# Schematics of a PWR reactor coolant system and the secondary side of the steam generator are shown..

Schematics of a PWR reactor coolant system and the secondary
side of the steam generator are shown in the figure. The reactor is shutdown
and the decay power is being steadily removed by the residual heat removal
system (not shown in the figure). At this steady state operation, the average
temperature in the primary side is equal to the temperature of water in the
secondary side of the steam generator, hence, there is no heat transfer taking
place in the steam generator tubes. At time zero, we lose the cooling of the
residual heat removal system, we inject water at a specified flow rate and
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Schematics of a PWR reactor coolant system and the secondary
side of the steam generator are shown in the figure. The reactor is shutdown
and the decay power is being steadily removed by the residual heat removal
system (not shown in the figure). At this steady state operation, the average
temperature in the primary side is equal to the temperature of water in the
secondary side of the steam generator, hence, there is no heat transfer taking
place in the steam generator tubes. At time zero, we lose the cooling of the
residual heat removal system, we inject water at a specified flow rate and
enthalpy into the primary side, and we turn on the reactor coolant pumps (not
shown in the figure). a) Set up the governing differential equations. Use one
control volume for the primary side water and one for the secondary side water,
b) solve the differential equations to find the primary side and secondary side
temperatures as functions of time and other system parameters specified below,
c) use the given data and plot the surge flow rate (out of the primary side) as
a function of time for the first ten minutes from the start of the event. The
primary and the secondary sides are identified with subscripts P and S,
respectively.

a) The primary and secondary sides pressures remain constant
throughout the event,

b) water in both control volumes remains subcooled for the
duration of interest such that du _
dh _ cdT,

c) the overall heat transfer coefficient U remains constant,

d) no water enters or leaves the secondary side.

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