Aerodynamic detuning of a loaded airfoil cascade in an incompressible flow by a locally analytical method
A mathematical model is developed and utilized to demonstrate the enhanced aeroelastic stability and forced response behavior associated with aerodynamic detuning of a rotor operating in an incompressible flow field. The unsteady aerodynamic gust response and oscillating cascade aerodynamics are determined by developing a complete first order unsteady aerodynamic analysis. A locally analytical solution is developed in which the discrete algebraic equations which represent the flow field equations are obtained from analytical solutions in individual grid elements of a body fitted computational grid. Aerodynamic detuning is accomplished by means of alternate circumferential spacing, and also by the introduction of variable spacing splitters between each pair of full chord airfoils. An unsteady aerodynamic influence coefficient technique is then utilized, thereby enabling the torsion mode stability and forced response behavior of both conventional tuned rotors and aerodynamically detuned rotors to be determined.^ The validity of the tuned cascade model and solution technique are demonstrated by considering the steady and unsteady aerodynamics of both theoretical and experimental cascade configurations. To verify the detuned cascade model and influence coefficient technique, predictions from this model are compared to the steady theoretical results and also the tuned cascade unsteady aerodynamic model predictions. The capabilities of this detuned cascade model are then demonstrated by predicting the flutter stability and forced response behavior of detuned rotor configurations.^ Nonuniform circumferential airfoil spacing and alternate blade structural detuning are both shown to enhance stability. The greatest stability enhancement resulted from a combination of aerodynamic and structural detuning. Also, the unstable baseline configuration can be stabilized by the introduction of splitter blades. For the forced response behavior, both the alternate circumferential spaced detuning and the alternate blade structural detuning can be beneficial on the response amplitude of the airfoils. By including aspect ratio effects, the alternate splitter blade detuning results in significantly reduced amplitudes of response for most cases considered. In conclusion, this detuning analysis has demonstrated that both the aeroelastic stability and forced responsive behavior can be greatly enhanced by aerodynamic detuning. Therefore, aerodynamic detuning appears to be a viable passive control mechanism for aeroelastic problems of an incompressible cascade. ^
Major Professor: Sanford Fleeter, Purdue University.