Page 299 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Large-eddy simulation: Application to liquid metal fluid flow and heat transfer 269

6

5

4

Pr t
3

2

1

0
0 500 1000 1500 2000
y +

Fig. 6.1.2.13 Turbulent Prandtl number for the turbulent channel flow at Re τ ¼ 2000: LES Pr ¼
0.01 (solid), LES Pr ¼ 0.025 (dash).
(From Duponcheel, M., Bricteux, L., Manconi, M., Winckelmans, G., Bartosiewicz, Y., 2014.
Assessment of RANS and improved near-wall modeling for forced convection at low Prandtl
numbers based on LES up to Re τ ¼ 2000. Int. J. Heat Mass Transf. 75 (2), 470–482.)

0.025. However, the turbulent eddy viscosity ν t ¼ u v = du tends to decrease after
0
0
dy
reaching its peak. Consequently, the turbulent Prandtl number,
ν t
Pr t ¼ , (6.1.2.63)
α t
+
does not remain constant and tends to slightly decrease after y ¼ 500 (Fig. 6.1.2.13).
The turbulent Prandtl number profiles exhibit a narrow peak very close to the wall,
+
followed by a sharp decrease up to y ¼ 300, and then a slowly decreasing plateau:
around Pr t 1.22 at Pr ¼ 0.01 and Pr t 1.0 at Pr ¼ 0.025. Those profiles are quite
different to the single value used in RANS, Pr ¼ 0.85, whatever the molecular
Prandtl number.

6.1.2.5 Concluding remarks

This chapter briefly introduced the LES approach, with a focus on the implicit-filtered
LES or grid-LES. The closure problems for the momentum and the thermal field were
also presented in the frame of low Prandtl number fluid for the thermal field. Regard-
ing the momentum closure, there is no specificity related to liquid metals and such
LES does not differ from an LES of any fluid flow. Nevertheless, the hybrid approach