Integral properties of turbulent natural convection over a vertical flat plate

摘要

This paper investigates global integrals of the volumetric, momentum and temperature fluxes for turbulent natural convection over a vertical plate (TNCVP). The global integral of the mean continuity equation gives a relation for the mean wall-normal velocity outside the boundary layer as W_∞ = -d(∫_0~∞Udz)/dx where U is the mean velocity in the streamwise x direction and z is the wall-normal direction. The global integral of the mean momentum equation gives a relation for the specific wall momentum flux as u_τ~2=gβ∫_0~∞(Θ_∞-Θ)dz-d(∫_0~∞U~2dz)/ dx where u_τ is the friction velocity, g is the gravitational acceleration and β is the thermal expansion coefficient. Θ=T_w-T is the difference between the wall temperature T_w and the fluid temperature, and Θ_∞=T_w-T_∞ is the difference between the wall temperature and the ambient fluid temperature. Finally, the global integral of the mean heat equation gives a relation for the wall temperature flux as u_τθ_τ=-W_∞Θ_∞-d(∫_0~∞UΘdz)/dx where θ_τ is the frictional temperature. Based on the global integrals of the momentum and heat fluxes, we propose an indirect determination of u_τ and θ_τ. Given the extreme challenge in direct measurement of u_τ and θ_τ in wall-bounded turbulent flows, the indirect determination proposed here offers a powerful tool to subsequent experimental studies of TNCVP.