کاربرد معادلات دیفرانسیل کسری در تحلیل خط نشت در محیط‌های متخلخل درشت‌دانه

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی آبیاری و آبادانی، دانشکده مهندسی و فناوری کشاورزی، دانشگاه تهران، کرج، ایران.

2 گروه مهندسی آبیاری و آبادانی دانشکده مهندسی و فناوری کشاورزی، دانشگاه تهران، کرج، ایران.

3 گروه علوم خاک، دانشکده کشاورزی، دانشگاه یاسوج، یاسوج، ایران.

چکیده

در این تحقیق از معادلات دیفرانسیل مرتبه کسری برای مدل­سازی نیمرخ سطح آب درون محیط متخلخل در دامنه مرتبه­ی کسری صفر تا یک برای جریان متلاطم کاملاً توسعه‌یافته استفاده گردید و معادله توسعه­یافته تحت شرایط قانون دارسی، به روش تحلیلی حل گردید. مدل آزمایشگاهی شامل یک محیط متخلخل درشت‌دانه به طول 4/6 متر، عرض 8/0 متر و ارتفاع 1 متر و شامل مصالح گرد­گوشه می­باشد که آزمایش­ها برای حالت­های مختلف دبی جریان و سه شیب افقی، 4 و 3/20 درصد انجام شد. پارامترهای مدل و محیط متخلخل بر مبنای داده­های آزمایشگاهی واسنجی گردیدند. به‌منظور ارزیابی حل تحلیلی حاضر، نتایج با داده­های آزمایشگاهی مورد مقایسه قرار گرفت. نتایج به‌دست‌آمده توافق رضایت­بخشی با داده­های تجربی نیمرخ سطح آب را در هر سه شیب موردنظر نشان داد. به‌طوری‌که حداکثر خطای مدل پیشنهادی نسبت به داده­های تجربی 5/3 درصد است. طبق تحقیق حاضر، روش پیشنهادی می­تواند برای تجزیه و تحلیل نیمرخ سطح آب در شرایط جریان­های غیر دارسی توصیف بهتری نسبت به مدل دارسی در محیط­های متخلخل ارائه کند.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Application of Fractional Differential Equations in Analysis of Seepage Line in Coarse Porous Media

نویسندگان [English]

  • Nooshin Eslahi 1
  • Alireza Vatankhah 2
  • Mohammad Sedghi Asl 3
1 Department of Irrigation and Reclamation Engineering, Faculty of Agricultural Engineering and Technology, University College of Agriculture and Natural Resources, University of Tehran, P. O. Box 4111, Karaj, 31587-77871, Iran.
2 Associate Professor, Department of Irrigation and Reclamation Engineering, University College of Agriculture and Natural Resources, University of Tehran, P. O. Box 4111, Karaj, 31587-77871, Iran
3 Associate Professor, Soil Science Department, College of Agriculture, Yasouj University, P.O.BOX: 353, Yasouj, 75918-74831, Iran.
چکیده [English]

In this study, the fractional-order differential equations in range of (0,1) were used to model the water surface profile under Darcy's law condition in porous medium for a fully developed turbulent flow. The developed equation is solved analytically. The laboratory model used in this study consists of a coarse-grained porous medium with 6.4 m length, 0.8 m width and 1 m height, including rounded corner materials, which are tested for different flow rates and three longitudinal slopes of 0, 4, 20.3%. Then, parameters of model and porous media were calibrated based on laboratory data. In order to evaluate the proposed analytical solution, the obtained results from fractional-order differential model were compared with the laboratory data. The results showed a satisfactory agreement with experimental data of water surface profile (seepage line) in all three slopes. The maximum error of the proposed model is 3.5% compared to the experimental data. It can be concluded that the proposed method can provide better description of water surface profile analysis under non-Darcy flow conditions as compared to Darcy model in porous media.

کلیدواژه‌ها [English]

  • Fully developed turbulent flow
  • fractional-order differential model
  • free surface profile
  • Non-Darcian flow
  • analytical solution

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تحقیقات آب و خاک ایران
دوره 51، شماره 3
خرداد 1399
صفحه 563-574

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