It is clear that these three systems will have very different responses to flow perturbations and because of the high pressures involved, flow per­turbations in the gas — and steam-cooled systems due to system rupture are classified as depressurizations (Section 2.2.4).

2.2.1 System Modeling

The modeling of the coolant flow has been treated in the first chapter. The flow enters the core at a low temperature and is raised in temperature through the core. It then transfers the removed heat to a heat sink in the form of a heat exchanger or a turbine.

While in the core, the heat balance in the coolant is represented by an equation of the form

mccc dTJdt = hf(Tf— Tc) — mccct>c dTJdz (2.1)

where the heat-transfer coefficients are flow dependent, according to some correlation between the Nusselt and the Reynolds and Prandtl numbers:

К = a + 0.025(Re)°-8(Pr)0-8 = hfdJkA (2.2)

Thus a reduction of flow reduces the heat removal term in Eq. (2.1) directly through the velocity vc and so Tc increases. The flow reduction also decreases the heat transfer ht and the fuel temperature T{ increases by more than just the increase in T0. It is noted that the coolant temperature in­creases first and is a primary indication of flow reduction.

Flow perturbations arise from: (a) system malfunctions such as pump failures, a loss of system pressure, or blockages which might arise from isolation valve malfunction; and (b) local blockages within the subassembly or at its inlet. The latter cases of local blockages are treated in Section 4.4; this section is concerned with overall system malfunctions.