Acoustic measurement of boundary layer flow parameters

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Abstract

The principle of an ultrasonic method for measuring the parameters of a boundary layer flow is investigated using a mathematical model of the sound field created by a compact piston in a solid boundary, radiating into a parallel shear flow. The model, based on a wavenumber decomposition of the problem, is used to demonstrate that dispersive effects in the streamwise direction are a function of the free-stream flow velocity and the boundary layer displacement thickness, and that a multifrequency measurement of phase velocity between two wall-mounted transducers can in principle be used to determine these parameters. Results from a preliminary experiment to demonstrate the method are presented.

Introduction

Ultrasonic techniques for measuring flow speed based on a measurement of the convected speed of sound are well established for situations where uniform flow may be assumed over the propagation path, e.g. for fluid flowing in a duct where the measurement is made using the plane wave acoustic mode [1], or for anemometry in the atmosphere [2]. In these cases, sound propagation is non-dispersive and the time of flight of a pulse of sound as it travels from a source transducer to a receiver transducer may be measured unambiguously. Here, we consider a different application, where it is required to measure the free-stream velocity and boundary layer thickness non-invasively for steady flow over a flat boundary. The principle of the method considered here specifically exploits the dispersive behaviour of sound propagating in the non-uniform flow so as to determine the properties of the boundary layer.

A flow-measuring device based on this principle would comprise a source and one or more receiver transducers, flush mounted in the surface, with an electronic system for measuring phase velocity between source and each receiver. By measuring over a distance that is large compared with the thickness of the boundary layer the effect of unsteadiness in the boundary layer flow is averaged out to provide a measurement of the mean parameters.

Some preliminary measurements using a prototype system are described in Section 5 of this paper. Such a system could be useful in determining the characteristics and state of the flow over the wings or fuselage of an aircraft, the hull of a ship or sails of a boat, the aerodynamic surfaces of racing cars, etc., and may be useful for model scale wind tunnel testing or on full-scale vehicles.

Section snippets

Problem outline

The problem of interest for a mathematical model of the measurement device is shown in Fig. 1. A two-dimensional (2D) line or three-dimensional (3D) point source radiates sound into a parallel shear flow, comprising an idealised boundary layer which separates a solid surface at z=0 from a region of uniform flow in the region δ<z<. The model needs to predict the acoustic pressure distribution over the wall, including the phase change between source and receiver, but does not necessarily need to

Characteristics of the radiation impedance and the sound pressure field at the wall

In this section numerical results are presented to illustrate the effects of flow, first on the radiation impedance (Section 3.1) and then on the spatial characteristics of the modulus of the pressure field around a 2D line source (Section 3.2) and a 3D point source (Section 3.3). The phase information in the sound field, which is used for flow measurement, is considered in Section 4.

Measurement of mean velocity in pipe flow

Ultrasonic flow measurement for fluid flowing in pipes is a well-established technique, which is generally based on the concept of a one-dimensional (1D) model of the convected phase velocity of sound propagation in a moving medium [1], [2]. For a plane wave mode propagating in a rigid walled duct carrying a uniform flow, the phase velocity is c0(1+M0) in the downstream direction and c0(1−M0) in the upstream direction. Here, c0 is the speed of sound in stationary fluid and M0 is the Mach number

Experimental validation

This section describes an experiment that was undertaken as a consultancy project to test the concept of measuring mean flow over a surface using ultrasound. The original study was focussed on measurement of the free-stream flow, rather than the boundary layer parameters, so that no independent method of measuring boundary layer thickness was available. The project was carried out collaboratively between ISVR and Gill Electronic R&D and was funded by DERA (now QinetiQ).

Conclusions

A model of sound radiation into a shear flow has been used to predict the phase velocity of sound convected between a source and a downstream receiver. This has been used to demonstrate the principle of a flow-measuring device.

The model shows that an instrument working at a frequency where the boundary layer is thin on the wavelength scale would measure the free-stream Mach number of the flow. For boundary layers greater than one hundredth of a wavelength thick the phase velocity is reduced. It

Acknowledgements

The authors acknowledge the contribution of D. Greenwell, formerly of DERA (now Qinetiq) and now at Bristol University, who initiated and participated in the DERA funded project on which this paper is partly based. They also wish to thank Professor C.L. Morfey, Professor Emeritus at ISVR, who contributed to this work as academic supervisor to M.G. Smith during the course of the project and subsequent studies.

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