Numerical Analysis of Two- and Three-Dimensional 90-Degree Bend Flow
Liou, Ren-Jei
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https://hdl.handle.net/2142/68509
Description
Title
Numerical Analysis of Two- and Three-Dimensional 90-Degree Bend Flow
Author(s)
Liou, Ren-Jei
Issue Date
1980
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Language
eng
Abstract
The two basic methods of numerical viscous flow calculation--the vorticity-transport and primitive-variable schemes--are applied to the finite-difference analysis of flow through a two-dimensional 90-degree bend between sections of straight conduit. Additionally, the vorticity-transport method is employed in two approaches--one a direct calculation in rectangular and polar coordinates, the other via a non-orthogonal coordinate transform by which calculations are performed in a square mesh field. The solutions for all three methods were in agreement for (//R) = 72. The two-dimensional primitive-variable methodology was then successfully transferred to the three-dimensional 90-degree curved pipe problem and solutions have been generated up to (//R) = 100.
The two- and three-dimensional bend flows show many similarities except that no secondary flow occurs in two-dimensional bend. The axial velocity increases in the inner wall upstream junction region and outer wall downstream junction region while the axial pressure gradient increases in both regions. The axial velocity decreases in the outer wall upstream junction region and inner wall downstream junction region while the axial pressure gradient reverses in both regions. There is a strong secondary flow developed in the three-dimensional bend region and extends into the downstream straight pipe.
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