Flow reversal chambers are mainly used to accomplish a compact silencer design needed on a vehicle. Generally in this configuration the inlet and outlet ports are on the same face and the flow direction is reversed.
During many years different authors have tried to develop 1D and 3D models for evaluating the acoustic performance of circular and rectangular reversing chambers. Ih  categorizes four methods for evaluating the acoustic performance of the reversing chamber.
The first involves utilizing analysis techniques for other types of muffler elements having similar acoustic performances . Analysis techniques for extended inlet/outlet expansion chambers may be used to approximate the behavior of a reversing chamber in which the length-to-diameter ratio is large. When the length-to-diameter ratio is small, the reversing chamber approximates the behavior of a short expansion chamber. In this case, exact predictions of the acoustic performances cannot be made and, moreover, the method itself is a trial-and-error one.
The second is a mode-matching method at the discontinuities [3-5], but this is tedious to formulate and the transmission matrix for this type of muffler has not been obtained. A simplified version (third method) of this method has been developed for plane wave propagation, in which the sound pressures and particle velocities at the area discontinuities are matched [6, 7].
However, this method is restricted to a very small frequency range below the cut-off frequency of the first asymmetric mode, i.e., the (1, 0) mode, and the peaks of the transmission loss curves are not correctly predicted due to the disregard of the higher order modes. Furthermore, when the length-to-diameter ratio is small, the actual acoustic performance deviates appreciably from the theoretical transmission loss predicted by this one-dimensional analysis method.
The fourth method involves using numerical methods such as finite element analysis  and the finite difference method , or possibly, the boundary element method. These numerical techniques have some merits in the treatment of more complicated geometries, such as that of an elliptic cross-section and/or a chamber with a pass tube , but a great many mesh points or mesh elements are required to deal with the high frequency range, so that the execution time for computation is long and the costs are high.
It is also difficult to describe the total exhaust system by incorporating the transmission matrix of each silencer element.Lindborg et al.  modeled the flow reversal chamber by two port method. The system under study is broken down into a set of linear subcomponents that are described individually and then assembled in a network.
Each component is treated as a black box that is defined at the inlet and outlet ports where plane waves are assumed. This is an efficient tool, but for complicated geometries such as the flow reversal chamber the decomposition into subcomponents is not obvious.
Three different approaches are used for the two port modeling of a flow reversal ;
1- Large quarter wave resonator
2- More detailed representation consisting of cones and quarter wave resonators
3- A simplification of the second approach into a simple Pipe 6
Author: Qazizadeh, Alireza