5.8. Overall Solution and Time Step Control

5.8.1. Order of Calculation in PRIMAR

The computational sequence used in a time step in the primary and intermediate loops is as follows:

  1. Adjust the inlet and outlet plenum pressures for any errors between the estimated and the calculated core flows in the last step.

  2. Calculate \(b_{\text{o}}\), \(b_{1}\), and \(b_{2}\) for the compressible volumes in the primary loop.

  3. Calculate the contributions to \(a_{\text{o}}\), \(a_{1}\), \(a_{2}\), and \(a_{3}\) for each element in a liquid segment and sum them for all of the liquid segments in the primary loop.

  4. Calculate contributions to \(c_{\text{ij}}\) and \(d_{\text{j}}\) from all of the segments in the primary loop.

  5. Add the contributions to \(c_{\text{ij}}\) and \(d_{\text{j}}\) from the estimated core flow.

  6. Solve for \(\Delta p\).

  7. Calculate \(\Delta w\).

  8. Repeat steps 2, 3, 4, 6 and 7 for the intermediate loops, if any are present.

  9. Repeat steps 2, 3, 4, 6 and 7 for the DRACS loops, if any are present.

  10. Calculate the liquid temperatures.

  11. Recalculate the compressible volume pressures with the new liquid temperatures.

  12. Calculate the cover gas flows and the cover gas pressures.

In this sequence of events, the liquid flow hydraulics calculations are done first, followed by the liquid temperature calculations and then by the gas flow and temperature calculations. In order to reduce the sizes of the matrix equations that must be solved, the hydraulics calculations are done for the primary loop first, then for the intermediate loops, and finally for the DRACS loops, if any are present. Adiabatic compression of the cover gases is accounted for during the initial hydraulics calculations, but heat transfer to the gas and gas flows through connecting pipes are not accounted for until the gas calculations at the end of the computational sequence for a time step.

5.8.2. PRIMAR Time Step Size

The initial PRIMAR time-step size is entered as an input quantity. Then the time-step size is determined by the coupling with the coolant dynamics calculations for the core subassemblies. PRIMAR is called to calculate a new time step before the core coolant dynamics routines are called and, as a result, part of the PRIMAR calculation consists in estimating the new core flows based on information supplied by the coolant dynamics routines. Before the start of voiding, the core flows can be estimated accurately in PRIMAR because the single-phase subassembly flow calculations are relatively simple. Consequently, the time step can be fairly large before the start of voiding. After the start of voiding, the core flows are strongly influenced by the rapidly varying pressures in the voiding region, and the PRIMAR time-step size must be cut back to 20 milliseconds or less.

If PRIMAR predicts a large change in the inlet plenum pressure during a time step, the step size must be reduced and the quantities determined in the time step recalculated. Alternatively, if the pressure, temperature, or flow in the primary or intermediate loop change rapidly, but do not have a large effect on the inlet or outlet plenum pressures and temperatures, then the PRIMAR time step is subdivided into smaller intervals for the PRIMAR calculations without requiring additional coolant dynamics calculations in the core subassemblies.