FuelThermalPower

FuelThermalPower#

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.

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.

ThermoSysPro Version 4.2#

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