A finite element analysis of a free surface drainage problem of two immiscible fluids
作者:
Masatake Mori,
Makoto Natori,
Zhang Guo‐Feng,
期刊:
International Journal for Numerical Methods in Fluids
(WILEY Available online 1989)
卷期:
Volume 9,
issue 5
页码: 569-582
ISSN:0271-2091
年代: 1989
DOI:10.1002/fld.1650090507
出版商: John Wiley&Sons, Ltd
关键词: Flow analysis;Free surface problem;Finite element method;Blast furnace
数据来源: WILEY
摘要:
AbstractA sharp interface problem arising in the flow of two immiscible fluids, slag and molten metal in a blast furnace, is formulated using a two‐dimensional model and solved numerically. This problem is a transient two‐phase free or moving boundary problem, the slag surface and the slag–metal interface being the free boundaries. At each time step the hydraulic potential of each fluid satisfies the Laplace equation which is solved by the finite element method. The ordinary differential equations determining the motion of the free boundaries are treated using an implicit time‐stepping scheme. The systems of linear equations obtained by discretization of the Laplace equations and the equations of motion of the free boundaries are incorporated into a large system of linear equations. At each time step the hydraulic potential in the interior domain and its derivatives on the free boundaries are obtained simultaneously by solving this linear system of equations. In addition, this solution directly gives the shape of the free boundaries at the next time step. The implicit scheme mentioned above enables us to get the solution without handling normal derivatives, which results in a good numerical solution of the present problem. A numerical example that simulates the flow in a blast furnace i
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