Page 312 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

282 Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

is a challenging task, since it contains twice as many free parameters compared with
the equation for the dissipation rate of turbulence kinetic energy. Determining all the
new coefficients associated with the modeling of various terms in the ε θ equation
requires information that is not yet available for different flows. Once such type of
four equation model (Kenjeres and Hanjalic, 2000) was considered within the THINS
project. This AHFM-2000 has been implemented in the TransAt code of ASCOMP.
The code will allow the user to apply this model in combination with several
implemented nonlinear k-ε turbulence models. This model is originally developed
to provide improved solutions for the natural convection flow regime for fluids with
a Prandtl number close to unity (e.g., air). Validation of this model for a natural con-
vection heated cavity has shown good performance as mentioned by Roelofs et al.
(2015a). Further assessment of this model for low Prandtl numbers and for other flow
regimes should be performed in the near future.

AHFM-2005 (Kenjeres et al., 2005)
Another approach used to close the aforementioned system would be to evaluate the ε θ
from the thermal to mechanical timescale ratio R. It has been shown by Dol et al.
(1997), Hanjalic et al. (1996a,b), and Kenjeres and Hanjalic (2000) that the assump-
tion of the constant timescale ratio (implying a direct proportionality of the thermal
and mechanical scales) works reasonably well in a number of flows as compared with
DNS or experimental data, indicating that this parameter is not very influential. Nev-
2
ertheless, this approach reduces the model to three equations, k, ε, and θ . Kenjeres
and Hanjalic (2000) have shown that the three equation model with R¼ 0.5 gives very
similar results as the four equation model. Consequently, Kenjeres et al. (2005) pro-
posed a new model, which is based on three equations, here called AHFM-2005. The
expression for the turbulent heat flux is given as

∂T ∂U i

τ u βg i θ 2 a (6.2.1.10)
θu i ¼ C t 0 c C t 1 i u j + C t 2 θu j + C t 3 + C t 4 ij θu j
∂x j ∂x j
where g i is the gravity vector, a ij is the Reynolds stress anisotropy tensor, and τ c is the
characteristic timescale. In addition, C t0 , C t1 , C t2 , C t3 , and C t4 are the model coeffi-
cients that are given in Table 6.2.1.1.

Table 6.2.1.1 Model coefficients for the considered AHFM
R
Model C t0 C t1 C t2 C t3 C t4
AHFM-2005 0.15 0.6 0.6 0.6 1.5 0.5
AHFM-NRG 0.2 0.053 0.6 2.5 0 0.5
ln(Re Pr) 0.27
AHFM-NRG+ 0.2 0.25 0.6 4.5 10 9 log 7 0 0.5
(Ra Pr)+2.5