A view on the internal consistency of linear source identification for I.C. engine exhaust noise prediction

Considerable efforts have been devoted to the development of predictive models that, from a certain set of data related to an engine, and making use of an adequate representation of the effect of the silencing elements, provide an estimate of the exhaust noise emitted. Such models should allow for the consideration of the engine and its interaction with the exhaust system. This is properly achieved by gas-dynamic models, which are becoming the standard, but linear models solved in the frequency domain and representing the engine as a linear time-invariant source may still play a role in exhaust system design, as the engine is treated as a black box. Such a representation is very attractive for engine manufacturers, since it gives the possibility to provide data on the engine without any possibility to trace back to its real characteristics. In order to provide additional criteria for the suitability of the application of a linear time-invariant representation to an engine exhaust, in this paper a multi-load method has been used to extract source characteristics from gas-dynamic simulation results. The details of the method, in which the resulting over-determined system is solved by fitting the values of the source parameters in a least-squares sense, are described, and different approaches are used in order to check the internal consistency of the source representation: the identification of pressure and velocity sources, and the application of the least-squares criterion to the modulus or to the real and imaginary parts separately. In particular, eight different determinations of the source impedance are obtained and, considering the application of the formalism to an engine exhaust, the differences observed provide a suitable criterion for the evaluation of the suitability of the representation and of the particular set of loads chosen.