# Heat Release Rate Model

The cylinder gas is considered as a spatially homogeneous thermodynamic system occupying in a single zone for the compression, expansion, intake, exhaust processes and two zones (burned and unburned zone) for the combustion process. The instantaneous composition of cylinder gases are obtained from the mass fraction of fuel burned. The instantaneous thermodynamic properties are computed by the established equations [20-21, 28]. The instantaneous gas properties are calculated by the simultaneous numerical integration of the differential equations. The differential equations governing the gas pressure and temperature are resulting from the first law of thermodynamic analysis. The instantaneous

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Lapuerta et al [30] found a deviation of up to 34°C at the combustion produced temperature peaks of diesel engine with the ideal gas assumption and stated that the deviation of such a magnitude is considered important for emissions estimations only. Hence the ideal gas assumption is considered to be a good approximation as this work is concerned with performance estimation only. The ideal gas equation of state together with the first law of thermodynamics provides the equation (1) of net heat release rate [31]. A predictive Wiebe function combustion heat release rate model is first developed comprising two Wiebe functions each one for premixed combustion phase and diffusion combustion phase as in equation (2) [32]. The gross heat release rate is synthesized with an equation (3) having two separate Wiebe efficiency factors ap and ad in the two Wiebe functions often referred to as double Wiebe function [25, 33]. The direct experimental measurement of heat release rate is difficult. Therefore, a net apparent heat release rate calculated from the experimentally measured pressure-time profile and computationally calculated piston displacement profile along with heat loss to the cylinder wall using equation (1) is applied for validation. The diesel and DME oxidation reaction equations assuming complete

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The instantaneous concentration of reactants and products are calculated from the burn fraction of fuel synthesized by the Wiebe function. The aim of the proposed model is to provide accurate thermodynamic conditions in the cylinder to facilitate the pressure and temperature calculations for performance prediction alone. The fluid mass flow rate and changes in fluid properties during intake and exhaust processes are calculated by a gas exchange process analysis [51] and detailed model is available in the earlier paper