Page 120 - Dynamics and Control of Nuclear Reactors

10.5 Plenum and piping models 115

10.4 Boiling coolant
Modeling channels with boiling fluid is more complex than modeling channels with
single-phase fluid. Boiling heat transfer models are needed for BWRs and steam
generators.
Consider a heated channel into which liquid fluid is introduced into a channel
with boiling fluid. The fluid temperature in the sub-cooled region at the entrance
increases as it travels through the channel. At some point, the hotter fluid adjacent
to the heated surface reaches saturation temperature even though the fluid farther
from the heated surface remains sub-cooled. Boiling begins near the surface. The
heat transfer coefficient for this region is greater than in the sub-cooled region.
As the fluid continues through the channel, the bulk fluid temperature reaches sat-
uration and vigorous boiling throughout the fluid occurs. High heat transfer coeffi-
cients occur in this region. A mixture of liquid and vapor exists in this region. This
liquid-vapor mixture exits the core in BWRs and in U-tube steam generators. If all of
the liquid boils before exiting the heated region (as in once-through steam genera-
tors), continuing heat transfer results in superheating of the steam. In a transient,
the boundaries between the different regions move. Models have been developed
in which these boundaries are state variables.
Moving boundary models for BWRs and steam generators are quite complex, too
complex for inclusion in this introductory book. But the concept is important. Appen-
dix F illustrates the approach with a moving boundary model for the subcooled node
in a heated channel.

10.5 Plenum and piping models
Plenums are regions in which fluid enters and mixes with the existing fluid inventory.
Plenums exist at core inlets and outlets and at steam generator inlets and outlets.
Well-stirred-tank models are usually used for plenums. The model is as follows:

dθ p
M p C p ¼ WC p θ pin θ p (10.7)
dt
where
M p ¼mass of fluid in the plenum
C p ¼specific heat capacity of the fluid
W¼fluid flow rate
θ p ¼fluid temperature in the plenum (equal to plenum outlet temperature because
of well-stirred-tank approximation)
θ pin ¼temperature of fluid entering the plenum
Piping carries fluid from one reactor subsystem to another. Piping models are used
for hot leg and cold leg piping in PWRs and CANDU reactors, and feedwater for
BWRs and steam generators.