Neil A. Halliwell

Fluid dynamics of a flow excited resonance, Part II: Flow acoustic interaction

Abstract This is the second of two companion papers in which the physics and detailed fluid dynamics of a flow excited resonance are examined. The approach is rather different from those previously used, in which stability theory has been applied to small wavelike disturbances in a linearly unstable shear layer, with an equivalent source driving the sound field which provides the feedback. In the approach used here, the physics of the flow acoustic interaction is explained in terms of the detailed momentum and energy exchanges occurring inside the fluid . Gross properties of the flow and resonance are described in terms of the parameters necessary to determine the behaviour of the feedback system. In this second paper it is shown that two relatively distinct momentum balances can be considered in the resonator neck region. One can be identified with the vortically induced pressure and velocity fluctuations and the other with the reciprocating potential flow. The fluctuating Coriolis force caused by the interaction of the potential and vortical flows is shown to be the only term in the linearized momentum equation which is not directly balanced by a fluctuating pressure gradient. This force provides the mechanism for the exchange of the mean energies associated with the mean and fluctuating momenta, respectively. A source and sink of energy are identified in which mean energy associated with fluctuating momentum is extracted from and returned to the mean flow, respectively. The imbalance between the source and sink is responsible for both the radiated acoustic power and the power carried away by the vortices as they convect downstream. This radiated acoustic power and vortically convected power, and the source and sink powers, are all of the same order of magnitude. With the vortex shedding and reciprocating potential flow “phase locked” the amplitude of the steady state oscillations is determined by the condition that the net power produced in the resonator neck (the source power less the sink power) is equal to the sum of the radiated acoustic power and that carried by the vortices.

Fluid dynamics of a flow excited resonance, part I: Experiment

This is the first of two companion papers concerned with the physics and detailed fluid dynamics of a flow excited resonance. The phenomenon has been examined by using a rather different approach from others to date, in which usually stability theory has been applied to small wave-like disturbances in an unstable shear layer with an equivalent source to describe the radiation of sound providing the feedback. The physics of the flow acoustic interaction is explained in terms of the detailed momentum and energy exchanges occurring in the fluid itself. Gross properties of the flow and resonance are described in terms of the parameters necessary to determine the behaviour of the self-oscillatory system. In this first paper a full experimental investigation of a flow excited Helmholtz resonator is described, in which the detailed fluid dynamical and acoustic data necessary to develop a mathematical model for the flow was obtained, and a new theory of the interaction process is presented in the companion paper (Part II). The investigation described involved the use of a two-component Laser-Doppler Velocimeter (L.D.V.) and probe microphones to specify completely the velocity and pressure fields and a flow visualization to give qualitative information of the vortex shedding process. The overall aim of the work described in the two papers was to increase fundamental understanding of flow/acoustic interactions.

Laser vibrometry: pseudo-vibrations

The application of Laser Doppler Velocimetry (LDV) to the measurement ofnnormal-to-surface vibration of a solid surface is now established as a techniquencomplementary to the use of an accelerometer. Several practical systems have beenndeveloped and a number are now commercially available. Each velocirneter relies onnthe same principle of operation, namely the detection of a Doppler shift, fD, innthe light scattered from a vibrating target. Fig. 1 shows a typical vibrometernarrangement. Since the photodetector cannot respond quickly enough to detect thenlight frequency directly, scattered light from the vibrating surface is mixednwith a reference beam and heterodyned on the detector surface. In addition, innorder to resolve the sign of the vibration velocity, it is necessary to pre-shiftnthe reference beam by a known amount, fR, resulting in an optical beat at thendetector of frequency (fR ± fD). An appropriate Doppler signal processor thenndemodulates the detector signal to produce a time-resolved analogue of the targetnvibration velocity (in the direction of the incident beam). Systems differ in thenmethod adopted to produce the reference beam frequency shift. Bragg cells [1],ndiffraction gratings [2] rotating scattering discs [3] and frequency modulationnof the laser beam itself [4] have all been used successfully... (continues).

Particle image velocimetry: rapid transparency analysis using optical correlation

Particle image velocimetry (PIV) provides a means of measuring instantaneous 2-D velocity vector fields from a plane of interest within an unsteady flow. The technique was pioneered by Dudderar and Simpkins in 1977 and has since been used to study convection currents, flow around unexcited jets, and more recently breaking wave phenonema. In its simplest form, PIV uses double-exposure photography to record the position of seeding particles contained within a thin sheet of light illuminating a section of the flow. The resulting transparency is divided into a grid of small interrogation regions which are systematically analyzed to obtain the average displacement of the particle images recorded within each region. If the time interval between

Particle image velocimetry: theory of directional ambiguity removal using holographic image separation

On utilise la photographie a exposions multiples pour enregistrer les positions des particules densemencement dans lecoulement a des intervalles de temps donnes

Laser speckle photography and particle image velocimetry: photographic film noise

Laser speckle photography (LSP) applied in fluid mechanics is more appropriately named particle image velocimetry (PIV). Traditional use of holographic films requires the use of high powered pulsed lasers to arrest the flow and record the seeding particle images. If resolution limits are satisfied, the use of more sensitive films can remove this restriction. This paper examines the noise contributed by films used in PIV and LSP and shows that, although sensitive films exhibit high noise levels due to phase distortions, signal-to-noise ratios can be preserved with the use of an index matching liquid gate during analysis of the negative.

The laser vibrometer: A portable instrument

A portable laser vibrometer is described which allows the engineer to simply point a laser beam at a target surface in order to obtain a measure of its vibrational velocity level in amplitude and phase. This non-contacting transducer will complement the accelerometer in situations where use of the latter is precluded: i.e., hot, light or rotating surfaces. The instrument is compact, portable, robust, user friendly, inexpensive and is safe for general on-site use. An investigation of the mechanisms which determine the noise floor is presented and minimization procedures are defined. The first prototype constructed has a dynamic range of 60 dB and a frequency response of 20 kHz, which is adequate for general use. Two applications of use on rotating and lightweight surfaces are reported.

Jet engine liner impedance: An experimental investigation of cavity neck flow/acoustics in the presence of a Mach 0·5 tangential shear flow

In order to develop an accurate prediction method for the acoustic impedance and hence attenuation performance of jet engine liners in flow conditions, it is necessary to understand the detailed flow-acoustic interactions taking place at the liner surface. As a first step, a single cell of a perforate-faced cavity type of liner has been modelled by a rectangular cavity with a rectangular slot mouth set into the wall of the working section of a Mach 0·5 wind tunnel. By using microphones, hot wire anemometry and Laser-Doppler Velocimetry measurements have been made of the acoustically driven flow field in the mouth of the cavity when it is subjected to grazing flow and acoustic excitation in conditions approaching those found in a jet engine liner. (I.e., incident SPL>130 dB, boundary layer turbulence level ≊12%), in order to provide as much information as possible on the sort of pressure and velocity fields to be expected there. The results are discussed in the light of existing theoretical models concerning flow induced impedance changes of cavities. In general it is found that these models are inadequate in explaining phenomena in the real case but that certain features are worthy of further development. In particular the approach taken by Nelson et al. [1,2] in which the measured pressure and velocity fields are modelled as the superposition of those produced separately by the reciprocating potential flow (associated with the acoustic excitation) and the vorticity distribution lends itself most readily to explaining the presented results.

Particle Image Velocimetry: A new approach to fringe analysis

Abstract In recent years there has been a great deal of interest in automatic fringe analysis for Particle Image Velocimetry (PIV). To achieve this it is necessary to measure the wavelength and orientation of Youngs-type fringes which have inherently poor signal-to-noise ratio. Current methods can be classified into two groups. In the first the fringe orientation is found so that the wavelength can be determined using 1 -D algorithms, and in the second 2 -D algorithms are used to measure wavelength and orientation directly. Since the signal-to-noise ratio of PIV fringes is generally poor, full automation of either technique is fraught with difficulties and some interactive control is usually required. In this paper, a new technique is reported which uses the cross-correlation function calculated from two separated lines of data in the fringe pattern. It is shown that an efficient automatic data reduction system can be realised using this approach.

Automatic analysis of Young's fringes in speckle photography and particle-image velocimetry

Abstract Laser-speckle photography (LSP) and particle-image velocimetry (PIV) are two closely related optical techniques for the measurement of two-dimensional in-place displacement. LSP is primarily used for the measurement of solid-surface motion, whereas PIV is used in fluid-flow applications. In both cases, data are obtained from the optical-power spectrum of a double-exposure recording of the moving object by measuring the wavelength and orientation of Youngs-type fringes corresponding to the displacement magnitude and direction, respectively. Typically, in any single experiment, of the order of 10 4 fringe patterns must be analysed, and this would be extremely tedious to perform manually. For this reason, a number of schemes have been reported in the technical literature for automated analysis of Youngs fringes. In this paper, we examine two techniques, 1 -D integration and 2 -D autocorrelation, and discuss their application to LSP and PIV. A unified theoretical model is used to show important differences between the two techniques, and resulting implications with respect to analysis procedures are discussed.