Thesis for degree: Licentiate of Engineering

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Nomenclature a lattice direction, – AV surface area-to-volume ration, m 2 /m 3 Bi Biot number, – c lattice speed of sound, lu/ts c T total concentration, mol/m 3 c p specific heat at constant pressure, J/(kg·K) C concentration, mol/m 3 Da Darcy number, – D ij Maxwell-Stefan binary diffusion coefficient, m 2 /s D thermal diffusion coefficient, kg/(m·s) E activation energy, kJ/mol e lattice speed, lu/ts f a particle density distribution function, – f eq equilibrium distribution function, – F force vector, N/m 3 F Faraday constant, 96485 C/mol F gravitational force, mu·lu/ts 2 h enthalpy, kJ/mol h heat transfer coefficient, W/(m 2·K) h v volume heat transfer coefficient, W/(m 3·K) i current density, A/cm 2 i 0 exchange current density, A/cm 2 J mole flux, mol/(m 2 s 1 ) J* dimensionless mole flux, – k thermal conductivity, W/(m·K) k reaction rate constant, mol/(m 3·bar 2·s) k c mass transfer coefficient, m/s k´´ pre-exponential factor, 1/(·m 2 ) K e equilibrium constant, Pa 2 or dimensionless M j molecular weight of species j, kg/mol N number of grid points, – N iter number of iterations, – Nu Nusselt number, – n e number of electrons transferred per reaction, – P pressure, bar p partial pressure, Pa v
Q source term (heat), W/m3 q heat flux, W/m 2 r reaction rate, mol/(m 3·s), mol/(m 2·s) r mean pore radius, m R gas constant, 8.314 J/(mol·K) Re Reynolds number, – S i source term for the reaction rate, kg/(m 3·s) T temperature, K T viscous stress tensor, N/m 2 t time step, – u, v velocity, m/s w a weight factor, – w i mass fraction of species i, kg/kg x, y coordinate system, m x mole fraction, – z pixel point, – Greek symbols β dimensionless maximum temperature rise, – γ dimensionless activation energy, – δ reference step (time or length) ε porosity, – η overpotential, V κ permeability, m 2 κ dv deviation from thermodynamic equilibrium, Pa·s μ dynamic viscosity, Pa·s ρ density, kg/m 3 ζ ionic/electronic conductivity, Ω -1 m -1 η tortuosity, – η relaxation time υ kinematic viscosity, m 2 /s χ Damköhler number for the heat transfer, – ω Damköhler number for the mass transfer, – Ω D diffusion collision integral, – Φ phase function, – Subscripts 0 reference state or initial state a lattice direction in LBM act activation polarization D dimensionless system e electrode, ea,c eff el effective electrolyte vi
Page 1 and 2: SOFC modeling from micro to macrosc
Page 3 and 4: Abstract The purpose of this work i
Page 5 and 6: katalytisk omvandling av naturgas o
Page 7 and 8: List of publications Journal public
Page 9: 3.2 Governing equations for the mac
Page 13 and 14: 1 Introduction After some time of d
Page 15 and 16: 2 SOFC modeling at smaller scales T
Page 17 and 18: etween 0.3 and 1.5 mm. In this conf
Page 19 and 20: Volume Method (FVM) which adopt the
Page 21 and 22: 2.3 Lattice Boltzmann method LBM ha
Page 23 and 24: streaming [3]. The concentration ρ
Page 25 and 26: ease the correspondence between the
Page 27 and 28: applicable for a mixture of two spe
Page 29 and 30: Figure 2.6: Effective boundary arra
Page 31 and 32: Table 2.1: Comparison of previous w
Page 33 and 34: Figure 2.7: Schematic illustration
Page 35 and 36: model is presented after the data c
Page 37 and 38: 3.2.1 Mass transport In the electro
Page 39 and 40: where h v is the volume heat transf
Page 41 and 42: Achenbach [43], it was found that t
Page 43 and 44: cathode are assumed to be similar t
Page 45 and 46: (3.48) where, besides the parameter
Page 47 and 48: for an isothermal spherical particl
Page 49 and 50: Velocity carried out to check wheth
Page 51 and 52: Figure 4.4: Velocity field [lu/ts]
Page 53 and 54: Table 4.2: Parameters in the SOFC a
Page 55 and 56: eactions are safely fulfilled. This
Page 57 and 58: Figure 4.8: Mole fraction distribut
Page 59 and 60: Table 4.5: Inlet mole fractions for
Page 61 and 62:
Figure 4.12: Mole fraction distribu
Page 63 and 64:
5 Conclusions The physics and the t
Page 65 and 66:
7 References [1] Andersson M., Yuan
Page 67 and 68:
[25] Latt J., Hydrodynamic Limit of
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Thesis for degree: Licentiate of Engineering

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