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Modeling Dynamic Lift Response to Actuation

The dynamic lift response of an airfoil to sinusoidal amplitude variations from a synthetic jet actuator was studied. The wing was at a fixed angle of attack, and the actuator operated in a ‘burst-mode’ with a fixed duty cycle. The actuator burst amplitude was used as a control signal, which was varied between an ‘off’ condition and the actuator saturation voltage. Three dimensionless frequencies were examined, corresponding to k = πfc U∞ = 0.064, 0.128, and 0.25. Hysteresis loops in the lift increment were observed, whose shapes were dependent on the control frequency. Three different approaches to modeling the lift increment response were explored: a linear convolution approach, a nonlinear time delay and decay model, and a combination of those two. The linear convolution captures the high frequency content of the lift response, but becomes inaccurate when the actuator burst period is less than 3.5 convective times. The time delay and decay model reproduces the low frequency component of the lift response, but not the high frequency. When the control frequency becomes large, (k = 0.25), then the largest time-varying lift increment is produced near the minimum of the actuator voltage.