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

Abstract
This study is focused on the efficient computation of natural convection
flows. Numerical investigations have been carried out of turbulent natural
convection flow in cavities, using different strategies for the modelling of the
near-wall turbulence and also different levels of modelling of the turbulent
stresses and the turbulent heat fluxes. More specifically, for the modelling
of near-wall turbulence the low-Reynolds-number modelling approach, the
standard wall function (SWF) and the more recently developed analytical wall
function (AWF) strategies have been tested. For the turbulent stresses, the ef-
fective viscosity approximation (EVM), the basic Reynolds stress closure (RSM)
and a more recent variant, the two-component-limit version (TCL-RSM) of the
Reynolds stress closure have been tested. The turbulent heat fluxes have been
modelled through the effective diffusivity approximation when the EVM was
used for the Reynolds stresses, while for the RSM closures, the generalised gra-
dient diffusion hypothesis (GGDH) and a more elaborate algebraic expression
for the fluxes that involved the temperature variancet 2 and its dissipation rate,
εt, obtained from additional transport equations, have been tested. The stud-
ied cases are flow in high-aspect-ratio rectangular cavities inclined at angles of
60 ◦ (with stable and unstable heating configurations, both at Ra = 0.8×10 6 ),
15 ◦ (with stable and unstable heating configurations, at Ra = 1.4 × 10 6 and
Ra = 0.8 × 10 6 , respectively), 5 ◦ stable (Ra = 4.16 × 10 8 ). The cavities have
the longitudinal aspect ratio of 28.7 and spanwise aspect ratio of 6.8. All the
inclined cavities are computed as 2D while the 15 ◦ stable and unstable config-
urations are computed as 3D time-dependent as well. The final case studied
was a horizontal annular penetration (Ra = 4.5 × 10 8 and Ra = 3.1 × 10 13 ).
The horizontal annular penetration case is computed as 3D steady-state and
time-dependent.
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