On the nonlinear and time-varying acoustic modeling of the simplified intake or exhaust silencing system

The intake or exhaust noise of an internal combustion engine is usually predicted by the linear, time-invariant source model in frequency domain with reasonable precision. However, the actual finite amplitude pulsation involves the nonlinear, time-varying characteristics that are prominent in time-domain. To overcome the discrepancy between two source models, an approximate nonlinear and time-varying frequency domain source model can be employed by appending the nonlinear or time-varying terms to the linear, time-invariant source model. Proper selection of the nonlinear describing terms varying with time is important for the realistic and precise prediction of the radiated sound. For the selection of such terms, flow and motional characteristics in the valve and orifice of a simplified fluid machine comprised of very large reservoir, valve, and duct is considered. Effects of each describing term and the combined terms are investigated by comparing the sound spectrum predicted from nonlinear source model to that from linear source model. In the comparison, the sound spectrum calculated by the method of characteristics is used as a reference. It is found that the source model using only the velocityrelated terms yields the best result among all the models using various combinations of the terms with different characteristics. The best model yields a difference from the linear source model within ±5 dB in overall sound level. Change of acoustic loads results in a difference of 20–27 dB in linear source model from the reference data; however, maximum 10–22 dB deviations are observed in using the various nonlinear source models. It is concluded that more than 4 describing terms should be employed in the nonlinear model to obtain a realistic result of the radiated sound from the intake or exhaust system.