Page 155 - Dynamics and Control of Nuclear Reactors

152 CHAPTER 12 Pressurized water reactors

selected process variables to their set points in a timely and safe manner. The variation
of process variable set points with power level is called a steady-state program.

12.8.1 Heat transfer in a steam generator
Relationships that must exist at steady state can be used to define a steady-state pro-
gram. Simplified and approximate versions of these relations suffice here since the
purpose is explaining the development of a steady-state program. The relationship
for heat transfer in the steam generator is as follows:

P SG ¼ U SG A SG θ avg T S (12.1)
where

P SG ¼power extracted from the steam generator
θ avg ¼average primary coolant temperature in the core (and the steam generator)
T S ¼average steam temperature
U SG ¼steam generator overall heat transfer coefficient from primary coolant to
secondary side
A SG ¼steam generator heat transfer surface area.

Eq. (12.1) shows that average coolant temperature and steam temperature cannot
both be constant if the value of U SG is constant. Reactors with U-tube steam gener-
ators produce saturated steam and almost all of the heat transfer surface produces
boiling. The steam generator overall heat transfer coefficient varies only slightly
with changes in power level. Therefore, the choice is to hold either average coolant
temperature or steam temperature constant or to cause both to change in a
prescribed way.
Here, we make the assumption that the overall heat transfer coefficient is constant
at all power levels. This is not strictly true, but it is close enough for facilitating our
understanding of steady state programs.
Other relationships are necessary at steady state condition. They are stated in the
following.

12.8.2 Fuel-to-coolant heat transfer

P R ¼ U FC A FC T F θ avg (12.2)
where

U FC ¼average fuel-to-coolant heat transfer coefficient
A FC ¼fuel-to-coolant heat transfer surface area
T F ¼average fuel temperature
P R ¼reactor power (thermal power transferred from fuel to coolant).