Stability and transition in pitching wings

The aeroelastic stability of airplanes is one of the most important aspects of airplane design. Flutter or divergence instabilities arising out of the interaction of fluid forces and structural elasticity must be avoided by design or through the limitation of the flight envelope. Classical unsteady theories have been established since the 1930s however, recent investigations with laminar wings and in transitional flows have found the theories to be unreliable in these regimes. The current work investigates the flow around unsteady airfoils in these flow regimes. A linear framework for the stability analysis of fluid-structure-interaction (FSI) problems is derived and validated. The derived formulation is then used to investigate the changes in the structural sensitivity of an eigenvalue for an oscillating cylinder, which is found to change significantly when the fluid and structural systems are close to resonance. The linear stability analysis is then applied to investigate the aeroelastic stability of a NACA0012 airfoil with a free pitch-deegree-of-freedom at transitional Reynolds numbers. The stability results of the coupled FSI system are found to be in good agreement with previously performed experimental results and were able to predict the onset of aeroelastic pitch-oscillations. The boundary layer evolution for a natural laminar flow airfoil undergoing forced small-amplitude pitch-oscillations is investigated at Rec = 7.5×105. Large changes in laminar-to-turbulent transition location are found throughout the pitch cycle which cause a non-linear aerodynamic force response. The origins of the non-linear unsteady aerodynamic response is explained on the basis of the phase-lagged quasi-steady evolution of the boundary layer. A simple empirical model is developed using the phase-lag concept to model the unsteady aerodynamic forces which fits the experimental data very well. On the other hand, the forced pitching investigation at Rec = 1.0×105 for the same airfoil found abrupt changes in transition during the pitch-cycle. A local stability analysis in the reverse flow region indicates that the stability characteristics of the LSB change character from convective to absolute, and it is conjectured that this change in stability characteristics may be the cause of abrupt changes inboundary-layertransition.QC 20191028