Page 195 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

166 Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

In the following, the procedure adopted by the University of Pisa (UniPi) to imple-
ment the thermodynamic properties of lead, lead-bismuth, lead-lithium, and sodium in
the RELAP5/Mod3.3 is reported.

4.3.1 Liquid phase
From the work of Sobolev (2011), it is possible to find the density, isobaric specific
heat, and sound velocity, for liquid metals of interest in the nuclear field, given as a
5
function of the temperature at a reference pressure p ref of 10 Pa. Starting from these
three aforementioned properties, all the thermodynamic properties can be
reconstructed analytically as a function of temperature and pressure (Kolev, 2011).
Typically, the density at atmospheric pressure (reference pressure, p ref ) of a liquid
metal is given in literature as a linear function of temperature:

ρ l, ref T ðÞ ¼ r 0 + r 1 T

Sometimes, in the STH codes, the use a polynomial form for the specific volume cor-
relation is preferred instead of density:
2
v l, ref TðÞ ¼ b 0 + b 1 T + b 2 T + b 3 T 3

Similarly, the correlation for the isobaric specific heat can be set as a third-order poly-
nomial of temperature:

2
c pl, ref TðÞ ¼ d 0 + d 1 T + d 2 T + d 3 T 3
In the work of Sobolev, the sound velocity of a liquid metal is generally given by a
second-order polynomial function:

w sl, ref TðÞ ¼ c 0 + c 1 T + c 2 T 2

The specific volume of a liquid metal is generally weakly dependent from pressure;
thus, a linear dependence from it can be assumed:

∂v l
v l T, pð Þ ¼ v l, ref TðÞ + F 1 TðÞ p p ref with F 1 TðÞ ¼
∂p
T
Because the specific volume partial derivative with respect to the pressure is assumed
only as a function of temperature, it can be calculated using

Tβ 2 Tβ 2 !
∂v l 2 1 l 2 1 l, ref
¼ v l + ¼ v l, ref + with β l, ref
∂p T w 2 sl c pl w 2 sl, ref c pl, ref
1 dv l, ref
¼
v l, ref dT