Herschel-Bulkley Viscoplastic Flow in Tubes of Non-Circular Cross-Section

2016 ◽  
Author(s):  
Mario F. Letelier ◽  
Dennis A. Siginer ◽  
Felipe Godoy ◽  
César Rosas
Keyword(s):  
Cross Section ◽  
Power Index ◽  
Circular Cross Section ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Equation Of Motion ◽  
Arbitrary Cross Section ◽  
Viscoplastic Flow ◽  
The Cross ◽  
Tube Geometry

Flow of a Herschel-Bulkley (H-B) fluid in tubes of non-circular cross-section in investigated analytically. This study complements results presented in [1] where the equation of motion was solved in tubes of arbitrary cross-section for Bingham type of fluids, and the shapes of plug zones centered on the tube axis and stagnant zones attached to the corners were predicted when the cross-section is triangular and square. In this paper we investigate the effect of the power index in the H-B model on the flow for values greater and lesser than unity, considering thus the shear-thinning and shear-thickening effects, which could not be accounted for with the Bingham model. The equation of motion is solved when the cross-section is an equilateral triangle or a square by means of the shape factor method previously introduced in [2]. Thus, shear-thickening and shear-thinning effects are accounted for and related to the tube geometry in predicting the existence and the extent of undeformed regions in the flow field.

scholarly journals Asymptotic Behavior of Stable Structures Made of Beams

2021 ◽  
Author(s):  
Georges Griso ◽  
Larysa Khilkova ◽  
Julia Orlik ◽  
Olena Sivak
Keyword(s):  
Asymptotic Behavior ◽  
Cross Section ◽  
Cross Sections ◽  
Linear Elasticity ◽  
Circular Cross Section ◽  
Linear Elasticity Theory ◽  
Linear Elastic ◽  
The Cross ◽  
Small Rotation ◽  
Stable Structures

AbstractIn this paper, we study the asymptotic behavior of an $\varepsilon $ ε -periodic 3D stable structure made of beams of circular cross-section of radius $r$ r when the periodicity parameter $\varepsilon $ ε and the ratio ${r/\varepsilon }$ r / ε simultaneously tend to 0. The analysis is performed within the frame of linear elasticity theory and it is based on the known decomposition of the beam displacements into a beam centerline displacement, a small rotation of the cross-sections and a warping (the deformation of the cross-sections). This decomposition allows to obtain Korn type inequalities. We introduce two unfolding operators, one for the homogenization of the set of beam centerlines and another for the dimension reduction of the beams. The limit homogenized problem is still a linear elastic, second order PDE.

scholarly journals Validation of Welding Simulations Using Thermal Strains Measured with DIC

2011 ◽  
Vol 70 ◽  
pp. 129-134 ◽  
Author(s):  
Maarten De Strycker ◽  
Pascal Lava ◽  
Wim Van Paepegem ◽  
Luc Schueremans ◽  
Dimitri Debruyne
Keyword(s):  
Residual Stresses ◽  
Cross Section ◽  
Circular Cross Section ◽  
Welding Process ◽  
Weld Bead ◽  
Image Correlation ◽  
Steel Tubes ◽  
Element Analysis ◽  
Strain Evolution ◽  
The Cross

Residual stresses can affect the performance of steel tubes in many ways and as a result their magnitude and distribution is of particular interest to many applications. Residual stresses in cold-rolled steel tubes mainly originate from the rolling of a flat plate into a circular cross section (involving plastic deformations) and the weld bead that closes the cross section (involving non-uniform heating and cooling). Focus in this contribution is on the longitudinal weld bead that closes the cross section. To reveal the residual stresses in the tubes under consideration, a finite element analysis (FEA) of the welding step in the production process is made. The FEA of the welding process is validated with the temperature evolution of the thermal simulation and the strain evolution for the mechanical part of the analysis. Several methods for measuring the strain evolution are available and in this contribution it is investigated if the Digital Image Correlation (DIC) technique can record the strain evolution during welding. It is shown that the strain evolution obtained with DIC is in agreement with that found by electrical resistance strain gauges. The results of these experimental measuring methods are compared with numerical results from a FEA of the welding process.

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 The torsion and flexure of shafting with keyways or cracks

1932 ◽  
Vol 138 (836) ◽  
pp. 607-634 ◽  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Torsional Rigidity ◽  
Circular Cross Section ◽  
Transverse Load ◽  
Torsion Problem ◽  
Circular Section ◽  
Physical Conditions ◽  
The Cross ◽  
Straight Lines

The object of the paper is to investigate the properties of shafts of circular cross-section into which keyways or slits have been cut, first when subjected to torsion, and second when bent by a transverse load at one end. The torsion problem for similar cases has been treated by several writers. Filon has worked out an approximation to the case of a circular section with one or two keyways ; in his method the boundary of the cross-section was a nearly circular ellipse and the boundaries of the keyways were confocal hyperbolas. In particular he considered the case when the hyperbola degenerated into straight lines starting from the foci. The solution for a circular section with one keyway in the form of an orthogonal circle has been obtained by Gronwall. In each case the solution has been obtained by the use of a conformal trans­formation and this method is again used in this paper, the transformations used being ρ = k sn 2 t . ρ = k 1/2 sn t , ρ = k 1/2 sn 1/2 t where ρ = x + iy , t = ξ + i η. No work appears to have been done on the flexure problem which is here worked out for several cases of shafts with slits. 2. Summary of the Problems Treated . We first consider the torsional properties of shafts with one and with two indentations. In particular cases numerical results have been obtained for the stresses at particular points and for the torsional rigidity. The results for one indentation and for two indentations of the same width and approximately the same depth have been compared. We next consider the solution of the torsion problem for one, two or four equal slits of any depth from the surface towards the axis. The values of the stresses have not been worked out in these cases since the stress is infinite at the bottom of the slits. This in stress occurs because the physical conditions are not satisfied at the bottom of the slits, but as had been pointed out by Filon this does not affect the validity of the values of the torsional rigidity. We compare the effect on the torsional rigidity of the shaft of one, two and four slits of the same depth in particular cases. We also compare the results for one slit with those obtained by Filon by another method, and find very good agreement which is illustrated by a graph. The reduction in torsional rigidity due to a semicircular keyway is compared with that due to a slit of approximately the same depth. Finally the distortion of the cross-sections at right angles to the planes is investigated, and in this, several interesting and perhaps unexpected features appear. The relative shift of the two sides of the slits is calculated in several cases.

Torsion of Composite Elastic Bars of Arbitrary Cross Section

1968 ◽  
Vol 90 (3) ◽  
pp. 435-440 ◽  
Author(s):  
E. M. Sparrow ◽  
H. S. Yu
Keyword(s):  
Exact Solution ◽  
Closed Form ◽  
Elastic Properties ◽  
Cross Section ◽  
Excellent Agreement ◽  
Solution Method ◽  
Circular Cross Section ◽  
High Accuracy ◽  
Arbitrary Cross Section ◽  
Closed Form Solutions

A method of analysis is presented for determining closed-form solutions for torsion of inhomogeneous prismatic bars of arbitrary cross section, the inhomogeneity stemming from the layering of materials of different elastic properties. It is demonstrated that the solution method is very easy to apply and provides results of high accuracy. As an application, solutions are obtained for the torsion of a bar of circular cross section consisting of two materials separated by a plane interface. The results are compared with those of various limiting cases and excellent agreement is found to exist. Among the limiting cases, an exact solution was derived by Green’s functions for the problem in which the interface between the materials coincides with a diameter of the circular cross section.

The pancaking of coronal mass ejections: an in situ attestation

2020 ◽  
Vol 493 (1) ◽  
pp. L16-L21 ◽  
Author(s):  
Anil N Raghav ◽  
Zubair I Shaikh
Keyword(s):  
Cross Section ◽  
Space Weather ◽  
Coronal Mass Ejections ◽  
Arrival Time ◽  
Interplanetary Space ◽  
Morphological Evolution ◽  
Circular Cross Section ◽  
Primary Concern ◽  
The Cross

ABSTRACT The interplanetary counterparts of coronal mass ejections (ICMEs) are the leading driver of severe space weather. Their morphological evolution in interplanetary space and the prediction of their arrival time at Earth are the ultimate focus of space weather studies, because of their scientific and technological effects. Several investigations in the last couple of decades have assumed that ICMEs have a circular cross-section. Moreover, various models have also been developed to understand the morphology of ICMEs based on their deformed cross-section. In fact, simulation studies have suggested that the initial circular cross-section flattens significantly during their propagation in the solar wind and this is referred to as ‘pancaking’. However, an observational verification of this phenmenon is still pending and it will eventually be the primary concern of several morphological models. Here, we report the first unambiguous observational evidence of extreme flattening of the cross-section of ICMEs, similar to pancaking, based on in situ measurements of 30 ICME events. In fact, we conclude that the cross-section of ICME flux ropes transformed into a two-dimensional planar magnetic structure. Such a deformed morphological feature not only alters the prediction of their arrival time but also has significant implications in solar-terrestrial physics, the energy budget of the heliosphere, charged particle energization, turbulence dissipation and enhanced geo-effectiveness, etc.

Modeling the Phonon Transport in Nanowire with Different Cross-Section

2013 ◽  
Vol 401-403 ◽  
pp. 852-855
Author(s):  
Gao Hui Su ◽  
Zi Chun Yang ◽  
Feng Rui Sun
Keyword(s):  
Thermal Conductivity ◽  
Cross Section ◽  
Diffuse Reflection ◽  
Silicon Nanowire ◽  
Circular Cross Section ◽  
Phonon Transport ◽  
Reflection Mode ◽  
Section Shape ◽  
Section Size ◽  
The Cross

The phonon transport in silicon nanowire was simulated by Monte Carlo Method (MCM). The effect on the phonon transport of the boundary reflection mode, cross-section size and cross-section shape was studied. Analysis shows that diffuse reflection can result in phonon accumulation at the circumferential boundary. As the cross-section size decrease, the nonuniformity of the temperature distribution within the cross-section becomes more severe. When the area of the square cross-section silicon nanowire (SCSN) is equal to that of the circular cross-section silicon nanowire (CCSN), the thermal conductivity of them is more close to each other.

Modeling of Strain and Stress States for Straight Rods with Particular Cross Sections Subjected to Torsion

2013 ◽  
Vol 837 ◽  
pp. 699-704
Author(s):  
Marilena Glovnea ◽  
Cornel Suciu
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Circular Cross Section ◽  
Segment Length ◽  
Circular Arc ◽  
Tangential Stresses ◽  
Applied Torque ◽  
The Cross ◽  
Stress States ◽  
Model Strain

In the case of shaft-hub joints with cylindrical pins found in both macro and micro-devices, a longitudinal gutter with an almost half-circular cross section is practiced along the length of the shaft segment. The center of the circular arc is placed on the circular edge of the cross section. The present paper aims to model strain and stress states within such a shaft, when the material elastic properties are known along with shaft segment length and applied torque. Using the MathCad environment, 3D and constant stress level plots were obtained for the distribution of tangential stresses over the cross section. After application of torque, the transverse cross sections shift and become anti-symmetric as illustrated by the obtained 3D and constant strain plots.

Combined Bending and Compression of a Pressurized Circular Cylindrical Membrane Column

1965 ◽  
Vol 87 (3) ◽  
pp. 372-378
Author(s):  
W. E. Jahsman
Keyword(s):  
Compressive Strength ◽  
Cross Section ◽  
Compressive Load ◽  
Circular Cross Section ◽  
Bending Moment ◽  
Maximum Load ◽  
Bending Moments ◽  
Lateral Deflection ◽  
The Cross

Load-lateral deflection curves are developed for a pressurized tube of circular cross section under combined bending and compression. The tube walls are assumed to have negligible compressive strength so that wrinkling develops if the stress tends to become negative. It is found that for a given bending moment, the load increases monotonically with deflection until a maximum is reached beyond which the load decreases with increasing deflection. An interaction curve of the maximum load versus bending moment shows that the presence of only a small amount of bending significantly decreases the maximum compressive load below the classical Euler load. Conversely, for bending moments which produce almost complete wrinkling of the cross section, only very small amounts of compressive load can be supported.

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