3.12. Interaction with Other Models

As mentioned in Section 3.1, the heat-transfer routines interact with a number of other models. These interactions are indicated in Figure 3.1.1.

If PRIMAR-4 is being used, then the subassembly coolant outlet temperatures calculated in the heat-transfer routines are used by PRIMAR-4 to calculate the outlet plenum temperature. Also, if flow reversal occurs in a channel, then the temperature calculated in the heat-transfer routines for the coolant leaving the bottom of the subassembly is used by PRIMAR-4 in the calculation of the inlet plenum temperature. Section 3.3.6 describes how the inlet and outlet plenum temperatures are used in the calculations of the subassembly coolant inlet and reentry temperatures.

Before the onset of voiding, TSHTRN calculates the coolant temperatures used in the coolant channel hydraulics calculations, and the hydraulics routines calculate the coolant flow rates used by TSHTRN.

After the onset of voiding, coolant temperatures are calculate din TSBOIL. This module supplies the heat flux at the cladding outer surface, as defined in Eq. (3.5-2) and used in Eq. (3.5-9) to TSHTRV. TSBOIL uses the calculated cladding temperatures form TSHTRV to obtain extrapolated cladding temperatures, as in Eq. (3.5-3), for use in its coolant temperature calculations.

The point kinetics model supplies the power level used in the heat-transfer routines. In return, the heat-transfer routines supply the temperatures used to calculate reactivity feedback.

3.12.1. Reactivity Feedback

The temperatures calculated in the core thermal hydraulics routines are used to calculate various components of reactivity feedback. These reactivity components include Doppler feedback, axial expansion of the fuel and cladding, density changes in the sodium, core radial expansion and control rod drive expansion. These reactivity feedbacks are described in Chapter 4.

3.12.2. Coupling Between Core Channels and PRIMAR-4

As described in Section 5.2.2, the PRIMAR-4 calculations for a PRIMAR time step are carried out before the core channel coolant calculations. PRIMAR-4 must make estimates of the core flows for a new time step, and it also makes corrections for the differences between its estimates for the previous step and values computed by the core channel coolant routines. The coolant routines supply information to PRIMAR-4 for use in these estimates and corrections. Also, PRIMAR-4 supplies inlet and outlet coolant plenum pressures and temperatures for the use in the core channel calculations.

3.12.2.1. Supplied By PRIMAR-4

The information supplied by PRIMAR-4 is

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

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

\(\frac{\text{dp}_{\text{in}}}{\text{dt}}\) =time derivative of the inlet plenum pressure

\(\frac{\text{dp}_{\text{x}}}{\text{dt}}\) =time derivative of the outlet plenum pressure

\(\rho_{\text{cin}}\) =coolant density in the inlet plenum

\(\rho_{\text{cout}}\) =coolant density in the outlet plenum

\(T_{\text{cin}}\) =coolant temperature in the inlet plenum

and

\(T_{\text{cout}}\) = coolant temperature in the outlet plenum

The pressure \(p_{\text{in}}\) is at an elevation \(z_{\text{pll}}\) and \(p_{\text{x}}\) is at \(z_{\text{plu}}\). At any time, \(t\), during the PRIMAR time step, the inlet plenum pressure is

(3.12-1)\[p_{\text{in}}\left( t \right) = p_{\text{in}}\left( t_{\text{p}1} \right) + \left( t - t_{\text{p}1} \right)\frac{\text{dp}_{\text{in}}}{\text{dt}}\]

and the exit plenum pressure is

(3.12-2)\[p_{\text{x}}\left( t \right) = p_{\text{x}}\left( t_{\text{p}1} \right) + \left( t - t_{\text{p}1} \right)\frac{\text{dp}_{\text{x}}}{\text{dt}}\]

3.12.2.2. Supplied To PRIMAR-4

The information supplied to PRIMAR-4 by the core coolant routines for channel \(ic\) at the subassembly inlet \(\left( L=1 \right)\) or outlet \(\left( L=2 \right)\) is the following:

(3.12-3)\[\Delta m_{\text{c}}\left( L \right) = \sum_{\text{ic}}{N_{\text{ps}}\left( \text{ic} \right)}\int_{t_{\text{p}1}}^{t_{\text{p}2}}{w \left( L,ic \right) }\text{dt}~ ,\]

(3.12-4)\[\Delta m_{\text{c}}T_{\text{c}}\left( L \right) = \sum_{\text{ic}}{\ N_{\text{ps}}\left( \text{ic} \right) }\int_{t_{\text{p}1}}^{t_{\text{p}2}}{w\left( L,ic \right)\ T_{\text{ex}}\left( L,ic \right) }\text{dt}~ ,\]

where

\(w \left(L,ic,t=t_{\text{p}2} \right)\) = computed flow rate at \(t_{\text{p}2}\)

\(T_{\text{ex}} \left( L,ic \right)\) = coolant temperature at the subassembly inlet or outlet

Additionally, the core coolant routines supply the coefficients \(C_{\text{0}}' \left( L,ic \right)\), \(C_{\text{1}} \left( L,ic \right)\), \(C_{2} \left( L,ic \right)\), and \(C_{3}' \left( L,ic \right)\) used by PRIMAR-4 to estimate the core channel flow. PRIMAR-4 estimates the flow into or out of each subassembly using

(3.12-5)\[\begin{split}\frac{\Delta w_{\text{e}}\left( L,ic \right)}{\Delta \text{t}} = C_{0}'\left( L,ic \right) + C_{1} \left( L,ic \right) \left( p \left( \text{JIN} \right) + \theta_{2c} \Delta p\left( \text{JIN} \right) \right) \\ + C_{2} \left( L,ic \right) \left( p \left( \text{JX} \right) + \theta_{2c} \Delta p\left( \text{JX} \right) \right) \\ + 2 \theta_{2c} C_{3}' \left( L,ic \right) w_{\text{e}}\left( L,ic \right) \Delta w_{\text{e}}\left( L,ic \right)\end{split}\]

The core channel calculations use \(w\) as the flow rate per pin, whereas PRIMAR-4 estimates the total flow represented by a channel, so \(N_{\text{ps}} \left( ic \right)\), the number of pins per subassembly times the number of subassemblies represented by the channel, comes into Eq. (3.12-3), Eq. (3.12-4) and the calculations of the coefficients \(C_0'\), \(C_1\), \(C_2\), and \(C_3'\). In the pre-voiding module the coefficients are calculated as

(3.12-6)\[\begin{split}C_{0}' = -\frac{N_{ps}}{I_1} \left( w_{2}^{2} I_{2} + A'_{\text{fL}} w_{2}I_{\text{3L}} + A'_{\text{fr}}w_{2}\left| w_{2} \right|^{1 + b_{\text{fr}}} I_{\text{3T}} + w_{2}\left| w_{2} \right|I_{4} \right. \\ \left. + g\left\lbrack I_{5} + \rho_{\text{cin}}\left( z_{\text{c}}\left( 1 \right) - z_{\text{pll}} \right) + \rho_{\text{cout}} \left( z_{\text{plu}} - z \left( \text{MZC} \right) \right) \right\rbrack\right)\end{split}\]

(3.12-7)\[ C_{1} = \frac{N_{\text{ps}}}{I_{1}}\]

(3.12-8)\[ C_{2} = - C_{1}\]

and

(3.12-9)\[ C_{3}' = - \frac{\left( I_{2}w_{2} + 0.5A'_{\text{fL}}I_{\text{3L}} + \left(1+0.5b_{\text{fr}}\right)A'_{\text{fr}}I_{\text{3T}}\left| w_{2} \right|^{1 + b_{\text{fr}}} + I_{4}\left| w_{2} \right| \right)}{\left| w_{2} \right|I_{1}N_{\text{ps}}}\]

In this case, the coefficients for \(L=2\) are equal to those for \(L=1\).