Several improvements to the mathematical model of the indicator process, taking place in a diesel engine cylinder, are proposed. The thermodynamic behavior of working media is described by the equation of state, valid for real gases. Analytical mathematical dependencies between thermal parameters (pressure, temperature, volume) and caloric parameters (internal energy, enthalpy, specific heat capacities) have been obtained. These equations have been applied to the various products encountered during the burning of fuel and the gas mixture as a whole in the engine cylinder under conditions of high pressures and temperatures. An improved mathematical model, based on the first law of thermodynamics, has been developed by taking into account imperfections in the working media that appear under high pressures and temperatures. The numerical results show that there are significant differences between the values calculated using ideal gas behavior and the real gas, in particular at high pressure and high temperature conditions. The numerical experiments show that if the pressure is above 8 to 9 MPa, the imperfections in working medium must be taken into consideration. The results obtained from the mathematical dependency of the caloric parameters can also be used to model any energy conversion and combustion process, such as, advanced gas turbine engines which operate at high pressure ratios, rockets.

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