Fourier–Bessel theory on flow acoustics in inviscid shear pipeline fluid flow

•A new wave equation is mathematically formulated based on potential theory.•A new solution based on Fourier–Bessel theory is proposed.•Calculation procedure of axial wave number is given.•Wave propagation in laminar and turbulent flow is numerically analyzed.

Flow acoustics in pipeline is of considerable interest in both industrial application and scientific research. While well-known analytical solutions exist for stationary and uniform mean flow, only numerical solutions exist for shear mean flow. Based on potential theory, a general mathematical formulation of flow acoustics in inviscid fluid with shear mean flow is deduced, resulting in a set of two second-order differential equations. According to Fourier–Bessel theory which is orthogonal and complete in Lebesgue Space, a solution is proposed to transform the differential equations to linear homogeneous algebraic equations. Consequently, the axial wave number is numerically calculated due to the existence condition of non-trivial solution to homogeneous linear algebraic equations, leading to the vanishment of the corresponding determinant. Based on the proposed method, wave propagation in laminar and turbulent flow is numerically analyzed.