General Solution of Acoustic Wave Equation for Circular Reversing Chamber with Temperature Gradient

A general solution for transmission loss in a circular reversing chamber with the effects of temperature gradient, offset, and twisting angle variations of inlet/outlet ports is obtained by using the mode matching technique. The assumptions included in the solution method are division of the reversing chamber into segments, continuity of pressure and velocity at the boundaries of adjacent elements, constant temperature along each segment, and rigid wall boundary condition. Furthermore, the general solution can reduce to the existing solution of acoustic wave equation for a reversing chamber when no mean flow of exhaust gas and temperature gradient are present. The numerical simulation results based upon the obtained governing equation have the same trough frequencies and shapes of transmission loss curves as the experimental results performed on various types of reversing chambers. From these simulations, it is determined that the diameter of the reversing chamber dictates that cutoff frequencies in the transmission loss curves, and its length controls the number of standing waves in the chamber. Reversing chambers exhibit the acoustic characteristics of simple expansion chambers when the ratios of length over diameter are small. Even for limiting cases, i.e., Helmholtz resonators and close ended pipes, simulations produce the predicted results derived by other existing theories for silencers.