Page 116 - Dynamics and Control of Nuclear Reactors

CHAPTER

Reactor thermal-

hydraulics 10

10.1 Introduction
Temperature and pressure of reactor fluids and solids are important variables in
steady state and transient operation. Along with associated coefficients of reactivity,
they determine the magnitude of reactivity feedbacks. Conservation of mass, energy,
and momentum are the basis for thermal-hydraulics models. However, since pressure
transients reach a new steady state so much faster in a transient than mass or energy,
the differential equation for momentum is usually unnecessary. Much of the infor-
mation in this chapter comes from Ref. [1].
This chapter includes short descriptions of major heat transport systems in
nuclear power reactors. Chapters 12, 13, and 14 provide more detailed information
about power reactor characteristics and control systems.

10.2 Heat conduction in fuel elements
Most of the reactors addressed in this book use cylindrical UO 2 fuel rods clad in zir-
caloy and have a gas-filled gap between the UO 2 and the cladding. Fuel heat transfer
in reactors with non-cylindrical fuel elements (such as high temperature gas cooled
reactors and molten salt reactors).is not addressed here.
A complete heat transfer model would require a partial differential equation in
two spatial dimensions (axial and radial … azimuthal is not required) and time. Solu-
tions of such a model equation are known, but they are not suitable for coupling with
models for cooling fluid. Instead, lumped parameter models (also, sometimes
referred to as nodal models) must be used. Lumped parameter models involve break-
ing the system into regions with uniform internal properties and coupling to adjacent
regions. It is possible to model fuel rods with concentric radial lumps, but the sim-
plest and most common lumped parameter model for cylindrical fuel elements uses a
single radial node.
Consider a single radial node model for a fuel element with heat transfer to fluid
coolant. The fuel has mass, M f , and specific heat capacity, C f . The model equation is
as follows:
dT f
M f C f ¼ UA T f θ avg + P f (10.1)
dt
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