Abstract
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.
Highlights
In low free-stream turbulence conditions, the transition to turbulence in a flat-plate boundary layer is dominated by Tollmien–Schlichting (TS) instabilities
We have shown that reactive linear adaptive control can efficiently delay the laminar-to-turbulent transition in a realistic low-amplitude disturbance environment
It is shown that the drag reduction that results from the transition delay leads to a net power saving up to the order of 103, when an ideal-actuator model is considered
Summary
In low free-stream turbulence conditions, the transition to turbulence in a flat-plate boundary layer is dominated by Tollmien–Schlichting (TS) instabilities. By increasing even further the disturbance amplitude, the laminar-to-turbulent transition reaches the actuation location and the control does not effectively control the perturbation field. Control strategy The control action is performed by a row of localised, equispaced actuators forcing the flow in the proximity of the wall Their action ul(t) is computed based on the measurements ym(t) by a row of sensors upstream of the actuators: in this study, the number of sensors is equal to the number of actuators and they are aligned with the flow direction (figure 1). In the current study the secondary path is obtained via a linear DNS of the impulsive response of one actuator
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