Perturbation theory applied to sound propagation in flowing media confined by a cylindrical waveguide

First-order perturbation theory is employed to examine sound propagation in flowing media confined by a cylindrical waveguide. The use of perturbation theory allows examination of mode phase-speed changes due to any radially dependent flow w(r) as long as the flow magnitude is sufficiently small. The condition to be fulfilled is satisfied in the flow range: 0-0.3 m/s for the specific values of cylinder radius, ultrasound frequency, and sound speed analyzed in the present work [in the general case, however, the condition in Eq. (1) of the present work must be fulfilled]. This freedom of choice, i.e., the possibility to handle any radial flow profile, is used to analyze two flow profile cases: (1) where w(r) is a linear combination of a laminar flow profile and a flat profile corresponding to turbulent flow, and (2) where w(r) is a linear combination of a laminar flow profile and a more realistic logarithmic-dependent turbulent flow profile. In both cases, it is shown that large errors may result in ultrasound flow measurements if several modes are excited by the transmitting transducer, and that a logarithmic flow profile in the turbulent regime leads to somewhat larger measurement errors at high flow values as compared to assuming a simple flat profile in the turbulent regime.