Machine Learning Control of Jet Noise | Computational Flow Physics

Selected Publications

2025

Spectral dynamics of natural and forced supersonic twin-rectangular jet flow

B. Yeung, and O. T. Schmidt

Journal of Fluid Mechanics, 2025, 1018, A34

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Nonlinear dynamics of vortex pairing in transitional jets

A. Nekkanti, T. Colonius, and O. T. Schmidt

Journal of Fluid Mechanics, 2025, 1018, A32

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2024

Nonlinear Interactions in Turbulent Jets

A. Nekkanti, E. Pickering, T. Colonius, and 1 more author

AIAA Paper 2024-3414, 2024

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Bispectral mode decomposition is used to investigate triadic interactions within a Mach 0.4 turbulent jet. We explore its potential to identify dominant triadic interactions and their associated spatial structures in an unforced turbulent jet. The bispectral measure is broadband in frequency for each azimuthal wavenumber triad. The [1,1,2] and [0,0,0] azimuthal wavenumber triads are dominant, emphasizing the importance of the self-interactions of the helical and axisymmetric components. Bispectral modes reveal that streaky structures are fed by the interaction of a Kelvin-Helmholtz wavepacket with its conjugate. Streaks are also observed in other frequency interactions, occurring in regions where the structures of these frequencies are spatially active. Furthermore, integral interaction maps and nonlinear transfer terms are computed to determine the direction of energy transfer and to pinpoint the spatial regions where nonlinearity is most active. As the shear layer develops, small scales interact nonlinearly, transferring energy to larger scales. Moving downstream, near the potential core closure, larger scales become more active, resulting in a forward energy cascade.
Space-Time Proper Orthogonal Decomposition of Actuation Transients of a Plasma-Controlled Twin-Rectangular Jet

B. Yeung, and O. T. Schmidt

AIAA Paper 2024-4192, 2024

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The transient dynamics of a turbulent supersonic twin-rectangular jet flow, forced symmetrically at a Strouhal number of 0.9, are investigated using large-eddy simulations (LES). The forcing is provided by localized arc filament plasma actuators (LAFPA), modeled as source terms in the energy equation. Under plasma-actuated control, the statistically stationary jet evolves towards a cyclostationary state over a transient phase. Forcing-induced perturbations of the natural jet are extracted using synchronized simulations of the natural and forced jets. A database is collected that captures an ensemble of realizations of the perturbations within the initial transient. The spatiotemporal dynamics and statistics of the transient are investigated using space-time proper orthogonal decomposition (space-time POD) for each D2 symmetry component. The eigenvalue spectra unveil low-rank dynamics in the symmetric component. The spatial and temporal structures of the leading modes indicate that the initial pulse of the actuators produces large, impulsive perturbations to the flow field. The symmetric mode reveals the contraction of the shock cells due to the forcing, and shows the evolution of the mean flow deformation transient.
On the role of eddy viscosity in resolvent analysis of turbulent jets

J. G. R. Saldern, O. T. Schmidt, P. Jordan, and 1 more author

Journal of Fluid Mechanics, 2024, 1000, A51

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2023

Bispectral mode decomposition of axisymmetrically and non-axisymmetrically forced turbulent jets

A. Nekkanti, O. T. Schmidt, I. Maia, and 3 more authors

AIAA Paper 2023-3651, 2023

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View Video Presentation: https://doi.org/10.2514/6.2023-3651.vidLarge-eddy simulations (LES) of a turbulent unforced jet at \Re = 50,000 and \M_j = 0.4 and jets forced at azimuthal wavenumbers \m=0 \m=\pm1 \m=\pm2 and \m=\pm6 are performed. The objective of this study is to characterize the nonlinear interactions that are initiated by the forcing. To achieve this, we used the bispectral mode decomposition (BMD) technique, which is tailored to extract flow structures associated with triadic interactions. Azimuthal wavenumber triads are investigated using the cross-spectral variant of BMD. Axisymmetric forcing generates peaks at the forcing frequency and its harmonics in the \m=0 component only, whereas non-axisymmetric forcing generates peaks at different azimuthal wavenumbers. The latter aspect is investigated using cross-BMD. Forcing the jet at \m=\pm1 the only odd-\m forcing case considered, creates a cascade of triads that generates peaks at the forcing frequency and its odd harmonics at odd azimuthal wavenumbers and even harmonics at even azimuthal wavenumbers. Forcing the jet at \m = \pm m_f azimuthal wavenumbers produces peaks at the odd harmonics in the odd integer multiples of \m_f and at even harmonic frequencies in the even integer multiples of \m_f\.
Cyclostationary analysis of forced turbulent jets

L. Heidt, T. Colonius, A. Nekkanti, and 3 more authors

AIAA Paper 2023-3652, 2023

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View Video Presentation: https://doi.org/10.2514/6.2023-3652.vidA variety of actuation methods have been applied to turbulent jets with the aim of reducing far-field sound. However, a detailed understanding of the mechanisms by which actuation alters the turbulence and far-field sound is lacking. We investigate the effect of periodic acoustic forcing by performing a series of large-eddy simulations of turbulent axisymmetric subsonic and supersonic jets subjected to periodic forcing at several frequencies and amplitudes. To analyze data from the forced jets, we employ cyclostationary analysis, which is an extension of the statistically stationary framework to processes that have periodically varying statistics. Both low- St_f=0.3 and high-frequency St_f=1.5 forcing generate an energetic tonal response but have limited effect on the time-averaged mean with a forcing amplitude greater than 1% required to achieve a small change. Similar trends were seen for the turbulent kinetic energy and the energy transfer between the mean and turbulent components. By applying cyclostationary spectral proper orthogonal decomposition (CS-SPOD), we investigate how the dominant coherent structures are modified and modulated by the forcing. For St_f=0.3, a broadband increase in the energy of the dominant coherent structures was found. The low-frequency coherent structures were found to be strongly phase dependent, with substantial energy coupled to the high-velocity and high-shear regions of the mean flow. In contrast, forcing at St_f=1.5 resulted in a broadband decrease in the energy of the dominant coherent structures. No phase-dependent modulation of the low-frequency coherent structures was seen due to a large difference in the wavelength and spatial support between the coherent structures and the mean field. A reduced impact of the St_f=0.3 forcing on the supersonic jet is seen, while the St_f=1.5 forcing results in a similar impact.
Plasma Actuation and Bispectral Mode Decomposition of Supersonic Twin-Rectangular Jet Flow

B. Yeung, and O. T. Schmidt

AIAA Paper 2023-4177, 2023

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View Video Presentation: https://doi.org/10.2514/6.2023-4177.vidLarge-eddy simulations (LES) of a Mach 1.5, nominally ideally-expanded, twin-rectangular jet are performed, with and without forcing. The numerical implementation of the periodic forcing is based on companion experiments at Ohio State University that utilize localized arc filament plasma actuators (LAFPA) to control twin-jet coupling and influence jet screech. In the forced jet LES, twelve independently-controlled energy sources, which model LAFPAs, generate bursts of thermal and pressure perturbations in a pattern that is symmetric about the major and minor axes of the jet, or symmetric-symmetric for short. For rigorous statistical analysis, the natural and forced jet data are decomposed into their \D_2\-symmetry components, which are either symmetric or antisymmetric about the major and/or minor axes. To identify large-scale structures involved in triadic interactions, bispectral mode decomposition (BMD) is applied to the forced case, leading to a complex mode bispectrum and three-dimensional BMD modes for each \D_2 symmetry component (auto-BMD) or set of components (cross-BMD). The BMD analyses reveal dominant triadic interactions between symmetric-symmetric modes, associated with the forcing, and between antisymmetric-symmetric modes, associated with the natural screech tone. Both classes of symmetry-self interactions generate superharmonics and mean flow distortions that are symmetric-symmetric. In contrast, symmetry-cross interactions between the symmetric-symmetric forcing and antisymmetric-symmetric screech form superharmonics and mean flow deformations that are antisymmetric-symmetric. Summed mode spectra, obtained from the average along each diagonal of the BMD bispectra, suggest that under the present forcing, consistent symmetry (i.e., either both symmetric, or both antisymmetric) about the minor axis is a prerequisite for two modes to interact quadratically.

2022

Three-Dimensional Spectral POD of Supersonic Twin-Rectangular Jet Flow

B. C. Y. Yeung, O. T. Schmidt, and G. A. Brès

AIAA Paper 2022-3345, 2022

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View Video Presentation: https://doi.org/10.2514/6.2022-3345.vid The statistical analysis of non-axisymmetric turbulent jets using spectral proper orthogonal decomposition (SPOD) is computationally costly; in particular, their non-axisymmetry precludes Fourier decomposition of the three-dimensional flow field into two-dimensional azimuthal modes. Jets in the dihedral group \D_2 including rectangular, elliptic, and twin jets, are invariant under reflection about their major and minor axes. For these jets, we propose an SPOD workflow that exploits their \D_2 geometrical symmetry to obtain a reduction in computational effort, accelerate statistical convergence, and improve the interpretability of results. We decompose the three-dimensional snapshots into four symmetry components. For each symmetry component, we independently perform SPOD on one quadrant of the domain. We demonstrate an application of this \D_2\-symmetric SPOD workflow on a large-eddy simulation of a twin-rectangular supersonic jet. Our analysis indicates that the twin jet exhibits screech at Strouhal number 0.3, and that this screech is dominated by components which are antisymmetric along the minor axis. These observations are consistent with the results from companion experiments at Ohio State University. Furthermore, the same workflow is used to analyze the symmetry-dependence of far-field acoustics at low and high frequencies.
Triadic nonlinear interactions and acoustics of forced versus unforced turbulent jets

A. Nekkanti, I. Maia, P. Jordan, and 3 more authors

12th International Symposium on Turbulence and Shear Flow Phenomena, 2022

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Interaction between wavepackets and streaks in turbulent jets

P. A. S. Nogueira, A. V. G. Cavalieri, V. Jaunet, and 3 more authors

12th International Symposium on Turbulence and Shear Flow Phenomena, 2022

2021

Waves in screeching jets

D. Edgington-Mitchell, T. Wang, P. Nogueira, and 5 more authors

Journal of Fluid Mechanics, 2021, 913, A7

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Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets

E. Pickering, G. Rigas, O. T. Schmidt, and 2 more authors

Journal of Fluid Mechanics, 2021, 917, A29

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Analysis of forced subsonic jets using spectral proper orthogonal decomposition and resolvent analysis

L. Heidt, T. Colonius, A. Nekkanti, and 3 more authors

AIAA Paper 2021-2108, 2021

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View Video Presentation: https://doi.org/10.2514/6.2021-2108.vidVarious passive and active control strategies have been applied to turbulent jets and have achieved up to about a 5dB reduction in overall sound pressure level. However, the mechanisms by which forcing alters the turbulence and far-field sound are poorly understood. We investigate the effect of forcing by performing large-eddy simulations of turbulent axisymmetric jets subjected to periodic forcing at multiple frequencies and amplitudes. Spectral proper orthogonal decomposition is used to study the effect of the forcing on the linear spectrum. Low-frequency periodic forcing, with \St_f = 0.3 while producing highly energetic tonal structures and noise, has a limited effect upon the underlying turbulent spectrum of the jet and the most energetic modes. High levels of forcing, 1\% of the jet velocity, are required to achieve a small change to the turbulent mean flow and a minor shift in the turbulent spectrum. The changes in the overall spectrum and the shift in the modes are predicted well via the resolvent analysis performed on the new turbulent mean flow. This shows that the turbulent spectrum stems from the turbulent mean flow and not via interactions between phase-locked structures and the natural turbulence. High-frequency periodic forcing, with \St_f = 1.5 is less effective at altering the mean flow field compared to the low-frequency forcing at the same amplitude, but results in a nonlinear interaction, potentially associated with vortex pairing, amplifying the turbulence spectrum at \St ≈0.75\.
Towards large-eddy simulations of supersonic jets from twin rectangular nozzle with plasma actuation

G. A. Brès, B. Yeung, O. T. Schmidt, and 4 more authors

AIAA Paper 2021-2154, 2021

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View Video Presentation: https://doi.org/10.2514/6.2021-2154.vidLarge-eddy simulation of a jet issuing from rectangular nozzles of aspect ratio 2 is performed. The nozzles are operating at their nominal design Mach number of 1.5. This operating condition and the geometry match those of the companion experiment conducted at Ohio State University. The preliminary results show good agreement with near-field and far-field noise measurements in terms of broadband levels and predictions of screech tone frequencies and amplitudes. In particular, the main noise radiation towards the aft angles and the overall sound pressure level directivity are within 1dB for most relevant frequencies and angles. For future simulations of active control, a numerical model of a localized arc filament plasma actuator is implemented and tested in a small test domain inside one of the nozzles. A grid resolution study is conducted to investigate the minimum grid resolution required for correct energy transport within the boundary layer.
Nonlinear dynamics of forced wavepackets in turbulent jets

I. Maia, P. Jordan, L. Heidt, and 3 more authors

AIAA Paper 2021-2277, 2021

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View Video Presentation: https://doi.org/10.2514/6.2021-2277.vidWe study the dynamics of harmonically-forced jets under different forcing amplitudes covering linear and nonlinear response regimes. Using a combination of Particle Image Velocimetry (PIV) measurements, Spectral Proper Orthogonal Decomposition (SPOD) and Bispectral Mode Decomposition (BMD), we educe coherent structures on the different forcing regimes and analyse how strong nonlinear interactions affect their dynamics. The forced jets provide a simplified scenario where energy exchange between frequencies can be traced back to a few prominent triadic interactions. These are identified through the mode bispectrum and the associated BMD modes are found to be in good agreement with the most energetic structures computed through SPOD. The mode bispectrum also provides insight into the relative importance of linear and nonlinear mechanisms, with respect to the mean of the forced jet, in determining the amplitudes of velocity fluctuations at the forcing frequency and its harmonics. Unforced jets have a broad signature in the bispectrum, reflecting the broadband nature of nonlinear energy exchange in the unforced jets.

2020

Lift-up, Kelvin–Helmholtz and Orr mechanisms in turbulent jets

E. Pickering, G. Rigas, P. A. S. Nogueira, and 3 more authors

Journal of Fluid Mechanics, 2020, 896, A2

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Modal Analysis of Acoustic Directivity in Turbulent Jets

A. Nekkanti, and O. T. Schmidt

AIAA Journal, 2020, 0(0), 1-12

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The directivity of noise from three large-eddy simulations of turbulent jets at Mach 0.7, 0.9, and 1.5 is investigated using spectral proper orthogonal decomposition (SPOD). The most energetic patterns of acoustic radiation are extracted using the far-field pressure 2-norm. Specialization of the norm to the far field is accomplished through localized spatial weighting. Radiation patterns to specific jet inlet angles are isolated by further restricting the spatial weighting to small rectangular regions in the far field. The most energetic radiation pattern for all cases and relevant frequencies is a single superdirective acoustic beam in the downstream direction. The source region of these beams is traced back to the end of the potential core for low frequencies and the shear-layer region for higher frequencies. In the sideline direction, to low angles, the acoustic patterns consist of beams that propagate upstream or perpendicular to the jet axis. The sideline radiation patterns are found to originate from the same source locations as the dominant superdirective beams. Inspection of the SPOD modes reveals that sideline radiation is directly linked to directive downstream radiation. Within the restricted radial extent of the computational domain, these results indicate that the sources of sideline and downstream radiation are intimately linked.
Amplitude Scaling of Wave Packets in Turbulent Jets

L. A. Antonialli, A. V. G. Cavalieri, O. T. Schmidt, and 4 more authors

AIAA Journal, 2020, 0(0), 1-10

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This paper studies the amplitude of large-scale coherent wave-packet structures in jets, modeled by the parabolized stability equations (PSEs). Linear PSEs can retrieve the shape of the wave packets, but linearity leads to solutions with a free amplitude, which has traditionally been obtained in an ad hoc manner using limited data. We systematically determine the free amplitude as a function of frequency and azimuthal wave number by comparing the fluctuation fields retrieved from PSEs with coherent structures educed from large-eddy simulation data using spectral proper orthogonal decomposition. The wave-packet amplitude is shown to decay exponentially with the Strouhal number for axisymmetric and helical modes at both Mach numbers considered in the study: 0.4 and 0.9. Analytical fit functions are proposed, and the scaled wave packets provide reasonable reconstructions of pressure and velocity spectra on the jet centerline and lip line over a range of streamwise positions.
Modal analysis of the directivity of acoustic emissions from wavepackets in turbulent jets

A. Nekkanti, and O. T. Schmidt

AIAA Paper 2020-0745, 2020

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The directivity of noise from three large-eddy simulations of turbulent jets at Mach 0.7, 0.9 and 1.5 and the first three azimuthal wavenumbers is investigated using spectral proper orthogonal decomposition (SPOD). First, a weighting function for the pressure 2-norm that is localized to the far-field is employed to educe the overall most energetic radiation patterns. Second, we isolate radiation patterns to specific jet inlet angles by restricting the spatial weighting to small rectangular regions in the far-field. The most energetic radiation pattern for all cases and relevant frequencies is a single superdirective acoustic beam in the downstream direction. The source region of these beams is traced back to the end of the potential core for low frequencies and the shear-layer region for higher frequencies. In the sideline direction to low angles, the acoustic patterns consist of waves that propagate upstream or perpendicular to the jet axis. The sideline radiation patterns are found to originate from the same source locations as the dominant superdirective beams. Inspection of the SPOD modes reveals that sideline radiation is directly slaved to directive downstream radiation. These results indicate that large-scale coherent structures are the dominant source of acoustic radiation to all the angles.

2019

Eddy viscosity for resolvent-based jet noise models

E. M. Pickering, G. Rigas, D. Sipp, and 2 more authors

2019, 2454
Resolvent-based analysis of streaks in turbulent jets

P. A Nogueira, A. V. G. Cavalieri, O. T. Schmidt, and 5 more authors

AIAA Paper 2019-2569, 2019, 2569
Streaks and coherent structures in jets from round and serrated nozzles

G. Rigas, E. M. Pickering, O. T. Schmidt, and 4 more authors

AIAA Paper 2019-2597, 2019, 2597
An investigation of the Mach number dependence of trapped acoustic waves in turbulent jets

A. Towne, O. T. Schmidt, and G. A. Brès

2019, 2546
Real-Time Estimation in a Turbulent Jet Using Multiple-Input-Multiple-Output Transfer Functions

I. Maia, P. Jordan, E. Martini, and 4 more authors

AIAA Paper 2019-2535, 2019, 2535
A conditional space–time POD formalism for intermittent and rare events: example of acoustic bursts in turbulent jets

O. T. Schmidt, and P. J. Schmid

Journal of Fluid Mechanics, 2019, 867, R2

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2018

Jet–flap interaction tones

P. Jordan, V. Jaunet, A. Towne, and 4 more authors

Journal of Fluid Mechanics, 2018, 853, 333–358

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Importance of the nozzle-exit boundary-layer state in subsonic turbulent jets

G. Brès, P. Jordan, M. Le Rallic, and 6 more authors

Journal of Fluid Mechanics, 2018, 851, 83–124

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Spectral analysis of jet turbulence

O. T. Schmidt, A. Towne, G. Rigas, and 2 more authors

Journal of Fluid Mechanics, 2018, 855, 953–982

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Amplitude scaling of turbulent-jet wavepackets

L. A. Antonialli, A. V. G. Cavalieri, O. T. Schmidt, and 4 more authors

AIAA Paper 2018-2978, 2018

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Large-eddy simulations of co-annular turbulent jet using a Voronoi-based mesh generation framework

G. A. Brès, S. T. Bose, M. Emory, and 4 more authors

AIAA Paper 2018-3302, 2018

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2017

High-frequency wavepackets in turbulent jets

K. Sasaki, A. V. G. Cavalieri, P. Jordan, and 3 more authors

Journal of Fluid Mechanics, 2017, 830, R2

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Wavepackets and trapped acoustic modes in a turbulent jet: coherent structure eduction and global stability

O. T. Schmidt, A. Towne, T. Colonius, and 3 more authors

Journal of Fluid Mechanics, 2017, 825, 1153-1181

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Acoustic resonance in the potential core of subsonic jets

A. Towne, A. V. G. Cavalieri, P. Jordan, and 4 more authors

Journal of Fluid Mechanics, 2017, 825, 1113-1152

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Wavepacket intermittency and its role in turbulent jet noise

O. T. Schmidt, T. Colonius, and G. A. Brès

AIAA Paper 2016-3050, 2017

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Linear dynamics of large-scale structures in turbulent jets

O. T. Schmidt, T. Colonius, and G. A. Brès

10th International Symposium on Turbulence and Shear Flow Phenomena, 2017

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One-Way Navier-Stokes and resolvent analysis for modeling coherent structures in a supersonic turbulent jet

G. Rigas, O. T. Schmidt, T. Colonius, and 1 more author

AIAA Paper 2017-4046, 2017, 4046

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2016

Large eddy simulation for jet noise: azimuthal decomposition and intermittency of the radiated sound

G. A. Brès, V. J., M. Le Rallic, and 6 more authors

AIAA Paper 2016-3050, 2016

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High-frequency wavepackets in turbulent jets

A. V. G. Cavalieri, K. Sasaki, P. Jordan, and 3 more authors

AIAA Paper 2016-3056, 2016

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Tonal dynamics and sound in subsonic turbulent jets

V. Jaunet, P. Jordan, A. V. G. Cavalieri, and 4 more authors

AIAA Paper 2016-3016, 2016

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

O. T. Schmidt, A. Towne, T. Colonius, and 4 more authors

AIAA Paper 2016-2808, 2016

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Trapped acoustic waves in the potential core of subsonic jets

A. Towne, A. V. G. Cavalieri, P. Jordan, and 4 more authors

AIAA Paper 2016-2809, 2016

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