Effect of shell compliance on the axial transmission loss of concentric tube resonator

Veerababu, Dharanalakota and Balide, Venkatesham (2018) Effect of shell compliance on the axial transmission loss of concentric tube resonator. In: 13th Western Pacific Conference on Acoustics (WESPAC-2018), 11 – 15 November 2018, New Delhi, India.

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Abstract

A simple expansion chamber can be turned into a concentric tube resonator by connecting the inlet and outlet pipes through a perforated pipe. This arrangement will reduce the pressure drop and aerodynamic noise generated due to sudden area changes. It also improves the transmission loss through the inertance of the perforations. Thus, a concentric tube resonator offers a great advantage over a simple expansion chamber in flow, aerodynamics, and acoustics point of view. In general, while calculating the TL, the walls of the chamber are assumed to be acoustically rigid. However, in some applications, the walls are compliant to the sound waves incident on them. Thus, a part of the incident energy will break out of the chamber in the transverse direction, and the rest will propagate and gets attenuated in the axial direction. Therefore, the presence of compliant walls will influence the transmission loss of the chamber calculated in the axial direction. The current paper discusses an analytical methodology developed by using Green’s function to calculate the axial transmission loss of a concentric tube resonator having a compliant wall in transverse direction. In the analysis, end walls of the chamber are assumed to be acoustically rigid except at the inlet and outlet ports. The effect of the compliant wall, annular cavity, and perforated sheet together is transferred to the inner pipe as a reflection load coefficient. The Green’s function for this configuration is expressed as the summation of modal eigenfunctions of the inner pipe by using the division-of-region method. The modal amplitudes and the corresponding wavenumbers are calculated by substituting appropriate boundary conditions. The inlet and outlet ports are treated as hypothetical rigid pistons moving back and forth with uniform velocity. From the Kirchoff Helmholtz integral equation, the total velocity potential generated inside the chamber is calculated with the aid of the principle of superposition. By using the relation between the velocity potential and acoustic pressure, the total pressure acting on each piston is calculated. Thence, the transfer matrix relating the acoustic pressure and volume velocity at the inlet port to that of outlet port is evaluated to predict the transmission loss. A numerical model has been prepared by using the finite element method to validate the results obtained from the current methodology. The comparison shows that there is a good agreement between the results obtained from the proposed method and the numerical model.

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