شبيه‌سازي دوبُعدي جريان آب و رسوب در پديده شكست سد با استفاده از روش هيدروديناميك ذرات هموار (SPH)

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

روش هيدروديناميك ذرات هموار (SPH)، يك روش بدون شبكه بندي، لاگرانژي و ذره اي است كه به علت طبيعت بدون شبكه بندي و توانايي اين روش در شبيه‌سازي پديده هاي پيچيده، استفاده از آن در مكانيك سيالات و جامدات توسعه يافته است. اين مقاله شامل شبيه-سازي جريان دوفازي آب و رسوب در پديده شكست سد با استفاده از روش SPH است. معادلات حاكم بر جريان شامل معادله مومنتم، پيوستگي، معادله حالت فشار و معادله XSPH (براي محاسبه موقعيت ذرات) است. رسوبات به صورت سيالات غيرنيوتني رفتار مي كنند كه براي شبيه سازي آن‌ها از مدل هاي سيالات غيرنيوتني استفاده شده است. رسوبات با استفاده از روش تركيبي دو مدل كراس و بينگهام شبيه‌سازي شده اند. براي درستي آزمايي مدل، ابتدا نمونه تك فازي شكست سد بررسي و نتايج آن با نتايج آزمايشگاهي و عددي ساير پژوهشگران مقايسه شده است. سپس دو نمونه دو فازي شكست سد با ابعاد مختلف بررسي شده و نتايج آزمايشگاهي موجود مقايسه و ميزان خطا محاسبه شده است. مقدار خطاي به دست آمده از مقايسه تغييرات ارتفاع رسوبات در فواصل 5 و 14 سانتي‌متري مخزن در نمونه عددي و آزمايشگاهي به ترتيب برابر با 55/6 و 94/5 درصد است. مقايسه نتايج نشان مي دهد كه مطابقت خوبي بين نتايج عددي و آزمايشگاهي وجود دارد.

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 numericalsolutions 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.