Direct estimation and experimental validation of the acoustic source characteristics of two-cylinder naturally aspirated diesel engine exhaust system

Abstract

In this paper, acoustic source characteristics of the exhaust system of two-cylinder naturally aspirated engines are estimated using a novel direct method. Each cylinder (the cylinder cavity and exhaust valve) is a non-linear time-variant acoustic source for the exhaust system. The source impedance of each cylinder is estimated assuming that the other cylinder is not exhausting at the same time. In order to work with linear time-invariant model of the acoustic source, the impedance of each cylinder is assumed as the reciprocal of source admittance averaged over different crank-angle steps. The source pressure is product of acoustic mass velocity at the source-load junction and the sum of the source impedance and the load impedance. Computation of source impedance and acoustic mass velocity calls for the aero-thermodynamic computation in the time-domain making use of the values of pressure and temperature of the in-cylinder gas at the exhaust valve opening (EVO) along with the basic geometrical details of the cylinder, intake and exhaust valves and ports. The estimated source characteristics for each cylinder at the downstream of exhaust valve are then transferred downstream to the end of the runner. The source characteristics so obtained are then combined for the two cylinders. These values are then transferred to the beginning of the acoustic test load (exhaust pipe or exhaust muffler). The estimation of source characteristics is dependent on the exhaust mass flow rate which depends on the exhaust system to which cylinders are discharging. Thus, the IC engine acoustic source is load-dependent, not unique. Yet, the resultant source characteristics help to predict unmuffled sound pressure level (SPL) spectra that agree reasonably with the experimentally measured spectra.