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Abstract
The problem of scattering of airborne sound by a dynamically rough surface of a turbulent, open channel flow is poorly understood. In this work, a laser-induced fluorescence (LIF) technique is used to capture accurately a representative number of the instantaneous elevations of the dynamically rough surface of 6 turbulent, subcritical flows in a rectangular flume with Reynolds numbers of 10,800⩽Re⩽47,300 and Froude numbers of 0.36⩽Fr⩽0.69. The surface elevation data were then used in a finite difference time domain (FDTD) model to predict the directivity pattern of the airborne sound pressure scattered by the dynamically rough flow surface. The predictions obtained with the FDTD model were compared against the sound pressure data measured in the flume and against that obtained with the Kirchhoff approximation. It is shown that the FDTD model agrees with the measured data within 22.3%. The agreement between the FDTD model and stationary phase approximation based on Kirchhoff integral is within 3%. The novelty of this work is in the direct use of the LIF data and FDTD model to predict the directivity pattern of the airborne sound pressure scattered by the flow surface. This work is aimed to inform the design of acoustic instrumentation for non-invasive measurements of hydraulic processes in rivers and in partially filled pipes.
Highlights
Turbulent, depth-limited flows such as those in natural rivers and urban drainage systems always have patterns of waves on the air/water boundary which carry information about the mean flow velocity, depth, turbulent mixing and energy losses within that flow
The mean amplitude of the sound pressure calculated for the 500 surface realisations with the proposed finite differences time domain modelling (FDTD) method (Section 3.1) was compared against that predicted with the stationary phase approximation
In the stationary wave approximation we used the values of the mean roughness height listed in Table 2 and the absolute value of the sound pressure, jp0ðRÞj, predicted with the FDTD method for the flat, perfectly reflecting surface, which were substituted into Eq (4) to determine jpK ðRÞj
Summary
Depth-limited flows such as those in natural rivers and urban drainage systems always have patterns of waves on the air/water boundary which carry information about the mean flow velocity, depth, turbulent mixing and energy losses within that flow Monitoring of these flows is vital to predict accurately the timing and extend of floods, manage natural water resources, operate efficiently and safely waste water processing plants and manage underground sewer networks. It is impossible to measure remotely and in-situ the flow mixing ability, turbulence kinetic energy, Reynolds stress, sediment erosion rates and the volume fraction of suspended/transported sediment These characteristics are essential to calibrate accurately the existing and new computational fluid dynamics models, implement efficient real time control algorithms, forecast flooding and to estimate the potential impact of climate change on water infrastructure and the environment. The widely used particle image velocimetry [2] or LiDAR methods are notoriously expensive and difficult to set up, calibrate and make work to cover a representative area of flow either in the laboratory [3] or in the field [4]
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