Page 121 - Dynamics and Control of Nuclear Reactors

116 CHAPTER 10 Reactor thermal-hydraulics

Pure time delay models are often used. That is the formulation is simply as
follows:
ð
θ out tðÞ ¼ θ in t τÞ (10.8)
where

τ¼residence time in the piping.
Well-stirred-tank models are also used. The rationale for a well-stirred-tank model is
that some axial mixing does occur in piping. The more general dynamic formulation
of the temperature of the liquid in the piping has the form

dθ out 1
¼ ð θ in θ out Þ (10.9)
dt τ
The resident time is approximated as the ratio between the mass of fluid (M p ) in the
piping and the fluid flow rate (W p ).
τ ¼ M p =W p (10.10)

10.6 Pressurizer
A PWR pressurizer is a vessel with liquid water in the bottom section and saturated
steam in the top section. A pressurizer is used to regulate the primary coolant pres-
sure ( 150 bars) in PWRs and CANDU reactors. The pressurizer is connected to one
of the hot leg pipings with a long surge line. Fig. 10.4 shows a typical pressurizer.
Because of the contact between steam and liquid water, the water is also at the sat-
uration temperature at steady state. Spray of cooler water enters from the top and
electrical heaters at the bottom heat the liquid water. The steady state can be dis-
turbed by water inflow or outflow, changes in inlet water temperature, changes in
spray flow or changes in heater power.
A PWR pressurizer control system can alter the pressure by modulating heater
power and/or spray flow. A schematic representation of a pressurizer model structure
appears in Fig. 10.5.
As shown in Chapter 14, PWR and CANDU reactor pressurizers are slightly
different.

10.7 Heat exchanger model
Mann’s formulation also may be used in liquid-liquid heat exchangers. Fig. 10.6
shows the model. The equations are as follows:

dθ p1 UA
M p1 C p ¼ W p C p θ pin θ p1 + T t θ p1 (10.11)
dt 2

dθ p2 UA
M p2 C p ¼ W p C p θ p1 θ p2 + T t θ p1 (10.12)
dt 2