This content is not included in
your SAE MOBILUS subscription, or you are not logged in.
A New Approach to Newton-Raphson Method to Evaluate Thermodynamics Properties for a “In-Equilibrium” Combustion Mixture
Technical Paper
2007-01-0024
ISSN: 0148-7191, e-ISSN: 2688-3627
Annotation ability available
Sector:
Language:
English
Abstract
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.
Citation
Lanzafame, R. and Messina, M., "A New Approach to Newton-Raphson Method to Evaluate Thermodynamics Properties for a “In-Equilibrium” Combustion Mixture," SAE Technical Paper 2007-01-0024, 2007, https://doi.org/10.4271/2007-01-0024.Also In
References
- Benson, R. S. Annand, W. J. D. Baruah, P. C. A., A simulation model including intake and exhaust systems for a single cylinder four-stroke cycle spark ignition engine Int. J. Mech. Sci. 17 97 124 1975
- Benson, R. S. The Thermodynamics and Gas Dynamics of Internal - Combustion Engines I Clarendon Press Oxford. 1982
- Strehlow, R. A. Combustion Fundamentals McGraw Hill 1985
- U.S. National Bureau of Standards JANAF Thermochemical Tables 2nd ed. 1971
- Chase, M.W., Jr. NIST-JANAF Themochemical Tables 4th J. Phys. Chem. Ref. Data 1 1951 1998
- Gordon S. McBride B., “Thermodynamic Data to 20000 K for monatomic gas” 1999
- Gurvich L.V. et al. “Thermodynamic Properties of Individual Substances” 1 Nauka Moscow 1978
- Gurvich L.V. Veyts I.V. Alcock C.B. Thermodynamic Properties of Individual Substances 4th 1 Hemisphere Publishing Corp. 1989
- Cox, J.D. Wagman, D.D. Medvedev, V.A. CODATA Key Values for Thermodynamics Hemisphere Publishing Corp. New York 1984
- Lanzafame R. Messina M. 2005 “New Gases Thermodynamic Properties Models to Predict Combustion Phenomena” SAE Paper n. 2005-01-2112
- Lanzafame R. Messina M. Thermodynamics Property Models for Unburned Mixtures and Combustion Gases International Journal of Thermodynamics June 2006