Mathematical simulation of passive scalar impurity in the transverse jet
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Keywords:
Navier-Stokes equations, mass transfer, numerical simulation, air pollution, concentrationAbstract
The active development of the industry leads to an increase in the number of factories, plants, thermal power plants and nuclear power plants, thereby there are increasing the amount of emissions into the atmosphere. Harmful chemicals are deposited and remain in the ground surface layers of the atmosphere, which leads to a variety of environmental problems which are harmful to human health and the environment. Considering the above problems, it is very important to control emissions, to keep them at a safe level for the environment. That is why it is necessary to investigate the spreading of harmful emissions. The best way to assess is the compilation of the mathematical model of the gaseous substances motion. Such model includes various physical, chemical and weather factors. In the present paper is considered a model problem, which allows to validate the correctness of the chosen mathematical models and numerical solution algorithm. The model takes into account the physical parameters of the materials, allows to calculate the chemical reaction between the reactants and the distribution of mass fractions of emission depending on the wind velocity. The calculations were performed using the ANSYS Fluent software package. In the end there are given results of numerical solutions and the graphs. This task allows to test the existing mathematical model in order to create in the further more accurate model of the emissions distribution in the atmosphere.
References
[1] Ekologicheskiy kodeks Respubliki Kazahstan (s izmeneniyami i dopolneniyami po sostojaniyu na 11.04.2014 g.).
[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.
[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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Issakhov, A. A., & Baitureyeva, A. R. (2018). Mathematical simulation of passive scalar impurity in the transverse jet. Journal of Mathematics, Mechanics and Computer Science, 91(3), 109–124. Retrieved from https://bm.kaznu.kz/index.php/kaznu/article/view/543
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