We develop a method for estimating the instantaneous lift coefficient on a rapidly pitching airfoil that uses a small number of pressure sensors and a measurement of the angle of attack. The approach assimilates four surface pressure measurements with a modified nonlinear state space model (Goman-Khrabrov model) through a Kalman filter. The error of lift coefficient estimates based only on a weighted-sum of the measured pressures are found to be noisy and biased, which leads to inaccurate estimates. The estimate is improved by including the predictive model in an conventional Kalman filter. The Goman-Khrabrov model is shown to be a linear parameter-varying system and can therefore be used in the Kalman filter without the need for linearization. Additional improvement is realized by modifying the algorithm to provide more accurate estimate of the lift coefficient. The improved Kalman filtering approach results in a bias-free lift coefficient estimate that is more precise than either the pressure-based estimate or the Goman-Khrabrov model on their own. The new method will enable performance enhancements in aerodynamic systems whose performance relies on lift.
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 = πf c 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.
The separated flow response to single and multiple burst mode actuation over a 2-D airfoil at 12 o angle of attack was studied experimentally. For the single-burst actuation case, surface pressure signals were correlated with the flowfield observations of the roll-up and convection of a large-scale vortex structure that follows the actuator burst input. A spatially localized region of high pressure occurs below and slightly upstream of a "kink" that forms in the shear layer, which is responsible for the lift reversal that occurs within 2.0t + after the burst signal was triggered. Proper orthogonal decomposition of the single-burst flow field shows that the time-varying coefficients of the first two modes correlate with the negative of the lift coefficient and pitching moment coefficient. The dynamic mode decomposition (DMD) of the single-burst flow field data identified the modes related to the kinetic energy growth of the disturbance. The mode with the largest growth rate had a Strouhal number close to that associated with the separation bubble dynamics. However, when multiple bursts are used to control the separation, the interactions between the bursts were observed which depend on the time intervals between the bursts. The convolution integral and DMD were performed on the multiburst flow field datasets. The results indicate that the nonlinear burst-burst interaction only affects the reverse flow strength within the separation bubble, which is related to the main trend of the lift. On the other hand, the linear burst-burst interaction contributes to the high-frequency lift variation associated with the bursts.Key words: Authors should not enter keywords on the manuscript, as these must be chosen by the author during the online submission process and will then be added during the typesetting process (see http://journals.cambridge.org/data/relatedlink/jfmkeywords.pdf for the full list) †
A feedforward controller is designed to attenuate the roll moment coefficients produced by forced roll motion of a delta-wing type model. Active flow control effectors in the form of variable strength pneumatic slot-jets are located along the trailing edge of the model. The control effectors produce a roll moment coefficient proportional to the momentum coefficient. Direct measurements of the roll moment are made with the model in a wind tunnel. Black-box models for the plant and disturbance are identified, and used in the design of the feedforward controller. The effectiveness of the feedforward controller in attenuating disturbance roll moments produced by forced roll maneuvers is evaluated with periodic and pseudo-random maneuvers. Near the design point of the for the controller the root-mean-square value of the net roll moment is four times smaller than the roll moment without control.
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