EXISTENCE AND UNIQUENESS OF STEADY, FULLY DEVELOPED FLOWS OF SECOND ORDER FLUIDS IN CURVED PIPES

2001 ◽  
Vol 11 (06) ◽  
pp. 1055-1071 ◽  
Author(s):  
V. COSCIA ◽  
A. M. ROBERTSON
Keyword(s):  
Cross Section ◽  
Existence And Uniqueness ◽  
Perturbation Methods ◽  
Second Order ◽  
Radius Of Curvature ◽  
Governing Equations ◽  
Curvature Ratio ◽  
Curved Pipes ◽  
Second Order Fluids ◽  
Perturbation Equations

Steady, fully developed flows of second order fluids in curved pipes of circular cross-section have previously been studied using regular perturbation methods.2,3,12,20 These perturbation solutions are applicable for pipes with small curvature ratio: The cross sectional radius of the pipe divided by the radius of curvature of the pipe centerline. It was shown by Jitchote and Robertson12 that perturbation equations could be ill-posed when the second normal stress coefficient is nonzero. Motivated by the singular nature of the perturbation equations, here, we study the full governing equations without introducing assumptions inherent in perturbation methods. In particular, we examine the existence and uniqueness of solutions to the full governing equations for second order fluids. We show rigorously that a solution to the full problem exists and is locally unique for small non-dimensional pressure drop, in agreement with earlier results obtained using a formal expansion in the curvature ratio.12 The results obtained here are valid for arbitrarily shaped cross-section (sufficiently smooth) and for all curvature ratios. An operator splitting method has been employed which may be useful for numerical studies of steady and unsteady flows of second order fluids in curved pipes.

The Bending of Curved Pipes With Variable Wall Thickness

2003 ◽  
Vol 70 (2) ◽  
pp. 253-259 ◽  
Author(s):  
V. P. Cherniy
Keyword(s):  
Cross Section ◽  
Wall Thickness ◽  
Shell Theory ◽  
Neutral Line ◽  
Radius Of Curvature ◽  
Curved Pipes ◽  
Variable Wall Thickness ◽  
Previous Solution ◽  
Variable Wall ◽  
Thin Shell Theory

A general solution is presented for the in-plane bending of short-radius curved pipes (pipe bends) which have variable wall thickness. Using the elastic thin-shell theory, the actual radius of curvature of the pipe’s longitudinal fibers and displacement of the neutral line of the cross section under bending are taken into account. The pipe’s wall thickness is assumed to vary smoothly along the contour of the pipe’s cross section, and is a function of an angular coordinate. The solution uses the minimization of the total energy, and is compared to our previous solution for curved pipes with constant wall thickness.

Flow of second order fluids in curved pipes

2000 ◽  
Vol 90 (1) ◽  
pp. 91-116 ◽  
Author(s):  
W. Jitchote ◽  
A.M. Robertson
Keyword(s):  
Second Order ◽  
Curved Pipes ◽  
Second Order Fluids

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.

First and Second Order Elastoplastic Analyses of Thin-Walled Metal Members using Generalized Beam Theory

2018 ◽  
Author(s):  
Miguel Abambres
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Cross Section ◽  
Beam Theory ◽  
Second Order ◽  
Flow Rule ◽  
Non Linear ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalized Beam Theory

Original Generalized Beam Theory (GBT) formulations for elastoplastic first and second order (postbuckling) analyses of thin-walled members are proposed, based on the J2 theory with associated flow rule, and valid for (i) arbitrary residual stress and geometric imperfection distributions, (ii) non-linear isotropic materials (e.g., carbon/stainless steel), and (iii) arbitrary deformation patterns (e.g., global, local, distortional, shear). The cross-section analysis is based on the formulation by Silva (2013), but adopts five types of nodal degrees of freedom (d.o.f.) – one of them (warping rotation) is an innovation of present work and allows the use of cubic polynomials (instead of linear functions) to approximate the warping profiles in each sub-plate. The formulations are validated by presenting various illustrative examples involving beams and columns characterized by several cross-section types (open, closed, (un) branched), materials (bi-linear or non-linear – e.g., stainless steel) and boundary conditions. The GBT results (equilibrium paths, stress/displacement distributions and collapse mechanisms) are validated by comparison with those obtained from shell finite element analyses. It is observed that the results are globally very similar with only 9% and 21% (1st and 2nd order) of the d.o.f. numbers required by the shell finite element models. Moreover, the GBT unique modal nature is highlighted by means of modal participation diagrams and amplitude functions, as well as analyses based on different deformation mode sets, providing an in-depth insight on the member behavioural mechanics in both elastic and inelastic regimes.

Acoustic streaming in second-order fluids

2020 ◽  
Vol 32 (12) ◽  
pp. 123103
Author(s):  
Pradipta Kr. Das ◽  
Arthur David Snider ◽  
Venkat R. Bhethanabotla
Keyword(s):  
Acoustic Streaming ◽  
Second Order ◽  
Second Order Fluids

Optimal Solutions for Nonhomogeneous Multiply-Connected Torsional Sections

1989 ◽  
Vol 111 (1) ◽  
pp. 87-93 ◽  
Author(s):  
A. Mioduchowski ◽  
M. G. Faulkner ◽  
B. Kim
Keyword(s):  
Numerical Simulation ◽  
Boundary Value Problem ◽  
Cross Section ◽  
Boundary Value ◽  
Optimization Procedure ◽  
Second Order ◽  
External Boundary ◽  
Optimal Solutions ◽  
Torsion Problem ◽  
Multiply Connected

Optimization of a second-order multiply-connected inhomogeneous boundary-value problem was considered in terms of elastic torsion. External boundary and material proportions are the applied constraints in finding optimal internal configurations of the cross section. The optimization procedure is based on the numerical simulation of the membrane analogy and the results obtained indicate that the procedure is usable as an engineering tool. Optimal solutions are obtained for some representative cases of the torsion problem and they are presented in the form of tables and figures.

Sign in / Sign up

Export Citation Format

Share Document