Establishment of the Wake Behind a Disk

Abstract

An air-tunnel study of the establishment of the wake behind a disk at a Reynolds number of approximately 7 × 104 was undertaken. On the basis of the measured data, such a wake is fully established, that is, similarity profiles of the flow characteristics are formed, within 15 diameters of the disk, and approximately 95 percent of the transfer of energy from the mean motion to the turbulence motion takes place within 3 diameters of the disk, in the region of the mean standing eddy. The measured mean ambient-pressure and mean total-pressure distributions, mean velocity distributions, turbulence-intensity and shear-stress distributions, and the mean streamline pattern are presented in graphical form, as are the quantitative balances of the integrated momentum and mean-energy relationships. A stream function consisting of a continuous distribution of doublets is introduced to extend the radial limit of understanding of the flow characteristics to a very large if not infinite radius. Considerable attention is given to the problem of obtaining and interpreting turbulence shear-stress data immediately downstream from the point of flow separation. The applicability of a local diffusion coefficient or virtual viscosity of the Boussinesq or Prandtl type for relating the turbulence shear stress to the radial gradient of mean axial velocity is discussed. The Bernoulli sum and the energy changes along individual streamlines investigated in an associated study are incorporated herein to obtain a quantitative estimate of the local errors involved in the turbulence-shear-stress measurements.