Page 76 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Rod bundle and pool-type experiments in water serving liquid metal reactors 51

U ch ∂U V ch ∂V
+ ¼ 0: (3.1.9)
L ∂X H ∂Y

Limiting the analysis to values of H/L close to unity and considering normalized hor-
izontal component of velocity U of the same order of magnitude V (incompressible
flow), the order of magnitude analysis suggests

X Oð1Þ; Y Oð1Þ; V Oð1Þ; U V

being the characteristic quantities chosen to normalize variables to 1. The dimension-
less continuity equation becomes

V ch
U ch L : (3.1.10)
H

Replacing this expression and the normalized quantities in the y-momentum equation
and energy transport, we obtain

2
2 2
∂V ∂V 1 ΔP ch ∂P y ν H ∂ V ∂ V Hgβ T h T c Þ
ð
U + V ¼ + + θ
2
2
2
∂X ∂Y ρ V ch ∂Y V ch H L ∂X 2 ∂Y 2 V ch
0
(3.1.11)
2 2
2
2 2
2
∂θ ∂θ k H ∂ V ∂ V α H ∂ V ∂ V
U + V ¼ + ¼ + : (3.1.12)
2
2
∂X ∂Y ρc p V ch H L ∂X 2 ∂Y 2 V ch H L ∂X 2 ∂Y 2
The choice of a value for the characteristic velocities and characteristic pressures
depends strongly on the phenomena under analysis. For this reason, the forced con-
vection and the natural convection case will be treated separately.
3.1.2.1 Forced convection for pool-type investigation
In forced convection, the prediction of a typical velocity value can be easily made
considering the mass conservation in a section of the primary loop: the mass is deter-
mined by the power of the pumps, designed accordingly to the coolant heat capacity
and the core power, and designed with the purpose of keeping the maximum value of
temperature below a certain level. In this case, the similarities with respect to scale
down the reactor are directly the dimensionless groups appearing in Eqs. (3.1.11),
(3.1.12):

V ch H 1 ΔP ch Hgβ T h T c Þ
ð
Re ¼ Reynolds; Eu ¼ Euler; Ri ¼ Richardson;
ν ρ V 2 ch V 2 ch
0
V ch H H
Pe ¼ P eclet; Geometrysimilarity:
α L