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Abstract :
In this article, application of the novel direct estimation method developed recently by the authors for naturally aspirated engines [Applied Acoustics 135, 70-84 (2018)] is extended here to turbocharged engines. The direct estimation method needs knowledge of the transfer matrices of the elements constituting the exhaust system (downstream of each cylinderâ€™s exhaust port). Thus, the acoustic modelling of passive transmission properties of turbine of the turbocharger is needed. In the present study, turbine is modelled as a one-dimensional blackbox across which the isentropic expansion occurs. Transfer matrix of the turbine is derived using the known static pressure ratio of the turbine, and the mass continuity across the turbine. Four-pole parameters of the turbine turn out to be simple functions of the turbine pressure ratio. Each cylinder of the engine is an acoustic source, the characteristics of which are computed assuming that the cylinders are discharging to an ideal pressure release boundary condition (the constant pressure against which the cylinders are assumed to discharge is the product of turbine pressure ratio and mean exhaust pressure in exhaust runners). The acoustic source impedance of each cylinder is the sum of the valve impedance (inertance and resistance) and cylinder cavity compliance, which vary with the crank angle. Average acoustic source impedance of each cylinder is computed as reciprocal of source admittance averaged over one complete engine cycle. The acoustic source pressure of each cylinder is the product of the average source impedance and the acoustic mass velocity downstream of the exhaust valve. The resultant source characteristics of each cylinder are transferred and combined appropriately as per the formulae developed by Munjal and Doige [Journal of Sound and Vibration 121(1), 25-35 (1988)] to estimate the source characteristics of the engine downstream of the exhaust manifold. The estimated source characteristics are shown to predict the unmuffled exhaust sound pressure level (SPL) spectrum which compares well with the measured spectrum. Unlike in the literature on indirect multi-load methods of source characterization, the source resistance is shown to be positive at all frequencies. The direct evaluation method proposed here needs only the basic geometrical parameters of cylinders, the exhaust and intake valves, exhaust gas mass flow rate, and the in-cylinder gas pressure and temperature at the start of blowdown. These data would be available at the design stage itself; we do not wait for the engine prototype to be ready. Thus, the muffler design process can be integrated with the engine design process.