Page 267 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Direct numerical simulations for liquid metal applications 237

x = 0.3 x = 0.7 x = 1.3 x = 1.7
2

1.6
y 1.2
0.8
0.4
0
0 2 4 0 2 4 0 2 4 0 2 4

0.2
y
0.1
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x

0 0
Fig. 6.1.1.6 Profiles of turbulent heat fluxes, u θ : solid line (Pr ¼ 0.71); dashed line (Pr ¼
0.20); dash-dot line (Pr ¼ 0.025).

turbulent Prandtl number for the modeling of turbulent heat transfer for Pr ≪ 1 is not
expected to be accurate, especially in flow separation conditions.
Flow over a backward-facing step (BFS) is another geometry relevant for several
applications. The paper by Oder et al. (2015) describes preliminary DNS results of
thermal fluctuations in walls and in turbulent flow of liquid metal flowing over a
BFS with finite dimensions and solid walls. The BFS geometry is shown in
Fig. 6.1.1.8 and is as close as possible to the Kasola experimental device that is
planned at Karlsruhe Institute of Technology ( Jaeger et al., 2017). The Pr ¼ 0.01 fluid
is flowing from the narrower part into the wider part. The realistic heated wall is
assumed behind the step. The temperature field is a passive scalar, which means that
the natural convection is not simulated, although it can be relevant. For the inflow BC
over the BFS, a fully developed turbulent velocity field with constant temperature is
used. To obtain the inflow, a recycling BC is used. The values for velocity and tem-
perature from a plane parallel and downstream from the inflow are imposed as the
inflow BC. The streamwise component of velocity is scaled at this operation to ensure
a constant mass flow rate. Simulations are performed with the Open Source Code
Nek5000 (ANL, 2017), based on spectral element method.
Strong 3D nature of the resulting temperature field makes the recirculating vortex
behind the step rather complicate, although that cannot be clearly seen from
Fig. 6.1.1.8, where the instantaneous field is shown in the plane of symmetry. It turns
out that one of the key problems in DNS of statistically 3D turbulence is the very long
computational times that are needed to obtain reasonably low statistical uncertainty.
Discussion of the BFS simulations can be concluded with a reference to a recent paper
by Niemann and Froehlich (2016) where DNS of vertical buoyant flow over the step
was analyzed, although the results were not supported by the measurements.