**3.2 Boundary conditions**

This section presents the boundary conditions used to solve each balance. The symmetry existing in the geometry allows the solver to consider half of the mesh. The following **Figure 2** summarizes the different boundary conditions defined. The present multiphysics problem uses partial derivative equations that need boundary

conditions to be solved, such as electric and ionic charge balances Eq. (4) or the mass balance Eq. (13). Such conditions are expressed by the set of equations

*Cathode inlet composition* [H2O]0 = 10.09 mol m�<sup>3</sup> (90%molar)

[H2]0 = 1.12 mol m�<sup>3</sup> (10%molar)

*Gas insulation n:*ð�*D* ∇*Ci* þ *Ci u*Þ ¼ 0

*Anode inlet composition* [O2]0 = 2.35 mol m�<sup>3</sup>

*Mathematical expressions and numerical values of the boundary conditions.*

**Boundary condition Expression** *Vcell ϕelec* ¼ *Vpol Ground ϕelec* ¼ 0 *Electric insulation n:i* ¼ 0 *Continuity n:*ð Þ¼ *i*<sup>1</sup> � *i*<sup>2</sup> 0

*Solid Oxide Steam Electrolyzer: Gas Diffusion Steers the Design of Electrodes*

The simulations obtained with the multiphysics model previously described have been developed to investigate the impact of diffusion on the SOEC performance and to quantify the location of current sources within functionally graded

The diffusion phenomenon was investigated via four simulation cases, referred to with letters A to D. A is the reference case, based on the set of parameters and geometry as described in **Tables 2**–**4**. This set was modified to give simulations B, C, and D. Case B considers a perfectly collected current without the collector pin: the boundary conditions of mass balance and electronic charge balance are merged. The effect of electrode thickness on gas diffusion and reaction distribution within the electrode was studied with case C considering an electrode thickness of 80 μm instead of the previous 40 μm (case A). Finally, case D displays a steam diffusion coefficient 10 times lower than in the standard case A. **Figure 3** shows the results obtained for case A (left), taken as a reference for the discussion, and case B (right),

The distribution of current sources (*ibv*) appears to be neither continuous nor homogeneous. **Figure 4** exhibits the steam concentration distribution along the electrode at varying abscissa. Whereas high current densities are reached in the vicinity of the interfaces electrode/electrolyte under the gas canals, a low fraction of the total current is produced under the current collector. The water concentration under the cathodic current collector is very low, and this shortage is close to depletion.

Consequently, most of the current source terms are located below the gas channel, and these sources are rather small below the current collector. Since most of the current is generated below the gas channels, the convergence of the electrons toward the collector pin causes hot spots where high current densities are observed. To separate the role of diffusion from other phenomena, such as conduction of charged species, additional simulations were performed. In order to complete the investigation of diffusion process, additional simulation cases B to D were

presented in **Table 5** that are to be satisfied.

*DOI: http://dx.doi.org/10.5772/intechopen.90352*

where the collector pin has been removed.

**4. Results and discussion**

**4.1 Control by diffusion**

electrodes.

**101**

**Table 5.**

#### **Figure 1.**

*Model geometry.*


#### **Table 4.**

*Cell dimensions and computational parameters.*

#### **Figure 2.**

*Type and localization of the model's boundary conditions.*

*Solid Oxide Steam Electrolyzer: Gas Diffusion Steers the Design of Electrodes DOI: http://dx.doi.org/10.5772/intechopen.90352*


#### **Table 5.**

**3.2 Boundary conditions**

*Electrodialysis*

**Figure 1.** *Model geometry.*

**Table 4.**

**Figure 2.**

**100**

e [μm] 100

*Cell dimensions and computational parameters.*

*Type and localization of the model's boundary conditions.*

This section presents the boundary conditions used to solve each balance. The symmetry existing in the geometry allows the solver to consider half of the mesh. The following **Figure 2** summarizes the different boundary conditions defined. The present multiphysics problem uses partial derivative equations that need boundary

**SRU dimensions Mesh parameter**

a [mm] 1 Degrees of freedom 63,982 b [mm] 2 Number of mesh point 13,757 c [mm] 1 Number of boundary elements 1352 d [μm] 40 Minimum element quality 0.5505 *Mathematical expressions and numerical values of the boundary conditions.*

conditions to be solved, such as electric and ionic charge balances Eq. (4) or the mass balance Eq. (13). Such conditions are expressed by the set of equations presented in **Table 5** that are to be satisfied.

#### **4. Results and discussion**

The simulations obtained with the multiphysics model previously described have been developed to investigate the impact of diffusion on the SOEC performance and to quantify the location of current sources within functionally graded electrodes.

#### **4.1 Control by diffusion**

The diffusion phenomenon was investigated via four simulation cases, referred to with letters A to D. A is the reference case, based on the set of parameters and geometry as described in **Tables 2**–**4**. This set was modified to give simulations B, C, and D. Case B considers a perfectly collected current without the collector pin: the boundary conditions of mass balance and electronic charge balance are merged. The effect of electrode thickness on gas diffusion and reaction distribution within the electrode was studied with case C considering an electrode thickness of 80 μm instead of the previous 40 μm (case A). Finally, case D displays a steam diffusion coefficient 10 times lower than in the standard case A. **Figure 3** shows the results obtained for case A (left), taken as a reference for the discussion, and case B (right), where the collector pin has been removed.

The distribution of current sources (*ibv*) appears to be neither continuous nor homogeneous. **Figure 4** exhibits the steam concentration distribution along the electrode at varying abscissa. Whereas high current densities are reached in the vicinity of the interfaces electrode/electrolyte under the gas canals, a low fraction of the total current is produced under the current collector. The water concentration under the cathodic current collector is very low, and this shortage is close to depletion.

Consequently, most of the current source terms are located below the gas channel, and these sources are rather small below the current collector. Since most of the current is generated below the gas channels, the convergence of the electrons toward the collector pin causes hot spots where high current densities are observed. To separate the role of diffusion from other phenomena, such as conduction of charged species, additional simulations were performed. In order to complete the investigation of diffusion process, additional simulation cases B to D were
