3.6. Fuel-Cladding Bond Gap Conductance

A number of gap-size-dependent bond gap correlations are available in SAS4A/SASSYS‑1. The bond gap conductance depends on two main factors: the gap size or the contact pressure between fuel and cladding after the gap has closed, and the correlation for bond gap conductance as a function of gap size or contact pressure. Since small differences in differential expansion between fuel and cladding can make the difference between an open gap and a closed gap, and since gap conductance correlations are strongly dependent on gap size, the models used for fuel and cladding thermal expansion and swelling might have a much larger impact on computed bond gap conductances than the choice of the particular correlation used for bond gap conductance as function of gap size.

There are a number of options for computing the gap size. One common option for oxide fuel is to use DEFORM-IV to compute the steady-state and transient dimensions. Chapter 8 describes DEFORM-IV and the bond gap conductance correlations that can be used with it. A second option would be to use DEFORM-IV for the steady-state but not for the transient. In this case, the gap size and gap conductance determined in the steady-state calculations would be constant during the transient. A third option is not to use DEFORM-IV at all. In this case the gap size is constant, based on the user-specified pin dimensions, and the bond gap conductance is constant. The fourth option is to use a simple thermal expansion model for the transient bond gap size. For a metal fuel, the DEFORM-5 model described in Chapter 9 can be used to obtain the bond gap conductance.

The simple thermal expansion model applies only to the transient calculation. It can be used either with or without the DEFORM-IV steady-state calculations, but it cannot be used with the transient DEFORM-IV. In this model, it is assumed that the gap size, \(\Delta r_{\text{g}}\), is determined by simple thermal expansion of the fuel and cladding from their steady-state dimensions:

(3.6‑1)

\[\begin{split}\begin{matrix} \Delta r_{\text{g}} = r_{\text{o}}\left( \text{NE} \right) - r_{\text{o}}\left( \text{NR} \right) \\ + \frac{\left\lbrack r_{\text{o}}\left( \text{NE} \right) + r_{\text{o}}\left( \text{NE}' \right) \right\rbrack}{2} \alpha_{\text{e}} \left\lbrack T \left( \text{NE} \right) - T_{\text{o}}\left( \text{NE} \right) \right\rbrack \\ - r_{\text{o}}\left( \text{NR} \right) \alpha_{\text{f}} \left( {\overline{T}}_{\text{f}} - {\overline{T}}_{\text{fo}} \right) \\ \end{matrix}\end{split}\]

where

\(r_{\text{o}}\) = steady-state radii,

\({\overline{T}}_{\text{o}}\) = steady-state temperature,

\({\overline{T}}_{\text{f}}\) = average fuel temperature, mass-weighted average,

\({\overline{T}}_{\text{fo}}\) = average steady-state fuel temperature,

\(\alpha_{\text{e}}\) = cladding thermal expansion coefficient, and

\(\alpha_{\text{f}}\) = fuel thermal expansion coefficient

The bond gap conductance then has the form

(3.6‑2)

\[h_{\text{b}} = \frac{{\overline{h}}_{\text{b}}}{\Delta r_{\text{g}}}\]

or

(3.6‑3)

\[h_{\text{b}} = A_{\text{g}} + \frac{1}{B_{\text{g}} + \frac{\Delta r_{\text{g}} + C_{\text{g}}}{{\overline{h}}_{\text{b}}}}\]

depending on the correlation chosen. In these correlations \({\overline{h}}_{\text{b}}\), \(A_{\text{g}}\), \(B_{\text{g}}\), and \(C_{\text{g}}\) are user-supplied correlation coefficients. For either correlation, the bond gap conductance is also constrained to lie between user-supplied minimum and maximum values; so if a value outside this range is calculated using Eq. 3.6-2 or 3.6-3, the minimum or the maximum value is used instead.