A REVERSE FLOW THEOREM AND ACOUSTIC RECIPROCITY IN COMPRESSIBLE POTENTIAL FLOWS IN DUCTS

✍ Scribed by W. EVERSMAN

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 380 KB
• Volume: 246
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2000.3608

✦ Synopsis

A reverse #ow theorem for acoustic propagation in compressible potential #ow has been obtained directly from the "eld equations without recourse to energy conservation arguments. A reciprocity theorem for the scattering matrix for the propagation of acoustic modes in a duct with either acoustically rigid walls or acoustically absorbing walls follows. It is found that for a source at a speci"c end of the duct, suitably scaled re#ection matrices in direct and reverse #ow have a reciprocal relationship. Scaled transmission matrices obtained for direct #ow and reversed #ow with simultaneous switching of source location from one end to the other also have a reciprocal relationship. A related reverse #ow theorem specialized to one-dimensional acoustic propagation has also been obtained. Reciprocity relationships for the scattering coe$cients for propagation are derived, and are found to be similar though much simpler than in the case of multi-mode propagation. In one-dimensional #ow, reciprocal relations and power conservation arguments are used to show that scaled power re#ection and transmission coe$cients are invariant to #ow reversal and switching of source location from one end of the duct to the other. Numerical veri"cation of the reciprocal relationships is given in a companion paper.

2001 Academic Press