Page 256 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Direct numerical simulations for liquid metal applications 227

6.1.1.3 Boundary and initial conditions

6.1.1.3.1 Periodic boundary conditions
In hydrodynamically and thermally fully (time) developed conditions and also for
periodically fully developed conditions (Stalio and Piller, 2007), where homogeneity
of the flow in the streamwise direction can be assumed (see Section 6.1.1.1), periodic
BCs can be implemented on all variables along the streamwise direction, including
pressure and temperature.
One of the most frequently used geometries in DNS, where periodic BCs are
imposed, is the channel flow. Simulations of a turbulent flow in a channel of infinite
length (x) and width (z) are performed by approximating the infinite extent of the
domain in the streamwise and spanwise directions with a computational domain of
finite length (also called unit cell) and by applying periodic BCs in these directions.
Such conditions theoretically entail the dependent variable fields to be periodic along
the selected direction. In practice, their implementation depends on the specific
method itself: for instance, periodicity is inherent to the basis functions of spectral
methods, while in finite volume/finite difference methods, it is achieved by imposing
a circular topology of the computational stencils at the two ends of the domain. Special
care should be taken when choosing the extent of the unit cell, which should be large
enough to encompass the largest scales of the flow. If these conditions are satisfied,
the flow in the computational domain can be considered as an accurate representation
of the flow in the infinite channel. Section 6.1.1.4 reports some qualitative criteria for
the choice of the channel length and width.

6.1.1.3.2 Inflow open boundary conditions
Periodic BCs can be applied in the streamwise direction to the computed variables
when fully developed conditions are met. In case the interest is a spatially developing
flow, the DNS approach requires resorting to an inflow turbulence generation method
for both the velocity and the temperature fields. Inflow turbulence generation methods
for the velocity field have been recently classified and reviewed by Wu (2017). A short
auxiliary periodic domain, where turbulence is computed in parallel to the main cal-
culation, is providing results that are used as inflow condition for the target simulation.
This type of inflow BCs is known as a recycling method. Synthetic methods represent
an alternative attempt to fully model the inflow.

6.1.1.3.3 Outflow open boundary conditions
Devising appropriate BCs at open boundaries when the mean flow is exiting the
domain can be a difficult task (Sani and Gresho, 1994). The most common problems
of outflow open BCs is that they produce spurious reflection of the velocity and of
transported scalars, they tend to produce wiggles at the domain boundary and might
affect the stability of the solution algorithm.