بررسي عددي و تجربي حركت يك جسم جامد تغيير شكل‌پذير و برخورد آن با يك سطح صلب

Numerical and Experimental Investigation of the Motion of a Deformable Solid Body and its Impact on a Rigid Substrate

در تحقيق حاضر به بررسي عددي و آزمايشگاهي برهمكنش بين يك جسم جامد تغيير شكل پذير و محيط سيال توسعه داده شده خواهيم پرداخت. مدل توسعه يافته از روش اويلري براي سيال و جسم جامد، و از روش نسبت حجمي سيال براي تعيين موقعيت جسم جامد بهره مي‌برد. براي محاسبات مربوط به جسم جامد از يك تانسور كرنش استفاده شده كه در هر گام زماني، توسط يك رابطه‌ي انتقال محاسبه مي‌‌شود. براساس مقادير كرنش به دست آمده و نيز معادله‌ي مشخصه‌ي جسم جامد، تنش هاي كشسان در ناحيه‌ي جسم جامد محاسبه مي‌شود. به‌منظور بهبود شرط مرزي ديناميكي، گرانروي (گران‌روي‌ي) جسم جامد افزايش يافته كه اين امر با كاهش تاثير تنش‌هاي كشسان در فصل مشترك سيال/ جامد، سبب پايداري شبيه‌سازي مي‌شود. در ادامه، آزمايشِ تجربي حركت جسم جامد در هوا و برخورد آن با سطح صلب انجام شد. همين مورد با استفاده از برنامه‌ي عددي توسعه‌يافته نيز شبيه سازي و نتايج حاصله با نتايج آزمايشگاهي مقايسه شد.

In this study, a numerical model for simulation of the interaction between a deformable solid body and an incompressible fluid is developed. The solid object is assumed to be a hyperelastic material which has many applications in biological systems. The developed model uses an Eulerian approach for both fluids and solids and the volume of fluid method, to obtain the position of the solid object. For treating the solid object, a deformation tensor is employed, which is computed by means of a transport equation at each time step. Based on the obtained value of deformation and, also, the constitutive equation of the solid object, elastic stresses can be calculated. This term, which has a nonzero value only in the solid zone, is added to the fluid governing equations. The elastic stresses have discontinuities across the fluid/solid interface. Therefore, the dynamic boundary condition is not completely satisfied. For improving this boundary condition, the viscosity in the solid object is increased, which reduces the effects of the elastic stresses in the fluid/ solid interface; resulting in a stable simulation. For validating the numerical results, a simple experiment is performed, in which the movement of a spherical deformable solid object in air and its impact on a rigid substrate are studied. In this experiment, a CCD camera is employed to capture images from the movement of the solid object. Next, an image processing technique is used to obtain the required data. The same case is also simulated using the developed numerical program, and the obtained results are compared with those of the experiments. The numerical results are in good agreement with those of the experiments performed in this study.