This work deals with the feedforward active control of Tollmien-Schlichting instability waves over incompressible 2D and 3D boundary layers. Through an extensive numerical study, two strategies are evaluated; the optimal linear-quadratic-Gaussian (LQG) controller, designed using the Eigensystem realization algorithm, is compared to a wave-cancellation scheme, which is obtained using the direct inversion of frequency-domain transfer functions of the system. For the evaluated cases, it is shown that LQG leads to a similar control law and presents a comparable performance to the simpler, wave-cancellation scheme, indicating that the former acts via a destructive interference of the incoming wavepacket downstream of actuation. The results allow further insight into the physics behind flow control of convectively unstable flows permitting, for instance, the optimization of the transverse position for actuation. Using concepts of linear stability theory and the derived transfer function, a more efficient actuation for flow control is chosen, leading to similar attenuation of Tollmien-Schlichting waves with only about 10% of the actuation power in the baseline case.

This work deals with the closed-loop control of streaky structures induced by free-stream turbulence (FST) in a zero-pressure gradient, transitional boundary layer, by means of localized sensors and actuators. A linear quadratic gaussian regulator is considered along with a system identification technique to build reduced-order models for control. Three actuators are developed with different spatial supports, corresponding to a baseline shape with only vertical forcing, and to two other shapes obtained by different optimization procedures. A computationally efficient method is derived to obtain an actuator which aims to induce the exact structures which are inside the boundary layer, given in terms of their first spectral proper orthogonal decomposition (SPOD) mode, and an actuator that maximizes the energy of induced downstream structures. Two free-stream turbulence levels were evaluated, corresponding to 3.0% and 3.5%, and closed-loop control is applied in large-eddy simulations of transitional boundary layers. All three actuators lead to significant delays in the transition to turbulence and were shown to be robust to mild variations in the free-stream turbulence levels. Differences are understood in terms of the SPOD of actuation and FST-induced fields along with the causality of the control scheme when a cancellation of disturbances is considered. The actuator optimized to generate the leading downstream SPOD mode, representing the streaks in the open-loop flow, leads to the highest transition delay, which can be understood due to its capability of closely cancelling structures in the boundary layer. However, it is shown that even with the actuator located downstream of the input measurement it may become impossible to cancel incoming disturbances in a causal way, depending on the wall-normal position of the output and on the actuator considered, which limits sensor and actuator placement capable of good closed-loop performance.

No abstract

The current work presents a realizable method to control streaky disturbances in boundary layer flows and delay transition to turbulence by means of active flow control. Numerical simulations of the nonlinear transitional regime in a Blasius boundary layer are performed where streaks are excited in the boundary layer by means of a high level of free-stream turbulence. The occurring disturbances are measured by means of localized wall-shear-stress sensors and damped out using near-wall actuators, which resemble ring plasma actuators. Each actuator is powered by a time-varying signal whose amplitude is computed by processing signals from the sensors. The processed signal is the result of two control laws: the Linear Quadratic Gaussian regulator (LQG) and the Inverse Feed-Forward Control technique (IFFC). The use of the first control method, LQG, requires a state-space representation of the system dynamics, so the flow is described by means of a linear time-invariant operator that captures only the most relevant information of the dynamics and results in a reduced order model (ROM). The ROM is computed by means of the eigensystem realization algorithm (ERA), which is based on the impulse responses of the real system. Collecting such impulse responses may be unfeasible when considering free-stream turbulence because of the high dimensionality of the input forcing needed for a precise description of such a phenomenon. Here, a new method to identify the relevant system dynamics and generate the needed impulse responses is proposed, based on additional shear-stress measurements in an upstream location. Transfer functions between such measurements and other downstream sensors are obtained and allow the derivation of the ERA system, in a data-driven approach that would be realizable in experiments. Finally, the effectiveness of the technique in delaying bypass transition is shown. The work (i) presents a systematic and straightforward way to deal with high dimensional disturbances in order to build ROMs for a feasible control technique, and (ii) shows that even when considering practical constraints such as the type and size of actuators and sensors, it is possible to achieve at least as large delay of bypass transition as that obtained in more idealized cases found in literature.

Three methods are considered for estimating the downstream evolution of wavepackets in turbulent jets based on upstream measurements. The parabolised stability equations are used to compute a transfer function between axially and radially separated points in the flow, and the performance of this theoretical model is compared with that of two empirical approaches, direct transfer function calculation and autoregressive moving-average exogenous system identification, both of which require unsteady experimental data. The three approaches, which perform equally well, prove suitable for estimation of the downstream evolution of wavepackets using pressure data measured in the near-nozzle region. Over distances of the order of a couple of jet diameters, correlations of up to 80 % are observed between estimation and measurement. The performance deteriorates as axial separation between input and output is increased. While the two empirical approaches are limited in terms of both the number of input–output pairs and the number of flow variables that can be reasonably considered, the parabolised stability equations-based approach has no such limitation and can be used to perform full-field estimates comprising all of the dependent variables; in this it constitutes a potentially formidable means by which to perform single-input–multiple-output estimation. It has the further advantage of not requiring unsteady data for its construction, the only necessary ingredients being the mean flow and the linearised equations of motion.

Wavepackets obtained as solutions of the flow equations linearised around the mean flow have been shown in recent work to yield good agreement, in terms of amplitude and phase, with those educed from turbulent jets. Compelling agreement has been demonstrated, for the axisymmetric and first helical mode, up to Strouhal numbers close to unity. We here extend the range of validity of wavepacket models to Strouhal number $St=4.0$ and azimuthal wavenumber $m=4$ by comparing solutions of the parabolised stability equations with a well-validated large-eddy simulation of a Mach 0.9 turbulent jet. The results show that the near-nozzle dynamics can be correctly described by the homogeneous linear model, the initial growth rates being accurately predicted for the entire range of frequencies and azimuthal wavenumbers considered. Similarly to the lower-frequency wavepackets reported prior to this work, the high-frequency linear waves deviate from the data downstream of their stabilisation locations, which move progressively upstream as the frequency increases.

Three methods are evaluated to estimate the streamwise velocity fluctuations of a zero-pressure-gradient turbulent boundary layer of momentum-thickness-based Reynolds number up to $Re_{\unicode[STIX]{x1D703}}\simeq 8200$, using as input velocity fluctuations at different wall-normal positions. A system identification approach is considered where large-eddy simulation data are used to build single and multiple-input linear and nonlinear transfer functions. Such transfer functions are then treated as convolution kernels and may be used as models for the prediction of the fluctuations. Good agreement between predicted and reference data is observed when the streamwise velocity in the near-wall region is estimated from fluctuations in the outer region. Both the unsteady behaviour of the fluctuations and the spectral content of the data are properly predicted. It is shown that approximately 45 % of the energy in the near-wall peak is linearly correlated with the outer-layer structures, for the reference case $Re_{\unicode[STIX]{x1D703}}=4430$. These identified transfer functions allow insight into the causality between the different wall-normal locations in a turbulent boundary layer along with an estimation of the tilting angle of the large-scale structures. Differences in accuracy of the methods (single- and multiple-input linear and nonlinear) are assessed by evaluating the coherence of the structures between wall-normally separated positions. It is shown that the large-scale fluctuations are coherent between the outer and inner layers, by means of an interactions which strengthens with increasing Reynolds number, whereas the finer-scale fluctuations are only coherent within the near-wall region. This enables the possibility of considering the wall-shear stress as an input measurement, which would more easily allow the implementation of these methods in experimental applications. A parametric study was also performed by evaluating the effect of the Reynolds number, wall-normal positions and input quantities considered in the model. Since the methods vary in terms of their complexity for implementation, computational expense and accuracy, the technique of choice will depend on the application under consideration. We also assessed the possibility of designing and testing the models at different Reynolds numbers, where it is shown that the prediction of the near-wall peak from wall-shear-stress measurements is practically unaffected even for a one order of magnitude change in the corresponding Reynolds number of the design and test, indicating that the interaction between the near-wall peak fluctuations and the wall is approximately Reynolds-number independent. Furthermore, given the performance of such methods in the prediction of flow features in turbulent boundary layers, they have a good potential for implementation in experiments and realistic flow control applications, where the prediction of the near-wall peak led to correlations above 0.80 when wall-shear stress was used in a multiple-input or nonlinear scheme. Errors of the order of 20 % were also observed in the determination of the near-wall spectral peak, depending on the employed method.

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...