Difference between revisions of "SuperFINIX theory manual"
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{{NumBlk|:|<math> P = \int\limits_{r_i}^{r'_{i}} \rho_i \cdot 2\pi r h \text{d}r + \int\limits_{r'_i}^{r_{i+1}} \rho'_{i} \cdot 2\pi r h \text{d}r= \int\limits_{r_i}^{r_{i+1}} \left(\rho_i + (r - r_i) \cdot \frac{\rho_{i+1} - \rho_i}{r_{i+1} - r_{i}} \right)\, \cdot 2\pi r h \text{d}r</math>|<xr id="eqn:MassConservation2" nolink />}} | {{NumBlk|:|<math> P = \int\limits_{r_i}^{r'_{i}} \rho_i \cdot 2\pi r h \text{d}r + \int\limits_{r'_i}^{r_{i+1}} \rho'_{i} \cdot 2\pi r h \text{d}r= \int\limits_{r_i}^{r_{i+1}} \left(\rho_i + (r - r_i) \cdot \frac{\rho_{i+1} - \rho_i}{r_{i+1} - r_{i}} \right)\, \cdot 2\pi r h \text{d}r</math>|<xr id="eqn:MassConservation2" nolink />}} | ||
</equation> | </equation> | ||
| + | |||
| + | where: | ||
| + | :{| | ||
| + | |<math> P </math> | ||
| + | |The total power in a volume element [-], | ||
| + | |- | ||
| + | |<math> \gamma_{pq} </math> | ||
| + | |volumetric mass transfer rate from phase ''p'' to ''q'' [kg/m<sup>3</sup>s], | ||
| + | |- | ||
| + | |} | ||
[[File:SuperFINIXDiscretizationGraph.png]] | [[File:SuperFINIXDiscretizationGraph.png]] | ||
=== Temperature from FINIX to SuperFINIX === | === Temperature from FINIX to SuperFINIX === | ||
Revision as of 13:11, 12 July 2019
Field transfers from SuperFINIX meshes to FINIX meshes
Power from SuperFINIX to FINIX
SuperFINIX receives power densities in blocks that have to be discretized in the radial nodes of FINIX. This discretization is based on assumption that the number of axial elements remains unchanged before and after the discretization. Therefore the discretization is only performed in the radial dimension. The main solvers in FINIX assume linear scaling of power density (and most other variables) between two nodal points. Because of this assumption, the power densities in nodes have to adjusted when integrating over a volume element that is spanned by two radial nodes in different power density blocks. This conserves the total power over the volumes of single elements as well as the whole fuel rod volume. As such, the following condition has to hold true:
-
(1)
where:
The total power in a volume element [-], 
volumetric mass transfer rate from phase p to q [kg/m3s],
