Numerical simulation of wakes, blade-vortex interaction, flutter, and flutter suppression by feedback control

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Virginia Tech


A general aerodynamic model for two-dimensional inviscid flows is developed. This model is used to simulate wakes and blade-vortex interaction. This model is also coupled with dynamics and feedback controls to simulate flutter and flutter suppression.

The flow is assumed to be attached and incompressible. The present aerodynamic model is based on a vorticity-panel method coupled with vortex dynamics.

The present aerodynamic model is used to simulate some actual experiments: wakes generated by oscillating airfoils and blade-vortex interactions in which one airfoil is placed in or near the wake generated by another oscillating airfoil upstream. The present numerical model predicts wake structures, vorticity strength, and velocity profiles across the wake that compare very favorably with the experiments. The present numerical results of the blade-vortex interaction show good agreement with the experiments when separation does not occur. If separation is involved, the present model fails to accurately simulate blade-vortex interaction because separation is not considered in the present model.

Flutter is studied by means of numerical simulations. In an incompressible flow, an airfoil is mounted on an elastic support. The airfoil can pitch (rotate) and plunge (translate vertically). The dynamic equations that describe this two-degree-of-freedom motion are general and nonlinear. To calculate the aerodynamic loads on the airfoil, the aerodynamic model is coupled with this dynamic model. The motions of the airfoil and flowing air are calculated interactively and simultaneously.

The coupled aerodynamic/dynamic model accurately predicts the critical flutter speed of the freestream, the speed at which the motion of the airfoil grows spontaneously. The contributions of the phase difference and energy exchange to the flutter motion are discussed. The effect of the static angle of attack on the critical flutter speed is investigated. Also the effect of the nonlinearity of the elastic support (cubic term in the hardening spring) is studied.

A feedback control is coupled with aerodynamics/dynamics to suppress the flutter motion of the airfoil. A flap is added at the trailing edge of the airfoil as a control surface, and its deflection (rotation) about the hinge point is commanded by a feedback-control law. The flow, airfoil, elastic support, and control device are considered as one system, and the flow, the motions of the airfoil, and the flap deflections are calculated simultaneously.

With carefully designed control laws, oscillations that would be unstable (i.e., growing) without control are suppressed. The numerical results show different control variables can be used. The model of aerodynamics/dynamics/control is also used to successfully suppress the response to a wind gust with the same control laws as used for the suppression of flutter.