Calculation of Turbulent Boundary Layers Using Equilibrium Thermal Wakes

Abstract

The combined thermal law of the wall and wake is used as the approximating sequence for the boundary layer temperature profile to solve an integral thermal energy equation for the local Stanton number distribution. The velocity profile in the turbulent boundary layer was taken to be the combined law of the wall and wake of Coles. This allows the solution of an integral form of the x-momentum equation to give the skin friction coefficient distribution. This, along with the velocity profile, is used to solve the thermal energy equation using inner coordinates. The strength of the thermal wake was found by analysis of earlier research results, in the literature, for equilibrium, constant property, turbulent boundary layers. Solutions for the Stanton number distribution with position are found for some adverse pressure gradient boundary layers as well as for those having zero pressure gradient. The zero pressure gradient results cover both fully heated plates and those with unheated starting lengths, including both isothermal surfaces and constant flux surfaces. Comparison of predictions of the present work is made with experimental data in the literature.