Page 128 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Design of experimental liquid-metal facilities 101

3.2.6 Test section pressure drop

This paragraph reports the analytic calculation for the evaluation of the pressure drops
along the main flow path of the test section in forced circulation. For a closed loop in
steady-state conditions, by the momentum transport equation (Rozzia, 2014), it is pos-
sible to write the following relationship:

Δp ¼ Δp (3.2.4)
DF fric
where Δp DF represents the driving force available and Δp fric indicates the overall fric-
tional pressure drop along the loop.
The driving force, in the case of gas-enhanced circulation, can be expressed as
follows:

Δp DF ¼ ΔρgH r ¼ ρ LBE ρ r,TP gH r (3.2.5)
where H r is the riser height; ρ LBE is the average density of the LBE; and ρ r, TP is the
two-phase density inside the riser, which can be evaluated through the average void
fraction α, the LBE average density ρ LBE , and the gas average density ρ :
g
ρ ¼ αρ +1 αÞρ (3.2.6)
ð
r,TP g LBE
The Δρ can be expressed as
h i

Δρ ¼ ρ ρ ¼ ρ αρ +1 αÞρ ¼ α ρ ρ
ð
LBE r,TP LBE g LBE LBE g
αρ (3.2.7)
LBE
assuming to neglect the gas average density ρ because it is much smaller than
g
ρ LBE , and then, the Δp DF can be written as follows:
Δp DF ¼ αρ LBE gH r (3.2.8)
obtaining a value of 38kPa, as the riser length is 3.8m.
The overall frictional pressure drop along the circuit can be evaluated with the fol-
lowing correlation:

1 M _ 2
Δp ¼ (3.2.9)
fric 2 K eff
2ρ A
eff eff
where

M is the LBE mass flow rate,
l _
A eff is the effective flow area,
l
ρ eff is the effective LBE density,
l
K eff is the effective pressure drop coefficient.
l