Investigation of flutter suppression by active control

Flutter and active trailing edge flap control, in two dimensions, is simulated by coupling independent structural dynamic and inviscid aerodynamic models, in the time domain using the time-synchronised, strong coupling procedure. The computational method developed is used to perform transonic aeroelastic and aeroservoelastic calculations in the time domain, and used to compute stability (flutter) boundaries of 2-D wing sections. Previous works have considered the implementation of a simple control law within the aeroelastic solver, to investigate active means of flutter suppression via control surface motion. Open and closed loop simulations show that active control can successfully suppress the flutter and results in a significant increase in the allowable speed index in the transonic regime. This is due to the rapid effect the flap deflection has on shock wave position, but the control system was found to have little effect in subsonic flow. This paper takes this concept further, by considering a more detailed analysis of the control law, to optimise it for both subsonic and transonic flow. Introduction The accurate aeroelastic prediction of flutter boundaries over the entire flight envelope is essential, since underprediction of the boundary (due to inaccurate methods, or large safety margins due to lack of confidence in methods) results in unnecessary structural stiffness and hence weight. In the pure subsonic or supersonic regimes it has been normal industry practice to use linear aerodynamic theory, such that the aerodynamic forces depend upon the body motion in linear fashion, thus permitting uncoupling of the structural and fluid equations.1 However, this can not be applied in the transonic regime due to the high non-linearity of the flow field. The aerofoil thickness was often neglected in linear theory, but the aerofoil geometry plays an important role in the deCopyright c 2003 by C.B. Allen. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission Reader in Computational Aerodynamics. MAIAA. Corresponding author Postgraduate student. Postdoctoral researcher. Former postgraduate student. Now at Airbus U.K. velopment and motion of shock waves in the transonic region.2 There are other nonlinear phenomena associated with aeroelastics, for example aileron buzz or limit cycle oscillations (LCO), and none of these phenomena can be predicted directly by traditional linear theoretical methods, since they are interactions between nonlinear aerodynamic forces and structures. Hence, more advanced aeroelastic simulation methods, applicable to transonic flows, are essential. It is possible, with current computational power, to develop coupled aerodynamic-structural dynamic methods using the Euler and Navier-Stokes equations as the aerodynamic model. Euler solvers have been coupled with structural models previously, see for example3.8 The Navier-Stokes equations are still rarely used in computational transonic aeroelasticity due mainly to their excessive CPU demands. Simplified forms of the Navier-Stokes equations have been used for aeroelastic applications, see for example9 -,13 but results show that for two degree of freedom aerofoil motions little difference was found between using inviscid and viscous aerodynamic models. Reviews of computational aeroelasticity are presented in14 and.15 The time-accurate interaction between structural dynamics, the flight control system and aerodynamics, known as aeroservoelasticity, has recently received attention, see for example16-.29 Active Control Technology (ACT) can be implemented within an aeroelastic solver in order to simulate any the following: flutter suppression, gust alleviation or manoeuver enhancement. Previous work has relied mainly on transonic small disturbance theory as the aerodynamic solver,24–26 or has been performed in the frequency domain20 -.30 For example, Nissim20, 30 performed flutter boundary calculations in the frequency domain by considering the sign of the work done by the structural system on its surroundings. There are limitations to this approach, but the energy analysis is extremely useful and is used here. Active control systems normally have constant (with time) control laws. However, the use of adaptive control in active flutter suppression has started to appear in the literature, see for example.27–29 This approach is attractive since the parameters of the system often change with time or under load, which is the usual limitations of control using fixed-structures, fixed-parameter controllers. The added complexity of adaptive control is 1 American Institute of Aeronautics and Astronautics 21st Applied Aerodynamics Conference 23-26 June 2003, Orlando, Florida AIAA 2003-3510 Copyright © 2003 by C. B. Allen. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. often justified by reduced hardware requirements, but it is very difficult to prove the stability properties of controllers whose parameters can vary. In addition, it is almost impossible to get certification for civil aircraft equipped with adaptive control. Hence, the approach of using fixed-parameter controllers is preferred in this research, although it should also be noted that fixedparameter active controllers are also difficult to certify. This paper presents a computational method to simulate aeroelastic and aeroservoelastic behaviour of a two and three degree of freedom aerofoil. The aerodynamic model is described by the Euler equations, which is coupled with a structural model. A control law is implemented within the aeroelastic solver to investigate active means of flutter suppression via control surface (flap) motion, and the effect on the stability (flutter) boundary presented. Previous work31–33 has concentrated on transonic flutter suppression, and an increase in the allowable speed index of 19% was demonstrated in the transonic regime, using heave rate and pitch rate as the control signals in a simple linear control law. However, this had little or no effect in the subsonic regime. This paper extends the previous studies, by considering more advanced control laws and optimisation schemes, in an attempt to increase the stability margin throughout the entire flight envelope. Aerodynamic Model A finite-volume Euler code is used for the aerodynamic model. The two-dimensional unsteady Euler equations on a moving grid in integral form are : ! #"$ &% ' ( (1) where is the vector of conserved variables, is the flux vector, " is the outward cell face unit normal, and % the peripheral length of the cell face. and are given by: ' )* + *,.--0/ -01 -&2 3 *4* 5 6 ' )* + *, 798 : ; = -0/ 798 : ; = @DC -&2 798 : ; <?= @ 8 3 *4* 5 (2) where 8 is the velocity vector, ;.< the grid velocity vector, and @ 6 6 / 6 1 and 2 are pressure, density, Cartesian xand y-component velocities and total specific energy respectively. The equation set is closed by @ ' 7FEG: HI=KJ -&2 : 8$L M N (3) Discretisation The unsteady Euler equations are solved using a Jameson34 type cell-centred finite-volume method. Equation 1 is applied to each cell of the mesh. Following Jameson et al,34 the spatial and time dependent terms are decoupled and a set of ordinary differential equations is obtained. Artificial dissipation needs to be added to stabilise the solution.34, 35 It is expensive to use explicit time-stepping for unsteady flows. To maintain time-accuracy the whole domain must be integrated by the same time-step, and this is limited to the smallest value over the domain. Hence, an implicit scheme is used, based on that proposed by Jameson.36 This solves unsteady flows as a series of pseudo-steady cases, and is extremely efficient compared to an explicit scheme37, 38 The flow-solver is used in conjunction with a structured moving mesh, which allows the cell volumes to distort as the aerofoil moves or deforms. An algebraic moving grid generator based on transfinite interpolation39 is used. This approach is extremely efficient, as it allows instantaneous grid positions and speeds to be computed directly at any time.40, 41 The cell areas required in the time-stepping scheme are computed to satisfy a geometric conservation law.42 More details of the flow-solver can be found in.31 Structural Model Figure 1 shows the typical wing section used to derive the structural equations of motion. This model has been well established for two dimensional aeroelastic analysis.43 The degrees of freedom associated with the aerofoil are shown in figure 1. The pitching and heaving displacements are restrained by a pair of spring attached to the elastic axis (EA) with spring constants OQP and OGR respectively. A torsional spring is also attached at the hinge axis whose spring constant is OTS .