Bessel-fourier theory for acoustic propagation in inviscid fluid flow confined by rigid cylindrical waveguide

To theoretically analyze the performance of ultrasonic flow meter for circular pipeline flow, acoustic wave propagation in inviscid fluid confined by the rigid cylindrical waveguide in the presence of axial shear mean flow is investigated. After a detailed review of contributions in the literature, a comprehensive mathematical model of flow acoustics is deduced based on the conservation of mass and momentum where fluid viscosity and thermal conductivity is not considered. Then a novel solution based on the Bessel-Fourier theory, which is orthogonal and complete in Lebesgue Space, is proposed which can transform the second-order differential equation to algebraic equations. For uniform mean flow profile, the simplified solution deduced from the present method is consistent with the contribution in the literature.