is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. This is an author-deposited version published in: https://sam.ensam.eu Handle IDAbstract 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 Communicated by 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. IntroductionThe manipulation of flow dynamics through active or passive control strategies represents a challenge with several industrial and technological applications. Reduction in drag and consequently of fuel consumption, delay in the transition to turbulence of laminar flows, and reduction in noise levels are but a few of the foreseeable applications of flow control [29]. Over the last years, passive and active flow manipulation has been accomplished. Passive control has been achieved, for boundary layers, via the introduction of roughness elements, as in the work of [49] or by means of chevrons in turbulent jets which attenuate large scale structures [8,31]. For the active, open-loop case, Biringen [7] used suction and blowing in order to obtain the delay in transition in a channel flow. Koenig et al. [30] and Le Rallic et al. [32] use the continuous injection of air in the core of a turbulent jet in order to diminish the radiated acoustic emission. Active closed-loop control is also possible, as the initial stages of the transition of laminar shear flows is a linear pro...
In this work we perform reactive control of stochastic disturbances in forced turbulent jets based on destructive interference. The study is motivated by the success of recent studies in applying this type of control on instability waves in transitional boundary layers and free-shear flows. Linear convective mechanisms in the initial region of turbulent jets are explored in order to perform reactive control, wherein the actuation signal is updated in real time based on sensor measurements performed upstream, resulting in an inverse feedforward approach. The control law is based on empirical transfer functions of the jet response to stochastic forcing and actuation, which are measured experimentally. Since turbulent jets have energy content spread in a number of azimuthal wavenumbers, we apply axisymmetric forcing at the nozzle lip in order to be able to perform control using a reduced number of sensors and actuators. The external forcing produces axisymmetric wavepackets which possess stochastic phases and amplitudes, akin to turbulent fluctuations found in unforced jets. We demonstrate the successful implementation of real-time reactive control of these disturbances, achieving order-of-magnitude attenuations of associated velocity fluctuations. Control is shown to reduce fluctuation levels over an extensive streamwise range.
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 estimation 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 between 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.
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