On the theory of acoustic flow measurement

Abstract

The motivation for this paper arises from problems frequently encountered in acoustic flow measurement. Of primary concern is that acoustic flow meters, rather than directly measuring the volume flow rate, measure some biased average of fluid velocity in a duct. That is, the average is usually not equal to the volume flow rate divided by the duct cross-sectional area, and is influenced by alterations in the flow profile. In this paper perturbation analysis is used to characterize nontrivial situations under which a sound field may be convected to first order by the unbiased cross-sectionally averaged flow. Perturbation analysis previous to this paper has considered only the plane-wave approach to the problem. This paper will examine the use of higher-order duct modes. It will be shown that under certain circumstances these modes are less prone to distortion by the flow field than the plane wave, and will still average the flow to an approximation which improves with mode order. The study is restricted to the consideration of rectangular section ducts and cylindrical ducts with axisymmetric flow fields. As an aside, the two-dimensional viscous convective wave equation by Mungur and Gladwell [J. Sound Vib. 9, 28–48 (1969)], has been extended to three dimensions in this paper. In deriving this form it was noticed that an error existed in the original equation. This error has been corrected in the present three-dimensional version of the equation.