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Development of the Membrane Transport Model for PEMFC Simulations
Available online at www.sciencedirect.com
Procedia Engineering 44 (2012) 388 – 390
Euromembrane Conference 2012 [OC19] Development of the membrane transport model for PEMFC simulations 1 1 1 2 2 2 L.V. Karpenko-Jereb* , P. Innerwinkler , A-M. Kelterer , C. Fink , P. Prenninger , R. Tatschl 1 2 Graz University of Technology, Austria, AVL List Gmbh, Austria The aim of the work was to carry out the comparison of the membrane transport models published in the scientific literature for the past ten years and to create an improved 1D transport membrane model. The main objective of the membrane model is the calculation of the water flux and the ohmic potential. The analysis of eleven published membrane transport models [1] showed that the calculation of the membrane over-potential can be performed using the following equations: 1) Stefan-Maxwell; 2) Nernst-Planck or 3) Ohm´s Law. The existing models also differ in assumptions for the total water flux in PEM as well as in the formulation of boundary conditions like the definition of the water concentration at interfaces of PEM/CL, CL/GDL. The membrane transport model developed in this work considers three types of water transport processes in PEM: 1) water diffusion due to a water concentration difference between cathode and anode; 2) electro-osmosis caused by conjugated transport of the water molecules with the protons in the electric field; 3) convection caused by pressure gradient. The main governing and auxiliary equations of the developed model are presented in Table 1.
Table 1. Main equations of developed transport membrane model Magnitude 1
Equations
Membrane potential
Lmem
³
K mem
0
2
Water transport in PEM
3
Boundary conditions of water transport at 'p=0
Jw
a Dw
a Dw a Dw
4
Electro-osmotic coefficient
5
Water coefficient
6
Membrane conductivity
7
Water sorption isotherm
2 C Tdrag
diffusion
1877-7058 © 2012 Published by Elsevier Ltd. doi:10.1016/j.proeng.2012.08.426
D Tw2
i
V mem
dz
dC w i dp C drag k p dz F dz
dC w i C drag dz F
a J H 2O ,ano C w,ano C w* ,ano
dC w 2C drag 1 i dz 2F
a J H 2O ,cat C w,cat C w* ,cat
ª E adrag T1 c drag , 0 C w exp « R ¬
ª E dif d Tw1 C w exp« a ¬ R
§1 1 ·º ¨¨ ¸¸» T T 1 ¹¼ © 2
ª E aV ¬ R
T V mem V 0T (C wm C wcr ) t exp« 2
C w*
1
§ 1 1 ·º ¨¨ ¸¸» T T 1 ¹¼ © 2
§ 1 1 ·º ¨¨ ¸¸» © T2 T1 ¹¼
a b RH c RH 2 d RH 3
L.V. Karpenko-Jereb et al. / Procedia Engineering 44 (2012) 388 – 390
The membrane potential
K mem is calculated by Ohm´s Law; the total water flux through PEM Jw
represents the sum of diffusion, electro-osmotic and convection fluxes; boundary conditions of water transport utilize the modified equations from Berg´s model [2]; the electro-osmotic coefficient Cdrag and the water diffusion coefficient Dw in the membrane are functions of the local water concentration in PEM; the membrane specific conductivity, Vmem is defined from *
percolation equation; the water concentration C w at boundaries GDL/CL are calculated from water sorption isotherm. The programming of the developed model was carried out in Fortran95. In this program the total water flux Jw is found iteratively by Newton’s method and the calculation of water concentration profile Cw(z) is performed by Runge-Kutta´s method. Analyses have been made for the water concentration profile in PEM, the total water flux and the membrane over-potential as functions of the following membrane characteristics: water sorption isotherm; electro-osmotic coefficient and water diffusion coefficient. The calculations were carried out at T=70°C for different water humidification conditions, RH a/RHc: 0,0/0,9; 0,5/0,9; 0,9/0,9; 0,9/0,5; 0,9/0,0. The results showed that the change of the water sorption isotherm causes a noticeable change in all investigated values (Jw, Cw(z), Vmem). The variations of electro-osmotic and water diffusion coefficients caused some changes in total water flux but insignificant alterations in the water concentration profile and as consequence no noticeable changes in the membrane over-potential. The new developed PEM Model was implemented in CFD Code AVL FIRE [3]. The primary validation of CFD Code AVL FIRE with new developed PEM Model has been carried out using the Single Channel Cell (SCC) simulation geometry (Figure 1a). The polarization curve calculated using SCC is in good agreement with experimental data (Figure 2). Figure 1b presents the simulation geometry of Full Coupled Cell (FCC), which is exactly corresponding to the experimental Test st Cell and used for advanced validation of the PEM Model.
a)
b)
Fig.1. Simulation geometries of PEMFC used to validate the developed PEM Model: a) Single Channel Cell; b) Full Coupled Cell
389
390
L.V. Karpenko-Jereb et al. / Procedia Engineering 44 (2012) 388 – 390
1,0V U, Experiment Simulation
0,9
Fig.2. Polarization curves of PEMFC with MEA Gore Primea 5620. Oa/Oc=2,2/1,5; T=70°C; RH=0,9; p=1 atm
0,8 0,7 0,6 0
0,2
0,4
0,6
0,8
1
1,2 i,
The experimental data were obtained in Laboratory of Fuel Cell Systems (TU Graz), Prof.
The new PEM Model has been carefully validated at different operating conditions and will be commercially available in future releases of CFD Code AVL FIRE.
Acknowledgment: This work is financially supported by Austrian Research Promotion Agency (FFG) and AVL List GmbH in the framework of Bridge1 Program, Project No. 827559. Abbreviation: CL – catalyst layer; GDL – gas diffusion layer; PEM - polymer electrolyte membrane; PEMFC – polymer electrolyte membrane fuel cell; RH – relative humidity References: [1] Karpenko-Jereb L., Kelterer A.-M., Grampp G., Fink C., Prenninger P., Tatschl R. International Congress on Membrane and Membrane Processes, Amsterdam, Netherlands, Jul 23-29, 2011, 282; [2] Berg P., Promislow K., Pierre J., Stumper J., Wetton B. J. Electrochem. Soc., 151 (2004), 3, A341-A353; [3] General Purpose Modules AVL FIRE VERSION 2010. Edition 11/2010. AVL List Gmbh 2010. 91 pp Keywords: polymer electrolyte membrane fuel cell, transport model, AVL FIRE, CFD Simulation
Procedia Engineering 44 (2012) 388 – 390
Euromembrane Conference 2012 [OC19] Development of the membrane transport model for PEMFC simulations 1 1 1 2 2 2 L.V. Karpenko-Jereb* , P. Innerwinkler , A-M. Kelterer , C. Fink , P. Prenninger , R. Tatschl 1 2 Graz University of Technology, Austria, AVL List Gmbh, Austria The aim of the work was to carry out the comparison of the membrane transport models published in the scientific literature for the past ten years and to create an improved 1D transport membrane model. The main objective of the membrane model is the calculation of the water flux and the ohmic potential. The analysis of eleven published membrane transport models [1] showed that the calculation of the membrane over-potential can be performed using the following equations: 1) Stefan-Maxwell; 2) Nernst-Planck or 3) Ohm´s Law. The existing models also differ in assumptions for the total water flux in PEM as well as in the formulation of boundary conditions like the definition of the water concentration at interfaces of PEM/CL, CL/GDL. The membrane transport model developed in this work considers three types of water transport processes in PEM: 1) water diffusion due to a water concentration difference between cathode and anode; 2) electro-osmosis caused by conjugated transport of the water molecules with the protons in the electric field; 3) convection caused by pressure gradient. The main governing and auxiliary equations of the developed model are presented in Table 1.
Table 1. Main equations of developed transport membrane model Magnitude 1
Equations
Membrane potential
Lmem
³
K mem
0
2
Water transport in PEM
3
Boundary conditions of water transport at 'p=0
Jw
a Dw
a Dw a Dw
4
Electro-osmotic coefficient
5
Water coefficient
6
Membrane conductivity
7
Water sorption isotherm
2 C Tdrag
diffusion
1877-7058 © 2012 Published by Elsevier Ltd. doi:10.1016/j.proeng.2012.08.426
D Tw2
i
V mem
dz
dC w i dp C drag k p dz F dz
dC w i C drag dz F
a J H 2O ,ano C w,ano C w* ,ano
dC w 2C drag 1 i dz 2F
a J H 2O ,cat C w,cat C w* ,cat
ª E adrag T1 c drag , 0 C w exp « R ¬
ª E dif d Tw1 C w exp« a ¬ R
§1 1 ·º ¨¨ ¸¸» T T 1 ¹¼ © 2
ª E aV ¬ R
T V mem V 0T (C wm C wcr ) t exp« 2
C w*
1
§ 1 1 ·º ¨¨ ¸¸» T T 1 ¹¼ © 2
§ 1 1 ·º ¨¨ ¸¸» © T2 T1 ¹¼
a b RH c RH 2 d RH 3
L.V. Karpenko-Jereb et al. / Procedia Engineering 44 (2012) 388 – 390
The membrane potential
K mem is calculated by Ohm´s Law; the total water flux through PEM Jw
represents the sum of diffusion, electro-osmotic and convection fluxes; boundary conditions of water transport utilize the modified equations from Berg´s model [2]; the electro-osmotic coefficient Cdrag and the water diffusion coefficient Dw in the membrane are functions of the local water concentration in PEM; the membrane specific conductivity, Vmem is defined from *
percolation equation; the water concentration C w at boundaries GDL/CL are calculated from water sorption isotherm. The programming of the developed model was carried out in Fortran95. In this program the total water flux Jw is found iteratively by Newton’s method and the calculation of water concentration profile Cw(z) is performed by Runge-Kutta´s method. Analyses have been made for the water concentration profile in PEM, the total water flux and the membrane over-potential as functions of the following membrane characteristics: water sorption isotherm; electro-osmotic coefficient and water diffusion coefficient. The calculations were carried out at T=70°C for different water humidification conditions, RH a/RHc: 0,0/0,9; 0,5/0,9; 0,9/0,9; 0,9/0,5; 0,9/0,0. The results showed that the change of the water sorption isotherm causes a noticeable change in all investigated values (Jw, Cw(z), Vmem). The variations of electro-osmotic and water diffusion coefficients caused some changes in total water flux but insignificant alterations in the water concentration profile and as consequence no noticeable changes in the membrane over-potential. The new developed PEM Model was implemented in CFD Code AVL FIRE [3]. The primary validation of CFD Code AVL FIRE with new developed PEM Model has been carried out using the Single Channel Cell (SCC) simulation geometry (Figure 1a). The polarization curve calculated using SCC is in good agreement with experimental data (Figure 2). Figure 1b presents the simulation geometry of Full Coupled Cell (FCC), which is exactly corresponding to the experimental Test st Cell and used for advanced validation of the PEM Model.
a)
b)
Fig.1. Simulation geometries of PEMFC used to validate the developed PEM Model: a) Single Channel Cell; b) Full Coupled Cell
389
390
L.V. Karpenko-Jereb et al. / Procedia Engineering 44 (2012) 388 – 390
1,0V U, Experiment Simulation
0,9
Fig.2. Polarization curves of PEMFC with MEA Gore Primea 5620. Oa/Oc=2,2/1,5; T=70°C; RH=0,9; p=1 atm
0,8 0,7 0,6 0
0,2
0,4
0,6
0,8
1
1,2 i,
The experimental data were obtained in Laboratory of Fuel Cell Systems (TU Graz), Prof.
The new PEM Model has been carefully validated at different operating conditions and will be commercially available in future releases of CFD Code AVL FIRE.
Acknowledgment: This work is financially supported by Austrian Research Promotion Agency (FFG) and AVL List GmbH in the framework of Bridge1 Program, Project No. 827559. Abbreviation: CL – catalyst layer; GDL – gas diffusion layer; PEM - polymer electrolyte membrane; PEMFC – polymer electrolyte membrane fuel cell; RH – relative humidity References: [1] Karpenko-Jereb L., Kelterer A.-M., Grampp G., Fink C., Prenninger P., Tatschl R. International Congress on Membrane and Membrane Processes, Amsterdam, Netherlands, Jul 23-29, 2011, 282; [2] Berg P., Promislow K., Pierre J., Stumper J., Wetton B. J. Electrochem. Soc., 151 (2004), 3, A341-A353; [3] General Purpose Modules AVL FIRE VERSION 2010. Edition 11/2010. AVL List Gmbh 2010. 91 pp Keywords: polymer electrolyte membrane fuel cell, transport model, AVL FIRE, CFD Simulation