Nonlinear airfoil torsional response induced by separated flows

Abstract

Stall-induced vibrations are nonlinear aeroelastic phenomena. Helicopter rotors, wind turbine blades, or other rotating components interacting with an airow may vibrate in stall condition. Despite a signiffcant effort to model the aerodynamics associated to the stall or separated flows, nonlinear aeroelastic behavior prediction and analysis in such flow regime remain a formidable challenge. Another source of nonlinearity with inuence to aeroelastic response may be associated to the structure dynamic response. The combi- nation of both separated flow aerodynamics and structural nonlinearities lead to complex dynamics, for instance, bifurcations and chaos. The purpose of this work is to present the analysis of stall-induced vibrations, or separated flow effects, of an airfoil in pitching when concentrated nonlinearities are associated to the structural dynamics. Limit cycles oscillations at higher angles of attack and complex nonlinear features are analyzed for different representations for concentrated restoring pitching moment. The pitching-only typical section dynamics is coupled with an unsteady aerodynamic model based on Beddoes- Leishmann semi-empirical approach to produce the proper framework for gathering time series of aeroelastic responses. The analyses are performed by checking the amplitude of the aeroelastic responses in limit cycle oscillations. Evolutions on limit cycles amplitudes are used to reveal bifurcation points also admitting Mach numbers range up to 0.7, thereby providing important information to assess, characterize, and qualify the nonlinear behavior associated with combinations of different forms to represent concentrated pitching spring of the typical section. The concentrate structural nonlinearities under investigation are the hardening and softening cubic, free-play, and hysteresis. Results reinforce that oscillations under the effects of stall are mostly determined by the flow ffeld. The structural nonlinear- ities are most relevant at lower airspeeds. Different bifurcations can be observed in Mach evolutions of LCOs, in which structural effects can be important to delay its onset.