André V. Cavalieri

Intermittent sound generation and its control in a free-shear flow

Comparisons are made between direct numerical simulations (DNS) of uncontrolled and optimally noise-controlled two-dimensional mixing layers in order to identify the physical mechanism responsible for the noise reduction. The analysis is carried out in the time domain to identify events that are significant in sound generation and which are acted upon by the control. Results show that a triple vortex interaction in the uncontrolled mixing layer radiates high-amplitude pressure waves to the far acoustic field; the elimination of this triple merging accounts for 70% of the noise reduction accomplished by a body force control applied normal to the shear layer. The effect of this control is shown to comprise vertical acceleration of vortical structures; the acceleration, whose action on the structures is convected across the control volume, leads to changes in their relative convection velocities and a consequent regularization of their evolution, which prevents the triple merger. Analysis of a longer time se...

Near-field Wavepackets and the Far-field Sound of a Subsonic Jet

David E. S. Breakey1∗, Peter Jordan2†, Andre V. G. Cavalieri3‡, Olivier Leon4§, Mengqi Zhang2¶, Guillaume Lehnasch2‖, Tim Colonius5∗∗ , and Daniel Rodŕiguez6†† Trinity College Dublin, Ireland CNRS – Universite de Poitiers – ENSMA, France Instituto Tecnologico de Aeronautica, Sao Jose dos Campos, Brazil ONERA, Toulouse, France California Institute of Technology, Pasadena, CA Universidad Politecnica de Madrid, Spain

Farfield filtering and source imaging for the study of jet noise

We present an analysis of the sound field radiated by a high Mach number subsonic jet. The spatial and temporal structures of the sound field are filtered and studied, respectively, by means of Proper Orthogonal Decomposition (POD) and wavelet transforms. The first POD mode is shown to give a near-perfect representation of the fluctuation energy radiation at low angles (in the range 30 ◦ ≤ θ ≤ 50 ◦ ), larger numbers of modes being necessary to completely reproduce the radiation characteristics at higher angles. The wavelet analysis shows, in agreement with previous studies, that the temporal structure of the sound field is characterised by localised high-amplitude events. We implement two threshold intermittency metrics which we use to filter the pressure signals based on the scalogram topology. By varying these metrics we characterise the intermittency of the pressure signals as a function of emission angle. We again find that the sound field can be divided into two families: the fluctuations radiated at low angles (30 ◦ ≤ θ ≤ 50 ◦ ) are characterised by higher levels of global intermittency (an intermittency metric defined with respect to the overall fluctuation energy) than the fluctuations radiated in the angular range θ ≥ 60 ◦ . However, when Farge’s Local Intermittency Measure (defined with respect to the local fluctuation energy at each scale) is used to analyse the data, the fluctuations at all angles show identical behaviour. Results also show that the spectral shapes associated with the high-amplitude events, at all emission angles, are less broadband than those of the unfiltered field, suggesting that the most important source dynamics are not as broadband as the Fourier spectrum would have one believe. Using both the POD and wavelet-filtered signals we decompose the acoustic field into two components: a component which we loosely attribute to coherent structures (CS) and a residuum (R). We compare the CS and R components with the LSS and FSS proposed by Tam et al. 1 We find that neither of these filtering criteria produce a natural division of the acoustic field into two components which match the LSS and FSS shapes. We also show, in the appendix, that the three-microphone approach proposed by Nance & Ahuja 2 to split the acoustic field into two such pieces is very sensitive to the three microphones which are chosen to perform the operation. Finally, we implement a source imaging algorithm, using the CS part of the farfield signature, for both the POD and wavelet-based filtering, in order to establish if our socalled CS signal ensemble can be associated with wavepacket-like sources. Results show that the CS component of our filtering can be associated with a wavepacket-like source mechanism.

Parabolized stability equation models for predicting large-scale mixing noise of turbulent round jets

Parabolized stability equation (PSE) models are being developed to predict the evolution of low-frequency, large-scale wavepacket structures and their radiated sound in highspeed turbulent round jets. Linear PSE wavepacket models were previously shown to be in reasonably good agreement with the amplitude envelope and phase measured using a microphone array placed just outside the jet shear layer. 1,2 Here we show they also in very good agreement with hot-wire measurements at the jet centerline in the potential core, for a different set of experiments. 3 When used as a model source for acoustic analogy, the predicted far field noise radiation is in reasonably good agreement with microphone measurements for aft angles where contributions from large-scale structures dominate the acoustic field. Nonlinear PSE is then employed in order to determine the relative importance of the mode interactions on the wavepackets. A series of nonlinear computations with randomized initial conditions are use in order to obtain bounds for the evolution of the modes in the natural turbulent jet flow. It was found that nonlinearity has a very limited impact on the evolution of the wavepackets for St � 0.3. Finally, the nonlinear mechanism for the generation of a low-frequency mode as the difference-frequency mode 4,5 of two forced frequencies is investigated in the scope of the high Reynolds number jets considered in this paper.

Stochastic and nonlinear forcing of wavepackets in a Mach 0.9 jet

This note contains a correction to equation (16) in AIAA Paper 2015-2217: ”Stochastic and nonlinear forcing of wavepackets in a Mach 0.9 jet,” as well as some additional clarification of the empirical resolvent mode (ERM) method described in the same paper. The notation and terminaology used in this note follows that of the paper. Before turning attention to ERM, it’s useful to write proper orthogonal decomposition (POD) as an optimization problem in a form similar to that used later for ERM.

Numerical solution of acoustic scattering by finite perforated elastic plates

We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k0 based on the plate length. However, at low k0, finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k0. The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k0 for perforated elastic plates.

Super- and multi-directive acoustic radiation by linear global modes of a turbulent jet

The mean flow stability of a Mach 0.9 turbulent jet is investigated by means of global linear theory with a focus on acoustic effects. A novel class of resonant acoustic modes that are trapped within the potential core, and whose eigenvalues appear as discrete branches in the global stability spectrum, is studied in detail. A dispersion relation is reconstructed from the global modes, and shown to accurately predict energy bands observed in the PSD of a high-fidelity LES. Similarly, the acoustic far-field radiation patterns of the trapped modes are compared to the LES. A favorable agreement between the global mode waveforms and coherent structures educed from the LES is found for both the trapped acoustic wave component inside the core and the far-field radiation.

Trapped acoustic waves in the potential core of subsonic jets

The purpose of this paper is to characterize and model waves that are observed within the potential core of subsonic jets and that have been previously detected as tones in the near-nozzle region. Using three models (the linearized Euler equations, a cylindrical vortex sheet, and a cylindrical duct with pressure release boundary conditions), we show that these waves can be described by linear modes of the jet and correspond to acoustic waves that are trapped within the potential core. At certain frequencies, these trapped waves resonate due to repeated reflection between end conditions provided by the nozzle and the streamwise contraction of the potential core. Our models accurately capture numerous aspects the potential core waves that are extracted from large-eddy-simulation data of a Mach 0.9 isothermal jet. Furthermore, the vortex sheet model indicates that this behavior is possible for only a limited range of Mach numbers that is consistent with previous experimental observations.

Intermittency of the azimuthal components of the sound radiated by subsonic jets

We apply a filtering procedure, based on a continuous wavelet transform, to acoustic pressure and to the velocity field of an experimental Mach 0.6 jet in order to extract the intermittent bursts in the signals. With an intermittency measure based on this filter, it is possible to quantify the significance of these events in the total acoustic intensity. The acoustic pressure is measured by a ring of six azimuthal microphones, allowing decomposition of the sound field into azimuthal Fourier modes. The wavelet filtering is applied to each azimuthal mode, and the results show that the intermittent bursts occur mostly for the axisymmetric mode and for low polar angles. When high energy thresholds are used for the filtering, so as to retain only the most energetic bursts, more than 80 percent of the intermittent radiation is axisymmetric.

Intermittent sound generation in a free-shear flow

Comparisons are made between direct numerical simulations of uncontrolled and optimally controlled mixing layers in order to understand what it is about the controlled flows that makes them substantially quieter. Special attention is paid to the possibility that the essential details of the source mechanism may be spatially and/or temporally localised: such features are hidden when second-order statistics such as spectra are considered; and indeed these are almost identical for the two flows. Analysis is thus performed in the time domain, in order to search for intermittent sound-producing events. The results show that a large-amplitude pressure wave associated with a triple vortex merger in the uncontrolled mixing layer contributes significantly to the farfield, and that this event has been eliminated in the controlled flow. The large amplitude pressure wave associated with this event appears to be due to two things: the axial concentration of a low-pressure zone associated with the merging of the three vortical structures on one hand, and an axially-extended high-pressure region which opens up in the low-vorticity region immediately upstream of the three said structures. These pressure distributions can be mechanistically understood in terms of centripetal forces associated with the vortex dynamics, and the sound production associated with this can be mechanistically understood in terms of the axial imbalance that occurs between the spatially-localised low pressure and the spatially extended highpressure. Having understood the above, we proceed to analyse a longer time-run simulation of the uncontrolled flow, to see if we can objectively extract similar events. We apply a wavelet transform to the radiated pressure field, and by means of this we identify a collection of similar signatures. In each case we find that these correspond to a similar mechanism. The results highlight the importance of considering sound-producing flows in the time domain, and using appropriately adapted signal processing. The implications for noisesource modelling, which are often based on second-order statistics, are also discussed.