An asymptotic solution for transpired incompressible turbulent boundary layers

Abstract

In this work perturbation techniques are used to study the equations of mean motion for transpired incompressible turbulent boundary layers. One of the features of this approach is the use of multiple scales. Indeed, the solution of this problem requires the use of three distinct scales associated with the three flow regions : the inviscid region, the defect layer and the wall layer. In the construction of the wall and defect solutions, a new law of the wake is determined by comparison of these two solutions in an interval of common domain of validity. The matching conditions also yield a skin-friction equation for transpired turbulent boundary layers. The velocity profiles obtained from the law of the wake expression, and the values of the skin-friction coefficient predicted by the skin-friction equation for flows with both injection and suction of fluid, are compared with experimental data showing good agreement.