Abstract
It is very important to analyze the polluted water that streams transfer around them by diffusion. Dirty water leaking from streams like this causes soil and water pollution. The protection of surface and underground water resources is very important given the decreasing water resources. How deep a pollutant has infiltrated can be found by solving the diffusion equation. In this study, the concentration amount of the pollutant passing from a long-polluted stream to the soil was investigated by the finite difference method. Instead of using expensive packet programs, a widespread program Matlab used by engineers and scientists to analyze data, develop algorithms, solve problems analytically and numerically, and create models is preferred in this study. The cross-section of the stream is rectangular and its length is considered to be quite long. Therefore, the problem has been examined in two dimensions. First, the necessary finite difference equations are derived and this problem is analyzed using appropriate boundary conditions. A numerical solution has been obtained for two cases in which the bottom of the stream is permeable and it is not. The mass flow rate of both of the cases was calculated and it is found that the mass flow rate in the first case in which the bottom of the stream is permeable is almost double of the second case. The flow velocities on the boundaries have been found to be less in the case in which the bottom of the stream is impermeable.
References
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- Flynn G, Yalkowsky SH, Roseman T. Mass transport phenomena and models: theoretical concepts. Journal of Pharmaceutical Sciences 1974;63:479–510.
- Desai CS, Zaman M. Advanced geotechnical engineering: Soil-structure interaction using computer and material models. CRC Press; 2013.
- Das BM, Das B. Advanced soil mechanics. vol. 270. Taylor & Francis New York; 2008.
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- Chatwin P, Allen C. Mathematical models of dispersion in rivers and estuaries. Annual Review of Fluid Mechanics 1985;17:119–49.
- Dehghan M. Weighted finite difference techniques for the one-dimensional advection–diffusion equation. Applied Mathematics and Computation 2004;147:307–19.
- Ott WR. Environmental statistics and data analysis. Routledge; 2018.
- Tychon B, Vander Borght P, De Backer LW. Water and nitrogen transfer study through soils of a small agricultural water catchment. Water Science and Technology 1999;39:69–76.
- Johnes PJ. Evaluation and management of the impact of land use change on the nitrogen and phosphorus load delivered to surface waters: the export coefficient modelling approach. Journal of Hydrology 1996;183:323–49.
- Woitke P, Wellmitz J, Helm D, Kube P, Lepom P, Litheraty P. Analysis and assessment of heavy metal pollution in suspended solids and sediments of the river Danube. Chemosphere 2003;51:633–42.
- Shackelford CD. Diffusion of contaminants through waste containment barriers. Transportation Research Record 1989.
- Weeks EP, Earp DE, Thompson GM. Use of atmospheric fluorocarbons F‐11 and F‐12 to determine the diffusion parameters of the unsaturated zone in the southern high plains of Texas. Water Resources Research 1982;18:1365–78.
- Noye B, Tan H. A third‐order semi‐implicit finite difference method for solving the one‐dimensional convection‐diffusion equation. International Journal for Numerical Methods in Engineering 1988;26:1615–29.
- Noye B, Tan H. Finite difference methods for solving the two‐dimensional advection–diffusion equation. International Journal for Numerical Methods in Fluids 1989;9:75–98.
- Lardner R, Song Y. An algorithm for three‐dimensional convection and diffusion with very different horizontal and vertical length scales. International Journal for Numerical Methods in Engineering 1991;32:1303–19.
- Sankaranarayanan S, Shankar N, Cheong H. Three-dimensional finite difference model for transport of conservative pollutants. Ocean Engineering 1998;25:425–42.
- Kaczmarek M, Hueckel T, Chawla V, Imperiali P. Transport through a clay barrier with the contaminant concentration dependent permeability. Transport in Porous Media 1997;29:159–78.
- Lastochkin D, Favelukis M. Bubble growth in a variable diffusion coefficient liquid. Chemical Engineering Journal 1998;69:21–5.
- Kačur J, Malengier B, Remešíková M. Solution of contaminant transport with equilibrium and non-equilibrium adsorption. Computer Methods in Applied Mechanics and Engineering 2005;194:479–89.
- Craig JR, Rabideau AJ. Finite difference modeling of contaminant transport using analytic element flow solutions. Advances in Water Resources 2006;29:1075–87.
- Sayed M, Serrer M, Mansard E. Oil spill drift and fate model. Oil Spill Response: A Global Perspective, Springer; 2008, 205–20.
- Zhang Y, Wang Q, Zhang ST. Numerical simulation of Benzene in soil contaminant transport by finite difference method. vol. 414, Trans Tech Publ; 2012, 156–60.
- Ordu S, Ordu E, Mutlu R. Axisymmetric spilled pollutant analysis in steady-state using finite difference method. Feb-Fresenius Environmental Bulletin 2022:9587-9592.
- Gündoğdu Ö, Kopmaz O, Ceviz MA. Mühendislik ve fen uygulamalarıyla Matlab. Nobel Yayıncılık; 2004.
- Halliday D, Resnick R, Walker J. Fundamentals of physics. John Wiley & Sons; 2013.
- Cengel YA. a Afshin J. Ghajar A. Heat and Mass Transfer, 4th Edition in SI Units, Special Indian Edition, Mcgraw Hill Education, New York, United States, 2011.
- Karaoğlan HC, Mutlu R. A Water Level Sensor Design Using Finite Difference Solution and Its Coding in Matlab. European Journal of Engineering and Applied Sciences. 2020; 3(1), 37-45.
Abstract
Akarsuların etraflarına difüzyon yolu ile aktardıkları kirli suyun analizi oldukça önemlidir. Bu akarsulardan sızan kirli su toprak ve su kirliliğine neden olmaktadır. Yüzey ve yeraltı su kaynaklarının korunması giderek azalan su kaynakları dikkate alındığında çok önemlidir. Bir kirleticinin ne kadar derine sızdığı difüzyon denklemi çözülerek bulunabilir. Bu çalışmada atıksularla kirlenmiş uzun bir dereden toprağa geçen kirleticinin konsantrasyon miktarı sonlu farklar yöntemi ile incelenmiştir. Bu çalışmada pahalı paket programlar kullanmak yerine mühendisler ve bilim insanlarının verileri analiz etmek, algoritma geliştirmek, problemleri analitik ve sayısal olarak çözmek ve model oluşturmak için kullandıkları yaygın bir program olan Matlab tercih edilmiştir. Derenin kesiti diktörtgen alınmış ve boyu oldukça uzun kabul edilmiştir. Bundan dolayı problem iki boyutta incelenmiştir. Önce gerekli sonlu farklar denklemleri türetilmiş ve uygun sınır şartları kullanılarak problem analiz edilmiştir. Akarsuyun tabanının geçirimli olduğu ve olmadığı iki durum için sayısal çözüm elde edilmiştir. Her iki durumun kütlesel debisi hesaplanmış ve akarsuyun tabanının geçirimli olduğu birinci durumdaki kütlesel debinin, ikinci durumun neredeyse iki katı olduğu bulunmuştur. Akarsu tabanının geçirimsiz olması durumunda sınırlardaki akış hızlarının daha az olduğu tespit edilmiştir.
References
- Davis ML, Cornwell DA. Introduction to environmental engineering. WCB McGraw-Hill; 1998.
- Flynn G, Yalkowsky SH, Roseman T. Mass transport phenomena and models: theoretical concepts. Journal of Pharmaceutical Sciences 1974;63:479–510.
- Desai CS, Zaman M. Advanced geotechnical engineering: Soil-structure interaction using computer and material models. CRC Press; 2013.
- Das BM, Das B. Advanced soil mechanics. vol. 270. Taylor & Francis New York; 2008.
- Wanielista M, Kersten R, Eaglin R. Hydrology: Water quantity and quality control. John Wiley and Sons; 1997.
- Das BM, Sobhan K. Principles of geotechnical engineering, Cengage Learning. Stamford, Connecticut 2010.
- Kiusalaas J. Numerical methods in engineering with Matlab®. Cambridge university press; 2005.
- Chatwin P, Allen C. Mathematical models of dispersion in rivers and estuaries. Annual Review of Fluid Mechanics 1985;17:119–49.
- Dehghan M. Weighted finite difference techniques for the one-dimensional advection–diffusion equation. Applied Mathematics and Computation 2004;147:307–19.
- Ott WR. Environmental statistics and data analysis. Routledge; 2018.
- Tychon B, Vander Borght P, De Backer LW. Water and nitrogen transfer study through soils of a small agricultural water catchment. Water Science and Technology 1999;39:69–76.
- Johnes PJ. Evaluation and management of the impact of land use change on the nitrogen and phosphorus load delivered to surface waters: the export coefficient modelling approach. Journal of Hydrology 1996;183:323–49.
- Woitke P, Wellmitz J, Helm D, Kube P, Lepom P, Litheraty P. Analysis and assessment of heavy metal pollution in suspended solids and sediments of the river Danube. Chemosphere 2003;51:633–42.
- Shackelford CD. Diffusion of contaminants through waste containment barriers. Transportation Research Record 1989.
- Weeks EP, Earp DE, Thompson GM. Use of atmospheric fluorocarbons F‐11 and F‐12 to determine the diffusion parameters of the unsaturated zone in the southern high plains of Texas. Water Resources Research 1982;18:1365–78.
- Noye B, Tan H. A third‐order semi‐implicit finite difference method for solving the one‐dimensional convection‐diffusion equation. International Journal for Numerical Methods in Engineering 1988;26:1615–29.
- Noye B, Tan H. Finite difference methods for solving the two‐dimensional advection–diffusion equation. International Journal for Numerical Methods in Fluids 1989;9:75–98.
- Lardner R, Song Y. An algorithm for three‐dimensional convection and diffusion with very different horizontal and vertical length scales. International Journal for Numerical Methods in Engineering 1991;32:1303–19.
- Sankaranarayanan S, Shankar N, Cheong H. Three-dimensional finite difference model for transport of conservative pollutants. Ocean Engineering 1998;25:425–42.
- Kaczmarek M, Hueckel T, Chawla V, Imperiali P. Transport through a clay barrier with the contaminant concentration dependent permeability. Transport in Porous Media 1997;29:159–78.
- Lastochkin D, Favelukis M. Bubble growth in a variable diffusion coefficient liquid. Chemical Engineering Journal 1998;69:21–5.
- Kačur J, Malengier B, Remešíková M. Solution of contaminant transport with equilibrium and non-equilibrium adsorption. Computer Methods in Applied Mechanics and Engineering 2005;194:479–89.
- Craig JR, Rabideau AJ. Finite difference modeling of contaminant transport using analytic element flow solutions. Advances in Water Resources 2006;29:1075–87.
- Sayed M, Serrer M, Mansard E. Oil spill drift and fate model. Oil Spill Response: A Global Perspective, Springer; 2008, 205–20.
- Zhang Y, Wang Q, Zhang ST. Numerical simulation of Benzene in soil contaminant transport by finite difference method. vol. 414, Trans Tech Publ; 2012, 156–60.
- Ordu S, Ordu E, Mutlu R. Axisymmetric spilled pollutant analysis in steady-state using finite difference method. Feb-Fresenius Environmental Bulletin 2022:9587-9592.
- Gündoğdu Ö, Kopmaz O, Ceviz MA. Mühendislik ve fen uygulamalarıyla Matlab. Nobel Yayıncılık; 2004.
- Halliday D, Resnick R, Walker J. Fundamentals of physics. John Wiley & Sons; 2013.
- Cengel YA. a Afshin J. Ghajar A. Heat and Mass Transfer, 4th Edition in SI Units, Special Indian Edition, Mcgraw Hill Education, New York, United States, 2011.
- Karaoğlan HC, Mutlu R. A Water Level Sensor Design Using Finite Difference Solution and Its Coding in Matlab. European Journal of Engineering and Applied Sciences. 2020; 3(1), 37-45.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | April 30, 2023 |
| Submission Date | July 28, 2022 |
| Published in Issue | Year 2023 Volume: 10 Issue: 19 |
