Page 275 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Large-eddy simulation: 6.1.2

Application to liquid metal
fluid flow and heat transfer

Y. Bartosiewicz*, M. Duponcheel*
*Institute of Mechanics, Materials and Civil Engineering, UCLouvain,
Louvain-la-Neuve, Belgium

6.1.2.1 Introduction

Liquid metal reactors are characterized, from the thermal-hydraulic point of view, by a
very low Prandtl number coolant, Pr 0.01. At such Prandtl number, the temperature
field is much smoother than the velocity field, that is, the smallest temperature scales
are much larger than those of the velocity, and, for moderate Reynolds numbers, the
heat transfer in a channel could be essentially molecular while the flow is fully tur-
bulent. Consequently, simulation tools and in particular computational fluid dynamics
(CFD) should account for such peculiar behavior.
We can classify CFD by three distinct approaches according the level of modeling/
simulating the flow physics: the direct numerical simulation (DNS), the large-eddy
simulation (LES), and the Reynolds averaged numerical simulation (RANS). The
flow physics of interest is essentially characterized by turbulent transfers (e.g.,
momentum and energy transfers). Turbulent flows are characterized by a full spec-
trum of space and time scales, ranging from large scales, driven by the geometry
and boundary conditions, down to the smallest scales where the energy is finally dis-
sipated. This feature is illustrated by the so-called energy cascade introduced by
Kolmogorov (1941). This statistic-based theory relies on local isotropy and similarity
assumptions. The energy cascade means that, because of the nonlinear interactions
between the different scales, an energy transfer takes place from the large scales to
the small ones. At some point, depending on the Reynolds number, the energy transfer
competes with the viscous dissipation of the energy into heat, and this latter effect
becomes dominant. The final dissipation occurs at a scale defined by Kolmogorov
and called the Kolmogorov scale. This energy cascade is represented by a relation
between the local characteristic wavenumber k of eddies and the turbulent kinetic
energy contained by such eddies E(k) (see Fig. 6.1.2.1).
The large wavenumber range (e.g., the large scales) is the production range where
the energy is injected to turbulence because of existing gradients in the mean flow or
any external forcing. Thus, we find here the largest eddies containing most of the
energy; these eddies are characterized by a length scale l 0 and a velocity scale u 0 pro-
portional to the geometric length scale L and to the characteristic velocity scale of the

Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors. https://doi.org/10.1016/B978-0-08-101980-1.00017-X
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