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Viscothermal Longitudinal Wave Propagation in Non-Uniform Shear Liquid Flow Confined by Constant Temperature Pipeline and Implications for Ultrasonic Flow Meter

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Viscothermal longitudinal wave propagation in incompressible viscous liquid with non-uniform shear flow confined by rigid pipeline wall of constant temperature is mathematically formulated, which is a set of coupled fourth-order nonlinear differential equations. Based on Bessel-Fourier theory, a general solution in the form of Bessel-Fourier sequences, which are orthogonal and complete in Lebesgue Space, is proposed to transform the fourth-order nonlinear differential equations to a set of homogeneous linear algebraic equations. Then acoustic wave number can be solved using the existence condition of non-trivial solution to the homogeneous linear algebraic equations, leading to the vanishment of the corresponding determinant which can be numerically calculated by various iteration methods. Based on the proposed scheme, phase velocity and attenuation of viscothermal longitudinal wave is numerically analysed in shear flow. In the end, measurement performance of ultrasonic flow meter based on wave propagation is investigated.
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Document Type: Research Article

Publication date: November 1, 2013

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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