Tuning of the extended concentric tube resonators

Abstract

It has been shown recently that the acoustic performance of the extended tube expansion chambers can be improved substantially by making the extended inlet and outlet equal to half and quarter chamber lengths, duly incorporating the end corrections due to the evanescent higher order modes that would be generated at the discontinuities. Such chambers, however, suffer from the disadvantages of high back pressure and generation of aerodynamic noise at the area discontinuities. These two disadvantages can be overcome by means of a perforated bridge between the extended inlet and extended outlet. This paper deals with design or tuning of these extended concentric tube resonators. One dimensional control volume approach is used to analyze this muffler configuration. It is validated experimentally making use of the two source-location method. It is thus shown that the inertance of holes plays a role similar to the lumped inertance generated by evanescent 3-D modes at the terminations of the quarter wave resonators in the case of the double-tuned extended tube chambers. The effect of mean flow is also investigated. The resultant transfer matrix is then used to carry out a systematic parametric study in order to arrive at empirical expressions for the correction lengths. Thus, an extended concentric tube resonator can be tuned such that the first three troughs, which characterize the corresponding simple chamber transmission loss (TL) curve, may be eliminated making use of the proposed procedure. In fact, the entire TL curve at low and medium frequencies may be substantially lifted, making the tuned extended concentric tube resonator a viable design option.