Математическое моделирование распространения пассивной скалярной примеси в поперечной струе
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Ключевые слова:
уравнения Навье-Стокса, перенос веществ, численное моделирование, загрязнение воздуха, концентрацияАннотация
Активное развитие промышленности приводит к увеличению количества заводов, фабрик, ТЭС и АЭС, вследствие чего повышается объем выбросов примеси в атмосферу. Вредные химические соединения оседают и остаются в приземных слоях атмосферы, что влечет за собой различные экологические проблемы, наносящие вред здоровью населения и окружающей среде. Учитывая вышеуказанные проблемы, очень важно контролировать объем выбросов, чтобы поддерживать их на безопасном для окружающей среды уровне. Для этого необходимо исследовать распространение вредных выбросов. Наиболее оптимальным способом оценки является составление математической модели движения газообразных веществ. Подобная модель предусматривает различные физические, метеорологические и химические факторы. В представленной работе рассматривается модельная задача, позволяющая произвести валидацию корректности выбранной математической модели и алгоритма численного решения. Модель учитывает физические параметры веществ, позволяет рассчитать химическую реакцию реагентов и распространение массовых долей выбросов в зависимости от скорости ветра. Расчеты выполнялись с помощью программного комплекса ANSYS Fluent. В итоге приведены результаты численных решений и построены графики. Подобная задача позволяет протестировать имеющуюся математическую модель и в дальнейшем построить максимально корректную модель распространения выбросов в атмосфере.
Библиографические ссылки
[1] Ekologicheskiy kodeks Respubliki Kazahstan (s izmeneniyami i dopolneniyami po sostojaniyu na 11.04.2014 g.).
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[19] Shan, J. W., Dimotakis, P. E. Reynolds-number effects and anisotropy in transverse-jet mixing // J. Fluid. Mech. 566.- 2006. - 47-96 pp.
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[25] Chochua, G., Shyy, W., Thakur, S., Brankovic, A., Lienau, K., Porter, L., Lischinsky, D. A computational and experimental investigation of turbulent jet and crossflow interaction. Numer. Heat Transfer A 38.- 2000. - 557-572 pp.
[26] Acharya, S., Tyagi, M., Hoda, A. Flow and heat transfer predictions for film-cooling. Ann. NY Acad. Sci. 934.- 2001. - 110-125 pp.
[27] Yuan, L. L., Street, R. L., Ferziger, J. H. Large-eddy simulations of a round jet in crossflow // J. Fluid Mech. 379.- 1999. - 71-104 pp.
[28] Schluter, J. U., Schonfeld, T. LES of jets in crossflow and its application to a gas turbine burner // Flow Turbulence Combust. 65.- 2000. - 177-203 pp.
[29] Chai, X., Iyer, P. S.,Mahesh, K. Numerical study of high speed jets in crossflow // Journal of Fluid Mechanics, Volume 785.- 2015. - 152-188 pp.
[30] Muppidi, S., Mahesh, K. Direct numerical simulation of round turbulent jets in crossflow // J. Fluid. Mech. 574, 2007,- 59-84 pp.
[31] Livescu, D., Jaberi, F. A., Madnia C. K. Passive-scalar wake behind a line source in grid turbulence // Journal of Fluid Mechanics. Volume 416.- 2000. - 117-149 pp.
[32] Camussi R., Guj G., Stella A. Experimental study of a jet in a crossflow at very low Reynolds number // Journal of Fluid Mechanics. Volume 454. - 2002. - 113-144 pp.
[33] Chung T. J. Computational Fluid Dynamics. Cambridge University Press, 2002 - p. 1012.
[34] Ferziger J. H., Peric M. Computational Methods for Fluid Dynamics. Springer; 3rd edition, 2013, -p. 426
[35] Issakhov A. Large eddy simulation of turbulent mixing by using 3D decomposition method. Issue 4 // J. Phys.: Conf. Ser. 318. pp. 1282-1288. -2011. doi:10.1088/1742-6596/318/4/042051.
[36] Issakhov A. Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal power plant // International Journal of Nonlinear Science and Numerical Simulation, 16(5). -2015, -229-238 pp., doi:10.1515/ijnsns-2015-0047.
[37] Issakhov A. Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal power plant under various operational capacities // Applied Mathematical Modelling (2015), Volume 40, Issue 2, -2016, - 1082- 1096 pp. http://dx.doi.org/10.1016/j.apm.2015.06.024.
[2] Ryzhkin V. Ya. Teplovye elektricheskie stancii, / red V.Ya. Girshfelda .- M: Energoatomizdat.- 1987 g.- 321 s.
[3] Dukenbaev K. Energetika Kazahstana. Tehnicheskiy aspekt, - Almaty, 2001 g.-312 s.
[4] U.S. Environmental Protection Agency, Clean Air Markets Division, available at: https://ampd.epa.gov/ampd/
[5] Zavila O. Physical Modeling of Gas Pollutant Motion in the Atmosphere, Advances in Modeling of Fluid Dynamics, Dr. Chaoqun Liu (Ed.), InTech, 2012, DOI: 10.5772/48405.
[6] Goyal P., Kumar A. Mathematical Modeling of Air Pollutants: An Application to Indian Urban City, Air Quality-Models and Applications, Prof. Dragana Popovic (Ed.), InTech, 2011, DOI: 10.5772/16840.
[7] Kozic, M. S. A numerical study for the assessment of pollutant dispersion from kostolac b power plant to viminacium for different atmospheric conditions // THERMAL SCIENCE, Vol. 19, No. 2.-2015.- pp. 425-434.
[8] Falconi C. J., Denev J. A., Frohlich J. and Bockhorn H. A test case for microreactor flows - a two-dimensional jet in crossflow with chemical reaction, Internal Report, available at: http://www.ict.uni- karlsruhe.de/index.pl/themen/dns/index.html: "2d test case for microreactor flows. Internal report. 2007 July 20, 2007.
[9] Schonauer, W., Adolph, T. FDEM: The Evolution and Application of the Finite Difference Element Method (FDEM) Program Package for the Solution of Partial Differential Equations, Abschlussbericht des Verbundprojekts FDEM, UniversitЁat Karlsruhe.- 2005.- available at http://www.rz.uni-karlsruhe.de/rz/docs/FDEM/Literatur/fdem.pdf
[10] Margason, R. J. Fifty years of jet in crossflow research. In AGARD Symp. on a Jet in Cross Flow, Winchester, UK.- AGARD CP . - 1993.- p. 534.
[11] Kamotani, Y., Greber, I. Experiments on turbulent jet in a crossflow // AIAA J. 10.-1972. - 1425-1429 pp.
[12] Fearn, R. L., Weston, R. P. Vorticity associated with a jet in crossflow // AIAA J. 12.-, 1974. - 1666-1671 pp.
[13] Andreopoulos, J., Rodi, W. Experimental investigation of jets in a crossflow // J. Fluid Mech. 138.- 1984. - 93-127 pp.
[14] Krothapalli, A., Lourenco, L., Buchlin, J. M. Separated flow upstream of a jet in a crossflow // AIAA J. 28.- 1990. - 414-420 pp.
[15] Fric, T. F., Roshko, A. Vortical structure in the wake of a transverse jet // J. Fluid Mech. 279.- 1994. - 1-47 pp.
[16] Kelso, R. M., Lim, T. T., Perry, A. E. An experimental study of round jets in cross-flow // J. Fluid Mech. 306.- 1996. - 111-144 pp.
[17] Smith, S. H., Mungal, M. G. Mixing, structure and scaling of the jet in crossflow // J. Fluid Mech. 357.- 1998. - 83-122 pp.
[18] Su, L. K., Mungal, M. G. Simultaneous measurement of scalar and velocity field evolution in turbulent crossflowing jets // J. Fluid Mech. 513.-2004. - 1-45 pp.
[19] Shan, J. W., Dimotakis, P. E. Reynolds-number effects and anisotropy in transverse-jet mixing // J. Fluid. Mech. 566.- 2006. - 47-96 pp.
[20] Broadwell, J. E., Breidenthal, R. E. Structure and mixing of a transverse jet in incompressible flow // J. Fluid Mech. 148.- 1984.- 405-412 pp.
[21] Karagozian, A. R. An analytical model for the vorticity associated with a transverse jet // AIAA J. 24.- 1986.- 429-436 pp.
[22] Hasselbrink, E. F., Mungal, M. G. Transverse jets and jet flames. Part 1. Scaling laws for strong transverse jets // J. Fluid Mech, 443.- 2001.- 1-25 pp.
[23] Muppidi, S., Mahesh, K. Study of trajectories of jets in crossflow using direct numerical simulations. J. Fluid. Mech. 530.- 2005. - 81-100 pp.
[24] Muppidi, S., Mahesh, K. Direct numerical simulation of passive scalar transport in transverse jets. J. Fluid Mech., 598.- 2008. - 335-360 pp.
[25] Chochua, G., Shyy, W., Thakur, S., Brankovic, A., Lienau, K., Porter, L., Lischinsky, D. A computational and experimental investigation of turbulent jet and crossflow interaction. Numer. Heat Transfer A 38.- 2000. - 557-572 pp.
[26] Acharya, S., Tyagi, M., Hoda, A. Flow and heat transfer predictions for film-cooling. Ann. NY Acad. Sci. 934.- 2001. - 110-125 pp.
[27] Yuan, L. L., Street, R. L., Ferziger, J. H. Large-eddy simulations of a round jet in crossflow // J. Fluid Mech. 379.- 1999. - 71-104 pp.
[28] Schluter, J. U., Schonfeld, T. LES of jets in crossflow and its application to a gas turbine burner // Flow Turbulence Combust. 65.- 2000. - 177-203 pp.
[29] Chai, X., Iyer, P. S.,Mahesh, K. Numerical study of high speed jets in crossflow // Journal of Fluid Mechanics, Volume 785.- 2015. - 152-188 pp.
[30] Muppidi, S., Mahesh, K. Direct numerical simulation of round turbulent jets in crossflow // J. Fluid. Mech. 574, 2007,- 59-84 pp.
[31] Livescu, D., Jaberi, F. A., Madnia C. K. Passive-scalar wake behind a line source in grid turbulence // Journal of Fluid Mechanics. Volume 416.- 2000. - 117-149 pp.
[32] Camussi R., Guj G., Stella A. Experimental study of a jet in a crossflow at very low Reynolds number // Journal of Fluid Mechanics. Volume 454. - 2002. - 113-144 pp.
[33] Chung T. J. Computational Fluid Dynamics. Cambridge University Press, 2002 - p. 1012.
[34] Ferziger J. H., Peric M. Computational Methods for Fluid Dynamics. Springer; 3rd edition, 2013, -p. 426
[35] Issakhov A. Large eddy simulation of turbulent mixing by using 3D decomposition method. Issue 4 // J. Phys.: Conf. Ser. 318. pp. 1282-1288. -2011. doi:10.1088/1742-6596/318/4/042051.
[36] Issakhov A. Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal power plant // International Journal of Nonlinear Science and Numerical Simulation, 16(5). -2015, -229-238 pp., doi:10.1515/ijnsns-2015-0047.
[37] Issakhov A. Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal power plant under various operational capacities // Applied Mathematical Modelling (2015), Volume 40, Issue 2, -2016, - 1082- 1096 pp. http://dx.doi.org/10.1016/j.apm.2015.06.024.
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Как цитировать
Issakhov, A. A., & Baitureyeva, A. R. (2018). Математическое моделирование распространения пассивной скалярной примеси в поперечной струе. Вестник КазНУ. Серия математика, механика, информатика, 91(3), 109–124. извлечено от https://bm.kaznu.kz/index.php/kaznu/article/view/543
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Прикладная математика
