Study of thermoviscous dissipation on axisymmetric wave propagating in a shear pipeline flow confined by rigid wall. Part I. theoretical formulation

Abstract

Axisymmetric acoustic wave propagation in a shear pipeline flow confined by a rigid wall is studied in the two-part paper. The effects of viscous friction and thermal conduction on the acoustic wave propagating in the liquid and perfect gas are respectively analyzed under different configurations of acoustic frequency and shear flow profile. In Part 1 of this paper, mathematical models of non-isentropic and isentropic acoustic waves are formulated based on the conservation of mass, momentum and energy for both liquid and perfect gas. Meanwhile, comprehensive solutions based on the Fourier-Bessel theory are provided, which gives a general methodology of iteratively calculating features of the acoustic wave. Numerical comparisons with previous simplified models verify the validity of the proposed models and solutions.