Etude de la combustion de gaz de synthèse issus d'un processus de ...
Etude de la combustion de gaz de synthèse issus d'un processus de ... Etude de la combustion de gaz de synthèse issus d'un processus de ...
References tel-00623090, version 1 - 13 Sep 2011 186. Wang D. Czernik S., Montane D., Mann M., Chornet E. Biomass to hydrogen via fast pyrolysis and catalytic steam reforming of the pyrolysis oil or its fractions. Ind. Eng. Chem. Res. 36, 1507-1518 (1997). 187. Warnatz J., Peters N. Stretch effects in plane premixed hydrogen-air-flames. Progress in Astronautics and Aeronautics 95, 61-74 (1984). 188. Wei S. W., kim Y.Y., kim H.J., Lee J.T. A study on transient heat transfer coefficient of in-cylinder gas in the hydrogen fuelled engine. 6th Korea-Kapan Joint Symposium on Hydrogen Energy, 2001. 189. Westbrook C.K., Adamczyk A.A., Lavoie G.A. A numerical study of laminar flame wall quenching. Combustion and Flame 40, 81-89 (1981). 190. Williams F.A. Combustion Theory, 2 nd ed., Adison Wesley. 1985. 191. Woschni G. A universal applicable equation for the instantaneous heat transfer coefficient in the internal combustion engine. SAE Technical Paper 670931, (1967). 192. Zeleknik F.J. Combustion modeling in internal combustion engines. Combustion Sci Technol 12, 159–164 (1976). 193. Zimont V.L. Gas premixed combustion at high turbulence. Turbulent flame closure combustion model. Experimental Thermal Fluid Science 21, 179-186 (2000). 214
Appendix A – Overdetermined linear equations systems Appendix A - OVERDETERMINED LINEAR EQUATIONS SYSTEMS The system of linear algebraic equations of the form: AX = b , (A-1) m× n Where A ∈IR , X ∈IR n , and b∈ IR n is said to be an overdetermined system if m>n i.e., there are more equations than unknowns. tel-00623090, version 1 - 13 Sep 2011 This type of systems appears as a consequence of experimental errors; in order to obtain a more accurate result one requires more measurements than the strictly necessary ones. For example, curve fitting which is the process of constructing a curve that has the best fit to a series of data points. Given m data points (x i , y j ) for i = 1,…m, we want to adjust these points to a curve of the form: n = 0 0 + 1 1 + + n n =∑ j j j = 1 ( ) ( ) ( ) ( ) Px ( ) au x au x au x au x (A-2) Where u j (j=0,…,n) are linearly independent given functions and a j (j=0,…,n) parameters to be determine. The linear systems (A-1) only as a solution when b belongs to the column space of A. However, it is also possible to determine X such that it minimizes some vector norm of the residual r = b−AX (A-3) i.e., determine X such that the residual vector r is as small as possible. Due to the differentiability of the Euclidean norm, allowing determining the minimum by the usual process is in general the used norm to minimize the residual. This is called least squares method. The goal of the least squares method is to determine the vector X which minimizes the sum of the squared residuals, i.e., 215
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References<br />
tel-00623090, version 1 - 13 Sep 2011<br />
186. Wang D. Czernik S., Montane D., Mann M., Chornet E. Biomass to hydrogen via<br />
fast pyrolysis and catalytic steam reforming of the pyrolysis oil or its fractions. Ind.<br />
Eng. Chem. Res. 36, 1507-1518 (1997).<br />
187. Warnatz J., Peters N. Stretch effects in p<strong>la</strong>ne premixed hydrogen-air-f<strong>la</strong>mes.<br />
Progress in Astronautics and Aeronautics 95, 61-74 (1984).<br />
188. Wei S. W., kim Y.Y., kim H.J., Lee J.T. A study on transient heat transfer<br />
coefficient of in-cylin<strong>de</strong>r gas in the hydrogen fuelled engine. 6th Korea-Kapan<br />
Joint Symposium on Hydrogen Energy, 2001.<br />
189. Westbrook C.K., Adamczyk A.A., Lavoie G.A. A numerical study of <strong>la</strong>minar f<strong>la</strong>me<br />
wall quenching. Combustion and F<strong>la</strong>me 40, 81-89 (1981).<br />
190. Williams F.A. Combustion Theory, 2 nd ed., Adison Wesley. 1985.<br />
191. Woschni G. A universal applicable equation for the instantaneous heat transfer<br />
coefficient in the internal <strong>combustion</strong> engine. SAE Technical Paper 670931,<br />
(1967).<br />
192. Zeleknik F.J. Combustion mo<strong>de</strong>ling in internal <strong>combustion</strong> engines. Combustion<br />
Sci Technol 12, 159–164 (1976).<br />
193. Zimont V.L. Gas premixed <strong>combustion</strong> at high turbulence. Turbulent f<strong>la</strong>me<br />
closure <strong>combustion</strong> mo<strong>de</strong>l. Experimental Thermal Fluid Science 21, 179-186<br />
(2000).<br />
214
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