Out-of-Plane Pipe Whip for a Bent Cantilever Pipe: Comparison Between Experiment and FEM Models

2011 ◽  
Vol 79 (1) ◽  
Author(s):  
S. R. Reid ◽  
M. Aleyaasin ◽  
B. Wang
Keyword(s):  
Cross Section ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Plastic Response ◽  
Nonlinear Dynamic Model ◽  
Accurate Analysis ◽  
Shell Elements ◽  
Rigorous Approach ◽  
Significant Difference ◽  
Out Of Plane

The three-dimensional, dynamic, elastic-plastic response of a right-angle bent cantilever pipe, with an initially uniform, circular cross section, subjected to out-of-plane loading is examined using finite element beam and shell models in ABAQUS. The large-deflection behavior involves both bending and torsional elastoplastic deformations of the pipe, phenomena which have not been previously studied in the context of the dynamic problem of pipe whip. Initially, neglecting ovalization and local collapse (kinking), the bent pipe is modeled as a beam, using spatial beam elements in ABAQUS. This enables the basic three-dimensional kinematic behavior of the pipe to be analyzed. A similar, but potentially more accurate, analysis was then performed using shell elements. It is shown that there is no significant difference in the global dynamic plastic response. However the ovalization of the pipe cross section and formation and movement of the plastic zones (hinges) can be captured by using shell elements. This provides data which could form the basis for examining local failures in the pipe run. Previously unpublished experimental results, obtained in an earlier study by some of the present authors, are compared with the simulated results. Good agreement is observed and it is concluded that a nonlinear dynamic model using finite elements provides a rigorous approach for estimating the hazard zone (HZ) and, also, for treating the kinematics of a whipping pipe for this complex three-dimensional situation.

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

On the Flexural-Torsional Behavior of a Straight Elastic Beam Subject to Terminal Moments

1993 ◽  
Vol 60 (2) ◽  
pp. 498-505 ◽  
Author(s):  
Z. Tan ◽  
J. A. Witz
Keyword(s):  
Coordinate System ◽  
Cross Section ◽  
Equilibrium Equation ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elastic Beam ◽  
Cartesian Coordinate System ◽  
Kinematic Constraints ◽  
Torsional Behavior ◽  
Cartesian Coordinate

This paper discusses the large-displacement flexural-torsional behavior of a straight elastic beam with uniform circular cross-section subject to arbitrary terminal bending and twisting moments. The beam is assumed to be free from any kinematic constraints at both ends. The equilibrium equation is solved analytically with the full expression for curvature to obtain the deformed configuration in a three-dimensional Cartesian coordinate system. The results show the influence of the terminal moments on the beam’s deflected configuration.

Geometry Effects in Eulerian/Granular Simulation of a Turbulent FCC Riser with a (kg-?g)-KTGF Model

2010 ◽  
Vol 8 (1) ◽  
Author(s):  
Hamid Reza Nazif ◽  
Hassan Basirat Tabrizi ◽  
Farhad A Farhadpour
Keyword(s):  
Cross Section ◽  
Large Scale ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Good Prediction ◽  
Model Predictions ◽  
Secondary Circulations ◽  
Sharp Corners ◽  
Granular Simulation

Three-dimensional, transient turbulent particulate flow in an FCC riser is modeled using an Eulerian/Granular approach. The turbulence in the gas phase is described by a modified realizable (kg-?g) closure model and the kinetic theory of granular flow (KTGF) is employed for the particulate phase. Separate simulations are conducted for a rectangular and a cylindrical riser with similar dimensions. The model predictions are validated against experimental data of Sommerfeld et al (2002) and also compared with the previously reported LES-KTGF simulations of Hansen et al (2003) for the rectangular riser. The (kg-?g)-KTGF model does not perform as well as the LES-KTGF model for the riser with a rectangular cross section. This is because, unlike the more elaborate LES-KTGF model, the simpler (kg-?g)-KTGF model cannot capture the large scale secondary circulations induced by anisotropic turbulence at the corners of the rectangular riser. In the cylindrical geometry, however, the (kg-?g)-KTGF model gives good prediction of the data and is a viable alternative to the more complex LES-KTGF model. This is not surprising as the circulations in the riser with a circular cross section are due to the curvature of the walls and not due to the presence of sharp corners.

Three-dimensional wakes behind cylinders of square and circular cross-section: early and long-time dynamics

2019 ◽  
Vol 870 ◽  
pp. 419-432 ◽  
Author(s):  
G. Agbaglah ◽  
C. Mavriplis
Keyword(s):  
Circular Cylinder ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Early Time ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Square Cylinder ◽  
Saturation Regime ◽  
Time Dynamics ◽  
Significant Difference

The flow in the near wake of a square cylinder at Reynolds numbers of 205 and 225, corresponding to three-dimensional wake instability modes $A$ and $B$, respectively, and that of the square’s circumscribed circular cylinder are examined by using three-dimensional Navier–Stokes numerical simulations. At small times, prior to the streamwise vortex shedding, a self-similar velocity is observed in the wake and no significant difference is observed in the dynamics of the flows past the square and the circular cylinders. The exponential growth of the three-dimensional instability reaches a saturation regime during this early time for the considered Reynolds numbers. Vortical structures in the wake at long times and shedding frequencies are very close for the square and the circular cylinders. The flow separation on the forward top and bottom corners of the square cylinder have the effect of increasing its effective width, making it comparable with the diameter of the circumscribed circular cylinder. Thus, Floquet multipliers and modes of the associated three-dimensional instabilities are shown to be very close for the two cylinders when using the circumscribed circular cylinder as the basis for a characteristic length scale. Most importantly, the wavenumber with the maximum growth rate, for modes $A$ and $B$, is approximately identical for the two cylinders.

scholarly journals Computational Study of Zigzag Spacer Design with Elliptical Cross-Section Filaments

2020 ◽  
Vol 307 ◽  
pp. 01047
Author(s):  
Gohar Shoukat ◽  
Farhan Ellahi ◽  
Muhammad Sajid ◽  
Emad Uddin
Keyword(s):  
Mass Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Computational Study ◽  
Flow Direction ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Two Dimensional ◽  
Permeate Flux ◽  
Elliptical Cross

The large energy consumption of membrane desalination process has encouraged researchers to explore different spacer designs using Computational Fluid Dynamics (CFD) for maximizing permeate per unit of energy consumed. In previous studies of zigzag spacer designs, the filaments are modeled as circular cross sections in a two-dimensional geometry under the assumption that the flow is oriented normal to the filaments. In this work, we consider the 45° orientation of the flow towards the three-dimensional zigzag spacer unit, which projects the circular cross section of the filament as elliptical in a simplified two-dimensional domain. OpenFOAM was used to simulate the mass transfer enhancement in a reverse-osmosis desalination unit employing spiral wound membranes lined with zigzag spacer filaments. Properties that impact the concentration polarization and hence permeate flux were analyzed in the domain with elliptical filaments as well as a domain with circular filaments to draw suitable comparisons. The range of variation in characteristic parameters across the domain between the two different configurations is determined. It was concluded that ignoring the elliptical projection of circular filaments to the flow direction, can introduce significant margin of error in the estimation of mass transfer coefficient.

Three-dimensional vibration of a ring with a noncircular cross-section on an elastic foundation

2017 ◽  
Vol 232 (13) ◽  
pp. 2381-2393 ◽  
Author(s):  
Zhe Liu ◽  
Fuqiang Zhou ◽  
Christian Oertel ◽  
Yintao Wei
Keyword(s):  
Elastic Foundation ◽  
Cross Section ◽  
Three Dimensional ◽  
Theoretical Formula ◽  
Variation Principle ◽  
Displacement Fields ◽  
Element Analysis ◽  
Noncircular Cross Section ◽  
Truck Tire ◽  
Out Of Plane

The three-dimensional dynamic equations of a ring with a noncircular cross-section on an elastic foundation are obtained using the Hamilton variation principle. In contrast to the previous rings on elastic foundation model, the developed model incorporates both the in-plane and out-of-plane bend and the out-of-plane torsion in displacement fields. The errors in the derivation of the initial stress and the work of the internal pressure in previous rings on elastic foundation models have been corrected. The mode expansion was used to obtain the analytical solution of the natural frequency. The initial motivation is to develop a theoretical model for car tire dynamics. Therefore, to validate the proposed model, the in-plane and out-of-plane vibrations of a truck tire have been analyzed using the proposed method. To further verify the accuracy of the model, the results of the theoretical formula are compared with the finite element analysis and modal test, and good agreement can be found.

Axially Symmetric Waves in Elastic Rods

1960 ◽  
Vol 27 (1) ◽  
pp. 145-151 ◽  
Author(s):  
R. D. Mindlin ◽  
H. D. McNiven
Keyword(s):  
Cross Section ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elastic Rods ◽  
Axially Symmetric ◽  
Elastic Rod ◽  
One Dimensional ◽  
Axial Shear ◽  
Wave Numbers ◽  
Complex Wave

A system of approximate, one-dimensional equations is derived for axially symmetric motions of an elastic rod of circular cross section. The equations take into account the coupling between longitudinal, axial shear, and radial modes. The spectrum of frequencies for real, imaginary, and complex wave numbers in an infinite rod is explored in detail and compared with the analogous solution of the three-dimensional equations.

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