Application of Reciprocity to Calculating the Scattering Matrix of a Complex Muffler Without and With Nonuniform Meanflow

The internal meanflow with nonuniform distributions of velocity and temperature is a major challenge for acoustic analysis of a muffler in the frequency domain. On the other hand, the three-dimensional time-domain numerical method is well suited for solving the influence of meanflow on the muffler, but it is time-consuming, especially for calculating the transfer matrix that requires two sets of boundary conditions. We proposed a more efficient time-domain method to calculate the scattering matrix (SM) of an actual engine muffler using a numerical model with only one set of boundary conditions. The reciprocity, as a basic property of waves, was for the first time demonstrated in such a complex muffler with hot nonuniform flow exhausted from the engine and used to reduce the procedures for calculating the SM. The reciprocal relationship was not only expressed in the modules of the transmission coefficients in the SM but also corrected in the phases using the time delay between the incident and transmitted waves observed with the time-domain method. At last, the SM was adopted to obtain the performance of the muffler, which was validated with the measurement. The proposed method shall make the time-domain method more efficient for calculating the characterizing matrix of a muffler without or with meanflow.