A new approach to the velocity field investigation in case of the entry flow in curved pipes with circular cross section

2000 ◽  
Vol 140 (1-2) ◽  
pp. 103-117 ◽  
Author(s):  
R. Šašić ◽  
S. Šašić
Keyword(s):  
Velocity Field ◽  
Cross Section ◽  
Circular Cross Section ◽  
Field Investigation ◽  
New Approach ◽  
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.

Velocity Field and Energy Dissipation in Viscoplastic Flow in Tubes of Non-Circular Cross-Section

2014 ◽  
Author(s):  
Mario F. Letelier ◽  
Dennis A. Siginer ◽  
Felipe Godoy
Keyword(s):  
Energy Dissipation ◽  
Velocity Field ◽  
Yield Stress ◽  
Cross Section ◽  
Mechanical Energy ◽  
Longitudinal Velocity ◽  
Circular Cross Section ◽  
Viscoplastic Flow ◽  
Entire Cross Section ◽  
Cross Sectional

An analytical method for determining the velocity field, shear stress and energy dissipation in viscoplastic flow in non-circular straight tubes is presented. Bingham’s model of fluid is used for the case of tubes with several cross-sectional contours that can be arbitrarily chosen through a shape factor imposed in the solution for the longitudinal velocity. The analysis is extended to steady flow in tubes in which the cross-section contour exhibits sharp corners. In these cases three flow zones are distinguished: stagnant, non-zero deformation, and plug zones. The method provides the expressions for determining the boundaries and characteristics of those three zones for a wide variety of cross-section shapes. In particular the dynamics of plug-zones for large values of the yield stress and for contours that markedly differ from circumferences is analyzed. Energy dissipation is determined throughout the entire cross-section, so that the effect of shape on mechanical energy loss is assessed in terms of the yield stress and viscosity of the fluid. Some general expressions that help understand energy dissipation mechanisms are derived by using natural coordinates for the velocity field and related variables. These results draw on several recent works from other researchers and the present authors, which have highlighted the significant difficulty of determining the zones of zero deformation in viscoplastic flow when the related solid boundaries are not elementary.

scholarly journals Flow of a new class of non-Newtonian fluids in tubes of non-circular cross-sections

2019 ◽  
Vol 377 (2144) ◽  
pp. 20180069 ◽  
Author(s):  
Juan P. Gomez-Constante ◽  
Kumbakonam R. Rajagopal
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Cross Section ◽  
Cross Sections ◽  
Applied Mathematics ◽  
Constitutive Relations ◽  
Maximum Shear Stress ◽  
Circular Cross Section ◽  
Secondary Flows ◽  
Shear Stresses

Fluids described by constitutive relations wherein the symmetric part of the velocity gradient is a function of the stress can be used to describe the flows of colloids and suspensions. In this paper, we consider the flow of a fluid obeying such a constitutive relation in a tube of elliptic and other non-circular cross-sections with the view towards determining the velocity field and the stresses that are generated at the boundary of the tube. As tubes are rarely perfectly circular, it is worthwhile to study the structure of the velocity field and the stresses in tubes of non-circular cross-section. After first proving that purely axial flows are possible, that is, there are no secondary flows as in the case of many viscoelastic fluids, we determine the velocity profile and the shear stresses at the boundaries. We find that the maximum shear stress is attained at the co-vertex of the ellipse. In general tubes of non-circular cross-section, the maximum shear stress occurs at the point on the boundary that is closest to the centroid of the cross-section. This article is part of the theme issue ‘Rivlin's legacy in continuum mechanics and applied mathematics’.

Peg-bush alignment under elastic vibrations

2014 ◽  
Vol 34 (4) ◽  
pp. 349-356 ◽  
Author(s):  
Edvardas Sadauskas ◽  
Bronius Baksys
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Feedback Systems ◽  
Piezoelectric Resonator ◽  
New Approach ◽  
Content Type ◽  
Elastic Vibrations ◽  
Alignment Process ◽  
Novel Method

Purpose – The paper aims to theoretically and experimentally investigate vibratory peg-bush alignment using elastic vibrations of the peg, when the peg is axially excited by a pressed piezoelectric vibrator on the upper end. Design/methodology/approach – Experimental research of part alignment using elastic vibrations was performed and dependencies of alignment duration on excitation signal parameters and initial pressing force were defined for rectangular and circular cross-section parts. Mathematical model of two-mass dynamic systems with elastic contact model representing alignment process was created. Dependencies of system parameters on the alignment duration were obtained by numerically solving systems differential equations. Findings – Theoretical and experimental investigation approved the usage of elastic vibrations for alignment of chamferless circular and rectangular cross-section parts. This novel method of part alignment compensates axial misalignment between mating parts by directional displacement of movably based bush. Research limitations/implications – Impact and non-impact interaction between bush and peg is possible; however, only non-impact regime was investigated. Static and dynamic coefficients of friction between the parts are equivalent and do not depend on relative velocity of parts. Practical implications – The results are useful in designing reliable and effective assembly equipment with vibratory assistance alignment for peg-bush operations, which do not require auxiliary sensors and feedback systems. Use of a piezoelectric resonator for peg excitation makes this system easily adaptable to the existing automated assembly equipment. Originality/value – The proposed method is a new approach to vibratory alignment. The data obtained during investigation expand the insight of the physical processes that drive bush to the axial alignment direction.

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.

A New Approach to the Demonstration of Oxidase-Localization Using Tannic Acid Or Catechin

1973 ◽  
Vol 31 ◽  
pp. 698-699
Author(s):  
V. Mizuhira ◽  
Y. Futaesaku
Keyword(s):  
Cross Section ◽  
Tannic Acid ◽  
Elastic Fiber ◽  
The Other ◽  
New Approach ◽  
Tissue Block ◽  
Active Reaction ◽  
The Cross

Previously we reported that tannic acid is a very effective fixative for proteins including polypeptides. Especially, in the cross section of microtubules, thirteen submits in A-tubule and eleven in B-tubule could be observed very clearly. An elastic fiber could be demonstrated very clearly, as an electron opaque, homogeneous fiber. However, tannic acid did not penetrate into the deep portion of the tissue-block. So we tried Catechin. This shows almost the same chemical natures as that of proteins, as tannic acid. Moreover, we thought that catechin should have two active-reaction sites, one is phenol,and the other is catechole. Catechole site should react with osmium, to make Os- black. Phenol-site should react with peroxidase existing perhydroxide.

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