Opposition control within the resolvent analysis framework

Luhar, Mitul; Sharma, A. S.; McKeon, Beverley

doi:10.1017/jfm.2014.209

Cited by 89 publications

(116 citation statements)

References 39 publications

(80 reference statements)

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“…Therefore, the fact that the fast wall pressure reflects an integral of the wall-normal velocity (2.24) could prove useful in inferring velocity information from wall-based pressure measurements. In addition, recent work by the present authors (Luhar et al 2013(Luhar et al , 2014 suggests that the performance of opposition control can be improved through the inclusion of a phase lag between the sensed wall-normal velocity and the blowing and suction generated at the wall. In this context, the consistent π/2 phase difference between the fast pressure and wall-normal velocity may be useful in determining the phase of the wall-based actuation.…”

Section: Resultsmentioning

confidence: 78%

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On the structure and origin of pressure fluctuations in wall turbulence: predictions based on the resolvent analysis

2014

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We generate predictions for the fluctuating pressure field in turbulent pipe flow by reformulating the resolvent analysis of McKeon and Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336-382) in terms of the so-called primitive variables. Under this analysis, the nonlinear convective terms in the Fourier-transformed Navier-Stokes equations (NSE) are treated as a forcing that is mapped to a velocity and pressure response by the resolvent of the linearized Navier-Stokes operator. At each wavenumber-frequency combination, the turbulent velocity and pressure field are represented by the most-amplified (rank-1) response modes, identified via a singular value decomposition of the resolvent. We show that these rank-1 response modes reconcile many of the key relationships among the velocity field, coherent structure (i.e. hairpin vortices), and the high-amplitude wall-pressure events observed in previous experiments and direct numerical simulations (DNS). A Green's function representation shows that the pressure fields obtained under this analysis correspond primarily to the fast pressure contribution arising from the linear interaction between the mean shear and the turbulent wall-normal velocity. Recovering the slow pressure requires an explicit treatment of the nonlinear interactions between the Fourier response modes. By considering the velocity and pressure fields associated with the triadically consistent mode combination studied by Sharma and McKeon (J. Fluid Mech., vol. 728, 2013, pp. 196-238), we identify the possibility of an apparent amplitude modulation effect in the pressure field, similar to that observed for the streamwise velocity field. However, unlike the streamwise velocity, for which the large scales of the flow are in phase with the envelope of the small-scale activity close to the wall, we expect there to be a π/2 phase difference between the large-scale wall-pressure and the envelope of the small-scale activity. Finally, we generate spectral predictions based on a rank-1 model assuming broadband forcing across all wavenumber-frequency combinations. Despite the significant simplifying assumptions, this approach reproduces trends observed in previous DNS for the wavenumber spectra of velocity and pressure, and for the scale-dependence of wall-pressure propagation speed.

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Section: Resultsmentioning

confidence: 78%

“…This extension permits direct access to pressure information, and it also allows consideration of alternative boundary conditions (e.g. Luhar, Sharma & McKeon 2013, 2014.…”

Section: Resolvent Analysismentioning

confidence: 99%

On the structure and origin of pressure fluctuations in wall turbulence: predictions based on the resolvent analysis

2014

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“…While the global stability analysis reveals how perturbations in the flow behave through the setup of an initial value problem, the resolvent analysis uncovers the flow response as a particular solution for a sustained harmonic forcing input. The insights gained from resolvent analysis are powerful and have supported studies focusing on transitions, transient growth, and flow control [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Resolvent Analysis of Compressible Laminar and Turbulent Cavity Flows

et al. 2020

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The present work demonstrates the use of resolvent analysis to obtain physical insights for open-cavity flows. Resolvent analysis identifies the flow response to harmonic forcing, given a steady base state, in terms of the response and forcing modes and the amplification gain. The response and forcing modes reveal the spatial structures associated with this amplification process. In this study, we perform resolvent analysis on both laminar and turbulent flows over a rectangular cavity with length-to-depth ratio of L/D = 6 at a free stream Mach number of M ∞ = 0.6 in a spanwise periodic setting. Based on the dominant instability of the base state, a discount parameter is introduced to resolvent analysis to examine the harmonic characteristics over a finite-time window. We first uncover the underlying flow physics and interpret findings from laminar flow at Re D = 502. These findings from laminar flow are extended to a more practical cavity flow example at a much higher Reynolds number of Re D = 10 4 . The features of response and forcing modes from the laminar and turbulent cavity flows are similar to the spatial structures from the laminar analysis. We further find that the large amplification of energy in flow response is associated with high frequency for turbulent flow, while the flow is

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“…However, the distribution of the nonlinear forcing is unknown in this model and assumptions must be taken with respect to this. Examples of this are the work of Sharma and McKeon [2], who successfully assigned weightings to the modes according to their relative importance based on observation in the existing literature in order to model hairpin packets, and the work of Luhar et al [3], in which a broad unit forcing is assumed across all wavenumbers for the prediction of the effectiveness of opposition control in pipe flow. Additional efforts to unveil the distribution of nonlinear forcing have been carried out by Moarref et al [4], who applied optimization methods to weight resolvent modes in order to reconstruct a given turbulent spectra, and by Gómez et al [5] who compared the most amplified resolvent modes with the most energetic modes arising from a dynamical mode decomposition (DMD) of direct numerical simulation (DNS) data.…”

Section: Introductionmentioning

confidence: 99%

On the Coupling of Direct Numerical Simulation and Resolvent Analysis

Gómez

Blackburn

Rudman

et al. 2016

Springer Proceedings in Physics

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The present contribution explores the relationship between response and forcing via amplification mechanisms in the Navier-Stokes equations applied to a turbulent pipe flow. A novel numerical method coupling direct numerical simulation with the resolvent model [J. Fluid Mech. 658, 336-382 (2010)] is developed in order to reveal the exact distribution of the nonlinear forcing terms, originally unknown in the model. The obtained results highlight the major role of the nonlinear terms in the energy spectra.

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Opposition control within the resolvent analysis framework

Cited by 89 publications

References 39 publications

On the structure and origin of pressure fluctuations in wall turbulence: predictions based on the resolvent analysis

On the structure and origin of pressure fluctuations in wall turbulence: predictions based on the resolvent analysis

Resolvent Analysis of Compressible Laminar and Turbulent Cavity Flows

On the Coupling of Direct Numerical Simulation and Resolvent Analysis

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