The radiation of sound from a propeller at angle of attack

The mechanism by which the noise generated at the blade passing frequency by a propeller is altered when the propeller axis is at an angle of attack to the freestream is examined. The measured noise field is distinctly non axially symmetric under such conditions with far field sound pressure levels both diminished and increased relative to the axially symmetric values produced with the propeller at zero angle of attack. Attempts have been made to explain this non axially symmetric sound field based on the unsteady (once per rev) loading experienced by the propeller blades when the propeller axis is at non zero angle of attack. A calculation based on this notion appears to greatly underestimate the measured azimuthal asymmetry of noise for high tip speed, highly loaded propellers. A new mechanism is proposed; namely, that at angle of attack, there is a non axially symmetric modulation of the radiative efficiency of the steady loading and thickness noise which is the primary cause of the non axially symmetric sound field at angle of attack for high tip speed, heavily loaded propellers with a large number of blades. A calculation of this effect to first order in the crossflow Mach number (component of freestream Mach number normal to the propeller axis) is carried out and shows much better agreement with measured noise data on the angle of attack effect

Investigation of a Parabolic Iterative Solver for Three-dimensional Configurations

A parabolic iterative solution procedure is investigated that seeks to extend the parabolic approximation used within the internal propagation module of the duct noise propagation and radiation code CDUCT-LaRC. The governing convected Helmholtz equation is split into a set of coupled equations governing propagation in the positive and negative directions. The proposed method utilizes an iterative procedure to solve the coupled equations in an attempt to account for possible reflections from internal bifurcations, impedance discontinuities, and duct terminations. A geometry consistent with the NASA Langley Curved Duct Test Rig is considered and the effects of acoustic treatment and non-anechoic termination are included. Two numerical implementations are studied and preliminary results indicate that improved accuracy in predicted amplitude and phase can be obtained for modes at a cut-off ratio of 1.7. Further predictions for modes at a cut-off ratio of 1.1 show improvement in predicted phase at the expense of increased amplitude error. Possible methods of improvement are suggested based on analytic and numerical analysis. It is hoped that coupling the parabolic iterative approach with less efficient, high fidelity finite element approaches will ultimately provide the capability to perform efficient, higher fidelity acoustic calculations within complex 3-D geometries for impedance eduction and noise propagation and radiation predictions

Quasi Two-Dimensional Flows Through Cascades

The present thesis is an attempt to develop a thin airfoil theory for an airfoil which spans the gap between a pair of stream surfaces which are slowly diverging or converging, the motivation being to predict, theoretically, the effect of varying axial velocity on cascade performance of axial flow compressor rows. The procedure involves, firstly, derivation of approximate equations satisfied by suitably defined average potentials and stream functions in such quasi two-dimensional flows. The flow is assumed to be inviscid, irrotational, and incompressible, but as will be argued later, the quasi two-dimensional type equations also result from less restrictive assumptions. Next, fundamental solutions to these equations, corresponding to bound, line sources and vortices, are found. A distribution of such solutions is used to formulate the airfoil problem, using the condition that the flow be tangential to the airfoil contour. The vorticity distribution appears as the solution to a singular integral equation, which is solved by an approximate method. Simple yet physically realistic assumptions are made concerning the gap width as a function of the streamwise length, to obtain numerical results for the effect of contraction of the stream surfaces. Varying degrees of approximation, later discussed, are used in the calculation procedures. A wide variety of the location and the extent of the contraction, with respect to the airfoil, is investigated. In all cascade calculations the contraction of the stream surfaces was assumed to be in the same direction as the cascade axis. The main conclusions of the thesis can be summarized as below: 1. The theory predicts a lesser circulation round an airfoil in a contracting flow as compared to the circulation round the same airfoil in a plane flow. There is a similar reduction of circulation for a cascade of airfoils. The percentage reduction of circulation is greater for the cascade case as compared to the isolated case, assuming the contractions to be geometrically similar in both cases. The effect on the circulation of contractions, considered physically reasonable in extent and magnitude, either fully upstream or fully downstream of the airfoil, is quite small. 2. As a very rough rule of thumb, it may be stated that the reduction of circulation as compared to the two-dimensional theory, in the range of parameters applicable to compressors, has about the same magnitude as the reduction of gap between the stream surfaces taking place across the airfoil chords. 3. In a comparison with fixed mean angle of attack, the change in flow turning and deviation angles of the flow are much smaller than changes of circulation and may be stated to be of the order of one degree or less for contraction extents and magnitudes considered realistic for compressor cascades.</p

The calculation of sound propagation in nonuniform flows: suppression of instability waves

Acoustic waves propagating through nonuniform flows are subject to convection and refraction. Most noise prediction schemes use a linear wave operator to capture these effects. However, the wave operator can also support instability waves that, for a jet, are the well-known Kelvin-Helmholtz instabilities. These are convective instabilities that can completely overwhelm the acoustic solution downstream of the source location. A general technique to filter out the instability waves is presented. A mathematical analysis is presented that demonstrates that the instabilities are suppressed if a time-harmonic response is assumed, and the governing equations are solved by a direct solver in the frequency domain. Also, a buffer-zone treatment for a nonreflecting boundary condition implementation in the frequency domain is developed. The outgoing waves are damped in the buffer zone simply by adding imaginary values of appropriate sign to the required real frequency of the response. An analytical solution to a one-dimensional model problem, as well as numerical and analytical solutions to a two-dimensional jet instability problem, are provided. They demonstrate the effectiveness, robustness, and simplicity of the present technique