Hsiao-Wei D. Chiang

Oscillating aerodynamics and flutter of an aerodynamically detuned cascade in an incompressible flow

A mathematical model is developed and utilized to demonstrate the enhanced torsion mode stability associated with alternate blade circumferential aerodynamic detuning of a rotor operating in an incompressible flow field. The oscillating cascade aerodynamics, including steady loading effects, are determined by developing a complete first order unsteady aerodynamic analysis. An unsteady aerodynamic influence coefficient technique is then utilized, thereby enabling the stability of both conventional uniformly spaced rotors and detuned nonuniform circumferentially spaced rotors to be determined. To demonstrate the enhanced flutter aeroelastic stability associated with this aerodynamic detuning mechanism, this model is applied to a baseline unstable rotor with a Gostelow flow geometry.

UNSTEADY AERODYNAMIC GUST RESPONSE INCLUDING STEADY FLOW SEPARATION

A series of experiments are performed to investigate and quantify the unsteady aerodynamic response of an airfoil to a high reduced frequency gust including the effects of the gust forcing function waveform, airfoil loading and steady flow separation. this is accomplished by using an axial flow research compressor to experimentally model the high reduced frequency gust forcing function and replacing the last stage stator row with isolated instrumented airfoils. Appropriate data are correlated with predictions from flat plate and chambered airfoil convected gust models. The airfoil surface steady loading is shown to have a large effect on the unsteady aerodynamic response. Also the steady flow separation has a significant influence on the gust response, particularly upstream of the separation point and in the airfoil trailing-edge region.

Prediction of loaded airfoil unsteady aerodynamic gust response by a locally analytical method

A complete first-order model is formulated to analyze the effects of steady loading on the incompressible unsteady aerodynamics generated by a two-dimensional gust convected with the steady mean flow past an arbitrary airfoil at finite nonzero angle of attack. A locally analytical solution is then developed in which the discrete algebraic equations which represent the flow field equations are obtained from analytical solutions in individual grid elements. The unsteady flow field is rotational and is linearized about the full potential steady flow past the airfoil. Thus, the effects of airfoil geometry and angle of attack are completely accounted for through the mean potential flow field. The steady flow is independent of the unsteady flow. However, the strong dependence of the unsteady flow on the steady effects of airfoil geometry and finite angle of attack are manifested in the unsteady boundary conditions which are coupled to the steady flow. A body-fitted computational grid is utilized. Analytical solutions to the transformed flow equations in individual grid elements are then developed, with the complete solution obtained by assembling these locally analytical solutions. This model and locally analytical solution are then applied to a series of airfoil and flow configurations. The results demonstrate that accurate predictions for the unsteady aerodynamic gust response are obtained only by including the coupled steady flow effects on the unsteady aerodynamics. Thus for cambered, or cambered and thick airfoils at zero or finite angle of attack, or a thin flat plate airfoil at a nonzero angle of attack, the model and solution developed herein accurately predict the gust response. It was also demonstrated that the classical small perturbation combined transverse and chordwise gust models yield accurate predictions only for the special case of a thin flat plate airfoil at zero angle of attack, i.e. only when the chordwise gust is zero.

Passive Control of Flow Induced Vibrations by Splitter Blades

Splitter blades as a passive control technique for flow induced vibrations is investigated by developing an unsteady aerodynamic model to predict the effect of incorporating splitter blades into the design of an axial flow blade row operating in an incompressible flow field. The splitter blades, positioned circumferentially in the flow passage between two principal blades, introduce aerodynamic and/or combined aerodynamic-structural detuning into the rotor. The unsteady aerodynamic gust response and resulting oscillating cascade unsteady aerodynamics, including steady loading effects, are determined by developing a complete first-order unsteady aerodynamic analysis together with an unsteady aerodynamic influence coefficient technique. The torsion mode flow induced vibrational response of both uniformly spaced tuned rotors and detuned rotors are then predicted by incorporating the unsteady aerodynamic influence coefficients into a single-degree-of-freedom aeroelastic model. This model is then utilized to demonstrate that incorporating splitters into axial flow rotor designs is beneficial with regard to flow induced vibrations. NOMENCLATURE

Aerodynamically forced Response of an Airfoil Including Profile and Incidence Effects

A structural dynamics model is developed and utilized to predict and assess the effects of airfoil thickness, camber, mean flow incidence angle, and two-dimensional gust direction on the aerodynamically induced forced response of an airfoil in an incompressible flow. An energy balance is performed between the unsteady aerodynamic work and the energy dissipated through the airfoil structural and aerodynamic damping. Predictions of the airfoil unsteady aerodynamics are obtained f rom a complete first order model, i.e. the thin airfoil approximation is not applied. It is then demonstra ted that the steady aerodynamic loading on the airfoil and the direction of the gust strongly affect the ampli tude of response. It is also shown tha t the classical thin airfoil unsteady aerodynamic models result in significantly underpredicted airfoil response amplitudes, i.e., the thin airfoil predictions are nonconservative.

Unsteady incompressible aerodynamics and forced response of detuned blade rows

A mathematical model is developed and utilized to demonstrate the enhanced forced response behavior associated with aerodynamic, structural, and combined aerodynamic-structural detuning of a loaded rotor operating in an incompressible flow field. The unsteady aerodynamic gust response and oscillating cascade aerodynamics are determined by developing both a complete first-order unsteady aerodynamic analysis and a locally analytical solution in individual grid elements of a body fitted computational grid. The aerodynamic detuning is accomplished by means of alternate circumferential airfoil spacing, with alternate blade structural detuning also considered. The beneficial forced response effects of these detuning techniques are then demonstrated by applying this model to various detuned rotor configurations.

Locally analytical prediction of the steady inviscid incompressible flow through an airfoil cascade

A mathematical model and locally analytical solution technique are developed to analyze the steady, inviscid, incompressible, flow through a two-dimensional turbomachinery cascade. The velocity potential is separated into circulatory and non-circulatory components, each individually described by a Laplace euation. A body fitted computational grid is utilized. General analytical solutions in the transformed computational plane are determined by separation of variables. The validity of this locally analytical solution and the flow modeling are then demonstrated by correlating predictions with cascade data.

Prediction of the oscillating incompressible aerodynamics of a loaded airfoil cascade by a locally analytical method

A complete first order model is developed to predict the oscillating incompressible aerodynamics of an airfoil cascade, including the effects of steady loading. The cascade steady and unsteady flow fields are analyzed by considering a periodic flow channel. The velocity potential is separated into steady and unsteady harmonic components each of which is described by a Laplace equation. An analytical solution in individual grid elements of a body fitted computational grid is then determined, with the complete solution obtained by assembling these local solutions. The capabilities and validity of this model and solution technique are demonstrated by considering the steady and unsteady aerodynamics of both theoretical and experimental cascade configurations.