Axisymmetric superdirectivity in subsonic jets

Abstract

We present experimental results for the acoustic field of jets with Mach numbers between 0.35 and 0.6. An azimuthal ring array of six microphones, whose polar angle, θ , was progressively varied, allows the decomposition of the acoustic pressure into azimuthal Fourier modes. In agreement with past observations, the sound field for low polar angles (measured with respect to the jet axis) is found to be dominated by the axisymmetric mode, particularly at the peak Strouhal number. The axisymmetric mode of the acoustic field can be clearly associated with an axially non-compact source, in the form of a wavepacket: the sound pressure level for peak frequencies is found be superdirective for all Mach numbers considered, with exponential decay as a function of (1 − M c cos θ ) 2 , where M c is the Mach number based on the phase velocity U c of the convected wave. While the mode m = 1 spectrum scales with Strouhal number, suggesting that its energy content is associated with turbulence scales, the axisymmetric mode scales with Helmholtz number -the ratio between source length scale and acoustic wavelength. The axisymmetric radiation has a stronger velocity dependence than the higher-order azimuthal modes, again in agreement with predictions of wavepacket models. We estimate the axial extent of the source of the axisymmetric component of the sound field to be of the order of six to eight jet diameters. This estimate is obtained in two different ways, using, respectively, the directivity shape and the velocity exponent of the sound radiation. The analysis furthermore shows that compressibility plays a significant role in the wavepacket dynamics, even at this low Mach number. Velocity fluctuations on the jet centreline are reduced as the Mach number is increased, an effect that must be accounted for in order to obtain a correct estimation of the velocity dependence of sound radiation. Finally, the higher-order azimuthal modes of the sound field are considered, and a model for the low-angle sound radiation by helical wavepackets is developed. The measured sound for azimuthal modes 1 and 2 at low Strouhal numbers is seen to correspond closely to the predicted directivity shapes.

Potential-core closing of temporally developing jets at Mach numbers between 0.3 and 2: Scaling and conditional averaging of flow and sound fields

“…For instance, this is the case for the dependence of its peak frequency on the velocity. This frequency was indeed found to remain around a Strouhal number of St D = f D/u j = 0.15, where f and D are the frequency and the jet diameter, in a number of work [21,22], but scalings as the Helmholtz number Hm = f D/c 0 , with [23] or without [11,24] a correction by a Doppler factor, were also reported in the literature.…”

“…7(c), they are multiplied by M 7.5 . In all cases, the axisymmetric mode dominates [10,11] and contains between 57.5% of the total energy for M = 0.3 and 47.3% for M = 2. As a result, Figs.…”

“…Some questions, however, are still unanswered about the strong mixing-noise component prevailing in the downstream direction of jets, whose properties are quite distinct from those of the omnidirectional, broadband mixing-noise component dominant in the upstream and sideline directions [9]. This downstream component is mainly axisymmetric [10,11], and appears to be generated by large-scale structures and/or instability waves over a wide range of Mach numbers [12], typically from M = u j /c 0 = 0.5 up to M = 2, where u j and c 0 are the jet velocity and the speed of sound in the ambient medium. On the basis of the results of noise source localizations [13][14][15] and flow-noise crosscorrelations [16][17][18], it was also found to originate at the end of the jet potential core where the shear layers merge.…”

“…On the basis of the results of noise source localizations [13][14][15] and flow-noise crosscorrelations [16][17][18], it was also found to originate at the end of the jet potential core where the shear layers merge. Its generation mechanism is most likely not to depend significantly on the Reynolds number [18][19][20] but is not yet clearly understood [9,11]. Some of the basic characteristics of the noise component themselves continue to be matters of debate.…”

Sensitivity of wavepackets in jets to nonlinear effects: the role of the critical layer

“…In the experimental results, upstream of x/D ∼ 5, the first POD mode of the TRPIV data for m = 0 shows that the turbulent jet flow comprises a vortex-like signature in this region. 2 We can also see that, in this region, the linear wavepacket models (PSE and LEE) correctly capture this structure, as these curves collapse with the TRPIV data. This means that the homogeneous linear wavepacket model is able to predict the near-nozzle behaviour of the K-H instability, which presents exponential growth in x.…”