ACOUSTIC RESONANCES IN THE PRESENCE OF RADIAL FINS IN CIRCULAR CYLINDRICAL WAVE-GUIDES

This paper presents a method, based on matched eigenfunction expansion s, for the determination of the frequencies of the acoustic resonances that can occur in a circular cylindrical waveguide in the presence of a number of thin radial fins of finite length in the axial direction. The fins are evenly distributed around the guide and we find that the re are significant differences in the possible modes depending on whet her the number of fins is even or odd and also that the qualitative be haviour of the mode frequencies changes when the number of fins passes a certain critical value. Simple approximate formulas are derived for the low-frequency modes under the assumption that the number of fins is large. The implications of our results are discussed for the case w hen the circular cross-section is replaced by an annular one, a situat ion of practical importance in the design of turbomachinery. (C) 1998 Elsevier Science B.V. All rights reserved.