A New Approach to Newton-Raphson Method to Evaluate Thermodynamics Properties for a “In-Equilibrium” Combustion Mixture 2007-01-0024
In order to estimate the combustion process inside an Internal Combustion Engine it is fundamental to evaluate the molar fractions of the gases which constitute the burned mixture. A non linear set of equations must be solved to evaluate the mixture composition. The present paper deals with the study about the thermodynamics of combustion, using a new approach to solve the set of non linear equations by the Newton-Raphson method. In order to solve the non-linear set of equations describing the combustion process, a new first attempt solution for the Newton-Raphson numerical method has been evaluated and implemented. Starting from the combustion model presented in scientific literature by Benson, a new first attempt solution has been evaluated in order to have the numerical convergence of the model for a wide set of fuels and for a wide range of thermodynamic conditions. The combustion model is able to evaluate the molar fractions of the products of combustion. The new first attempt solution, that offers the possibility of solving the equation set in a wide range of pressure, temperature and equivalence ratio combinations, has been determined by using fifth order logarithmic polynomials. The fifth order logarithmic polynomials has been determined for a fuel with a high value of the Carbon Hydrogen mass ratio, and has been modified in order to be utilized also for the combustion of other twenty-eight fuels. This first version of the model is based on chemical equilibrium, and does not take into account the chemical kinetics. Future developments will take into account also chemical kinetics and the possible presence of unburned hydrocarbons.