.. _section-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. :numref:`Chapter %s<section-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 :numref:`Chapter %s<section-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,
:math:`\Delta r_{\text{g}}`, is determined by simple thermal expansion of the
fuel and cladding from their steady-state dimensions:

(3.6‑1)

.. _eq-3.6-1:

.. math::

    \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}

where

:math:`r_{\text{o}}` = steady-state radii,

:math:`{\overline{T}}_{\text{o}}` = steady-state temperature,

:math:`{\overline{T}}_{\text{f}}` = average fuel temperature,
mass-weighted average,

:math:`{\overline{T}}_{\text{fo}}` = average steady-state
fuel temperature,

:math:`\alpha_{\text{e}}` = cladding thermal expansion coefficient, and

:math:`\alpha_{\text{f}}` = fuel thermal expansion coefficient

The bond gap conductance then has the form

(3.6‑2)

.. _eq-3.6-2:

.. math::

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

or

(3.6‑3)

.. _eq-3.6-3:

.. math::

    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
:math:`{\overline{h}}_{\text{b}}`, :math:`A_{\text{g}}`, :math:`B_{\text{g}}`,
and :math:`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. :ref:`3.6-2<eq-3.6-2>` or :ref:`3.6-3<eq-3.6-3>`, the minimum or the
maximum value is used instead.