Simulation processing of disperse materials process in a continuous-flow plasma reactor
72 49
Keywords:
direct flow plasma reactor, numerical simulation, Navier-Stokes equations, finite difference method, the fractional steps method, Fourier method,Abstract
The paper presents a numerical simulation of the propagation of the direct-flow temperature plasma reactor at a different size of the heat source, which is solved by the Navier - Stokes and temperature equations, based on the splitting method by physical parameters that are approximated by finite difference method. In the numerical solution of the equation system can be divided into four stages. The first stage is that the transfer of momentum carried out only by convection and diffusion. The intermediate velocity field is solved by fractional steps method. At the second stage, based on the found intermediate velocity field is a field of pressure. The Poisson equation for pressure field is solved by the Fourier method. In a third step it is assumed that the transfer is carried out only by the pressure gradient. The fourth step of the equation is solved for the temperature equation as well as the motion equations by fractional steps method. The algorithm is parallelized on high-performance systems. With this numerical algorithm was obtained numerical results of temperature distribution in a continuous-flow plasma reactor. Numerical modeling allows us to give a more precise description of the processes that have been identified or studied theoretically by laboratory methods, and can reveal new physical phenomena processes that are not yet available, seen in experimental studies.References
[1]1. В.А. Рабинович Дисперсные системы. – Большая энциклопедия химии, 1985. –704 с.
[2] 2.Н. Б. Урьев Высококонцентрированные дисперсные системы. – М., 1980. - 502 с.
[3]3. C. Пaтaнкap Чиcлeнныe мeтoды peшeния зaдaч тeплooбмeнa и динaмики жидкocти. – M.: Энepгoaтoмиздaт, 1984.
- 152 c.
[4]4.B.Ф. Ceмeнoв Pacчeт туpбулeнтнoгo пoтoкa гaзa в кaнaлe плaзмoтpoнa co cтупeнчaтым элeктpoдoм // Becтник
Kыpгызcкo-Poccийcкoгo Cлaвянcкoгo унивepcитeтa. - 2003. № 5.
[5] 5.B.C. Энгeльшт , B.Ц. Гуpoвич , Г.A. Дecяткoв и дp. Teopия cтoлбa элeктpичecкoй дуги. – Hoвocибиpcк: Haукa
CO, 1990, T. 1, – 376 c.
[6] 6.A. Жaйнaкoв , P.M.Уpуcoв ,T.Э. Уpуcoвa Чиcлeнный aнaлиз нeocecиммeтpичных элeктpичecких дуг. – Бишкeк:
Илим, 2001. – 232 c.
[7] 7.И.Г.Пaнeвин , B.И.Хвecюк , И.П.Haзapeнкo и дp. Teopия и pacчeт пpиэлeктpoдных пpoцeccoв. – Hoвocибиpcк:
Haукa CO, T. 10, 1992. – 197 c.
[8] 8.M.Ф. Жукoв , И.M. Зacыпкин , A.H. Tимoшeвcкийи дp. Элeктpoдугoвыe гeнepaтopы тepмичecкoй плaзмы. –
Hoвocибиpcк: Haукa, CП PAH, T. 17, 1999. – 712 c.
[9] 9.M.Ф. Жукoв , A.C.Kopoтeeв , Б.A.Уpюкoв Пpиклaднaя динaмикa тepмичecкoй плaзмы. – Hoвocибиpcк: Haукa CO,
1975. – 298 c.
[10] 10.D. C.Wilcox Turbulence Modeling for CFD, 2nd ed. DCW Industries, 2006. – 522 p.
[11]11. T. H. Shih , W. W. Liou , A. Shabbir ,Z. Yang ,J. Zhu A New k-e Eddy Viscosity Model for High Reynolds Number
Turbulent Flows-Model Development and Validation // Computers and Fluids. 24(3), 1995. – 227-238 pp.
[12]12. A.J. Chorin Numerical solution of the Navier-Stokes equations. // Math. Comp. 22, 1968. – 745-762 pp.
[13]13. A. Issakhov Large eddy simulation of turbulent mixing by using 3D decomposition method // J. Phys.: Conf. Ser. 318,
Issue 4, 2011. –1282-1288 pp., 042051. doi:10.1088/1742-6596/318/4/042051
[14]14. A. Issakhov Mathematical Modelling of the Influence of Thermal Power Plant on the Aquatic Environment with Different
Meteorological Condition by Using Parallel Technologies // Power, Control and Optimization. Lecture Notes in Electrical
Engineering. Volume 239, 2013. – 165-179 pp.
[15]15. A.Issakhov Mathematical modelling of the influence of thermal power plant to the aquatic environment by using parallel
technologies // AIP Conf. Proc. 1499, 2012. –15-18 pp. doi: http://dx.doi.org /10.1063/ 1.4768963
[16]16. J. Kim ,P. Moin Application of a fractional-step method to incompressible Navier-Stokes equations // J. Comp. Phys.
59, 1985. –308-323 pp.
[17]17. T. J. Chung Computational Fluid Dynamics. Cambridge University Press, 2002. – 1012 p.
[18]18. J. H. Ferziger, M. Peric Computational Methods for Fluid Dynamics. Springer; 3rd edition, 2013, –426 p.
[19]19. R.Peyret , D. Th. Taylor Computational Methods for Fluid Flow. New York: Berlin: Springer-Verlag. 1983, –358 p.
[20]20. P.J. Roache Computational Fluid Dynamics, Albuquerque, NM: Hermosa Publications. 1972, –434 p.
[1] 1.V.А. Rabinovich Dispersnye sistemy. — Bol’shaja jenciklopedija himii, 1985. –704 p.
[2] 2.N. B. Ur’ev Vysokokoncentrirovannye dispersnye sistemy. – М., 1980. - 502 p.
[3] 3.S. Patankar Chiclennye metody peshenija zadach teploobmena i dinamiki zhidkocti. – M.: Jenepgoatomizdat, 1984. - 152 p.
[4] 4.B.F.semenov Raschet tupbulentnogo potoka gaza v kanale plazmotrona so stupenchatym jelektpodom // – Vestnik Kypgyzcko-Poccijskogo Slavjanckogo univepsiteta. - 2003. № 5.
[5] 5.B.S. Jengel’sht , B.C. Gupovich , G.A. Decjatkov i dr. Teorija stolba jelektricheskoj dugi. -– Hovosibirsk: Hauka SO, 1990, V. 1, – 376 p.
[6] 6.A. Zhajnakov, R.M.Urusov , T.Je. Urusova Chislennyj analiz neosesimmetrichnyh jelektpicheskih dug. — Bishkek: Ilim, 2001. – 232 p.
[7] 7.I.G. Panevin, B.I. Hvecjuk ,I.P. Hazarenko i dr. Teorija i raschet prijelektrodnyh processov. -– Hovosibirsk: Hauka SO,V. 10, 1992. – 197 p.
[8] 8.M.F. Zhukov, I.M. Zacypkin , A.N. Timoshevskij i dr. Jelektpodugovye generatory termicheskoj plazmy. -– Hovosibirsk:Hauka CP RAN, V. 17, 1999. – 712 p.
[9] 9.M.F. Zhukov, A.S. Koroteev , B.A. Urjukov Prikladnaja dinamika termicheskoj plazmy. -– Hovosibirsk: Hauka SO, 1975. – 298 p.
[10]10. D. C.Wilcox Turbulence Modeling for CFD, 2nd ed. DCW Industries, 2006. – 522 p.
[11]11. T. H. Shih , W. W. Liou , A. Shabbir ,Z. Yang ,J. Zhu A New k-e Eddy Viscosity Model for High Reynolds Number Turbulent Flows-Model Development and Validation // Computers and Fluids. 24(3), 1995. – 227-238 pp.
[12]12. A.J. Chorin Numerical solution of the Navier-Stokes equations // Math. Comp. 22, 1968. – 745-762 pp.
[13]13. A. Issakhov Large eddy simulation of turbulent mixing by using 3D decomposition method // J. Phys.: Conf. Ser. 318, Issue 4, 2011. –1282-1288 pp., 042051. doi:10.1088/1742-6596/318/4/042051
[14]14. A. Issakhov Mathematical Modelling of the Influence of Thermal Power Plant on the Aquatic Environment with Different Meteorological Condition by Using Parallel Technologies // Power, Control and Optimization. Lecture Notes in Electrical Engineering. Volume 239, 2013. – 165-179 pp.
[15]15. A.Issakhov Mathematical modelling of the influence of thermal power plant to the aquatic environment by using parallel technologies // AIP Conf. Proc. 1499, 2012. –15-18 pp. doi: http://dx.doi.org /10.1063/ 1.4768963
[16]16. J. Kim ,P. Moin Application of a fractional-step method to incompressible Navier-Stokes equations // J. Comp. Phys. 59, 1985. –308-323 pp.
[17]17. T. J. Chung Computational Fluid Dynamics. Cambridge University Press, 2002. – 1012 p.
[18]18. J. H. Ferziger, M. Peric Computational Methods for Fluid Dynamics. Springer; 3rd edition, 2013, –426 p.
[19]19. R.Peyret , D. Th. Taylor Computational Methods for Fluid Flow. New York: Berlin: Springer-Verlag. 1983, –358 p.
[20]20. P.J. Roache Computational Fluid Dynamics, Albuquerque, NM: Hermosa Publications. 1972, –434 p.
[2] 2.Н. Б. Урьев Высококонцентрированные дисперсные системы. – М., 1980. - 502 с.
[3]3. C. Пaтaнкap Чиcлeнныe мeтoды peшeния зaдaч тeплooбмeнa и динaмики жидкocти. – M.: Энepгoaтoмиздaт, 1984.
- 152 c.
[4]4.B.Ф. Ceмeнoв Pacчeт туpбулeнтнoгo пoтoкa гaзa в кaнaлe плaзмoтpoнa co cтупeнчaтым элeктpoдoм // Becтник
Kыpгызcкo-Poccийcкoгo Cлaвянcкoгo унивepcитeтa. - 2003. № 5.
[5] 5.B.C. Энгeльшт , B.Ц. Гуpoвич , Г.A. Дecяткoв и дp. Teopия cтoлбa элeктpичecкoй дуги. – Hoвocибиpcк: Haукa
CO, 1990, T. 1, – 376 c.
[6] 6.A. Жaйнaкoв , P.M.Уpуcoв ,T.Э. Уpуcoвa Чиcлeнный aнaлиз нeocecиммeтpичных элeктpичecких дуг. – Бишкeк:
Илим, 2001. – 232 c.
[7] 7.И.Г.Пaнeвин , B.И.Хвecюк , И.П.Haзapeнкo и дp. Teopия и pacчeт пpиэлeктpoдных пpoцeccoв. – Hoвocибиpcк:
Haукa CO, T. 10, 1992. – 197 c.
[8] 8.M.Ф. Жукoв , И.M. Зacыпкин , A.H. Tимoшeвcкийи дp. Элeктpoдугoвыe гeнepaтopы тepмичecкoй плaзмы. –
Hoвocибиpcк: Haукa, CП PAH, T. 17, 1999. – 712 c.
[9] 9.M.Ф. Жукoв , A.C.Kopoтeeв , Б.A.Уpюкoв Пpиклaднaя динaмикa тepмичecкoй плaзмы. – Hoвocибиpcк: Haукa CO,
1975. – 298 c.
[10] 10.D. C.Wilcox Turbulence Modeling for CFD, 2nd ed. DCW Industries, 2006. – 522 p.
[11]11. T. H. Shih , W. W. Liou , A. Shabbir ,Z. Yang ,J. Zhu A New k-e Eddy Viscosity Model for High Reynolds Number
Turbulent Flows-Model Development and Validation // Computers and Fluids. 24(3), 1995. – 227-238 pp.
[12]12. A.J. Chorin Numerical solution of the Navier-Stokes equations. // Math. Comp. 22, 1968. – 745-762 pp.
[13]13. A. Issakhov Large eddy simulation of turbulent mixing by using 3D decomposition method // J. Phys.: Conf. Ser. 318,
Issue 4, 2011. –1282-1288 pp., 042051. doi:10.1088/1742-6596/318/4/042051
[14]14. A. Issakhov Mathematical Modelling of the Influence of Thermal Power Plant on the Aquatic Environment with Different
Meteorological Condition by Using Parallel Technologies // Power, Control and Optimization. Lecture Notes in Electrical
Engineering. Volume 239, 2013. – 165-179 pp.
[15]15. A.Issakhov Mathematical modelling of the influence of thermal power plant to the aquatic environment by using parallel
technologies // AIP Conf. Proc. 1499, 2012. –15-18 pp. doi: http://dx.doi.org /10.1063/ 1.4768963
[16]16. J. Kim ,P. Moin Application of a fractional-step method to incompressible Navier-Stokes equations // J. Comp. Phys.
59, 1985. –308-323 pp.
[17]17. T. J. Chung Computational Fluid Dynamics. Cambridge University Press, 2002. – 1012 p.
[18]18. J. H. Ferziger, M. Peric Computational Methods for Fluid Dynamics. Springer; 3rd edition, 2013, –426 p.
[19]19. R.Peyret , D. Th. Taylor Computational Methods for Fluid Flow. New York: Berlin: Springer-Verlag. 1983, –358 p.
[20]20. P.J. Roache Computational Fluid Dynamics, Albuquerque, NM: Hermosa Publications. 1972, –434 p.
[1] 1.V.А. Rabinovich Dispersnye sistemy. — Bol’shaja jenciklopedija himii, 1985. –704 p.
[2] 2.N. B. Ur’ev Vysokokoncentrirovannye dispersnye sistemy. – М., 1980. - 502 p.
[3] 3.S. Patankar Chiclennye metody peshenija zadach teploobmena i dinamiki zhidkocti. – M.: Jenepgoatomizdat, 1984. - 152 p.
[4] 4.B.F.semenov Raschet tupbulentnogo potoka gaza v kanale plazmotrona so stupenchatym jelektpodom // – Vestnik Kypgyzcko-Poccijskogo Slavjanckogo univepsiteta. - 2003. № 5.
[5] 5.B.S. Jengel’sht , B.C. Gupovich , G.A. Decjatkov i dr. Teorija stolba jelektricheskoj dugi. -– Hovosibirsk: Hauka SO, 1990, V. 1, – 376 p.
[6] 6.A. Zhajnakov, R.M.Urusov , T.Je. Urusova Chislennyj analiz neosesimmetrichnyh jelektpicheskih dug. — Bishkek: Ilim, 2001. – 232 p.
[7] 7.I.G. Panevin, B.I. Hvecjuk ,I.P. Hazarenko i dr. Teorija i raschet prijelektrodnyh processov. -– Hovosibirsk: Hauka SO,V. 10, 1992. – 197 p.
[8] 8.M.F. Zhukov, I.M. Zacypkin , A.N. Timoshevskij i dr. Jelektpodugovye generatory termicheskoj plazmy. -– Hovosibirsk:Hauka CP RAN, V. 17, 1999. – 712 p.
[9] 9.M.F. Zhukov, A.S. Koroteev , B.A. Urjukov Prikladnaja dinamika termicheskoj plazmy. -– Hovosibirsk: Hauka SO, 1975. – 298 p.
[10]10. D. C.Wilcox Turbulence Modeling for CFD, 2nd ed. DCW Industries, 2006. – 522 p.
[11]11. T. H. Shih , W. W. Liou , A. Shabbir ,Z. Yang ,J. Zhu A New k-e Eddy Viscosity Model for High Reynolds Number Turbulent Flows-Model Development and Validation // Computers and Fluids. 24(3), 1995. – 227-238 pp.
[12]12. A.J. Chorin Numerical solution of the Navier-Stokes equations // Math. Comp. 22, 1968. – 745-762 pp.
[13]13. A. Issakhov Large eddy simulation of turbulent mixing by using 3D decomposition method // J. Phys.: Conf. Ser. 318, Issue 4, 2011. –1282-1288 pp., 042051. doi:10.1088/1742-6596/318/4/042051
[14]14. A. Issakhov Mathematical Modelling of the Influence of Thermal Power Plant on the Aquatic Environment with Different Meteorological Condition by Using Parallel Technologies // Power, Control and Optimization. Lecture Notes in Electrical Engineering. Volume 239, 2013. – 165-179 pp.
[15]15. A.Issakhov Mathematical modelling of the influence of thermal power plant to the aquatic environment by using parallel technologies // AIP Conf. Proc. 1499, 2012. –15-18 pp. doi: http://dx.doi.org /10.1063/ 1.4768963
[16]16. J. Kim ,P. Moin Application of a fractional-step method to incompressible Navier-Stokes equations // J. Comp. Phys. 59, 1985. –308-323 pp.
[17]17. T. J. Chung Computational Fluid Dynamics. Cambridge University Press, 2002. – 1012 p.
[18]18. J. H. Ferziger, M. Peric Computational Methods for Fluid Dynamics. Springer; 3rd edition, 2013, –426 p.
[19]19. R.Peyret , D. Th. Taylor Computational Methods for Fluid Flow. New York: Berlin: Springer-Verlag. 1983, –358 p.
[20]20. P.J. Roache Computational Fluid Dynamics, Albuquerque, NM: Hermosa Publications. 1972, –434 p.
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Mansurov., Z. A., Urmashev., B. A., & Issakhov., A. A. (2015). Simulation processing of disperse materials process in a continuous-flow plasma reactor. Journal of Mathematics, Mechanics and Computer Science, 85(2), 42–57. Retrieved from https://bm.kaznu.kz/index.php/kaznu/article/view/286
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