Wavepackets in the velocity field of turbulent jets

Abstract

We study the velocity fields of unforced, high Reynolds number, subsonic jets, issuing from round nozzles with turbulent boundary layers. The objective of the study is to educe wavepackets in such flows and to explore their relationship with the radiated sound. The velocity field is measured using a hot-wire anemometer and a stereoscopic, time-resolved PIV system. The field can be decomposed into frequency and azimuthal Fourier modes. The low-angle sound radiation is measured synchronously with a microphone ring array. Consistent with previous observations, the azimuthal wavenumber spectra of the velocity and acoustic pressure fields are distinct. The velocity spectrum of the initial mixing layer exhibits a peak at azimuthal wavenumbers m ranging from 4 to 11, and the peak is found to scale with the local momentum thickness of the mixing layer. The acoustic pressure field is, on the other hand, predominantly axisymmetric, suggesting an increased relative acoustic efficiency of the axisymmetric mode of the velocity field, a characteristic that can be shown theoretically to be caused by the radial compactness of the sound source. This is confirmed by significant correlations, as high as 10 %, between the axisymmetric modes of the velocity and acoustic pressure fields, these values being significantly higher than those reported for two-point flow-acoustic correlations in subsonic jets. The axisymmetric and first helical modes of the velocity field are then compared with solutions of linear parabolized stability equations (PSE) to ascertain if these modes correspond to linear wavepackets. For all but the lowest frequencies close agreement is obtained for the spatial amplification, up to the end of the potential core. The radial shapes of the linear PSE solutions also agree with the experimental results over the same region. The results suggests that, despite the broadband character of the turbulence, the evolution of Strouhal numbers 0.3 St 0.9 and azimuthal modes 0 and 1 can be modelled as linear wavepackets, and these are associated with the sound radiated to low polar angles.

Resolvent-based modeling of coherent wave packets in a turbulent jet

“…The study is based on jet experiments conducted at the Bruit et Vent jet-noise facility of the Pprime Institute in Poitiers. Technical details of the experimental apparatus, as well as measurement validation, are thoroughly described in past publications [13,31].…”

“…The transition to turbulence of the incoming boundary layer is forced using an azimuthally homogeneous carborandum strip, such that a fully turbulent boundary layer is obtained at the exit section of the nozzle (see Fig. 1 in [13]).…”

“…Free-jet mean flow measurements from this setup, obtained with a Pitot tube, are available from the experiments by Cavalieri et al [13], and excellent reproducibility has been demonstrated in the more recent experiments by Jaunet et al [31]. These experimental data are used to construct a parametric model of the mean flow, providing smooth variations of axial and radial velocity, density and temperature [33].…”

“…Twenty-one experimental velocity profiles in the free jet are available between x = 0.1D and x = 10D; some of these are compared in [33]. The distribution has been modelled such as to closely reproduce the experimental measurements [13]. The pipe wall is represented as a white line, and only a portion of the numerical domain is shown.…”

Prediction of Near-Field Jet Cross Spectra

“…Reba et al [32] used two-point statistics of a nearfield array close to various jets and projected sound to the midfield using the wave equation. Cavalieri et al [33] studied the velocity field of subsonic jets and discerned instability waves modeled as wave packets. These wave packets were connected to the radiated sound of the jet using measurements of the velocity field.…”