High Rayleigh number convection in a three-dimensional porous medium
High-resolution numerical simulations of statistically steady convection in a three-dimensional porous medium are presented for Rayleigh numbers $Ra \leqslant 2 \times 10^4$ . Measurements of the Nusselt number $Nu$ in the range $1750 \leqslant Ra \leqslant 2 \times 10^4$ are well fitted by a relati...
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Veröffentlicht in: | Journal of fluid mechanics 2014-06, Vol.748, p.879-895 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | High-resolution numerical simulations of statistically steady convection in a three-dimensional porous medium are presented for Rayleigh numbers
$Ra \leqslant 2 \times 10^4$
. Measurements of the Nusselt number
$Nu$
in the range
$1750 \leqslant Ra \leqslant 2 \times 10^4$
are well fitted by a relationship of the form
$Nu = \alpha _3 Ra + \beta _3$
, for
$\alpha _3 = 9.6 \times 10^{-3}$
and
$\beta _3 = 4.6$
. This fit indicates that the classical linear scaling
$Nu \sim Ra$
is attained, and that
$Nu$
is asymptotically approximately
$40\, \%$
larger than in two dimensions. The dynamical flow structure in the range
$1750 \leqslant Ra \leqslant 2\times 10^4$
is analysed, and the interior of the flow is found to be increasingly well described as
$Ra \to \infty $
by a heat-exchanger model, which describes steady interleaving columnar flow with horizontal wavenumber
$k$
and a linear background temperature field. Measurements of the interior wavenumber are approximately fitted by
$k\sim Ra^{0.52 \pm 0.05}$
, which is distinguishably stronger than the two-dimensional scaling of
$k\sim Ra^{0.4}$
. |
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ISSN: | 0022-1120 1469-7645 |
DOI: | 10.1017/jfm.2014.216 |