Page 264 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

234 Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Second specific behavior of the passive scalar turbulence at Pr ¼ 0.01 is shown in
Fig. 6.1.1.3 (right): Solid line DNS results in this figure are obtained at Re τ ¼ 180 with
the same resolution and in the same computational domain size as in the DNS
described in Moser et al. (1999) (solid line). Other two profiles are obtained with
the same spatial resolution but in larger computational domains: the “large” domain
and the “very large” domain results were obtained in 3 3 and 6 6 larger compu-
tational domains in streamwise/spanwise direction, respectively. These large domains
thus allowed tracking of larger turbulent structures. Fig. 6.1.1.3 (right) shows that tem-
perature fluctuations at the wall in the “very large” domain are 20% larger than in the
“normal” computational domain. This is another result that is not observed at moder-
ate Prandtl numbers. The explanation lies in the very large turbulent structures, which
are too weak to have any kind of influence on velocity field statistics and also on tem-
perature field statistics at Pr around unity (Tiselj, 2014). However, in low Pr number
flows the relative importance of these structures grows, because high thermal diffu-
sion eliminates smaller structures much more effectively than the larger structures
with longer wave lengths. It is a rather well known fact from mathematical physics,
that diffusion typically dumps higher frequencies (short wave lengths) of any kind of
wave motions more efficiently than lower frequencies (long wave lengths). It is
important to emphasize that velocity statistics were not influenced by the enlarged
computational domain and the mean temperature profiles at Pr ¼ 0.01 also remained
unaffected. The same effect of computational domain size is visible (Tiselj, 2014) also
at Re τ ¼ 395, but remains to be confirmed at higher Reynolds numbers.
Two of the more important statistical quantities are streamwise and spanwise tur-
bulent heat fluxes, as they are usually needed in development of the LES/RANS
(Reynolds Averaged Navier-Stokes) turbulent models. Fig. 6.1.1.4 shows that turbu-
lent heat fluxes in liquid metal flow at low Re represent only a small fraction of the
total heat flux q w ¼ 1. Profiles in Fig. 6.1.1.4 show differences between the fluctuating

0.05 0.03
F-normal
F-normal F-large
0.04 F-large 0.025 F-very large
F-very large N-normal
N-normal
N-large
N-large 0.02 N-very large
0.03
<u′θ′> x,z,t <v′θ′> x,z,t 0.015
N-very large
0.02
0.01
0.01
0.005
0
0 20 40 60 80 100 120 140 160 180 0
y + 0 20 40 60 80 100 120 140 160 180
y +
Fig. 6.1.1.4 Streamwise (left) and wall-normal (right) turbulent heat flux profiles at Pr ¼ 0.01
computed in “normal,” “large,” and “very large” computational domains. Results are shown for
ideal fluctuating (F) and ideal nonfluctuating (N) temperature boundary condition.
(Figures from Tiselj, I., 2014. Tracking of large-scale structures in turbulent channel with DNS
of low Prandtl number passive scalar. Phys. Fluids 26 (12), 125111.)