Investigation of the PSE Approach for Subsonic and Supersonic Hot Jets. Detailed Comparisons with LES and Linearized Euler Equations Results

Piot, Estelle; Casalis, Grégoire; Muller, Frederic; Bailly, Christophe

doi:10.1260/147547206779379877

Cited by 43 publications

(39 citation statements)

References 44 publications

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“…This eigenmode decomposition can be achieved by making use of the bi-orthogonality between the eigenfunctions of the direct and adjoint LST problems. [21][22][23] The approach of modeling wave packets as linear instability waves has been widely employed in the study of forced supersonic jets, 5,10,12,[24][25][26] for which the measured near-field fluctuations were found to be in good agreement with the predictions of linear stability theory. 9 In the case of subsonic natural jets, this approach has only recently begun to deliver satisfactory quantitative predictions, both in the near pressure and velocity fields.…”

Section: -3mentioning

confidence: 99%

“…A further improvement in the linear model can be achieved with the introduction of ad hoc eddy viscosity models. [5][6][7] Following diverse assumptions on the characteristics of the mean flow and wave packets, different approaches to the computation of instability waves have been employed in the past, including locally parallel stability analysis based on the Orr-Sommerfeld equation, 8 multiple-scales analysis, 4,9 parabolized stability equations (PSE), [10][11][12][13] global eigenmode analysis, 14 and boundaryvalue problems. 15 Independent of the particular approach followed for the wave packet modeling, the governing equations are deterministic and the solution depends on prescribed inlet conditions.…”

Section: Introductionmentioning

confidence: 99%

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Inlet conditions for wave packet models in turbulent jets based on eigenmode decomposition of large eddy simulation data

et al. 2013

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This paper makes contributions towards reduced-order models of wave packets in supersonic, turbulent jets. Wave packets are large-scale turbulent structures that are correlated and advected over distances that are large compared to the integral scales of turbulence, i.e., many jet diameters at the lowest frequencies. They are thought to be responsible for the peak noise radiated at shallow angles to the jet axis. Linear wave packet models based on the Parabolized Stability Equations (PSE) have been shown in the past to be in excellent agreement with statistical structures educed from experimental pressure and velocity data in subsonic jets. Here, we extend these models to supersonic jets and validate them using a Large Eddy Simulation (LES) database for an isothermal and a moderately heated Mach 1.5 turbulent jets. For supersonic jets, inlet conditions for PSE models are ambiguous, as a parallel flow stability analysis shows several unstable modes at the inlet cross section. We develop a bi-orthogonal decomposition and project the LES data onto the relevant families of instability waves. These serve as inlet conditions, including the amplitude and shape functions, for PSE solutions which are then favorably compared to the near-field pressure fields educed from LES. C 2013 AIP Publishing LLC. [http://dx

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Section: -3mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Inlet conditions for wave packet models in turbulent jets based on eigenmode decomposition of large eddy simulation data

et al. 2013

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“…The modelling of wavepackets in unforced jets was also attempted (e.g. Tam & Chen 1994;Balakumar 1998;Yen & Messersmith 1998;Piot et al 2006), but this was hampered owing, in hindsight, to a lack of detailed spatiotemporal data. Furthermore, none of these studies showed how a linear instability wave could be consistent with the fluctuations of a real turbulent jet.…”

Section: Introductionmentioning

confidence: 99%

“…There were many attempts to validate this theory that were viewed as successful (e.g. Troutt & McLaughlin 1982;Tam & Hu 1989;Tam & Chen 1994;Balakumar 1998;Yen & Messersmith 1999;Lin et al 2004;Piot et al 2006), and the earlier efforts were reviewed by Tam (1991Tam ( , 1995. However, the comparisons were actually based on limited measurements, and the lack of consistent identification of both the near and far sound fields prevented a more rigourous test of the theory.…”

Section: Introductionmentioning

confidence: 99%

Wavepacket models for supersonic jet noise

et al. 2014

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Gudmundsson and Colonius (J. Fluid Mech., vol. 689, 2011, pp. 97-128) have recently shown that the average evolution of low-frequency, low-azimuthal modal large-scale structures in the near field of subsonic jets are remarkably well predicted as linear instability waves of the turbulent mean flow using parabolized stability equations. In this work, we extend this modelling technique to an isothermal and a moderately heated Mach 1.5 jet for which the mean flow fields are obtained from a high-fidelity large-eddy simulation database. The latter affords a rigourous and extensive validation of the model, which had only been pursued earlier with more limited experimental data. A filter based on proper orthogonal decomposition is applied to the data to extract the most energetic coherent components. These components display a distinct wavepacket character, and agree fairly well with the parabolized stability equations model predictions in terms of near-field pressure and flow velocity. We next apply a Kirchhoff surface acoustic propagation technique to the near-field pressure model and obtain an encouraging match for far-field noise levels in the peak aft direction. The results suggest that linear wavepackets in the turbulence are responsible for the loudest portion of the supersonic jet acoustic field.

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“…First, we employ parabolized stability equations (PSE), introduced by Bertolotti & Herbert (1991). This approach represents a refinement of the locally parallel approach whereby both nonparallel and nonlinear effects can be retained in the analysis of slowly spreading, convectively unstable flows such as boundary layers (Bertolotti & Herbert 1991;Bertolotti, Herbert & Spalart 1992;Chang et al 1993), planar mixing layers (Day, Mansour & Reynolds 2001;) and jets (Balakumar 1998;Yen & Messersmith 1998;Malik & Chang 2000;Piot et al 2006;Gudmundsson & Colonius 2009;Ray & Cheung 2009). While it is computationally feasible nowadays to perform a global stability analysis of the jet mean flow field (Chomaz 2005), we prefer PSE with an eye towards developing rapidly computable, reduced-order models for the farfield sound associated with large-scale structures (Colonius, Samanta & Gudmundsson 2010;Reba, Narayanan & Colonius 2010).…”

Section: Introductionmentioning

confidence: 99%

Instability wave models for the near-field fluctuations of turbulent jets

2011

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Previous work has shown that aspects of the evolution of large-scale structures, particularly in forced and transitional mixing layers and jets, can be described by linear and nonlinear stability theories. However, questions persist as to the choice of the basic (steady) flow field to perturb, and the extent to which disturbances in natural (unforced), initially turbulent jets may be modelled with the theory. For unforced jets, identification is made difficult by the lack of a phase reference that would permit a portion of the signal associated with the instability wave to be isolated from other, uncorrelated fluctuations. In this paper, we investigate the extent to which pressure and velocity fluctuations in subsonic, turbulent round jets can be described as linear perturbations to the mean flow field. The disturbances are expanded about the experimentally measured jet mean flow field, and evolved using linear parabolized stability equations (PSE) that account, in an approximate way, for the weakly nonparallel jet mean flow field. We utilize data from an extensive microphone array that measures pressure fluctuations just outside the jet shear layer to show that, up to an unknown initial disturbance spectrum, the phase, wavelength, and amplitude envelope of convecting wavepackets agree well with PSE solutions at frequencies and azimuthal wavenumbers that can be accurately measured with the array. We next apply the proper orthogonal decomposition to near-field velocity fluctuations measured with particle image velocimetry, and show that the structure of the most energetic modes is also similar to eigenfunctions from the linear theory. Importantly, the amplitudes of the modes inferred from the velocity fluctuations are in reasonable agreement with those identified from the microphone array. The results therefore suggest that, to predict, with reasonable accuracy, the evolution of the largest-scale structures that comprise the most energetic portion of the turbulent spectrum of natural jets, nonlinear effects need only be indirectly accounted for by considering perturbations to the mean turbulent flow field, while neglecting any non-zero frequency disturbance interactions.

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Investigation of the PSE Approach for Subsonic and Supersonic Hot Jets. Detailed Comparisons with LES and Linearized Euler Equations Results

Cited by 43 publications

References 44 publications

Inlet conditions for wave packet models in turbulent jets based on eigenmode decomposition of large eddy simulation data

Inlet conditions for wave packet models in turbulent jets based on eigenmode decomposition of large eddy simulation data

Wavepacket models for supersonic jet noise

Instability wave models for the near-field fluctuations of turbulent jets

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