12.8. Time Step Controls

In order to operate the voiding model as efficiently and accurately as possible, provision is made for varying the coolant time-step size. This allows a large step size to be used in portions of the transient when no rapid changes are taking place, with a transfer to small time steps when changes occur more rapidly. The size of the step is bounded from below by a user-input minimum value (variable TPDMIN) and is limited above by the user-input maximum heat-transfer (DTMXB), primary-loop (DTPBOI), and main (DTMMXB) time step sizes. Within this rather broad range, the actual step size is determined as the largest value which will satisfy several limiting criteria on other quantities involved in the calculation. These criteria require the time-step size to be small enough so that all of the following are satisfied:

  1. No bubble which is decreasing in size will shrink to less than half its size from the start to the end of the time step. This prevents collapsing bubbles from disappearing in the middle of the time step and allows them to be removed by the bubble-size criterion at a point in the coding at which the loss of the bubble may be properly accounted for.

  2. Neither the highest not the lowest liquid slug is ejected from the subassembly over the span of the time step. As in item 1, such an event must be recorded at the end of a time step in a specific section of the coding.

  3. Neither the liquid-sodium nor sodium-vapor temperature anywhere in the channel changes by more than a user-input amount (DTLMAX and DTVMAX, respectively) over the time step.

  4. The liquid-slug mass flow rate in any slug does not change by more than thirty percent over the time step.

  5. Neither the highest nor the lowest vapor bubble is ejected from the subassembly over the span of the time step.

  6. No vapor-liquid interface travels more than a user-supplied distance (DZIMAX) over the time step.

  7. No vapor-liquid interface crosses more than one axial mesh segment boundary during the time step.

  8. No liquid slug shrinks to less than a minimum length (SLMIN) over the time step.

In addition to satisfying these criteria, the time-step selection must obey the following rules:

  1. No time step can be less than 10-7 seconds.

  2. The new time step cannot be more than four times as large as the old step, even if it satisfies the eight criteria listed above.

  3. The coolant time step cannot extend past the end of the heat-transfer or primary-loop time steps.

Not that it is possible that the time step which satisfied the eight limiting criteria may be less than 10-7 seconds long, which violates the first rule shown above. In this case, the time step is simply set to 10-7 seconds, even though one or more of the criteria may not be satisfied.

The size of the new time step is set in subroutine TSC9 at the end of the voiding calculation over the old time step. This subroutine determines the time step which will satisfy the rules and criteria just discussed. In addition, checks are made on several of the criteria during the course of the calculation; if the time step fails to meet any of these checks, it is reset at the point at which the check was made and the calculation for that step is started over again.

A special case exists when boiling is initiated in any channel. In this instance, the coding will iterate to try to determine the exact time of voiding onset, and so the time step must be adjusted repeatedly so as to locate the beginning of boiling exactly. The time-step adjustment is made from a linear extrapolation based on the amount of liquid superheat.