The interaction of sound with turbulent flow

Abstract

Introduction: In the now classical theory of sound from turbulent flow by Lighthill boundaries were not considered. Further, it was assumed that the turbulent flow field was not altered by sound emission. For closed systems, such as cavities and waveguides, discrete modes may be excited. It is possible that the coupling between the flow field and acoustic modes is strong enough to alter the primary flow field. Under such conditions acoustically induced flow instabilities such as whistles occur. The objective of this thesis is to study the turbulent excitation of duct modes and the conditions for possible instabilities. Chapter One reviews the theory of turbulent excitation of sound in free space. The induced acoustic field is calculated in three ways. The sound field is determined by time-domain Green's function technique for both Lighthill's quadrupole source model and Ribner's equivalent distribution of monopoles.

The omission of turbulent shear interactions in an isotropic monopole model of the turbulence is demonstrated. The sound field is also determined by a frequency-domain Green's function technique for a monopole distribution. Time and frequency domain calculations yield identical results for the monopole source distribution. However, the frequency domain technique allows the analysis to be extended to Chapter Two examines the excitation of axial pipe modes by turbulent flow theoretically and experimentally. The experiment is performed by drawing air through a cylindrical pipe. The observations demonstrate that mode excitation diminishes as the flow speed increases. This is attributed to end losses which increase with flow speed. A Green's function, based on the measured pressure reflection coefficients, is used to predict the variation in spectra with flow. Chapter Three demonstrates the excitation of transverse modes in pipes experimentally.

Air is drawn through a small orifice into a rectangular duct. Pronounced asymmetric peaks are observed at the first few cutoff frequencies. The asymmetric nature of the peaks and relative spectral intensity are again explained by Green's function techniques. For high frequencies, where a large number of modes can propagate, the spectra resembles the free-space jet spectra. In this frequency range, the duct radiation impedance asymptotically approaches the free space impedance, hence the similar response to similar source distributions. Chapter Four examines feedback instabilities, cases where the emitted sound field alters the jet flow itself. The chapter concentrates on screech tones of circular orifices having length to diameter ratios between one half and two. The frequency dependence of the screech on Mach number and length is explained by a kinematic analysis of the feedback loop.

It is further demonstrated that the frequency of the feedback instability must be approximately equal to that of an acoustic made for screech to occur. Similar observations are presented with regard to air jets impinging on plates. In conclusion two mechanisms exist whereby the acoustic energy from a turbulent jet can be concentrated at select frequencies. The first is the selective response of a medium with boundaries to a random source. The spectral line shape for such cases is accounted for by Green's function techniques. The second mechanism is the feedback instability which requires coupling of the jet flow to the acoustic field. Here the modification of the jet flow must be considered to determine the excitation frequencies. It is recommended that future work be done on the screech instability. The influence of the acoustic cavity mode on the feedback instability should be examined in greater detail.

In particular, the convection speed of jet column disturbances with and without adjacent resonators should be determined experimentally. Furthermore, the mechanism which limits the amplitude of the screech should be determined.