Scaling high Rayleigh number natural convection boundary layer statistics: A vertical water tunnel experiment

Abstract

A high Rayleigh number natural convection boundary layer adjacent to the vertical heated wall was investigated at a large-scale facility. The global Rayleigh number (Rax) measured by the temperature difference between the wall and ambient water and the distance from the bottom of the heated wall reached 1013. Experimental results confirm that the global Nusselt number Nux is scaled by power 1/3 of Rax, which is similar to the well-known asymptote of the previously achieved Rax. The velocity field obtained using particle image velocimetry (PIV) indicated that the buoyancy-dominant outer-layer scaling suggested by Wells and Worster [A geophysical-scale model of vertical natural convection boundary layers, J. Fluid Mech. 609, 111–137 (2008)] was not only applicable to scale the lower-order velocity statistics but was also valid as a reasonable measure of the spatial correlation, probability distribution, and quadrant contribution features in the outer layer. The dynamical behavior of fluid motion captured by PIV supported a robust momentum transfer to positive wall-normal direction, which was sustained by the Q1 and Q3 quadrants. In addition, merging the existing literature and current data suggested that near-wall function can be applied at a moderate Rax; the universality of this wall-function model was confirmed around z×∼0.7 (where z× represents the near-wall scaled wall-normal distance, Kiš and Herwig [The near wall physics and wall functions for turbulent natural convection, Int. J. Heat Mass Transfer 55, 2625–2635 (2012)]). At a larger buoyancy regime, it was expected to follow a canonical boundary layer flow.