C.L. Morfey

Acoustic energy in non-uniform flows

Abstract The concept of acoustic energy is extended to non-uniform fluid flows. In general, the resulting energy balance equation exhibits acoustic energy production or dissipation within the flow, but in an important special case the production term is zero, implying conservation of acoustic energy. The acoustic energy equations used in classical and geometric acoustics are recovered from the general formulation by making the appropriate assumptions.

Sound transmission and generation in ducts with flow

Abstract Sound generation in hard-walled ducts with flow is treated theoretically. Axial standing waves are allowed for in the theoretical model, by applying an impedance boundary condition at the ends of the duct. The results show the effects of axial and swirling flow on the radiated sound power, for different types of source contained in the duct. Suggestions are also put forward for analysing the generation of sound by sources at a mean-flow discontinuity.

Amplification of aerodynamic noise by convected flow inhomogeneities

Lighthills acoustic analogy is used to study the sound radiated from free flows without dissipation, in the limit as the sound speed tends to infinity. If the flow is of non-uniform density, the most efficient source is not the velocity quadrupole term discussed by Lighthill, but a dipole-order term whose radiated intensity scales on the sixth power of velocity. The physical mechanism is the same as that described by Rayleigh, in his work on sound scattering.

Developments in jet noise modelling—theoretical predictions and comparisons with measured data

Abstract Spectral information on the sound radiated from turbulent shock-free jets is now available over a wide range of Strouhal numbers, for jet densities ranging from 0·3 to 2 times the ambient density and jet velocities ranging from 0·3 to 2 times the ambient sound speed. In order to account for some of the trends observed, a jet noise model is developed which takes account of acoustic-mean flow interaction. The model is based on a shear flow analogy, for which the governing equation is Lilleys equation, and numerical solutions are obtained for sources representative of turbulent mixing noise. Analytic solutions developed for low- and high-frequency excitation show good agreement with the numerical results. Finally, the model predictions are compared with measurements on hot and isothermal jets.

Sound radiation from a point force in circular motion

Abstract This paper is a theoretical study of sound radiation from a time-varying point force in accelerative motion, where the acceleration arises from steady rotation in a circle. The study is prompted by the question of whether such effects are significant in fan or helicopter rotor noise at subsonic tip speeds. Closed-form expressions are found for the overall radiation at a point in the far field, and for the radiated sound power, showing the acceleration effect as an additive term in each case. The effect of rotation on the broad-band far-field spectrum is demonstrated by a series expansion for rotational frequencies small compared with the radiated frequency.

New scaling laws for hot and cold jet mixing noise based on a geometric acoustics model

Abstract New scaling laws are presented for hot turbulent jet mixing noise outside the cone of silence. These account for mean flow field effects on sound radiation via an analytical high frequency approximate solution to Lilleys equation. Numerical calculations for sound radiation from sources in a cylindrical shear flow are used to test the validity of the approximation. The proposed scaling laws yield an excellent collapse of jet noise measurements over a wide range of conditions. The resulting information has been incorporated into a jet mixing noise prediction scheme which, with appropriate modifications to the analytical high frequency approximation, can be applied both inside and outside the cone of silence. The prediction scheme for angles inside the cone of silence will be described in a subsequent paper.

Rotating blades and aerodynamic sound

The history of research on rotating blade noise is reviewed, from early studies of propeller radiation to current work on aircraft-engine fans. The survey is selective, with emphasis on fundamental aspects of aerodynamic sound generation by blades. The topics covered include the following: early research on propeller noise, unsteady airfoil theory, acoustic radiation and cut-off, aerodynamic sound generation, scattering by airfoils at arbitrary chord/wavelength ratios, boundary layer and vortex shedding noise from isolated rotors, rotor/tip-vortex interaction, interaction between moving blade rows, sound transmission through blade rows, the instantaneous Kutta condition, supersonic rotor noise, in-duct measurement techniques, and centrifugal flow machines.

Multimode radiation from an unflanged, semi-infinite circular duct

Theoretical expressions for sound radiation from a single incident duct mode, arriving at the open end of a semi-infinite circular unflanged duct with rigid walls, are used to obtain numerical results for (1) the single-mode sound power transmission coefficient, and (2) the multimode far-field directivity factor. For the multimode calculations the modes are assumed incoherent, and a weighting model is adopted which includes, as special cases, equal power per mode (above cutoff), and excitation by incoherent monopoles or axial dipoles uniformly distributed over a duct cross section. High-frequency asymptotic features of the results are explored in detail and analytical approximations are given. The findings have practical application to sound power measurement from tall exhaust stacks.

Multi-mode sound transmission in ducts with flow

Abstract Exhaust mufflers, large exhaust stacks, and turbofan engines are common examples of ducted noise. The most useful measure of the sound produced by these noise sources is the sound power transmitted along the duct. When airflow is present, sound power flow can no longer be uniquely determined from the usual measurements of acoustic pressure and particle velocity. One approach to sound power determination from in-duct pressure measurement, and the one discussed in this paper, is to predict the relationship between the sound power and pressure based upon an assumed mode amplitude distribution. This paper investigates the relationship between acoustic pressure and power for a family of idealized source distributions of arbitrary temporal and spatial order. Incoherent monopole and dipole sources uniformly distributed over a duct cross-section can be obtained as special cases. This paper covers the sensitivity of the pressure–power relationship to source multipole order, frequency and, in particular, flow speed. It is shown that the introduction of flow in a hard-walled duct can have a substantial effect on the behavior of the pressure–power relationship for certain source distributions. Preliminary experimental results in a no-flow facility are presented in order to verify some of the main results.

A note on the radiation efficiency of acoustic duct modes

Abstract Graphs are presented for the radiation efficiency of higher-order acoustic modes in a baffled annular opening. The variation of radiation efficiency with frequency is generalized in terms of mode cut-off.