Nozzle dynamics and wavepackets in turbulent jets

Kaplan, Oguzhan; Jordan, Peter; Cavalieri, André V. G.; Brès, Guillaume A.

doi:10.1017/jfm.2021.566

Cited by 19 publications

(12 citation statements)

References 71 publications

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“…2020; Kaplan et al. 2021), which we elaborate now. Before that, we note that this different approach here is due to our primary objective being to construct models that accurately capture the far-field sound from twin jets, for which it was realized that preserving the three-dimensionality of the wavepackets in the calculated SPOD modes would be of utmost importance.…”

Section: Simulation Configuration and Methodologiesmentioning

confidence: 87%

“…2020; Kaplan et al. 2021), such structures were extracted from the primitives, while our approach here is to extract them directly from the sound sources of (2.4) with the advantage of a more accurate description of potentially radiating structures. This may be understood from the fact that in acoustic analogies, the far-field sound pressure is directly related to the corresponding source terms, so that a superposition of various components of Lighthill's stress tensors yield the total sound.…”

Section: Simulation Configuration and Methodologiesmentioning

confidence: 99%

“…2020; Kaplan et al. 2021) is to construct a separate CSD matrix using data from each pair of the transformed quantity. This yields a CSD matrix that is devoid of the information pertaining to all other azimuthal modes necessary to capture the three-dimensional nature of the wavepackets.…”

Section: Simulation Configuration and Methodologiesmentioning

confidence: 99%

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Reduced-order models of aeroacoustic sources for sound radiated in twin subsonic jets

Muthichur,

Vempati,

Hemchandra

et al. 2023

J. Fluid Mech.

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We construct reduced-order models of aeroacoustic sources for single and twin subsonic jets ( $M_j=0.9$ , $Re=3600$ ), with the goal of accurately recovering the far-field sound over a wide band of frequencies $St=[0.07,1.0]$ and directivity angles $\phi = [30^{\circ },120^{\circ }]$ within a subdecibel level accuracy. These models are realized via combining spatio-temporally coherent spectral proper orthogonal decomposition (SPOD) modes extracted directly from Lighthill's stress tensor, itself calculated using large-eddy simulation (LES). We consider two sets of twin subsonic jets of diameter $D$ each, with spacings of $0.1D$ and $1D$ , where the jets merge upstream and downstream of breakdown, respectively. The closely spaced twin jet decays the slowest due to reduced turbulent stresses which are, however, more broadband due to early merging. Such jets show strong shielding in the plane of jets, especially at shallow directivity angles where sound levels may drop below that of the single jet. The farther spaced twin jets have dynamics more akin to the constituent single jet with turbulent fluctuations peaking here at $St=0.34$ , but showing very little shielding, with their overall sound pressure level (OASPL) mostly linked to the nature of extra flow structures created during merging. Three-dimensional, energy-ranked, coherent structures for twin jets exhibit rather poor low-rank behaviour, especially at the far-field spectral peak $St=0.14$ . At $St \gtrsim 0.3$ , the SPOD wavepackets show strong visual coherence, resembling Kelvin–Helmholtz instability modes upstream of breakdown, while at the lower frequencies, there is very little spatial coherence with wavepackets peaking downstream of breakdown. Although the leading SPOD modes radiate poorly, reduced-order models using a subset of them, up to $45$ SPOD modes per frequency, show a remarkable match (within $1$ dB) against the LES-predicted sound over $0.1 \lesssim St \lesssim 0.5$ , at all angles investigated. At other frequencies, the closely spaced twin jet shows more error, due to its greater hierarchy of spatio-temporal structures, showing slower convergence at the shallower angles.

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Section: Simulation Configuration and Methodologiesmentioning

confidence: 87%

Section: Simulation Configuration and Methodologiesmentioning

confidence: 99%

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Reduced-order models of aeroacoustic sources for sound radiated in twin subsonic jets

Muthichur,

Vempati,

Hemchandra

et al. 2023

J. Fluid Mech.

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show abstract

“…With the purpose of providing a deeper insight of the intrinsic dynamics of the boundary layer system, global resolvent modes, computed according to the method presented in Kaplan et al. (2021) and Abreu et al. (2021), are compared with the available SPOD modes.…”

Section: Convergence Analysis Of Spodmentioning

confidence: 99%

“…The details of this method are described in Kaplan et al. (2021). Results of the global resolvent analysis for the same and as in the LES are displayed in figure 17.…”

Section: Convergence Analysis Of Spodmentioning

confidence: 99%

Improved convergence of the spectral proper orthogonal decomposition through time shifting

Blanco

Martini²,

Sasaki³

et al. 2022

J. Fluid Mech.

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Spectral proper orthogonal decomposition (SPOD) is an increasingly popular modal analysis method in the field of fluid dynamics due to its specific properties: a linear system forced with white noise should have SPOD modes identical to response modes from resolvent analysis. The SPOD, coupled with the Welch method for spectral estimation, may require long time-resolved datasets. In this work, a linearised Ginzburg–Landau model is considered in order to study the method's convergence. Spectral proper orthogonal decomposition modes of the white-noise forced equation are computed and compared with corresponding response resolvent modes. The quantified error is shown to be related to the time length of Welch blocks (spectral window size) normalised by a convective time. Subsequently, an algorithm based on a temporal data shift is devised to further improve SPOD convergence and is applied to the Ginzburg–Landau system. Next, its efficacy is demonstrated in a numerical database of a boundary layer subject to bypass transition. The proposed approach achieves substantial improvement in mode convergence with smaller spectral window sizes with respect to the standard method. Furthermore, SPOD modes display growing wall-normal and spanwise velocity components along the streamwise direction, a feature which had not yet been observed and is also predicted by a global resolvent calculation. The shifting algorithm for the SPOD opens the possibility for using the method on datasets with time series of moderate duration, often produced by large simulations.

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Eduction of coherent structures from schlieren images of twin jets using SPOD informed with momentum potential theory in the spectral domain

Padilla-Montero,

Rodríguez,

Jaunet

et al. 2024

Theor. Comput. Fluid Dyn.

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This work presents a methodology to extract coherent structures from high-speed schlieren images of turbulent twin jets which are more physically interpretable than those obtained with currently existing techniques. Recently, Prasad and Gaitonde (J Fluid Mech 940:1–11, 2022) introduced an approach which employs the momentum potential theory of Doak (J Sound Vib 131(1):67–90, 1989) to compute potential (acoustic and thermal) energy fluctuations from the schlieren images by solving a Poisson equation, and combines it with spectral proper orthogonal decomposition (SPOD) to educe coherent structures from the momentum potential field instead of the original schlieren field. While the latter field is dominated by a broad range of vortical fluctuations in the turbulent mixing region of unheated high-speed jets, the momentum potential field is governed by fluctuations which are intimately related to acoustic emission, and its spatial structure in the frequency domain is very organized. The proposed methodology in this paper improves the technique of Prasad and Gaitonde (J Fluid Mech 940:1–11, 2022) in three new ways. First, the solution of the Poisson equation is carried out in the frequency-wavenumber domain instead of the time-space domain, which simplifies and integrates the solution of the Poisson equation within the SPOD framework based on momentum potential fluctuations. Second, the issue of solving the Poisson equation on a finite domain with ad hoc boundary conditions is explicitly addressed, identifying and removing those unphysical harmonic components introduced in the solution process. Third, the solution of the SPOD problem in terms of momentum potential fluctuations is used to reconstruct schlieren SPOD fields associated with each mode, allowing the visualization of the obtained coherent structures also in terms of the density gradient. The method is applied here to schlieren images of a twin-jet configuration with a small jet separation at two supersonic operation conditions: a perfectly-expanded and an overexpanded one. The SPOD modes based on momentum potential fluctuations retain the wavepacket structure including the direct Mach-wave radiation, together with upstream- and downstream-traveling acoustic waves, similar to SPOD modes based on the schlieren images. However, for the same dataset, they result in a lower-rank decomposition than schlieren-based SPOD and provide an effective separation of twin-jet fluctuations into independent toroidal and flapping oscillations that are recovered as different SPOD modes. These coherent structures are more consistent with twin-jet wavepacket models available in the literature than those originally obtained with direct schlieren-based SPOD, facilitating their interpretation and comparison against theoretical analyses. Graphical abstract

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Nozzle dynamics and wavepackets in turbulent jets

Abstract: Abstract

Cited by 19 publications

References 71 publications

Reduced-order models of aeroacoustic sources for sound radiated in twin subsonic jets

Reduced-order models of aeroacoustic sources for sound radiated in twin subsonic jets

Improved convergence of the spectral proper orthogonal decomposition through time shifting

Eduction of coherent structures from schlieren images of twin jets using SPOD informed with momentum potential theory in the spectral domain

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