The Axisymmetric Turbulent Jet

Doctoral thesis, 2002

This thesis aims at understanding the downstream evolution of the most energetic features of a turbulent axisymmetric jet. The study was conducted from 2 to 69 diameters downstream, using 3 different jet exit diameters with air flowing at a wide range of velocities to ensure a reasonable span of Reynolds numbers, while still keeping it in a high range, from 40,000 to 156,700. Proper Orthogonal Decomposition (POD) techniques were used to decompose the acquired flow field. Instantaneous measurements of the streamwise velocity component were acquired using two different arrays of single hot-wires. A large array comprising 138 or 139 wires was used to acquire the signals simultaneously in order to reconstruct the velocity using only the most energetic modes in the flow. A second array of 15 wires, placed in two wings rotating from one another, was used to check the veracity of the previous results. The Proper Orthogonal Decomposition applied to the double Fourier transform in time and azimuthal direction of the two-point velocity correlation tensor, was very efficient in decomposing the energy, since more than 60% (50% with the 15 wires-array) of the resolved streamwise energy was picked up by the first eigenspectrum alone. The lowest azimuthal mode for all POD modes dominates the dynamics very close to the jet, but dies off rapidly downstream. This is consistent with a trend toward homogeneity in the downstream evolution, and suggests that some residual value may control the growth rate of the far jet. On the other hand, a secondary peak for higher azimuthal modes shifts to lower mode numbers and actually increases in amplitude with downstream distance. By the end of the potential core, the general form of the eigenspectra seems not to evolve anymore, and is seen to follow equilibrium similarity scalings much sooner than the two-point statistics from which they were generated. The eigenspectra for the far jet exhibited three major peaks: a dominant one at azimuthal mode-2 for near zero frequency, another at mode-1 at a constant local Strouhal number, f .delta.1/2 /Uc, and a third smaller one for azimuthal mode-0 at near-zero frequency. If regarded as resulting from an amplified disturbance around the mean flow, the peak at mode-1 seems to be a convected instability, while the maximum at mode-2 might be a global instability associated with a precession of the mean. When normalized to reflect the energy distribution per mode number only, all the eigenspectra past the potential core peaked at azimuthal mode-2, and were independent of downstream positions thereafter. In light of these new experimental results, the classical temporal stability analysis was re-examined and shown to be unstable to azimuthal modes-0, 1, and 2, contrary to the previous belief that only mode-1 is unstable far downstream.