Piscaglia, F., Montorfano, A., and Onorati, A., "Improving the Simulation of the Acoustic Performance of Complex Silencers for ICE by a Multi-Dimensional Non-Linear Approach," SAE Int. J. Engines 5(2):633-648, 2012, doi:10.4271/2012-01-0828.
In this paper a three-dimensional time-domain CFD approach has been employed to predict and analyze the acoustic attenuation performance of complex perforated muffler geometries, where strong 3D effects limit the validity of the use of one-dimensional models. A pressure pulse has been imposed at the inlet to excite the wave motion, while unsteady flow computation have been performed to acquire the time histories of the pressures upstream and downstream of the silencer. Pressures in the time domain have been then transformed to acoustic pressures in the frequency domain, to predict the transmission loss. In order to achieve reliable predictions of the acoustic attenuation, especially above the plane wave cut-off frequency, an advanced non-reflecting boundary condition to model the anechoic termination, based on the NSCBC characteristic theory, has been implemented in a multidimensional open-source CFD code and it has been used together with a time dependent compressible Navier Stokes equation solver. The original local one dimensional inviscid relations (LODI) in Cartesian coordinates presented in  have been extended to local coordinates and have been applied for unsteady calculations in a multistage time stepping scheme. Numerical results show that the agreement between simulations and experiments strongly improves at high frequency when the novel boundary condition is applied. A comparative study with a 1D non-linear model for unsteady compressible flows is shown on four different configuration of reverse flow chambers and on a single-plug perforated muffler for internal combustion engine applications. Advantages and drawbacks of the proposed approach are discussed.