Direct numerical simulation of free convection over a heated plate
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hdl:2117/190424
Tipus de documentArticle
Data publicació2012-12-10
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Abstract
Direct numerical simulations of free convection over a smooth, heated plate are
used to investigate unbounded, unsteady turbulent convection. Four different boundary
conditions are considered: free-slip or no-slip walls, and constant buoyancy or constant
buoyancy flux. It is first shown that, after the initial transient, the vertical structure
agrees with observations in the atmospheric boundary layer and predictions from
classical similarity theory. A quasi-steady inner layer and a self-preserving outer layer
are clearly distinguished, with an overlap region between them of constant turbulent
buoyancy flux. The extension of the overlap region reached in our simulations is
more than 100 wall units (¿3/Bs)
1/4
, where Bs is the surface buoyancy flux and ¿
the corresponding molecular diffusivity (the Prandtl number is one). The buoyancy
fluctuation inside the overlap region already exhibits the 1/3 power-law scaling
with height for the four types of boundary conditions, as expected in the local, freeconvection regime. However, the mean buoyancy gradient and the vertical velocity
fluctuation are still evolving toward the corresponding power laws predicted by the
similarity theory. The second major result is that the relation between the Nusselt and
Rayleigh numbers agrees with that reported in Rayleigh–Benard convection when the ´
heated plate is interpreted as half a convection cell. The range of Rayleigh numbers
covered in the simulations is then 5 ¿ 107–109. Further analogies between the two
problems indicate that knowledge can be transferred between steady Rayleigh–Benard ´
and unsteady convection. Last, we find that the inner scaling based on {Bs, ¿} reduces
the effect of the boundary conditions to, mainly, the diffusive wall layer, the first
10 wall units. There, near the plate, free-slip conditions allow stronger mixing than
no-slip ones, which results in 30 % less buoyancy difference between the surface
and the overlap region and 30–40 % thinner diffusive sublayers. However, this local
effect also entails one global, substantial effect: with an imposed buoyancy, free-slip
systems develop a surface flux 60 % higher than that obtained with no-slip walls,
which implies more intense turbulent fluctuations across the whole boundary layer and
a faster growth.
CitacióMellado, J. P. Direct numerical simulation of free convection over a heated plate. "Journal of fluid mechanics", 10 Desembre 2012, vol. 712, p. 418-450.
ISSN0022-1120
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