Page 289 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Large-eddy simulation: Application to liquid metal fluid flow and heat transfer 259

Indeed, a first class of models uses the complete LES field for the subgrid-scale vis-
cosity while using the small field to express the strain tensor:

SGS s
τ ¼ 2ν SGS S : (6.1.2.47)
ij ij
This class of models is called “complete-small.”
A second class of models uses the small field for both the strain tensor and the
subgrid-scale viscosity:
SGS s s
τ ¼ 2ν S , (6.1.2.48)
ij SGS ij
s s 1=2
2
where using Smagorinsky scaling, ν s ¼ C S Δ 2S S . This class is called
SGS ij ij
“small-small.”
6.1.2.3.3.2 The multiscale WALE model
The regularized multiscale version of the WALE model or RVMS-WALE has been
proposed by Bricteux et al. (2009). This model belongs to the “small-small” class.
Hence, this formulation is based on Eq. (6.1.2.48) with,

3=2
sd sd
S S
ij ij
2
ν s ¼ C W Δ , (6.1.2.49)
SGS
s s
5=2 sd sd 5=4
S S + S S
ij ij ij ij
s s s s
s 1 ∂~ u ∂~ u k ∂~ u ∂~ u k
j
i
S ¼ + : (6.1.2.50)
ij
2 ∂x k ∂x j ∂x k ∂x i
This multiscale model has the proper near-wall behavior and does not dissipate
resolved large scales as well as vortex cores. Bricteux et al. (2009) successfully used
this model for channel flow at Re τ ¼ 395 (calibration of C W ¼ 0.56) and Re τ ¼ 590
(calibration of C W ¼ 1.4) as well as for vortical flows. This model has been also used
by Duponcheel et al. (2014) for LES of liquid metal heat transfer in a channel flow at
Re τ ¼ 2000. The case of heat transfer of liquid metal in the channel at Re τ ¼ 2000 is
presented in Section 6.1.2.4.
6.1.2.3.4 Modeling subgrid-scale heat flux

6.1.2.3.4.1 The Reynolds analogy and the eddy heat diffusivity
approach

The molecular Prandtl number of a given fluid is defined as
ν
Pr ¼ , (6.1.2.51)
α