A reactive control technique with localised actuators and sensors is used to delay the transition to turbulence in a flat-plate boundary-layer flow. Through extensive direct numerical simulations, it is shown that an adaptive technique, which computes the control law on-line, is able to significantly reduce skin-friction drag in the presence of random three-dimensional perturbation fields with linear and weakly nonlinear behaviour. An energy budget analysis is performed in order to assess the net energy saving capabilities of the linear control approach. When considering a model of the dielectric-barrier-discharge (DBD) plasma actuator, the energy spent to create appropriate actuation force inside the boundary layer is of the same order as the energy gained from reducing skin-friction drag. With a model of an ideal actuator a net energy gain of three orders of magnitude can be achieved by efficiently damping small-amplitude disturbances upstream. The energy analysis in this study thus provides an upper limit for what we can expect in terms of drag-reduction efficiency for linear control of transition as a means for drag reduction.

This manuscript demonstrates the first successful application of the delayed-x-LMS (dxLMS) control algorithm for TS-wave cancelation. Active wave cancelation of two-dimensional broadband Tollmien–Schlichting (TS) disturbances is performed with a single DBD plasma actuator. The experiments are conducted in flight on the pressure side of a laminar flow wing glove, mounted on a manned glider. The stability properties of the controller are investigated in detail with experimental flight data, DNS and stability analysis of the boundary layer. Finally, a model-free approach for dxLMS operation is introduced to operate the controller as a ‘black-box’ system, which automatically adjusts the controller settings based on a group speed measurement of the disturbance wave packets. The modified dxLMS controller is operated without a model and is able to adapt to varying conditions that may occur during flight in atmosphere.

Friction drag is reduced in a two-dimensional (2D) boundary-layer flow by delaying the laminar-to-turbulence transition. A localised forcing in the wall region is used to attenuate the growing 3D disturbances that eventually trigger the turbulent regime farther downstream. An adaptive filtered-X least-mean-squared (FXLMS) algorithm is used to process the information of the flow gathered from two rows of surface hot-wires sensors and compute the forcing, performed by a row of plasma actuators. LES simulations are used to evaluate and analyze the performance of the described control strategy: in particular, a study on the streamwise position of the sensor and an actual transition delay scenario are presented.

In boundary layer flows, one may reduce skin friction drag by delaying the onset of laminar-to-turbulent transition via the attenuation of small-amplitude Tollmien Schlichting (TS) waves In this work, we use numerical simulations and experiments to compare the robustness of adaptive and model-based techniques for reducing the growth of two-dimensional TS disturbances. In numerical simulations, the optimal linear quadratic Gaussian (LQG) regulator shows the best performance under the conditions it was designed for However, it is found that the performance deteriorates linearly with the drift of the Reynolds number from its nominal value. As a result, an order-of-magnitude loss of performance is observed when applying the computation-based I.QG controller in wind-tunnel experiments In contrast, it is shown that the adaptive filtered-X least-mean-squares (FXLMS) algorithm is able to maintain an essentially constant performance for significant deviations of the nominal values of the disturbance amplitude and Reynolds number.

Research on active control for the delay of laminar-turbulent transition in boundary layers has made a significant progress in the last two decades, but the employed strategies have been many and dispersed. Using one framework, we review model-based techniques, such as linear-quadratic regulators, and model-free adaptive methods, such as least-mean square filters. The former are supported by a elegant and powerful theoretical basis, whereas the latter may provide a more practical approach in the presence of complex disturbance envi- ronments, that are difficult to model. We compare the methods with a particu- lar focus on efficiency, practicability and robustness to uncertainties. Each step is exemplified on the one-dimensional linearized Kuramoto-Sivashinsky equa- tion, that shows many similarities with the initial linear stages of the transition process of the flow over a flat plate. Also, the source code for the examples are provided. 

We use linear control theory to construct an output feedback controller for the attenuation of small-amplitude three-dimensional Tollmien-Schlichting (TS) wavepackets in a flat-plate boundary layer. A three-dimensional viscous, incompressible flow developing on a zero-pressure gradient boundary layer in a low Reynolds number environment is analyzed using direct numerical simulations. In this configuration, we distribute evenly in the spanwise direction up to 72 localised objects near the wall (18 disturbances sources, 18 actuators, 18 estimation sensors and 18 objective sensors). In a fully three-dimensional configuration, the interconnection between inputs and outputs becomes quickly unfeasible when the number of actuators and sensors increases in the spanwise direction. The objective of this work is to understand how an efficient controller may be designed by connecting only a subset of the actuators to sensors, thereby reducing the complexity of the controller, without comprising the efficiency. If n and m are the number of sensor-actuator pairs for the whole system and for a single control unit, respectively, then in a decentralised strategy, the number of interconnections deceases mn compared to a centralized strategy, which has n (2) interconnections. We find that using a semi-decentralized approach - where small control units consisting of 3 estimation sensors connected to 3 actuators are replicated 6 times along the spanwise direction - results only in a 11 % reduction of control performance. We explain how "wide" in the spanwise direction a control unit should be for a satisfactory control performance. Moreover, the control unit should be designed to account for the perturbations that are coming from the lateral sides (crosstalk) of the estimation sensors. We have also found that the influence of crosstalk is not as essential as the spreading effect.