5.11. Interaction With Other Models

5.11.1. Information Received by PRIMAR from Other Models

PRIMAR-1 receives no information from other routines. It is driven entirely by the input regardless of what happens elsewhere in the code. Three kinds of input can be supplied: a pressure drop as a function of time, a normalized channel flow rate as a function of time, or the parameters for an exponentially decreasing pressure drop. These are described in Section 5.10 and mentioned in the input listing in Chapter 3.

PRIMAR-4 receives $C_{0}'$, $C_{1}$, $C_{2}$, and $C_{3}'$ and also the inlet and outlet temperatures for each core channel from the coolant dynamics routines. These are the variables described in Section 5.2.2. The coolant dynamics routines also supply PRIMAR with the net mass flow and the net mass flow times temperature from all of the core channels to each outlet plenum, as well as the net mass flow and the net mass flow times temperature into all of the core channels from each inlet plenum during the last PRIMAR time step. The PRIMAR model then adjusts the inlet and outlet plenum mass, pressure, and cover-gas interface to account for differences between the estimated channel flows (PRIMAR) and the computed channel flows (coolant dynamics routines) for the last PRIMAR time step. Symbolically,

(5.11-1) $$\Delta m = \int{w_{\text{c}} \text{dt}} - \int{w_{\text{e}} \text{dt}}$$

where

$\Delta m$ = the mass adjustment

$w_{\text{c}}$ = the total calculated mass flow rate from all the core channels

$w_{\text{e}}$ = the total estimated mass flow rate from all the core channels

The integration is over the time step. Then

$m_{\text{l}} = m + \Delta m$

$V_{\text{l}} = m_{\text{l}}/\rho_{\text{l}}$

$z_{\text{inter}} = z_{\text{ref}} + V_{\text{l}}/A_{\text{inter}}$

where

$m_{\text{l}}$ = the adjusted liquid mass in the plenum

$m$ = the liquid mass in the plenum before adjustment

$V_{\text{l}}$ = the liquid volume in the plenum

$\rho_{\text{l}}$ = the liquid density in the plenum

$z_{\text{inter}}$ = the liquid interface height in the plenum

$z_{\text{ref}}$ = the reference height input for the plenum

$A_{\text{inter}}$ = the area of the liquid interface input for the plenum

The coefficients $C_{0}'$, $C_{1}$, $C_{2}$, and $C_{3}'$, supplied to the PRIMAR model by the coolant dynamics routines, are used to estimate the rate of change in the mass flow rate for each channel, as indicated in Eq. (5.2-21) and written more simply for a particular channel as

(5.11-2) $$\frac{\text{dw}}{\text{dt}} = C_{0}' + C_{1} \left( p_{in} + \theta_2 \Delta p_{in} \right) + C_{2} \left( p_{\text{x}} + \theta_2 \Delta p_{\text{x}} \right) + 2 \theta_2 C_{3}' w \Delta w$$

where the symbols have the same meaning as in Eq. (5.2-26). Before boiling begins in a core channel, $\text{dw}/\text{dt}$ depends on $p_{\text{in}} - p_{\text{x}}$, and $C_{1}$ is set equal to $- C_{2}$. After boiling starts, the inlet flow is independent of $p_{\text{x}}$, and depends on $p_{\text{in}} - p_{\text{b}}$, where $p_{\text{b}}$ is the bubble pressure. Also after boiling starts, the outlet flow is independent of $p_{\text{in}}$, and depends on $p_{\text{b}} - p_{\text{x}}$. The bubble pressure $p_{\text{b}}$ is included in $C_{0}'$.

5.11.2. Information Supplied by PRIMAR to Other Models

PRIMAR supplies information to the pre-voiding coolant dynamics routines, the boiling model, LEVITATE and PLUTO-2. Both PRIMAR-1 and PRIMAR-4 supply the same information, but it is arrived at differently by the two options. The information supplied is

$p_{\text{in}}\left( t_{\text{P}1} \right)$ = the inlet plenum pressure at the beginning of the PRIMAR time step

$p_{\text{out}}\left( t_{\text{P}1} \right)$ = the outlet plenum pressure at the beginning of the PRIMAR time step

$\frac{\text{dp}_{\text{in}}}{\text{dt}},\ \frac{\text{dp}_{\text{out}}}{\text{dt}}$ = the time derivatives of the inlet and outlet plenum pressures

$T_{\text{in}} T_{\text{out}}$ = the inlet and outlet plenum temperatures

At any time t during the PRIMAR time step, the inlet and outlet plenum pressures are taken as

(5.11-3) $$p_{\text{in}}\left( t \right) = p_{\text{in}} \left( t_{\text{P}1} \right) + \left( t - t_{\text{P}1} \right) \text{dp}_{\text{in}}/\text{dt}$$

and

(5.11-4) $$p_{\text{out}}\left( t \right) = p_{\text{out}}\left( t_{\text{P}1} \right) + \left( t - t_{\text{P}1} \right) \text{dp}_{\text{out}}/\text{dt}$$

The plenum pressures $p_{\text{in}}$ and $p_{\text{out}}$ that PRIMAR supplies to the coolant routines are at the plenum reference heights $z_{\text{PLENL}}$ and $z_{\text{PLENU}}$, and the coolant routines compute the core channel inlet and outlet pressures from these by the formula:

(5.11-5) $$p\left( z_{\text{ci}} \right) = p_{\text{in}} + \rho_{\text{in}} g\left( z_{\text{PLENL}} - z_{\text{ci}} \right)$$

and

(5.11-6) $$p\left( z_{\text{co}} \right) = p_{\text{out}} + p_{\text{out}} g\left( z_{\text{PLENU}} - z_{\text{co}} \right)$$

It should be noticed that in the PRIMAR-4 input (ZCVL) a reference height is entered for each compressible volume, including the compressible volumes that are the inlet and outlet plenums. In addition, inlet and outlet plenum reference heights, $z_{\text{PLENL}}$ and $z_{\text{PLENU}}$, are also entered as input (ZPLENL and ZPLENU, or ZPLENC). If these two sets of reference are different, the PRIMAR-4 code calculates the appropriate adjustments and passes the inlet and outlet plenum pressures at $z_{\text{PLENL}}$ and $z_{\text{PLENU}}$ to the coolant routines.

The inlet and outlet plenum temperatures are discussed in Section 3.3.6 of Chapter 3.