Page 266 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

236 Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

periodic computational domain. Jimenez and Moin (1991) have shown that even
+
+
domain with dimensions L ¼ 300 and L ¼ 100 is sufficient to correctly reproduce
x y
the mean velocity profiles, profiles of the velocity fluctuations, and small scale veloc-
ity spectra. Authors of the present chapter are not aware of similar test for passive
scalars at low Prandtl numbers.
Many other turbulent quantities, spectra of the temperature fluctuations, and bud-
get terms of the turbulent quantities are relevant for development of the LES or RANS
models or empirical heat transfer correlations. The reader is referred to the references
in Table 6.1.1.1 for details about these statistics.
For the conjugate heat transfer results, the reader is referred to Tiselj and Cizelj
(2012): where channel flow results are available at Re τ ¼ 180, 395, and 590, and
at Pr ¼ 0.01 for variable fluid-solid properties. All turbulent statistics are somewhere
between the values provided by the limiting thermal BCs discussed earlier.

6.1.1.5 Results: Nonplanar geometries

When geometries become more complex, also the flow and temperature fields gain
specific, relevant features that are not observed over planar walls. Errico and Stalio
(2014, 2015) performed DNS of the fully developed low Prandtl number forced con-
vective heat transfer in a channel of high aspect ratio, having one wavy wall and one
flat wall. The flow is forced and no buoyancy effects are accounted for. The simulated
friction Reynolds number is Re τ ¼ 282, corresponding to a Reynolds number of the
bulk velocity and the hydraulic diameter, Re 18, 900. Three fluids of different ther-
mal conductivities, corresponding to Pr ¼ 0.71, 0.20, 0.025 are considered in the
research. The fluid flow displays separation, reattachment, and a shear layer down-
stream the wave peak, these are conditions relevant for turbulent heat transfer and pas-
sive scalar transport applications.
Low Prandtl number fluids are characterized by comparatively low Nusselt num-
bers, but results reveal that heat transfer is enhanced by the wall undulation.
A minimum Nusselt number is found in the flow separation region, where the rec-
irculating bubble acts as a barrier to the advection of heat, a peak heat transfer rate
is instead located in the flow reattachment region for all fluids investigated.
A detailed investigation of the components of heat flux in vertical direction reveals
that the main contribution to heat transfer is always to be ascribed to the mean advec-
tive term, at least within the range of parameters investigated. Profiles of turbulent
heat flux in Fig. 6.1.1.6 show that turbulent transport of heat almost vanishes at
Pr ¼ 0.025; as a consequence mean temperature profiles at those low P eclet number
values are typically laminar.
Instantaneous contours of the streamwise velocity component and three tempera-
ture fields corresponding to the different Prandtl numbers simulated are shown in
Fig. 6.1.1.7, together with the fluctuation fields. It appears that the mean temperature
profiles of laminar characteristics at Pr ¼ 0.025 derive from an unsteady temperature
field, a small range of spatial scales and weak turbulent heat flux in vertical direction.
The additional discussion in Errico and Stalio (2014) reveals that the use of a uniform