Page 202 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

System thermal hydraulics for liquid metals 173

where the first term represents the distributed friction pressure losses through the
single-phase region (usually negligible), the second term represents the loss localized
in singularities (such as the effect of sudden expansion or contraction, valves, and ori-
fices), and the third represents the distributed friction pressure losses along the two-
phase region (usually negligible).
The first and the third terms are characterized by an own characteristic length,
equivalent diameter, flow pattern, and then friction coefficient. Introducing the liquid
flow rate and assuming a constant riser cross section A R , the previous equation can be
written as

2 2
X L X 2 H R _ m l _ m l
Δp fric ¼ f lo + K j + Φ f lo ffi K t
i D e i j lo D e,r 2ρ A 2 2ρ A 2
l R
l R
Since the single-phase and the two-phase distributed pressure losses are negligible in
comparison with the singular pressure drops along the path, K t is independent from the
mass flow rate for turbulent flow regime.
Moreover, under the tested conditions, it can be assumed

ρ ρ g gH R ρ ρ g gH R
l
l
Δp DF ¼ ffi
1 x ρ g _ m l ρ g
1+ S S
x ρ _ m g ρ
l l
So, it is possible to write

ρ ρ g gH R 2
_ m
l
l
ρ ¼ K t 2
_ m l g 2ρ A R
l
S
_ m g ρ l |fflfflfflfflffl{zfflfflfflfflffl}
|fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} Δp fric
Δp DF
Rearranging the previous equation, we have
v ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

u 2 2
3 l g l R
u 2 ρ ρ gH R ρ A
t 0:33
_ m l ¼ _ m g ) _ m l ffi const _ m g
SK t ρ
g
Moreover, the primary LBE side is coupled to the water secondary side by means of a
“tube in tube” counterflow-type heat exchanger (HX) fed by liquid water at low pres-
sure (about 1.5bar) and designed assuming a thermal duty of 30kW. The HX essen-
tially consists of three coaxial tubes with different thicknesses and with an active
length of 1.5m (see Fig. 4.8).
LBE flows downward into the HX inner pipe, while water flows upward in the
annular region between the middle and the outer pipe allowing a countercurrent flow