NUMERICAL INVESTIGATION OF TWO DIMENSIONAL SEDIMENT TRANSPORT IN NON-EQUILIBRIUM CONDITIONS

Öz

A two-dimensional model, under non equilibrium condition, consists of three components has been developed to determine suspended load over an erodible layer. The first component, prepares unstructured triangular meshes. The second component, employs the shallow water equation system to calculate flow treatment, is hydrodynamic component. The last component, determines suspended sediment and bed deformation, is morphodynamic component. The governing equations solved by explicit Finite volume method and discretized by Total Variation Diminishing scheme. In addition, in order to obtain a more accurate solution, two turbulence models has been adjoined to the governing equation. The numerical results of developed model are compared with the results of Flower 3D software. The model was examined for two hypothetical cases. The acceptable compatibility between numerical results of developed model and Flow3D software had been recognized. However, results of mixing length turbulence model are compatible than eddy viscosity model

Anahtar Kelimeler

• Finite Volume Method, Total Variation Diminishing scheme, Sediment Transport, Turbulence model, Non-Equilibrium condition

DENGEDE OLMAYAN ŞARTLAR ALTINDA KATI MADDE TAŞINIMININ İKİ BOYUTLU OLARAK SAYISAL İNCELENMESİ

Öz

Askıda katı madde içeren hareketli tabanlı bir yatakta dengede olmayan şartlar altında taban profilinin değişiminin belirlenmesi için üç bileşenden oluşan iki boyutlu bir model geliştirilmiştir. Birinci bileşen çözüm için düzensiz üçgen ağlar oluşturmaktadır. İkinci bileşen sığ su denklemlerini kullanarak akımı modelleyen hidrodinamik bileşendir. Son bileşen ise tabandaki değişimi ve askıdaki katı madde hareketini hesaplayan morfodinamik bileşendir. Denklemler açık Sonlu Hacimler Yöntemi, Toplam Değişim Azalması şeması kullanılarak çözülmüştür. Ayrıca, daha doğru çözüm elde edebilmek için genel denklemlere iki tane çalkantı modeli eklenmiştir. Geliştirilen modelin sonuçlarını denemek amacıyla iki tane hipotez örnek çözülmüştür. Geliştirilen modelden elde edilen sayısal sonuçlar Flow3D yazılımı sonuçlarıyla karşılaştırılmış ve uyumlu olduğu görülmüştür. Ancak, karışım uzunluğu çalkantı modeli sonuçları eddy viskozitesi modeline göre daha uyumludur

Anahtar Kelimeler

• Sonlu Hacimler Yöntemi, Toplam Değişim Azalması Şeması, katı Madde Taşınımı

Kaynakça

1. Kaya B, Gharehbaghi A. Modelling of sediment transport with Finite volume method under unsteady conditions, Journal of the Faculty of Engineering and Architecture of Gazi University, Cilt.27, 2012, s.827-836.
2. Fe J, Cueto-Felgueroso L, Navarrina F, Puertas J. Numerical viscosity reduction in the resolution of the shallow water equations with turbulent term, International Journal for Numerical Methods in Fluids, Cilt.58, 2008, s.781–802.
3. Whipple K.X, Parker G, Paola C, Mohrig D. Channel Dynamics, Sediment Transport, and the Slope of Alluvial Fans: Experimental Study, The Journal of Geology, Cilt.106, 1998, s.677–693.
4. Seo I.W, Jun I, Choi H.S. One-dimensional Finite Element Model for Suspended Sediment Transport Analysis, World City Water Forum, Cilt.24, 2009, s.3107-3112.
5. Kaya B, Gharehbaghi A. Implicit solutions of advection diffusion equation by various numerical methods, Australian Journal of Basic and Applied Sciences, Cilt.8, 2014, s.381- 391.
6. Bradford S.F, Sanders B. F. Finite-Volume Model for Shallow-Water Flooding of Arbitrary Topography, Journal of Hydraulic Engineering, Cilt.128, 2002, s.289-298.
7. Farsirotou E.D, Soulis J.V., Dermissis V.D. A Numerical Method for 2-D Bed Morphology Calculations, International Journal of Computational Fluid Dynamics, Cilt 16, 2002, s.187–200.
8. Liu X, Landry B.J, García M.H. Two-dimensional scour simulations based on coupled model of shallow water equations and sediment transport on unstructured meshes, Coastal Engineering, Cilt.55, 2008, s.800–810.

9. Castro Diaz M.J, Fernández-Nieto E.D, Ferreiro A.M, Parés C. Two-dimensional sediment transport models in shallow water equations. A second order finite volume approach on unstructured meshes, Computer Methods in Applied Mechanics and Engineering, Cilt.198, 2009, s.2520–2538.
10. Kuang C.P, hang Y, Gu J, Pan Y, Huang J. A two-dimensional morphological model based on a next generation circulation solver I: Formulation and validation.” Coastal Engineering, Cilt.59, 2011, s.1–13.
11. Cea L, Vázquez-Cendón M.E. Unstructured Şnite volume discretisation of bed friction and convective flux in solute transport models linked to the shallow water equations, Journal of Computational Physics, Cilt.231, 2012, s.3317–3339.
12. Wu W, Sanchez A, Zhang M. An implıcit 2-d depth-averaged finite-volume model of flow and sediment transport in coastal waters, Journal of Coastal Research, Cilt.59, 2011 ,s.15-26.
13. Gharehbaghi A, Kaya B. Modelling of two dimensional sediment transport phenomenon under unsteady conditions, DSI technical bulletin, Cilt.119, 2015, s.1-9.
14. Abdelaziz S, Bui M.D, Rutschmann P. Numerical investigation of flow and sediment transport around a circular bridge pier, 34th IAHR World Congress, Balance and Uncertainty, Brisbane, Australia, 2011.
15. Vasquez J, Hurtig K, Hughes B. Computational Fluid Dynamics (CFD) Modeling of Run-of-River Intakes, Hydrovision 2013 Conference Proceedings, Denver, 2013.
16. Yulistiyanto B. Numerical modeling on shallow water 2d equations applied on flow around a cylinder, proceeding of The 6th International Conference on Numerical Analysis in Engineering, Lombok Island, Mataram City, West Nusa Tenggara Province – INDONESIA, 2009.
17. Tayfur G, Singh P. Kinematic wave model for transient bed profiles in alluvial channels under nonequilibrium conditions. Water Resources Research, Cilt.43, 2007, s.1- 11.
18. Meyer-Peter E, Müller R. Formulas for bed load transport, International Association of Hydraulic Research, IAHR. 1948, s.39-64.
19. Chien N. The present status of research on sediment transport, Transactions of the American Society of Civil Engineers, Cilt.121, 1956 , s.833–868.
20. Yang C.T. Sediment Transport Theory and Practice, New York:McGraw-Hill, 1996.
21. Anastasiou k, Chan C.T. Solutin of the 2d shallow water equatıons using the finite volume method on unstructured triangular meshes, International journal for numerical methods in fluids, Cilt.24, 1997 ,s.1225-1245.
22. Wu W, Wang P, Chiba N. Comparison of Five Depth-Averaged 2-D Turbulence Models for River Flows, Archives of Hydro-Engineering and Environmental Mechanics, Cilt.51, 2004, s.183-200.
23. Yafei J, Wang, S.S.Y. CCHE2D: Two-dimensional Hydrodynamic and Sediment Transport Model For Unsteady Open Channel Flows Over Loose Bed, Technical Report No. NCCHE-TR-2001-1, 2001.
24. Versteeg H.K, Malalasekera W. An introduction to computational fluid, Glasgow: Bell & Bain Limited, 2007.