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Slow flow past a weakly permeable spheroidal particle in a hypothetical cell

Bucha Tina, Madasu Krishna Prasad

Archive of Mechanical Engineering

2021

LXVIII, nr 2

119--146

The perspective of the current analysis is to represent the incompressible viscous flow past a low permeable spheroid contained in a fictitious spheroidal cell. Stokes approximation and Darcy’s equation are adopted to govern the flow in the fluid and permeable zone, respectively. Happel’s and Kuwabara’s cell models are employed as the boundary conditions at the cell surface. At the fluid porous interface, we suppose the conditions of conservation of mass, balancing of pressure component at the permeable area with the normal stresses in the liquid area, and the slip condition, known as Beavers-Joseph-Saffman-Jones condition to be well suitable. A closed-form analytical expression for hydrodynamic drag on the bounded spheroidal particle is determined and therefore, mobility of the particle is also calculated, for both the case of a prolate as well as an oblate spheroid. Several graphs and tables are plotted to observe the dependence of normalized mobility on pertinent parameters including permeability, deformation, the volume fraction of the particle, slip parameter, and the aspect ratio. Significant results that influence the impact of the above parameters in the problem have been pointed out. Our work is validated by referring to previous results available in literature as reduction cases.

Projektowanie geometrii rdzenia aluminiowego odlewu szkieletowego o komórkach otwartych

Dziuba M.

Archiwum Technologii Maszyn i Automatyzacji

2006

Vol. 26, nr 1

15-23

Obiektem zainteresowania są metalowe materiały szkieletowe o regularnych komórkach otwartych. Analiza regularnych elementarnych komórek ułatwia projektowanie właściwości mechanicznych odlewów szkieletowych. Celem badań był dobór geometrii szkieletu aluminiowego do wytwarzania odlewów szkieletowych. Plan zaprojektowania rdzenia odlewu szkieletowego obejmował: podział rdzenia na najmniejsze powtarzalne elementy, wyznaczenie geometrycznych cech komórek szkieletu metalowego, wytypowanie modelu kształtowego odlewu próbnego. Zaproponowano trzy koncepcje kształtu pojedynczych komórek. Są to osiemnastościan z płaskimi ścianami, osicmnastościan o minimalnych oporach hydraulicznych przepływu metalu oraz czternastościan Kelvina. Na podstawie analizy geometrii pojedynczej komórki wyznaczono kształt rdzenia.

Cast skeleton materials with regular opened cells were studied. The analysis of elementary regular cells enables to design mechanical properties of various materials used for skeleton cast ings. The main aim of this work was cell geometry selection for creation the skeleton castings. The schedule of skeleton cast core included: division of the core for the smallest reproducible elements, determine of the geometric characteristics of the metal skeleton cells, creation of the shape model of the test model. Three concepts for elementary cells were presented. There are: oktadekahedron-with flat walls, oktadekahedron about minimal hydraulic contumacies flows of metal and Kelvin's tetradekahedon. On base of elementary cell geometrical analysis the core shape was determined.