Page 124 - Dynamics and Control of Nuclear Reactors

10.8 Steam generator model 119

dT t
ð
M t C t ¼ UA T t θ p1 + UA T t θ s1 Þ (10.13)
dt
dθ s1 UA
ð
M s1 C s ¼ W s C s θ sin θ s1 Þ + ð T t θ s1 Þ (10.14)
dt 2
dθ s2 UA
ð
M s2 C s ¼ W s C s θ s1 θ s2 Þ + ð T t θ s1 Þ (10.15)
dt 2
where
M p1 ¼mass of primary fluid node-1
M p2 ¼mass of primary fluid node-2
M t ¼mass of metal node (heat exchanger tubing)
M s1 ¼mass of secondary fluid node-1
M s2 ¼mass of primary fluid node-2
W p ¼flow rate of primary fluid
W s ¼flow rate of secondary fluid
C p ¼specific heat capacity of the primary fluid
C s ¼specific heat capacity of the secondary fluid
C t ¼specific heat capacity of the tube metal
U¼overall heat transfer coefficient from primary fluid to metal, or from metal to
secondary fluid
A¼heat transfer area from primary fluid to metal node, or from metal node to
secondary fluid
θ pin ¼temperature of primary fluid inflow
θ sin ¼temperature of secondary fluid inflow
θ p1 ¼temperature of primary fluid node-1
θ p2 ¼temperature of primary fluid node-2
θ s1 ¼temperature of secondary fluid node-1
θ s2 ¼temperature of secondary fluid node-2
T t ¼temperature of metal (tube) node

10.8 Steam generator model
Steam generator modeling can be simple or complex. Fig. 10.7 shows a typical
U-tube steam generator. Different requirements for secondary system modeling
determine the detail required for steam generators.
For example, if the simulation focuses on reactor behavior, then a simple steam
generator model that adequately simulates heat removal is adequate. A simple
model, called the “teakettle model” represents steam generator dynamics with only
three Eqs. A schematic representation of a teakettle model appears in Fig. 10.8. This
approach has been found to represent heat transfer to the secondary fluid quite well in
overall system simulations [1].