Geodesic
Variational formulation of the problem of steady flame spread rate prediction using the generalized thermodynamic functional
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2011), pp. 80-85 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The variational statement for the generalized form of thermodynamic functional has been formulated consisting in its minimization relatively to the sought steady flame spread rate treated as additional variable. An integral relationship for the flame spread rate has been achieved for the stationary state of considered functional.
Keywords: flame spread, stationary state, variational principle, thermodynamic functional. 
@article{VUU_2011_4_a5,
     author = {A. V. Kudrin and A. I. Karpov},
     title = {Variational formulation of the problem of steady flame spread rate prediction using the generalized thermodynamic functional},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {80--85},
     year = {2011},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2011_4_a5/}
}
TY  - JOUR
AU  - A. V. Kudrin
AU  - A. I. Karpov
TI  - Variational formulation of the problem of steady flame spread rate prediction using the generalized thermodynamic functional
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2011
SP  - 80
EP  - 85
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VUU_2011_4_a5/
LA  - ru
ID  - VUU_2011_4_a5
ER  - 
%0 Journal Article
%A A. V. Kudrin
%A A. I. Karpov
%T Variational formulation of the problem of steady flame spread rate prediction using the generalized thermodynamic functional
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2011
%P 80-85
%N 4
%U http://geodesic.mathdoc.fr/item/VUU_2011_4_a5/
%G ru
%F VUU_2011_4_a5
A. V. Kudrin; A. I. Karpov. Variational formulation of the problem of steady flame spread rate prediction using the generalized thermodynamic functional. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2011), pp. 80-85. http://geodesic.mathdoc.fr/item/VUU_2011_4_a5/

[1] Williams F. A., Combustion theory, 2nd Edition, Addison-Wesley, Redwood, CA, 1985

[2] Peters N., Warnatz J. (Eds.), Numerical methods in laminar flame propagation A GAMM workshop, Notes on numerical fluid mechanics, 6, Vieweg, Braunschweig, 1982 | MR | Zbl

[3] Lovachev L. A., Kaganova Z. I., “Raschet kharakteristik bromo-vodorodnogo plameni”, Doklady AN SSSR, 188:5 (1969), 1087–1089

[4] Spalding D. B., Stephenson P. L., “Laminar flame propagation in hydrogen+bromine mixtures”, Proceedings of the Royal Society of London (A), 324 (1971), 315–337 | DOI

[5] Smooke M. D., “Solution of burner stabilized premixed laminar flames by boundary value methods”, Journal of Computational Physics, 48 (1982), 72–105 | DOI | Zbl

[6] Smooke M. D., Miller J. A., Kee R. J., “Determination of adiabatic flame speeds by boundary value methods”, Combustion Science and Technology, 34 (1983), 79–90 | DOI

[7] Basevich V. Ya., Belyaev A. A., Novozhilov B. V., Posvyanskii V. S., “Chislennoe issledovanie laminarnogo rasprostraneniya plameni dlya opredeleniya fiziko-khimicheskikh kharakteristik goryuchei smesi”, Gorenie geterogennykh i gazovykh sistem, Materialy VIII Vsesoyuznogo simpoziuma po goreniyu i vzryvu, Institut khimicheskoi fiziki AN SSSR, Chernogolovka, 1986, 8–11

[8] Mukunda H. S., Deshpande S. M., Bhashyam A. T., “New formulation for one-dimensional premixed flames”, AIAA Journal, 24 (1986), 1127–1128 | DOI

[9] Sermange M., “Contribution to the numerical analysis of laminar stationary flames”, Numerical Simulation of Combustion Phenomena, Lecture Notes in Physics, 241, eds. Glowinski R., Larrouturou B., Temam R., Springer, Berlin–Heidelberg, 1985, 375–388 | DOI | MR

[10] Karpov A. I., “O formulirovke termodinamicheskogo variatsionnogo printsipa dlya zadachi o statsionarnom rasprostranenii plameni”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye Nauki, 2008, no. 3, 61–68

[11] Karpov A. I., Kudrin A. V., “Metod lokalnogo potentsiala dlya rascheta statsionarnoi skorosti rasprostranenii plameni”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye Nauki, 2010, no. 4, 87–95

[12] de Groot S., Mazur P., Neravnovesnaya termodinamika, Mir, M., 1964, 456 pp.

[13] Glensdorf P., Prigozhin I., Termodinamicheskaya teoriya struktury, ustoichivosti i fluktuatsii, Mir, M., 1973, 280 pp. | MR

[14] Karpov A. I., Bulgakov V. K., “Ob odnom netraditsionnom algoritme rascheta skorosti rasprostraneniya plameni”, Fizika goreniya i vzryva, 26:5 (1990), 137–138

[15] Gerasev A. P., “Neravnovesnaya termodinamika teplovykh voln v sloe katalizatora. Funktsional avtovolnovogo resheniya”, Fizika goreniya i vzryva, 36:3 (2000), 51–59