Page 221 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

192 Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

For the hexagonal lattice fuel assembly in Fig. 5.1, each interior subchannel faces
three fuel rods with one-sixth surface each and thus shares one-half fuel rod surface in
total. The boundary of the edge subchannel and the corner subchannel consists of both
the fuel rod surface and the box surface. The edge subchannel shares also one-half fuel
rod surface, whereas the corner subchannel corresponds only one-sixth fuel rod sur-
face. It is easily concluded that the total number of subchannels in a hexagonal fuel
assembly is

N sc ¼ 2N R + 4 (5.2)

For the square lattice fuel assembly in Fig. 5.6, each interior subchannel faces four fuel
rods with one-fourth surface each and shares one fuel rod surface in total, whereas the
edge subchannel shares one-half fuel rod surface, and the corner subchannel corre-
sponds only one-fourth fuel rod surface. Thus, the total number of subchannels in a
square lattice fuel assembly is

p p
ffiffiffiffiffiffi 2 ffiffiffiffiffiffi
N sc ¼ N R 1 +4 N R 1 + 4 (5.3)
In addition to the average values of the thermal-hydraulic parameters in each sub-
channel, most SCTH programs solve also the thermal conduction equation for the fuel
rod, to calculate the temperature distribution in the fuel rod. For this purpose, various
approaches are possible, starting from simple one-dimensional to complex three-
dimensional methods. In this chapter, the focus is put on the calculation of the
thermal-hydraulic parameters of the fluid.

5.2.1 Basic equations
Asdiscussedinthepreviouschapter,forSCTHanalysis,onefuelassemblyisdividedinto
a large number of subchannels. In the x-y plane perpendicular to the main flow direction,
eachsubchannelrepresentsonemesh.Inthemainflowdirection,thatis,z-coordinate,the
total length is divided into N z meshes. Fig. 5.7 presents one control volume in the SCTH
program.Intheviewpointofmeshstructure,subchannelanalysiscanbetreatedasathree-
dimensional approach with specific coarse mesh in the x-y plane.
However, a subchannel analysis program solves only the conversation equations in
the main flow direction (z-coordinate). The transversal exchange of mass, momentum,
and energy between subchannels (or neighboring meshes in the x-y plane) is consid-
ered with additional source term in the conservation equations for the z-coordinate. In
the following equations, the subscript k presents the identification number of the axial
node, i and j the number of the subchannel in x-y plane, in the axial inlet into the con-
trol volume, out the axial outlet from the control volume, and int the exchange at the
interface between two neighboring subchannels. The conservation equations for one
control volume are summarized below.