2020年4月19日

# Ultimate heat transfer in `wall-bounded' convective turbulence

• Koki Kawano
• ,
• Shingo Motoki
• ,
• Masaki Shimizu
• ,
• Genta Kawahara

Direct numerical simulations have been performed for turbulent thermal
convection between horizontal no-slip, permeable walls with a distance $H$ and
a constant temperature difference $\Delta T$ at the Rayleigh number
$Ra=3\times10^{3}-10^{10}$. On the no-slip wall surfaces $z=0$, $H$ the
wall-normal (vertical) transpiration velocity is assumed to be proportional to
the local pressure fluctuation, i.e. $w=-\beta p'/\rho, +\beta p'/\rho$
(Jiménez et al., J. Fluid Mech., vol. 442, 2001, pp. 89-117), and the
property of the permeable wall is given by the permeability parameter $\beta U$
normalised with the buoyancy-induced terminal velocity $U={(g\alpha\Delta TH)}^{1/2}$, where $\rho$, $g$ and $\alpha$ are mass density, acceleration due
to gravity and volumetric thermal expansivity, respectively. A zero net mass
flux through the wall is instantaneously ensured, and thermal convection is
driven only by buoyancy without any additional energy inputs. The critical
transition of heat transfer in convective turbulence has been found between the
two $Ra$ regimes for fixed $\beta U=3$ and fixed Prandtl number $Pr=1$. In the
subcritical regime at lower $Ra$ the Nusselt number $Nu$ scales with $Ra$ as
$Nu\sim Ra^{1/3}$, as commonly observed in turbulent Rayleigh-Bénard
convection. In the supercritical regime at higher $Ra$, on the other hand, the
ultimate scaling $Nu\sim Ra^{1/2}$ is achieved, meaning that the wall-to-wall
heat flux scales with $U\Delta T$ independent of the thermal diffusivity,
although the heat transfer on the wall is dominated by thermal conduction. The
physical mechanisms of the achievement of the ultimate heat transfer are
presented.

リンク情報
arXiv
http://arxiv.org/abs/arXiv:2004.08831
URL
http://arxiv.org/abs/2004.08831v1
URL
http://arxiv.org/pdf/2004.08831v1 本文へのリンクあり

エクスポート