Development and application of a generalized dynamic wake theory for lifting rotors.

摘要

Rotorcraft aeroelasticity and aeromechanics analysis requires a consistent mathematical model that has an appropriate combination of structural dynamics and unsteady aerodynamics. Unfortunately, existing rotor unsteady induced flow theories, a key part of rotorcraft unsteady aerodynamics, are either too simple to capture necessary physical reality or too involved to carry out any system eigenvalue analysis or system design. To provide rotorcraft dynamists with an efficient unsteady wake model, this research aims at development of an intermediate level unsteady induced-flow theory suitable for rotorcraft aeroelastic stability, vibration, control, and aeroelastic tailoring studies. The unsteady wake theory is developed for lifting rotors based on an acceleration potential for an actuator disk. The induced inflow at the rotor disk is expressed in terms of a Fourier series azimuthally and a polynomial distribution radially. A system of first-order, ordinary differential equations in the time domain, formulated from first principles, describes the flow. The pressure at the rotor disk is discretized at each rotor blade to allow for the effect of finite number of blades. This formulation is well fitted to rotor aeroelastic analysis.;The research has resulted in closed-form, analytical expressions for the induced-flow influence coefficients, one of the most critical parts in the development of the theory in forward flight. The theory has also been applied to the computation of the induced-flow distribution of helicopter rotors in forward flight. Encouragingly, the results have shown an overall good correlation with recent measurement data, both time-averaged and time-dependent, from the Army's Langley facility. The theory correctly predicts such essential characteristics as fore-to-aft induced-flow gradient, dissymmetric side-to-side induced-flow distribution in forward flight, and saw-tooth, triangular wave form of unsteady inflow associated with the passage of rotor blades. The theory also reveals the significant difference between time-averaged induced flow at points fixed in space and instantaneous induced flow in the blade-fixed rotating system.