Page 192 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

System thermal hydraulics for liquid metals 163

Control No exchange due to fluid motion can occur
volume in this case

Generally, the Lagrangian approach is more familiar (e.g., thermodynamics makes an
extensive use of it), but STH and computational fluid dynamic (CFD) codes often
adopt the Eulerian approach. Moreover, two-phase conditions may further complicate
the problem no matter of the considered point of view. Two-phase conditions can be
due to the presence of vapor of the same coolant fluid or for the presence of incon-
densable gases.
In the case of two-phase flow, even more complicating aspects come into play,
owing to the fact that at each spatial location, either phase may be present at a given
time. This is customarily accounted for by the phase density function (see Todreas and
Kazimi, 2012):

!
! 1, if the k thphase is present in r attime t
α k r , t ¼ !
0, if thek thphase is not present in r attime t
The local instantaneous form of balance equations for phase k (k¼f for liquid phase or
k¼g for vapor phase) is

∂ ! !
ð ρ ψ Þ ¼ — ρ ψ w k — J ψ,k + ρ S ψ,k
k
k
k
k
k
∂t |fflfflfflfflfflffl{zfflfflfflfflfflffl} |fflffl{zfflffl}
|fflfflfflfflffl{zfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflffl}
diffusion volumetric
variation convection advectionÞ
ð
source
in time due to fluid motion
!
where the expression of the intensive property ψ k , diffusion flux J ψ,k , and the source
term S ψ,k depends on the particular accounted balance equation (see Table 4.2).
To be used in STH codes, these equations must be subjected to.
l time averaging, to filter the fluctuations due to turbulence;
l space averaging, to operate in terms of area-averaged variables and to obtain 1-D versions of
the equations.

Table 4.2 Specific terms of the differential fluid transport equations
Mass balance ψ k ¼1 ! S ψ,k ¼0
J ψ,k ¼ 0
Momentum ! ! ! S ψ,k ¼g
!
k
ψ ¼ w k ! ! !
balance J ψ,k ¼ p k I τ k
2
Energy ψ k ¼u k +w k /2 ! ! ! q 000 ! !
! ! S ψ,k ¼
! 00 ! ! + g w k
balance J ψ,k ¼ q + p k I τ k w k ρ k