# Theoretical prediction of pressure drop and under rib velocity of single serpentine and repetitive five pass spiral flow fields for polymer electrolyte membrane fuel cells.

INTRODUCTIONHigh efficiency, low emissions and scalability are some of the various advantages that make fuel cell a promising energy conversion device [1]. Internal-combustion engines and power generators in stationary and portable power applications are the two fields where fuel cells can be a potential replacement. A polymer electrolyte membrane fuel cell (PEMFC) operates at low temperatures of less than 100oC. This feature when coupled with relatively high power density has made these type of fuel cells highly suitable for transportation applications [2]. Among the various technological problems that hinder the commercialization of PEM fuel cells, severe water flooding of cathode and induced mass transport losses are some of the most critical. The other acute challenges that PEMFCs have to overcome are associated with durability, performance and cost [3].

The design of the flow field channel plays a crucial role in the performance of a fuel cell. Variation of the flow field design was reported to cause a differences of 300% in peak power densities among analogous fuel cell systems [4]. The flow field takes care of various critical issues that affect the performance of a fuel cell. The main purpose of the flow field is to uniformly distribute the reactant gases throughout the reaction site. This prevents the formation of hot spots or areas having higher chemical reaction rates which lead to more heat generation. A non-uniform distribution of reactant gases tends to reduce the performance and life of the fuel cell. Along with the delivery of reactant gases, the flow field is also responsible for the movement of byproducts away from the reaction sites. Another responsibility of the flow field design is to promote the transit of electrons that are produced in the cell. This is done by increasing the contact area between the gas diffusion layer and the bipolar plate. An effective flow field must facilitate the free movement of electrons from the reaction area. Apart from the above mentioned responsibilities, the flow field should also take care of reducing the pressure drop that occurs between the inlet and outlet. The various flow field patterns that are commonly in use today are the serpentine, parallel, pin type, spiral and inter-digitated patterns [5]. Among these patterns, the most frequently used pattern is the serpentine type. This can be attributed to the reduced blockage of flow path due to gas or liquid formation in the serpentine pattern [6]. In the past it was widely speculated that diffusion was the most prevalent mechanism for mass transport that took place in the gas diffusion layer. Later, more and more researchers began to recognise the role played by convection for the transport of reactant gases in the porous diffusion layer. This transporting mechanism is commonly referred to as under rib convection or channel bypass [7]. PEMFCs and direct methanol fuel cells (DMFC) suffer from mass transport limitations when operated at high current densities which affect their performance. The mass transport limitations occur mainly in the form of reactant deficiency below the rib regions of the flow field plate and due to flooding in the porous transport layers. The flow field design plays an inevitable role in the design of a fuel cell system due to its impact on mass transport limitations [8]. As a consequence, under rib convection has garnered considerable recognition as a potential method for improving the performance of PEMFCs and DMFCs.

Experimental studies have established that enhancing the under rib convection improved the performance of PEMFCs. Xu and Zhao [9] proposed a convection enhanced serpentine flow field (CESFF) which they experimentally proved to achieve better performance and more stable operation in a DMFC. They credited the remarkable performance of CESFF to the enriched under rib convection which improved its mass transport capacity [9]. Various mathematical models have been developed by researchers to study the flow field designs of PEM fuel cells. Compared to the numerical models, network based models have the advantage of building complicated networks. Such networks can be applied with ease to various flow field configurations. In the case of such models, channel structure is analogous to electric circuit networks. Due to its similarity with Ohm's law, pressure drop can be assumed to be proportional to the flow rate. The relationship that exists between pressure drop, flow rate and the resistance of flow can be constructed using the Hagen-Poiseuille equation. The consumption of reactants plays a pivotal role in flow field designs as it creates a significant change in the flow distribution inside the fuel cell. Due to reactant consumption, the flow rate gradually decreases as the reactant gases flow through the active cell area. For a typical stoichiometry of 2.0, the difference between the flow rates at inlet and outlet could be as high as 50% [10]. In the present study, a network based model was developed to predict the pressure distribution and under rib convection that occur in a serpentine flow field. Hagen-Poiseuille flow is considered in the gas flow channels while Darcy flow is taken account of in the porous GDL. The model also takes into account the effect of reactant consumption throughout the flow network.

11. Network based pressure distribution model:

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

The network model was constructed by building the flow correlation over the entire channel network which was then solved using the Thomas algorithm. The flow correlation was established based on the following valid assumptions: a) the reactant gases are viscous b) the flow is laminar; c) a constant resistance coefficient exists at each channel junction which can be estimated empirically; d) reactants are consumed uniformly over the entire active area. The highlight of using the network approach is that the flow field configuration can be represented by a channel network where each channel is evaluated as a link that connects two nodes. The channel structure of the single serpentine flow pattern (SSFF) and the repetitive five pass spiral flow pattern (RFPSFF) are shown in Fig. 1. In both the design, A x B = 13 x 13 nodes were used. Channel (m,n) is designated as the channel connecting two neighboring nodes denoted by m and n. The relationship between the pressure drop and flow rate in each channel (m,n) in the case of Hagen-Poiseuille flow is given by [11]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where [L.sub.mn] is the length of the channel, [mu] is the viscosity of the fluid, [q.sub.mn] is the flow rate of the fluid, [D.sup.h.sub.mn] is the hydraulic diameter of the flow channel. Due to its equivalence with an electric circuit, the pressure drop in Equation (1) can be represented in terms of flow resistance and flow rate as shown below:

[DELTA][p.sup.mn] = [r.sup.mn][q.sup.mn] (2)

where [r.sub.mn] is the flow channel resistance. The flow channel resistance in terms of the channel's dimensions is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

To account for the pressure losses that occur at the interconnection of channel fragments, a constant [r.sub.k] of 3.6 x [10.sup.5] [12] is introduced to the flow resistance, [r.sub.mn] in equation (3).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

Equations for mass conservation were developed for uniform reactant consumption. During the operation of the fuel cell, the reactant gases are gradually consumed by electrochemical reactions. This results in the decrease of local flow rate in the channels from inlet to outlet. Thus it becomes imperative to consider the reactant consumption for predicting the pressure drop along the flow channel. Reactant consumption is assumed to be uniform over the entire active cell area, i.e., at each node, an amount of Q /([lambda](AxB)) is consumed, where Q is the inlet flow rate and [lambda] stands for the stoichiometry of the reactant gas [10]. Therefore, for a given node m, the sum of all the inflow rates and the outflow rates should be equal to the constant amount that is consumed at each node.

[[summation].sub.m] [q.sub.mn] = [Q/[lambda](A x B)] (5)

[[summation].sub.m] [[DELTA][p.sup.mn]/[r.sup.mn]] = [P.sup.n] - [P.sup.m]/[r.sup.mn] = Q/[lambda](AxB) (6)

This system of equations has A x B equations and A x B unknowns, which represents the pressure at each node. The A x B equations are solved to determine the pressure at each node. The flow networks that were investigated here consisted of two types of interconnections, namely the straight connection and the L connection. The two types of interconnections were expressed respectively as

Straight connection:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

L connection:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

where subscripts (i, j) represents the node coordinates of the flow network. Due to the presence of a porous GDL below the inter connector rib, under rib convection occurs as a result of the flow of reactants through the GDL. The driving force for this under rib convection is the pressure difference [DELTA][p.sub.r] that exists across the rib structure.

According to Darcy's law, the under rib convection velocity, [u.sub.r] can be determined as [13]:

[u.sub.r] = [[K.sup.gdl]/[mu][w.sub.r]] [DELTA][p.sub.r] (9)

where [K.sub.gdl] is the permeability of GDL and [w.sub.r] is the rib of the width.

The network model was formulated in MATLAB based on the Thomas algorithm. The calculation was started by first fixing the pressure at the exit of both the SSFF and the RFPSFF to atmospheric pressure (101325 Pa). By using equation (4), the flow resistance of each channel was determined. The pressure at each node was then subsequently calculated by solving the system of linear equations given by equation (6). The pressure drop was calculated for the adjacent nodes in the adjacent channels. Subsequently, the under rib velocity was obtained by using equation (9).

RESULTS AND DISCUSSIONS

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

The conventional pattern was designed for a small reactive area of 5 [cm.sup.2] (2.5 cmx2.5 cm). It consists of 13 straight flow channels and 24 mitered 90o elbows. In the flow network model, the length of the channel connecting two nodes is 2 mm. Thus, the entire flow field of both the flow patterns, namely the conventional serpentine flow field and the repetitive five pass serpentine flow field was decomposed into a 13x13 matrix consisting of 169 nodes. Fig.4 depicts the variation of pressure with respect to the flow channel length [x.sub.c] in the case of a conventional serpentine flow field. The channel length [x.sub.c] represents the distance travelled by the reactant gas along the flow channel starting from the inlet. Thus, [x.sub.c] spans a length of 33.6 cm covering 13 passes of 2.4 cm length. From Fig.4, it can be observed that the pressure distribution along the flow channel length exhibits a stair case shaped profile that decreases from the inlet to the outlet. It can also be inferred that the pressure drop shows a decreasing trend from inlet to the outlet. The pressure distribution in the straight channel regions exhibited less steep gradient lines. The mitered elbows brought about the steep fall that occurred at various junctions of the pressure distribution curve.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

For the same cell area of 5 [cm.sup.2] (2.5 cmx2.5 cm) a unique multiple pass serpentine flow field was designed. The proposed design was created by connecting three five pass spiral flow pattern in series. Fig.6 depicts the pressure distribution curve that was obtained for the RFPSFF for the same parameters at which the SSFF was modelled. From Fig.6, it can be observed that the RFPSFF had a pressure drop of 3.32 kPa between the inlet and outlet. The SSFF was also found to have the same pressure drop between its inlet and outlet. Fig.7 represents the mean under rib velocity [[bar.u].sub.r] for the RFPSFF and the SSFF. The RFPSFF displayed a higher [[bar.u].sub.r] of 5.4[cms.sup.-1] compared to the 2.7 [cms.sup.-1] of SSFF. This result is consistent with the prediction done by Nam et al. [14] which was based on the geometrical characterization of multiple pass serpentine flow field.

[FIGURE 7 OMITTED]

Conclusion:

The repetitive five pass spiral flow field (RFPSFF) that was studied in this work exhibited a 97.7% increase in the mean under rib convection velocity when compared to that of a conventional single serpentine flow field (SSFF) for the same operating parameters. Another noteworthy feature of the RFPSFF when compared to the SSFF is that the pressure drop between the inlet and outlet is the same. This can be explained by the fact that width, depth, total length and other flow channel dimensions were the same for both the flow fields. Since enhanced under rib convection is associated with increased mass transport capability, it is safe to conclude that the RFPSFF will display a superior mass transport capability without increasing the pumping power.

ACKNOWLEDGEMENT

The authors of this project are grateful to the Department of Mechanical Engineering, National Institute of Technology Calicut, India for their support and for providing facilities for this work.

REFERENCES

[1.] Larminie, J., A. Dicks and M.S. McDonald, 2003. Fuel cell systems explained (Vol. 2). New York: Wiley.

[2.] Ahluwalia, R.K. and X. Wang, 2008. Fuel cell systems for transportation: status and trends. Journal of power sources, 177(1): 167-176.

[3.] Arvay, A., J. French, J.C. Wang, X.H. Peng and A.M. Kannan, 2013. Nature inspired flow field designs for proton exchange membrane fuel cell.International Journal of Hydrogen Energy, 38(9): 3717-3726.

[4.] Spernjak, D., A.K. Prasad and S.G. Advani, 2010. In situ comparison of water content and dynamics in parallel, single-serpentine, and interdigitated flow fields of polymer electrolyte membrane fuel cells. Journal of Power Sources, 195(11): 3553-3568.

[5.] Liu, H., P. Li, D. Juarez-Robles, K. Wang and A. Hernandez-Guerrero, 2014. Experimental study and comparison of various designs of gas flow fields to PEM fuel cells and cell stack performance. Frontiers in Energy Research, 2(2).

[6.] Ye, Q., T.S. Zhao and C. Xu, 2006. The role of under-rib convection in mass transport of methanol through the serpentine flow field and its neighboring porous layer in a DMFC. Electrochimica Acta, 51(25): 54205429.

[7.] Feser, J.P., A.K. Prasad and S.G. Advani, 2006. On the relative influence of convection in serpentine flow fields of PEM fuel cells. Journal of Power Sources, 161(1): 404-412.

[8.] Hamilton, P.J. and B.G. Pollet, 2010. Polymer electrolyte membrane fuel cell (PEMFC) flow field plate: design, materials and characterisation. Fuel cells, 10(4): 489-509.

[9.] Xu, C. and T.S. Zhao, 2007. A new flow field design for polymer electrolyte-based fuel cells. Electrochemistry communications, 9(3): 497-503.

[10.] Guo, N., M.C. Leu and U.O. Koylu, 2014. Optimization of parallel and serpentine configurations for polymer electrolyte membrane fuel cells. Fuel Cells, 14(6): 876-885.

[11.] Kothandaraman, C.P., 2007. Fluid mechanics and machinery. New Age International.

[12.] Tondeur, D., Y. Fan, J.M. Commenge and L. Luo, 2011. Uniform flows in rectangular lattice networks. Chemical engineering science, 66(21): 5301-5312.

[13.] Kaviany, M., 2012. Principles of heat transfer in porous media. Springer Science & Business Media.

[14.] Nam, J.H., K.J. Lee, S. Sohn and C.J. Kim, 2009. Multi-pass serpentine flow-fields to enhance under-rib convection in polymer electrolyte membrane fuel cells: Design and geometrical characterization. Journal of Power Sources, 188(1): 14-23.

(1) Anup Johnson and (2) A. Shaija

(1,2) Mechanical Engineering, National Institute of Technology Calicut, India.

Received February 2016; Accepted 18 April 2016; Available 25 April 2016

Address For Correspondence: Anup Johnson, Mechanical Engineering, National Institute of Technology Calicut, India

E-mail: anupjpt@gmail.com

Table 1: Parameters used in the network model Active area ([mm.sup.2]) 25 x 25 Ratio of surface area to land area 1:1 Channel depth (mm) 1.0 Inlet flow rate of hydrogen ([cm.sup.3][s.sup.-1]) 4.3 Stoichiometry 2.0 Absolute viscosity of hydrogen 9.742 x [10.sup.-6] at 70[degrees]C, [mu] (Ns[m.sup.-1]) Permeability of GDL, [K.sub.gdl] ([m.sup.2]) 1 x [10.sup.-12]

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Author: | Johnson, Anup; Shaija, A. |
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Publication: | Advances in Natural and Applied Sciences |

Date: | Apr 1, 2016 |

Words: | 2751 |

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