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

Inclined Cavity-2D simulations 152
profiles between the two thermally active walls, at the middle of the cavity, at
different angles of inclination, with the k-ε model, using LRN, AWF and SWF
and also with the Basic RSM using AWF. As is shown in the diagrams, all the
turbulence models predict that the highest turbulent kinetic energy is found
in the vertical cavity case. This is contrary to what it might be expected, that
the turbulence level would increase as the cavity is tilted toward the unsta-
bly stratified case. The explanation, as mentioned in the previous sections, is
that based on the experimental study of the 15 ◦ unstable inclined tall cavity,
there are significant 3-dimensional flow structures within the cavity, whereas
the numerical simulations are purely 2-dimensional. In the case where the cav-
ity is tilted to give stably stratified flow, all the turbulence models behave as
expected. They show that the turbulence level is reduced as the angle of incli-
nation of the tall cavity is reduced, until the flow becomes fully stagnant at 0 ◦
stable.
Regarding the mean velocity distribution between the two thermally ac-
tive walls at the middle of the cavity, again all turbulence models predict
velocity profiles as expected for the vertical and stably stratified cases. It is
worth to note that there might be some discrepancies between 2D numerical
simulations of unstable flows and the real thermally unstable flows. This is
based on the fact that in reality in unstably stratified cases, there are signifi-
cant 3-dimensional flow structures, whereas the numerical results are based on
purely 2-dimensional simulations. The other source of discrepancy in the ve-
locity profiles for the unstably stratified flows is related to the fact that at some
of the angles of inclinations some turbulence models return multiple cell circu-
lations. The velocity profiles between the two thermally active walls shown in
Figures 6.20-6.23, which are shown along the section at the middle of the cav-
ity, which in the cases with multiple circulation cells, may lie on the weaker or
stronger part of cells, or even the direction of the circulation may be different
from one turbulence model to another along the section at the middle of the
cavity.
In Figure 6.24, the turbulent kinetic energy distributions along the line nor-
mal to the insulated end-walls, at the middle of the cavity are shown. The