Page 196 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

System thermal hydraulics for liquid metals 167

and then

v T _ v
2 2
∂v l l, ref l, ref dv l, ref 2
¼ F 1 TðÞ ¼ with _ v l, ref ¼ b 1 +2b 2 T +3b 3 T
∂p w 2 dT
T sl, ref c pl, ref
Deriving again with respect to the temperature, the following correlation is obtained:

_ dF 1 TðÞ d ∂v l
F 1 TðÞ ¼
dT dT ∂p
T
2v l, ref _ v l, ref w sl, ref 2 _ w sl, ref v 2 l, ref
¼
w 3
sl, ref
2 2
_ v +2T _ v l, ref € v l, ref c pl, ref T _ v _ c
l, ref l, ref pl, ref
2
c
pl, ref
where:
2
d v l, ref dw sl, ref
€ v l, ref 2 ¼ 2b 2 +6b 3 T, _ w sl, ref ¼ c 1 +2c 2 T, and _ c pl, ref
dT dT
2
dc pl, ref ¼ d 1 +2d 2 T +3d 3 T .
dT
Finally, the partial derivative of the specific volume with respect to the temperature is

∂v l _
¼ _ v l, ref + F 1 TðÞ p p ref
∂T
p
The thermal expansion coefficient and the isothermal coefficient of compressibility
can be then calculated according to their definitions:
_

1 ∂v l _ v l, ref TðÞ + F 1 TðÞ p p ref
ð
β T, pð Þ ) β T, pÞ ¼
l
l
v l T, pð Þ ∂T v l T, pð Þ
p

1 ∂v l F 1 TðÞ
ð
κ l T, pð Þ ) κ l T, pÞ ¼
v l T, pð Þ ∂p v l T, pð Þ
T
Similar derivations can be used to obtain the specific enthalpy, the specific internal
energy, and the specific entropy of the liquid phase as a function of both temperature
and pressure.
4.3.2 Vapor phase
In principle, in STH codes, the properties of coolants in vapor phase are also needed.
Apart from the sodium, the other liquid metals foreseen in the nuclear field as possible
coolants (such as lead and lead-bismuth) have the boiling temperature so high that