This dissertation presents the aeroelastic study of lifting surfaces in proximity and investigates the effect of aerodynamic interaction on the potential aeroelastic instabilities. Moreover, the effect of structural coupling between the lifting surfaces is considered as well, along with the ground effect. Aeroelastic modeling and analysis of lifting surfaces in proximity are numerically approached in two and three dimensions. In the two-dimensional (2D) approach, rigid wing sections are used as a two-dimensional representation of lifting surfaces. The rigid section model offers simplicity and tractability in the aeroelastic analysis, hence ideal in the preliminary studies to draw insight into the physical nature of the phenomenon. In the three-dimensional (3D) approach, swept and unswept flat plate flexible wings are considered. It is also assumed that the wings are elastically connected by a bracing structure. Bracing structure such as struct bar provides structural coupling between the wings which could mathematically be modeled using a spring. A potential-based aerodynamic model is used to simulate the unsteady aerodynamic characteristics of lifting surfaces. Three different aerodynamic models were established to compute the aerodynamic loads namely, unsteady discrete vortex method (UDVM), unsteady source and vortex panel method (USVPM), and unsteady vortex lattice method (UVLM). These methods are extended to account for aerodynamic interaction between multiple lifting bodies; UDVM for thin rigid airfoil sections, USVPM for thick rigid airfoil sections, and UVLM for the thin flexible wings. USVPM has been introduced in this study mainly to investigate the effect of thickness on the aeroelastic behavior of closely coupled airfoil sections. In the 2D approach, coupled aeroelastic equations of motion of elastically supported airfoils are formulated in a state-space form and solved explicitly using the predictor-corrector numerical scheme. In the 3D approach, a finite element analysis program is used to model the wing structure and the interactive aeroelastic simulation environment is established using the multibody dynamic program (MSC. Adams) and UVLM. Primarily the aeroelastic behaviors of a two-airfoil system and two wings in proximity are investigated. But, the present method applies to any number of lifting surfaces in proximity. Hence, this study also presents the aeroelastic investigation of multiple vanes of a ducted vane system.
From the 2D and 3D aerodynamic analyses, results have revealed that the effect of aerodynamic interaction is significant in the aerodynamic characteristics of either airfoils or wings in proximity. The magnitude of lift and moment forces that the airfoils or wings generate in the presence of aerodynamic interaction is mainly affected by the gap and phase of the motion between them. The aerodynamic interaction effect was magnified by decreasing the gap but the positive and negative influences on the aerodynamic loads are due to the phase of the motion between them. It was shown that the wings in proximity generates more lift when their motions are out-of-phase and less lift when their motions are in-phase as compared to the single wing case. In the case of three wings in proximity, the interaction effect was significant for the middle one. Therefore, the middle wing was generating more lift when oscillating in out-of-phase with lower and upper wings whereas less lift when oscillating in in-phase with other wings. Likewise, for any number of lifting surfaces in proximity, the aerodynamic loads they generate are determined by the gap and the relative motions between the adjacent lifting surfaces. While considering the effect of thickness, it was found that the thickness tends to magnify the interaction effects. The ground effect on the other hand increases the magnitude of lift and moment forces and destroys the symmetry of the loads. As a result, the lifting bodies tend to produce average positive lift and negative moment forces. Results also showed that the thickness effect contributes more to the average positive lift and negative moment forces as compared to thin airfoil near the ground.
The 2D and 3D aeroelastic results have revealed that the airfoils or wings in proximity were destabilized at a lower speed due to the effect of aerodynamic interaction. With only the structural coupling, the two-airfoil system showed a considerable change in the flutter speed due to changes in the modal characteristics, especially for lower coupling stiffness values. When both aerodynamic interaction and structural coupling effects were taken into account, improvement in the flutter instability was observed. This was mainly observed for coupling stiffness of larger values while for lower coupling stiffness values flutter speed was further degraded for decreasing the gap. Essentially for the gap less than the chord length between the lifting surfaces, the interaction effect seemed to be critical with an exponential decrease in the flutter speed for decreasing the gap. This was even worse with the inclusion of the thickness effect where the airfoils were destabilized at a much lower speed with the increase in the thickness. It was also observed that the aeroelastic responses in the presence of only the aerodynamic interaction always reach out of phase irrespective of the initial disturbances. As a consequence, the larger lift and moment forces were generated which was responsible for destabilizing the system at a lower speed. Similarly, when structural coupling was introduced and especially for larger coupling stiffness, the oscillations were in in-phase, thus decreasing the magnitude of aerodynamic loads and improving the flutter instability. From the ground effect study, it was shown that the thin airfoil or wing operating near the ground could suffer from aeroelastic instability at a lower speed. And again, the effect was significant for the height less than the chord length above the ground. The presence of ground was shown to alter the wake shape and was responsible for increasing the magnitude of the aerodynamic loads and consequently destabilizing the airfoil or wing at a lower speed. As opposed to that, the inclusion of thickness demonstrated the delay in the flutter instability when height was less than the chord length above the ground. From the analysis, it was found that the ground effect produces average positive lift and negative moment forces and in the case of the thick airfoil, the generated average negative moment was large enough to stabilize the airfoil and increase the flutter speed. The example of the multiple vanes of the ducted vane system strongly suggested the significance of the aerodynamic interaction effects. The study indicated that the flutter instability is mostly influenced by the gap between the adjacent vanes as well as the flutter characteristics of the individual vane. Overall, this study suggests the significance of aerodynamic interaction in the aeroelastic design of the multiple lifting surfaces in proximity.