Page 295 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Large-eddy simulation: Application to liquid metal fluid flow and heat transfer 265

3

2.5

2

θ + 1.5

1

0.5

0
−1 0 1 2
10 10 10 10
y +

Fig. 6.1.2.7 Mean temperature profile for the turbulent channel flow at Re τ ¼ 590 and Pr ¼
+
+
0.01. present work LES (bullets), DNS (solid), theoretical near-wall behavior θ ¼ Pr y (dash).
(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.)
model. However, the temperature field is fully resolved by the LES grid as it is much
smoother than the flow. A more quantitative validation is provided in Figs. 6.1.2.7 and
6.1.2.8 with the comparison with the DNS results. Both the mean temperature profile
(Fig. 6.1.2.7) and the RMS temperature profile (Fig. 6.1.2.8) correspond very well to
those of the DNS, which completely validates the V-LES/T-DNS approach. In
Fig. 6.1.2.7, it is also interesting to note the absence of the logarithm range, which
proves the nonvalidity of the Reynolds analogy for such Prandtl number. Furthermore,
one can observe that the linear behavior of the temperature profile is verified up to
+
y 60, this value would tend to increase by increasing the Re or decreasing the
Pr (e.g., for sodium). This results are crucial in wall-function RANS modeling for
+
which a first grid point at y Oð100Þ is advised according the Re, that is, where
the log-region is supposed to prevail for both the velocity and temperature. For such
considerations, the reader is invited to refer to Duponcheel et al. (2014).

6.1.2.4.3 V-LES/T-DNS at higher Reynolds

In this section we apply the V-LES/T-DNS previously validated to a higher Reynolds
case, that is, Re τ ¼ 2000 (Re ¼ 84, 000) and for Pr ¼ 0.025 and Pr ¼ 0.01. The domain
is the same as described in the previous section and the mesh is N x N y N z ¼ 384
+
256 384 and the stretching factor is γ ¼ 2.4, corresponding to a resolution of Δx ¼