Fundamental Studies of Turbulent Boundary Layers with Injection or Suction through Porous Walls : 2nd Report, Theoretical and Experimental Analysis of Turbulent Boundary Layers with Injection and Adverse Pressure Gradients

Abstract

In this report, Truckenbrodt's method of analyzing the turbulent boundary layer with adverse pressure gradients has been extended to explain the properties of the turbulent boundary layers with injection. Applying the Truckenbrodt's method, and based on the fact of the One-Parameter Family advocated by Doenhoff and the others, the author intended to find a method of calculating the velocity profiles from the momentum thickness θ and the shape parameter H(=δ*/θ). As it was confirmed through many experiments that the concept of One-Parameter Family is applicable to the velocity profiles of turbulent boundary layers with injection, the author established a simple analytical method of calculating θand H from the momentum equation and the energy equation. Accordingly, the velocity profiles are easily determined as functions of given Reynolds number (R_x=u₀ x/ν). Here, the theoretical equations of θ and H were examined by the author, and it is confirmed that the semi-empirical values of θ and H are in good agreement with measured ones. Moreover shearing stress at the wall and frictional work in the turbulent boundary layer were examined for the turbulent boundary layer with injection.