Viscous Sublayer and Adjacent Wall Region in Turbulent Pipe Flow

TLDR

The study constructed a boundary‑layer facility using glycerine to enable detailed experimental investigation of the viscous sublayer. Hot‑film anemometry measured streamwise velocity fluctuations in the viscous sublayer and transition region, from which space‑time correlations were computed and eigenfunction decomposition was performed to analyze flow structures. At Re = 8700 the viscous sublayer thickness was 0.110 in, and analysis revealed a dominant eigenfunction matching the mean velocity and a large‑scale structure of randomly distributed counter‑rotating elongated eddy pairs.

Abstract

The boundary-layer research facility utilizing the highly viscous fluid, glycerine, was constructed to permit detailed experimental investigation of the viscous sublayer. At a pipe Reynolds number of 8700 the sublayer thickness corresponding to a nondimensional distance from the wall of yuτ/ν = 5.00 was 0.110 in. Detailed measurements of the streamwise fluctuating velocities were obtained with hot-film anemometers within the viscous sublayer as well as in the transition region between the linear and logarithmic mean velocity profiles. These data were used to form the space-time correlation function of the streamwise fluctuating velocities. An eigenfunction decomposition of the streamwise fluctuating velocity into a sum of products of eigenfunctions in the inhomogeneous coordinate direction, with random coefficients dependent on the homogeneous and stationary variables, was obtained from the correlation data. One dominant eigenfunction with a structure nearly identical to the mean velocity in the wall region was found. The dominant large scale structure of the flow in the wall region, obtained with the aid of a mixing length approximation, consisted of randomly distributed counterrotating eddy pairs of elongated streamwise extent.