The computation of turbulent natural convection flows - Turbulence ...

Turbulence modelling 88
For moderate to low Reynolds-number flows, this is not an accurate repre-
sentation of dissipation rate. To some extent, because the anisotropic compo-
nent,εij− 1
2 εδij has some of the same mathematical properties as the pressurestrain
term, it can be argued that the modelling of the pressure-strain term can
be interpreted as compensating for the lack of accuracy in the local isotropy
assumption.
Two-Component-Limit Version
The basic Reynolds-stress closure can capture many important physical
processes and is more general than the EVM, but it has some disadvantages
as well.
One important weakness of the basic Reynolds-stress closure is that it does
not work properly in the situation of the two component limit. The two com-
ponent limit refers to a situation where one of the normal stress components
becomes zero. For instance, this may occur in free shear flows at the region be-
tween the stagnant fluid and the jet of fluid. The other disadvantage of the ba-
sic Reynolds-stress closure is that φij requires corrections in near-wall regions
to reduce the stress normal to the wall. The wall reflection terms developed
for this correction are calibrated for plane surfaces and are dependent on the
ratio of the turbulent length scale to the normal distance from the wall. In the
case of complex geometries, it may be difficult to define the normal distance to
the wall.
An alternative method is to develop a more general pressure-strain term so
that it can comply with the two component limit situation. An added benefit
may be that there is no need to apply a wall correction term.
The φij1 term of the TCL pressure-strain model was presented by Craft et
al. [53] as:
φij1 = −c1ε aij +c ′
1 aikajk − 1
3 A2δij
−A 0.5 εaij
(3.58)
whereAis termed the flatness factor andA2 andA3 are stress invariants. They