An improved thermodynamic open Dual cycle is proposed to simulate the working of internal combustion engines. It covers both spark ignition and Diesel types through a sequential heat release. This study proposes a procedure that includes (i) the composition change caused by internal combustion, (ii) the temperature excursions, (iii) the combustion efficiency, (iv) heat and pressure losses, and (v) the intake valve timing, following well-established methodologies. The result leads to simple

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... tical expressions, valid for portable models, optimization studies, engine transformations, and teaching. The proposed simplified model also provides the working gas properties and the amount of trapped mass in the cylinder resulting from the exhaust and intake processes. This allows us to yield explicit equations for cycle work and efficiency, as well as exhaust temperature for turbocharging. The model covers Atkinson and Miller cycles as particular cases and can include irreversibilities in compression, expansion, intake, and exhaust. Results are consistent with the real influence of the fuel-air ratio, overcoming limitations of standard air cycles without the complex calculation of fuel-air cycles. It includes Exhaust Gas Recirculation, EGR, external irreversibilities, and contemporary high-efficiency and low-polluting technologies. Correlations for heat ratio γ are given, including renewable fuels.