Page 296 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

266 Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

0.25

0.2

0.15
+
θ rms
0.1

0.05

0
−1 0 1 2
10 10 10 10
y +

Fig. 6.1.2.8 RMS of the temperature fluctuation profile for the turbulent channel flow at Re τ ¼
590 and Pr ¼ 0.01: present work LES (bullets), DNS (solid).
(From Bricteux, L., Duponcheel, M., Winckelmans, G., Tiselj, I., Bartosiewicz, Y., 2012. Direct
and large eddy simulation of turbulent heat transfer at very low Prandtl number: application to
lead-bismuth flows. Nucl. Eng. Des. 246, 91–97.)

+
32.7, Δz ¼ 16.4, Δy + ¼ 1:25, and Δy + ¼ 38:22. This resolution is typical of high-
min max
quality wall-resolved LES. The criteria of Gr€ otzbach (2011), as introduced in
Section 6.1.2.3.4.2, can be verified a posteriori. Characterizing the mesh size as
1/3
Δ ¼ (ΔxΔyΔz) , the LES grid is such that Δ/η < 6, which corresponds to a highly
resolved LES. For the temperature, Δ/η T < 0.2 at Pr ¼ 0.01 and Δ/η T < 0.4 at Pr ¼
0.025. This shows that the temperature field is well-resolved and its simulation does
not require a subgrid-scale flux model. The mean temperature profiles are shown in
Fig. 6.1.2.9 together with the linear law. A log-region is still not present at this Reyn-
+ +
olds and the linear behavior is verified up to y ¼ 60 at Pr ¼ 0.01 and y ¼ 35 at Pr ¼
0.025. At this Reynolds, the effect of the molecular Prandtl number on the heat trans-
port is illustrated by the heat flux decomposition (Figs. 6.1.2.10 and 6.1.2.11). At Pr ¼
0.01, the turbulent heat flux is of the same order of magnitude as the molecular flux
(Fig. 6.1.2.10) whereas, at Pr ¼ 0.025, the turbulent flux is dominant (Fig. 6.1.2.11)
and approximately four times larger than the molecular flux. The important role that
the molecular heat diffusivity still plays in the heat transfer explains the strong differ-
ences between the temperature and the velocity statistics. This is confirmed by the
0
profiles of effective turbulent diffusivity α t ¼ θ v = dθ (Fig. 6.1.2.12), which reach
0
dy
a plateau at y/δ 0.5 and remain nearly constant up to the center of the channel.
The plateau is slightly above α t /α ¼ 1at Pr ¼ 0.01 and slightly below 4 at Pr ¼