Informed by large-eddy simulation (LES) data and resolvent analysis of the mean flow, we examine ... more Informed by large-eddy simulation (LES) data and resolvent analysis of the mean flow, we examine the structure of turbulence in jets in the subsonic, transonic and supersonic regimes. Spectral (frequency-space) proper orthogonal decomposition is used to extract energy spectra and decompose the flow into energy-ranked coherent structures. The educed structures are generally well predicted by the resolvent analysis. Over a range of low frequencies and the first few azimuthal mode numbers, these jets exhibit a low-rank response characterized by Kelvin-Helmholtz (KH) type wavepackets associated with the annular shear layer up to the end of the potential core and that are excited by forcing in the very-near-nozzle shear layer. These modes too have been experimentally observed before and predicted by quasi-parallel stability theory and other approximations-they comprise a considerable portion of the total turbulent energy. At still lower frequencies, particularly for the axisymmetric mode, and again at high frequencies for all azimuthal wavenumbers, the response is not low-rank, but consists of a family of similarly amplified modes. These modes, which are primarily active downstream of the potential core, are associated with the Orr mechanism. They occur also as subdominant modes in the range of frequencies dominated by the KH response. Our global analysis helps tie together previous observations based on local spatial stability theory, and explains why quasi-parallel predictions were successful at some frequencies and azimuthal wavenumbers, but failed at others.
In this article, we report the results of an experimental sensitivity analysis on a vertical elec... more In this article, we report the results of an experimental sensitivity analysis on a vertical electrically heated Rijke tube. We examine the stability characteristics of the system due to the introduction of a secondary heat source. The experimental sensitivity analysis is quantified by measuring the shift in linear growth and decay rate as well as the shift in the linear frequency during periods of growth and decay of thermoacoustic oscillations. Linear growth and decay rate measurements agree qualitatively well with the theoretical predictions from adjoint-based methods. A discrepancy in the linear frequency measurements highlight deficiencies in the model used for those predictions and shows that the experimental measurement of sensitivities is a stringent test of any thermoacoustic model. The findings suggest that adjoint-based methods are, in principle, capable of providing industry with a cheap and efficient tool for developing optimal control strategies for more complex thermoacoustic systems.
The dynamics of a three-dimensional axisymmetric bluff-body wake are examined at low Reynolds reg... more The dynamics of a three-dimensional axisymmetric bluff-body wake are examined at low Reynolds regimes where transitions take place through spatio-temporal symmetry breaking. A linear stability analysis is employed to identify the critical Reynolds number associated with symmetry breaking, and the associated eigenmodes, known as global modes. The analysis shows that the axisymmetric stable base flow breaks the rotational symmetry through a pitchfork m = 1 bifurcation, in agreement with previously reported results for axisymmetric wakes. Above this threshold, the stable base flow is steady and three-dimensional with planar symmetry. A three-dimensional global stability analysis around the steady reflectionally symmetric base flow, assuming no homogeneous directions , predicts accurately the Hopf bifurcation threshold, which leads to asymmetric vortex shedding. DNS simulations validate the stability results and characterize the flow topology during the early chaotic regime.
In this study we present a theoretical weakly nonlinear framework for the prediction of thermoaco... more In this study we present a theoretical weakly nonlinear framework for the prediction of thermoacoustic oscillations close to Hopf bifurcations. We demonstrate the method for a thermoacoustic network that describes the dynamics of an electrically heated Rijke tube. We solve the weakly nonlinear equations order by order, discuss their contribution on the overall dynamics and show how solvability conditions at odd orders give rise to Stuart–Landau equations. These equations, combined together, describe the nonlinear dynamical evolution of the oscillations' amplitude and their frequency. Because we retain the contribution of several acoustic modes in the thermoacoustic system, the use of adjoint methods is required to derive the Landau coefficients. The analysis is performed up to fifth order and compared with time domain simulations, showing good agreement. The theoretical framework presented here can be used to reduce the cost of investigating oscillations and subcritical phenomena close to Hopf bifurcations in numerical simulations and experiments and can be readily extended to consider, e.g. the weakly nonlinear interaction of two unstable thermoacoustic modes.
Adjoint-based sensitivity analysis methods are powerful tools for engineers who use flow simulati... more Adjoint-based sensitivity analysis methods are powerful tools for engineers who use flow simulations for design. However, the conventional adjoint method breaks down for scale-resolving simulations like large-eddy simulation (LES) or direct numerical simulation (DNS), which exhibit the chaotic dynamics inherent in turbulent flows. Sensitivity analysis based on least-squares shadowing (LSS) avoids the issues encountered by conventional methods, but has a high computational cost. The following report outlines a new, more computationally efficient formulation of LSS, non-intrusive LSS, and estimates its cost for several canonical flows using Lyapunov analysis.
A specific feature of three-dimensional bluff body wakes, flow bistability, is a subject of parti... more A specific feature of three-dimensional bluff body wakes, flow bistability, is a subject of particular recent interest. This feature consists of a random flipping of the wake between two asymmetric configurations and is believed to contribute to the pressure drag of many bluff bodies. In this study we apply the modelling approach recently suggested for axisymmetric bodies by Rigas et al. (J. Fluid Mech., vol. 778, 2015, R2) to the reflectional symmetry-breaking modes of a rectilinear bluff body wake. We demonstrate the validity of the model and its Reynolds number independence through time-resolved base pressure measurements of the natural wake. Further, oscillating flaps are used to investigate the dynamics and time scales of the instability associated with the flipping process, demonstrating that they are largely independent of Reynolds number. The modelling approach is then used to design a feedback controller that uses the flaps to suppress the symmetry-breaking modes. The controller is successful, leading to a suppression of the bistability of the wake, with concomitant reductions in both lateral and streamwise forces. Importantly, the controller is found to be efficient, the actuator requiring only 24 % of the aerodynamic power saving. The controller therefore provides a key demonstration of efficient feedback control used to reduce the drag of a high-Reynolds-number three-dimensional bluff body. Furthermore, the results suggest that suppression of large-scale structures is a fundamentally efficient approach for bluff body drag reduction.
A high-frequency periodic jet, issuing immediately below the point of separation, is used to forc... more A high-frequency periodic jet, issuing immediately below the point of separation, is used to force the turbulent wake of a bluff axisymmetric body, its axis aligned with the free stream. It is shown that the base pressure may be varied more or less at will: at forcing frequencies several times that of the shear layer frequency, the time-averaged area-weighted base pressure increases by as much as 35 %. An investigation of the effects of forcing is made using random and phase-locked two-component particle image velocimetry (PIV), and modal decomposition of pressure fluctuations on the base of the model. The forcing does not target specific local or global wake instabilities: rather, the high-frequency jet creates a row of closely spaced vortex rings, immediately adjacent to which are regions of large shear on each side. These shear layers are associated with large dissipation and inhibit the entrainment of fluid. The resulting pressure recovery is proportional to the strength of the vortices and is accompanied by a broadband suppression of base pressure fluctuations associated with all modes. The optimum forcing frequency, at which amplification of the shear layer mode approaches unity gain, is roughly five times the shear layer frequency.
Informed by large-eddy simulation (LES) data and resolvent analysis of the mean flow, we examine ... more Informed by large-eddy simulation (LES) data and resolvent analysis of the mean flow, we examine the structure of turbulence in jets in the subsonic, transonic and supersonic regimes. Spectral (frequency-space) proper orthogonal decomposition is used to extract energy spectra and decompose the flow into energy-ranked coherent structures. The educed structures are generally well predicted by the resolvent analysis. Over a range of low frequencies and the first few azimuthal mode numbers, these jets exhibit a low-rank response characterized by Kelvin-Helmholtz (KH) type wavepackets associated with the annular shear layer up to the end of the potential core and that are excited by forcing in the very-near-nozzle shear layer. These modes too have been experimentally observed before and predicted by quasi-parallel stability theory and other approximations-they comprise a considerable portion of the total turbulent energy. At still lower frequencies, particularly for the axisymmetric mode, and again at high frequencies for all azimuthal wavenumbers, the response is not low-rank, but consists of a family of similarly amplified modes. These modes, which are primarily active downstream of the potential core, are associated with the Orr mechanism. They occur also as subdominant modes in the range of frequencies dominated by the KH response. Our global analysis helps tie together previous observations based on local spatial stability theory, and explains why quasi-parallel predictions were successful at some frequencies and azimuthal wavenumbers, but failed at others.
In this article, we report the results of an experimental sensitivity analysis on a vertical elec... more In this article, we report the results of an experimental sensitivity analysis on a vertical electrically heated Rijke tube. We examine the stability characteristics of the system due to the introduction of a secondary heat source. The experimental sensitivity analysis is quantified by measuring the shift in linear growth and decay rate as well as the shift in the linear frequency during periods of growth and decay of thermoacoustic oscillations. Linear growth and decay rate measurements agree qualitatively well with the theoretical predictions from adjoint-based methods. A discrepancy in the linear frequency measurements highlight deficiencies in the model used for those predictions and shows that the experimental measurement of sensitivities is a stringent test of any thermoacoustic model. The findings suggest that adjoint-based methods are, in principle, capable of providing industry with a cheap and efficient tool for developing optimal control strategies for more complex thermoacoustic systems.
The dynamics of a three-dimensional axisymmetric bluff-body wake are examined at low Reynolds reg... more The dynamics of a three-dimensional axisymmetric bluff-body wake are examined at low Reynolds regimes where transitions take place through spatio-temporal symmetry breaking. A linear stability analysis is employed to identify the critical Reynolds number associated with symmetry breaking, and the associated eigenmodes, known as global modes. The analysis shows that the axisymmetric stable base flow breaks the rotational symmetry through a pitchfork m = 1 bifurcation, in agreement with previously reported results for axisymmetric wakes. Above this threshold, the stable base flow is steady and three-dimensional with planar symmetry. A three-dimensional global stability analysis around the steady reflectionally symmetric base flow, assuming no homogeneous directions , predicts accurately the Hopf bifurcation threshold, which leads to asymmetric vortex shedding. DNS simulations validate the stability results and characterize the flow topology during the early chaotic regime.
In this study we present a theoretical weakly nonlinear framework for the prediction of thermoaco... more In this study we present a theoretical weakly nonlinear framework for the prediction of thermoacoustic oscillations close to Hopf bifurcations. We demonstrate the method for a thermoacoustic network that describes the dynamics of an electrically heated Rijke tube. We solve the weakly nonlinear equations order by order, discuss their contribution on the overall dynamics and show how solvability conditions at odd orders give rise to Stuart–Landau equations. These equations, combined together, describe the nonlinear dynamical evolution of the oscillations' amplitude and their frequency. Because we retain the contribution of several acoustic modes in the thermoacoustic system, the use of adjoint methods is required to derive the Landau coefficients. The analysis is performed up to fifth order and compared with time domain simulations, showing good agreement. The theoretical framework presented here can be used to reduce the cost of investigating oscillations and subcritical phenomena close to Hopf bifurcations in numerical simulations and experiments and can be readily extended to consider, e.g. the weakly nonlinear interaction of two unstable thermoacoustic modes.
Adjoint-based sensitivity analysis methods are powerful tools for engineers who use flow simulati... more Adjoint-based sensitivity analysis methods are powerful tools for engineers who use flow simulations for design. However, the conventional adjoint method breaks down for scale-resolving simulations like large-eddy simulation (LES) or direct numerical simulation (DNS), which exhibit the chaotic dynamics inherent in turbulent flows. Sensitivity analysis based on least-squares shadowing (LSS) avoids the issues encountered by conventional methods, but has a high computational cost. The following report outlines a new, more computationally efficient formulation of LSS, non-intrusive LSS, and estimates its cost for several canonical flows using Lyapunov analysis.
A specific feature of three-dimensional bluff body wakes, flow bistability, is a subject of parti... more A specific feature of three-dimensional bluff body wakes, flow bistability, is a subject of particular recent interest. This feature consists of a random flipping of the wake between two asymmetric configurations and is believed to contribute to the pressure drag of many bluff bodies. In this study we apply the modelling approach recently suggested for axisymmetric bodies by Rigas et al. (J. Fluid Mech., vol. 778, 2015, R2) to the reflectional symmetry-breaking modes of a rectilinear bluff body wake. We demonstrate the validity of the model and its Reynolds number independence through time-resolved base pressure measurements of the natural wake. Further, oscillating flaps are used to investigate the dynamics and time scales of the instability associated with the flipping process, demonstrating that they are largely independent of Reynolds number. The modelling approach is then used to design a feedback controller that uses the flaps to suppress the symmetry-breaking modes. The controller is successful, leading to a suppression of the bistability of the wake, with concomitant reductions in both lateral and streamwise forces. Importantly, the controller is found to be efficient, the actuator requiring only 24 % of the aerodynamic power saving. The controller therefore provides a key demonstration of efficient feedback control used to reduce the drag of a high-Reynolds-number three-dimensional bluff body. Furthermore, the results suggest that suppression of large-scale structures is a fundamentally efficient approach for bluff body drag reduction.
A high-frequency periodic jet, issuing immediately below the point of separation, is used to forc... more A high-frequency periodic jet, issuing immediately below the point of separation, is used to force the turbulent wake of a bluff axisymmetric body, its axis aligned with the free stream. It is shown that the base pressure may be varied more or less at will: at forcing frequencies several times that of the shear layer frequency, the time-averaged area-weighted base pressure increases by as much as 35 %. An investigation of the effects of forcing is made using random and phase-locked two-component particle image velocimetry (PIV), and modal decomposition of pressure fluctuations on the base of the model. The forcing does not target specific local or global wake instabilities: rather, the high-frequency jet creates a row of closely spaced vortex rings, immediately adjacent to which are regions of large shear on each side. These shear layers are associated with large dissipation and inhibit the entrainment of fluid. The resulting pressure recovery is proportional to the strength of the vortices and is accompanied by a broadband suppression of base pressure fluctuations associated with all modes. The optimum forcing frequency, at which amplification of the shear layer mode approaches unity gain, is roughly five times the shear layer frequency.
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Papers by Georgios Rigas