3.11. Subassembly-to-subassembly Heat Transfer

SAS4A/SASSYS‑1 contains a model for transferring heat from the duct wall of one subassembly, through the interstitial sodium, to the duct wall of an adjacent subassembly. During normal, full power operation the subassembly-to-subassembly heat flow is usually small compared to the power generation rate, but at decay heat power levels the heat flow between a subassembly and its neighbors can be comparable to the power generation rate within the subassembly. This heat flow between adjacent subassemblies will affect subassembly-to-subassembly flow re-distribution at low flow rates; and at low powers and flow rates it will tend to cause all subassemblies to have similar temperature rises.

The subassembly duct wall is normally represented by the structure in a SAS4A/SASSYS‑1 channel; so this mode is implemented by transferring heat from the outer structure nodes of a SAS4A/SASSYS‑1 channel to the outer structure nodes of other SAS4A/SASSYS‑1 channels or to a constant temperature heat sink. Also, it is possible to transfer heat from the outer structure node of one channel to the coolant of another channel. This option was included in the code in order to treat the thimble flow region shown in Figure 3.10.1. The equation for the structure to structure heat flux, \(Q_{\text{I,M}} (j)\), from channel I to channel M at axial node j is

(3.11‑1)

\[Q_{\text{I,M}}\left( j \right) = \frac{\left( \text{HA} \right)_{\text{I,M}}}{N_{\text{PI}}N_{\text{SI}}S_{\text{st}1}} \left\lbrack \ T_{\text{sto}}\left( I,J \right) - T_{\text{sto}}\left( M,j \right)\ \right\rbrack\]

where

\(\left( \text{HA} \right)_{\text{I,M}}\) = heat transfer coefficient times area per unit height, between channels I and M

\(T_{\text{sto}}\) = structure outer node temperature

\(N_{\text{PI}}\) = number of pins per subassembly in channel I

\(N_{\text{SI}}\) = number of subassemblies represented in channel I

\(S_{\text{stI}}\) = structure perimeter per pin in channel I

The SAS4A/SASSYS‑1 channel treatment only accounts for one structure per channel; so the channel-to-channel heat flux seen by the structure in a channel will be a sum of the heat fluxes to all adjacent channels. This heat flux is

(3.11‑2)

\[Q_{\text{I}}\left( j \right) = \sum_{\text{M}}{ Q_{\text{I,M}}\left( j \right)}\]

Each SAS4A/SASSYS‑1 channel can transfer heat to up to eight other channels. A subassembly has six nearest neighbors, but a channel can represent more than one subassembly. Therefore, a channel can be in contact with more than six other channels.

If the constant temperature heat sink option is used, then the user supplies values of \(T_{\text{snk}}\) and \(H_{\text{snk}}\) for each axial zone in the channel, and these values are held constant during the calculations.

In contrast to many of the other temperature calculations in the code, explicit forward time differencing is used for the channel to channel heat transfer. The channel to channel heat fluxes are calculated at the beginning of each main time step using the temperatures at that time. These heat fluxes are then held constant during a time step. This explicit forward differencing imposes stability limits on the time step size. The stability limit is typically in the range of .2-.5 seconds.

At this point, the subassembly-to-subassembly heat transfer model has only been implemented in the transient single phase heat transfer calculations. It is necessary to run a null transient to obtain the current steady-state temperatures when subassembly-to-subassembly heat transfer is used.