5.10. PRIMAR-1 Option

PRIMAR-4 contains both a simple PRIMAR-1 type option and the more detailed PRIMAR-4 treatment. The PRIMAR-1 option supplies only the minimum quantities required to drive the subassembly coolant dynamics module. It is often used when the more detailed treatment is not required. The minimum information consists of the inlet and outlet plenum pressures, the subassembly inlet temperatures, and the outlet reentry temperatures. All of these quantities are supplied as a function of time by PRIMAR-1 from user-supplied information, independent of what is happening in the core or in the rest of the primary loop.

The inlet pressure \(p_{\text{in}} \left( t \right)\) is calculated as

(5.10‑1)

\[p_{\text{in}}\left( t \right) = p_{\text{x}} + p_{\text{gr}} + \Delta p_{\text{p}} \left( t \right)\]

where \(p_{\text{x}}\) is the user-specified exit plenum pressure, \(p_{\text{gr}}\) is the gravity head, and \(\Delta p_{\text{p}} \left( t \right)\) is the pump head. The gravity head is calculated as

(5.10‑2)

\[p_{\text{gr}} = \left\lbrack \rho_{\text{HOT}} \left( z_{\text{PU}} - z_{\text{IHX}} \right) + \rho_{\text{COLD}} \left( z_{\text{IHX}} - z_{\text{PL}} \right) \right\rbrack g\]

where \({\rho}_{\text{HOT}}\) is the average steady-state outlet density, \({\rho}_{\text{COLD}}\) is the average steady-state inlet density, \(z_{\text{PU}}\) is the reference height at which the outlet plenum pressure is calculated, \(z_{\text{PL}}\) is the reference height at which the inlet plenum pressure is calculated, and \(z_{\text{IHX}}\) is the reference height of the thermal center of the intermediate heat exchanger. The quantity \(p_{\text{gr}}\) is calculated in subroutine SSPRIM as PINGR and placed in a COMMON block.

The pump head is calculated as

(5.10‑3)

\[\Delta p_{\text{p}} \left( t \right) = \Delta p_{\text{o}} f_{\text{p}}\left( t \right)\]

where \(\Delta p_{\text{o}}\) is the steady-state pump head, taken as

(5.10‑4)

\[\Delta p_{\text{o}} = p_{\text{in}} \left( t = 0 \right) - p_{\text{gr}} - p_{\text{x}}\]

and \(f_{\text{p}} \left( t \right)\) is the user-supplied time dependence of the pump head, which should be normalized so that

(5.10‑5)

\[f_{\text{p}} \left( t = 0 \right) = 1.0\]

There are two options for specifying \(f_{\text{p}} \left( t \right)\). One option is for the user to supply a table of \(f_{\text{p}}\) as a function of time. With this option, the code interpolates linearly between table entries. The other option is for the user to supply the three coefficients \(p_{\text{d}}\), \(p_{\text{d}1}\), \(p_{\text{d}2}\) for use in the equation

(5.10‑6)

\[f_{\text{p}}\left( t \right) = \exp{\left\lbrack - \left( p_{\text{d}}t + p_{\text{d}1}t^{2} + p_{\text{d}2} t^{3} \right) \right\rbrack}\]

In addition, the time derivatives of the inlet and exit plenum pressures are calculated as

(5.10‑7)

\[\frac{\text{dp}_{\text{x}}}{\text{dt}} = 0.0\]

and

(5.10‑8)

\[\frac{\text{dp}_{\text{in}}}{\text{dt}} = \frac{p_{2} - p_{1}}{\Delta t}\]

where \(p_{1}\) and \(p_{2}\) are the pump head values at the beginning and end of the time interval \(\Delta t\).