Page 224 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Subchannel analysis for LMR 195

The cross flow enthalpy h* is determined as follows:

∗ ∗
h ¼ h i , if G 0 (5.12)
ij ij
∗ ∗
h ¼ h J , if G 0 (5.13)
ij
ij

5.2.2 Closure models

To solve the equation system listed above, closure equations for the friction coeffi-
cient f, local pressure-drop coefficient ε, heat-transfer coefficient α, and transversal
mass fluxes G and G* are required.
0

5.2.2.1 Pressure drop
In a control volume, the total pressure drop consists of four parts, that is, pressure drop
due to acceleration, gravitational force, friction, and local hydraulic resistance. The
first two terms can be accurately calculated by knowing the geometric parameters
and the density variation, whereas the determination of the last two parts requires clo-
sure equations.
The friction pressure drop is usually defined as

Δp f 1 ρ u 2
¼ f (5.14)
Δz D h 2
Closure equation is needed to compute the friction factor f. For bare rod bundles, the
following correlation is recommended (Todreas and Kazimi, 2012):
" #
2
1 P P
f b ¼ n a + b 1 1 + b 2 1 (5.15)
Re D D
with n¼1.0 for laminar flow and n¼0.18 for turbulent flow. The coefficients a, b 1 ,
and b 2 are dependent on the lattice arrangement and SC types and can be found in
Todreas and Kazimi (2012).
For high Reynolds number, Re>100,000, experimental measurements pointed out
that the prediction models for circular tubes provide reasonable results also for bare
rod bundles, if hydraulic diameter is applied (Todreas and Kazimi, 2012). The friction
coefficient in circular tubes of the same hydraulic diameter is computed with the cor-
relation of Colebrook (1939):

1 2δ 18:7
p ffiffiffi ¼ 1:74 2 log + p ffiffiffi (5.16)
f D h Re f

In many SCTH code, the general form of equation is provided: