STRUCTURE OF TURBULENT FREE-CONVECTION BOUNDARY LAYERS ALONG A VERTICAL PLATE

Abstract

Abstract : A non-local differential phenomenological theory for turbulent free-convection boundary layers along a two-dimensional heated vertical plate is described, in which both eddy viscosity and eddy thermal diffusivity are considered unknown. The total viscosity (molecular plus eddy) is taken to be governed by a parabolic rate equation which takes into account turbulent convection, diffusion, generation and decay, while the turbulent thermal diffusivity is based on a constant turbulent Prandtl number. Based on this closed system of partial differential equations, the mean velocity and temperature field as well as the eddy viscosity and the turbulent thermal diffusivity distribution can be mapped out. It is shown for the vertical-plate problem that the generation of turbulence is essentially shear induced, and that the gravity force only influences the mean velocity and temperature fields. A degenerated local theory is developed to interpret and compare with existing experimental data. Calculations show that the turbulent free-convection boundary layer consists essentially of three distinct regions, namely, the viscous sublayer, the inner layer, and the outer layer. The viscous sublayer defined by vanishing eddy viscosity, is shown to have a nonlinear velocity distribution. The inner layer is dominated by the balance of turbulent generation and decay. The outer layer is governed mainly by turbulent convection and diffusion. It is shown that Corrsin's viscous superlayer also exists in the turbulent free-convection case and that temperature fluctuations tend to reduce the sharpness of the turbulent-non-turbulent interface. It has also been found that Grashof number has strong effects on turbulent generation and decay. (Author)