Difference between revisions of "SuperFINIX theory manual"

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(→‎Power from SuperFINIX to FINIX)
(→‎Power from SuperFINIX to FINIX)
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By solving the <xr id="eqn:PowerConservationSuperFINIX"/>, the power densities at radial nodes can be solved for FINIX as:  
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<xr id="eqn:PowerConservationSuperFINIX"/> can be solved for <math> \rho_{i+1} </math>: to obtain the power densities at all radial nodes as:
  
 
[[File:SuperFINIXDiscretizationGraph_2.png]]
 
[[File:SuperFINIXDiscretizationGraph_2.png]]
  
 
=== Temperature from FINIX to SuperFINIX ===
 
=== Temperature from FINIX to SuperFINIX ===

Revision as of 14:36, 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:

P = \int\limits_{r_i}^{r_{j+1}} \rho_j \cdot 2\pi r h \text{d}r + \int\limits_{r_{j+1}}^{r_{i+1}} \rho_{j+1} \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

 

 

 

 

(???)

where:

P The total power in a volume element,
r Radial coordinate,
r_i Radial coordinate of a radial node in FINIX,
r_j Radial coordinate at the beginning of a power density block in SuperFINIX,
\rho Power density,
\rho_i Power density of a radial node in FINIX,
\rho_j Power density of a block in SuperFINIX,
h Axial length of the volume element,

Equation 1 can be solved for \rho_{i+1} : to obtain the power densities at all radial nodes as:

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Temperature from FINIX to SuperFINIX

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