Transverse Gust Research Articles

Compressor unsteady aerodynamic response to rotating stall and surge excitations

A series of experiments are performed in an extensively instrumented three-stage axial flow research compressor to investigate the fundamental aeromechanics of compressor flow instabilities, including pure rotating stall, classic surge, and the stable modified surge flow regimes between these two modes. In particular, the flow-induced vibration forcing functions together with the resulting blade row unsteady aerodynamic response generated by these various compressor flow instabilities are measured with a rotating cross hot-wire, with the resulting blade row gust response measured with dynamic pressure transducers embedded in the first-stage rotor blading. The forcing function data are analyzed in terms of the streamwise and transverse gust components and the mean rotor relative velocity, with the unsteady rotor blade row gust response specified by the unsteady lift response to each instability mode. The data show that rotating stall excites a relatively constant rotor blade response, approximately 27% of the steady loading. Surge excites an unsteady response proportional to the level of surge present in the instability mode, thereby increasing as the B parameter increases. However, the absolute level of the response resulting from surge is considerably less than the rotating stall generated response, approximately 37-67%.

Rotor Blade Unsteady Aerodynamic Gust Response to Inlet Guide Vane Wakes

A series of experiments is performed in an extensively instrumented axial flow research compressor to investigate the fundamental flow physics of wake-generated periodic rotor blade row unsteady aerodynamics at realistic values of the reduced frequency. Unique unsteady data are obtained that describe the fundamental unsteady aerodynamic gust interaction phenomena on the first-stage rotor blades of a research axial flow compressor generated by the wakes from the inlet guide vanes. In these experiments, the effects of steady blade aerodynamic loading and the aerodynamic forcing function, including both the transverse and chordwise gust components, and the amplitude of the gusts, are investigated and quantified.

Viscous unsteady gust aerodynamics of a flat plate airfoil by a locally analytical method

A mathematical model is developed to analyze the unsteady viscous transverse gust aerodynamics of a flat plate airfoil in an incompressible laminar flow at moderate values of the Reynolds number. The steady flow is described by the Navier-Stokes equations. The unsteady viscous flow is assumed to be a small perturbation to this steady viscous flow, with the resulting system of linear partial differential equations coupled to the steady flow field through the unsteady boundary conditions. Solutions for both the steady and unsteady viscous flow fields are obtained by developing locally analytical solutions. For the steady flow, this is accomplished by first locally linearizing the nonlinear convective terms in the Navier-Stokes equations. The significant effects of Reynolds number and reduced frequency on the transverse gust generated unsteady aerodynamics on the airfoil are then demonstrated.

Experimental Investigation of Multistage Interaction Gust Aerodynamics

The fundamental flow physics of multistage blade row interactions are experimentally investigated at realistic reduced frequency values. Unique data are obtained that describe the fundamental unsteady aerodynamic interaction phenomena on the stator vanes of a three-stage axial flow research compressor. In these experiments, the effect on vane row unsteady aerodynamics of the following are investigated and quantified: (1) steady vane aerodynamic loading; (2) aerodynamic forcing function waveform, including both the chordwise and transverse gust components; (3) solidity; (4) potential interactions; and (5) isolated airfoil steady flow separation.

Prediction of incidence effects on oscillating airfoil aerodynamics by a locally analytical method

AbstractA complete mathematical model is formulated to analyse the effects of mean flow incidence angle on the unsteady aerodynamics of an oscillating airfoil in an incompressible flow field. A velocity potential formulation is utilized. The steady flow is independent of the unsteady flow field. However, the unsteady flow is coupled to the steady flow field through the boundary conditions on the oscillating airfoil. The numerical solution technique for both the steady and unsteady flow fields is based on a locally analytical method. In this method, analytical solutions are incorporated into the numerical technique, with the discrete algebraic equations which represent the differential flow field equations obtained from analytic solutions in individual local computational grid elements. This flow model and locally analytic numerical solution method are then verified through the excellent correlation obtained with the Theodorsen oscillating flat plate and Sears transverse gust classical solutions. The effects of mean flow incidence on the steady and oscillating airfoil aerodynamics are then investigated.

Forced Response Analysis of an Aerodynamically Detuned Supersonic Turbomachine Rotor

High-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 maldistributions in inlet ducts. In this paper, an analysis is developed to predict the flow-induced forced response behavior 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, due to the convection of the transverse gust past the airfoil cascade and the resulting motion of the cascade, is developed in terms of influence coefficients. This analysis is then utilized to investigate the effect of aerodynamic detuning on the forced response characteristics of a 12-bladed rotor, 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 generally very beneficial, resulting in significantly decreased maximum amplitude blade responses for many interblade phase angles.

The effects of gusts on the fluctuating airloads of airfoils in transonic flow

Unsteady interactions of distributed and sharp-edged gusts with a stationary airfoil have been analyzed in two-dimensional transonic flow.A simple method of introducing such disturbances has been numerically implemented within the framework of unsteady, transonic small-disturbance theory. Representative solutions for various airfoils subjected to chordwise and transverse gusts show that the strength and unsteady motion of the shock wave on the airfoil significantly affect the flowfield development and, consequently, the dynamic airloads. Also a study was made of the reductions in the unsteady airloads that can be achieved by the proper active control motion of a trailing-edge flap, and a simple gust-alleviation strategy was developed. However, the chordwise pressure distributions associated with gusts are very different from those produced by trailing-edge flap oscillations. Consequently, the fluctuating lift and the unsteady pitching moments cannot both be eliminated simultaneously.

Unsteady Pressure on a Cambered Blade Under Periodic Gust

An analysis is given for determining the unsteady pressure on a cambered blade with angle of attack moving through both longitudinal and transverse gusts. The nondimensional unsteady pressure functions are defined for seven combinations of the effects of longitudinal and transverse gusts, angle of attack and camber. Based on these functions, examples of obtained results describing the unsteady pressure distribution on the blade are presented.

SOLUTION OF THE UNSTEADY SUBSONIC THIN AIRFOIL PROBLEM

The problem of a thin airfoil subject to simple harmonic disturbances in a uniform subsonic free stream is solved by extension of a technique developed earlier for a stationary strip vibrating in a uniform fluid. Explicit expressions are given for the lift and moment, acoustic directivity pattern, and total acoustic power for arbitrary upwash and, in particular, for the 'elementary disturbances': plunge, pitch and a stationary transverse gust. Numerical results for a simple skewed gust are presented and compared to the high-frequency asymptotic theory of Martinez and Widnall.

Discrete frequency noise reduction modeling for application to fanjet engines

A model for the generation of discrete frequency noise due to rotor–stator interactions in a fanjet engine is examined to ascertain its relevance to noise reduction studies. Predictions are obtained for the noise reduction between a base fan stage and one redesigned to achieve reduced discrete frequency noise utilizing response functions corresponding to incompressible flow isolated airfoil transverse and longitudinal gust analyses as well as incompressible and compressible flat plate airfoil cascade transverse gust analyses. The correlation of the various predictions with the actual fan test results demonstrated that the viscous wake-generated noise model utilizing the compressible flow cascade response function was the one most appropriate for noise reduction studies of fanjet engines. The significant parameters and their relative importance were then identified by means of a parametric study of the base fan based on the compressible flow cascade response analysis. This study showed that the dominant parameter relevant to discrete frequency noise generation is the interblade phase angle, equal to the ratio of the number of upstream rotor blades to downstream stator vanes. Other parameters of importance included the Mach number, reduced frequency, and vane solidity.

The Time-Variant Aerodynamic Response of a Stator Row Including the Effects of Airfoil Camber

An experimental investigation was conducted to quantitatively determine the validity and applicability of state-of-the-art transverse gust cascade analyses. This was accomplished by obtaining fundamental time-variant forced response data at realistic values of key parameters in a large-scale, low-speed, single-stage research compressor. The forcing function, the velocity defect created by the rotor blade wakes, was measured with a crossed hot-wire probe. The resulting time-variant aerodynamic response was measured by means of flush mounted high response pressure transducers on both flat plate and cambered airfoil stator vane rows over a wide range of incidence angles. These dynamic data were then analyzed to determine the chordwise variation of the unsteady pressure difference in terms of a dimensionless dynamic pressure coefficient and an aerodynamic phase lag referenced to a transverse gust at the leading edge of the vanes. These dimensionless pressure difference data were all correlated with predictions obtained from a state-of-the-art compressible transverse gust, flat plate cascade analysis. Correlation of the classical flat plate unsteady data with the predictions permitted the range of validity of the analysis to be assessed in terms of incidence angle. Correlation of the cambered vane unsteady data with those for the flat plate and with the predictions allowed the effects of airfoil camber as well as the applicability of the flat plate prediction to realistic cambered airfoils to be quantitatively determined.

Rotor Wake Generated Unsteady Aerodynamic Response of a Compressor Stator

An experimental investigation was conducted to determine the fluctuating pressure distribution on a stationary vane row, with the primary source of excitation being the wakes from the upstream rotor blades. This was accomplished in a large scale, low speed, single stage research compressor. The forcing function, the velocity defect created by the rotor wakes, was measured with a crossed hot-wire probe. The aerodynamic response on the vanes was measured by means of flush mounted high response dynamic pressure transducers. The dynamic data were analyzed to determine the chordwise distribution of the dynamic pressure coefficient and aerodynamic phase lag as referenced to a transverse gust at the vane leading edge. Vane suction and pressure surface data as well as the pressure difference across the vane were obtained for reduced frequency values ranging from 3.65 to 16.80 and for an incidence angle range of 35.5 deg. The pressure difference data were correlated with a state-of-the-art aerodynamic cascade transverse gust analysis. The correlation was quite good for all reduced frequency values for small values of incidence. For the more negative incidence angle data points, it was shown that a convected wake phenomena not modeled in the analysis existed. Both the first and second harmonic unsteady pressure differential magnitude data decrease in the chordwise direction. The second harmonic magnitude data attains a value very nearly zero at the vane trailing edge transducer location, while the first harmonic data is still finite, albeit small, at this location. That the magnitude of the unsteady pressure differential data approaches zero near to the trailing edge, particularly the second harmonic data which has reduced frequency values to 16.8, is significant in that it reflects upon the validity of the Kutta condition for unsteady flows.

Lift and Pressure Fluctuations of a Cambered Airfoil Under Periodic Gusts and Applications in Turbomachinery

Previous authors have considered the unsteady lift of a flat-plate (zero-cambered) airfoil travelling through sinusoidal gusts. The present paper extends the analysis to cambered airfoils with angle of attack moving through both longitudinal and transverse gusts. Closed-form analytical solutions are obtained. The results are used to calculate the unsteady lift on a blade moving through periodic wakes in an axial-flow turbomachine. Knowledge gained by this analysis clearly indicates design trends to obtain minimum lift fluctuations. Since the interference effects of neighboring blades are ignored in this analysis, the conclusions on turbomachinery are strictly valid only for cascades with low solidity.