Wind Tunnel Studies of Damaged-Wing-Induced Limit Cycle Oscillations

Abstract

The influence of damage on the performance of the lifting surface of an aircraft has been an area of interest to the military for over half a century. Some of the earlier studies of this subject focused on the impact that structural damage resulting in the loss of lifting surface structural strength, stiffness, and mass might have on imparting catastrophic aeroelastic failures to the lifting surface. Discouraging mixed results arose over the next 30 years in these investigations that employed only structural damage models. As time passed, it was finally noticed that if the often neglected, usually second-order, drag term was now included (as aerodynamic damage often creates a high, unsteady, localized drag rise) in the earlier aeroelastic damaged-wing analyses, more encouraging results were obtained. That is, the realistic asymmetric damaged lifting surfaces flutter and divergence analysis did show lowered, and not raised, flutter and divergence speeds over that of the undamaged lifting surface. This occurred both in the presence of or in the absence of structural damage as in the case of icing or external wing stores. In essence, it was determined at this time that the resulting high and unsteady drag rise caused by the damage could do more than just cause an energy deficiency in the aircraft mission. It could, in fact, cause shorter term catastrophic or stiffness failure events in terms of reduced flutter and divergence speeds as well as give rise to limit cycle oscillations embedded within what was shown to be that part of the damaged-aircraft flight envelope free from classic flutter and divergence. The present experimental wind-tunnel study was carried out to confirm these past theoretical findings by employing a one-twelfth-scale F-111 aeroelastic model and (third-order) higher-order statistical signal processing to identify the frequency ordering that occurs in these additional damaged-induced limit cycle oscillations. These limit cycle oscillations were also found to exhibit the classic lock-in/lock-out phenomenon that occurs in the well-known F/A-16 and F/A-18 wing store induced limit cycle oscillations. Nomenclature C = modal damping matrix Ft = classical forcing function H C i; j; l = cubic frequency-domain Volterra transfer function H L k = linear frequency-domain Volterra transfer function H Q i; j = quadratic frequency-domain Volterra transfer function Kt = modal stiffness matrix which may vary with time M = modal mass matrix P C k = output of the cubic component of the Volterra model P L k = output of the linear component of the Volterra model P Q k = output of the quadratic component of the Volterra model P Y k = true observed response power spectrum PŶk = estimated response power spectrum of the Volterra model q = set of generalized coordinates S XX = power Spectrum of Xl S XXX = bispectrum of Xl S XXXX = trispectrum of Xl Xl = calculated value of the discrete Fourier transform of xn xn = nth sampled value of a digital time series Yl = calculated value of the discrete Fourier transform of yn yn= ...

Proper orthogonal decomposition-based spectral higher-order stochastic estimation

“…Therefore, the technique is being presented here in the context of stochastic estimation as spectral Higher-Order Stochastic Estimation (HOSE) but with the added benefit of including multiple points on the input and output sides of the system by way of POD. 28 A thirdorder Volterra approach was successfully applied by Park et al, 29 who considered the fluid-structure lock-in phenomena of a damaged fighter wing inducing unsteady flow. Linear, quadratic, and cubic coherence were obtained between the flow field (pressure) and structural response (acceleration) to characterize a nonlinear limit cycle oscillation of the wing.…”

POD based spectral Higher-Order Stochastic Estimation

“…A more recent application of the second-order Volterra approach was performed by Baars et al (2009) 23 to investigate ice-induced stability upsets of small general aviation aircraft. Similarly, a third-order Volterra approach has been applied successfully in the work by Park et al (2008). 24 The study considers a classic fluid-structure lock-in phenomena of a damaged fighter wing inducing an unsteady flow field.…”

“…Similarly, a third-order Volterra approach has been applied successfully in the work by Park et al (2008). 24 The study considers a classic fluid-structure lock-in phenomena of a damaged fighter wing inducing an unsteady flow field. Linear, quadratic and cubic coherences were obtained between the unsteady flow field (pressures) and unsteady structural response (acceleration) to characterize the nonlinear limit cycle oscillation of the wing.…”