A comparison of full non‐linear and reduced order aerodynamic models in control law design using a two‐dimensional aerofoil model

Abstract

SUMMARYThe prediction of the flutter boundary of an aircraft is a necessary but time consuming process, particularly as for the most realistic results a time accurate simulation of the interaction between the non-linear aerodynamic and structural forces is required. Extension of the flight envelope by the design of active control laws to suppress flutter further increases the demands on computational time, to presently unrealistic levels. Use of a reduced order model (ROM) derived from, and in place of, the full non-linear aerodynamics greatly reduces the time required for calculation of aerodynamic forces. However, this is necessarily accompanied by some loss in accuracy, and hence the method must be verified by comparison with results obtained by the full aerodynamic model before it may be used with confidence.Such a comparison is presented here, using a two-dimensional aerofoil and control surface combination as a test case. Active control of the deflectable surface is used to attempt to increase the flutter speed across the complete Mach range, feedback control being achieved by gains acting on heave and pitch proportional and differential signals, interpreted as a hinge moment demand. Full non-linear and reduced order aerodynamic models are then used to obtain optimum control law gain for flutter suppression. The results demonstrate that the ROM accurately predicts the open loop flutter boundary, gives a good approximation to the increase in flutter speed that may be produced by gain optimization, and produces a similar response given the identical gain values in each system for a significantly reduced cost.

Efficient Predictions of Unsteady Viscous Flows Around Bluff Bodies by Aerodynamic Reduced Order Models

“…A= t/,Si //(I) E^l/J (16) where, the symbol * stands for pseudoinverse. By using orthonormality of matrices UR and VR in Eq.…”

“…Efficient CFD tools of this nature will not be available for many years to come. To overcome tbis drawback of bigh fidelity CFD analysis, reduced order models have been applied since tbe 1980s and developed in tbe last few years [11][12][13][14][15][16][17]. A ROM is a representation of a system that, despite its reduced order form, maintains the dominant dynamical features of the original system.…”

Study of the conditions that cause chaotic motion in a two-dimensional airfoil with structural nonlinearities in subsonic flow

“…Additionally, the lack of visibility of the full nonlinear equations in state space form makes various forms of control law design and stability analysis extremely difficult if not impossible. A reduced order model (ROM) of the Euler code was then created (Allen et al, 2005), and the full nonlinear and reduced order aerodynamic models in control law design were compared. With an equivalent accuracy to the CFD method, the ROM requires a computational time that is much more comparable with traditional linear methods.…”

Unified fluid–structure interpolation and mesh motion using radial basis functions

“…When considering the coupled problem of aeroelasticity, two approaches have emerged, one using a tailored aero-structural solver [1,2] (the monolithic approach) and the other favouring the coupling of existing structural and fluid solvers [3][4][5][6][7][8][9][10] (the partitioned approach). The partitioned approach has received much more attention, including within the computational fluid dynamics (CFD) group at the University of Bristol [6][7][8][9][10], because it allows the use of existing software and grids, but synchronization of the structure and fluid at each time level must be done iteratively [6,7,10]. In comparison, the monolithic approach allows exact time synchronization but requires a new solver and mesh.…”