Symmetry-Breaking and Bifurcation Study on the Laminar Flows through Curved Pipes with a Circular Cross Section

1996 ◽  
Vol 127 (1) ◽  
pp. 73-87 ◽  
Author(s):  
Zhong-hua Yang ◽  
Rui-song Ye
Keyword(s):  
Symmetry Breaking ◽  
Cross Section ◽  
Circular Cross Section ◽  
Laminar Flows ◽  
Curved Pipes

Effect of Precompression on Thickness of Pipe During Bending

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
A. V. Kale ◽  
H. T. Thorat
Keyword(s):  
Cross Section ◽  
Wall Thickness ◽  
Horizontal Plane ◽  
Circular Cross Section ◽  
Thickness Variation ◽  
Parallel Plates ◽  
Thickness Change ◽  
Maximum Deformation ◽  
Curved Pipes ◽  
Tension And Compression

Straight pipes with a circular cross section are processed into smooth bends by various pipe bending techniques. After bending, the initial circular cross section is deformed with thickness change. These changes from ideal are normally referred to as “ovality” and “thinning.” Their influence on the subsequent behavior of curved pipes is not yet fully understood. The aim of this paper is to present a factual method to reduce thinning of the wall thickness of pipe during bending. A new mechanism is developed for bending of pipes. This mechanism has a provision of precompression (radial squeeze) of the pipe along the directrix of maximum deformation during bending. This is achieved by clamping the pipe using two parallel plates from top and bottom. In fact, the pipe is wrapped using two rollers—one from inside and one from outside in the horizontal plane—and two plates parallel to the horizontal plane—one from the top and one from the bottom. Experimentation is carried out on this mechanism, and thicknesses are measured at the grid points along the length of the pipe. From the experimental values of thicknesses on the tension and compression sides, dimensionless variations in wall thickness of various groups of pipes are computed for different precompression values. In order to represent the thickness at any point, a mathematical equation is derived. Analytical values of thickness variations on tension and compression sides are computed using this equation. Experimental and analytical results are compared, and its methodical approach is presented in this paper. Results show that precompression reduces thickness variation of the pipe after bending.

Investigation of the symmetry-breaking instability in a T-mixer with circular cross section

2020 ◽  
Vol 32 (12) ◽  
pp. 124106
Author(s):  
Claudio Chicchiero ◽  
Lorenzo Siconolfi ◽  
Simone Camarri
Keyword(s):  
Symmetry Breaking ◽  
Cross Section ◽  
Circular Cross Section

On the steady laminar flow of an incompressible viscous fluid in a curved pipe of elliptical cross-section

1985 ◽  
Vol 158 ◽  
pp. 329-340 ◽  
Author(s):  
H. C. Topakoglu ◽  
M. A. Ebadian
Keyword(s):  
Secondary Flow ◽  
Cross Section ◽  
Circular Cross Section ◽  
Elliptical Cross Section ◽  
Radius Of Curvature ◽  
Elliptical Cross ◽  
Curved Pipe ◽  
Curved Pipes ◽  
Ellipticity Ratio ◽  
Explicit Expressions

A literature survey (Berger, Talbot & Yao 1983) indicates that laminar viscous flow in curved pipes has been extensively investigated. Most of the existing analytical results deal with the case of circular cross-section. The important studies dealing with elliptical cross-sections are mainly due to Thomas & Walters (1965) and Srivastava (1980). The analysis of Thomas & Walters is based on Dean's (1927, 1928) approach in which the simplified forms of the momentum and continuity equations have been used. The analysis of Srivastava is essentially a seminumerical approach, in which no explicit expressions have been presented.In this paper, using elliptic coordinates and following the unsimplified formulation of Topakoglu (1967), the flow in a curved pipe of elliptical cross-section is analysed. Two different geometries have been considered: (i) with the major axis of the ellipse placed in the direction of the radius of curvature; and (ii) with the minor axis of the ellipse placed in the direction of the radius of curvature. For both cases explicit expressions for the first term of the expansion of the secondary-flow stream function as a function of the ellipticity ratio of the elliptic section have been obtained. After selecting a typical numerical value for the ellipticity ratio, the secondary-flow streamlines are plotted. The results are compared with that of Thomas & Walters. The remaining terms of the expansion of the flow field are not included, but they will be analysed in a future paper.

A direct theory of viscous fluid flow in pipes II. Flow of incompressible viscous fluid in curved pipes

1993 ◽  
Vol 342 (1666) ◽  
pp. 543-572 ◽  
Keyword(s):  
Experimental Data ◽  
Analytical Solution ◽  
Viscous Fluid ◽  
Cross Section ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Incompressible Viscous Fluid ◽  
Elliptical Cross ◽  
Curved Pipes

This paper is a companion to Part I under the same title and is concerned with the development of an analytical solution (via a direct formulation) for flow of an incompressible viscous fluid in curved pipes. Although a major portion of the analysis is presented for circular pipes of elliptical cross section, detailed calculations are carried out only for pipes of circular cross section. These calculations include the friction loss factor and the velocity contours, both of which are presented over a range of Dean number th a t significantly goes beyond the corresponding range of recent numerical solutions and the available experimental data. The results obtained show very favourable agreements with existing experimental data and several recent numerical solutions of the same problem based on the Navier—Stokes equations. Also included (for pipes of circular cross section) is a comparison of the multiple solutions and bifurcation points, as predicted by the present analytical solution, with corresponding available inform ation from several recent num erical solutions of the problem.

SAF file: It's really three dimensional file

2018 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Prof. Dr. Jamal Aziz Mehdi
Keyword(s):  
Cross Section ◽  
Root Canal ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Circular Motion ◽  
Root Canal Treatment ◽  
Metal Core ◽  
Rotating Blade

The biological objectives of root canal treatment have not changed over the recentdecades, but the methods to attain these goals have been greatly modified. Theintroduction of NiTi rotary files represents a major leap in the development ofendodontic instruments, with a wide variety of sophisticated instruments presentlyavailable (1, 2).Whatever their modification or improvement, all of these instruments have onething in common: they consist of a metal core with some type of rotating blade thatmachines the canal with a circular motion using flutes to carry the dentin chips anddebris coronally. Consequently, all rotary NiTi files will machine the root canal to acylindrical bore with a circular cross-section if the clinician applies them in a strictboring manner

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