SOUND PROPAGATION IN A MOVING FLUID CONFINED BY CYLINDRICAL WALLS—A COMPARISON BETWEEN AN EXACT ANALYSIS AND THE LOCAL-PLANE-WAVE APPROXIMATION
✍ Scribed by M. WILLATZEN
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 301 KB
- Volume
- 247
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
A discussion of sound propagation in a moving #uid con"ned by cylindrical walls is presented. Based on the continuity equation and the Euler equation, a single &&exact'' ordinary di!erential equation in the acoustic pressure is derived for the case where the medium #ow v (r) depends on the radial co-ordinate only and points in the axial direction. This &&exact'' pressure wave equation is solved semi-analytically by means of the Frobenius method and compared with the conventional approximative wave equation known as the local-plane-wave (LPW) approximation for a range of #ow values. In this way, information about mode phase-speed changes with #ow and #ow-meter performance is obtained. It is found that the LPW approximation works well only for mode propagation parallel or nearly parallel to the direction of #ow. Based on the &&exact'' acoustic pressure wave equation, it is also concluded that #ow-meter errors become independent of ultrasound frequency and cylinder radius, a point that the LPW approximation fails to predict. Furthermore, an &&exact'' procedure shows that #ow-meter errors depend on the Reynolds number and the mode number only. In actual fact, it is found that #ow measurement based on the fundamental mode is approximately free of errors while all other modes are characterized by the same (and, generally, non-vanishing) deviation of measurement.
2001 Academic Press