# Assessing the operation impact of thermal power plants on the environment by mathematical modeling method

### Abstract

The paper presents an assessment of the operation impact of thermal power plants on the environment by mathematical modeling method, which is solved by the Navier - Stokes and temperature equations for an incompressible fluid in a stratified medium, based on the projection method which are approximated by control volume method. A numerical algorithm for solving the Navier-Stokes and the temperature transport equations are as follows: in the first stage it is assumed that the transfer of momentum is carried out only by convection and diffusion. The intermediate velocity field is solved by 5-step Runge - Kutta method. In the second stage, based on the found intermediate velocity field, is solved the pressure field. Poisson equation for the pressure field is solved by Jacobi method. In a third step it is assumed that the transfer is carried out only by the pressure gradient. The fourth step numerically solved temperature transfer equation as the momentum equation by 5-step Runge - Kutta method. The algorithm is parallelized on high-performance systems. The obtained numerical results of three-dimensional stratified turbulent flow reveals qualitatively and quantitatively approximate the basic laws of hydrothermal processes occurring in the aquatic environment.### References

[1] Z. Yang , T. Khangaonkar Modeling Tidal Circulation and Stratification in Skagit River Estuary Using an Unstructured Grid Ocean Model // Ocean Modelling. 2008. 28(1-3), – 34-49 pp.

[2] C. Chen , H. Liu , R. C. Beardsley An Unstructured Grid, Finite-Volume, Three-Dimensional, Primitive Equations Ocean Model: Application to Coastal Ocean and Estuaries // Journal of Atmospheric and Oceanic Technology. 2003. 20(1), – 159-186 pp.

[3] L. Zheng , C. Chen, H. Liu A modeling study of the Satilla River estuary, Georgia. I: Flooding-drying process and water exchange over the salt marsh-estuary-shelf complex // Estuaries and Coasts. 2003. 26(3), – 651-669 pp.

[4] A. Isobe , R. C. Beardsley An estimate of the cross-frontal transport at the shelf break of the East China Sea with the Finite Volume Coastal Ocean Model // Journal of Geophysical Research. 111:C03012. doi:10.1029/2005JC 003290.

[5] K. Aoki , A. Isobe Application of finite volume coastal ocean model to hindcasting the wind-induced sea-level variation in Fukuoka bay // Journal of Oceanography. 2007. 63(2), – 333-339 pp.

[6] R. H. Weisberg , L. Zheng The circulation of Tampa Bay driven by buoyancy, tides, and winds, as simulated using a finite volume coastal ocean model // Journal of Geophysical Research. 111:C01005, doi:10.1029/2005JC003067, 2006.

[7] W. Lick Numerical models of lakes currents. EPA-60013-76-020, 1976. – 140 p.

[8] Y. Sheng , W. Lick , R.T. Gedney , F.B. Molls ANumerical computation of three-dimensional circulation of Lake Erie: A comparison of a free-surface model and rigid-Lid. Model. // J. of Phys. Ocean. 1978. 8, – 713 - 727 pp.

[9] 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.2013. 239, – 165-179 pp.

[10] A.Issakhov Mathematical modelling of the influence of thermal power plant to the aquatic environment by using parallel technologies // AIP Conf. Proc. 2012. 1499, –15-18 pp. doi: http://dx.doi.org /10.1063/ 1.4768963

[11] A. Issakhov Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal power plant // International Journal of Nonlinear Science and Numerical Simulation. 2015. 16(5), – 1082-1096 pp.

[12] A. Issakhov Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal power plant under various operational capacities // Applied Mathematical Modelling. 2016. 40(2), – 229-238 pp.

[13] M. Lesieur , O. Metais , P. Comte Large eddy simulation of turbulence. New York, Cambridge University Press, 2005. – 219 p.

[14] T. J. Chung Computational Fluid Dynamics. Cambridge University Press, 2002. – 1012 p.

[15] J. H. Ferziger, M. Peric Computational Methods for Fluid Dynamics. Springer; 3rd edition, 2013, –426 p.

[16] A. Issakhov Large eddy simulation of turbulent mixing by using 3D decomposition method // J. Phys.: Conf. Ser. 2011. 318(4), –1282-1288 p., 042051. doi:10.1088/1742-6596/318/4/042051

[17] Issakhov A. Mathematical modeling of influence of the thermal power plant with considering the meteorological condition at the reservoir-cooler // Bulletin KazNU. 2012. 3(74), p. 50-59.

[2] C. Chen , H. Liu , R. C. Beardsley An Unstructured Grid, Finite-Volume, Three-Dimensional, Primitive Equations Ocean Model: Application to Coastal Ocean and Estuaries // Journal of Atmospheric and Oceanic Technology. 2003. 20(1), – 159-186 pp.

[3] L. Zheng , C. Chen, H. Liu A modeling study of the Satilla River estuary, Georgia. I: Flooding-drying process and water exchange over the salt marsh-estuary-shelf complex // Estuaries and Coasts. 2003. 26(3), – 651-669 pp.

[4] A. Isobe , R. C. Beardsley An estimate of the cross-frontal transport at the shelf break of the East China Sea with the Finite Volume Coastal Ocean Model // Journal of Geophysical Research. 111:C03012. doi:10.1029/2005JC 003290.

[5] K. Aoki , A. Isobe Application of finite volume coastal ocean model to hindcasting the wind-induced sea-level variation in Fukuoka bay // Journal of Oceanography. 2007. 63(2), – 333-339 pp.

[6] R. H. Weisberg , L. Zheng The circulation of Tampa Bay driven by buoyancy, tides, and winds, as simulated using a finite volume coastal ocean model // Journal of Geophysical Research. 111:C01005, doi:10.1029/2005JC003067, 2006.

[7] W. Lick Numerical models of lakes currents. EPA-60013-76-020, 1976. – 140 p.

[8] Y. Sheng , W. Lick , R.T. Gedney , F.B. Molls ANumerical computation of three-dimensional circulation of Lake Erie: A comparison of a free-surface model and rigid-Lid. Model. // J. of Phys. Ocean. 1978. 8, – 713 - 727 pp.

[9] 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.2013. 239, – 165-179 pp.

[10] A.Issakhov Mathematical modelling of the influence of thermal power plant to the aquatic environment by using parallel technologies // AIP Conf. Proc. 2012. 1499, –15-18 pp. doi: http://dx.doi.org /10.1063/ 1.4768963

[11] A. Issakhov Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal power plant // International Journal of Nonlinear Science and Numerical Simulation. 2015. 16(5), – 1082-1096 pp.

[12] A. Issakhov Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal power plant under various operational capacities // Applied Mathematical Modelling. 2016. 40(2), – 229-238 pp.

[13] M. Lesieur , O. Metais , P. Comte Large eddy simulation of turbulence. New York, Cambridge University Press, 2005. – 219 p.

[14] T. J. Chung Computational Fluid Dynamics. Cambridge University Press, 2002. – 1012 p.

[15] J. H. Ferziger, M. Peric Computational Methods for Fluid Dynamics. Springer; 3rd edition, 2013, –426 p.

[16] A. Issakhov Large eddy simulation of turbulent mixing by using 3D decomposition method // J. Phys.: Conf. Ser. 2011. 318(4), –1282-1288 p., 042051. doi:10.1088/1742-6596/318/4/042051

[17] Issakhov A. Mathematical modeling of influence of the thermal power plant with considering the meteorological condition at the reservoir-cooler // Bulletin KazNU. 2012. 3(74), p. 50-59.

Published

2017-11-24

How to Cite

ИСАХОВ, A. A..
Assessing the operation impact of thermal power plants on the environment by mathematical modeling method.

**Journal of Mathematics, Mechanics and Computer Science**, [S.l.], v. 89, n. 2, p. 55-64, nov. 2017. ISSN 1563-0277. Available at: <http://bm.kaznu.kz/index.php/kaznu/article/view/353>. Date accessed: 20 jan. 2019.
Section

Mathematics

Keywords
stratified environment, Navier-Stokes equations, operational capacity, Ekibastuz GRES-2, finite volume method, Runge-Kutta method, Shandaksor lake