Study of mean velocity profiles in three-dimensional incompressible turbulent boundary layers

Abstract

This thesis is concerned with the description of mean velocity profiles in three-dimensional incompressible turbulent boundary layers. The principal features of the study are an examination of the Preston tube technique and the inner law, some detailed measurements of mean velocity profiles with a parametric correlation for the outer region, and a self-preservation analysis in two different orthogonal coordinate systems.

Normal Preston tubes, single-chamfered tubes, and Conrad probes of different sizes have been tested in a rectangular channel and on the wall of a boundary layer tunnel in both two- and three-dimensional flows. Results indicate that even in the presence of crossflow, a correct estimate of wall shear stress (at least in magnitude) is obtained when the pressure gradients are not severe. The pressure gradient effects on the inner law are similar to what has been observed in two-dimensional flows. Universal calibration curves have also been obtained for the different types of wall tubes used.

Mean velocity and pressure gradient data have been obtained along external streamlines and streamlines close to the wall in a flow caused by an obstruction mounted normal to a flat plate. Measurements have also been made in the same configuration with disturbed upstream conditions. Some features of the flow close to three-dimensional separation and streamline inflexion points have been indicated. Velocity profiles both in the main stream and the wall flow directions agree well with Thompson's two-parameter profile family.

Velocity distributions in the outer region, suitably non-dimensionalized, may be expressed as a one-parameter family of profiles in directions parallel and normal to the wall flow. This result is valid both for suddenly skewed flows and three-dimensional boundary layers developing more gradually. The profile given by the wake law of Coles is one such parametric curve in the direction normal to the wall flow.

A self-preserving three-dimensional turbulent boundary layer is postulated in two intrinsic coordinate systems - one formed by the external streamlines and their orthogonal trajectories, and the other given by wall shear lines and their normals (x and z directions). In the external streamline coordinate system, the limit of vanishing skin friction (or infinite Reynolds number) not only linearizes the equations, but also decouples them in the X and Z directions. A similar set of equations is obtained for infinite Reynolds number and small crossflow in the case of wall shear coordinates. Using the eddy viscosity hypothesis, solutions have been obtained for the limiting equations for different values of self-preservation parameters. Comparison of these solutions with experimental profiles, on the basis of a local similarity concept (governed by profile shape factors), shows fairly good agreement.