Page 249 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

220 Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

6.1.1.1.1.1 Historical context

As referenced in Moin and Mahesh (1999) and Kasagi and Iida (1999), the first tur-
bulent flow and heat transfer simulations date back to the end of the 1980s. Particular
attention was focused on the DNS of the near-wall flows, which is most relevant also
for the present chapter focused on heat transfer. Another type of turbulent flow sim-
ulations is homogeneous isotropic turbulence, see Pope (2000) for a review, which is
historically also very important for investigating turbulent cascade mechanisms of
energy, but is not considered in the present text.
Two main types of DNS heat transfer studies, both important for liquid metal
applications, must be distinguished: the first is the passive scalar hypothesis
(the scalar field T does not affect the velocity field) applicable for forced convec-
tion studies, and the second type of studies represents natural and mixed convec-
tion phenomena.
The focus of this chapter is on simulations of near-wall turbulence as they reveal
the basic mechanisms of the convective heat transfer between the fluid and the solid
wall. In the past decade, this topic became important also in the field of thermal fatigue
problems (Brillant et al., 2006; Aulery et al., 2012). It is important to stress that agree-
ments between the DNS results and measurements in turbulent heat transfer studies
cannot be as good as for the pure fluid dynamics problems, because the material prop-
erties of many fluids show nonnegligible variations with temperature. Most of the
state-of-the-art DNS studies assume constant material properties and only some of
them are considering the buoyancy effects. Thus, most of the results in this chapter
are shown for the passive scalar approximation approaches.
First, DNSs of heat transfer in the channel flow geometry were made at low
Reynolds numbers and at Prandtl numbers of around one by Kim and Moin (1989)
and Kasagi et al. (1992). Later, Kawamura et al. (1998) and Na and Hanratty
(2000) performed DNS of the turbulent channel flow at Prandtl numbers up to 10.
All these studies considered temperature as a passive scalar. Low Prandtl number
DNSs of channel flows, which are relevant for liquid metal heat transfer and can
be found in the database of Kawamura (2017), were performed at Pr ¼ 0.025 in
2003 and 2004. Tiselj and Cizelj (2012) created a DNS database at Pr ¼ 0.01, which
is closer to the lead and sodium properties. Their simulations took into account the
detailed heat transfer in the solid heated walls of the channel and were performed
for variable combinations of the liquid and solid material properties.

6.1.1.1.2 The scalar transport equation

When the flow is not isothermal, conservation of thermal energy implies the following
dimensionless transport equation for the temperature field that is solved together with
Eqs. (6.1.1.1)
∂T ! 1 2
+ U rT ¼ r T + S (6.1.1.2)
∂t Re τ Pr