| مستخلص: |
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 T at the Rayleigh number Ra = 3 × 10³–1010. 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). Here ρ is mass density, and the property of the permeable wall is given by the permeability parameter βU normalised with the buoyancy-induced terminal velocity U = (gαTH)1/2, where g and α are acceleration due to gravity and volumetric thermal expansivity, respectively. 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 ∼ Ra1/3, as commonly observed in turbulent Rayleigh–Bénard convection. In the supercritical regime at higher Ra, on the other hand, the ultimate scaling Nu ∼ Ra1/2 is achieved, meaning that the wall-to-wall heat flux scales with UT independent of the thermal diffusivity, although the heat transfer on the wall is dominated by thermal conduction. In the supercritical permeable case, large-scale motion is induced by buoyancy even in the vicinity of the wall, leading to significant transpiration velocity of the order of U. The ultimate heat transfer is attributed to this large-scale significant fluid motion rather than to transition to turbulence in boundary-layer flow. In such ‘wall-bounded’ convective turbulence, a thermal conduction layer still exists on the wall, but there is no near-wall layer of large change in the vertical velocity, suggesting that the effect of the viscosity is negligible even in the near-wall region. The balance between the dominant advection and buoyancy terms in the vertical Boussinesq equation gives us the velocity scale of O(U) in the whole region, so that the total energy budget equation implies the Taylor dissipation law ε ∼ U³/H and the ultimate scaling Nu ∼ Ra1/2. [ABSTRACT FROM AUTHOR] |
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