fuel Cell at two different levels: single cells and stacks.

reactant distribution over the different cells. This will be addressed in section 4.

**3.1 Description of a single cell: Main components and processes** 

2 2 *O H e HO* <sup>442</sup> + − + +→ (2)

22 2 2 2 *H O HO* + → (3)

electrons at the cathode catalyst layer:

in the field of fuel cell research.

**2. Fluid flow in PEM fuel cells** 

**3. Fluid flow in a single cell** 

Therefore, the overall reaction taking place in the cell is:

gas to the electrode surface are usually imprinted in the plate.

the gases over the entire surface. In order to provide a better uniformity of the reactants over the electrode, a Gas Diffusion Layer (GDL) is placed between Bipolar Plate and electrode. The main components of a cell are depicted in Figure 1.

Fig. 1. Main components of a single fuel cell

The following processes take place inside the fuel cell:


The design of the cell components must comprise a trade-off of these processes with minimum losses. A typical example is the porosity of the GDL: while high porosity would help the gas diffusion, this would hinder the electric conductivity and thus the cell performance. In general, the processes depicted above are tightly coupled in the cell. For

Fluid Flow in Polymer Electrolyte Membrane Fuel Cells 269

The performance of a given fuel cell is affected by the parameters listed below (Barbir, 2005):

From thermodynamics and electrochemical reaction kinetics, the Fuel Cell performance is higher when the operating pressure and temperature is increased. However, the complete system and balance of plant must be considered for the appropriate selection of the

Regarding reactant flow rates, generally speaking higher flow rates result in improved performance of the fuel cell, as higher flow rate helps remove liquid water from the cell and maintain a high oxygen concentration within the catalyst layer. However, when hydrogen is considered, a too high flow rate will reduce the system efficiency as part of the hydrogen

In Nafion membranes, reactants must be supplied humidified in order to keep the membrane sufficiently hydrated and enhance its protonic conductivity. A complex water transport and management issues arises, with water being generated at the cathode, and transported by means of different mechanisms through the cell. The degree of humidification required depends on the cell design and membrane type. For example, thinner membranes such as Nafion-111 present a better cathode to anode water transport via diffusion. Water management is one of the most active research fields in PEM Fuel Cells, and detailed reviews can be found in the work of Dai et al. (Dai et al., 2009) and Jiao and Li

The real potential obtained in a fuel cell is always less than the theoretical maximum, as certain irreversible losses exist. The main contributions to the losses are (Barbir, 2005;

Activation losses area caused the activation energy needed for the electrochemical reactions at the electrodes. The kinetics of the reactions results in part of the voltage

generated being used as driving force for the chemical reaction.



operating parameters (compression power, water management, etc.).

Fig. 3. Polarization curve of a single PEM fuel cell




would be wasted.

(Jiao & Li, 2011).

Mench 2008):


example, at the cathode side of the MEA a complex interrelation between various transport phenomena take place. The processes occurring at the cathode are (Djilali, 2007):


On the cathode, the reaction is likely to suffer from mass transport limitations at high current densities, when depletion of oxygen in the air stream becomes significant. This limitation can be further extended by flooding of the electrode pores by the product water and blocking of pathways for oxygen transport to the reaction sites. Effective removal of excess water is thus essential, but must be balanced against the need to prevent drying of the adjacent proton conducting media (membrane), which not only causes deterioration in protonic conductivity (and thus higher ohmic losses and lower efficiency), but also impacts durability.

The performance of a fuel cell is usually represented by means of a polarization curve I-V as shown in Figure 3.

In the polarization curve, three different regions can be generally observed. The cell performance is dominated by kinetic or activation losses at low current densities, while at high current densities mass transport limitations have a major effect given the high amount of reactants required to maintain the intensity and the pore blockage produced by the water flooding the cathode. At medium current densities and voltages, ohmic losses become an important factor in the fuel cell performance.

Fig. 3. Polarization curve of a single PEM fuel cell

The performance of a given fuel cell is affected by the parameters listed below (Barbir, 2005):


268 Fluid Dynamics, Computational Modeling and Applications

example, at the cathode side of the MEA a complex interrelation between various transport

On the cathode, the reaction is likely to suffer from mass transport limitations at high current densities, when depletion of oxygen in the air stream becomes significant. This limitation can be further extended by flooding of the electrode pores by the product water and blocking of pathways for oxygen transport to the reaction sites. Effective removal of excess water is thus essential, but must be balanced against the need to prevent drying of the adjacent proton conducting media (membrane), which not only causes deterioration in protonic conductivity

The performance of a fuel cell is usually represented by means of a polarization curve I-V as

In the polarization curve, three different regions can be generally observed. The cell performance is dominated by kinetic or activation losses at low current densities, while at high current densities mass transport limitations have a major effect given the high amount of reactants required to maintain the intensity and the pore blockage produced by the water flooding the cathode. At medium current densities and voltages, ohmic losses become an

(and thus higher ohmic losses and lower efficiency), but also impacts durability.

phenomena take place. The processes occurring at the cathode are (Djilali, 2007): - Conduction of electrons between the current collectors and the reaction sites.


Hydrogen Oxygen (air)

Anode Membrane Cathode

H+ H+

Back-diffusion

Channel GDL CL Mem CL\* GDL Channel

H+ H+

Electroosmotic drag e-

e<sup>e</sup> <sup>e</sup> - -

O2 transport (voids): diffusion

e- transport (conductive fibers)

\* Water generation (catalyst sites) and transport

e- e-

e- e-

Water transport (voids): diffusion, capillary, phase change




Fig. 2. Main processes within a single PEM fuel cell

e- e<sup>e</sup> <sup>e</sup> - -

H2 transport (voids): diffusion e- transport (conductive fibers)

important factor in the fuel cell performance.

shown in Figure 3.

e-

e- e-

e- <sup>e</sup> <sup>e</sup> - -


From thermodynamics and electrochemical reaction kinetics, the Fuel Cell performance is higher when the operating pressure and temperature is increased. However, the complete system and balance of plant must be considered for the appropriate selection of the operating parameters (compression power, water management, etc.).

Regarding reactant flow rates, generally speaking higher flow rates result in improved performance of the fuel cell, as higher flow rate helps remove liquid water from the cell and maintain a high oxygen concentration within the catalyst layer. However, when hydrogen is considered, a too high flow rate will reduce the system efficiency as part of the hydrogen would be wasted.

In Nafion membranes, reactants must be supplied humidified in order to keep the membrane sufficiently hydrated and enhance its protonic conductivity. A complex water transport and management issues arises, with water being generated at the cathode, and transported by means of different mechanisms through the cell. The degree of humidification required depends on the cell design and membrane type. For example, thinner membranes such as Nafion-111 present a better cathode to anode water transport via diffusion. Water management is one of the most active research fields in PEM Fuel Cells, and detailed reviews can be found in the work of Dai et al. (Dai et al., 2009) and Jiao and Li (Jiao & Li, 2011).

The real potential obtained in a fuel cell is always less than the theoretical maximum, as certain irreversible losses exist. The main contributions to the losses are (Barbir, 2005; Mench 2008):


Activation losses area caused the activation energy needed for the electrochemical reactions at the electrodes. The kinetics of the reactions results in part of the voltage generated being used as driving force for the chemical reaction.

Fluid Flow in Polymer Electrolyte Membrane Fuel Cells 271

mechanism, the third term represents the transport of φ by diffusion, and the fourth term

The different transport equations are assembled by using the appropriate variables, as

x-momentum u (velocity in x-direction) y-momentum v (velocity in y-direction) z-momentum w (velocity in z-direction) Energy h (enthalpy) Chemical specie i yi (mass fraction of i)

There are different types of flow field designs for Bipolar Plates. Pin-type and parallel flow fields are found in many fuel cells, although the most widely used design in industry is the serpentine flow field (Li & Sabir, 2005). Some experimental techniques are available for flow visualization in Bipolar Plates (Barreras et al., 2005), but numerical modelling has been established as a powerful tool for flow analysis and cell components design (Djilali, 2007). For example, Fig. 4 presents CFD results for the flow distribution in the channels of a parallel flow field Bipolar Plate. The corresponding pressure fields are depicted in Fig. 5. Preferential paths that may lead to an uneven reactant distribution over the electrode are clearly observed, enabling the researcher to redesign the flow field for the cell improvement. The results correspond to the work done by Iranzo et al. (Iranzo et al, 2010, 2011a), where a commercial 50 cm2 fuel cell was modelled by means of Computational Fluid Dynamics (CFD), and the numerical results were experimentally validated in a test station for different bipolar plate designs and operating conditions, using the real cells. The details of the CFD model, simulation, and results validation can be found in Iranzo et

Fig. 4. Computational Fluid Dynamics simulation of the velocity distribution in a 50 cm2 Bipolar Plate with parallel flow field design (cathode side). Left: 100 mA/cm2. Right: 600

Equation Variable φ Continuity 1

represents the source (or sink) of φ.

Table 1. Main transport equations

al. (Iranzo et al, 2010, 2011a).

mA/cm2.

shown in Table 1.

Therefore these losses depend on the reactions taking place, the properties of the electro-catalyst material and its microstructure, among others.


The voltage drop caused by ohmic losses represents the resistance to the flow of electrons through the materials and contact resistance, and the ionic resistance in the electrolyte. This is mainly proportional to the current density, and also depends on the material properties, cell geometry and working temperature.


Both fuel and oxidant must be transported to the electrodes surface as they are being consumed. There are transport limitations depending of the current density, reactant activity and electrode and GDL microstructure, and therefore the concentration of the reactants at the surface of the electrodes is reduced. At high current densities where water generation at the cathode is significant, liquid water being transported through the catalyst layer and GDL partially blocks the pores and the catalyst sites (flooding), thus leading to a limitation in the oxygen transport and reaction. This is considerably affecting the output voltage lowering the performance of the cell at high current densities (Li et al., 2008).

The high degree of coupling between all of the processes occurring within the cell makes necessary an overall approach for the analysis of the fuel cell. A well-established approach must account for all these processes, otherwise severe errors in the design can occur. For example, consider a design criteria based on the reactant transport from the channel to the catalytic layer. If no current transport is considered, no electric contact resistance between the GDL and the BP will be included in the study, and therefore the designer will probably reach the conclusion that a high channel-to land ratio optimises the performance. However, with a too high channel-to land ratio, the electric contact resistance between GDL and BP is increasing and the cell performance drops significantly.

The following subsections provide an insight into the main fluid flow phenomena within a single cell.

#### **3.2 Fluid flow in the bipolar plate channels**

The fluid flow in Bipolar Plate channels is always laminar in PEM Fuel Cells given the low Reynolds number found, generally in the range 50-500.

$$\text{Re} = \rho \text{VD/} \text{\(\mu\)}\tag{4}$$

where Re is the Reynolds number (dimensionless), ρ and μ are the fluid density and dynamic viscosity, V is the fluid velocity and D the channel hydraulic diameter. For anode and cathode, channel square section is around 1 mm x 1mm, with gas velocities in the range 0.1-5 m/s. Laminar flow is therefore found in the flow field of Bipolar Plates.

The equations governing the general fluid flow are the Navier-Stokes equations, also known as conservation or transport equations, which can be written in its general form as:

$$\frac{\partial}{\partial t} \int\_{V} \rho \Phi dV + \oint\_{A} \rho \Phi V \cdot dA = \oint\_{A} \Gamma \nabla \Phi \cdot dA + \int\_{V} \text{ S}\_{\Psi} dV \tag{5}$$

Where φ is the transported quantity, t is the time, A the superficial area, V the volume, Γ is transported quantity diffusivity, and Sφ is the source of φ. The first term in the equation corresponds to the transient transport of φ, the second term to the transport by convection

electro-catalyst material and its microstructure, among others.

material properties, cell geometry and working temperature.


densities (Li et al., 2008).

single cell.

increasing and the cell performance drops significantly.

Reynolds number found, generally in the range 50-500.

**3.2 Fluid flow in the bipolar plate channels** 

�


Therefore these losses depend on the reactions taking place, the properties of the

The voltage drop caused by ohmic losses represents the resistance to the flow of electrons through the materials and contact resistance, and the ionic resistance in the electrolyte. This is mainly proportional to the current density, and also depends on the

Both fuel and oxidant must be transported to the electrodes surface as they are being consumed. There are transport limitations depending of the current density, reactant activity and electrode and GDL microstructure, and therefore the concentration of the reactants at the surface of the electrodes is reduced. At high current densities where water generation at the cathode is significant, liquid water being transported through the catalyst layer and GDL partially blocks the pores and the catalyst sites (flooding), thus leading to a limitation in the oxygen transport and reaction. This is considerably affecting the output voltage lowering the performance of the cell at high current

The high degree of coupling between all of the processes occurring within the cell makes necessary an overall approach for the analysis of the fuel cell. A well-established approach must account for all these processes, otherwise severe errors in the design can occur. For example, consider a design criteria based on the reactant transport from the channel to the catalytic layer. If no current transport is considered, no electric contact resistance between the GDL and the BP will be included in the study, and therefore the designer will probably reach the conclusion that a high channel-to land ratio optimises the performance. However, with a too high channel-to land ratio, the electric contact resistance between GDL and BP is

The following subsections provide an insight into the main fluid flow phenomena within a

The fluid flow in Bipolar Plate channels is always laminar in PEM Fuel Cells given the low

where Re is the Reynolds number (dimensionless), ρ and μ are the fluid density and dynamic viscosity, V is the fluid velocity and D the channel hydraulic diameter. For anode and cathode, channel square section is around 1 mm x 1mm, with gas velocities in the range

The equations governing the general fluid flow are the Navier-Stokes equations, also known

Where φ is the transported quantity, t is the time, A the superficial area, V the volume, Γ is transported quantity diffusivity, and Sφ is the source of φ. The first term in the equation corresponds to the transient transport of φ, the second term to the transport by convection

�� � �∅�� � <sup>+</sup> <sup>∮</sup> �∅� � �� � � <sup>∮</sup> ��∅ � �� � <sup>+</sup> � �∅�� � (5)

0.1-5 m/s. Laminar flow is therefore found in the flow field of Bipolar Plates.

as conservation or transport equations, which can be written in its general form as:

Re = ρVD/μ (4)

mechanism, the third term represents the transport of φ by diffusion, and the fourth term represents the source (or sink) of φ.

The different transport equations are assembled by using the appropriate variables, as shown in Table 1.


Table 1. Main transport equations

There are different types of flow field designs for Bipolar Plates. Pin-type and parallel flow fields are found in many fuel cells, although the most widely used design in industry is the serpentine flow field (Li & Sabir, 2005). Some experimental techniques are available for flow visualization in Bipolar Plates (Barreras et al., 2005), but numerical modelling has been established as a powerful tool for flow analysis and cell components design (Djilali, 2007). For example, Fig. 4 presents CFD results for the flow distribution in the channels of a parallel flow field Bipolar Plate. The corresponding pressure fields are depicted in Fig. 5. Preferential paths that may lead to an uneven reactant distribution over the electrode are clearly observed, enabling the researcher to redesign the flow field for the cell improvement. The results correspond to the work done by Iranzo et al. (Iranzo et al, 2010, 2011a), where a commercial 50 cm2 fuel cell was modelled by means of Computational Fluid Dynamics (CFD), and the numerical results were experimentally validated in a test station for different bipolar plate designs and operating conditions, using the real cells. The details of the CFD model, simulation, and results validation can be found in Iranzo et al. (Iranzo et al, 2010, 2011a).

Fig. 4. Computational Fluid Dynamics simulation of the velocity distribution in a 50 cm2 Bipolar Plate with parallel flow field design (cathode side). Left: 100 mA/cm2. Right: 600 mA/cm2.

Fluid Flow in Polymer Electrolyte Membrane Fuel Cells 273

Fig. 6. Computational Fluid Dynamics simulation of the liquid water saturation (liquid water mass fraction) in a 50 cm2 PEMFC with parallel flow field design (cathode side) operating at 600 mA/cm2. Left: CL-GDL interface. Right: GDL-channel interface.

**3.3 Fluid flow in the porous components: Gas diffusion layer and catalytic layer**  The modelling of flow in porous media is a key issue in fuel cells, as both GDL and catalytic layers are porous materials. Typically, the porous media is represented by adding a negative source in the momentum equations, so that a pressure drop is generated accordingly. The consequent flow acceleration produced by the volume blockage or porosity can be accounted for. The source term is decomposed in two parts as in Eq. (6), the first one representing the viscous loss as in Darcy´s law, and the second one

ଶܥ ݒ <sup>ఈ</sup>

where Si is the source term in i direction, α is the permeability, µ the kinematic viscosity, ρ the fluid density, C2 the inertial resistance factor, vi the velocity in i direction and vmag the velocity magnitude. For the velocity ranges typically found in fuel cell GDL and catalytic

One of the main transport mechanisms within the cell porous components is diffusion. Binary diffusion is generally considered, although multicomponent diffusion (Maxwell-Stefan diffusion) is also used for non-dilute mixtures with more than two components. The need for an effective diffusivity stems from the fact that porous media presents important geometric restrictions (pores, etc.). The Bruggemann correction is the most used

 Deff = ε1.5 D (7) The pores of the catalyst layer (CL) and the Microporous layer (MPL, a fine layer serving as an effective interface between CL and GDL) are significantly smaller than the pores in the GDL. In such porous media where the continuum regime can be not valid (when Kn>1), it is

ଵ

(6) ቁݒݒߩ <sup>ଶ</sup>

ܵ ൌെቀ<sup>ఓ</sup>

correction factor for the diffusion coefficient (Sundén & Faghri, 2005), where:

representing inertial losses.

**3.3.1 Diffusion mechanisms** 

layers only the viscous loss is significant.

Fig. 5. Computational Fluid Dynamics simulation of pressure distribution in a 50 cm2 Bipolar Plate with parallel flow field design (cathode side). Left: 100 mA/cm2. Right: 600 mA/cm2.

However, as the physical and electrochemical phenomena within a fuel cell is highly coupled, it is in general necessary to work with a more complete model considering the fundamental phenomena, in order to accurately represent the cell.

For that, the N-S equations listed above (Eq. 5) can be augmented to account for different physical and chemical phenomena relevant to fuel cells such as electrochemistry, flow in porous media and multiphase flow. An excellent review on computational heat and mass transfer modelling for PEMFCs is found in the work by Siegel (Siegel, 2008).

#### **3.2.1 Multiphase flow in the bipolar plate channels**

The flow in the Bipolar Plate channels is not always a single flow problem. Especially at high current densities the water generation (Eq. 2, Eq. 3) can be large enough for establishing a two-phase flow. This is particularly important in the catalyst layer and GDL, as the liquid water blocks the catalyst sites and GDL pores, inducing a high resistance for the oxygen transport. Regarding the channels, liquid water emerges from the GDL and enters the channel in the form of droplets. A complex droplet dynamics is established then in the channel, where the water is dragged by the reactant flow towards the exit. Depending on the gas flow rate and the wall contact angle, the flow regime in the channel can be a mist, a plug or slug flow, or a film flow. Liquid water must be efficiently evacuated from the cell, in order to ensure an adequate path for the oxygen to reach the catalyst sites. The two-phase flow can be visualized by means of advanced experimental techniques such as neutron imaging (Park et al., 2008; Wu et al., 2008b), but again Computational Fluid Dynamics is used by many researchers for the investigation of twophase flow in fuel cells, although it is one of the most complex modelling tasks currently (Wang, 2004).

Fig.6 presents results for the liquid water concentration in a fuel cell with parallel flow field. This particular flow field design is known to be inadequate for handling liquid water, as droplets typically collapse one of the channels (red spots in the Fig. 6), the gas flow finds a high local resistance, and as other channels are still empty the flow is unable to flush the accumulated water (Li & Sabir, 2005).

Fig. 5. Computational Fluid Dynamics simulation of pressure distribution in a 50 cm2 Bipolar Plate with parallel flow field design (cathode side). Left: 100 mA/cm2. Right: 600

fundamental phenomena, in order to accurately represent the cell.

**3.2.1 Multiphase flow in the bipolar plate channels** 

transfer modelling for PEMFCs is found in the work by Siegel (Siegel, 2008).

However, as the physical and electrochemical phenomena within a fuel cell is highly coupled, it is in general necessary to work with a more complete model considering the

For that, the N-S equations listed above (Eq. 5) can be augmented to account for different physical and chemical phenomena relevant to fuel cells such as electrochemistry, flow in porous media and multiphase flow. An excellent review on computational heat and mass

The flow in the Bipolar Plate channels is not always a single flow problem. Especially at high current densities the water generation (Eq. 2, Eq. 3) can be large enough for establishing a two-phase flow. This is particularly important in the catalyst layer and GDL, as the liquid water blocks the catalyst sites and GDL pores, inducing a high resistance for the oxygen transport. Regarding the channels, liquid water emerges from the GDL and enters the channel in the form of droplets. A complex droplet dynamics is established then in the channel, where the water is dragged by the reactant flow towards the exit. Depending on the gas flow rate and the wall contact angle, the flow regime in the channel can be a mist, a plug or slug flow, or a film flow. Liquid water must be efficiently evacuated from the cell, in order to ensure an adequate path for the oxygen to reach the catalyst sites. The two-phase flow can be visualized by means of advanced experimental techniques such as neutron imaging (Park et al., 2008; Wu et al., 2008b), but again Computational Fluid Dynamics is used by many researchers for the investigation of twophase flow in fuel cells, although it is one of the most complex modelling tasks currently

Fig.6 presents results for the liquid water concentration in a fuel cell with parallel flow field. This particular flow field design is known to be inadequate for handling liquid water, as droplets typically collapse one of the channels (red spots in the Fig. 6), the gas flow finds a high local resistance, and as other channels are still empty the flow is unable to flush the

mA/cm2.

(Wang, 2004).

accumulated water (Li & Sabir, 2005).

Fig. 6. Computational Fluid Dynamics simulation of the liquid water saturation (liquid water mass fraction) in a 50 cm2 PEMFC with parallel flow field design (cathode side) operating at 600 mA/cm2. Left: CL-GDL interface. Right: GDL-channel interface.

#### **3.3 Fluid flow in the porous components: Gas diffusion layer and catalytic layer**

The modelling of flow in porous media is a key issue in fuel cells, as both GDL and catalytic layers are porous materials. Typically, the porous media is represented by adding a negative source in the momentum equations, so that a pressure drop is generated accordingly. The consequent flow acceleration produced by the volume blockage or porosity can be accounted for. The source term is decomposed in two parts as in Eq. (6), the first one representing the viscous loss as in Darcy´s law, and the second one representing inertial losses.

$$\mathcal{S}\_l = -\left(\frac{\mu}{a}\upsilon\_l + \mathcal{C}\_2 \frac{1}{2}\rho v\_{mag}\upsilon\_l\right) \tag{6}$$

where Si is the source term in i direction, α is the permeability, µ the kinematic viscosity, ρ the fluid density, C2 the inertial resistance factor, vi the velocity in i direction and vmag the velocity magnitude. For the velocity ranges typically found in fuel cell GDL and catalytic layers only the viscous loss is significant.

#### **3.3.1 Diffusion mechanisms**

One of the main transport mechanisms within the cell porous components is diffusion. Binary diffusion is generally considered, although multicomponent diffusion (Maxwell-Stefan diffusion) is also used for non-dilute mixtures with more than two components.

The need for an effective diffusivity stems from the fact that porous media presents important geometric restrictions (pores, etc.). The Bruggemann correction is the most used correction factor for the diffusion coefficient (Sundén & Faghri, 2005), where:

$$\mathbf{D}\_{\rm eff} = \mathbf{g}^{1.5} \,\mathrm{D} \tag{7}$$

The pores of the catalyst layer (CL) and the Microporous layer (MPL, a fine layer serving as an effective interface between CL and GDL) are significantly smaller than the pores in the GDL. In such porous media where the continuum regime can be not valid (when Kn>1), it is

Fluid Flow in Polymer Electrolyte Membrane Fuel Cells 275

Where σ is the surface tension, ε is the porosity, θc is the contact angle and K is the absolute

Such approach enables the modelling of various physical processes such as condensation, vaporization, capillary diffusion, and surface tension. Also the blocking of the porous media and the flooding of the reaction surface can be modelled by multiplying the porosity and the

The saturation model presented here is used by a number of groups, although it misses the main phenomena associated to liquid water transport and multiphase flow effects. The saturation model is in fact an enhanced multicomponent flow model, where different

Other approaches for the modelling of water transport have been developed and applied by other research groups. Euler-Euler multiphase-flow is found in many fuel cell models

In order to solve the governing equations for the fuel cell it is required to implement expressions for the various transport properties, especially in the membrane. The membrane phase is usually modelled as a porous media. There are many physical properties that must be correctly modelled in order to predict the fuel cell behaviour with accuracy, in particular: gas phase diffusivities, electrical conductivity, water diffusivity, and osmotic drag

As seen in the modelling equations, the water content is a key variable. It represents a driving force and an integral part of PEMFC water management, and it is also a crucial parameter as almost all property expressions depends on it, such as conductivity. Because of the importance of water content, it has received more modelling attention than other membrane properties. Such models span from simple curve fits to more elaborate

There are different methods to determine the transport properties: empirically, semiempirically, or by means of modelling. The semi-empirical method is used by most models. In particular, the polynomial fit of Springer et al. (Springer et al., 1991) is used in many fuel

���0.04� + 1�.1�� − �9.���� + �6���(� < 1)

� � �� � � �� � � �� � ��

where λ is the membrane water content, and a is the water activity, defined as Pwv/Psat. The gas species diffusivities can be modelled as a function of the water saturation s in order to account for the pore blockage when liquid water is present. An expression is given in Um

�� � ��.�(1 − �)����

14 + 1.4(�−1)�(� > 1) (11)

(12)

species coexist in a single-phase medium, rather than a true multi-phase flow model.

�.� (1.42(1−�) − 2.12(1−�)� + 1.26(1−�)�)��� < 90°

�.� (1.42� − 2.12�� + 1.26��)��� > 90°

(10)

�� � ������� �� ��

active surface area by a factor (1- s), respectively.

**3.4 Membrane property models** 

permeability.

coefficient.

cell models:

chemically based models.

et al. (Um et al., 2000):

������ �� ��

reported in the literature, as well as Lattice-Boltzmann methods.

necessary to account for the Knudsen diffusion mechanism. The transition is determined by the Knudsen number:

$$\mathbf{Kn} = \lambda \wedge \mathbf{d}\_{\text{pore}} \tag{8}$$

The diffusion coefficient is then determined from the kinetic theory of gases (Sundén & Faghri, 2005).

#### **3.3.2 Multiphase flow in porous components: Capillary forces**

Multiphase flow on the cathode side represents a main concern for the practical operation and performance of a fuel cell, given the potential flooding of the porous CL and GDL, and represents currently one of the main areas of research in the field of PEM fuel cells.

PEM fuel cells operate under 100 °C, thus water vapour formed during the operation of the cell may condense to liquid water. This is especially true at higher current densities when the reaction rates are higher and therefore water production becomes important. An excess of reactant in the cathode side helps evacuating liquid water, but increases the parasitic power associated to gas compressors.

The production of water takes place in the cathode catalyst layer due to the oxygen reduction reaction (ORR). Another source of water is the humidification of the reactants. Different transport mechanisms through the membrane are available for water: electroosmotic drag, proportional to the protonic flux, and diffusion, proportional to the water molar concentration gradient. Both effects operate in opposite directions and a correct water management implies a zero net water transport so that membrane and electrodes becomes neither flooded nor dried-out. Water management depends as well on the membrane thickness. Thin membranes such as Gore or Nafion-111 enhances the water back-diffusion from cathode to anode, but thick membranes such as Nafion-112 or 117 reduces the diffusion transport.

A correct amount of water is needed to keep the membrane hydrated, but excessive water blocks the porous media and reduces the mass transport rate by diffusion and also reduces the active reacting surface area, and therefore the cell performance. This is why correctly modelling water formation and transport is a key issue in predicting the cell behaviour with accuracy. Different types of multi-phase models have been used in the literature, such as the mixture model, the multifluid model, and the saturation model. A complete revision of the different modelling approaches can be found in the work by Wang (Wang, 2004). One of the modelling approaches is the saturation model, where a multi-component single phase system is resolved, with an additional equation accounting for the liquid saturation. The conservation equation for the liquid water volume fraction or water saturation, s, is solved:

$$\frac{\partial(\varepsilon\rho\_l\mathbf{s})}{\partial t} + \nabla \cdot \left(\rho\_l \overrightarrow{V\_l}\mathbf{s}\right) = r\_{\mathbf{w}}\tag{9}$$

where the subscript l stands for liquid water, and rw is the condensation rate, modelled as a function of the difference between vapour partial pressure and saturation pressure.

As a first approach the liquid velocity Vl can be assumed to be equivalent to the gas velocity inside the gas channel, so that the liquid droplets would be a fine mist. Inside the porous zones the use of the capillary diffusion term allows the replacement of the convective term in Equation (9).

The capillary pressure can be calculated as a function of s, depending on the wetting phase:

necessary to account for the Knudsen diffusion mechanism. The transition is determined by

 Kn = λ / dpore (8) The diffusion coefficient is then determined from the kinetic theory of gases (Sundén &

Multiphase flow on the cathode side represents a main concern for the practical operation and performance of a fuel cell, given the potential flooding of the porous CL and GDL, and

PEM fuel cells operate under 100 °C, thus water vapour formed during the operation of the cell may condense to liquid water. This is especially true at higher current densities when the reaction rates are higher and therefore water production becomes important. An excess of reactant in the cathode side helps evacuating liquid water, but increases the parasitic

The production of water takes place in the cathode catalyst layer due to the oxygen reduction reaction (ORR). Another source of water is the humidification of the reactants. Different transport mechanisms through the membrane are available for water: electroosmotic drag, proportional to the protonic flux, and diffusion, proportional to the water molar concentration gradient. Both effects operate in opposite directions and a correct water management implies a zero net water transport so that membrane and electrodes becomes neither flooded nor dried-out. Water management depends as well on the membrane thickness. Thin membranes such as Gore or Nafion-111 enhances the water back-diffusion from cathode to anode, but thick membranes such as Nafion-112 or 117

A correct amount of water is needed to keep the membrane hydrated, but excessive water blocks the porous media and reduces the mass transport rate by diffusion and also reduces the active reacting surface area, and therefore the cell performance. This is why correctly modelling water formation and transport is a key issue in predicting the cell behaviour with accuracy. Different types of multi-phase models have been used in the literature, such as the mixture model, the multifluid model, and the saturation model. A complete revision of the different modelling approaches can be found in the work by Wang (Wang, 2004). One of the modelling approaches is the saturation model, where a multi-component single phase system is resolved, with an additional equation accounting for the liquid saturation. The conservation equation for the liquid water volume fraction or water saturation, s, is solved:

where the subscript l stands for liquid water, and rw is the condensation rate, modelled as a

As a first approach the liquid velocity Vl can be assumed to be equivalent to the gas velocity inside the gas channel, so that the liquid droplets would be a fine mist. Inside the porous zones the use of the capillary diffusion term allows the replacement of the convective term

The capillary pressure can be calculated as a function of s, depending on the wetting phase:

function of the difference between vapour partial pressure and saturation pressure.

డ௧ ൫ߩܸ ሬሬሬԦݏ൯ ൌ ݎ௪ (9)

డሺఌఘ௦ሻ

represents currently one of the main areas of research in the field of PEM fuel cells.

**3.3.2 Multiphase flow in porous components: Capillary forces** 

the Knudsen number:

power associated to gas compressors.

reduces the diffusion transport.

in Equation (9).

Faghri, 2005).

$$p\_c = \begin{cases} \frac{\sigma \cos \theta\_c}{\binom{K}{c}^{0.5}} \{1.42(1-\text{s}) - 2.12(1-\text{s})^2 + 1.26(1-\text{s})^3\} \, \theta\_c < 90^\circ\\ \frac{\sigma \cos \theta\_c}{\binom{K}{c}^{0.5}} \{1.42\text{s} - 2.12\text{s}^2 + 1.26\text{s}^3\} \, \theta\_c > 90^\circ \end{cases} \tag{10}$$

Where σ is the surface tension, ε is the porosity, θc is the contact angle and K is the absolute permeability.

Such approach enables the modelling of various physical processes such as condensation, vaporization, capillary diffusion, and surface tension. Also the blocking of the porous media and the flooding of the reaction surface can be modelled by multiplying the porosity and the active surface area by a factor (1- s), respectively.

The saturation model presented here is used by a number of groups, although it misses the main phenomena associated to liquid water transport and multiphase flow effects. The saturation model is in fact an enhanced multicomponent flow model, where different species coexist in a single-phase medium, rather than a true multi-phase flow model.

Other approaches for the modelling of water transport have been developed and applied by other research groups. Euler-Euler multiphase-flow is found in many fuel cell models reported in the literature, as well as Lattice-Boltzmann methods.

#### **3.4 Membrane property models**

In order to solve the governing equations for the fuel cell it is required to implement expressions for the various transport properties, especially in the membrane. The membrane phase is usually modelled as a porous media. There are many physical properties that must be correctly modelled in order to predict the fuel cell behaviour with accuracy, in particular: gas phase diffusivities, electrical conductivity, water diffusivity, and osmotic drag coefficient.

As seen in the modelling equations, the water content is a key variable. It represents a driving force and an integral part of PEMFC water management, and it is also a crucial parameter as almost all property expressions depends on it, such as conductivity. Because of the importance of water content, it has received more modelling attention than other membrane properties. Such models span from simple curve fits to more elaborate chemically based models.

There are different methods to determine the transport properties: empirically, semiempirically, or by means of modelling. The semi-empirical method is used by most models. In particular, the polynomial fit of Springer et al. (Springer et al., 1991) is used in many fuel cell models:

$$
\lambda = \begin{cases}
0.043 + 17.18a - 39.85a^2 + 36a^3 \text{ ( $a < 1$ )} \\
14 + 1.4(a - 1) \text{ ( $a > 1$ )}
\end{cases}
\tag{11}
$$

where λ is the membrane water content, and a is the water activity, defined as Pwv/Psat. The gas species diffusivities can be modelled as a function of the water saturation s in order to account for the pore blockage when liquid water is present. An expression is given in Um et al. (Um et al., 2000):

$$D\_l = \varepsilon^{1.5} (1 - s)^{r\_s} D\_l^0 \left(\frac{p\_o}{p}\right)^{\chi\_p} \left(\frac{T}{T\_0}\right)^{\chi\_t} \tag{12}$$

Fluid Flow in Polymer Electrolyte Membrane Fuel Cells 277

In terms of the region of interest, numerical simulation can be divided into modelling at the electrode level or micro-modelling, or at cell or stack level (macro-modelling). The microscopic models provide the fundamental understanding of processes like diffusion and conduction in the membrane on a single-pore or even molecular level. They allow for the evaluation of small perturbations like pores heterogeneity as well as the incorporation of small-scale effects. Such models require a lot more knowledge of the microstructure. To allow modelling of entire PEFC behaviour, macroscopic models are more commonly used, where some microscopic details are included in the model. Computational Fluid Dynamics works at macro-modelling level, aiming at the optimization of different design alternatives and determining operational strategies, incorporating built-in models for the electrochemical performance of the given electrodes and electrolytes. CFD models work either for 2D or 3D problems, where during the last years a high increase in the number of

3D models allows for a complete representation of the real fuel cell geometry, thus enabling for the evaluation of different cell geometries and for the understanding of the influence of operating conditions. Given the wide range of possible geometries and operating parameters that influence the fuel cell performance, the use of a model representing the key physical and chemical characteristics of fuel cells is in general necessary for the optimization of cell design under specific application requirements. In all 3D models, the geometry is discretised into finite elements or volumes, and different physical and chemical properties

As discussed, single cell models are preferred for CFD analysis given the computing power requirements. Models thus focus on the representation of unit cells without considering stack or manifolding effects. However, their complexity is high as they consider in different degrees of detail the coupling between the different physical, chemical and electrochemical

A considerable body of literature exists for the modelling and simulation PEM fuel cells, as summarized in excellent review articles from Yao et al. (Yao et al., 2004), Biyikoglu (Biyikoglu, 2005), Cheddie and Munroe (Cheddie & Munroe, 2005), Siegel (Siegel, 2008), Djilali (Djillai, 2007), Weber and Newman (Weber & Newman, 2004), and Wang (Wang,

Wang (Wang, 2004) states the necessary steps in the development of the so-called CFCD

All these fronts must be developed in order to reach CFD models with a high degree of accuracy, confidence, and direct applicability to the understanding and design of

Fuel cell modelling comprises a tightly coupled combination of different physical and chemical phenomena: fluid flow, flow in porous media, multiphase flow, capillary forces, electrochemical reactions, heat transfer, membrane properties, etc., mostly acting in very small space and time scales. Experimental techniques are sometimes limited due to the small scales to be resolved, but however very detailed and useful information can be obtained.

(Computational Fuel Cell Dynamics) or CFD Fuel Cell modelling. The steps are:

3D models have been reported in the literature.

are assigned to the regions of the cell components.

phenomena occurring in a fuel cell.



**3.6.2 Experimental techniques for PEM fuel cells** 

advanced fuel cells.

2004).

where Di is the diffusivity of species i at reference temperature and pressure (P0, T0). The exponents and the pore blockage rs are model parameters. Nam and Kaviany (Nam & Kaviany, 2003) provides a detailed discussion on the values of rs.

The membrane electric conductivity can be modelled with the expression:

$$
\sigma\_{mem} = \varepsilon (0.514\lambda - 0.326)e^{126\theta\left(\frac{1}{303} - \frac{1}{7}\right)}\tag{13}
$$

where λ is the water content. The membrane osmotic drag coefficient follows the expression:

$$a\_d = 2.5 \frac{\lambda}{22} \tag{14}$$

#### **3.5 Transient effects**

Transient phenomena, such as the dynamic response of the cell with a load change or the cell start-up, adds additional challenges to the analysis of the flow and cell performance.

The different time scales associated with the main processes occurring within the cell must be considered. In fuel cells, the water transport phenomena are presenting larger timescales than electrochemical, mass transport, or gas flow timescales. Wang (Wang, 2004) compares the timescales for the different phenomena: the time constant for the electrochemical reaction is known to be typically in the range of micro- and milliseconds. Electrochemical reaction timescales can also be determined experimentally (Iranzo et al, 2011b). The time constant for the transport of the reactant gas through the GDL is estimated by its diffusion time:

$$
\pi\_{\rm MT} = \delta\_{\rm GDF}^2 \Big/ \mathcal{D}\_{\rm g} \tag{15}
$$

Where δGDL is the GDL thickness and Dg is the diffusion coefficient. For typical cells, the time constant is in the range between 0.1 and 1 s as stated by Wang (Wang, 2004). Finally, the time constant for the membrane hydration process, associated to multiphase and water transport effects, can be estimated by (Wang, 2004):

$$
\pi\_H = \frac{\rho \mathcal{S}\_m \Delta \mathcal{X}}{E \mathcal{W}} \Bigg/ \left(\frac{I}{2F}\right) \tag{16}
$$

Where EW is the membrane equivalent weight, I the intensity, F the Faraday constant, δ<sup>m</sup> the membrane thickness, and λ the water content. This results in a typical time constant of several seconds.

Therefore, the differences in the physical and chemical phenomena timescales in a fuel cell are at least within a 103 range.

#### **3.6 Numerical and experimental analysis of fluid flow in PEM fuel cells**

The main tools available for the analysis of the fluid flow inside fuel cells are the numerical modelling of the system and specific experimental techniques.

#### **3.6.1 Numerical modelling of PEM fuel cells**

Fuel cell modelling has received much attention over the past 15 years in an attempt to better understand the phenomena occurring within the cell.

Models can be used for a wide range of situations and problems within fuel cells, from very simple pre-dimensioning models to complex three-dimensional models covering different physical and chemical phenomena. Therefore, very different models have been developed.

where Di is the diffusivity of species i at reference temperature and pressure (P0, T0). The exponents and the pore blockage rs are model parameters. Nam and Kaviany (Nam &

���� = �(�.5��� � �.�2�)������ �

where λ is the water content. The membrane osmotic drag coefficient follows the expression:

�� = 2.5 �

Transient phenomena, such as the dynamic response of the cell with a load change or the cell start-up, adds additional challenges to the analysis of the flow and cell performance. The different time scales associated with the main processes occurring within the cell must be considered. In fuel cells, the water transport phenomena are presenting larger timescales than electrochemical, mass transport, or gas flow timescales. Wang (Wang, 2004) compares the timescales for the different phenomena: the time constant for the electrochemical reaction is known to be typically in the range of micro- and milliseconds. Electrochemical reaction timescales can also be determined experimentally (Iranzo et al, 2011b). The time constant for

2

Where δGDL is the GDL thickness and Dg is the diffusion coefficient. For typical cells, the time constant is in the range between 0.1 and 1 s as stated by Wang (Wang, 2004). Finally, the time constant for the membrane hydration process, associated to multiphase and water

2

*EW F*

<sup>Δ</sup> <sup>=</sup>

Where EW is the membrane equivalent weight, I the intensity, F the Faraday constant, δ<sup>m</sup> the membrane thickness, and λ the water content. This results in a typical time constant of

Therefore, the differences in the physical and chemical phenomena timescales in a fuel cell

The main tools available for the analysis of the fluid flow inside fuel cells are the numerical

Fuel cell modelling has received much attention over the past 15 years in an attempt to

Models can be used for a wide range of situations and problems within fuel cells, from very simple pre-dimensioning models to complex three-dimensional models covering different physical and chemical phenomena. Therefore, very different models have been developed.

*I*

 δ

the transport of the reactant gas through the GDL is estimated by its diffusion time:

*<sup>m</sup> <sup>H</sup>*

τ

**3.6 Numerical and experimental analysis of fluid flow in PEM fuel cells** 

modelling of the system and specific experimental techniques.

better understand the phenomena occurring within the cell.

**3.6.1 Numerical modelling of PEM fuel cells** 

ρδ λ

τ

transport effects, can be estimated by (Wang, 2004):

����� ��

(13)

�� (14)

*MT GDL g* = *D* (15)

(16)

Kaviany, 2003) provides a detailed discussion on the values of rs.

**3.5 Transient effects** 

several seconds.

are at least within a 103 range.

The membrane electric conductivity can be modelled with the expression:

In terms of the region of interest, numerical simulation can be divided into modelling at the electrode level or micro-modelling, or at cell or stack level (macro-modelling). The microscopic models provide the fundamental understanding of processes like diffusion and conduction in the membrane on a single-pore or even molecular level. They allow for the evaluation of small perturbations like pores heterogeneity as well as the incorporation of small-scale effects. Such models require a lot more knowledge of the microstructure. To allow modelling of entire PEFC behaviour, macroscopic models are more commonly used, where some microscopic details are included in the model. Computational Fluid Dynamics works at macro-modelling level, aiming at the optimization of different design alternatives and determining operational strategies, incorporating built-in models for the electrochemical performance of the given electrodes and electrolytes. CFD models work either for 2D or 3D problems, where during the last years a high increase in the number of 3D models have been reported in the literature.

3D models allows for a complete representation of the real fuel cell geometry, thus enabling for the evaluation of different cell geometries and for the understanding of the influence of operating conditions. Given the wide range of possible geometries and operating parameters that influence the fuel cell performance, the use of a model representing the key physical and chemical characteristics of fuel cells is in general necessary for the optimization of cell design under specific application requirements. In all 3D models, the geometry is discretised into finite elements or volumes, and different physical and chemical properties are assigned to the regions of the cell components.

As discussed, single cell models are preferred for CFD analysis given the computing power requirements. Models thus focus on the representation of unit cells without considering stack or manifolding effects. However, their complexity is high as they consider in different degrees of detail the coupling between the different physical, chemical and electrochemical phenomena occurring in a fuel cell.

A considerable body of literature exists for the modelling and simulation PEM fuel cells, as summarized in excellent review articles from Yao et al. (Yao et al., 2004), Biyikoglu (Biyikoglu, 2005), Cheddie and Munroe (Cheddie & Munroe, 2005), Siegel (Siegel, 2008), Djilali (Djillai, 2007), Weber and Newman (Weber & Newman, 2004), and Wang (Wang, 2004).

Wang (Wang, 2004) states the necessary steps in the development of the so-called CFCD (Computational Fuel Cell Dynamics) or CFD Fuel Cell modelling. The steps are:


All these fronts must be developed in order to reach CFD models with a high degree of accuracy, confidence, and direct applicability to the understanding and design of advanced fuel cells.

#### **3.6.2 Experimental techniques for PEM fuel cells**

Fuel cell modelling comprises a tightly coupled combination of different physical and chemical phenomena: fluid flow, flow in porous media, multiphase flow, capillary forces, electrochemical reactions, heat transfer, membrane properties, etc., mostly acting in very small space and time scales. Experimental techniques are sometimes limited due to the small scales to be resolved, but however very detailed and useful information can be obtained.

Fluid Flow in Polymer Electrolyte Membrane Fuel Cells 279

the cathode and manifolds for discharge of gases (hydrogen and air or oxygen). The design of these manifolds is one of most difficult engineering design in fuel cell stacks. The



Another design issue is the need to remove the heat produced by a PEM fuel cell, and prevent a too high increase of the temperature in the stack. Therefore it is necessary to use a refrigerant flow like air or water. For this reason, an additional plate is inserted to provide a coolant path between each cell, or the cooling path could be integrated in to the bipolar plate. The result is a block in which the electric current must pass efficiently

An important approach to determine the flow and the pressure distribution within the stack is the flow network analysis. Various authors (Baschuk & Li, 2004; Ma et al., 2002; Park & Li, 2006; Karimi et al., 2005; Chang et al., 2006; Kohn et al., 2003) have developed this type

Apart from ageing and durability issues, the performance degradation in a fuel cell stack is


The fuel cell performance is sensitive to the flow rate of reactants therefore it is necessary that each cell in a stack receives approximately the same amount of reactant gases. It is important that the manifolds that feed the gases to the cells and the manifolds that collect the unused gases are properly sized. The cross-sectional area of the manifolds determines the velocity of gas flow and the pressure drop. As a rule of thumb, the pressure drop through the manifolds should be an order of magnitude lower than the pressure drop

The problem of flow and pressure distribution within the stack is coupled, and for this reason the mass and pressure distribution must be solved simultaneously (Baschuk & Li, 2004). Some mathematical techniques and computer software have been developed for solving the problem of flow and pressure distribution within the stack (Baschuk & Li, 2004; Ma et al., 2022; Park & Li, 2006; Karimi et al., 2005; Chen et al., 2007; Chang et al.,

manifolds must have the following three characteristics (Mench, 2008):

plates in the stack.

**4.2 Flow network approach** 


2006; Kohn et al., 2003).

known to be caused by (Barbir, 2005):

of mathematic method to resolve this problem.



during handling and operation, including shocks and vibrations).

through each cell in order to ensure uniform flow distribution (Barbir, 2005).

through the cells.

Apart from the determination of the cell polarization curve, more detailed and advanced techniques are available for fuel cell research and design:


Electrochemical Impedance Spectroscopy (EIS) or AC Impedance consists of sending an AC signal through the cell and monitor the response signal for a wide range of frequencies. The signal is recorded by a Frequency Response Analyzer (FRA). The imaginary and real impedances of the signal can be plotted in a Nyquist diagram (ZIm vs ZRe), where the characteristics of the diagram can be interpreted in order to assess the different phenomena occurring within of the cell. At high frequencies, the value of ZRe at ZIm = 0 represents the total resistance of cell (electronic of the bulk materials and contact resistances, and protonic of the membrane). This value is known as High Frequency Resistance (HFR). The first semicircle at medium frequencies represents the charge transfer resistance of the electrochemical reaction, and the next semicircle at low frequencies represents the mass transport resistance of the reactant reaching the active sites of the electrode (Mench, 2008).

EIS can be used for a wide range of fuel cell research activities (Wu et al., 2008a; Fouquet et al., 2006), including the determination of diffusion and reactant mass transport within the porous media.


This technique consists of measuring the in-plane spatial distribution of the generated current. Different technologies are used, such as the printed circuit board approach using segmented current collectors, anode catalysts, and anode GDLs. Segmented cells are necessary as the uneven current distribution resulting at the reaction sites in the catalyst layers can quickly equalizes in the bipolar plates, especially if the conductivity in the in-plane direction is larger than in the through-plane direction. To map the current distribution the measurement must be taken using a segmented cell, where each segment is isolated from the others.

The current distribution measured in this way provides useful information about the local phenomena influencing the cell performance such as reactant starvation or electrode flooding (Higier & Liu, 2010; Hwnag et al., 2008).


Neutron imaging is a more sophisticated technique where a beam of neutrons are sent through the cell. A neutron detector provide the contrast necessary to image the hydrogen and water in the cell, allowing for real-time images that provides information about the water distribution within the cell (Park et al., 2008b; Wu et al., 2008).

#### **4. Fluid flow in fuel cell stacks**

#### **4.1 Description of a fuel cell stack: Main components**

A single PEM fuel cell can provide a voltage of 0,6 -0,8 V when drawing a useful current. In order to sufficiently increase the voltage for practical operation, many cells have to be connected in series. A collection of fuel cells in series is known as a ``stack´´. For stack, the total current is proportional to the active electrode area of each cell in the stack and it is the same through all cells. The total stack voltage is the sum of the individual cell voltage.

$$V\_{stack} = \Sigma\_{j=1}^{Ncell} V\_j \approx N\_{cell} V\_{cell} \tag{17}$$

One of the most important components in the stack are the manifolds. The stack has manifolds for feeding hydrogen over the anode, manifolds for feeding oxygen (or air) over

Apart from the determination of the cell polarization curve, more detailed and advanced

Electrochemical Impedance Spectroscopy (EIS) or AC Impedance consists of sending an AC signal through the cell and monitor the response signal for a wide range of frequencies. The signal is recorded by a Frequency Response Analyzer (FRA). The imaginary and real impedances of the signal can be plotted in a Nyquist diagram (ZIm vs ZRe), where the characteristics of the diagram can be interpreted in order to assess the different phenomena occurring within of the cell. At high frequencies, the value of ZRe at ZIm = 0 represents the total resistance of cell (electronic of the bulk materials and contact resistances, and protonic of the membrane). This value is known as High Frequency Resistance (HFR). The first semicircle at medium frequencies represents the charge transfer resistance of the electrochemical reaction, and the next semicircle at low frequencies represents the mass transport resistance of the reactant reaching the active sites of the electrode (Mench, 2008). EIS can be used for a wide range of fuel cell research activities (Wu et al., 2008a; Fouquet et al., 2006), including the determination of diffusion and reactant mass transport within the

This technique consists of measuring the in-plane spatial distribution of the generated current. Different technologies are used, such as the printed circuit board approach using segmented current collectors, anode catalysts, and anode GDLs. Segmented cells are necessary as the uneven current distribution resulting at the reaction sites in the catalyst layers can quickly equalizes in the bipolar plates, especially if the conductivity in the in-plane direction is larger than in the through-plane direction. To map the current distribution the measurement must be

The current distribution measured in this way provides useful information about the local phenomena influencing the cell performance such as reactant starvation or electrode

Neutron imaging is a more sophisticated technique where a beam of neutrons are sent through the cell. A neutron detector provide the contrast necessary to image the hydrogen and water in the cell, allowing for real-time images that provides information about the

A single PEM fuel cell can provide a voltage of 0,6 -0,8 V when drawing a useful current. In order to sufficiently increase the voltage for practical operation, many cells have to be connected in series. A collection of fuel cells in series is known as a ``stack´´. For stack, the total current is proportional to the active electrode area of each cell in the stack and it is the same through all cells. The total stack voltage is the sum of the individual cell voltage.

One of the most important components in the stack are the manifolds. The stack has manifolds for feeding hydrogen over the anode, manifolds for feeding oxygen (or air) over

��� � ���������� (17)

������ = ∑ �� �����

taken using a segmented cell, where each segment is isolated from the others.

water distribution within the cell (Park et al., 2008b; Wu et al., 2008).

**4.1 Description of a fuel cell stack: Main components** 

flooding (Higier & Liu, 2010; Hwnag et al., 2008).

**4. Fluid flow in fuel cell stacks** 

techniques are available for fuel cell research and design:


porous media.



the cathode and manifolds for discharge of gases (hydrogen and air or oxygen). The design of these manifolds is one of most difficult engineering design in fuel cell stacks. The manifolds must have the following three characteristics (Mench, 2008):


Another design issue is the need to remove the heat produced by a PEM fuel cell, and prevent a too high increase of the temperature in the stack. Therefore it is necessary to use a refrigerant flow like air or water. For this reason, an additional plate is inserted to provide a coolant path between each cell, or the cooling path could be integrated in to the bipolar plate. The result is a block in which the electric current must pass efficiently through the cells.

An important approach to determine the flow and the pressure distribution within the stack is the flow network analysis. Various authors (Baschuk & Li, 2004; Ma et al., 2002; Park & Li, 2006; Karimi et al., 2005; Chang et al., 2006; Kohn et al., 2003) have developed this type of mathematic method to resolve this problem.

#### **4.2 Flow network approach**

Apart from ageing and durability issues, the performance degradation in a fuel cell stack is known to be caused by (Barbir, 2005):


The fuel cell performance is sensitive to the flow rate of reactants therefore it is necessary that each cell in a stack receives approximately the same amount of reactant gases. It is important that the manifolds that feed the gases to the cells and the manifolds that collect the unused gases are properly sized. The cross-sectional area of the manifolds determines the velocity of gas flow and the pressure drop. As a rule of thumb, the pressure drop through the manifolds should be an order of magnitude lower than the pressure drop through each cell in order to ensure uniform flow distribution (Barbir, 2005).

The problem of flow and pressure distribution within the stack is coupled, and for this reason the mass and pressure distribution must be solved simultaneously (Baschuk & Li, 2004). Some mathematical techniques and computer software have been developed for solving the problem of flow and pressure distribution within the stack (Baschuk & Li, 2004; Ma et al., 2022; Park & Li, 2006; Karimi et al., 2005; Chen et al., 2007; Chang et al., 2006; Kohn et al., 2003).


$$
\dot{m}\_{ln}^{stack} = \Sigma\_{f=1}^{Ncell} \dot{m}\_{cell,in}^{J} \tag{18}
$$

$$
\dot{m}\_{top}^l = \dot{m}\_{ln}^{\text{stack}} - \sum\_{j=1}^{l} \dot{m}\_{cell,in}^j \tag{19}
$$

$$
\dot{m}\_{bottom}^{l} = \begin{cases}
\Sigma\_{j=1}^{l} \dot{m}\_{cell,out}^{l} \text{ for Z configuration} \\
\Sigma\_{j=1\pm 1}^{\text{Ncell}} \dot{m}\_{cell,out}^{l} \text{ for U configuration}
\end{cases}
\tag{20}
$$

$$
\hbar \dot{\mathfrak{m}}\_{cell,in}^{j} = \dot{\mathfrak{m}}\_{cell,out}^{j} - \Delta \dot{\mathfrak{m}}\_{consumed} \tag{21}
$$

$$
\Delta\dot{m}\_{\text{consumed}} = \begin{cases}
\frac{I\mathcal{A}\_{\text{cell}}}{2F}\mathcal{M}\_{\text{H}\_2} \text{ In the anode} \\
\frac{I\mathcal{A}\_{\text{cell}}}{4F}\mathcal{M}\_{\text{O}\_2} - \frac{I\mathcal{A}\_{\text{cell}}}{2F}\mathcal{M}\_{\text{H}\_2\text{O}} \text{ In the cathode}
\end{cases}
\tag{22}
$$

$$
\Delta P\_{cell}^{j} - \Delta P\_{top\,\,small\,\,fold}^{j} - \Delta P\_{cell}^{j+1} - \Delta P\_{bottom\,\,small\,\,fold}^{j} = 0 \text{ for } \text{U} \text{ configurational} \tag{23}
$$

$$
\Delta P\_{cell}^{f} - \Delta P\_{top\,\,manifold}^{f} - \Delta P\_{cell}^{f+1} + \Delta P\_{bottom\,\,manifold}^{f} = 0 \text{ for Z-configurations} \tag{24}
$$

$$
\Delta P = \Delta P\_m + \Delta P\_f \tag{25}
$$

$$
\Delta P\_m = \frac{m}{A\_{manfotd}} (\upsilon\_{out} - \upsilon\_{ln}) \tag{26}
$$

$$
\Delta P\_f = \frac{2C\_f L\_{manfold} \rho\_{ave} (v\_{ave})^2}{\theta\_h^{manfold}} \tag{27}
$$

$$\mathcal{C}\_{f} = \begin{cases} 16(Re\_{\theta\_{\hbar}})^{-1} \text{ if } Re\_{\theta\_{\hbar}} \le 2000 \\ 0,079(Re\_{\theta\_{\hbar}})^{-1/4} \text{ if } Re\_{\theta\_{\hbar}} \ge 4000 \end{cases} \tag{28}$$

$$
\Delta P\_m = \frac{1}{A\_{flow\ channel}} \{ \dot{m}\_{cell\ out} \upsilon\_{cell\ out} - \dot{m}\_{cell\ in} \upsilon\_{cell\ in} \} \tag{29}
$$

$$Q\_{reactant} = \mathcal{W}\_{electricity} + Q\_{generated} \tag{30}$$

$$Q\_{generated} = n\_{cell} \ I \left( E\_{th} - E\_{cell} \right) = Q\_{conduction} + Q\_{convection} + Q\_{coolant} \tag{31}$$

$$Q\_{conduction} = kA \frac{dT}{dx} \tag{32}$$

$$Q\_{convection} = A\_{environment} \ln{\left(T\_{cell} - T\_{environment}\right)} \tag{33}$$

$$Q\_{\text{coolant}} = \dot{m}\_{\text{coolant}} \mathcal{L}\_{p\_{\text{coolant}}} (T\_{\text{out}\_{\text{coolant}}} - T\_{\text{In}\_{\text{coolant}}}) \tag{34}$$

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**13** 

*Malaysia* 

**Heat Transfer Enhancement in Microchannel** 

The microchannel heat sink (MCHS) cooling concept is first proposed by Tuckerman and Pease [1] in 1981. MCHSs are the most common and cost-effective hardware employed for the thermal management of MEMS devices. Tuckerman and Pease [1] pointed out that decreasing liquid cooling channel dimensions to the micron scale will lead to increase the heat transfer rate. They demonstrated experimentally a forty-fold improvement in heatsinking capability in Si-base microchannels anodically bonded to Pyrex cover plates. Since then, intense research on MCHS have been conducted to study the heat transfer and fluid

There are two main configurations for the application of microchannel cooling which are direct cooling and indirect cooling. Direct cooling requires a direct contact between the surface to be cooled and the coolant fluid as illustrated in Fig.1.1a. This scheme reduces the thermal resistance between the surface and the coolant and thus, enhances the cooling effectiveness. However, electrical and chemical compatibility between the coolant and device itself needs to be ensured for this system to work [2]. An alternative to the above configuration is the use of a metallic heat sink to conduct the heat away from the device to a coolant which is forced through circular or noncircular grooves in the heat sink. Such an indirect cooling configuration shown in Fig.1.1b allows for a greater flexibility in coolant selection at the cost of increased thermal resistance between the device and the heat sink due

Microchannels are very fine channels of the width of a normal human hair and are widely used for electronic cooling purposes. In a MCHS, multiple microchannels are stacked together as shown in Fig.1.1 (b) which can increase the total contact surface area for heat transfer enhancement and reduce the total pressure drop by dividing the flow among many channels. Liquid or gas is used as a coolant to flow through these microchannels. The large surface area of MCHS enables the coolant to take away large amounts of energy per unit time per unit area while maintaining a considerably low device temperature. Using these

MCHS, heat fluxes can be dissipated at relatively low surface temperatures.

**1. Introduction** 

flow characteristics of MCHS.

**1.1 Introduction to microchannel heat sink (MCHS)** 

to the heat diffusion resistance in the heat sink itself [3].

**Heat Sink Using Nanofluids** 

M.F. Abdul Jalal and E. Sandhita

*Universiti Tenaga Nasional, Km7 Jalan Kajang-Puchong, Selangor* 

P. Gunnasegaran, N.H. Shuaib, H.A. Mohammed,

*Department of Mechanical Engineering, College of Engineering* 

