Three-Component Vectorial Proper Orthogonal Decomposition of Axisymmetric Wake Behind a Disk

Abstract

One-component scalar, two-component vectorial, and three-component vectorial proper orthogonal decompositions of the axisymmetric turbulent wake have been studied to investigate possible effects of the number of components comprising the two-point correlation tensor forming the kernel of the proper orthogonal decompositions integral equation. A wind-tunnel experiment has been performed 50 diameters downstream of the wake generator, which was a disk of 20 mm in diameter. The Reynolds number based on the disk diameter was 20,400. Twelve cross hot wires were used to obtain the simultaneous multipoint measurements. Six of the probes were located on a fixed rake and the other six probes were located on a movable rake, which was traversed from 10 to 180 deg in 10 deg increments. Two experiments were carried out to obtain first the streamwise and azimuthal components of the velocity, and second to obtain the streamwise and radial components of the velocity. Seven out of nine components of the two-point correlation tensor were computed using measured velocities and the remaining two two-point correlations were extracted from the data using the continuity equations. The one-component scalar, and two- and three-component vectorial decomposition results were essentially in agreement. Eigenvalues for the full vector proper orthogonal decompositions integrated over frequency showed that Fourier mode 2 was the largest in both the streamwise and azimuthal velocity. Azimuthal mode 2 peaks at the near-zero frequency, whereas azimuthal mode 1 peaks at a frequency which corresponds to the vortex shedding frequency. Similar features in turbulence kinetic energy distributions were also observed in the modally decomposed two-point cross-spectra and two-point cross-correlations. Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.