توسعه‌ي روش «هيدروديناميك ذره‌ي هموار» تعميم‌يافته براي شبيهسازي حركت اجسام جامد معلق در سيال نيوتني

DEVELOPING AN IMPROVED SMOOTHED PARTICLE HYDRODYNAMICS METHOD FOR SIMULATING THE MOTION OF SOLID BODIES IN A NEWTONIAN FLUID

در اين نوشتار با ارايه‌ي روشي جديد در اعمال شرط مرزي جامد و استفاده از رويههاي اصلاح‌شده‌ي مشتقگيري مكاني، قابليت‌هاي روش هيدروديناميك ذره‌ي هموار در حل مسايل جريان سيال حاوي اجسام معلق افزايش يافته است. روش معرفي‌شده به‌منظور اعمال مرز جامد امكان محاسبه‌ي بهينه‌ي نيروهاي تعاملي سيال ـ جامد را فراهم مي‌كند، و رويههاي اصلاح‌شده‌ي گسستهسازي مشتقات مكاني موجب حفظ سازگاري روش و نيز تسهيل اعمال روش جديد در مرز جامد مي‌شود. نوسانات غيرفيزيكي فشار نيز با اصلاح معادله‌ي پيوستگي كاهش يافته است. نتايج حاصل از شبيهسازي دوبعدي سقوط اجسام جامد دايره‌يي‌شكل در كانال حاوي سيال نيوتني تراكم‌ناپذير، با نتايج موجود در ساير مقالات مقايسه و اعتبار روش ارزيابي شده است.

In this paper, a Smoothed Particle Hydrodynamics method is introduced to simulate particulate flow problems seen in, for example, biological or refinery industries. To this end, the capability of the Smoothed Particle Hydrodynamics method has been improved using a new solid boundary treatment method, along with the so-called renormalized spatial derivative schemes. In this method, a sufficiently accurate pressure is obtained at the solid surface using the fluid equation of motion. As a result of this, the fluid-solid interaction forces can be efficiently calculated. In order to alleviate the problems caused by deficiencies in the SPH particle distribution in the neighborhood of the solid surfaces, renormalized schemes are acquired for the first and second order spatial derivatives. These schemes lead to a consistent method and facilitate the implementation of the proposed solid boundary treatment method. Using a weakly compressible SPH scheme can potentially lead to severe pressure oscillations that eventually cause a failure in the solution procedure. Here, the spurious pressure oscillations are reduced by using a modified continuity equation, in which the first and second order derivations of the pressure field are taken into account. The proposed method is verified by comparing the results of the simulations of falling circular cylinders with the available data, in a two-dimensional closed channel, filled with an incompressible Newtonian fluid. The falling of a single solid body comes as the first benchmark problem in the context of particulate flows. It is shown that the result has good agreement with those previously reported, while it is independent from the resolution of the domain discretization. In the second benchmark, the so-called drafting-kissing and tumbling of two falling cylinders is simulated. The solid-solid collision is treated by using a simple repulsive force. Good agreement with the available data is achieved. The last simulation in this paper shows the resulting deviation in the falling path of a single solid body in the presence of an obstacle placed on the side wall of the closed channel.