scholarly journals The influence of secondary flow in a two-phase gas-solid system in straight channels with a non-circular cross-section

2016 ◽  
Vol 20 (suppl. 5) ◽  
pp. 1419-1434
Author(s):  
Sasa Milanovic ◽  
Milos Jovanovic ◽  
Boban Nikolic ◽  
Vladislav Blagojevic
Keyword(s):  
Turbulent Flow ◽  
Secondary Flow ◽  
Cross Section ◽  
Circular Cross Section ◽  
Channel Cross Section ◽  
Two Phase ◽  
Cross Sectional ◽  
Specific Flow ◽  
Sectional Plane ◽  
The Cross

The paper considers two-phase gas-solid turbulent flow of pneumatic transport in straight horizontal channels with a non-circular cross-section. During turbulent flow, a specific flow phenomenon, known as secondary flow, occurs in these channels in the cross-sectional plane. The existence of strong temperature gradients in the cross-sectional plane of the channel or the cases of curved channels result in the appearance of the secondary flow of the first kind. However, in straight channels with a non-circular cross-section, in the developed turbulent flow mode, a secondary flow, known as Prandtl?s secondary flow of the second kind, is induced. The paper presents a numerical simulation of a developed two-phase turbulent flow by using the PHOENICS 3.3.1 software package. Reynolds stress model was used to model the turbulence. The paper provides the data on the changes in turbulent stresses in the channel cross-section as well as the velocities of solid particles transported along the channel.

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

scholarly journals A Spectral Finite Element Model for Vibration Analysis of a Beam Based on General Higher-Order Theory

2008 ◽  
Vol 15 (2) ◽  
pp. 179-192 ◽  
Author(s):  
Jiao Sujuan ◽  
Li Jun ◽  
Hua Hongxing ◽  
Shen Rongying
Keyword(s):  
Cross Section ◽  
Spectral Element ◽  
Higher Order ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Coupled Equations ◽  
Aspect Ratios ◽  
Sectional Plane ◽  
The Cross ◽  
Element Matrix

The spectral element matrix is derived for a straight and uniform beam element having an arbitrary cross-section. The general higher-order beam theory is used, which accurately accounts for the transverse shear deformation out of the cross-sectional plane and antielastic-type deformation within the cross-sectional plane. Two coupled equations of motion are derived by use of Hamilton's principle along with the full three-dimensional constitutive relations. The theoretical expressions of the spectral element matrix are formulated from the exact solutions of the coupled governing equations. The developed spectral element matrix is directly applied to calculate the exact natural frequencies and mode shapes of the illustrative examples. Numerical results of the thick isotropic beams with rectangular and elliptical cross-sections are presented for a wide variety of cross-section aspect ratios.

scholarly journals Effect of inertial lift on a spherical particle suspended in flow through a curved duct

2019 ◽  
Vol 875 ◽  
pp. 1-43 ◽  
Author(s):  
Brendan Harding ◽  
Yvonne M. Stokes ◽  
Andrea L. Bertozzi
Keyword(s):  
Reynolds Number ◽  
Spherical Particle ◽  
Cross Section ◽  
Bend Radius ◽  
Cross Sectional ◽  
Particle Reynolds Number ◽  
Curved Duct ◽  
Sectional Plane ◽  
Flow Through ◽  
The Cross

We develop a model of the forces on a spherical particle suspended in flow through a curved duct under the assumption that the particle Reynolds number is small. This extends an asymptotic model of inertial lift force previously developed to study inertial migration in straight ducts. Of particular interest is the existence and location of stable equilibria within the cross-sectional plane towards which particles migrate. The Navier–Stokes equations determine the hydrodynamic forces acting on a particle. A leading-order model of the forces within the cross-sectional plane is obtained through the use of a rotating coordinate system and a perturbation expansion in the particle Reynolds number of the disturbance flow. We predict the behaviour of neutrally buoyant particles at low flow rates and examine the variation in focusing position with respect to particle size and bend radius, independent of the flow rate. In this regime, the lateral focusing position of particles approximately collapses with respect to a dimensionless parameter dependent on three length scales: specifically, the particle radius, duct height and duct bend radius. Additionally, a trapezoidal-shaped cross-section is considered in order to demonstrate how changes in the cross-section design influence the dynamics of particles.

On Saint-Venant’s Problem for an Inhomogeneous, Anisotropic Cylinder—Part II: Cross-Sectional Properties

2000 ◽  
Vol 68 (3) ◽  
pp. 382-391 ◽  
Author(s):  
J. B. Kosmatka ◽  
H. C. Lin ◽  
S. B. Dong
Keyword(s):  
Cross Section ◽  
Symmetry Plane ◽  
Material Symmetry ◽  
Shear Center ◽  
Cross Sectional ◽  
Mean Values ◽  
Anisotropic Cylinder ◽  
Sectional Plane ◽  
Weighted Integrals ◽  
The Cross

Cross-sectional properties of a prismatic inhomogeneous, anisotropic cylinder are determined from Saint-Venant solutions for extension-bending-torsion and flexure, whose method of construction was presented in a previous paper. The coupling of extensional, bending, and twisting deformations due to anisotropy and inhomogeneity leads to some very interesting features. Herein, it is shown that for an inhomogeneous, anisotropic cylinder whose cross-sectional plane is not a material symmetry plane, distinct modulus-weighted and compliance-weighted centroids and distinct principal bending axes are possible. A line of extension-bending centers is given on which an axial force causes extension and bending only but no twist. Two shear centers are given, one using the Griffith-Taylor definition that ignores cross-sectional warpages and the other by stipulating a zero mean rotation over the cross section. The center of twist is discussed, and this property depends on root end fixity conditions that are prescribed in terms of their mean values based on integrals over the cross section rather than by a pointwise specification. While these shear center and center of twist definitions have some rational bases, it is recognized that other definitions are possible, for example those based on modulus or compliance-weighted integrals. Two examples, an angle and a channel, both composed of a two-layer ±30 deg angle-ply composite material, illustrate the procedures for determining these cross-sectional properties.

scholarly journals Cross-Section Deformation and Bending Moment of a Steel Square Tubular Section

Materials ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 5170
Author(s):  
Stanisław Kut ◽  
Feliks Stachowicz
Keyword(s):  
Numerical Modeling ◽  
Cross Section ◽  
Circular Cross Section ◽  
Bending Moment ◽  
Experimental Tests ◽  
Cross Sectional ◽  
Cold Bending ◽  
Bending Process ◽  
The Cross ◽  
Sectional Shape

When bending thin-walled profiles, significant distortion of the cross-section occurs, which has a significant impact on the course of the bending moment characteristics and on the value of allowable bending curvatures. This paper presents the results of experimental and numerical modeling of the box profile bending process, which was carried out in order to determine the dependence of the cross-sectional shape and bending moment of bending curvature. Extensive numerical calculations were used to model the process of shaping a square pipe from a circular tube and to model the bending process, especially when taking into account the effects of such a deformation path. The pure bending moment characteristics and the deformation of the cross-section were performed for a 25 × 25 × 2 mm square tube made of S235JR structural steel. The innovative approach for determining the parameters of cold bending square tubes pertained to considering the stress state in the preserved material in individual areas of their cross-section. The results of numerical modeling—after considering the history of deformation (i.e., the process of forming a square pipe from a pipe with a circular cross-section)—gave a satisfactory agreement with the results of experimental tests, both in terms of the degree of pipe wall deflection and the characteristics of the bending moment.

scholarly journals Suppression of Brazier Effect in Multilayered Cylinders

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hiroyuki Shima ◽  
Motohiro Sato ◽  
Sung-Jin Park
Keyword(s):  
Cross Section ◽  
Circular Cross Section ◽  
Interlayer Coupling ◽  
Theoretical Formulation ◽  
Cross Sectional ◽  
Quantitative Manner ◽  
Hollow Cylinders ◽  
The Common ◽  
The Cross ◽  
Brazier Effect

When a straight hollow tube having circular cross-section is bent uniformly into an arc, the cross-section tends to ovalize or flatten due to the in-plane stresses induced by bending; this ovalization phenomenon is called the Brazier effect. The present paper is aimed at theoretical formulation of the Brazier effect observed in multilayered cylinders, in which a set of thin hollow cylinders are stacked concentrically about the common axis. The results indicate that mechanical couplings between stacked cylinders are found to yield pronounced suppression of the cross-sectional ovalization. Numerical computations have been performed to measure the degree of suppression in a quantitative manner and to explore how it is affected by the variations in the bending curvature, the number of stacked cylinders, and the interlayer coupling strength.

Fiber Stabilization of Bent Cylinders, With an Application to Intervertebral Disks

1983 ◽  
Vol 105 (3) ◽  
pp. 294-295 ◽  
Author(s):  
K. E. Schreiner
Keyword(s):  
Cross Section ◽  
Pure Bending ◽  
Cross Sectional ◽  
Intervertebral Disks ◽  
Reinforcing Fibers ◽  
Sectional Plane ◽  
The Cross

Fibers cannot carry compression, and reinforcing fibers in a cylinder can only carry load if they are kept taut by the deformations of the cylinder. In the present study it is found that in pure bending, deformations that change the pitch, i.e., the angle between the fibers and the cross-sectional plane, towards 30 deg will slacken the fibers. With an initial pitch different than 30 deg, fibers in one half of the cross section will then be slackened by bending, and this half of the cylinder becomes unstable. Applied to the mechanics of the intervertebral disks, this may help explain mechanisms leading to nucleus prolaps.

A General Model for Predicting Low Reynolds Number Flow Pressure Drop in Non-Uniform Microchannels of Non-Circular Cross Section in Continuum and Slip-Flow Regimes

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
M. Akbari ◽  
A. Tamayol ◽  
M. Bahrami
Keyword(s):  
Pressure Drop ◽  
Cross Section ◽  
General Model ◽  
Circular Cross Section ◽  
Numerical Data ◽  
Creeping Flow ◽  
Geometrical Parameters ◽  
Cross Sectional ◽  
Flow Pressure ◽  
The Cross

A general model that predicts single-phase creeping flow pressure drop in microchannels of a noncircular cross section under slip and no-slip regimes is proposed. The model accounts for gradual variations in the cross section and relates the pressure drop to geometrical parameters of the cross section, i.e., area, perimeter, and polar moment of inertia. The accuracy of the proposed model is assessed by comparing the results against experimental and numerical data collected from various studies in the literature for a wide variety of cross-sectional shapes. The suggested model can be used for the design and optimization of microsystems that contain networks of microchannels with noncircular cross sections resulting from different fabrication techniques.

Laminar Mixed Convection in a Concentric Annulus With Horizontal Axis

1985 ◽  
Vol 107 (4) ◽  
pp. 902-909 ◽  
Author(s):  
A. O. Nieckele ◽  
S. V. Patankar
Keyword(s):  
Rayleigh Number ◽  
Secondary Flow ◽  
Cross Section ◽  
Numerical Study ◽  
Secondary Flows ◽  
Cross Sectional ◽  
Laminar Mixed Convection ◽  
The Cross ◽  
Annular Pipe ◽  
Rayleigh Numbers

Axial laminar flow in a horizontal annular pipe is influenced by the presence of buoyancy-induced secondary flows that are caused by the heat flow from the inner cylinder. A numerical study is presented for the fully developed region of the buoyancy-affected flow. The distributions of the axial and cross-sectional velocities are calculated along with the temperature variation in the cross section. Results are presented for a range of values of the Rayleigh number, the Prandtl number, and the radius ratio of the annulus. The Nusselt number increases significantly with the Rayleigh number; yet the corresponding increase in the friction factor is found to be rather small. Distributions of secondary flow and isotherms over the cross section are presented for different values of the parameters. In each half of the annulus on either side of the vertical centerline, the secondary flow displays a single-eddy pattern at low Rayleigh numbers and changes to a double-eddy pattern at high values.

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