Trabajo presentado al 10th European Solid Oxide Fuell Cell Forum celebrado en Lucerna (Suiza) del 26 al 29 de Junio de 2012.In this work, the authors introduce a comprehensive model and the corresponding 3D numerical tool for the simulation of reversible micro-tubular solid oxide fuel cells. It is based on a previous in-house model for SOFC [1], to which some new features has been added to extend its applicability to SOEC. The model considers the following physical phenomena: (i) fluid flow through channels and porous media; (ii) multicomponent mass transfer within channels and electrodes; (iii) heat transfer due to conduction, convection and radiation; (iv) charge motion; and (v) electrochemical reaction. The numerical algorithm to solve this mathematical model is implemented in OpenFOAM, an open source CFD toolbox based on the finite-volume method.Peer reviewe

Fueyo, Norberto

García-Camprubí, M.

Laguna-Bercero, M. A.

Digital.CSIC

 10th European SOFC Forum 2012 26 – 29 June 2012, Lucerne Switzerland  B0715 / Page 1-13    B0715  CFD simulation of a reversible solid oxide microtubular cell   María García-Camprubí (1), Miguel Laguna-Bercero (2), Norberto Fueyo (1) (1) Fluid Mechanics Group (University of Zaragoza) and LIFTEC (CSIC);  C/ María de Luna 3, 50.018, Zaragoza, Spain. (2) Instituto de Ciencia de Materiales de Aragón, ICMA, CSIC-Universidad de Zaragoza; C/ Pedro Cerbuna 12, 50009, Zaragoza, Spain.  Tel.: +34-976-762-153 Fax: +34-976-761-882 Norberto.Fueyo@unizar.es   Abstract  In this work, the authors introduce a comprehensive model and the corresponding 3D numerical tool for the simulation of reversible micro-tubular solid oxide fuel cells. It is based on a previous in-house model for SOFC [1], to which some new features has been added to extend its applicability to SOEC. The model considers the following physical phenomena: (i) fluid flow through channels and porous media; (ii) multicomponent mass transfer within channels and electrodes; (iii) heat transfer due to conduction, convection and radiation; (iv) charge motion; and (v) electrochemical reaction. The numerical algorithm to solve this mathematical model is implemented in OpenFOAM, an open source CFD toolbox based on the finite-volume method. The model accurately describes the characteristic curve (J-V) of the performance of a reversible solid oxide fuel cell, in both SOEC and SOFC modes, as shown in the Figure 1, where experimental data [2] (lines) is plotted versus the numerical results (dots).  Figure 1: J-V curves, numerical versus experimental data [2].  The model is used to determine the electrochemical-model parameters and to study the physics taking place in both modes of operation. The role of the physical phenomena involved in the performance of a solid-oxide device depending on the operation mode (fuel cell or electrolyser) will be discussed, aiming at providing a basis for the cell optimization.  10th European SOFC Forum 2012 26 – 29 June 2012, Lucerne Switzerland  B0715 / Page 2-13     Introduction  Reversible solid oxide fuel cells, also known as solid oxide regenerative fuel cells (SORFCs), are electrochemical devices that can operate either as an electrolyser (SOEC mode), generating hydrogen if water and electricity are supplied, or as a fuel cell (SOFC mode), consuming hydrogen and producing electricity.   SORFC technology is currently researched by many experimental groups [2,4,5]. However, numerical modeling is scarce in this field. Although there are many numerical works for solid oxide fuel cells (SOFCs) and  several for solid oxide electrolyser cells (SOECs), there are hardly any regarding both operating modes simultaneously [6].   In this work, a numerical study of a microtubular anode-supported SORFC is presented. The simulations are performed using a comprehensive numerical tool previously developed by the authors [1,3]. The analysis of the results provide a better understanding of the differences between the SOFC and SOEC operating modes, aiming at helping to the optimization of the cell structure and cell design.    1. Scientific Approach  The numerical study is performed using a comprehensive model that describes the operating principle of SOFCs and SOECs. The model has been described in detail elsewhere [3] and only its relevant features are thus summarised in this section.  The model consists of five submodels, three of which describe the volumetric phenomena taking place within the cell components (channels, electrodes and electrolyte), and the remaining two represent the superficial phenomena, such as the surface-to-surface radiation and the electrochemical reactions.  The channel model describes the fluid flow and the species, mass and heat transfer within the channels; main equations of this model are summarised in Table 1. The electrode model stands for the physics occurring at the fuel and air electrodes, namely: fluid flow, species, mass and heat transfer through a porous medium; the equation set included in this model is shown in Table 2. The electrolyte is an impervious solid where charge and heat transfer are considered, as stated in Table 3.    Table 4 and Table 5 show the algebraic equations used to describe the superficial electrochemical reactions at the electrode-electrolyte interfaces, and the surface-to-surface radiation between the external cell surfaces and the internal furnace surfaces, respectively. For further details see [1,3].  The mathematical model is used to simulate the performance of an in-house fabricated microtubular anode-supported reversible solid oxide fuel cell, shown in Figure 2. The reversible operation of this cell has been experimentally demonstrated [2], and it is numerically studied in this work.     10th European SOFC Forum 2012 26 – 29 June 2012, Lucerne Switzerland  B0715 / Page 3-13     Phenomenon Equation Label Mass conservation 0· v (1) Momentum conservation pIvtrvvvvTT32)()(  (2) Species conservation 0)·()·(· yDyyDvy mm  (3) Enthalpy conservation hjvCTTTvC pp····  (4) Table 1: Channel model equations    Phenomenon Equation Label Species conservation Sppp Np *** ··· (5)  Pressure pp (6) Darcy’s Law pBv o (7) Enthalpy conservation radpeffpqNWhCNWTTTCNW···· cconccactrcrc i ,,  aconcaactrararafuelocKTrra inNnFVH ,,,)0( (8)  Table 2: Electrode model equations    Phenomenon Equation Label Charge conservation 0)~( *  (9) Enthalpy conservation radqiT~)(2 (10) Table 3: Electrolyte model equations     10th European SOFC Forum 2012 26 – 29 June 2012, Lucerne Switzerland  B0715 / Page 4-13    Phenomenon Equation Label Cell Voltage cconactaconactohmVOHrefOHoocvppppFRTEV  222/ln2 (11) Activation overpotential RTFRTFiiaactaaactaaora,,, expexp; SOFCaSOECaSOFCaSOECa ,,,, (12)  RTFRTFiicactccactccorc,,, expexp; SOFCcSOECcSOFCcSOECc ,,,, (13) Exchange current density RTEppppiaactrefraOHrefraHaao,67.0,11.0,, exp22  (14)  RTEppicactrefrcOcco,25.0,, exp2  (15) Concentration overpotential SOFC:raHOHraOHHaconppppFRT,,,2222ln2; SOEC: 2222,,, ln2 HraOHOHraHaconppppFRT (16)  SOFC:  rcOOcconppFRT,,22ln2; SOEC:  22 ,, ln2OrcOcconppFRT (17)  Ohmic overpotential SOFC: ** rarcohm  SOEC: **rcraohm  (18)  Table 4: Electrochemical model equations   Phenomenon Equation Label Radiative heat flux jjradjijradiojjbjiibiradirad qFHEFEq ,,,,,,, 11 (19) View Factor jjiji dArF2coscos (20)  Table 5: Radiation model equations     10th European SOFC Forum 2012 26 – 29 June 2012, Lucerne Switzerland  B0715 / Page 5-13    2. Numerical Simulations     Figure 2: Picture of the microtubular SORFC [2] on the top and sketch of the test rig on the bottom.   Numerical simulations reproducing the experimental test rig shown in Figure 2 (bottom) were carried out considering the following five adjacent numerical subdomains: (i) “Fuel channel” represents the void space inside the electrode-electrolyte tube, it is a 10 cm long cylindrical channel; (ii) “Fuel electrode” represents the 10 cm long porous hollow tube of Ni-YSZ; (iii) “Electrolyte” domain stands for the impervious hollow tube made of YSZ; (iv) “Air electrode” is about 1 cm long porous hollow tube made of LSM-YSZ (active area of 1 cm2); and “Air channel” represents the void space between the SORFC and the heated wall of the furnace.  On the experimental side, the reversible operation of the cell has been successfully tested for different fuel compositions and the results are reported in [2]. In this work the reference experimental data set is that reported in [2] for 70% steam concentration in the fuel stream (i.e. 15 % H2, 70 % H2O, 15 % N2).   The numerical and experimental J-V curves of the reversible solid oxide cell operating at the reference conditions are shown in Figure 1; numerical results agree with experimental data.  Furnace:  10th European SOFC Forum 2012 26 – 29 June 2012, Lucerne Switzerland  B0715 / Page 6-13    Further numerical results are presented and analysed below.   3. Results  A numerical tool such the one developed by the authors does not only provide J-V curves that allow the prediction of the cell global performance. It also provides a wide range of interesting results that may be even more useful for experimentalist than the prediction of j-V curve itself. A selection of these complementary results is presented and analysed in this section.  The microstructure of the porous electrodes is closely related to the species mass transfer to the reaction sites, which is essential to avoid fuel depletion in the triple phase boundaries and the corresponding failure in performance. In Figure 3, Figure 4 and Figure 5 the reactants and products concentrations along the electrodes-electrolyte interfaces (i.e. reacting walls) are shown for both operating modes at different cell voltages.   Figure 3 shows the hydrogen molar fraction along the fuel electrode for SOEC and SOFC modes, the analysis of the latter being of interest. In SOFC mode, hydrogen concentration remains constant from the inlet (x=0) to the air electrode position (4.5 cm). Hydrogen is then consumed within a distance of about 1 cm (air electrode length) and then it reaches a concentration, lower that the feeding one, that remains constant until the electrode end (x=10cm). For low voltages, it can be seen how hydrogen is about to be depleted within the 1cm long reactive area, despite the fact that the hydrogen at the end of the electrode is far from depleted. Moreover, significant concentration differences along the reactive wall may be found for low voltages.   Figure 4 shows the H2O concentration distribution along the fuel electrode. As pointed out in Figure 3, the species is consumed (SOFC) or produced (SOEC) only in the central area of the fuel electrode, corresponding to the position of the air electrode. Most interesting results are those for the SOEC mode, where it can be observed how the concentration of H2O decreases in the active area to lower values than that found at the electrode outlet, and steep concentration gradients are found for high operating voltages.  From the above analysis of Figure 3 and Figure 4, it can be stated that mass transfer within the fuel electrode is strongly impeded both in SOFC and SOEC modes when operating the cell at high current densities. This indicates that a modification on the fuel electrode microstructure such as an increase of the porous diameter or the porosity could improve the cell performance.   Likewise Figure 5 shows the oxygen molar fraction along the air electrode for both SOEC and SOFC modes and several operating voltages. The oxygen distribution in both operating modes and for any voltage remains almost flat, indicating that mass transport of oxygen is not as critical as in the fuel electrode. Thus, the air electrode microstructure should not be a matter of concern for such a thin air electrode.    10th European SOFC Forum 2012 26 – 29 June 2012, Lucerne Switzerland  B0715 / Page 7-13      Figure 3: Numerical H2 molar-fraction distribution along the reaction wall of the fuel electrode for SOFC and SOEC modes at different operating voltages              10th European SOFC Forum 2012 26 – 29 June 2012, Lucerne Switzerland  B0715 / Page 8-13      Figure 4: Numerical H2O molar-fraction distribution along the reaction wall of the fuel electrode for SOFC and SOEC modes at different operating voltages       10th European SOFC Forum 2012 26 – 29 June 2012, Lucerne Switzerland  B0715 / Page 9-13      Figure 5: Numerical O2 molar-fraction distribution along the reaction wall of the air electrode for SOFC and SOEC modes at different operating voltages              10th European SOFC Forum 2012 26 – 29 June 2012, Lucerne Switzerland  B0715 / Page 10-13      Other interesting information that can be extracted from the numerical simulations is the temperature distribution inside the cell. Figure 6 shows the temperature distribution along the air electrode for both operating modes and for the given operating voltages. Here, the study of the different thermal behavior between the direct and reverse operating modes is of relevance. In the SOFC mode the predicted? cell temperature is on average close to the measured temperature (Tsetup), while in SOEC mode the predicted? cell temperature is at any case lower than the measured one. Additionally, it is clear that the SOFC temperature increases as the cell voltage is decreased (i.e the current density is increased). In the SOEC mode temperature decreases as the current density is increased (higher voltages) due to the endothermic nature of the reverse reaction. However, at a given point the temperature starts increasing if the current density (i.e. the voltage) is further increased. This indicates that Joule heating together with radiation heat transfer can balance and even exceed the heat sink due to the electrochemical reaction. This is an interesting result that must be considered for a deeper study of the thermally self-sustaining SOEC operation.   References  [1]   García-Camprubí, M., Jasak, H., Fueyo, N. Journal of Power Sources, 196 (17), 7290-7301, 2011. [2]  Laguna-Bercero, M.A., Campana, R., Larrea, A., Kilner, J.A., Orera, V.M. Journal of the Electrochemical Society, 157 (6), B852-B855, 2010. [3]     García-Camprubí, M., Fueyo, N. Journal of Power Sources, Submitted, 2012. [4]   Jensen, S. H., Sun, X., Ebbesen, S. D., Knibbe, R., Mogensen M. International Journal of Hydrogen Energy, 35 (18), 9544 – 9549, 2010. [5]   Hashimoto, S., Liu, Y., Mori, M., Funahashi, Y., Fujishiro, Y. International Journal of Hydrogen Energy 34 (3), 1159 – 1165, 2009. [6] Jin, X., Xue, X. Journal of Power Sources 195 (19) 6652 – 6658, 2010.   10th European SOFC Forum 2012 26 – 29 June 2012, Lucerne Switzerland  B0715 / Page 11-13       Figure 6: Numerical temperature distribution along the reaction wall of the air electrode, for SOFC and SOEC modes at different operating voltages      10th European SOFC Forum 2012 26 – 29 June 2012, Lucerne Switzerland  B0715 / Page 12-13     Nomenclature oB   Permeability of the porous-medium, m2 pC   Specific heat at constant pressure of the fluid, m2 s-2 K-1 mD   Diffusion coefficient of species  in the gas mixture, m2 s-1 oE   Standard electrochemical cell voltage, V bE   Blackbody emissive power, kg s-3 F   Faraday’s constant, A s kmol-1 jiF   View factor between surface i  and surface j , -’ h   Sensible enthalpy of the fluid, m2 s-2 h   Sensible enthalpy of the species  in the fluid , m2 s-2 oH   External radiation , kg s-3 i   Current density, A m-2 oi   Exchange current density, A m-2 j  Mass diffusive flux of species , kg m-2 s-1 Bk   Boltzmann’s constant, kg m2 s-2 K-1 n  Number of electrons to convert a single molecule of species , - n Normal unit-vector, - N  Total molar flux of species , kmol m-2 s-1 p  Pressure, kg m-1 s-2 p   Partial pressure of species , kg m-1 s-2 q  Energy flux, kg s-3 Q   Volumetric heat sources, Joule heat, kg m-1 s-3 r  Vector from channel surface to enclosure, m R   Ideal gas constant, kg m2 s-2 kmol-1 K-1 S   Volumetric molar source of species , kmol m-3 s-1 T  Temperature, K  v  Fluid velocity, m s-1 V  Voltage, V W   Molecular weight of species , kg kmol-1 x   Molar fraction of species in the gas mixture, - y   Mass fraction of the species , - Greek Symbols  Gas mixture species, -  10th European SOFC Forum 2012 26 – 29 June 2012, Lucerne Switzerland  B0715 / Page 13-13     Backward transfer coefficient, -   Forward transfer coefficient, -  Gas mixture species, -   Pre-exponential coefficient, A m-2 * Dusty-gas model parameter, m2 s-1   Porosity, - rad   Emissivity of the surface, -  Overpotential, V  Angle, -   Thermal conductivity of the fluid, kg m s-3 K-1 s   Thermal conductivity of the solid, kg m s-3 K-1 eff  Effective thermal conductivity of the fluid and porous medium as a continuum, kg m s-3 K-1   Viscosity of the fluid, kg m-1 s-1   Viscosity of species , kg m-1 s-1   Fluid density, kg m3   Anionic conductivity, A V-1 m-1   Tortuosity factor, - *p  Dusty-gas model parameter, m s-1 *N Dusty-gas model parameter, m s-1   Heat of reaction, kg m-1 s-3  Subscripts  a  Fuel electrode act  Activation c  Air electrode con  Concentration e  Electrolyte fuel  Fuel i  Index of surface element, - j  Index of surface element, - ocv  Open circuit voltage ohm  Ohmic rad  Radiation ref  Reference rw  Reaction wall, active electrode-electrolyte interface  

CFD simulation of a reversible solid oxide microtubular cell

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