Bypass transition is a subcritical transition pathway that a boundary layer may follow from laminar to turbulent state. The latter is associated with higher drag. Prolonging the laminar boundary can therefore enhance efficiency in applications such as the flow over aircraft. Bypass transition is caused by the growth of streaks of low and high velocity in the laminar boundary.Spanwise arrays of plasma actuators have shown promise in experimental demonstrations of the active cancelation of these streaks in an open-loop and also closed-loop feedback control framework to delay transition in the past. However, when the plasma actuators were given a step input to model a fast response to a detected streak, a non-minimum phase response of the far-field velocity and shear stress was detected. Experiments were limited to only the streamwise velocity component and to regions considered in the far fields given physical sensor limitations.

The unsteady output of a spanwise array of plasma actuators, arranged to generate laminar streaks of streamwise vorticity in a Blasius boundary layer, are modelled numerically. When the forcing by the actuators undergoes a step change from off to on, the flow response downstream of the actuators is initially inverted in terms of the streamwise vorticity, disturbance velocity, and wall shear stress before approaching the steady-state behaviour. The present study considers the effect of the length of the actuator in the streamwise direction and the effect of the rate change of the output of the actuator with respect to the non-minimum phase behaviour. Four different actuator lengths are considered. For the gradually applied force, the body force increases linearly from zero to the same maximum value of the step, which simulates a reduced slew rate or ramped output. It is shown that the inverse response remains for the gradually applied input, however, the peak magnitude is less and the overall response appears more damped. As the actuator length is reduced, while forcing was compensated for the shorter convective time over the actuator, the peak inverse response was enhanced.

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In this study, simulations of the laminar boundary layer response to forcing by an array of streamwise oriented plasma actuators are performed. The objective of this study is to evaluate a method to mitigate the non-minimum phase behaviour of the flow that occurs during the step response to input by the actuators. It was recently shown that when the actuators are abruptly started the non-minimum phase response of the wall shear and near-wall disturbance velocity is detected downstream of the actuators. This was shown to be caused by a secondary flow generated between the wall and the front of the tilted vortex structure that is advected downstream [1]. In the present study the step input response is compared to gradually applied inputs. For the step response, the actuators are abruptly activated for 0.2 s followed by a rest period for the flow to return to the undisturbed Blasius condition. For the gradually applied input, the body force of the actuators increases linearly from zero for either 0.005 s, 0.01 s, 0.02 s and 0.04 s to the same maximum value of the step, which simulates a reduced slew rate applied to the physical actuator. The value is held constant and then linearly decreases over a total duration of 0.2 s. It is shown the that inverse response remains for the gradually applied input. However, the peak magnitude is less for the lower ramp rates and the overall response appears more damped.