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224 Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

The largest time scales are also important, because they determine the time inter-
val, which is needed to obtain statistically acceptable averaged values of turbulent
quantities. Typical averaging times in domains with inlet and outlet are several dozens
flow-through times, where the flow-through time is defined as the time needed by a
fluid particle to travel along the whole domain. For fully developed flows, a time scale
based on the mean velocity and the reference length should be considered. More about
the largest length and time scales relevant for DNS is given in Section 6.1.1.2, dis-
cussing periodic BCs, and in Section 6.1.1.3, discussing autocorrelation functions,
which are used to determine the required minimum length of periodic domains
in DNS.

6.1.1.2 Direct numerical simulation techniques

The first DNS studies of homogeneous and near-wall turbulence were performed with
spectral schemes. Authors of the first turbulent channel DNS studies, which were per-
formed 30 years ago, are still maintaining their databases with open access data
(Moser, 2017; Jimenez, 2017). Spectral schemes are known as the most accurate tech-
niques for DNS studies and are computationally very efficient; however, they are lim-
ited to rather simple geometries (cuboid, cylinder) and BCs.
A typical DNS approach for turbulent channel flow and heat transfer is based on
pseudospectral schemes, using Fourier series in the x (streamwise) and z (spanwise)
directions, and Chebyshev polynomials in the wall-normal y-direction (Tiselj et al.,
2001b). Second-order accurate time differencing (Crank-Nicholson scheme for diffu-
sive terms and Adams-Bashfort scheme for other terms) is used with maximum CFL
numbers of approximately 0.1. The aliasing error can be removed by computing the
nonlinear terms on a number of modes 1.5 times larger in each direction (Kim and
Moin, 1989).
DNS heat transfer results obtained with this type of codes can be found in various
papers (Kasagi and Iida, 1999; Kasagi et al., 1992; Tiselj et al., 2001b, 2004; Bergant
and Tiselj, 2007). Some of the DNS studies include also conjugate heat transfer, which
accounts for the penetration of the turbulent temperature fluctuations into the heated
wall (Tiselj et al., 2001a, 2013; Flageul et al., 2015). The channel flow database
obtained at friction Reynolds numbers Re τ ¼ 180, 395, and 590 with liquid metal
Prandtl number Pr ¼ 0.01 was prepared within the EU project THINS (Tiselj and
Cizelj, 2012).
Typical resolution (i.e., the distance between the collocation points of the spectral
scheme) in DNS studies of turbulent channel flows at friction Reynolds numbers
+
between 180 and 2000 (Hoyas and Jimenez, 2006; Moser et al., 1999)is Δx ¼
+
+
10 18, Δz ¼ 5, and Δy ¼ 8 (channel center), in the streamwise, spanwise, and
wall-normal directions, respectively. This resolution guarantees the accuracy of