论文标题
在“壁挂”对流湍流中的最终传热
Ultimate heat transfer in `wall-bounded' convective turbulence
论文作者
论文摘要
直接数值模拟已经进行了水平无滑动，距离$ h $的渗透性墙和恒定温度差的易热对流，rayleigh number $ ra = 3 \ times10^{3} {3} -10^{10} $。在无滑动壁上$ z = 0 $，$ h $假定壁正常（垂直）蒸腾速度与当地压力波动成正比，即$ w =-βp'/ρ， +βp'/ρ， +βp'/ρ'/ρ$（Jiménez等由渗透性参数$βu$给出，浮力诱导的末端速度$ u = {（gαΔth）}^{1/2} $，其中$ρ$，$ g $和$ g $和$ g $和$ g $和$ g $和$ g $是质量密度，由于引力和体积的热量膨胀，分别是加速度。瞬时确保了通过墙壁的零净质量通量，并且热对流仅由浮力驱动，而没有任何额外的能量输入。在对流湍流中传热的关键过渡已经在固定$βu= 3 $的两个$ ra $ regimes和固定的prandtl Number $ pr = 1 $之间发现了关键的过渡。在较低$ ra $的亚临界体制中，nusselt number $ ra $ a $ a $ ra $ as $ nu \ sim ra^{1/3} $，如Turbulen Rayleigh-Bénard对流中所观察到的那样。另一方面，在较高$ ra $的超临界方案中，实现了最终的缩放$ nu \ sim ra^{1/2} $，这意味着，尽管壁传热率独立于热传递，但具有$uΔt$的壁到壁热量尺度，尽管受热传输占主导地位。提出了实现最终传热的物理机制。
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 $ΔT$ 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. $w=-βp'/ρ, +βp'/ρ$ (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 $βU$ normalised with the buoyancy-induced terminal velocity $U={(gαΔTH)}^{1/2}$, where $ρ$, $g$ and $α$ 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 $βU=3$ 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 $UΔT$ 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.
