modelFuelThermalPower

Information

# Fuel Heat Transfer1

This module resolve the heat transfer equation in the fuel rod, based on the fuel properties, *cp* and "k",
 computed in [FuelProperties](modelica://ThermoSysPro.NuclearCore.FuelProperties).

## Heat Transfer Resolution

The Finite Volumes approach is used, leading to the following equation for each node (axial thermal conduction is neglected):

$$Mnode*cp_{i,j}\frac{dT_{i,j}}{dt} = W_{i,j} + Wcond_{i,j}-Wcond_{i,j+1}$$

where the radial themal conduction term is:

$$Wcond_{i,j+1} = \frac{k_{i,j}+k_{i,j+1}}2 * \frac{T_{i,j}-T_{i,j+1}}{rvi_{j+1}-rvi_j} * S_{i,j}$$

and where *i* is the axial index, *j* the radial index, *T* the temperature in the node, *S* the radial surface between two nodes,
 *Mnode* the mass in the node and *W* the power generated in the node.

It has to be noticed that the discretization is based on constant volumes, instead of constant radial steps; 
*rsi* is the radial coordinate of the volumes boundary, *rvi* the radial coordinate of the volumes centers (centers in volumic terms).

## Doppler Effect

The effective temperature used for the Doppler effect can be computed, for each axial section, using the Rowlands weighting function [1]:

$$T_{i,eff} = \frac59T_{i,surface} + \frac49T_{i,center}$$

then, weighted axially as a function of the generated power:

$$T_{effg} = \frac{W_i}{W_T}*T_{i,eff} $$

To improve the the representativity of the *center* and *surface* temperatures, they are linearly extrapolated from the volume node temperature:

$$ T_{i,center} = T_{i,1}*1.5 - T_{i,2}*0.5 $$
$$ T_{i,surface} = T_{i,end}*1.5 - T_{i,end-1}*0.5 $$

The *linear* extrapolation is possible because of the constant volume discretization which give a linear solution under certains hypotheses 
(constant and homogenoeus power, constant conductivity). Under the same assomptions, it is also possible to compare the results in with the analytical solution [2]:

$$ T_{i,center}-T_{i,surface}=\frac{W_i}{4\pi k} $$

and thus validate the extrapolation of the *center* and *surface* values.

## Gap Heat Trasfer
For the gap, the following thermal convection equation is used, where \\(h_{gap}\\) is a user defined constant:

$$ Wcond_{i,end} = h_{gap} * S_{i,end} * (T_{i,surface} - T_{i,clad}) $$

- [1]. G. Rowlands, *Resonance absorption and non-uniform temperature distributions*, Journal of Nuclear Energy, 1962.
- [2]. N.E. Todreas, M. S. Kazimi, Nuclear System I, Thermal Hydraulics Fundamentals. Taylor&Francis, 1798.

## Copyright © EDF 2002 - 2026  


## ThermoSysPro Version 4.2

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