Effects Of Steady Loading Research Articles

Combined/Simultaneous Gust and Oscillating Compressor Blade Unsteady Aerodynamics

Experiments are performed in a three-stage axial flow research compressor to investigate and quantify the simultaneous/combined gust- and motion-induced unsteady aerodynamic response of the first-stage rotor blades of thecompressor. The gust-response unsteady aerodynamics are experimentally modeled with a 2 per revolution forcing function. The torsion mode unsteady aerodynamics is investigated utilizing an experimental influence coefficient technique in conjunction with a unique drive system. Combined gust and oscillating unsteady aerodynamics are obtained by the superposition of the oscillating blade row and the gust-response unsteady aerodynamics. Simultaneous gust- and motion-induced unsteady aerodynamic responses are obtained by driving the torsion mode oscillation in the presence of the 2 per revolution forcing function. The effects of steady loading are quantified. Airfoil oscillation amplitude effects are also studied. The combined unsteady aerodynamics establishes superposition limitations at high oscillation amplitudes and high loading. In addition, the gust-blade motion phase angle is identified as a key parameter.

Incidence Effects on Chordwise Bending Cascade Unsteady Aerodynamics

Experiments directed at investigating and quantifying the effects of off-design conditions, including mean flow incidence and leading-edge flow separation, on chordwise bending mode unsteady aerodynamics are described. An n influence coefficient technique is used wherein a single airfoil in the cascade is oscillated in a chordwise bending mode, accomplished with a piezoelectric crystal-based drive system. The resulting unsteady surface pressures on the oscillating airfoil and its stationary neighbors are measured and the unsteady aerodynamic influence coefficients determined, with the cascade unsteady aerodynamics defined through a vector summation. Unsteady aerodynamic data are obtained over a range of reduced frequency values and mean flow incidence angles, with the effects of steady loading and leading-edge separation examined. Significant effects of mean incidence on cascade unsteady aerodynamics that deviate significantly from linearized theory occur near the leading edge, with the nonlinear region increasing with increasing mean incidence. The large-scale effects of mean incidence on the leading-edge unsteady aerodynamic loading are attributable to both steady loading and suction surface separation

Passive Control of Flow-Induced Vibrations by Splitter Blades

Splitter blades as a passive control technique for flow-induced vibrations are 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 aero-elastic model. This model is then utilized to demonstrate that incorporating splitters into axial flow rotor designs is beneficial with regard to flow induced vibrations.

Forcing function generator fluid dynamic effects on compressor blade gust response

To investigate the fundamental flow forcing function phenomena generating different blade row gust responses, in particular attached and separated flow forcing functions, a series of experiments are performed in an extensively instrumented axial flow research compressor. In these experiments, the gust ratio magnitude is controlled without affecting the forcing function fluid dynamics, i.e., attached or separated flow, thereby enabling a controlled study of the effect of steady loading. Periodic 2-E unsteady aerodynamic forcing functions to the first stage rotor are generated by fundamentally equivalent honeycomb sections and flat plate airfoils, with unsteady linear theory gust requirements considered. Then the resulting rotor blade row gust response is measured over a range of steady loading levels and the gust response data correlated with the appropriate linear theory predictions. These experiments show that the forcing function generator fluid dynamics is significant with regard to the resulting unsteady aerodynamic gust response. Also demonstrated is the decreased correlation of the gust response data with linear theory predictions as the steady loading is increased.

Turbine Rotor Generated Forcing Functions for Flow Induced Vibrations

A series of experiments are performed to investigate the effect of steady loading on the unsteady aerodynamic gust forcing functions generated by turbine rotor blade rows and the validity of the vortical and potential gust splitting techniques. Both the downstream vortical-potential gusts and, for the first time, the upstream generated potential gust are considered. Note that these upstream gusts are in fact the potential field of the rotor and not the nozzle wakes. This is accomplished by measuring the downstream and upstream unsteady forcing functions generated by the first stage rotor of the low speed research turbine over a range of steady loading levels. These forcing functions are then split into vortical and potential gusts utilizing both the V-Method using only velocity data and the P-Method which also incorporates unsteady static pressure data. The results clearly show an increase in potential effects for the downstream gust forcing functions with increased blade loading. The rotor blade gusts upstream of the first rotor are theoretically purely potential gusts since no vorticity can be conducted upstream. These potential disturbances do not appear to be a function of the blade loading. The results of the linear theory splitting show that both splitting methods have discrepancies in their recombined forcing functions. The V-Method either under or over estimates the unsteady static pressure and has trouble duplicating the phase. The P-Method tends to skew the recombined velocity in the lift force direction. The upstream potential gusts posed a particular problem for the splitting, with neither method able to fully reconcile the measured pressure and velocity perturbations.Copyright © 1994 by ASME

Flutter control of incompressible flow turbomachine blade rows by splitter blades

Splitter blades as a passive flutter control technique is investigated by developing a mathematical model to predict the stability of an aerodynamically loaded splittered-rotor 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 two-dimensional 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 flutter of both uniformly spaced tuned rotors and detuned rotors are predicted by incorporating the unsteady aerodyamic influence coefficients into a single-degree-of-freedom aeroelastic model. This model is then utilized to demonstrate that incorporating splitters into unstable rotor configurations results in stable splittered-rotor configurations.

The Effect of Steady Aerodynamic Loading on the Flutter Stability of Turbomachinery Blading

An aeroelastic analysis is presented that accounts for the effect of steady aerodynamic loading on the aeroelastic stability of a cascade of compressor blades. The aeroelastic model is a two-degree-of-freedom model having bending and torsional displacements. A linearized unsteady potential flow theory is used to determine the unsteady aerodynamic response coefficients for the aeroelastic analysis. The steady aerodynamic loading was caused by the addition of (1) airfoil thickness and camber and (2) steady flow incidence. The importance of steady loading on the airfoil unsteady pressure distribution is demonstrated. Additionally, the effect of the steady loading on the tuned flutter behavior and flutter boundaries indicates that neglecting either airfoil thickness, camber, or incidence could result in nonconservative estimates of flutter behavior.

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.

Cascade aerodynamic gust response including steady loading effects

AbstractTo predict the unsteady convected gust aerodynamic response of a cascade comprised of arbitrary thick and cambered aerofoils in an incompressible, inviscid, flow field, a complete first‐order model is formulated. The flow is analysed by considering a periodic flow channel. The velocity potential is separated into steady and unsteady harmonic components, each described by a Laplace equation. The strong dependence of the unsteady aerodynamics on the steady effects of aerofoil and cascade geometry and incidence angle is manifested in the coupling of the unsteady and steady flow fields through the unsteady boundary conditions. Analytical solutions in individual grid elements of a body‐fitted computational grid are then determined, with the complete solution obtained by assembly of these local solutions. The validity and capabilities of this model and solution technique are then demonstrated by analysing the steady and unsteady aerodynamics of both theoretical and experimental cascade configurations.

Wake-induced unsteady aerodynamic interactions in a multistage compressor

The effects of steady loading and the detailed aerodynamic forcing function on airfoil row unsteady aerodynamics are investigated and quantified at high reduced frequency values. For the first time, both parallel and normal gust components of the forcing function are considered. This is accomplished by a series of experiments that quantify the unsteady aerodynamics of the first stage vane row of a research compressor. The effects of steady vane aerodynamic loading with both nonconstant and constant aerodynamic forcing functions are quantified. These data show that the steady loading affects only the magnitude of the complex dynamic pressure coefficient, whereas the ratios of the maximum amplitudes of the parallel and normal components of the aerodynamic forcing function affect both the magnitude and the phase lag. The relative effects of the two components of the time-variant inlet velocity field on the resulting vane row unsteady aerodynamics are also investigated, showing that the parallel component of the aerodynamic forcing function affects only the dynamic pressure coefficient phase lag. The correlation of the dynamic pressure coefficient data with flat plate predictions is also considered. The level and chordwise distribution of the steady aerodynamic loading, not the incidence angle, are revealed to be the key parameters to obtain good correlation with such mathematical models.

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 developed in which the discrete algebraic equations which represent the flow field equations are obtained from analytical solutions in individual grid elements. This model and locally analytical solution are then applied to a series of airfoil and flow configurations.

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.

Unsteady Flow through a Cascade of Airfoils with Steady Loading

Incompressible potential flow through a cascade of staggered thin airfoils with steady loading in general, unsteady, in-phase motion is considered. With the assumptions of the Kutta condition and linearized wakes, exact analytical expressions are derived for pressure distribution, lift and moment, using conformal mapping applied to the velocity field. Mean attack angle and parabolic camber are considerd to give steady loading, and then the results are expressed in closed-form as quadratures, and reduce to the well-known relations for thin airfoil theory, as the solidity decreases to zero. Typical results are given in the figures. They should serve as a measure of the accuracy of numerical or approximate solutions, as well as representing in a simple way the effects of steady loading, stagger and solidity on unsteady cascade aerodynamics.