3.8. Heat-transfer Time Step Control

Each channel uses its own separate heat-transfer time step size, so that channels in which temperatures are changing rapidly or in which boiling is occurring can use small heat-transfer time steps while other channels use larger steps.

After each heat-transfer time step, the size of the next step is determined, based on number of criteria. Most of these criteria are based on user-supplied values for maximum time step sizes and maximum temperature changes per step. The time step used in the smallest of the various criteria. If not other factor is more limiting, then the next heat-transfer step size is set equal to the initial main time-step size. This is usually in the range of .05-1.0 s. After the onset of boiling in a channel, a maximum boiling heat-transfer time step size, typically .01-.02 s, is used. In addition, a heat-transfer time step cannot go past the end of a main time step. Also, if the channel has not started boiling yet, then an attempt is made to end a heat-transfer time step right at, or very close to, the time when the first bubble is formed. For this purpose, the pre-boiling coolant routines make an estimate of the boiling time at the end of each coolant time step. The boiling time estimate is based on linear extrapolations in time for the coolant temperature and the saturation temperature at each axial node. The other criteria are based on the rate of change of the temperatures. The user supplies values of the maximum change per time step for the fuel and clad temperatures. Typical values are in the range of 30-50K. The rate of change of the fuel center-line temperature, the fuel surface temperature, and the clad mid-point temperature at each axial node are used to determine maximum time step sizes. After the minimum of the various time-step criteria has been found, the time step size is rounded to eight decimal places to minimize differences in results caused by different round-off errors on different computers. These criteria are summarized below:

  1. Initial time step size

  2. Maximum boiling time step size, if boiling

  3. End of a main time step

  4. Initiation of boiling

  5. Maximum fuel center-line temperature change

  6. Maximum fuel surface temperature change

  7. Maximum clad mid-point temperature change