Dynamically Rough Boundary Scattering Effect on a Propagating Continuous Acoustical Wave in a Circular Pipe with Flow.

Anna Romanova,Anton Krynkin,Kirill Horoshenkov

doi:10.3390/s18041098

Anna Romanova, Anton Krynkin + Show 1 more

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https://doi.org/10.3390/s18041098

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Abstract

The pattern of the free surface of the turbulent flow in a partially filled circular pipe contains information on the underlying hydraulic processes. However, the roughness of the free surface of flow and its temporal variation in a pipe is a dynamic and non-stationary process that is difficult to measure directly. This work examines a new acoustic method that is used to study the characteristics of the free surface roughness under controlled laboratory conditions. The acoustic method makes use of a continuous sine wave that is transmitted through the air above the turbulent flow of water over a section of the pipe instrumented with an array of wave probes and microphones. The results obtained for a representative range of flow regimes and variety of pipe bed conditions illustrate that it is possible to unambiguously relate variations in the recorded acoustic field to the standard deviation in the free surface roughness and mean flow depth. These variations are clearly linked to the hydraulic friction factor of the pipe, which is shown to be related to airborne acoustic data obtained non-invasively.

Highlights

There is a general lack of evidence on the relationship between the airborne acoustic field in a partially filled pipe and the behaviour of the free water surface of the hydraulic flow in the presence of discrete bed roughness
A simple theoretical way to account for the flow surface roughness in a partly filled pipe is to introduce the notion of the eigenvalue correction (ξ 0,2 ) to the acoustic wavenumber (k = ω0 /c) in the airborne section of the pipe affected by the roughness of the dynamic surface, (ω0 ) being the angular frequency and (c) is the sound speed in air
Lw is the flow free surface width measured across the pipe, Pa is the perimeter of the dry section of the pipe, Sa is the dry cross-sectional area of the pipe and S p is the cross section of the whole pipe

Summary

Introduction

There is a general lack of evidence on the relationship between the airborne acoustic field in a partially filled pipe and the behaviour of the free water surface of the hydraulic flow in the presence of discrete bed roughness. Theories exist for sound propagation in the presence of a rough boundary [1,2,3,4,5], but not for a partially filled round pipe in which the flow surface is dynamically rough. We consider the case, when: (i) the acoustic wavelength (λ) is sufficiently large compared to the diameter of the pipe (d = 2Rc , Rc being the pipe radius); and (ii) the mean roughness height (σh ) is much smaller than the acoustic wavelength.

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