A panel method study of vortex sheets with special emphasis on sheets of axisymmetric geometry

The self induced evolution of a vortex sheet was simulated by modeling the sheet using an integration of discrete elements of vorticity. Replacing small sections of a vortex sheet by flat panels of constant vorticity is found to reproduce more accurately the initial conditions for the Lagrangian simulation technique than replacement by point vortices. The flat panel method for the vortex sheet was then extended to model axisymmetric vortex sheets. The local and far field velocities induced by the axisymmetric panels were obtained using matched asymptotic analysis, and some of the uncertainties involved in other models of the axisymmetric vortex sheet have been eliminated. One important result of this analysis is the determination of the proper choice of core size for a circular vortex filament which may replace a section of an axisymmetric vortex sheet. Roll-up of both two dimensional and axisymmetric vortex sheets was computed using the panel methods developed in the report

Aeroacoustic theory for noncompact wing-gust interaction

Three aeroacoustic models for noncompact wing-gust interaction were developed for subsonic flow. The first is that for a two dimensional (infinite span) wing passing through an oblique gust. The unsteady pressure field was obtained by the Wiener-Hopf technique; the airfoil loading and the associated acoustic field were calculated, respectively, by allowing the field point down on the airfoil surface, or by letting it go to infinity. The second model is a simple spanwise superposition of two dimensional solutions to account for three dimensional acoustic effects of wing rotation (for a helicopter blade, or some other rotating planform) and of finiteness of wing span. A three dimensional theory for a single gust was applied to calculate the acoustic signature in closed form due to blade vortex interaction in helicopters. The third model is that of a quarter infinite plate with side edge through a gust at high subsonic speed. An approximate solution for the three dimensional loading and the associated three dimensional acoustic field in closed form was obtained. The results reflected the acoustic effect of satisfying the correct loading condition at the side edge

The effect of tip vortex structure on helicopter noise due to blade/vortex interaction

A potential cause of helicopter impulsive noise, commonly called blade slap, is the unsteady lift fluctuation on a rotor blade due to interaction with the vortex trailed from another blade. The relationship between vortex structure and the intensity of the acoustic signal is investigated. The analysis is based on a theoretical model for blade/vortex interaction. Unsteady lift on the blades due to blade/vortex interaction is calculated using linear unsteady aerodynamic theory, and expressions are derived for the directivity, frequency spectrum, and transient signal of the radiated noise. An inviscid rollup model is used to calculate the velocity profile in the trailing vortex from the spanwise distribution of blade tip loading. A few cases of tip loading are investigated, and numerical results are presented for the unsteady lift and acoustic signal due to blade/vortex interaction. The intensity of the acoustic signal is shown to be quite sensitive to changes in tip vortex structure

A group-velocity criterion for breakdown of vortex flow: An application to measured inlet profiles

Vortex flows exhibiting breakdown in a slightly divergent duct were measured. The slowly varying vortex flow field downstream of the entrance and upstream of the breakdown region is obtained numerically by using the inviscid quasi-cylindrical approximation. In these calculations, the Faler and Lebovich's experimental data were used as the starting conditions at the entrance of the duct. The group velocity of wave propagation for the axisymmetric mode (n = 0) and the asymmetric modes (n = + or - 1 and n = + or - 2) are calculated for the entrance conditions. For the theoretically predicted slowly varying flow field downstream of the entrance, the wave characteristics of the n = 0 and n = + or - 1 modes are presented. It was concluded that the flows which subsequently undergo vortex breakdown are all predicted to be supercritical and stable to infinitesimal inviscid disturbances, including the axially symmetric as well as the nonsymmetric perturbations

Calculations of axisymmetric vortex sheet roll-up using a panel and a filament model

A method for calculating the self-induced motion of a vortex sheet using discrete vortex elements is presented. Vortex panels and vortex filaments are used to simulate two-dimensional and axisymmetric vortex sheet roll-up. A straight forward application using vortex elements to simulate the motion of a disk of vorticity with an elliptic circulation distribution yields unsatisfactroy results where the vortex elements move in a chaotic manner. The difficulty is assumed to be due to the inability of a finite number of discrete vortex elements to model the singularity at the sheet edge and due to large velocity calculation errors which result from uneven sheet stretching. A model of the inner portion of the spiral is introduced to eliminate the difficulty with the sheet edge singularity. The model replaces the outermost portion of the sheet with a single vortex of equivalent circulation and a number of higher order terms which account for the asymmetry of the spiral. The resulting discrete vortex model is applied to both two-dimensional and axisymmetric sheets. The two-dimensional roll-up is compared to the solution for a semi-infinite sheet with good results

An examination of a group-velocity criterion for the breakdown of an idealized vortex flow

The phenomenon of vortex breakdown is believed to be associated with a finite amplitude wave that has become trapped at the critical or breakdown location. The conditions at which the propagating waves become trapped at a certain axial location were examined by use of a group-velocity criterion implied by Landahl's general theory of wave trapping. An ideal vortex having constant vorticity and uniform axial velocity at the inlet of a slowly diverging duct was studied. The linear wave propagation analysis is applied to the base flow at several axial stations for several values of the ratio of swirl velocity to axial velocity at the inlet of the divergent duct, assuming a locally parallel flow. The dipsersion relations and hence the group velocities of both the symmetric (n = 0) and asymmetric modes (n = + or - 1) were investigated. The existence of a critical state in the flow (at which the group velocity vanishes), and its relationship to the stagnation point on the axis of the duct and to the occurrence of an irregular singularity in the equations governing wave propagation in the flow field are discussed

Prediction of low frequency and impulsive sound radiation from horizontal axis wind turbines

Theoretical models to predict the radiation of low frequency and impulsive sound from horizontal axis wind turbines due to three sources: (1) steady blade loads; (2) unsteady blade loads due to operation in a ground shear; (3) unsteady loads felt by the blades as they cross the tower wake. These models are then used to predict the acoustic output of MOD-1, the large wind turbine operated near Boone, N.C. Predicted acoustic time signals are compared to those actually measured near MOD-1 and good agreement is obtained

The development of a wind tunnel facility for the study of V/STOL noise

August 1972Includes bibliographical references (leaf 12)An open-jet wind tunnel operating within an anechoic chamber was developed for the purpose of the study of V/STOL noise mechanisms. An existing low-speed conventional hard-walled wind tunnel was modified to operate as an open-jet tunnel; an anechoic chamber was then constructed around the test section. The resulting aerodynamic and acoustic characteristics of the tunnel are discussed.Sponsored by ARO Durha

The role of fluctuating forces in the generation of compressor noise

The results of a theoretical and experimental study on the role of aerodynamically-induced fluctuating forces in the sound generation by axial-flow compressors are presented. Analytical models for the generation and radiation of sound by rotor/stator combinations were developed. For the experimental substantiation of the analytical results, the technology was developed to measure fluctuating forces directly on rotating airfoils using miniature differential-pressure sensors and FM telemetry. Under the assumption of full coherence of the force field on the blade, radiated sound power was predicted from the force measurements on blades and compared with measured sound power. Both broadband radiation from a single rotating airfoil and discrete frequency radiation due to interaction of multi-bladed stator/rotor configurations were investigated. The results indicate the necessity to obtain information on the details of the force field for accurate prediction of the radiated sound spectrum

The development of experimental techniques for the study of helicopter rotor noise

The features of existing wind tunnels involved in noise studies are discussed. The acoustic characteristics of the MIT low noise open jet wind tunnel are obtained by employing calibration techniques: one technique is to measure the decay of sound pressure with distance in the far field; the other technique is to utilize a speaker, which was calibrated, as a sound source. The sound pressure level versus frequency was obtained in the wind tunnel chamber and compared with the corresponding calibrated values. Fiberglas board-block units were installed on the chamber interior. The free field was increased significantly after this treatment and the chamber cut-off frequency was reduced to 160 Hz from the original designed 250 Hz. The flow field characteristics of the rotor-tunnel configuration were studied by using flow visualization techniques. The influence of open-jet shear layer on the sound transmission was studied by using an Aeolian tone as the sound source. A dynamometer system was designed to measure the steady and low harmonics of the rotor thrust. A theoretical Mach number scaling formula was developed to scale the rotational noise and blade slap noise data of model rotors to full scale helicopter rotors