UNIVERSITY OF CINCINNATI

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1 UNIVERSITY OF CINCINNATI Date: I,, hereby submit this work as part of the requirements for the degree of: in: It is entitled: This work and its defense approved by: Chair:

2 COMPUTATIONAL MODELING OF HEAT AND MASS TRANSFER IN PLANAR SOFC: EFFECTS OF VOLATILE SPECIES/OXIDANT MASS FLOW RATE AND ELECTROCHEMICAL REACTION RATE A thesis submitted to The Division of Research and Advanced Studies of the University of Cincinnati In partial fulfillment of the requirements for the degree of MASTER OF SCIENCE In the Department of Mechanical, Industrial and Nuclear Engineering of the College of Engineering February 29, 2008 By Padma Priya Venkata B.Tech. Mechanical Engineering Jawaharlal Nehru Technological University, India, 2004 Committee Chair: Dr. Raj M Manglik i

3 ABSTRACT A three dimensional computational model of an intermediate temperature planar, trilayered solid oxide fuel cell is considered for a steady incompressible fully developed laminar flow in the interconnect ducts of rectangular cross section. A constant supply of volatile species (80% H % H 2 O vapor) and oxidant (20% O % N 2 ) is maintained at the electrolyte surface on the anode and cathode side respectively. The governing equations of mass, momentum and energy coupled with the electrochemical species equations are solved computationally. Darcy-Forchheimer model is used to account for the porosity effects of the electrodes where the flow is in thermal equilibrium with the solid matrix. The anode-side triple phase boundary is resolved as a finite region to accurately capture the physics of electrochemical reaction which results in current generation and volumetric heat dissipation. Parametric effects of the interconnect contact design and channel aspect ratio on the variation of thermal-hydrodynamic and electrical performances of the cell are presented. The effect of the flow rate and duct aspect ratio on the area-specific resistance and its subsequent effects on current density, temperature and mass/species distributions, flow friction factor and convective heat transfer coefficient are presented. Interconnect channels of cross-section aspect ratio ~ and interconnect channel half width of 500 μm are compared for overall electrical and convective cooling performance of the planar anode-supported SOFC. ii

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5 ACKNOWLEDGEMENT I am truly indebted to my advisor, Dr. Raj M Manglik for giving me the opportunity to do research under his guidance. The experience of being part of his research group, and the advice, support and encouragement that he has extended have helped me grow into a better individual, both as a researcher and a person. I would also like to thank Dr. Milind Jog and Dr. Anastasios Angelopoulos for being part of my defense committee. This research project would not have been successful without the help from the members of the Thermal Fluids and Thermal-Processing lab and my friends at the University. I would like to specially thank Yogesh Magar, who helped me extensively in getting started on the project and shared his knowledge through all its intermediate stages. His composed and thoughtful approach to any situation never fails to inspire me. Sundeep Kasimsetty and Aravind Subramani have been wonderful companions in the research group and I thank them for their support. The discussions that we had, though not totally relevant to them, helped me immensely in clarifying my research queries. Also, the time spent in the lab would not have been as enjoyable if not for their company. I also wish to thank Larry Schartman of the MINE Department for helping me install the computational resources required for the successful completion of this project. My stay at the University has been an experience to cherish and I thank my roommates and friends for making Cincinnati a home away from home for me. I am grateful to my dear friend Ashwin Samarao, who in more ways that one has inspired me through his passion for electrical engineering. iv

6 Most of all, I thank my parents and brother for their love and support and for encouraging me in pursuing my aspirations. My brother has been my source of motivation and the confidence that he holds in me has driven me to achieve more from life. It is to them, that I dedicate this work. v

7 TABLE OF CONTENTS ABSTRACT.. i LIST OF TABLES AND FIGURES vi NOMENCLATURE viii CHAPTER 1: INTRODUCTION... 1 CHAPTER 2: MATHEMATICAL FORMULATION AND COMPUTATIONAL METHODOLOGY 2.1 Mathematical Model Computational Methodology. 16 CHAPTER 3: RESULTS AND DISCUSSION 3.1 Effect of interconnect geometry on Area-specific resistance Effect of interconnect duct aspect ratio on thermal-hydrodynamic behavior Effect of interconnect duct aspect ratio on electrical performance Optimization of interconnect geometry CHAPTER 4: CONCLUSION AND FUTURE RECOMMENDATIONS 4.1 Conclusions Future recommendations.. 39 BIBLIOGRAPHY APPENDIX A.. 42 APPENDIX B.. 43 vi

8 LIST OF TABLES AND FIGURES Tables Chapter 2 Table 2.1 Material thermo-physical and electrical properties of fuel cell components Table 2.2 Volatile species and oxidant thermo-physical properties Figures 7 9 Figure 1.1 Chapter 1 Figure Chapter 2 Figure Chapter 3 Figure Figure Figure Schematic of a planar solid oxide fuel cell (SOFC) stack, and co-current flow of fuel and oxidant depicting its structural components and basic working electrochemistry Two-dimensional schematic of anode-supported planar SOFC stack with fuel and oxidant side interconnectors Single-cell SOFC module illustrating the Co-flow arrangement of fuel and oxidant flows, geometrical features of its components, and midplane symmetry considered for the computational domain. Plot of area-specific resistance as a function of interconnect contact spacing for different interconnect half-width configurations Thermal boundary condition at heated interconnect-duct interface in a planar anodesupported SOFC Effect of interconnect flow channel aspect ratio on the variation in convective behavior with Reynolds number Figure Figure Effect of interconnect flow channel aspect ratio on the flow friction factor with Reynolds number Hydrogen Mass fraction distribution along the lateral cross-section of the anode-supported SOFC with for varying interconnect channel aspect ratios [(γ) = 0.5, 0.75, 1.0, 1.5, and 2.0] for (a) constant Reynolds number (b) constant mass flow rate vii

9 Figure Figure Figure Figure Figure Figure Temperature distribution along the lateral crosssection of the anode-supported SOFC with for varying interconnect channel aspect ratios [(γ) = 0.5, 0.75, 1.0, 1.5, and 2.0] for (a) constant Reynolds number (b) constant mass flow rate Effect of interconnect flow channel aspect ratio on the variation in laminar reaction rate of (a) electrochemical species reaction and, (b) fuel utilization for fuel (80% H % H 2 O) and oxidant (20% O % N 2 ) flows. Effect of interconnect flow channel aspect ratio on the variation on normalized Nernst potential, for change in fuel/oxidant inlet flow Reynolds number Variation of Nu and ( f Re) with interconnect duct aspect ratio for varying inlet fuel/oxidant stream for planar anode-supported SOFC with γ = 1.0, λ 2 = 0.05 Effects of γ on the optimal convective thermalhydrodynamic performance of interconnect flow channels. Variation in hydrogen mass fraction distribution along the lateral cross-section of the anodesupported SOFC with for varying Reynolds number [Re = 10, 30, 50 and 70] for γ =1.5 interconnect channel viii

10 NOMENCLATURE A pre-exponential factor A c cross-section area [m 2 ] C i molar concentration of the i th species [kmol/m 3 ] c D i,m d specific heat [kj/kg K] mass diffusion coefficient of the i th species [ m 2 /s] height or lateral depth of interconnect duct [m or mm] d h hydraulic diameter 4A / P ) [m or mm] E o E a E op e - F f g I i K k L M i Nu P p p i P w ( c w electro-motive force or EMF [V] activation energy [kj/kg mol] operating voltage [V] electron charge Faradays constant [96846 C/mol] Fanning friction factor specific Gibbs free energy [kj/mol] current [Amp] specific enthalpy [kj/mol] chemical reaction rate thermal conductivity of the material [W/m K] length of flow duct [mm] molecular weight of the i th species [kg/kmol] Nusselt Number pressure [Pa] center-to-center distance between adjacent interconnect contacts [mm] partial pressure of i th species [bar] wetted perimeter [m or mm] q volumetric heat source [W/m 3 ] R universal gas constant [kj/kmol K] Re Reynolds Number R ASR area specific resistance [Ω cm 2 ] viii

11 R ct,a Charge transfer resistance at the electrolyte-anode interface [Ω cm 2 ] R ct,c Charge transfer resistance at the electrolyte-cathode interface [Ω cm 2 ] R e R i S s s T V electrical resistance of the electrolyte layer [Ω] molar rate of creation/destruction of the i th species source term change in specific entropy [kj/kmol K] interconnect contact half-width [mm] temperature [K or C] velocity vector [m/s] V volume [m 3 ] u, v, w Velocity components in the x, y, and z directions, respectively [m/s] v i stoichometric coefficient of reactants v i U f w W x o Y stoichometric coefficient of products fuel utilization width of interconnect flow-duct [mm] frontal length of cell stack [m or mm] interconnect contact half width mass fraction Greek letters α permeability of the porous material [m 2 ] β temperature exponent γ aspect ratio of the flow duct W / d ) ( d d λ 1 anode-porous-layer thickness ratio d / d ) ( a d λ 2 cathode-porous-layer thickness ratio d / d ) ε μ ( c d porosity of the anode- and/or cathode-electrode material dynamic viscosity [kg/m s] ρ density [kg/m 3 ] ρ e ρ i electronic resistivity of anode material [Ω cm] electronic resistivity of anode material [Ω cm] ix

12 ν kinematic viscosity [m 2 /s] Ω electrical resistivity per unit length [Ω cm -1 ] Subscripts a anode electrode porous layer bulk c d e eff f H 2 O 2 H 2 O i p wall bulk fluid condition cathode electrode porous layer fuel/coolant flow duct electrolyte effective parameter fluid hydrogen oxygen water direction; interconnect porous layer wall surface x

13 CHAPTER 1: INTRODUCTION Solid Oxide fuel cells (SOFCs) are attractive alternate energy conversion devices for producing electrical energy by means of electrochemical reactions at the electrodeelectrolyte interface [1, 2]. They have many advantages compared to conventional electric power generation systems such as high energy conversion efficiency, power density coupled with low pollutant emissions. Among the different types of fuel cells give SOFCs the advantage of fuel adaptability and less sensitive to the fuel composition allowing for a variety of hydrocarbons and gasified coals beside hydrogen to be directly used as fuel. To overcome operation at high temperature which compromises material and structural integrity, a lot of research is now focused on developing intermediate temperature [823K and 1073K] and low temperature [700K-800K] SOFCs [3, 4]. This allows the use of traditional materials such as stainless steel for interconnects and metalceramic composites for the electrodes/electrolyte materials instead of more expensive precious metals. This decreases the system manufacturing costs and improves the robustness and mechanical reliability of the cell stack. Much of the current research is extensively focused on viable SOFC material and the associated electrochemical kinetics, flow distribution and temperature sensitivity [3-12]. The primary structural features of a planar solid oxide fuel cell (SOFC), consisting of an ion conducting electrolyte sandwiched between two electrically conducting electrodes, which are encompassed by interconnectors that house the flow ducts delivery of fuel and oxidant to the porous composite electrodes and provide electrical contacts between adjacent cells are schematically shown in Fig

14 Figure 1.1 Schematic of a planar solid oxide fuel cell (SOFC) stack, and co-current flow of fuel and oxidant depicting its structural components and basic working electrochemistry 2

15 Two main planar SOFC designs include electrode supported and electrolyte supported structures. In the latter a thick electrolyte supports the stack which is generally suitable for high temperature (1273K 1073K) applications where the usually high ohmic losses can be reduced. For intermediate temperatures (823K -1073K) the electrode supported structure is preferred for reducing ohmic losses. This configuration provides better [13-15] thermal-control as well as enhances the charge/gas transport micro kinetics [12]. This facilitates significantly lower operating temperatures of about 450K 600K [16, 17], which leads to improved structural integrity of the stack. A critical operating issue for SOFCs is to ensure higher power density and minimize the amount of material per kw of power supply. For this it has been shown [18] that the combined area-specific resistance (ASR) under ideal conditions should be closer to 0.5 Ωcm 2. This can be partly achieved by using Yttria stabilized Zirconia (YSZ) cermets and limiting the electrolyte thickness to 150 μm in an anode supported structure which reduces its contribution to ohmic resistances [18]. It is usually observed that the ASR for intermediate temperature SOFC is larger than high-temperature SOFC despite the reduced ohmic resistance from the thin electrolyte. This is attributable to the increased activation and concentration potentials in the fuel cell electrodes [16, 19]. The interconnect design plays a critical role in determining the power generating capacity of a fuel cell stack as it adds to the resistance of the unit cell. Its overall resistance depends on the material used and the area of contact with the electrode on both sides of the electrolyte. An important design parameter in this is the minimization of the ASR of a unit cell which generally depends on the activation polarization at the electrode-electrolyte interface, ionic resistivity of the electrolyte material, electronic 3

16 resistivities of the electrode material, and geometric attributes of the stack. In an analytical study [20], it has been shown that the ASR of a symmetric planar SOFC stack depends upon the interplay between the interconnect contact area and its spacing for fuel/oxidant flow channel width. Furthermore, the interconnect channel design can play a significant role in the thermal management of a planar SOFC stack [13]. The generally high temperature operation of SOFCs have structural stability and reliability implications as continuous heat generation and absorption in the fuel cell effects non-uniform temperature and species distributions. These coupled with different thermo-mechanical properties of electrode-electrolyte materials lead to thermal stresses and structural fracture or buckling [1, 13, 21]. To alleviate this, the fuel and oxidant flows through interconnect channels can be harnessed to promote effective convective cooling [13-15]. Several recent studies [14, 15, 22-29] have reported theoretical simulations of the convective behavior of interconnect channels. However, their findings are limited in scope and constrained by an oversimplification of the channel-electrode interface thermal boundary condition. Most models assume a constant heat flux or constant wall temperature boundary condition at the interface which has been shown to incorrectly represent the effects of electrochemical reaction rate and heat generation coupled with the porous-layer flow [13]. Furthermore, in some studies [14, 15, 29], the fuel and oxidant transport to the electrolyte has been simplified as a parametric mass transpiration boundary condition, instead of linking it to the electro-chemistry. In an earlier computational study [13] to look at the thermal management of planar anode-supported SOFCs via fuel and oxidant convection in the interconnect channel, the electrochemical reaction has been coupled 4

17 appropriately by an axially varying wall heat flux as well as wall temperature at the interface, which is distinct from the classical thermal boundary [37, 38] considered by others [14, 15, 22-29]. This work, however, considers uniform reaction rate and complete fuel utilization in the electrodes, which is the thermodynamic upper limit for the SOFC performance, in an effort to ascertain the interconnect channel flow cross-section aspect ratio on the thermal-hydrodynamic flow behavior. The interplay of fuel utilization relative to the reaction rate with different widths of interconnect channel in contact with the electrode-electrolyte composite alters the electromotive force produced. The varying flow duct width alters the interconnect electrode contact area as well, and hence the areaspecific resistance. The modeling of these effects in a three-dimensional simulation of the coupled electrochemical and flow convection behavior is addressed in the present study. 5

18 CHAPTER 2: MATHEMATICAL FORMULATION AND COMPUTATIONAL 2.1 Mathematical Formulation METHODOLOGY The unit cell configuration of an anode-supported planar SOFC with co-flow arrangement is shown in Fig 1.1. For the sake of simplicity geometric symmetry along the mid-plane is considered in the computational domain. The thermo-physical and electrical properties of the structural materials used for the cell components (interconnects-electrode-electrolyte) are listed in Table 2.1. Fixed electrode and electrolyte thicknesses are maintained based on the results from [13] and geometric variation of the interconnect flow duct is achieved by varying the duct aspect ratio γ = w/ d and interconnect contact spacing. In order to study the effect of interconnect design on the area specific resistance, thermo-hydrodynamic and electrochemical properties of the solid oxide fuel cell the duct aspect ratio is varied with a fixed interconnect contact half-width. For a given material, the ASR depends on the component thickness, charge transfer resistance, specific ionic conductivity, and operating temperature; interconnect contact spacing, and interconnect-electrode contact area. The thermo-physical and electrical properties of the structural materials used for the cell components (interconnectselectrode-electrolyte) are listed in Table 2.1. An analytical expression for calculation of the area specific resistance of the stack repeating unit proposed by [20], and is given as follows 6

19 R p ρ t + R + R ρ d = e e s s + δ s δ ( s p) δ e + e e e ct, c ct, a i ASR δ s δ ( s p) (1) where, δ ρ c / tc + ρ a = ρ e t e + R ct, c / t + R a ct, a Table 2.1 Material thermo-physical and electrical properties of different fuel cell elements. Material Porous layers: Nickel Electrolyte: Yttria stabilized Zirconium cermet Interconnector: Steel Density, ρ [kg/m 3 ] Specific heat, c [J/kg K] Thermal conductivity k [W/m K] Electrical Resistivity ρ j [Ω-cm] Charge transfer resistance, R ct,j [Ω-cm 2 ] E-05 Ω e [Ω-cm -1 ] exp(10300 /T) The above equation was derived considering the spacing between adjacent interconnect contacts (p); interconnect contact half width (2s), cell component thicknesses shown in Fig 2.1.1, electrode charge transfer resistances and ionic resistivity of the SOFC components. The numerator of the first term within the braces represents the single cell resistance and the second term represents the resistance contributed by the interconnect material. 7

20 Figure Geometrical description of anode-electrolyte-cathode stack, fuel- and oxidant-side interconnector flow ducts. 8

21 The ASR for the single cell module considered was estimated for fixed interconnect contact half-width using the above expression and the interconnect contact spacing was varied as a function of flow duct aspect ratio. The interconnect material is assumed to possess the highest electrical conductivity (i.e., lowest resistivity) amongst the SOFC components, and is thus neglected in further calculations. The porous anode and cathode layers are assumed to be homogeneous and characterized by uniform porosity, permeability and thermal conductivity, and the fluid in the porous layers is assumed to be in local thermal equilibrium with the solid matrix. A uniform supply of both the volatile species, constituting moist hydrogen (80% H % H 2 O vapor) at the fuel side, and oxidant air (20% O % N 2 ) at the oxidant side is maintained at the active electrolyte surface. The thermo-physical and electrical properties of the chemical species are given in Table 2.2. The electrochemical reaction rate is represented by an Arrhenius-type rate equation, which is coupled with the mass, momentum, heat, and species transport in the mathematical model. The mass injection/suction condition in the porous electrodes on either side of the electrolyte and the heat flux generated by the electrochemical reaction at the electrolyte are included as a mass/energy source terms within the iterative solution process. Table 2.2 Volatile species and oxidant thermo-physical properties Species ρ [kg/m 3 ] c [J/kg K] k [W/m K] μ [kg/m-s] Hydrogen /Oxygen /Water-vapor /Nitrogen Governed by ideal gas law for incompressible fluids Governed by ideal gas mixing law for incompressible fluids 9

22 Within the cell, the oxygen from the oxidant channel is transported to the porous cathode where it is reduced to oxygen ions (O 2- ) at the cathode-electrolyte interface. These oxygen ions migrate through the ion-conducting electrolyte to the anode side triple phase boundary (TPB), where it reacts with the oxidized hydrogen from the fuel channel. This exothermic electrochemical reaction results in water, releasing electrons that flow via the external circuit to the cathode side [30]. The electrochemical reaction at the triple phase boundaries (TPB) can thus be written as two half-cell reactions [5], with oxidation at the anode and reduction at the cathode, respectively, Anode: H O H 2O + e and Cathode: O 2 + 2e O (2) The overall reaction occurring in the SOFC can be expressed as: H H O (3) O2 2 2 The total enthalpy change in the system due to the electrochemical reaction is given as, Δ i=δ g+ TΔ s (4) where ( Δ g ) is the change in Gibbs free energy between the reactants and products. It contributes to the electromotive force (EMF) of the fuel cell as will be shown in Eq. (5), and the second term, ( TΔ s) accounts for the thermal energy released in the exothermic o chemical reaction. The EMF, E generated due to the electrochemical reaction is then given by the Nernst potential equation: 0.5 ( 2 ) ( ) ln( H O H O) o E g F RT F P P P = Δ + (5) 10

23 where P H 2 and P H2O are, respectively, the ratio of partial pressures of hydrogen and water vapor with the operating pressure, and P O 2 is the partial pressure ratio of oxygen at the triple phase boundary given in bar. The first term represents the ideal fuel cell electromotive force i.e., the maximum possible EMF. And the second term accounts for voltage losses in the fuel cell due to influence of gas flow, species generation/destruction and electrochemical reaction rate on the fuel utilization (U f ). The fuel utilization in the SOFC is defined as the ratio of the fuel spent in the electrochemical reaction to the inlet fuel fed at the entrance of the interconnect duct given by the expression, U f m FO = 1 (6) m FI The variation of volatile species and oxidant concentration at the triple phase boundary with change in fuel utilization is estimated and the EMF obtained is used to predict the current density of the SOFC. The current generated in the SOFC stack is obtained using the Nernst potential from Eq.(5) as follows, o ( op ) I = E E R (7) where E op represents the cell operating voltage and R e represents the electrolyte resistance. The ensuing volumetric heat generation in the electrolyte is given by e ( ) 2 2 q = I 2F ΔiH O T + I R e V (8) e The first term in the above expression represents the exothermic thermal energy released from the electrochemical reaction and the second term accounts for the heat generated due to ohmic losses in the electrolyte material. Complete fuel utilization sets the upper thermodynamic operational limit for the SOFC module, and hence the upper limit for thermal management which is used for comparison purposes in this study. 11

24 Incompressible, laminar fully-developed steady flow of fuel and oxidant in the interconnect channels are considered for modeling the heat and mass transport through the fuel cell. They are coupled with the species generation and transformation through the electrolytic reaction in order to describe the complex physics in the SOFC. The corresponding three-dimensional, non-linear, conservation equations describing the convective field of the reacting fuel and oxidant flows in the rectilinear domain of the SOFC module, are expressed as follows: u v w = S x y z ρ m (9) 2 2 u u u 1 P u u 1 u + v + w = + υ + S x y z ρ x y z ρ u (10a) 2 2 v v v 1 P v v 1 u + v + w = + υ + S x y z ρ y x z ρ v (10b) 2 2 w w w 1 P w w 1 u + v + w = + υ + S x y z ρ z x y ρ w (10c) ( ) ( ) ( ) u + v + w = + x y z ρcp x y 2 2 T T T k T T 2 2 uy vy wy Y Y Y = D + D + D + S x y z x x y y z z ρ i i i i i i im, im, im, Y (11) (12) The following set of equations give the boundary conditions applied at the interconnect channel walls: u = v= w= 0, [no slip] (13a) ( u y) = ( v y) = ( w y) = ( T y) = 0, [mid-plane symmetry] (13b) ( T x) 0 =, [thermal symmetry condition] (13c) 12

25 The interface boundary condition of the flow channel and porous electrode layer is implicitly obtained by means of coupling the mass, heat, and species transport through them. The appropriate source terms are iteratively applied at the respective structural regions of the fuel cell in order to account for mass transport through the porous media and species creation/destruction through the chemical reaction. The ionic transfer of oxidant through the electrolyte layer is modeled through the source term in the mass conservation eqaution Eq. (9). It is then coupled with the source term in species transport described by Eq. (12) as follows: ( 4 ) 2 S = I F M + S, and m O Y n S = M R (14) Y i i 1 The first term characterizes the wall suction condition at the cathode-oxidant flow duct interface while the second term or S Y, is the mass source term that produces a wall blowing effect at the anode-fuel flow duct interface. It accounts for consumption of the reactants and formation of products in the chemical reaction stated in Eq. (3) The molar rate of creation/destruction of the i th species given by [31] is expressed as ( ) ( ) i i i i 1 n vi R = K v v C (15) where C i represents the mole-mass ratio of the reactants, and K is the chemical reaction rate determined from the Arrhenius rate equation expressed as, ( ) K = Aexp E RT (16) A and E a are constants for a given chemical reaction [31]. Darcy-Forchheimer model for flow through porous media [32] is used to represent the diffusion and/or convection of species through the porous electrode media. This model is a 13

26 provides the source terms for the momentum transport equations in the anode and cathode porous layers, S j μ eff ρeff ε 1.8 = V+ α 5 α 180ε V V (17) S j accounts for the linear relationship between the pressure gradient and the fluid flow rate as governed by the Darcy law and the second term represents the inertial energy of the fluid [32]. The above equation is limited to gas and reactant flows in the porous cathode- and anode-layers, while for forced convection in the fuel/oxidant interconnect channels S j (S u = S v = S w ) = 0. The thermal-hydraulic performance of the volatile species and oxidant flow can be represented by the dimensionless Fanning friction factor (f) and Nusselt number (Nu). There is a pressure drop in the ducts along the main flow direction due to the friction between the gas flow and the internal surfaces of the duct and the mass permeation across the duct- electrode interface. The friction factor is governed by the hydraulic diameter of the flow channel, d ( 4A P ) =, and the driving axial pressure gradient defined as h c w 2 ( h 2ρ bulk)( ) where the bulk or mean flow velocity is calculated as, f = d w dp dz (18) (19) wbulk = w dac da c and the Reynolds number of the flow is given as, ( ρw d μ ) Re bulk h = (20) The convective heat transfer in the interconnect flow channels is calculated via the Nusselt number given by 14

27 ( ) Nu = dt dy dh ( Twall Tbulk ) wall (21) where T wall is the average wall temperature, ( dt dy ) is the wall temperature gradient at the duct/ porous layer interface, and T bulk the bulk or mean stream-wise flow temperature in the cross section is evaluated as (22) Tbulk = wtdac w da c 15

28 2.2 Computational Methodology The governing partial differential equations for mass, momentum, energy and species transport Eqs (5)-(8) together with the discussed boundary conditions are solved in a three dimensional domain using standard finite volume techniques. Fig details the unit cell configuration and the mid-plane symmetry considered. The computational domain in Fig was represented by a uniform orthogonal mesh in the cross section geometries of the flow channels and electrode porous layers. The grid at the anode/electrolyte interface is uniquely resolved to accurately reflect the electrochemical reaction at the anode triple phase boundary, where the O 2- ions are oxidized in the presence of H + ions resulting in the dissipation of heat and current generation. Finite volume based methods were employed for discretization of the partial derivatives [33, 34]. Central differencing was used for the diffusion terms while the convective terms were treated via second-order upwind scheme. The pressure-velocity coupling was handled using the SIMPLEC (semi-implicit method for pressure linked equations consistent) algorithm. For handling the pressure interpolation in the porous medium flow the pressure staggering option, PRESTO, was used. Numerical solutions for mass, temperature and species distributions, flow friction factor, convective heat transfer coefficient, fuel utilization, species reaction rate and current density values were obtained for different channel cross-section aspect ratio (0.5 γ 2.0). For the volumetric species reaction rate calculations, the constants in Eq (16) were considered to be, A = , β = 0, and E a = J/kg mol [31], kj/mol and Δ g H 2 O = kj/mol [35]. Δ i H 2 O = 16

29 Figure Single-cell SOFC module illustrating the co-flow arrangement of fuel and oxidant flows, geometrical features of its components, and mid-plane symmetry considered for the computational domain. 17

30 The (x y z) mesh for the computational domain was chosen such that Δy = Δz = 0.1 and Δx = 0.13 always, and the consequent grid for the flow duct for a typical case of γ = 1.0 was Grid independence was established for the interconnect duct with γ =1 and λ 1 =λ 2 = 0 by selecting a grid size that matched ( f Re) values within 1% of the established value of for pure duct flows. Second-order accurate trapezoidal rule was used for evaluating the mean fluid velocity and temperature (Eq. (21) and Eq. (22)). The computational convergence criterion in all calculations was chosen such that the relative error between two successive iterations wass less than 10-5 in all the dependent variables. Flow over and through the anode-cathode porous media was resolved using the Darcy-Forchheimer model to predict the source term in the momentum transport equations [13]. The characteristic properties of porous layers for materials listed in Table 2.1 are as follows: effective dynamic viscosity μ = kg/m s, porosity ε = 0.5 eff and permeability α = m 2 [1]. The effective density ρ eff in the porous medium was determined by a local volume-averaging method along with the ideal gas law. The Nernst potential, current and oxidant source/sink terms were calculated by means of a cell-based iterative process using user defined functions (UDFs) in conjunction with the fluid flow solver. The partial pressures of the reactants and products at each node along the rectilinear computational domain are calculated and then used iteratively in Eq (5) in order to predict the above mentioned electrochemical parameters. 18

31 CHAPTER 3: RESULTS AND DISCUSSION 3.1 Effect of interconnect geometry on ASR The area-specific resistance of the SOFC is a very significant design parameter and as has been previously stated [18], it is important to minimize the ASR to maximize power density of the stack. Eqn (1) from [20] gives the ASR for a planar SOFC as a function of its material properties and geometry. The electrical properties of the cell components selected are R ct,c = R ct,a = 0.1Ωcm 2, r a = r c = 0.001Ωcm, t a = 1000μm, t e = 15μm, t c = 50μm. The two important geometrical parameters that effect the ASR are the interconnect contact spacing (p) and interconnect half-width (2s). It can be seen in Fig that as the interconnect contact half-width (i.e., contact area) is increased, the ASR of the unit cell decreases. This is due to the shorter flow path that the charge carriers encounter to complete the electrical circuit. By increasing the interconnect half-width and utilizing a low interconnect contact spacing, the ASR of the single unit can be reduced considerably increasing the power generating capacity the SOFC stack. The interconnect contact halfwidth cannot however, be indefinitely increased as this would leave no space for the flow of fuel/oxidant in the interconnect ducts for a given p. From Fig it can also be observed that the ASR of the unit increases linearly as the spacing between adjacent interconnects is increased and this increase is independent of the interconnect half-width of the unit cell. For larger interconnect contact spacing the resistance to flow of electrons within the electrode material on either side of the electrolyte increases leading to an overall increase in its ASR. Based on the material properties in Table 2.1 an interconnect contact spacing (p) ~ 1.5mm 4mm for interconnect half-width of 0.5mm is thus needed to achieve minimum possible ASR. 19

32 Figure Variation of area-specific resistance with interconnect contact spacing for different interconnect-half-width specifications 20

33 3.2 Effect of interconnect geometry on thermal-hydrodynamic behavior The thermal boundary condition at the interface of the porous layer and interconnect flow duct is characterized through the coupling of mass, momentum, heat and species transport equations. It can be clearly observed from the temperature and heat flux distribution in Fig that the interface has an axially varying wall-temperature and wall-heat-flux condition as previously presented in [13]. This is a due to the internal ohmic heating and volumetric heat generation resulting from the electrochemical reaction which is appropriately accounted for in the solution methodology of the transport equations. The temperature at the interface increases monotonically in the main flow direction as shown in the Fig 3.2.1, due to the chemical species reaction taking place at the electrode-electrolyte interface. The subsequent impact on the convective heat transfer coefficient (Nu) is shown in Fig The complex suction/blowing condition as a result of the electrochemical reaction at the electrode-electrolyte triple phase boundaries and the heat release from the exothermic reaction change the interface condition hence showing that it cannot be approximated to that of pure duct flows as previously considered in the literature [22-27]. The flow-friction losses of the fuel and oxidant flow streams in the interconnect channels are also greatly influenced by both the duct aspect ratio and its porous-layer interface condition. This is seen from the friction factor ( f Re) results for varying duct cross-sectional aspect ratio (γ) graphed in Fig At the porous-layer/flow-channel interface, besides the exothermic heat dissipation, the species creation and destruction due to the electrochemical reaction lends to a blowing-suction condition for the anodeside fuel-flow duct, with H 2 species depletion into and H 2 O vapor back permeation from 21

34 the anode layer. Likewise, the cathode-side oxidant flow sees a net suction condition due to the O 2 depletion in the cathode layer. The unequal Nu and ( f Re) values for fuel and oxidant flows significantly influence both the analysis of the electro-thermodynamic performance of a planar SOFC and its thermal management. Figure Thermal boundary condition at heated interconnect-duct interface in a planar anode-supported SOFC 22

35 Figure Effect of interconnect flow channel aspect ratio on the variation in convective behavior with Reynolds number 23

36 Figure Effect of interconnect flow channel aspect ratio on the flow friction factor with Reynolds number 24

37 3.3 Effect of interconnect channel aspect ratio on electrical performance The interconnect duct geometry also influences the diffusion rate of species in the porous electrodes. The hydrogen mass distribution contours for various duct aspect ratios are shown in Fig Interconnect channels with higher aspect ratios display larger concentration gradients in the anode and near the reaction site, showing almost uniform mass distribution of Hydrogen as the aspect ratio is increased. The converse is the case for H 2 O mass distribution, the ongoing chemical reaction at the anode-electrolyte interface increases the H 2 O concentration continuously along the main flow direction in the porous anode layer and the flow duct. From the contour plots in Fig it can be observed that the hydrogen mass fraction has minimum values closer to the bottom of the anode showing H 2 mass consumption by the electrochemical reaction at the triple phase boundary. When a constant flow of species/oxidant is maintained in the duct channels, wider ducts tend to have better distribution of species concentration. The narrower ducts run at a much higher Reynolds number for the same mass flow rate and have bulk of the fuel in the interconnect ducts due to reduced penetration and diffusion through the porous anode layer. The improved availability of Hydrogen in the porous anode layer aids the chemical reaction phenomenon, leading to higher volumetric reaction rates in ducts with higher aspect ratios. The rate of the laminar reaction at the electrolyte surface governed by an Arrhenius type relation described in Eq (16) is graphed in Fig 3.3.3a. Here the influence of the duct geometry on the electrochemical reaction can be clearly noticed. The ducts with higher aspect ratios and operated at lower flow inlet velocities tend to exhibit better 25

38 reaction rates. The reaction rate tends to decreases with increasing Reynolds number due to reduced availability of hydrogen within the porous anode layer. The increase in reaction rate also leads to higher operating temperatures in the SOFC module. The gradual increase in temperature for ducts with varying aspect ratios can be seen in the temperature distribution contours in Fig The interconnect duct the highest aspect ratio, γ = 2.0, has the highest operating temperature owing to the enhanced volumetric reaction in the anode-electrolyte interface, whereas, the flow duct with γ = 0.5 operates at the lowest temperature with a maximum of 900K reached in the anode layer. From Fig (b) it is evident that for the same species/oxidant mass flow rates the wider duct operates at a higher temperature due to the increased presence in product species. Though the same amount of fuel is passed through all the flow channels the nonuniform molar distribution of the species in the narrower channels reduces the fuel available for the reaction. 26

39 (a) (b) Figure Hydrogen Mass fraction distribution along the lateral cross-section of the anode-supported SOFC with for varying interconnect channel aspect ratios [(γ) = 0.5, 0.75, 1.0, 1.5, and 2.0] for (a) constant Reynolds number (b) constant mass flow rate 27

40 (a) (b) Figure Temperature distribution along the lateral cross-section of the anodesupported SOFC with for varying interconnect flow duct aspect ratios [(γ) = 0.5, 0.75, 1.0, 1.5, 2.0] for (a) constant Reynolds number (b) constant mass flow rate 28

41 (a) (b) Figure Effect of interconnect flow channel aspect ratio on the variation in laminar reaction rate of (a) electrochemical species reaction and, (b) fuel utilization for fuel (80% H % H 2 O) and oxidant (20% O % N 2 ) flows. 29

42 The effect of changing duct aspect ratio on the fuel utilization i.e., the amount of fuel consumed within the fuel cell is graphed in Fig 3.3.3b. At lower Reynolds number flows, the fuel consumption is the highest in the SOFC. This reflects better penetration and uniform mass distribution of the fuel through the porous anode and cathode layers making it easily available for consumption by means of the chemical reaction. As the flow velocities are increased there is a significant drop in fuel utilization which is consistent with the reduced H 2 mass concentration found in the anode (Fig 3.3.1). The Nernst potential reaches a maximum value closer to the duct entrance and then gradually tapers down as the fuel gets used. The depletion of fuel due to the electrochemical reaction along the flow length dilutes the fuel stream of the product species towards the end of the channel decreasing the current. The current generated from the electrochemical reaction is calculated by accounting for Nernst potential losses and fuel consumption in the porous electrodes. The species concentration of the products and reactants show a continuous variation in the electrode, and so need to be calculated by means of an iterative solution methodology. They are then used in Eq (5) to estimate the Nernst potential and subsequently contribute to the species source terms in the transport equations listed in Eq (9) Eq (12). The current density and Nernst potential for the planar anode-supported SOFC are estimated based on a cell operating voltage of 0.6V. Fig shows the Nernst potential variation with interconnect duct aspect ratio. As expected from the graphs of volumetric reaction rate and species mass distribution the duct with the highest aspect ratio, and hence higher interconnect contact spacing shows the maximum Nernst potential. This is a result of increased amount of fuel/oxidant species concentration at the reaction site as seen in the 30

43 hydrogen mass distribution contours in Fig 3.3.1a which in turn improves the efficacy of the electrochemical reaction. The current generation follows a similar pattern due to its direct proportionality with the Nernst potential of the cell as seen in Eq (7). Figure Effect of interconnect flow channel aspect ratio on the variation on normalized Nernst potential, for change in fuel/oxidant inlet flow Reynolds number 31

44 3.4 Optimization of interconnect geometry In promoting and optimizing effective thermal management of planar SOFCs, the aspect ratio of the rectangular interconnect flow channels plays a prominent role. The impact on the thermal-hydraulic behavior is clearly evident in Fig 3.4.1, where both Nu and ( f Re) vary with γ but display different trends. Due to the combined effects of the electrochemical-reaction induced thermal interface condition and ion transport across the porous layers, Nu monotonically increases with γ to a plateau, while ( f Re) first decreases to a minima and then increases to gradually attain a plateau. The altered temperature field and hydrogen mass-concentration distribution, as seen in Figs and 3.3.2, respectively, further reflect the effects of flow duct aspect ratio. Increasing the cross-section aspect ratio of the flow ducts, both for fuel and oxidant, promotes enhanced convective cooling in the interconnect channels due to the relative increase in the thermal interface. There is also a concomitant improvement in the H 2 concentration distribution across the anode in Fig , which shows better penetration and molar/mass uniformity with increasing aspect ratio (γ = 0.5 2) thereby aiding the electro-chemical reaction efficacy. 32

45 Figure Variation of Nu and ( f Re) with interconnect duct aspect ratio for varying inlet fuel/oxidant stream for planar anode-supported SOFC with γ = 1.0, λ 1 = 1.0, λ 2 =

46 While the lowest frictional losses are seen to be incurred in ducts with γ = 0.75 and higher ( f Re) are obtained when γ < 0.75 and γ > 0.75, the heat transfer coefficient (Nu) increases with γ to a maximum plateau with γ 1.5. To optimize the influence of flow duct geometry and interconnect contact spacing for enhanced convective cooling, the ratio ( Nu f Re) provides an effective performance figure of merit. It is a measure of the heat transfer efficiency and relative surface area compactness (or density) [36, 37]. Thus, as seen in Fig , channels with 1 γ 1.5 provide an optimal thermal performance. Though interconnect channels with γ = 2.0 are seen to provide higher current and power densities, channels with 1 γ 1.5 exhibit better thermal-hydrodynamic behavior irrespective of the fuel/oxidant mass flow rate. 34

47 Figure Effects of γ on the optimal convective thermal-hydrodynamic performance of interconnect flow channels. 35

48 Figure Variation in hydrogen mass fraction distribution along the lateral crosssection of the anode-supported SOFC with for varying Reynolds number [Re = 10, 30, 50 and 70] for γ =1.5 interconnect channel 36

49 Fig shows the hydrogen mass distribution in a planer anode-supported SOFC structure with interconnect duct aspect ratio γ =1.5 while As the species inlet velocity is increased, the bulk of the H 2 concentration is seen in the flow duct with lesser concentrations in the anode porous layer and increased overall cell operating temperatures. Though there is more uniform distribution of fuel in the anode layer for higher fuel/oxidant flow rates the decrease in fuel utilization is significant. This causes a drop in chemical reaction rate at the electrolyte surface and also significantly decreases the power generating capacity of the fuel cell. When the flow inlet velocity for the species through the fuel and oxidant flow ducts was further reduced, a 40% increase in fuel utilization with corresponding increase in current density was seen for the case of γ = 1.5. This configuration provides substantially high performance for effective convective cooling without much compromise of electrical behavior of the planar anode-supported SOFC. 37

50 CHAPTER 4: CONCLUSIONS AND FUTURE RECOMMENDATIONS 4.1 Conclusions A computational model of a planar anode-supported SOFC to study the effects of volatile species/oxidant mass flow rate and electrochemical reaction is presented. Fully developed laminar flow of fuel (80% H % H 2 O) and oxidant (20% O % N 2 ) in the interconnect channels is assumed. The combined effect of mass, momentum, heat, and species transfer through the flow ducts and porous electrodes, on the convective and electrochemical mechanisms are discussed. The thermal boundary condition at the interconnect duct porous electrode interface is shown to be an axially varying wall heat flux as well as wall temperature condition as opposed to that of pure duct flow. The influence of species mass flow rate on its convective cooling behavior along with the effect on its electrical performance is discussed. The cross-sectional aspect ratio γ of the interconnect flow channels is shown to effect the area-specific resistance and its optimization for overall performance of the anode-supported planar SOFC module is presented. The ASR of the SOFC unit is measured based on the SOFC unit cell transport properties and geometric dimensions [20]. A parametric analysis on the influence of interconnect contact spacing on the electrochemical performance showed that higher aspect ratio channels had better current generating capacity. Wider channels favor uniform species mass distributions and species penetration in the electrodes subsequently increasing the volumetric reaction rate in the SOFC unit. The optimal convective performance, measured by the figure of merit ( Nu Re) f or relative thermalhydrodynamic compactness [45], is seen to be higher for channels with 1 γ 1.5 while 38

51 channels with γ = 2.0 are seen to have better electrical performance. It is seen that for effective thermal management, interconnect ducts with 1 γ 1.5 that exhibit better convective cooling can be used without significant loss of electrical output. 4.2 Future recommendations The current study on intermediate temperature anode supported SOFC module combines the electrical performance with the thermal hydrodynamic performance of the fuel cell and presents a realistic model to predict the convective cooling behavior of the SOFC in conjunction with its power generating capacity. These results can be used in the design of interconnects and design optimization of the overall fuel cell. Improvements to the current model can be made to include, Stack level-modeling: The present model can be used as a basis for building a stack level model of an SOFC which would predict the overall performance of the SOFC stack and characterize the influence of thermal hydrodynamic parameters on the electrical performance of the fuel cell. Addition of other losses like activation and polarization losses incurred within the SOFC will further enhance the model capabilities. Introduction of internal reforming: Solid oxide fuel cells offer high fuel flexibility due to their ability to use hydrocarbons as fuel. The current study is performed using pure Hydrogen as fuel; a similar analysis can be performed for hydrocarbons by incorporating direct internal reforming capability within the computational model. 39