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

Literature Review 66
walls. For the Reynolds shear stress, there was improvement in the square
cavity case but there was no improvement for the tall cavity case.
Hanjalić[31] numerically studied one-point closure models for buoyancy-
driven turbulent flows. The thermal buoyancy-driven flows are considered
as a challenge for one-point-closure models. The buoyancy-driven flows are
difficult to model because of inherent unsteadiness, energy non-equilibrium,
counter gradient diffusion and high pressure fluctuations. He investigated
some specific turbulence modelling issues regarding buoyant flows within
the realm of one-point closures. Firstly, the disadvantages of isotropic eddy-
diffusivity models were discussed in the work. A major disadvantage is that
they are not capable of capturing interactions of turbulent heat flux and the ef-
fects of buoyancy. Another disadvantage is that the alignment of the turbulent
heat flux with the mean temperature-gradient vector leads to model failure
in many cases such as Rayleigh-Bénard convection. However, 3D and time-
dependent simulation using EVM is able to avoid this drawback. Then it was
shown that Algebraic models based on a rational truncation of the differential
second-moment closure is the minimum closure level for complex flows. The
algebraic second moment closure was found not to be adequate to capture the
structure of buoyancy driven flows but it was capable of predicting more phe-
nomena than the eddy-diffusivity models. He presented results regarding two
generic flows of the side heated vertical channel and Rayleigh-Bénard convec-
tion. It was concluded that in these cases the isotropic eddy-diffusivity model
leads to wrong results. The algebraic second-moment closure was found to
improve the results to some extent but still there was huge discrepancy with
DNS data. It was possible to modify the algebraic second-moment closure
term by term to re-produce the DNS data but, because of inherent nonlinearity,
the generalization to complex flows would be doubtful. Finally he proposed
using algebraic truncation of the second moment closure to determine an alge-
braic equation for the turbulent heat fluxes. It was shown that this will capture
a number of internal buoyancy-driven flows.
Hsieh and Lien[32] investigated the numerical modelling of buoyancy-driven
turbulent flows in enclosures. They carried out computations for enclosures