Page 252 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Direct numerical simulations for liquid metal applications 223

The smallest scale for the scalar field was given by Batchelor (Pope, 2000) for high
Pr flows:
η
η 1=2 (6.1.1.10)
θ
Pr
while for low Pr flows the Obukhov-Corrsin scale should be considered (Sagaut,
2006):

η
η (6.1.1.11)
θ
Pr 3=4
Thus, for high Prandtl (Schmidt) number heat (mass) transfer, the smallest length
scales of the thermal (mass concentration) field are smaller than the dimensions of
the smallest vortices (Bergant and Tiselj, 2007) and this must be taken into account
in true DNS studies. At Pr ¼ 1, both scales are of the same size, although some studies
(Galantucci and Quadrio, 2010) indicate that accurate simulation of a passive scalar
field at Pr around unity actually requires a finer resolution than the velocity field due
to the higher intermittency of the scalar field. Nevertheless, tiny differences might be
observed only in less relevant higher-order statistics.
Because liquid metal flows are characterized by low Prandtl numbers, the smallest
length scales of the scalar field are larger than the smallest length scales of the velocity
field, which consequentially determine the required resolution of the DNS studies.
This can be clearly shown in Fig. 6.1.1.1, which shows the very fine structures of
streamwise velocity and larger structures in temperature fluctuations in the
centerplane of a turbulent channel flow with Pr ¼ 0.01 (Tiselj, 2014). Further discus-
sion of the resolution is reported in Section 6.1.1.2.
The largest length scales in a given turbulent flow are in principle determined by
the geometry of the domain. However, for external flows and for flows with inlet and
outlet sections, these length scales cannot be easily determined. Simulations in the
simplest wall-bounded flow configuration (i.e., flow between infinite parallel plates),
also known as channel flow or Poiseuille flow, have shown that the streamwise and the
spanwise lengthscales might be unbounded (Tiselj, 2014).

Fig. 6.1.1.1 Instantaneous fluctuation fields of streamwise velocity (left) and temperature
(right) at the center of the channel. Re τ ¼180, Pr ¼ 0.01. Horizontal coordinate: streamwise
direction spanning from 0 to 13,751 wall units. Vertical coordinate: spanwise direction from 0 to
4523 wall units (Tiselj, 2014).