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## Numerical solution of curved pipes submitted to in-plane loading conditions

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

46.46%

An alternative formulation to current meshes dealing with finite shell elements is presented to solve the problem of stress analysis of curved pipes subjected to in-plane bending forces. The solution is based on finite curved elements, where displacements are defined from a total set of trigonometric functions or a fifth-order polynomial, combined with Fourier series. Global shell displacements are achieved through the one associated with curved arch bending and the other referred to the toroidal thin-walled shell distortion. Beam-type displacement and in-plane rotation are uncoupled and separately formulated, using trigonometric shape functions, as in Timoshenko or Mindlin beam theory. To build up the solution, a simple deformation model was adopted, based on the semi-membrane concept of the doubly curved shells behaviour. Several studies are presented and compared with experimental and numerical analyses reported by other authors.

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## Determination of flexibility factors in curved pipes with end restraints using a semi-analytic formulation

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

46.72%

#Curved pipe#Pure bending#Previous term#Flexibility factornext term#Semi-analytic formulation#Fourier series

Piping systems are structural sets used in the chemical industry, conventional or nuclear power plants and fluid transport in general-purpose process equipment. They include curved elements built as parts of toroidal thin-walled structures. The mechanical behaviour of such structural assemblies is of leading importance for satisfactory performance and safety standards of the installations. This paper presents a semi-analytic formulation based on Fourier trigonometric series for solving the pure bending problem in curved pipes. A pipe element is considered as a part of a toroidal shell. A displacement formulation pipe element was developed with Fourier series. The solution of this problem is solved from a system of differential equations using mathematical software. To build-up the solution, a simple but efficient deformation model, from a semi-membrane behaviour, was followed here, given the geometry and thin shell assumption. The previous termflexibility factorsnext term are compared with the ASME code for some elbow dimensions adopted from ISO 1127. The stress field distribution was also calculated.

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## The modal analysis of a pipe elbow with realistic boundary conditions

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

46.68%

A vibration analysis for the determination of the natural frequencies and the associated eigenmodes of a pipe elbow with end-flanges or tangent terminations was performed. A numerical investigation of this problem was achieved with a semi-analytic definition finite ring element and a commercial finite element code. To assess the accuracy of the numerical solution for the elbow vibration, an experimental modal analysis was performed on a curved and on a straight pipe. The responses were processed by a data acquisition system which performs a fast Fourier transform on the time histories to convert them from a time to frequency domain, these leading to the extraction of natural frequencies and mode shapes associated with the test-specimen. The results were compared with the corresponding ones from the numerical approach and discussion about the results completes the paper.

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## The modal analysis of a pipe elbow with realistic boundary conditions

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

46.68%

A vibration analysis for the determination of the natural frequencies and the associated eigenmodes of a pipe elbow with end-flanges or tangent terminations was performed. A numerical investigation of this problem was achieved with a semi-analytic definition finite ring element and a commercial finite element code. To assess the accuracy of the numerical solution for the elbow vibration, an experimental modal analysis was performed on a curved and on a straight pipe. The responses were processed by a data acquisition system which performs a fast Fourier transform on the time histories to convert them from a time to frequency domain, these leading to the extraction of natural frequencies and mode shapes associated with the test-specimen. The results were compared with the corresponding ones from the numerical approach and discussion about the results completes the paper.; (Not applicable)

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## A finite element formulation for piping structures based on thin shell displacements theory

Fonte: Nova Science
Publicador: Nova Science

Tipo: Parte de Livro

ENG

Relevância na Pesquisa

46.83%

This chapter deals with the more usual formulations in the numerical approaches to the problem of stress analysis of curved pipes under generalized bending loads. The application of curved pipe elements is critically necessary in any
piping structure, no matter which the project applications are. Depending on
the safety standards ruling the project, it is known that curved pipe elements
are much more vulnerable to excessive stressing than straight pipe elements. A
larger risk of accessory breakdown during continuous operation after a
situation where limiting forces are exceeded is likely to occur. The study of the
flexibility and stress state of curved pipes subjected to generalized forces has
been an area of interest of many engineers and physicists, given the high
interest of the theme in many structural applications.

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## The linear elastic stress analysis of curved pipes under generalized loads using a reduced integration finite ring element

Fonte: SAGE Journals
Publicador: SAGE Journals

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

46.81%

This paper consists of a linear elastic stress analysis of curved pipes having all the possible boundary conditions in structural engineering and submitted to a generalized in-plane or out-of-plane loading. A semi-analytic displacement formulation ring element was developed, where simple first-degree polynomials were used to interpolate the global shell displacements along the longitudinal direction, and Fourier series were used along the meridional direction. The deformed shape of the curved pipe results from the superposition of the beam-type displacement to that of a toroidal shell. For the first case, the curved pipe was considered as being a short thin-walled straight beam element joining two nodal sections. In this case, as the pipe element is not curved, it is natural to consider that the transverse section undergoes no ovalization or warping. A C0-continuity reduced integration beam element was adopted for this purpose, leading to a simple and economic definition for the stiffness terms. In the second case, the displacement field was assumed to result from a stressed toroidal shell, where the transverse section could ovalize and warp. The stiffness terms following these assumptions are combined with those of the straight beam to give the complete stiffness matrix. This element has the important advantage of generating a zero stress field along the curved centroidal line when submitted to pure in-plane bending and...

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## A reduced integration mindlin beam element for linear elastic stress analysis of curved pipes under generalized in-plane loading

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

46.7%

This paper presents a ring element for the analysis of in-plane bending of curved pipes. The element is derived from the arch bending theory using short, straight elements as an approach to the curved structure. Each curved pipe element is considered as a straight thin-walled C0-continuity beam element for the purpose of the derivation of the beam stiffness matrix terms. The assumption of the straight elements does not involve ovalization and warping of the transverse section; for the stiffness terms concerning the distortion of the transverse section, the pipe element is assumed curved. This method leads to the important advantage of generating a zero stress field along the curved centroidal line of the element under pure in-plane bending and to the satisfaction of the ‘patch test’.

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## A mixed formulation for the stress analysis of curved pipes with tangent terminations under in-plane forces

Fonte: Springer
Publicador: Springer

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

36.39%

Curved pipes connected to tangent terminations play an important role in process equipment design where there is fluid transport. They allow change in flow direction and simultaneously contribute to increase flexibility of the whole structure. The stress analysis of curved pipes (or pipe elbows) is an essential step in the project of piping systems. The method of hybrid formulation of the shell parameters (internal forces and displacements), is an alternative to the irreducible formulation, this last dealing with a totally assumed displacement field for the unknowns. The main advantage has incidence in the use of lower order formulations in the differential equations to set-up the solution compared with the irreducible formulation. The hybrid solution here proposed is based on a semi-analytic formulation, where the definition of the shell forces and displacements combines analytic and trigonometric functions. Tests for most usual loading cases are analysed and results for stress distribution are discussed.

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## Determination of flexibility factors in curved pipes with end restraints using a semi-analytic formulation

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

46.72%

Piping systems are structural sets used in the chemical industry, conventional or nuclear power plants and fluid transport in general-purpose process equipment. They include curved elements built as parts of toroidal thin-walled structures. The mechanical behaviour of such structural assemblies is of leading importance for satisfactory performance and safety standards of the installations. This paper presents a semi-analytic formulation based on Fourier trigonometric series for solving the pure bending problem in curved pipes. A pipe element is considered as a part of a toroidal shell. A displacement formulation pipe element was developed with Fourier series. The solution of this problem is solved from a system of differential equations using mathematical software. To build-up the solution, a simple but efficient deformation model, from a semi-membrane behaviour, was followed here, given the geometry and thin shell assumption. The flexibility factors are compared with the ASME code for some elbow dimensions adopted from ISO 1127. The stress field distribution was also calculated.

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## Flows of generalized Oldroyd- B fluids in curved pipes.

Fonte: Springer Basel
Publicador: Springer Basel

Tipo: Parte de Livro

POR

Relevância na Pesquisa

56.55%

The aim of this work is to present a numerical study of generalized
Oldroyd-B flows with shear-thinning viscosity in a curved pipe of circular cross
section and arbitrary curvature ratio. Flows are driven by a given pressure
gradient and behavior of the solutions is discussed with respect to different
rheologic and geometric flow parameters.

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## Numerical approximation of viscoelastic Oldroyd-B flows in curved pipes

Fonte: RIMS Kôkyûroku Bessatsu Kyoto
Publicador: RIMS Kôkyûroku Bessatsu Kyoto

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

46.55%

The aim of this paper is to study a finite element numerical approximation of steady flows of an incompressible viscoelastic Oldroyd-B fluid in curved pipes of arbitrary cross-section and curvature ratio. Using rectangular toroidal coordinates, existence and uniqueness of approximated solutions are proved as well as a priori error estimates, under a natural restriction on the pipe curvature ratio.

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## Viscosity effects on flows of generalized Newtonian fluids through curved pipes

Fonte: Pergamon Press, Inc. Tarrytown, Elsevier
Publicador: Pergamon Press, Inc. Tarrytown, Elsevier

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

56.55%

This paper is concerned with the application of finite element methods to obtain solutions for steady fully develloped generalized Newtonian flows in a curved pipe of circular cross-section and arbitrary curvature ratio, under a given axial pressure gradient

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## Numerical simulations of shear-thinning Oldroyd-B fluids in curved pipes

Fonte: WSEAS
Publicador: WSEAS

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

56.55%

The aim of this paper is to present a numerical study of steady generalized Newtonian and generalized Oldroyd-B flows with shear-thinning viscosity in a curved pipe of circular cross section and arbitrary curvature ratio. The combined effects of inertia, viscoelasticity and viscosity are studied, and the quantitative and qualitative behavior of the secondary motions are analyzed with respect to the corresponding characteristic parameters.

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## Secondary flows of shear-thinning generalized Newtonian fluids in curved pipes

Fonte: WSEAS
Publicador: WSEAS

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

56.55%

This paper presents a numerical study of the behavior of steady generalized Newtonian flows with shearthinning viscosity in a curved pipe. Finite element simulations show in particular that, for sufficiently small curvature ratio and within a certain range of viscosity parameters, the secondary streamlines rotate and the flow field loses symmetry.

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## Optimal design of curved and bifurcated flow pipes

Fonte: Pacific Center of Thermal-Fluids Engineering.
Publicador: Pacific Center of Thermal-Fluids Engineering.

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

36.33%

The present study focuses on flows in
three-dimensional curved and bifurcated pipes. Computational fluid dynamics is used to investigate fluid flow through these pipes. The occurrence of recirculation due to
curvature ratio, bend angle, diameter, length, and bifurcation level is studied and the flow resistance is computed. The validity of Dean’s relation for the enhancement of flow resistance in curved pipes is studied numerically.

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## The decay of suddenly blocked flow in a curved pipe

Fonte: Kluwer Academic Publ
Publicador: Kluwer Academic Publ

Tipo: Artigo de Revista Científica

Publicado em //2009
EN

Relevância na Pesquisa

46.45%

Richard J. Clarke and James P. Denier

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## Amplitude equations for a linear wave equation in a weakly curved pipe

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/10/2009

Relevância na Pesquisa

46.73%

We study boundary effects in a linear wave equation with Dirichlet type
conditions in a weakly curved pipe. The coordinates in our pipe are prescribed
by a given small curvature with finite range, while the pipe's cross section
being circular. Based on the straight pipe case a perturbative analysis by
which the boundary value conditions are exactly satisfied is employed. As such
an analysis we decompose the wave equation into a set of ordinary differential
equations perturbatively. We show the conditions when secular terms due to the
curbed boundary appear in the naive peturbative analysis. In eliminating such a
secularity with a singular perturbation method, we derive amplitude equations
and show that the eigenfrequencies in time are shifted due to the curved
boundary.; Comment: To appear in J Phys A: Math. Theor

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## Experimental investigation of transitional flow in a toroidal pipe

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/08/2015

Relevância na Pesquisa

36.68%

The flow instability and further transition to turbulence in a toroidal pipe
(torus) with curvature (tube-to-coiling diameter) 0.049 is investigated
experimentally. The flow inside the toroidal pipe is driven by a steel sphere
fitted to the inner pipe diameter. The sphere is moved with constant azimuthal
velocity from outside the torus by a moving magnet. The experiment is designed
to investigate curved pipe flow by optical measurement techniques. Using
stereoscopic particle image velocimetry, laser Doppler velocimetry and pressure
drop measurements, the flow is measured for Reynolds numbers ranging from 1000
to 15000. Time- and space-resolved velocity fields are obtained and analysed.
The steady axisymmetric basic flow is strongly influenced by centrifugal
effects. On an increase of the Reynolds number we find a sequence of
bifurcations. For Re=4075 a supercritical bifurcation to an oscillatory flow is
found in which waves travel in the streamwise direction with a phase velocity
slightly faster than the mean flow. The oscillatory flow is superseded by a
presumably quasi-periodic flow at a further increase of the Reynolds number
before turbulence sets in. The results are found to be compatible, in general,
with earlier experimental and numerical investigations on transition to
turbulence in helical and curved pipes. However...

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## Isentropic Fluid Dynamics in a Curved Pipe

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/11/2015

Relevância na Pesquisa

46.73%

In this paper we study isentropic flow in a curved pipe. We focus on the
consequences of the geometry of the pipe on the dynamics of the flow. More
precisely, we present the solution of the general Cauchy problem for isentropic
fluid flow in an arbitrarily curved, piecewise smooth pipe. We consider initial
data in the subsonic regime, with small total variation about a stationary
solution. The proof relies on the front-tracking method and is based on [1].

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## Particle transport in turbulent curved pipe flow

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 19/01/2015

Relevância na Pesquisa

46.61%

Direct numerical simulations (DNS) of particle-laden turbulent flow in
straight, mildly curved and strongly bent pipes are performed in which the
solid phase is modelled as small heavy spherical particles. The objective is to
examine the effect of the curvature on particle transport and accumulation, in
particular how the turbophoretic drift of the particles is affected by weak and
strong secondary motions of the carrier phase and geometry-induced centrifugal
forces. A total of seven populations of dilute particles with different Stokes
numbers, one-way coupled with their carrier phase, are simulated. Even a slight
non-zero curvature in the flow configuration shows a strong impact on the
particle dynamics. Near-wall helicoidal particle streaks are observed in the
curved configurations with their inclination varying with the strength of the
secondary motion of the carrier phase. A reflection layer, as previously
observed in particle laden turbulent S-shaped channels, is also apparent in the
strongly curved pipe with heavy particles. In addition, depending on the
curvature, the central regions of the mean Dean vortices appear to be
completely depleted of particles, as observed also in the largely
re-laminarised region at the inner bend. The current data-set will be useful
for modelling particles advected in wall-bounded turbulent flows where the
effects of the curvature are not negligible.; Comment: 26 pages...

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