H(2)/H9(infinity) controller design for a two-dimensional thin airfoil flutter suppression

The effect of a leading-edge vortex (LEV) on the lift, thrust and moment of a two-dimensional heaving and pitching thin airfoil is analysed within the unsteady linear potential theory. First, general expressions that take into account the effect of any set of unsteady point vortices interacting with the oscillating foil and unsteady wake are derived. Then, a simplified analysis, based on the Brown–Michael model, of the initial stages of the growing LEV from the sharp leading edge during each half-stroke is used to obtain simple expressions for its main contribution to the unsteady lift, thrust and moment. It is found that the LEV contributes to the aerodynamic forces and moment provided that a pitching motion exists, while its effect is negligible, in the present approximation, for a pure heaving motion, and for some combined pitching and heaving motions with large phase shifts which are also characterized in the present work. In particular, the effect of the LEV is found to decrease with the distance of the pivot point from the trailing edge. Further, the time-averaged lift and moment are not modified by the growing LEVs in the present approximation, and only the time-averaged thrust force is corrected, decreasing slightly in most cases in relation to the linear potential results by an amount proportional to$a_{0}^{2}k^{3}$for large$k$, where$k$is the reduced frequency and$a_{0}$is the pitching amplitude. The time-averaged input power is also modified by the LEV in the present approximation, so that the propulsion efficiency changes by both the thrust and the power, these corrections being relevant only for pivot locations behind the midchord point. Finally, the potential results modified by the LEV are compared with available experimental data.

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LPV modeling and controller design for body freedom flutter suppression subject to actuator saturation

Chinese Journal of Aeronautics ◽

10.1016/j.cja.2020.05.027 ◽

2020 ◽

Vol 33 (10) ◽

pp. 2679-2693

Author(s):

Wei TANG ◽

Yu WANG ◽

Jiawei GU ◽

Zhiwei SUN

Keyword(s):

Controller Design ◽

Actuator Saturation ◽

Flutter Suppression

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Educational Results Obtained Using an Improved Two-Dimensional Panel Method Code in Undergraduate Fluid Dynamics and Aerodynamics Courses

Volume 2, Fora: Cavitation and Multiphase Flow; Advances in Fluids Engineering Education ◽

10.1115/fedsm2017-69031 ◽

2017 ◽

Author(s):

Robert Spall ◽

Joshua Hodson

Keyword(s):

Fluid Dynamics ◽

Potential Flow ◽

Pressure Coefficient ◽

Panel Method ◽

Two Dimensional ◽

Student Survey ◽

Integral Analysis ◽

Thin Airfoil ◽

Survey Questions ◽

Momentum Integral

Undergraduate required fluid dynamics and elective aerodynamics courses include substantial material on analysis techniques for forces acting on bodies in external flows. These methods include momentum integral analysis, and, for aerodynamic applications, lift computed using circulation and the Kutta-Joukowski theorem. The author presented in a previous FED meeting code development and preliminary classroom results for the implementation of a fully interactive, two-dimensional potential flow solver for flow over both rigid and flexible thin-airfoil (or sail) geometries. The intent of the development was to design a code that could be used as a virtual wind tunnel. The solver was developed in Fortran 90/95 with user interface and graphics routines developed using the high-level plotting library DISLIN for use on Windows-based computers. The analysis code solves the potential flow equations for single or multiple airfoils using a vortex panel method in which the vortex strength varies linearly along the panel and is continuous from one panel to the next. A variety of controls are available to adjust airfoil shapes and angles-of-attack. The user may also specify either rigid thin airfoil shapes, or flexible airfoils in which the final equilibrium shapes are determined by the pressure distribution. Available graphics include velocity vectors, pressure coefficient contours, and streamlines. Lift, axial and normal force coefficients are also output in the form of bar graphs. Several improvements have been implemented in the code, based on early student feedback, to improve its suitability for educational purposes in fluid dynamics and aerodynamics classes. These include pressure plot distributions over the airfoils, the inclusion of standard NACA 4-digit airfoil definitions, the output of velocity and pressure data about a closed contour for use in circulation and momentum integral analysis calculations, and improvements regarding compatibility for use on computers of widely varying screen resolutions. In this work to be presented, recent improvements to the code, and subsequent educational/student learning results based on a series of Qualtrics online student survey questions are presented. These survey questions query the students understanding of a) momentum integral analysis, b) circulation, c) lift calculations using the Kutta-Joukowski theorem, d) airfoil-to-airfoil fluid flow interactions, e) the necessity for attention to details when performing engineering analysis. The code may be downloaded for use by educators and students at other universities.

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