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http://hdl.handle.net/10985/17783
Closed-loop control of a free shear flow: a framework using the parabolized stability equations
SASAKI, Kenzo; TISSOT, Gilles; CAVALIERI, André V. G.; SILVESTRE, Flávio J.; JORDAN, Peter; BIAU, Damien
In this study the parabolized stability equations (PSE) are used to build reduced-order-models (ROMs) given in terms of frequency and time-domain transfer functions (TFs) for application in closed-loop control. The control law is defined in two steps; first it is necessary to estimate the open-loop behaviour of the system from measurements, and subsequently the response of the flow to an actuation signal is determined. The theoretically derived PSE TFs are used to account for both of these effects. Besides its capability to derive simplified models of the flow dynamics, we explore the use of the TFs to provide an a priori determination of adequate positions for efficiently forcing along the direction transverse to the mean flow. The PSE TFs are also used to account for the relative position between sensors and actuators which defines two schemes, feedback and feedforward, the former presenting a lower effectiveness. Differences are understood in terms of the evaluation of the causality of the resulting gain, which is made without the need to perform computationally demanding simulations for each configuration. The ROMs are applied to a direct numerical simulation of a convectively unstable 2D mixing layer. The derived feedforward control law is shown to lead to a reduction in the mean square values of the objective fluctuation of more than one order of magnitude, at the output position, in the nonlinear simulation, which is accompanied by a significant delay in the vortex pairing and roll-up. A study of the robustness of the control law demonstrates that it is fairly insensitive to the amplitude of inflow perturbations and model uncertainties given in terms of Reynolds number variations.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/177832018-01-01T00:00:00ZSASAKI, KenzoTISSOT, GillesCAVALIERI, André V. G.SILVESTRE, Flávio J.JORDAN, PeterBIAU, DamienIn this study the parabolized stability equations (PSE) are used to build reduced-order-models (ROMs) given in terms of frequency and time-domain transfer functions (TFs) for application in closed-loop control. The control law is defined in two steps; first it is necessary to estimate the open-loop behaviour of the system from measurements, and subsequently the response of the flow to an actuation signal is determined. The theoretically derived PSE TFs are used to account for both of these effects. Besides its capability to derive simplified models of the flow dynamics, we explore the use of the TFs to provide an a priori determination of adequate positions for efficiently forcing along the direction transverse to the mean flow. The PSE TFs are also used to account for the relative position between sensors and actuators which defines two schemes, feedback and feedforward, the former presenting a lower effectiveness. Differences are understood in terms of the evaluation of the causality of the resulting gain, which is made without the need to perform computationally demanding simulations for each configuration. The ROMs are applied to a direct numerical simulation of a convectively unstable 2D mixing layer. The derived feedforward control law is shown to lead to a reduction in the mean square values of the objective fluctuation of more than one order of magnitude, at the output position, in the nonlinear simulation, which is accompanied by a significant delay in the vortex pairing and roll-up. A study of the robustness of the control law demonstrates that it is fairly insensitive to the amplitude of inflow perturbations and model uncertainties given in terms of Reynolds number variations.Restricted nonlinear model for high- and low-drag events in plane channel flow
http://hdl.handle.net/10985/18049
Restricted nonlinear model for high- and low-drag events in plane channel flow
ALIZARD, Frédéric; BIAU, Damien
A restricted nonlinear (RNL) model, obtained by partitioning the state variables into streamwise-averaged quantities and superimposed perturbations, is used in order to track the exact coherent state in plane channel flow investigated by Toh & Itano (J. Fluid Mech., vol. 481, 2003, pp. 67–76). When restricting nonlinearities to quadratic interaction of the fluctuating part into the streamwise-averaged component, it is shown that the coherent structure and its dynamics closely match results from direct numerical simulation (DNS), even if only a single streamwise Fourier mode is retained. In particular, both solutions exhibit long quiescent phases, spanwise shifts and bursting events. It is also shown that the dynamical trajectory passes close to equilibria that exhibit either low- or high-drag states. When statistics are collected at times where the friction velocity peaks, the mean flow and root-mean-square profiles show the essential features of wall turbulence obtained by DNS for the same friction Reynolds number. For low-drag events, the mean flow profiles are related to a universal asymptotic state called maximum drag reduction (Xi & Graham, Phys. Rev. Lett., vol. 108, 2012, 028301). Hence, the intermittent nature of self-sustaining processes in the buffer layer is contained in the dynamics of the RNL model, organized in two exact coherent states plus an asymptotic turbulent-like attractor. We also address how closely turbulent dynamics approaches these equilibria by exploiting a DNS database associated with a larger domain.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/180492019-01-01T00:00:00ZALIZARD, FrédéricBIAU, DamienA restricted nonlinear (RNL) model, obtained by partitioning the state variables into streamwise-averaged quantities and superimposed perturbations, is used in order to track the exact coherent state in plane channel flow investigated by Toh & Itano (J. Fluid Mech., vol. 481, 2003, pp. 67–76). When restricting nonlinearities to quadratic interaction of the fluctuating part into the streamwise-averaged component, it is shown that the coherent structure and its dynamics closely match results from direct numerical simulation (DNS), even if only a single streamwise Fourier mode is retained. In particular, both solutions exhibit long quiescent phases, spanwise shifts and bursting events. It is also shown that the dynamical trajectory passes close to equilibria that exhibit either low- or high-drag states. When statistics are collected at times where the friction velocity peaks, the mean flow and root-mean-square profiles show the essential features of wall turbulence obtained by DNS for the same friction Reynolds number. For low-drag events, the mean flow profiles are related to a universal asymptotic state called maximum drag reduction (Xi & Graham, Phys. Rev. Lett., vol. 108, 2012, 028301). Hence, the intermittent nature of self-sustaining processes in the buffer layer is contained in the dynamics of the RNL model, organized in two exact coherent states plus an asymptotic turbulent-like attractor. We also address how closely turbulent dynamics approaches these equilibria by exploiting a DNS database associated with a larger domain.A framework for closed-loop flow control using the parabolized stability equations
http://hdl.handle.net/10985/17797
A framework for closed-loop flow control using the parabolized stability equations
SASAKI, Kenzo; CAVALIERI, André V. G.; SILVESTRE, Flávio J.; JORDAN, Peter; TISSOT, Gilles; BIAU, Damien
We develop a reduced-order-model framework using the parabolized stability equations and identification techniques for the closed-loop control of unsteady fluctuations along fluidic systems. These models had been successfully applied to a turbulent jet as estimation techniques and to an incompressible shear-layer for the development of closed-loop control laws. Through this paper, we propose a further investigation of the PSE-based transfer functions, exploring its flexibility to educe different control schemes and to determine the most effective sensor/actuator positions. Emphasis is be given to the feedforward and feedback configurations for flow control, and differences are understood in terms of causality. A study of the robustness to uncertainties in Reynolds and mean flow velocity, along with external perturbations is also presented. These topics allow deeper insight into the active closed-loop flow control problem and therefore may lead to more effective schemes, particularly on what concerns the experimental implementation of closed-loop control.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/177972017-01-01T00:00:00ZSASAKI, KenzoCAVALIERI, André V. G.SILVESTRE, Flávio J.JORDAN, PeterTISSOT, GillesBIAU, DamienWe develop a reduced-order-model framework using the parabolized stability equations and identification techniques for the closed-loop control of unsteady fluctuations along fluidic systems. These models had been successfully applied to a turbulent jet as estimation techniques and to an incompressible shear-layer for the development of closed-loop control laws. Through this paper, we propose a further investigation of the PSE-based transfer functions, exploring its flexibility to educe different control schemes and to determine the most effective sensor/actuator positions. Emphasis is be given to the feedforward and feedback configurations for flow control, and differences are understood in terms of causality. A study of the robustness to uncertainties in Reynolds and mean flow velocity, along with external perturbations is also presented. These topics allow deeper insight into the active closed-loop flow control problem and therefore may lead to more effective schemes, particularly on what concerns the experimental implementation of closed-loop control.Closed-loop control of wavepackets in a free shear-flow
http://hdl.handle.net/10985/17802
Closed-loop control of wavepackets in a free shear-flow
SASAKI, Kenzo; TISSOT, Gilles; CAVALIERI, André V. G.; SILVESTRE, Flávio J.; JORDAN, Peter; BIAU, Damien
This study aims at the attenuation of the unsteady fluctuations along a two-dimensional mixing layer which may be considered as a prototypical problem for the evaluation of es- timation and control techniques, and also a canonical problem, when compressibility is considered, for sound radiation by low-Reynolds-number free shear flows. Two strategies are proposed for the estimation of the time evolution of wavepackets based on upstream data of the simulation: a Parabolised-stability-equation (PSE) based transfer function be- tween two positions and an empirical-transfer-function identification technique, which relies on the theoretical background established by the PSE. Both techniques present a similar performance for prediction of the fluctuations between streamwise-separated input and output positions. Furthermore, the identification method is used to determine the response of the flow to a body force actuation which allows for the elaboration of a Feedforward control framework for the fluctuations via a phase-opposition actuation. This strategy, which is evaluated with three different control laws, presents encouraging results both for the linearized system (i.e. described in terms of transfer functions) and for the non-linear, direct numerical simulation of the mixing layer, in which significant delays of vortex pairing are observed. The established framework is thus seen as a promising technique for real-time flow control aiming at the attenuation of wavepackets, and the corresponding reduction of the radiated sound.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/178022016-01-01T00:00:00ZSASAKI, KenzoTISSOT, GillesCAVALIERI, André V. G.SILVESTRE, Flávio J.JORDAN, PeterBIAU, DamienThis study aims at the attenuation of the unsteady fluctuations along a two-dimensional mixing layer which may be considered as a prototypical problem for the evaluation of es- timation and control techniques, and also a canonical problem, when compressibility is considered, for sound radiation by low-Reynolds-number free shear flows. Two strategies are proposed for the estimation of the time evolution of wavepackets based on upstream data of the simulation: a Parabolised-stability-equation (PSE) based transfer function be- tween two positions and an empirical-transfer-function identification technique, which relies on the theoretical background established by the PSE. Both techniques present a similar performance for prediction of the fluctuations between streamwise-separated input and output positions. Furthermore, the identification method is used to determine the response of the flow to a body force actuation which allows for the elaboration of a Feedforward control framework for the fluctuations via a phase-opposition actuation. This strategy, which is evaluated with three different control laws, presents encouraging results both for the linearized system (i.e. described in terms of transfer functions) and for the non-linear, direct numerical simulation of the mixing layer, in which significant delays of vortex pairing are observed. The established framework is thus seen as a promising technique for real-time flow control aiming at the attenuation of wavepackets, and the corresponding reduction of the radiated sound.The first-digit frequencies in data of turbulent flows
http://hdl.handle.net/10985/9977
The first-digit frequencies in data of turbulent flows
BIAU, Damien
Considering the first significant digits (noted image) in data sets of dissipation for turbulent flows, the probability to find a given number (image or 2 or …9) would be 1/9 for a uniform distribution. Instead the probability closely follows Newcomb–Benford’s law, namely image. The discrepancies between Newcomb–Benford’s law and first-digits frequencies in turbulent data are analysed through Shannon’s entropy. The data sets are obtained with direct numerical simulations for two types of fluid flow: an isotropic case initialized with a Taylor–Green vortex and a channel flow. Results are in agreement with Newcomb–Benford’s law in nearly homogeneous cases and the discrepancies are related to intermittent events. Thus the scale invariance for the first significant digits, which supports Newcomb–Benford’s law, seems to be related to an equilibrium turbulent state, namely with a significant inertial range. A matlab/octave program provided in appendix is such that part of the presented results can easily be replicated.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/99772015-01-01T00:00:00ZBIAU, DamienConsidering the first significant digits (noted image) in data sets of dissipation for turbulent flows, the probability to find a given number (image or 2 or …9) would be 1/9 for a uniform distribution. Instead the probability closely follows Newcomb–Benford’s law, namely image. The discrepancies between Newcomb–Benford’s law and first-digits frequencies in turbulent data are analysed through Shannon’s entropy. The data sets are obtained with direct numerical simulations for two types of fluid flow: an isotropic case initialized with a Taylor–Green vortex and a channel flow. Results are in agreement with Newcomb–Benford’s law in nearly homogeneous cases and the discrepancies are related to intermittent events. Thus the scale invariance for the first significant digits, which supports Newcomb–Benford’s law, seems to be related to an equilibrium turbulent state, namely with a significant inertial range. A matlab/octave program provided in appendix is such that part of the presented results can easily be replicated.Transient growth of perturbations in Stokes oscillatory flows
http://hdl.handle.net/10985/11246
Transient growth of perturbations in Stokes oscillatory flows
BIAU, Damien
Oscillatory Stokes flows, with zero mean, are subjected to subcritical transition to turbulence. The maximal energy growth of perturbations is computed in the subcritical regime through an optimisation method. The results show strong amplifications during half a period. The energy transfer from the base flow involves an Orr mechanism with two-dimensional vorticity waves, and the maximum energy scales exponentially with the Reynolds number. Nonlinear simulations show that low-energy perturbations are sufficient to trigger turbulent flow.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/112462016-01-01T00:00:00ZBIAU, DamienOscillatory Stokes flows, with zero mean, are subjected to subcritical transition to turbulence. The maximal energy growth of perturbations is computed in the subcritical regime through an optimisation method. The results show strong amplifications during half a period. The energy transfer from the base flow involves an Orr mechanism with two-dimensional vorticity waves, and the maximum energy scales exponentially with the Reynolds number. Nonlinear simulations show that low-energy perturbations are sufficient to trigger turbulent flow.