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Article information
2017 , Volume 22, ¹ 3, p.71-90
Pivovarov Y.V.
Calculation of motion of two solid spheres in a Bingham fluid under the action of gravitational force
The purpose of investigation is the development of algorithm and carrying out the research of flow regimes in axisymmetric non-stationary problem of the motion of two solid spheres in a Bingham fluid under the action of gravitational force. In the solution of problem the methods of finite differences and the method of alternating directions were emplyed. Solution of vortex problem uses the pentadiagonal matrix algorithm and for the solution of stream function problem so does the Zverev method. In the construction of orthogonal difference grid the alternate triangular method and the method of transfinite interpolation from the boundary were carried out. The derivation of movement equations was done with the help of the method of regularization with a small parameter. The vortex equation was approximated by the convective terms using the upwind differences of the second-order accuracy. Tom’s conditions were used as boundary conditions connecting vortex and stream function on the surfaces of spheres. The Reynolds number varies from 0.03 to 50 in the study. The results of research include the constructed fields of velocity in the flow domain, normal and tangent stresses on the boundaries of spheres, forces acting on the spheres, velocities of spheres, distance between the centers of spheres and the shape of fluid zone around spheres depending on time. For small radii of the spheres, the time of their impact depending on the initial distance between their centers was calculated. It is shown that, for a fixed initial distance between the centers of the spheres, they approach as quicker as their radii are greater. Conclusion. The mathematical model and numerical algorithm for solving the problem of motion of two solid spheres in a Bingham fluid are developed, the calculations for this model were carried out and qualitative effects of the process of spheres approach were revealed.
[full text]
Keywords: regularization, non-Newtonian fluid, conformally map, Navier - Stokes equations, vortex, stream function
Author(s):
Pivovarov Yurii Vladimirovich
Position: Research Scientist
Address: 630090, Russia, Novosibirsk
Phone Office: (3832) 33 30 46
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Bibliography link:
Pivovarov Y.V. Calculation of motion of two solid spheres in a Bingham fluid under the action of gravitational force // Computational technologies. 2017. V. 22. ¹ 3. P. 71-90
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