A mathematical model is developed to predict the enhanced coupled bending-torsion unstalled supersonic flutter stability due to alternate circumferential spacing aerodynamic detuning of a turbomachine rotor. The translational and torsional unsteady aerodynamic coefficients are developed in terms of influence coefficients, with the coupled bending-torsion stability analysis developed by considering the coupled equations of motion together with the unsteady aerodynamic loading. The effect of this aerodynamic detuning on coupled bending-torsion unstalled supersonic flutter as well as the verification of the modeling are then demonstrated by considering an unstable twelve-bladed rotor, with Verdon’s uniformly spaced Cascade B flow geometry as a baseline. It was found that with the elastic axis and center of gravity at or forward of the airfoil midchord, 10 percent aerodynamic detuning results in a lower critical reduced frequency value as compared to the baseline rotor, thereby demonstrating the aerodynamic detuning stability enhancement. However, with the elastic axis and center of gravity at 60 percent of the chord, this type of aerodynamic detuning has a minimal effect on stability. For both uniform and nonuniform circumferentially spaced rotors, a single degree of freedom torsion mode analysis was shown to be appropriate for values of the bending-torsion natural frequency ratio lower than 0.6 and higher than 1.2. However, for values of this natural frequency ratio between 0.6 and 1.2, a coupled flutter stability analysis is required. When the elastic axis and center of gravity are not coincident, the effect of detuning on cascade stability was found to be very sensitive to the location of the center of gravity with respect to the elastic axis. In addition, it was determined that when the center of gravity was forward of an elastic axis located at midchord, a single degree of freedom torsion model did not accurately predict cascade stability.

A new, and as yet unexplored, approach to passive flutter control is aerodynamic detuning, defined as designed passage-to-passage differences in the unsteady aerodynamic flow field of a rotor blade row. Thus, aerodynamic detuning directly affects the fundamental driving mechanism for flutter, i.e., the unsteady aerodynamic forces and moments acting on individual rotor blades. In this paper, a model to demonstrate the enhanced supersonic unstalled aeroelastic stability associated with aerodynamic detuning is developed. The stability of an aerodynamically detuned cascade operating in a supersonic inlet flow field with a subsonic leading edge locus is analyzed, with the aerodynamic detuning accomplished by means of nonuniform circumferential spacing of adjacent rotor blades. The unsteady aerodynamic forces and moments on the blading are defined in terms of influence coefficients in a manner that permits the stability of both a conventional uniformly spaced rotor configuration as well as the detuned nonuniform circumferentially spaced rotor to be determined. With Verdon’s uniformly spaced Cascade B as a baseline, this analysis is then utilized to demonstrate the potential enhanced aeroelastic stability associated with this particular type of aerodynamic detuning.

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A full potential steady flow solver (SFLOW) developed explicitly for use with an inviscid unsteady aerodynamic analysis (LINFLO) is described herein. The steady solver uses the nonconservative form of the nonlinear potential flow equations together with an implicit, least-squares, finite-difference approximation to solve for the steady flow field. The difference equations were developed on a composite mesh which consists of a C-grid embedded in a rectilinear (H-grid) cascade mesh. The composite mesh is capable of resolving blade-to-blade and far-field phenomena on the H-grid, while accurately resolving local phenomena on the C-grid. The resulting system of algebraic equations is arranged in matrix form using a sparse matrix package and solved by Newton's method.Steady and unsteady results are presented for two cascade configurations: a high-speed compressor and a turbine with high exit Mach number.

SUMMARYHigh-performance aircraft-engine fan and compressor blades are vulnerable to aerodynamically forced vibrations generated by inlet flow distortions due to wakes from upstream blade and vane rows, atmospheric gusts, and maldistribu tions in inlet ducts. In this report, an analysis is developed to predict the flow-induced forced response of an aerodynamically detuned rotor operating in a supersonic flow with a subsonic axial component. The aerodynamic detuning is achieved by alternating the circumferential spacing of adjacent rotor blades. The total unsteady aerodynamic loading acting on the blading, as a result of the convection of the transverse gust past the airfoil cascade and the result ing motion of the cascade, Is developed in terms of infl.uence coefficients. This analysis is used to investigate the effect of aerodynamic detuning on the forced response of a 12-blade rotori with Verdon's Cascade B flow geometry as a uniformly spaced baseline configuration. The results of this study indicate that, for forward-traveling wave gust excitations, aerodynamic detuning is very 0 beneficial, resulting in significantly decreased maximum-amplitude blade i responses for many interblade phase angles.