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

Literature Review 62
to the larger distance between the active walls of the square cavity, there is an
almost zero velocity region at the core of the square cavity. In this case, the
velocity near the hot and cold walls reaches a maximum and then reduces to
almost zero in the core region. Therefore, due to lack of velocity gradients
in the core, there is almost laminar flow in that region and turbulent flow is
located only near the hot and cold walls. That is why a clear temperature
stratification is usually observed at the core of the square cavities heated from
the side walls.
2.2 Numerical Studies
The other major body of studies related to buoyancy-driven turbulent flows
are those exploring numerical simulation techniques. The numerical predic-
tion of natural or mixed convection can be an economical method to use for
design purposes in industrial applications. However, because of the complex
nature of such convection flows, their numerical simulation is still a challenge
for researchers.
Ince and Launder[21] numerically studied buoyancy-driven flows in rect-
angular enclosures. In the numerical study, air was the working fluid. They
investigated two different aspect ratios, 30:1 and 5:1, which showed different
flow structures. The study is covered the range ofRa from 10 6 to10 10 . Isother-
mal hot and cold temperatures were imposed to the vertical walls of the cav-
ities while the horizontal walls were adiabatic. The generalized gradient dif-
fusion hypothesis (GGDH) was employed to compute turbulent heat fluxes,
which then appear in the buoyancy turbulence generation term. In the GGDH,
cross flow gradients are taken into account which might be important in buoy-
ancy driven flows, whereas in the simpler eddy-diffusivity scheme these make
no contribution. The other important point in their research was the applica-
tion of a near wall source term in the ε equation. The Jones-Launder [22] form
of the k-ε predicts length scales too large at locations near to separation points
and consequently gives wrong prediction of wall heat transfer. It was con-
cluded that the Jones-Launder low-Reynolds-number k-ε model with amend-
ment of GGDH for calculation of turbulent heat fluxes and a near wall source