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

Literature Review 64
Hanjalić et al.[25] carried out numerical investigations on natural convec-
tion in two-dimensional empty and partitioned rectangular enclosures at high
Rayleigh numbers. The range of Rayleigh numbers covered in this study was
from 10 10 to 10 12 . Three and four-equation models, k-ε-θ 2 and k-ε-θ 2 -εθ, were
applied to compute the thermo-fluid flow. The computations were performed
using a low-Reynolds-number near-wall treatment to resolve changes in the
buffer layer. They reported improvements in the turbulence field results by
using a extended algebraic model for the turbulent heat fluxes uiθ, as com-
pared with the eddy diffusivity hypothesis. They presented some results re-
garding mean values and turbulent field and Nusselt number. They concluded
that, unlike the eddy diffusivity model , such as typically employed in low-
Re-number k-ε models, which predicted the turbulent regime erratically and
underpredicted turbulent kinetic energy, the algebraic flux model was capable
of predicting turbulence at Ra numbers consistent with experimental findings.
They compared the computed Nusselt number results with experimental and
heat transfer correlations. Those comparisons proved that the three and four
equation model resulted in good agreement with experimental data and cor-
relations, always within 15%.
Dol et al[26] numerically studied turbulent natural convection. They pre-
sented a comparison between differential and algebraic second moment clo-
sures in the case of natural convection. DNS data of turbulent natural con-
vection between two differentially heated infinite vertical plates at a Rayleigh
numberRa = 5.4×10 5 (Versteegh and Nieuwstadt [27], Boudjemadi et al. [28])
were employed to carry out the comparisons. They converted the differential
equations for uiθ and θ 2 into algebraic forms using relevant hypotheses. Then
they carried out computations using the full differential form and a four equa-
tion k-ε-θ 2 -εθ algebraic model. They reported reasonable agreement between
the algebraic model predictions and available experimental and DNS data. It
was shown that the algebraic models predicted well the mean flow and tur-
bulence properties in the tall cavity case [18]. The algebraic model was tested
at different levels of truncation. They initially developed the algebraic equa-
tion for uiθ based on the assumption of weak equilibrium, which implies that
the anisotropy of the thermal flow uiθ/ θ2 1/2 k is approximately constant in