Page 303 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

P. 303

Turbulent heat transport 6.2.1

A. Shams
Nuclear Research & Consultancy Group (NRG), Petten, The Netherlands

Turbulence is considered as one of the unresolved phenomena of classical physics.
A turbulent flow field is characterized by velocity fluctuations in all directions and
has an infinite number of scales, that is, degrees of freedom. An analytic solution
of the Navier-Stokes equations, which govern the motion of fluids, for a turbulent flow
is impossible because the equations are elliptic, nonlinear, and coupled (pressure
velocity and temperature velocity). On the other hand, the direct numerical solution
of the Navier-Stokes equations, if properly resolved, can provide a real picture of tur-
bulence containing all scales of motion, from the largest scales to the smallest dissi-
pative scales. Since direct numerical simulation (DNS) resolves all sizes of motion;
the computational cost increases enormously with the Reynolds number. This limits
the application of the DNS to low Reynolds number flow configurations and for
relatively simple geometries. The most practical option for numerically solving the
complex turbulent flows at high Reynolds numbers is the Reynolds-averaged
Navier-Stokes (RANS) approach. In the RANS approach, the Reynolds equations
(obtained by averaging the Navier-Stokes equations) are solved, and the effects of tur-
bulence need to be modeled. However, there is not a single turbulence model that can
describe the appearance and maintenance of turbulence in all conditions. The idea to
develop a generalized turbulence model is a challenging task since turbulence appears
almost everywhere. For example, in liquid-metal fast reactors (LMFR), a wide range
of flow types and regimes (natural, mixed, and forced convection) are involved, such
as flow in the subassemblies and pool (Gr€ otzbach, 2007). These flow configurations
exhibit a wide spectrum of Reynolds numbers. In addition, the molecular Prandtl
number (Pr) of liquid metals is very low (Pr≪1), which poses additional difficulties
for the turbulence modeling.
There are huge numbers of different turbulence models available for the velocity
fields in literature; see, for example, Andersson et al. (2012), Piquet (1999), Rodi
(1993), and Wilcox (1998). However, on the other hand, there are a limited number
of models for the turbulent transfer of heat; see, for example, Gr€ otzbach (2007),
Hanjalic (2002), and Launder (1988). Turbulent heat transfer is an extremely complex
phenomenon and has challenged turbulence modelers for various decades. The mod-
elers have often assumed that turbulent heat transfer can be predicted only from the
knowledge of momentum transfer, in what is known as the Reynolds analogy.
Although this assumption is overly simplistic, it has been successfully adopted for
the last four decades in the majority of industrial applications of CFD that are based
on eddy diffusivity models (EDM). This success is justified by the fact that, for fluids
with a Prandtl number close to unity, this approach has provided reasonable

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