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Article information
2019 , Volume 24, ¹ 3, p.88-105
Pivovarov Y.V.
Computation of motion of viscous fluid partially filling a rotating cavity at large Reynolds numbers
The goal of the research is to simulate a hydrodynamic flow of semiconductor material melt during its purification from impurity by using the method of zone melting in a horizontal cylindrical rotating container. The container is not fully filled with melt, there is a free surface. The flow is considered to be plane-parallel and stationary. It is supposed that the flow domain with unperturbed free boundary is a semicircle. The melt is separated from a container wall by a thin layer of finely dispersed lubricant. Therefore, when stating a problem, the Navier slip condition is set on the boundary with a wall. The problem formulation in variables of vortex – stream function is performed. To solve it, the following methods are used, namely, relaxation method for time, the method of an approximate factorization for solution of an evolutionary equation for vortex, V.G. Zverev’s method is used to solve the problems for stream function, this method allows precise satisfying a boundary condition which connects a vortex on boundary and nearboundary values of stream function at each time step using finite-difference method and method of computation on the sequence of meshes, beginning with the mesh of dimension 32×8 and ending with the mesh of dimension 2048×512. The research results in constructed patterns of streamlines and vortex isolines along with the form of perturbed free boundary at various values of Reynolds number. The range of Reynolds number is from zero to three thousand that corresponds to the experimental data. Conclusions. 1. The problem on motion of viscous fluid filling half the cylindrical rotating cavityis solved. 2. A great number of mesh points made it possible to minimize the influence ofscheme viscosity and to obtain trustworthy results at large Reynolds numbers. 3. It is shown that the flow domain is divided into a vortex boundary layer, transitionzone and the zone of constant vortex.
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Keywords: conformal mapping, incompressible fluid, the Navier - Stokes equations, slip condition, vortex, stream function
doi: 10.25743/ICT.2019.24.3.007
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. Computation of motion of viscous fluid partially filling a rotating cavity at large Reynolds numbers // Computational technologies. 2019. V. 24. ¹ 3. P. 88-105
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