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Mckeon, Beverley J. - One of the best experts on this subject based on the ideXlab platform.
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Experiments and Modeling of a Compliant Wall Response to a Turbulent Boundary Layer with Dynamic Roughness Forcing
'MDPI AG', 2021Co-Authors: Huynh, David P., Huang Yuting, Mckeon, Beverley J.Abstract:The response of a compliant surface in a turbulent boundary layer forced by a dynamic roughness is studied using experiments and Resolvent analysis. Water tunnel experiments are carried out at a friction Reynolds number of Re_τ ≈ 410, with flow and surface measurements taken with 2D particle image velocimetry (PIV) and stereo digital image correlation (DIC). The narrow band dynamic roughness forcing enables analysis of the flow and surface responses coherent with the forcing frequency, and the corresponding Fourier modes are extracted and compared with Resolvent modes. The Resolvent modes capture the structures of the experimental Fourier modes and the Resolvent with eddy viscosity improves the matching. The comparison of smooth and compliant wall Resolvent modes predicts a virtual wall feature in the wall normal velocity of the compliant wall case. The virtual wall is revealed in experimental data using a conditional average informed by the Resolvent prediction. Finally, the change to the Resolvent modes due to the influence of wall compliance is studied by modeling the compliant wall boundary condition as a deterministic forcing to the smooth wall Resolvent framework
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Data-driven Resolvent analysis
'Cambridge University Press (CUP)', 2021Co-Authors: Herrmann Benjamin, Baddoo, Peter J., Semaan Richard, Brunton, Steven L., Mckeon, Beverley J.Abstract:Resolvent analysis identifies the most responsive forcings and most receptive states of a dynamical system, in an input–output sense, based on its governing equations. Interest in the method has continued to grow during the past decade due to its potential to reveal structures in turbulent flows, to guide sensor/actuator placement and for flow control applications. However, Resolvent analysis requires access to high-fidelity numerical solvers to produce the linearized dynamics operator. In this work, we develop a purely data-driven algorithm to perform Resolvent analysis to obtain the leading forcing and response modes, without recourse to the governing equations, but instead based on snapshots of the transient evolution of linearly stable flows. The formulation of our method follows from two established facts: (i) dynamic mode decomposition can approximate eigenvalues and eigenvectors of the underlying operator governing the evolution of a system from measurement data, and (ii) a projection of the Resolvent operator onto an invariant subspace can be built from this learned eigendecomposition. We demonstrate the method on numerical data of the linearized complex Ginzburg–Landau equation and of three-dimensional transitional channel flow, and discuss data requirements. Presently, the method is suitable for the analysis of laminar equilibria, and its application to turbulent flows would require disambiguation between the linear and nonlinear dynamics driving the flow. The ability to perform Resolvent analysis in a completely equation-free and adjoint-free manner will play a significant role in lowering the barrier of entry to Resolvent research and applications
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Mean and Unsteady Flow Reconstruction Using Data-Assimilation and Resolvent Analysis
'American Institute of Aeronautics and Astronautics (AIAA)', 2020Co-Authors: Symon Sean, Sipp Denis, Schmid, Peter J., Mckeon, Beverley J.Abstract:A methodology is presented that exploits both data-assimilation techniques and Resolvent analysis for reconstructing turbulent flows, containing organized structures, with an efficient set of measurements. The mean (time-averaged) flow is obtained using variational data-assimilation that minimizes the discrepancy between a limited set of flow measurements, generally from an experiment, and a numerical simulation of the Navier–Stokes equations. The fluctuations are educed from Resolvent analysis and time-resolved data at a single point in the flow. Resolvent analysis also guides where measurements of the mean and fluctuating quantities are needed for efficient reconstruction of a simple example case study: flow around a circular cylinder at a Reynolds number of Re=100. For this flow, Resolvent analysis reveals that the leading singular value, most amplified modes, and the mean profile for 47
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Resolvent-based study of compressibility effects on supersonic turbulent boundary layers
'Cambridge University Press (CUP)', 2020Co-Authors: Bae H. Jane, Dawson, Scott T. M., Mckeon, Beverley J.Abstract:The Resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) is applied to supersonic turbulent boundary layers to study the validity of Morkovin’s hypothesis, which postulates that high-speed turbulence structures in zero-pressure-gradient turbulent boundary layers remain largely the same as their incompressible counterparts. Supersonic zero-pressure-gradient turbulent boundary layers with adiabatic wall boundary conditions at Mach numbers ranging from 2 to 4 are considered. Resolvent analysis highlights two distinct regions of the supersonic turbulent boundary layer in the wave parameter space: the relatively supersonic region and the relatively subsonic region. In the relatively supersonic region, where the flow is supersonic relative to the free-stream, Resolvent modes display structures consistent with Mach wave radiation that are absent in the incompressible regime. In the relatively subsonic region, we show that the low-rank approximation of the Resolvent operator is an effective approximation of the full system and that the response modes predicted by the model exhibit universal and geometrically self-similar behaviour via a transformation given by the semi-local scaling. Moreover, with the semi-local scaling, we show that the Resolvent modes follow the same scaling law as their incompressible counterparts in this region, which has implications for modelling and the prediction of turbulent high-speed wall-bounded flows. We also show that the thermodynamic variables exhibit similar mode shapes to the streamwise velocity modes, supporting the strong Reynolds analogy. Finally, we demonstrate that the principal Resolvent modes can be used to capture the energy distribution between momentum and thermodynamic fluctuations
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Data-driven Resolvent analysis
2020Co-Authors: Herrmann Benjamin, Baddoo, Peter J., Semaan Richard, Brunton, Steven L., Mckeon, Beverley J.Abstract:Resolvent analysis identifies the most responsive forcings and most receptive states of a dynamical system, in an input--output sense, based on its governing equations. Interest in the method has continued to grow during the past decade due to its potential to reveal structures in turbulent flows, to guide sensor/actuator placement, and for flow control applications. However, Resolvent analysis requires access to high-fidelity numerical solvers to produce the linearized dynamics operator. In this work, we develop a purely data-driven algorithm to perform Resolvent analysis to obtain the leading forcing and response modes, without recourse to the governing equations, but instead based on snapshots of the transient evolution of linearly stable flows. The formulation of our method follows from two established facts: $1)$ dynamic mode decomposition can approximate eigenvalues and eigenvectors of the underlying operator governing the evolution of a system from measurement data, and $2)$ a projection of the Resolvent operator onto an invariant subspace can be built from this learned eigendecomposition. We demonstrate the method on numerical data of the linearized complex Ginzburg--Landau equation and of three-dimensional transitional channel flow, and discuss data requirements. The ability to perform Resolvent analysis in a completely equation-free and adjoint-free manner will play a significant role in lowering the barrier of entry to Resolvent research and applications
Colonius Tim - One of the best experts on this subject based on the ideXlab platform.
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Resolvent-based modeling of turbulent jet noise
2021Co-Authors: Pickering Ethan, Towne Aaron, Jordan Peter, Colonius TimAbstract:Resolvent analysis has demonstrated encouraging results for modeling coherent structures in jets when compared against their data-educed counterparts from high-fidelity large-eddy simulations (LES). We formulate Resolvent analysis as an acoustic analogy that relates the near-field forcing to the near-field pressure field and the far-field acoustics. We use an LES database of round, isothermal, Mach 0.9 and 1.5 jets to produce an ensemble of realizations for the acoustic field that we project onto a limited set of Resolvent modes. In the near-field, we perform projections on a restricted acoustic output domain, $r/D = [5,6]$, while the far-field projections are performed on a Kirchhoff surface comprising a 100-diameter arc centered at the nozzle. This allows the LES realizations to be expressed in the Resolvent basis via a data-deduced, low-rank, cross-spectral density matrix. We observe substantial improvements to the acoustic field reconstructions with the addition of a RANS-derived eddy-viscosity model to the Resolvent operator and find that a single Resolvent mode reconstructs the most energetic regions of the acoustic field across Strouhal numbers, $St = [0-1]$, and azimuthal wavenumbers, $m=[0,2]$. Finally, we present a simple function that results in a rank-1 Resolvent model agreeing within 2dB of the peak noise for both jets.Comment: 18 pages, 16 figures, Submitted to the Journal of the Acoustical Society of Americ
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Resolvent-based modeling of turbulent jet noise
2021Co-Authors: Pickering Ethan, Towne Aaron, Jordan Peter, Colonius TimAbstract:Resolvent analysis has demonstrated encouraging results for modeling coherent structures in jets when compared against their data-educed counterparts from high-fidelity large-eddy simulations (LES). We formulate Resolvent analysis as an acoustic analogy that relates the near-field forcing to the near-field pressure field and the far-field acoustics. We use an LES database of round, isothermal, Mach 0.9 and 1.5 jets to produce an ensemble of realizations for the acoustic field that we project onto a limited set of Resolvent modes. In the near-field, we perform projections on a restricted acoustic output domain, r/D=[5,6], while the far-field projections are performed on a Kirchhoff surface comprising a 100-diameter arc centered at the nozzle. This allows the LES realizations to be expressed in the Resolvent basis via a data-deduced, low-rank, cross-spectral density matrix. We observe substantial improvements to the acoustic field reconstructions with the addition of a RANS-derived eddy-viscosity model to the Resolvent operator and find that a single Resolvent mode reconstructs the most energetic regions of the acoustic field across Strouhal numbers, St=[0−1], and azimuthal wavenumbers, m=[0,2]. Finally, we present a simple function that results in a rank-1 Resolvent model agreeing within 2dB of the peak noise for both jets
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Optimal eddy viscosity for Resolvent-based models of coherent structures in turbulent jets
'Cambridge University Press (CUP)', 2021Co-Authors: Pickering Ethan, Rigas Georgios, Schmidt, Oliver T., Sipp Denis, Colonius TimAbstract:Response modes computed via linear Resolvent analysis of a turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in both wall-bounded and free shear flows. To make such Resolvent models predictive, the nonlinear forcing term must be closed. Strategies to do so include imposing self-consistent sets of triadic interactions, proposing various source models or through turbulence modelling. For the latter, several investigators have proposed using the mean-field eddy viscosity acting linearly on the fluctuation field. In this study, a data-driven approach is taken to quantitatively improve linear Resolvent models by deducing an optimal eddy-viscosity field that maximizes the projection of the dominant Resolvent mode to the energy-optimal coherent structure educed using spectral proper orthogonal decomposition (SPOD) of data from high-fidelity simulations. We use large-eddy simulation databases for round isothermal jets at subsonic, transonic and supersonic conditions and show that the optimal eddy viscosity substantially improves the agreement between Resolvent and SPOD modes, reaching over 90 % agreement at those frequencies where the jet exhibits a low-rank response. We then consider a fixed model for the eddy viscosity and show that with the calibration of a single constant, the results are generally close to the optimal one. In particular, the use of a standard Reynolds-averaged Navier–Stokes eddy-viscosity Resolvent model, with a single coefficient, provides substantial agreement between SPOD and Resolvent modes for three turbulent jets and across the most energetic wavenumbers and frequencies
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Optimal eddy viscosity for Resolvent-based models of coherent structures in turbulent jets
2021Co-Authors: Pickering Ethan, Rigas Georgios, Schmidt, Oliver T., Sipp Denis, Colonius TimAbstract:Response modes computed via linear Resolvent analysis of a turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in both wall-bounded and free shear flows. To make such Resolvent models predictive, the nonlinear forcing term must be closed. Strategies to do so include imposing self-consistent sets of triadic interactions, proposing various source models, or through turbulence modelling. For the latter, several investigators have proposed using the mean-field eddy viscosity acting linearly on the fluctuation field. In this study, a data-driven approach is taken to quantitatively improve linear Resolvent models by deducing an optimal eddy-viscosity field that maximizes the projection of the dominant Resolvent mode to the energy-optimal coherent structure educed using spectral proper orthogonal decomposition (SPOD) of data from high-fidelity simulations. We use large-eddy simulation databases for round isothermal jets at subsonic, transonic, and supersonic conditions and show that the optimal eddy viscosity substantially improves the alignment between Resolvent and SPOD modes, reaching over 90% alignment at those frequencies where the jet exhibits a low-rank response. We then consider a fixed model for the eddy viscosity and show that with the calibration of a single constant, the results are generally close to the optimal one. In particular, the use of a standard Reynolds-Averaged-Navier-Stokes (RANS) eddy-viscosity Resolvent model, with a single coefficient, provides substantial agreement between SPOD and Resolvent modes for three turbulent jets and across the most energetic wavenumbers and frequencies.Comment: 34 pages, 18 figures, under consideration for publication in the Journal of Fluid Mechanic
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Efficient global Resolvent analysis via the one-way Navier-Stokes equations. Part 1. Forced response
2021Co-Authors: Towne Aaron, Pickering Ethan, Rigas Georgios, Colonius TimAbstract:Resolvent analysis is a powerful tool for modeling and analyzing turbulent flows and in particular provides an approximation of coherent flow structures. Despite recent algorithmic advances, computing Resolvent modes for flows with more than one inhomogeneous spatial coordinate remains computationally expensive. In this two-part paper, we show how efficient and accurate approximations of Resolvent modes can be obtained using a well-posed spatial marching method for flows that contain a slowly varying direction. In this first part of the paper, we derive a well-posed and convergent one-way equation describing the downstream-traveling waves supported by the linearized Navier-Stokes equations. Integrating these equations, which requires significantly less CPU and memory resources than a direct solution of the linearized Navier-Stokes equations, approximates the action of the Resolvent operator on a forcing vector. This capability is leveraged in part 2 of the paper to compute approximate Resolvent modes. The method is validated and demonstrated using the examples of a simple acoustics problem and a supersonic turbulent jet
Kunihiko Taira - One of the best experts on this subject based on the ideXlab platform.
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Resolvent analysis based design of airfoil separation control
Journal of Fluid Mechanics, 2019Co-Authors: Chian Yeh, Kunihiko TairaAbstract:We use Resolvent analysis to design active control techniques for separated flows over a NACA 0012 airfoil. Spanwise-periodic flows over the airfoil at a chord-based Reynolds number of $23\,000$ and a free-stream Mach number of $0.3$ are considered at two post-stall angles of attack of $6^{\circ }$ and $9^{\circ }$ . Near the leading edge, localized unsteady thermal actuation is introduced in an open-loop manner with two tunable parameters of actuation frequency and spanwise wavelength. To provide physics-based guidance for the effective choice of these control input parameters, we conduct global Resolvent analysis on the baseline turbulent mean flows to identify the actuation frequency and wavenumber that provide large perturbation energy amplification. The present analysis also considers the use of a temporal filter to limit the time horizon for assessing the energy amplification to extend Resolvent analysis to unstable base flows. We incorporate the amplification and response mode from Resolvent analysis to provide a metric that quantifies momentum mixing associated with the modal structure. This metric is compared to the results from a large number of three-dimensional large-eddy simulations of open-loop controlled flows. With the agreement between the Resolvent-based metric and the enhancement of aerodynamic performance found through large-eddy simulations, we demonstrate that Resolvent analysis can predict the effective range of actuation frequency as well as the global response to the actuation input. We believe that the present Resolvent-based approach provides a promising path towards mean flow modification by capitalizing on the dominant modal mixing.
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Resolvent analysis based design of airfoil separation control
arXiv: Fluid Dynamics, 2018Co-Authors: Chian Yeh, Kunihiko TairaAbstract:We combine three-dimensional (3D) large-eddy simulations (LES) and Resolvent analysis to design active separation control techniques on a NACA 0012 airfoil. Spanwise-periodic flows over the airfoil at a chord-based Reynolds number of $23,000$ and a free-stream Mach number of $0.3$ are considered at two post-stall angles of attack of $6^\circ$ and $9^\circ$. Near the leading edge, localized unsteady thermal actuation is introduced in an open-loop manner with two tunable parameters of actuation frequency and spanwise wavelength. For the most successful control case that achieves full reattachment, we observe a reduction in drag by up to $49\%$ and increase in lift by up to $54\%$. To provide physics-based guidance for the effective choice of these control input parameters, we conduct global Resolvent analysis on the baseline turbulent mean flows to identify the actuation frequency and wavenumber that provide high energy amplification. The present analysis also considers the use of a temporal filter to limit the time horizon for assessing the energy amplification to extend Resolvent analysis to unstable base flows. We incorporate the amplification and response mode from Resolvent analysis to provide a metric that quantifies momentum mixing associated with the modal structure. By comparing this metric from Resolvent analysis and the LES results of controlled flows, we demonstrate that Resolvent analysis can predict the effective range of actuation frequency as well as the global response to the actuation input. Supported by the agreements between the results from Resolvent analysis and LES, we believe that this study provides insights for the use of Resolvent analysis in guiding future active flow control.
Pickering Ethan - One of the best experts on this subject based on the ideXlab platform.
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Resolvent-based modeling of turbulent jet noise
2021Co-Authors: Pickering Ethan, Towne Aaron, Jordan Peter, Colonius TimAbstract:Resolvent analysis has demonstrated encouraging results for modeling coherent structures in jets when compared against their data-educed counterparts from high-fidelity large-eddy simulations (LES). We formulate Resolvent analysis as an acoustic analogy that relates the near-field forcing to the near-field pressure field and the far-field acoustics. We use an LES database of round, isothermal, Mach 0.9 and 1.5 jets to produce an ensemble of realizations for the acoustic field that we project onto a limited set of Resolvent modes. In the near-field, we perform projections on a restricted acoustic output domain, $r/D = [5,6]$, while the far-field projections are performed on a Kirchhoff surface comprising a 100-diameter arc centered at the nozzle. This allows the LES realizations to be expressed in the Resolvent basis via a data-deduced, low-rank, cross-spectral density matrix. We observe substantial improvements to the acoustic field reconstructions with the addition of a RANS-derived eddy-viscosity model to the Resolvent operator and find that a single Resolvent mode reconstructs the most energetic regions of the acoustic field across Strouhal numbers, $St = [0-1]$, and azimuthal wavenumbers, $m=[0,2]$. Finally, we present a simple function that results in a rank-1 Resolvent model agreeing within 2dB of the peak noise for both jets.Comment: 18 pages, 16 figures, Submitted to the Journal of the Acoustical Society of Americ
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Resolvent-based modeling of turbulent jet noise
2021Co-Authors: Pickering Ethan, Towne Aaron, Jordan Peter, Colonius TimAbstract:Resolvent analysis has demonstrated encouraging results for modeling coherent structures in jets when compared against their data-educed counterparts from high-fidelity large-eddy simulations (LES). We formulate Resolvent analysis as an acoustic analogy that relates the near-field forcing to the near-field pressure field and the far-field acoustics. We use an LES database of round, isothermal, Mach 0.9 and 1.5 jets to produce an ensemble of realizations for the acoustic field that we project onto a limited set of Resolvent modes. In the near-field, we perform projections on a restricted acoustic output domain, r/D=[5,6], while the far-field projections are performed on a Kirchhoff surface comprising a 100-diameter arc centered at the nozzle. This allows the LES realizations to be expressed in the Resolvent basis via a data-deduced, low-rank, cross-spectral density matrix. We observe substantial improvements to the acoustic field reconstructions with the addition of a RANS-derived eddy-viscosity model to the Resolvent operator and find that a single Resolvent mode reconstructs the most energetic regions of the acoustic field across Strouhal numbers, St=[0−1], and azimuthal wavenumbers, m=[0,2]. Finally, we present a simple function that results in a rank-1 Resolvent model agreeing within 2dB of the peak noise for both jets
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Optimal eddy viscosity for Resolvent-based models of coherent structures in turbulent jets
'Cambridge University Press (CUP)', 2021Co-Authors: Pickering Ethan, Rigas Georgios, Schmidt, Oliver T., Sipp Denis, Colonius TimAbstract:Response modes computed via linear Resolvent analysis of a turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in both wall-bounded and free shear flows. To make such Resolvent models predictive, the nonlinear forcing term must be closed. Strategies to do so include imposing self-consistent sets of triadic interactions, proposing various source models or through turbulence modelling. For the latter, several investigators have proposed using the mean-field eddy viscosity acting linearly on the fluctuation field. In this study, a data-driven approach is taken to quantitatively improve linear Resolvent models by deducing an optimal eddy-viscosity field that maximizes the projection of the dominant Resolvent mode to the energy-optimal coherent structure educed using spectral proper orthogonal decomposition (SPOD) of data from high-fidelity simulations. We use large-eddy simulation databases for round isothermal jets at subsonic, transonic and supersonic conditions and show that the optimal eddy viscosity substantially improves the agreement between Resolvent and SPOD modes, reaching over 90 % agreement at those frequencies where the jet exhibits a low-rank response. We then consider a fixed model for the eddy viscosity and show that with the calibration of a single constant, the results are generally close to the optimal one. In particular, the use of a standard Reynolds-averaged Navier–Stokes eddy-viscosity Resolvent model, with a single coefficient, provides substantial agreement between SPOD and Resolvent modes for three turbulent jets and across the most energetic wavenumbers and frequencies
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Optimal eddy viscosity for Resolvent-based models of coherent structures in turbulent jets
2021Co-Authors: Pickering Ethan, Rigas Georgios, Schmidt, Oliver T., Sipp Denis, Colonius TimAbstract:Response modes computed via linear Resolvent analysis of a turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in both wall-bounded and free shear flows. To make such Resolvent models predictive, the nonlinear forcing term must be closed. Strategies to do so include imposing self-consistent sets of triadic interactions, proposing various source models, or through turbulence modelling. For the latter, several investigators have proposed using the mean-field eddy viscosity acting linearly on the fluctuation field. In this study, a data-driven approach is taken to quantitatively improve linear Resolvent models by deducing an optimal eddy-viscosity field that maximizes the projection of the dominant Resolvent mode to the energy-optimal coherent structure educed using spectral proper orthogonal decomposition (SPOD) of data from high-fidelity simulations. We use large-eddy simulation databases for round isothermal jets at subsonic, transonic, and supersonic conditions and show that the optimal eddy viscosity substantially improves the alignment between Resolvent and SPOD modes, reaching over 90% alignment at those frequencies where the jet exhibits a low-rank response. We then consider a fixed model for the eddy viscosity and show that with the calibration of a single constant, the results are generally close to the optimal one. In particular, the use of a standard Reynolds-Averaged-Navier-Stokes (RANS) eddy-viscosity Resolvent model, with a single coefficient, provides substantial agreement between SPOD and Resolvent modes for three turbulent jets and across the most energetic wavenumbers and frequencies.Comment: 34 pages, 18 figures, under consideration for publication in the Journal of Fluid Mechanic
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Efficient global Resolvent analysis via the one-way Navier-Stokes equations. Part 1. Forced response
2021Co-Authors: Towne Aaron, Pickering Ethan, Rigas Georgios, Colonius TimAbstract:Resolvent analysis is a powerful tool for modeling and analyzing turbulent flows and in particular provides an approximation of coherent flow structures. Despite recent algorithmic advances, computing Resolvent modes for flows with more than one inhomogeneous spatial coordinate remains computationally expensive. In this two-part paper, we show how efficient and accurate approximations of Resolvent modes can be obtained using a well-posed spatial marching method for flows that contain a slowly varying direction. In this first part of the paper, we derive a well-posed and convergent one-way equation describing the downstream-traveling waves supported by the linearized Navier-Stokes equations. Integrating these equations, which requires significantly less CPU and memory resources than a direct solution of the linearized Navier-Stokes equations, approximates the action of the Resolvent operator on a forcing vector. This capability is leveraged in part 2 of the paper to compute approximate Resolvent modes. The method is validated and demonstrated using the examples of a simple acoustics problem and a supersonic turbulent jet
Sipp Denis - One of the best experts on this subject based on the ideXlab platform.
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Optimal eddy viscosity for Resolvent-based models of coherent structures in turbulent jets
'Cambridge University Press (CUP)', 2021Co-Authors: Pickering Ethan, Rigas Georgios, Schmidt, Oliver T., Sipp Denis, Colonius TimAbstract:Response modes computed via linear Resolvent analysis of a turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in both wall-bounded and free shear flows. To make such Resolvent models predictive, the nonlinear forcing term must be closed. Strategies to do so include imposing self-consistent sets of triadic interactions, proposing various source models or through turbulence modelling. For the latter, several investigators have proposed using the mean-field eddy viscosity acting linearly on the fluctuation field. In this study, a data-driven approach is taken to quantitatively improve linear Resolvent models by deducing an optimal eddy-viscosity field that maximizes the projection of the dominant Resolvent mode to the energy-optimal coherent structure educed using spectral proper orthogonal decomposition (SPOD) of data from high-fidelity simulations. We use large-eddy simulation databases for round isothermal jets at subsonic, transonic and supersonic conditions and show that the optimal eddy viscosity substantially improves the agreement between Resolvent and SPOD modes, reaching over 90 % agreement at those frequencies where the jet exhibits a low-rank response. We then consider a fixed model for the eddy viscosity and show that with the calibration of a single constant, the results are generally close to the optimal one. In particular, the use of a standard Reynolds-averaged Navier–Stokes eddy-viscosity Resolvent model, with a single coefficient, provides substantial agreement between SPOD and Resolvent modes for three turbulent jets and across the most energetic wavenumbers and frequencies
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Optimal eddy viscosity for Resolvent-based models of coherent structures in turbulent jets
2021Co-Authors: Pickering Ethan, Rigas Georgios, Schmidt, Oliver T., Sipp Denis, Colonius TimAbstract:Response modes computed via linear Resolvent analysis of a turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in both wall-bounded and free shear flows. To make such Resolvent models predictive, the nonlinear forcing term must be closed. Strategies to do so include imposing self-consistent sets of triadic interactions, proposing various source models, or through turbulence modelling. For the latter, several investigators have proposed using the mean-field eddy viscosity acting linearly on the fluctuation field. In this study, a data-driven approach is taken to quantitatively improve linear Resolvent models by deducing an optimal eddy-viscosity field that maximizes the projection of the dominant Resolvent mode to the energy-optimal coherent structure educed using spectral proper orthogonal decomposition (SPOD) of data from high-fidelity simulations. We use large-eddy simulation databases for round isothermal jets at subsonic, transonic, and supersonic conditions and show that the optimal eddy viscosity substantially improves the alignment between Resolvent and SPOD modes, reaching over 90% alignment at those frequencies where the jet exhibits a low-rank response. We then consider a fixed model for the eddy viscosity and show that with the calibration of a single constant, the results are generally close to the optimal one. In particular, the use of a standard Reynolds-Averaged-Navier-Stokes (RANS) eddy-viscosity Resolvent model, with a single coefficient, provides substantial agreement between SPOD and Resolvent modes for three turbulent jets and across the most energetic wavenumbers and frequencies.Comment: 34 pages, 18 figures, under consideration for publication in the Journal of Fluid Mechanic
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Mean and Unsteady Flow Reconstruction Using Data-Assimilation and Resolvent Analysis
'American Institute of Aeronautics and Astronautics (AIAA)', 2020Co-Authors: Symon Sean, Sipp Denis, Schmid, Peter J., Mckeon, Beverley J.Abstract:A methodology is presented that exploits both data-assimilation techniques and Resolvent analysis for reconstructing turbulent flows, containing organized structures, with an efficient set of measurements. The mean (time-averaged) flow is obtained using variational data-assimilation that minimizes the discrepancy between a limited set of flow measurements, generally from an experiment, and a numerical simulation of the Navier–Stokes equations. The fluctuations are educed from Resolvent analysis and time-resolved data at a single point in the flow. Resolvent analysis also guides where measurements of the mean and fluctuating quantities are needed for efficient reconstruction of a simple example case study: flow around a circular cylinder at a Reynolds number of Re=100. For this flow, Resolvent analysis reveals that the leading singular value, most amplified modes, and the mean profile for 47
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Optimal eddy viscosity for Resolvent-based models of coherent structures in turbulent jets
2020Co-Authors: Pickering Ethan, Rigas Georgios, Schmidt, Oliver T., Sipp Denis, Colonius TimAbstract:Response modes computed via linear Resolvent analysis of the turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in both wall-bounded and free shear flows. To make such models predictive, the nonlinear forcing term must be closed either by including a self-consistent set of triadic interactions or through turbulence modeling. For the latter, several investigators have proposed using the mean-field eddy viscosity acting linearly on the fluctuation field. In this study, a data-driven approach is taken to quantitatively improve linear Resolvent models by deducing an optimal eddy-viscosity field that maximizes the projection of the dominant Resolvent mode to the energy-optimal coherent structure educed using spectral proper orthogonal decomposition (SPOD) of data from high-fidelity simulations. We use large-eddy simulation databases for round isothermal jets at subsonic, transonic, and supersonic conditions and show that the optimal eddy viscosity substantially improves the alignment between Resolvent and SPOD modes, reaching over 90% alignment at those frequencies where the jet exhibits a low-rank response. We then consider a fixed model for the eddy viscosity and show that with the calibration of a single constant, the results are generally close to the optimal one. In particular, the use of a standard Reynolds-Averaged-Navier-Stokes (RANS) eddy-viscosity Resolvent model, with a single scaling coefficient, provides substantial agreement between SPOD and Resolvent modes for three turbulent jets and across the most energetic wavenumbers and frequencies
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Optimal eddy viscosity for Resolvent-based models of coherent structures in turbulent jets
2020Co-Authors: Pickering Ethan, Rigas Georgios, Schmidt, Oliver T., Sipp Denis, Colonius TimAbstract:Response modes computed via linear Resolvent analysis of the turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in both wall-bounded and free shear flows. To make such models predictive, the nonlinear forcing term must be closed either by including a self-consistent set of triadic interactions or through turbulence modeling. For the latter, several investigators have proposed using the mean-field eddy viscosity acting linearly on the fluctuation field. In this study, a data-driven approach is taken to quantitatively improve linear Resolvent models by deducing an optimal eddy-viscosity field that maximizes the projection of the dominant Resolvent mode to the energy-optimal coherent structure educed using spectral proper orthogonal decomposition (SPOD) of data from high-fidelity simulations. We use large-eddy simulation databases for round isothermal jets at subsonic, transonic, and supersonic conditions and show that the optimal eddy viscosity substantially improves the alignment between Resolvent and SPOD modes, reaching over 90% alignment at those frequencies where the jet exhibits a low-rank response. We then consider a fixed model for the eddy viscosity and show that with the calibration of a single constant, the results are generally close to the optimal one. In particular, the use of a standard Reynolds-Averaged-Navier-Stokes (RANS) eddy-viscosity Resolvent model, with a single scaling coefficient, provides substantial agreement between SPOD and Resolvent modes for three turbulent jets and across the most energetic wavenumbers and frequencies.Comment: 30 pages, 17 figure, under consideration for publication in the Journal of Fluid Mechanic
