Page 156 - Dynamics and Control of Nuclear Reactors

12.8 Steady-state programs for PWRs 153

12.8.3 Equivalence between reactor power and power delivered to
the steam generator at steady state
At steady state operation the reactor power is equal to the heat transferred in the
steam generator.

P R ¼ P SG (12.3)
The average temperature in Eqs. (12.1) and (12.2) is defined as

ð θ HL + θ CL Þ
θ avg ¼ (12.4)
2
θ HL ¼ 2 θ avg θ CL
where
θ HL ¼average hot leg temperature.
θ CL ¼average cold leg temperature.

12.8.4 Energy change in the coolant
The energy carried by the flowing primary coolant is given by
P ¼ WC θ HL θ CL Þ (12.5)
ð
or

P ¼ WC 2θ avg 2θ CL (12.6)
Solving for the cold leg temperature gives
P
θ CL ¼ θ avg (12.7)
ð 2WCÞ
where
W¼mass flow rate of coolant
C¼specific heat capacity of coolant.
Now consider the case in which the average coolant temperature for power level, P, is
specified. Then θ CL is given by Eq. (12.7). The hot leg temperature, θ HL , is given by
(12.8)
θ HL ¼ 2 θ avg θ CL
Control rod action permits operation with constant average coolant temperature, con-
stant average steam temperature or prescribed changes in average coolant tempera-
ture and steam temperature as a function of steady state reactor power.

12.8.5 Development of a steady-state program
The development of a steady state program in which it is desired to specify average
coolant temperature proceeds as follows: