Mapping regional fields to global mesh

In order to solve the energy equation, regional values of thermal conductivity, heat capacity, density, velocity, etc., are required on the global mesh. Prior to any mapping, the internal values of the recipient fields on the global mesh are reset to zero by appSrc file mapToCell.H. Regional fields are then mapped to the global mesh by appSrc files map<Region>ToCell.H for each of the regions air, fuel, electrolyte, interconnect0 and interconnect1.

In the case of the solids, there is no convective heat transfer, so velocity and heat capacity for the corresponding space within the global mesh will simply be set to zero. Density and thermal conductivity are assumed uniform and are given by the values in their properties files. In the case of the electrolyte, the volumetric energy source terms computed there are also mapped to a global energy source field.

For the fluids, we have both convective and diffusive heat transfer. Mass based heat capacity of the mixture, cp, is calculated as a linear combination of the specie molar heat capacities, C_p,i, divided by their molar mass, M_i, using mass fraction, Y_i, as the linear coefficients:

$${{c}_{p}}=\underset{i}{\mathop \sum }\,\frac{{{Y}_{i}}{{C}_{p,i}}}{{{M}_{i}}}$$

Thermal conductivity is assumed to be uniform within each fluid zone. In the fluid channels it takes the value read from the fluid properties file, whereas in the porous zones it is a linear combination of the channel value and the porous zone value weighted by porosity. Porosity and porous zone thermal conductivity are obtained from the porous zone dictionary.

Rather than mapping velocity directly, it is the fluxes \(\phi =\rho \mathbf{U}\centerdot \mathbf{dA}\) (computed during the pressure-velocity calculation such that mass conservation is satisfied) that are required for the finite volume equations. The fluxes form a surface field on the mesh faces and are mapped onto the global faces corresponding to the regional meshes interior faces and also to the regional mesh boundary patches. At this stage, we have fluxes on the fluid sides of the fluid/electrolyte interfaces, but not on the electrolyte side, the electrolyte being a solid. This can result in heat leaving or entering a fluid through its boundary with the electrolyte, without a corresponding gain or loss within the electrolyte. This situation is remedied by zeroing all fluxes that touch the electrolyte and introducing an additional compensating source term into the energy equation. The zeroing of fluxes is done in mapElectrolyteToCell.H. The source term is equivalent to the continuity error introduced by the zeroing of the fluxes on the electrolyte boundaries.