Selected Statistical Properties in the Inner Region of a Transpired Turbulent Boundary Layer

Abstract

ISTORICALLY, the study of turbulence phenomena has developed along two quite independent paths. The study of boundary-layer phenomena proceeded from a need to understand surface shear stress and hence the basic analysis was cast in the form that had been successful in laminar flow, resulting in the introduction of an empirical eddy viscosity. Simultaneously, the study of uniform, iso tropic turbulence proceeded from a statistical basis yielding significant results concerning the spectral transfer of energy across the wave numbers. It has recently become apparent that solutions are imperative for problems in which the fluctuating characteristics of turbulence in addition to the mean profiles of the variables of interest are of paramount importance in an evaluation of the problem. It has, thus, become necessary for progress in the engineering solution of many problems in turbulent flow to involve more of the statistical description of the turbulence in the analysis of the problem. New methods for computing turbulent mixing and shear flows are being developed which attempt to overcome the limitations of the phenomenological approaches and which also attempt to incorporate more of the physics of turbulence into the solution. These new techniques have been largely based upon incorporating in one fashion or another the turbulent kinetic energy equation into the set of equations requiring solution. Usually this is accomplished by modeling the various terms in the turbulent kinetic energy equation in terms of the basic properties of turbulence and local flow conditions. This Note presents the results of a study directed toward the experimental evaluation of the turbulent modeling parameters utilized in the turbulent kinetic energy equation and their application in correlating the mean velocity distribution across the inner region of a turbulent boundary layer with surface mass addition. The case considered is that of a uniform two-dimensional incompressible turbulent boundary layer developed initially over an impermeable surface with mass injected uniformly over the surface into the boundary layer from a downstream station. The axial pressure gradient is considered zero. For this case, the turbulent kinetic energy equation may be written as