Page 294 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

264 Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

scheme in the wall-normal direction. This implicit time-stepping is required because
of the very small heat conduction time scale, which is, at very low Prandtl, more strin-
gent that the convective time scale (i.e., the CFL condition).

6.1.2.4.2 Validation of the V-LES/T-DNS approach

In this section, the results of a V-LES/T-DNS (as explained in Section 6.1.2.3.4.2) are
u τ δ
compared to those of a DNS (Tiselj, 2011) for Pr ¼ 0.01. For this case, Re τ ¼ ¼ 590,
ν
u hi 2δ
which corresponds to a bulk Reynolds number of Re ¼ ν ¼ 22,000 and Pe ¼ 220.
The grid sizes are N x N y N z ¼ 96 64 96. The stretching parameter used is
γ ¼ 2.8. The LES performed is of high quality, it is a wall-resolved LES (first cell such
+ + +
that y < 1) with fairly fine grid sizes: Δx ¼ 39 and Δz ¼ 20. The obtained results
concerning the velocity field agree very well with the DNS by Moser et al. (1999) as
+ T w T
reported in Bricteux et al. (2009). The temperature profile θ ¼ is normalized
T τ
q w
by the friction temperature T τ ¼ .
ρ cu τ
Fig. 6.1.2.6 illustrates an instantaneous temperature field compared with the veloc-
ity field together with the overlapped LES grid. It is clear that the velocity field con-
tains much smaller scales than the temperature field and it requires a subgrid-scale

Fig. 6.1.2.6 Heat transfer results for the turbulent channel flow at Re τ ¼ 590. Plane cut in the
temperature field and in the velocity magnitude field at a given time. The LES grid is
superimposed.
(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.)