Theory and Design of the Double-Tuned Coaxial and Flow-Reversal Mufflers: A New Perspective

Abstract

Double-tuning an expansion chamber consists in extending the inlet–outlet pipes into the chamber by certain specific lengths so that the TL peaks due to the quarter-wave resonances of the annular cavities cancel or tune out the TL troughs due to the axial standing waves in the simple expansion chamber. The transfer matrix method is combined with the direct electroacoustic analogies in this paper to derive simple analytical expressions for the TL spectra of the double-tuned coaxial chamber (DTCAC) muffler or the axial-inlet, axial-outlet muffler, the double-tuned flow-reversal chamber (DTFRC) muffler or the inlet–outlet same-end muffler and the semi-tuned coaxial chamber (STCAC) or axial-inlet, axial-outlet muffler. It has been shown that barring the rather inconsequential sharp narrow peaks, the underlying overarching wide-band TL curve corresponds to a hypothetical simple expansion chamber, the effective lengths and diameter of which for the DTCAC muffler, DTFRC muffler and STCAC muffler have been tabulated at the end of this paper. This novel approach would simplify analysis and facilitate synthesis of mufflers with more than one semi-tuned as well as double-tuned chambers. Finally, some guidelines for design of these tuned mufflers for the HVAC systems have been given where it has been emphasized that physical lengths of the extended pipes would be different from the acoustic lengths to the extent of the end corrections.