Hybrid CFD and equivalent-circuit impedance modeling of solid oxide electrochemical cells

Transcription

1 Risø campus Hybrid CFD and equivalent-circuit impedance modeling of solid oxide electrochemical cells Valerio Novaresio, Christopher Graves, Henrik Lund Frandsen, Massimo Santarelli Valerio Novaresio 11/12/2013

2 Attention curve ( a joke ) Attention level We are here Attention threshold level Lunch End day Time

3 Outline Chapter 1 SOC: relevance of geometry Nernstian effects vs. Butler- Volmer effects Chapter 2 EIS & FV: state of the art Hybrid model (focus on LF) Some results Future works

4 Voltage [mv] SOC modeling at high current density Experimental Simulation Current [A] Modeling mantra : good agreement with experimental data!

5 Voltage [mv] SOC modeling at high current density Experimental Simulation Current [A] At high current density sometimes (usually ) something s wrong

6 Assume a spherical cow U U U U With far field approximation we can usually obtain good results

7 or neglect the real SOC geometry

8 Voltage [mv] Experimental vs. Simulations H2 50%, H2O 50% H2 30%, H2O 70% Current [A] These effects are mainly Nernstian effects!

9 Nernstian vs. Butler-Volmer Two way to capture high current density behavior: Artificial denaturation of Butler- Volmer equation (extreme modification of symmetry factor and exponents in exchange current density) Simulation of right 3D geometry in order to feed the cell with the right local gas composition (tacking into account shadow effects) Ratio between Butler-Volmer non linearity effects and 3D Nernstian effects in complete SRU simulation 25% 75% 3D Nernstian effects Non linearity Butler- Volmer effects

10 EIS in SOC simulation Impedance spectroscopy is widely used to study the electrochemical performance of the individual components (electrodes, electrolytes, gas transport) of solid oxide cells and how the components degrade over time. Impedance spectra contain much more information than DC polarization curves. Nearly all SOC impedance studies are conducted at open circuit and use 0D impedance model. It would however be very valuable to be able to properly study impedance measured during cell operation (DC polarization).

11 MD & LBM CFD for electrodes CFD for stacks FV in SOC simulation Complex geometry Huge number of elements Good approximation of mass transport phenomena Poor (less good ) approximation of electrochemical phenomena Simple geometry Huge number of elements Good approximation of mass transport phenomena Good approximation of electrochemical phenomena Very simple geometry Huge (very ) number of elements (high parallelization) Excellent approximation of mass transport phenomena Excellent approximation of electrochemical phenomena

12 How can couple them? 1D EIS models: good results for electrochemical processes, not trivial mass transport process evaluations Frequency domain CFD models both at cell and stack level: accounting for cells performances (degradation, conversion rate, etc ) at stack level requires a huge amount of computational elements (~10 9 ) Time domain Series of 1D EIS model overlapping a fully 3D CFD mass transport model (also in porous supporting electrode)

13 Hybrid model: the idea Frequency domain Time domain 1D EIS models: good results for electrochemical processes, not trivial mass transport process evaluations CFD models both at cell and stack level: taking into account cells performances (degradation, conversion rate, etc ) at stack level requires a huge amount of computational elements (~10 15 ) Input: geometry and parameters Series of 1D EIS models overlapping a fully 3D CFD mass transport model (also in porous supporting electrode) Output: Variables distributions and spectrum impedance State of the art Improving step

14 Hybrid model approach Coupled code increases performance far from OCV and doesn t requires parameters tuning

15 Hybrid model: LF description Warburg Element Typical EIS models accounts mass transport only with an equivalent impedance through a fictitious equivalent circuit Transient PDE for species mass transport (+ compressible Navier Stokes)

16 Hybrid model: paradigm Focus on LF processes: mass transport Emulation (reproduction of the effects) vs. Simulation (reproduction of the causes) Extreme assumption in order to emphasize (and isolate) mass transfer LF effects: η act + η Ohm = const

17 Hybrid model: algorithm For all ω Navier Stokes and species equations are solved Local Nernst potential value is calculated Electrolyte function provides impedance only due to processes computed in frequency domain Impedance due to mass transfer is obtained Total impedance value is calculated from voltage and current peaks (magnitude and delay) do these steps in OpenFOAM

18 EIS SOFC: typical experimental data Impedance decreases as the frequency increases Picks move on the right as the frequency increases

19 EIS SOFC: simulation results (hybrid code) H2=97%, ohmic resistance + mass transport impedance

20 3D geometry aspects Outlet Electrode Inlet Gas channel Inlet Interconnector

21 3D geometry results Fu = 75% Small inductive effects

22 -Z imag [Ω cm 2 ] It seams ohmic resistance reduction 0,25 0,2 0,15 0,1 0,05 OCV FU = 13% 0 0,045 0,095 0,145 0,195 0,245 Z real [Ω cm 2 ] 10% difference (isothermal case)

23 but it could be a cathode Nernstian effect x O2 = % x O2 = % x O2 = % i 1 η 1 x H2 = % x H2 = % x H2 = % x H2O = % x H2O = % x H2O = % i 2 V OCV R OCV g = V i k η 2 i 3 η 3 k η 1 = 0.51 mv η 2 = 0,45 mv η 3 = 0.40 mv R 2 Ω < R1 Ω x O2 = % x O2 = % x O2 = % i 1 η 1 x H2 = % x H2 = % x H2 = % x H2O = % x H2O = % x H2O = % η 1 = mv η 2 = 221,56 mv η 3 = mv i 2 V 0.9 R 0,9 g = V i k η 2 i 3 η 3 k

24 -Z imag [Ω cm 2 ] -Z imag [Ω cm 2 ] OCV 0,3 0,2 0, ,05 0,1 0,15 0,2 0,25 Z real [Ω cm 2 ] OCV - With pin OCV - Without pin 0,2 Differences (little 5%) are present at OCV 0,15 0,1-0,05 0,15 0,35 0,55 0,75 Log(f) OCV - With pin OCV - Without pin

25 -Z imag [Ω cm 2 ] 13% FU FU 13% - With pin FU 13% - Without pin 0,035 0,03 0,025 0,02 0,015 0,01 0, ,045 0,055 0,065 0,075 0,085 Z real [Ω cm 2 ] Pins play the role of occlusions: the impedance is about 10% greater (FU 13%)

26 -Z imag [Ω cm 2 ] 13% FU 0,035 0,03 0,025 0,02 0,015 0,01 0,005 0 FU 13% - With pin FU 13% - Without pin 0 0,5 1 1,5 Log(f) Pins play the role of occlusions: the impedance is about 10% greater (FU 13%)

27 Some comments Fuel utilization effects can be taken into account Incipient occlusion effects can be analyzed Geometry can be further optimized High computational time required Coupling with reliable HF equivalent circuit is only in working progress ( definitive validation with experimental data still is a to do activity)

28 Outlook Start from experimental data Set up a fully 3D FV simulation Tune the FV parameters in order to fit experimental data Start transient simulation for different frequencies ω Different parameters set can fit the same experimental data Many (many ) computational elements that means a lot of computational time

29 Conclusions FV algorithm for impedance spectra analysis was built. LF spectrum (mass transfer) can be described starting from physical PDE. Does it make sense? Yes! Incipient occlusion or degradation (pore occlusion) problems can be showed and studied (with proper code addition). Good approximation of species concentration fields can provide a more realistic bulk values also for HF models. The model can be improved by adding other phenomena directly described by PDE.

30 People Valerio Novaresio (PhD student, Polytechnic of Turin) CFD simulations with open source tool (OpenFOAM ) Mass transport modeling in SOFC/SOEC Christopher Graves (Scientist, DTU) Impedance modeling Materials and microstructure development Henrik Lund Frandsen (Senior Scientist, DTU) Physical and mathematical modeling Mechanical testing and modeling Massimo Santarelli (Associated Professor, Polytechnic of Turin) Experimental analysis of SOFC/SOEC at cell and short-stack level Design, development and testing of FC-based complete systems System analysis of electro-chemical and thermo-chemical plants

31 The Occam razor...the simplest hypothesis proposed as an explanation of phenomena is more likely to be the true one than is any other available hypothesis, that its predictions are more likely to be true than those of any other available hypothesis, and that it is an ultimate a priori epistemic principle that simplicity is evidence for truth.. Swinburne Thank you for your attention!

32 Annex - Bibliography [1] J.I. Gazzarri, O. Kesler, Electrochemical AC impedance model of a solid oxide fuel cell and its application to diagnosis of multiple degradation modes, Journal of Power Sources. 167 (2007) [2] J.I. Gazzarri, O. Kesler, Non-destructive delamination detection in solid oxide fuel cells, Journal of Power Sources. 167 (2007) [3] J.I. Gazzarri, O. Kesler, Short-stack modeling of degradation in solid oxide fuel cells: Part I. Contact degradation, Journal of Power Sources. 176 (2008) [4] J.I. Gazzarri, O. Kesler, Short stack modeling of degradation in solid oxide fuel cells: Part II. Sensitivity and interaction analysis, Journal of Power Sources. 176 (2008) [5] S. Gewies, W.G. Bessler, Physically Based Impedance Modeling of Ni/YSZ Cermet Anodes, J. Electrochem. Soc. 155 (2008) B937 B952. [6] W.G. Bessler, A new computational approach for SOFC impedance from detailed electrochemical reaction diffusion models, Solid State Ionics. 176 (2005) [7] W.G. Bessler, Rapid Impedance Modeling via Potential Step and Current Relaxation Simulations, Journal of The Electrochemical Society. 154 (2007) B1186 B1191. [8] R. Barfod, M. Mogensen, T. Klemensø, A. Hagen, Y. Liu, P. V. Hendriksen, "Detailed Characterization of Anode-Supported SOFCs by Impedance Spectroscopy" J. Electrochem. Soc. 154 (4), B371-B378 (2007). [9] R. Mohammadi, M. Ghassemi, Y. Mollayi Barzi, M. H. Hamedi, Impedance simulation of a solid oxide fuel cell anode in time domain Journal of Solid State Electrochemistry volume 16, issue 10, pp (2012) [10] V. Novaresio, M. G. Camprubí, S. Izquierdo, P. Asinari, N. Fueyo, An open-source library for the numerical modeling of mass-transfer in solid oxide fuel cells, Computer Physics Communications, Volume 183, Issue 1, January 2012, Pages

33 Annex OpenFOAM code The code used in present work was developed using the open source tool OpenFOAM The mass transport library (that is part of the code) was release as an open source code in 2012 The first release of the code was presented at Piero Lunghi EFC 2009 The complete SOC code will be release soon as a open source code

34 Annex - Photos