2D Simulation of Water and Sediment Flow in Dam Break by Smoothed Particle Hydrodynamics (SPH)

Authors
S. L. Razavi Toosi
S. A. Ayyoubzadeh
A. Valizadeh
Abstract
Computational Fluid Dynamics (CFD) implementations are also classified as the Lagrangian and Eulerian methods. Smoothed Particle Hydrodynamics (SPH) is a mesh free particle method based on Lagrangian formulation with a number of advantages. This method is obtained approximate numerical solutions of the equations of the fluid dynamics by replacing the fluid with a set of particles. All particles carry their properties and then the advection is taken care automatically. In contrast, Eulerian mesh based numerical methods have difficulties such as the problem of numerical diffusion due to advection terms. Because of the simplicity and robustness of SPH, this numerical method has been extended to complex fluid and solid mechanics problems. The important advantage of SPH is that the muli-phase flows can be modeled by SPH and each particle can be assigned to a different phase. In this paper, the SPH method is used for simulating water and sediment flow in dam break problem. The government equations are momentum and continuity equations which are described in a Lagrangian framework. Also, the compressible flows are modeled as a weakly compressible flow via the equation of state. The XSPH equation is applied for each particle movement at each time step. The Wendland kernel is applied as smoothing function. Sediments are treated as non-Newtonian fluid and for simulating them the non-Newtonian models are used. In this paper, the combination of two rheological models named Bingham and Cross is used. The predictor- corrector algorithm is applied. The time step is controlled by Courant condition (CFL), the forcing terms and the viscous diffusion terms. On the other hand, the laboratory experiment of dam break is performed and the new experimental set up was built. At first, the column of water with a height of 0.5 m and the wide of 0.25 m is blocked by a partition gate. The bottom of the water column is covered with non cohesive sediments. The sediments are sands with d50=1.4 mm. The partition gate separates the water column from the downstream channel and the speed of partition gate is more important. Then the partition gate is removed with a specific velocity. The partition gate opens completely from above with a constant speed of 0.6 m/s. The flow motion is recorded by digital camera system. Finally, a comparison between experimental results and computational results is carried out and the errors are calculated. The error of sediment height variations in specific horizontal distances (x=5 cm and 14 cm) in reservoir are 6.55% and 5.94%, respectively. Also, the sediment surface profiles are shown in different times. The comparisons are shown good agreements between numerical and experimental results. The good agreement proves the ability of the present SPH model to simulating two phase flows.

Keywords

  1. .رضوی طوسی، س. ل. (1391) شبیه­سازی دوبعدی آب­شستگی سریع رسوبات ناشی از عملیات تخلیه رسوب با استفاده از روش هیدرودینامیک ذرات هموار. رساله دکتری. رشته سازه­های آبی. دانشگاه تربیت مدرس.


    2.ولی­زاده، ع. (1387) مدلسازی دوفازی پخش و انتقال آلودگی نفتی در دریا. رساله دکتری. رشته مهندسی عمران- سازه­های هیدرولیکی. دانشگاه تربیت مدرس.



    1. Abderrezzak, K. E. K., Paquier, A. and Gay, B. (2008). One-dimensional numerical modeling of dam-break waves over movable beds: Application to experimental and field cases. Environ Fluid Mech. 8. 169- 198.

    2. Ashtiani, B. A., Shobeyri, G. and Farhadi, L. (2007). Modified incompressible SPH method for simulating freesurface problems. Fluid Dynamics Research. http://dx.doi.org/10.1016/j.fluiddyn. 2007.12.001.

    3. Cao, Zh., Pender, G., Wallis, S. and Carling, P. (2004). Computational Dam-Break Hydraulics over Erodible Sediment Bed. Journal of Hydraulic Engineering. ASCE. PP: 689- 703.

    4. Costabile, P. and Macchione, F. (2006). One dimensional modeling of dam break flow over erodible sediment bed. Proceedings of the international conference on fluvial hydraulics. Lisbon. Purtugal.

    5. Crespo, A. J. C., Gómez-Gesteira, M. and R. A. and Dalrymple, F. (2008). Modeling Dam Break Behavior over a Wet Bed by a SPH Technique. Journal of waterway, port, coastal and ocean engineering. ASCE. PP: 313-320.

    6. Cummins, S. J. and Rudman, M. (1999). An SPH projection method. J. Comput. Phys. 152. pp: 584- 607.

    7. Dalrymple, R. A. and Knio, O. (2001). SPH modeling of water waves. Proceeding of coastal dynamics. 10. PP: 227-264.

    8. Falappi, S., Gallati, M. and Maffio, A. (2007). SPH simulation of sediment scour in reservoir sedimentation problems. SPHERIC- second international workshop. Madrid, May 23rd-25th.

    9. Gottardi, G. and Venutelli, M. (2004). Central scheme for two-dimensional dam-break flow simulation. Advances in Water Resources. 27. PP: 259–268.

    10. Gingold, R. A. and Monaghan, J. J. (1977). Smoothed Particle Hydrodynamics: Theory and application to non-spherical stars. Mon. Not. R. astr. Soc. 375- 389.

    11. Hirt, C.W. and Nichols, B.D. (1981). "Volume of fluid (VOF) method for the dynamics of free boundaries. " J Comput Phys, Vol. 39, No. 1, pp. 201-25.

    12. Hu, C. and Sueyoshi, M. (2010). Numerical Simulation and Experiment on Dam Break Problem. J. Marine. Sci. Appl. 9. PP:109-114.

    13. Issa, R., Boersma, B. J., Violeau, D. and Laurence, D. (2006). Modelling turbulence flows through larg eddy simulation in SPH. 1st SPHERIC workshop, Roome, 10th May.

    14. Kim, S. (2002). A Study of Non-Newtonian Viscosity and Yield Stress of Blood in a Scanning Capillary-Tube Rheometer. Ph.D. thesis. Faculty of Drexel University.

    15. Liu, G. R. and Liu, M. B. (2003). Smoothed Particle Hydrodynamics: A Meshfree Particle Method, World Scientific Publishing.

    16. Lucy, L. B. (1977). A numerical approach to the testing of the fission hypothesis. Astron. J. 82. pp: 1013-1024.

    17. Manenti, S., Di Monaco, A., Gallati, M., Sibilla, S., Agate, G., Guandalini, R., Maffio, G. (2009).Simulating rapid sediment scour by water flow with SPH, SPHERIC Conference.

    18. Martin, J.C, Moyce, W.J. (1952). "An experimental study of the collapse of liquid columns on a rigid horizontal plane. " Philos Trans R Soc London, Ser A., Vol. 244, No. 882, pp. 312-324.

    19. Monaghan, J. J. (1985). Particle methods for hydrodynamics. Physics reports. 3 (2). 71p.

    20. Monaghan, J. J. (1989). On the problem of penetration in particle methods. Journal of Computational physics. 82. pp:1-15.

    21. Monaghan, J. J. (1992). Smoothed particle hydrodynamics. Ann. Rev. Astronom. Astrophys. 30. pp:543–574.

    22. Monaghan, J. and Kos, A. (1999). Solitary Waves on a Cretan Beach. J.Waterway, Port, Coastal and Ocean Engineering. pp: 145– 154.

    23. Monaghan, J. J. (2005). Smoothed Particle Hydrodynamics, Rep. Prog. Phys. 68, 1703-1759.

    24. Pan, C.H., Xu, X.Z. and Lin, B.Y. (1993). "Simulating free surface flows by MAC method. " Estuar Coastal Eng., Vol. 1, No. 2, pp. 51-8.

    25. Rosatti, G., Murillo, J. and Fraccarollo, L. (2008). Generalized Roe schemes for 1D two-phase, free-surface flows over a mobile bed. Journal of Computational Physics. 227. PP: 10058–10077.

    26. Shakibaeinia, A. and Jin, Y. C. (2011). A mesh-free particle model for simulation of mobile-bed dam break. Advances in Water Resources. 34. PP: 794–807.

    27. Shao, S., Lo, E. Y. M. (2003). Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Advances in water resources.26. 787-800.

    28. Sibilla, S. (2008). An SPH method to simulate local scouring. SPHERIC- second international workshop. Madrid, May 23rd-25th.

    29. Spinewine, B. (2005). Two-layer flow behaviour and the effects of granular dilatancy in dam break induced sheet-flow, PhD thesis, Univerisité de Louvain.

    30. Tseng, M. H. and Chu, C. R. (2000). The simulation of dam-break flows by an improved Predictor-corrector TVD scheme. Advances in Water Resources. 23. PP: 637-643.

    31. Wendland, H. (1995). Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Advances in Computational Mathematics. 4(1). pp: 389-396.

    32. Zu, S. and Dalrymple, R. (2004). Sediment suspension modeling by smoothed particle hydrodynamics. Coastal engineering . 1948-1958.

Modares Civil Engineering journal
Volume 15, Issue 2
July and August 2015
Pages 23-34