Page 258 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Direct numerical simulations for liquid metal applications 229

Mean dimensionless temperature for the fluctuating temperature BC at the wall is still
fixed to zero, while the zero derivative is prescribed for the fluctuating part of the tem-
0
perature θ . This type of thermal BC is achieved when the thermal activity ratio K goes
to infinity; it can be reproduced in experiments with a water flume that is heated with a
very thin metal foil (Mosyak et al., 2001).
In 2001 when the first analysis of the BCs (6.1.1.13), (6.1.1.14) in turbulent channel
flow was performed by Tiselj et al. (2001b), these BCs were denoted as “isothermal”—
Eq. (6.1.1.13)—and “isoflux BC for dimensionless temperature”—Eq. (6.1.1.14).
Especiallythe“isoflux”namecausedconsiderableconfusion,becauseitwasfrequently
mixed withstandardisofluxBCforthephysicaltemperature.These twoBCsshouldnot
be mistaken: configuration with a constant volumetric heat source inside the solid walls
corresponds to the isoflux BC for the physical temperature. The detailed BC in this case
can be nonfluctuating (Eq. 6.1.1.13) or fluctuating (Eq. 6.1.1.14). Thus new names are
recommended for BCs (6.1.1.13), (6.1.1.14)by Tiselj and Cizelj (2012).
Animportant featureof different thermalBCs(6.1.1.13), (6.1.1.14)isthat inthepas-
sive scalar approximation they have almost negligible influence on the heat transfer
coefficient.Inotherwords,meantemperatureprofilesnearthewallarepracticallyinde-
pendent of the detailed thermal BC. Of course, a significant difference can be observed
in temperature fluctuations and other turbulent statistics (see results in Section 6.1.1.4).
For realistic fluid-solid systems the thermal BC is always in between the two lim-
iting BCs of Eqs. (6.1.1.13), (6.1.1.14). For the liquid sodium and steel combination
with K ¼ 1, the thermal BC is roughly in the middle between the fluctuating and non-
fluctuating temperature BC. Hence, in order to study the details of the temperature
fluctuations and their penetration into the solid wall, a conjugate heat transfer
approach is recommended for DNS of heat transfer in liquid metals.

6.1.1.3.5 Initial conditions
After all the equations, computational domain and BCs have been specified, initial
conditions are needed to start the simulations. Given that long-term statistics are inde-
pendent of initial conditions, and provided CPU time is not a limiting factor, it is often
sufficient to start with any kind of initial velocity that contains at least a few pertur-
bations of sufficiently long wavelengths. Because these initial stages of the simula-
tions can be run on rather coarse grids, the CPU time consumption should not be
too high. In most of the cases, if the geometry remains similar, it is sufficient to
use instantaneous fields obtained from simulations at other Reynolds or Prandtl num-
bers after appropriate scaling. In case the computational cost is a limiting factor, then
the initial transient can be shortened with some more sophisticated types of initial con-
ditions (Coleman and Sandberg, 2010).

6.1.1.3.6 Statistical treatment of numerical solutions
3
After a time interval, which typically spans over several flow-through times and 10 to
4
10 viscous time units, the flow in the computational domain should develop into a
turbulent flow with constant mean properties. This condition is known as