Numerical Simulating Open-Channel Flows with Regular and Irregular Cross-Section Shapes Based on Finite Volume Godunov-Type Scheme

2020 ◽  
pp. 2050047
Author(s):  
Xiaokang Xin ◽  
Fengpeng Bai ◽  
Kefeng Li
Keyword(s):  
Finite Volume ◽  
Cross Section ◽  
Cross Sections ◽  
Open Channel ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Cross Sectional ◽  
Shallow Flows ◽  
Natural Streams ◽  
Saint Venant Equations

A numerical model based on the Saint-Venant equations (one-dimensional shallow water equations) is proposed to simulate shallow flows in an open channel with regular and irregular cross-section shapes. The Saint-Venant equations are solved by the finite-volume method based on Godunov-type framework with a modified Harten, Lax, and van Leer (HLL) approximate Riemann solver. Cross-sectional area is replaced by water surface level as one of primitive variables. Two numerical integral algorithms, compound trapezoidal and Gauss–Legendre integrations, are used to compute the hydrostatic pressure thrust term for natural streams with arbitrary and irregular cross-sections. The Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and second-order Runge–Kutta methods is adopted to achieve second-order accuracy in space and time, respectively. The performance of the resulting scheme is evaluated by application in rectangular channels, trapezoidal channels, and a natural mountain river. The results are compared with analytical solutions and experimental or measured data. It is demonstrated that the numerical scheme can simulate shallow flows with arbitrary cross-section shapes in practical conditions.

Estimation of Nusselt Number in Microchannels of Arbitrary Cross-Section With Constant Axial Heat Flux

2008 ◽  
Author(s):  
Ehsan Sadeghi ◽  
Majid Bahrami ◽  
Ned Djilali
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Cross Section ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Thermal Systems ◽  
Cross Sectional ◽  
Axial Heat

In many practical instances such as basic design, parametric study, and optimization analysis of thermal systems, it is often very convenient to have closed form relations to obtain the trends and a reasonable estimate of the Nusselt number. However, finding exact solutions for many practical singly-connected cross-sections, such as trapezoidal microchannels, is complex. In the present study, the square root of cross-sectional area is proposed as the characteristic length scale for Nusselt number. Using analytical solutions of rectangular, elliptical, and triangular ducts, a compact model for estimation of Nusselt number of fully-developed, laminar flow in microchannels of arbitrary cross-sections with “H1” boundary condition (constant axial wall heat flux with constant peripheral wall temperature) is developed. The proposed model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The present model is verified against analytical and numerical solutions for a wide variety of cross-sections with a maximum difference on the order of 9%.

Vibration of Stress-Free Hollow Cylinders of Arbitrary Cross Section

1995 ◽  
Vol 62 (3) ◽  
pp. 718-724 ◽  
Author(s):  
K. M. Liew ◽  
K. C. Hung ◽  
M. K. Lim
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Arbitrary Cross Section ◽  
Mode Shapes ◽  
Width Ratio ◽  
Cross Sectional ◽  
Hollow Cylinders ◽  
Displacement Based ◽  
Bending Modes

A three-dimensional elasticity solution to the vibrations of stress-free hollow cylinders of arbitrary cross section is presented. The natural frequencies and deformed mode shapes of these cylinders are obtained via a three-dimensional displacement-based energy formulation. The technique is applied specifically to the parametric investigation of hollow cylinders of different cross sections and sizes. It is found that the cross-sectional property of the cylinder has significant effects on the normal mode responses, particularly, on the transverse bending modes. By varying the length-to-width ratio of these elastic cylinders, interesting results demonstrating the dependence of frequencies on the length of the cylinder have been concluded.

scholarly journals Shear Lag Analysis due to Flexure of Prismatic Beams with Arbitrary Cross-Sections by FEM

2021 ◽  
Author(s):  
Dang-Bao Tran ◽  
Jaroslav Navrátil
Keyword(s):  
Numerical Method ◽  
Cross Section ◽  
Cross Sections ◽  
Arbitrary Cross Section ◽  
Local Analysis ◽  
3D Analysis ◽  
Shear Lag ◽  
Isoparametric Element ◽  
Cross Sectional ◽  
The Cross

This paper presents the use of a finite element method (FEM) to analyze the shear lag effect due to the flexure of beams with an arbitrary cross-section and homogeneous elastic material. Beams are constrained by the most common types of supports, such as fixed, pinned, and roller. The transverse, concentrated, or distributed loads act on the beams through the shear center of the cross-section. The presented FEM transforms the 3D analysis of the shear lag phenomenon into separated 2D cross-sectional and 1D beam modeling. The characteristics of the cross-section are firstly derived from 2D FEM, which uses a 9-node isoparametric element. Then, a 1D FEM, which uses a linear isoparametric element, is developed to compute the deflection, rotation angle, bending warping parameter, and stress resultants. Finally, the stress field is obtained from the local analysis on the 2D-cross section. A MATLAB program is executed to validate the numerical method. The validation examples have proven the efficiency and reliability of the numerical method for analyzing shear lag flexure, which is a common problem in structural design.

scholarly journals Theory of “dissolution” and “condensation” of the physical geometric characteristics of an arbitrary cross-section under the action of torsion with bending

2019 ◽  
Vol 15 (4) ◽  
pp. 261-270
Author(s):  
Vladimir I. Kolchunov ◽  
Aleksej I. Demyanov ◽  
Nikolay V. Naumov
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Strain State ◽  
Rectangular Cross Section ◽  
Arbitrary Cross Section ◽  
Large Circle ◽  
Stress Strain ◽  
Cross Sectional ◽  
Tangential Stresses ◽  
Stress Strain State

Aim of research - to continue the development of methods for determining the stress-strain state of rods during torsion using materials resistance methods. Methods. A new approach for determining tangential torsional stresses for arbitrary cross sectional rods, based on simplified assumptions of material resistance, is proposed. The main feature of this approach is the approximation of rectangular or any complex cross section of reinforced concrete structures by describing a large circle around the cross section and splitting it into small squares with circles inscribed into them. Results. Three theorems have been formulated, the first of which relates the accumulation of tangential stresses (increments) from the edges of a rectangle to the middle of a rectangular section with the formula for determining tangent stresses for round sections. The second theorem allows to establish a connection between the tangential stresses calculated for each of the small squares-circles and the tangent stresses of the large circle through their increments. The third theorem makes it possible to find tangential stresses for each of the small square circles. The proposed approach allows to remove the need to use special tables for the calculation and not only in the elastic stage. It also makes it possible to separate the stress-strain state in the whole set of round cross-sections from the additional field caused by the deplanation of the rectangular cross-section. In addition, the proposed approach makes it possible to take into account the concentration of angular deformations in the incoming angles and other places with changing geometric parameters.

Automated 3D measurement of fiber cross section morphology in handsheets

2012 ◽  
Vol 27 (2) ◽  
pp. 264-269 ◽  
Author(s):  
Christian Lorbach ◽  
Ulrich Hirn ◽  
Johannes Kritzinger ◽  
Wolfgang Bauer
Keyword(s):  
Image Analysis ◽  
Cross Section ◽  
Cross Sections ◽  
Image Plane ◽  
3D Measurement ◽  
Cross Sectional ◽  
Fiber Cross Section ◽  
Fiber Wall ◽  
Sectional Shape ◽  
Cross Section Geometry

Abstract We present a method for 3D measurement of fiber cross sectional morphology from handsheets. An automated procedure is used to acquire 3D datasets of fiber cross sectional images using an automated microtome and light microscopy. The fiber cross section geometry is extracted using digital image analysis. Simple sample preparation and highly automated image acquisition and image analysis are providing an efficient tool to analyze large samples. It is demonstrated that if fibers are tilted towards the image plane the images of fiber cross sections are always larger than the true fiber cross section geometry. In our analysis the tilting angles of the fibers to the image plane are measured. The resulting fiber cross sectional images are distorted to compensate the error due to fiber tilt, restoring the true fiber cross sectional shape. We use an approximated correction, the paper provides error estimates of the approximation. Measurement results for fiber wall thickness, fiber coarseness and fiber collapse are presented for one hardwood and one softwood pulp.

scholarly journals Supplemental Material: Plate boundary trench retreat and dextral shear drive intracontinental fault-slip histories: Neogene dextral faulting across the Gabbs Valley and Gillis Ranges, Central Walker Lane, Nevada

2020 ◽  
Author(s):  
J. Lee ◽  
et al.
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Plate Boundary ◽  
Fault Slip ◽  
Cross Sectional ◽  
Walker Lane ◽  
Dextral Shear ◽  
The Cross

<div>Figure 6. Interpretative cross sections illustrating the cross-sectional geometry of several paleovalleys. See Figure 3 for location of all cross sections and Figure 8 for location of cross section CCʹ. Cross sections AAʹ and BBʹ are plotted at the same scale, and cross section CCʹ is plotted at a smaller scale. Figure 6 is intended to be viewed at a width of 45.1 cm.</div>

scholarly journals Load bearing capacity of thin-walled rectangular and I-shaped steel sections of short both empty and concrete-filled columns

2021 ◽  
Vol 15 (58) ◽  
pp. 77-85
Author(s):  
Amor Bouaricha ◽  
Naoual Handel ◽  
Aziza Boutouta ◽  
Sarah Djouimaa
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Load Capacity ◽  
Cross Sectional ◽  
Short Columns ◽  
Cross Section Area ◽  
Section Area ◽  
Specimen Height ◽  
Steel Sections ◽  
Thin Walled

In this experimental work, strength results obtained on short columns subjected to concentric loads are presented. The specimens used in the tests have made of cold-rolled, thin-walled steel. Twenty short columns of the same cross-section area and wall thickness have been tested as follows: 8 empty and 12 filled with ordinary concrete. In the aim to determine the column section geometry with the highest resistance, three different types of cross-sections have been compared: rectangular, I-shaped unreinforced and, reinforced with 100 mm spaced transversal links. The parameters studied are the specimen height and the cross-sectional steel geometry. The registered experimental results have been compared to the ultimate loads intended by Eurocode 3 for empty columns and by Eurocode 4 for compound columns. These results showed that a concrete-filled composite column had improved strength compared to the empty case. Among the three cross-section types, it has been found that I-section reinforced is the most resistant than the other two sections. Moreover, the load capacity and mode of failure have been influenced by the height of the column. Also, it had noted that the experimental strengths of the tested columns don’t agree well with the EC3 and EC4 results.

A shear center demonstration model using 3D-printing

2021 ◽  
pp. 030641902110574
Author(s):  
Lawrence N Virgin
Keyword(s):  
3D Printing ◽  
Cross Section ◽  
Cross Sections ◽  
Principal Axis ◽  
Practical Importance ◽  
Bending Moment ◽  
Shear Center ◽  
Cross Sectional ◽  
Thin Walls ◽  
Section Profile

Locating the shear, or flexural, center of non-symmetric cross-sectional beams is a key element in the teaching of structural mechanics. That is, establishing the point on the plane of the cross-section where an applied load, generating a bending moment about a principal axis, results in uni-directional deflection, and no twisting. For example, in aerospace structures it is particularly important to assess the propensity of an airfoil section profile to resist bending and torsion under the action of aerodynamic forces. Cross-sections made of thin-walls, whether of open or closed form are of special practical importance and form the basis of the material in this paper. The advent of 3D-printing allows the development of tactile demonstration models based on non-trivial geometry and direct observation.

scholarly journals A Finite Volume Method for Modeling Shallow Flows with Wet-Dry Fronts on Adaptive Cartesian Grids

2014 ◽  
Vol 2014 ◽  
pp. 1-20 ◽  
Author(s):  
Sheng Bi ◽  
Jianzhong Zhou ◽  
Yi Liu ◽  
Lixiang Song
Keyword(s):  
Shallow Water ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Second Order ◽  
Topographic Features ◽  
Shallow Flows ◽  
Local Complex ◽  
Proposed Model ◽  
Volume Method

A second-order accurate, Godunov-type upwind finite volume method on dynamic refinement grids is developed in this paper for solving shallow-water equations. The advantage of this grid system is that no data structure is needed to store the neighbor information, since neighbors are directly specified by simple algebraic relationships. The key ingredient of the scheme is the use of the prebalanced shallow-water equations together with a simple but effective method to track the wet/dry fronts. In addition, a second-order spatial accuracy in space and time is achieved using a two-step unsplit MUSCL-Hancock method and a weighted surface-depth gradient method (WSDM) which considers the local Froude number is proposed for water depths reconstruction. The friction terms are solved by a semi-implicit scheme that can effectively prevent computational instability from small depths and does not invert the direction of velocity components. Several benchmark tests and a dam-break flooding simulation over real topography cases are used for model testing and validation. Results show that the proposed model is accurate and robust and has advantages when it is applied to simulate flow with local complex topographic features or flow conditions and thus has bright prospects of field-scale application.

scholarly journals Precise SEM Cross Section Polishing via Argon Beam Milling

2006 ◽  
Vol 14 (3) ◽  
pp. 22-25 ◽  
Author(s):  
N. Erdman ◽  
R. Campbell ◽  
S. Asahina
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Soft Materials ◽  
Mechanical Polishing ◽  
Water Soluble ◽  
Staining Procedure ◽  
Fibrous Materials ◽  
Cross Sectional ◽  
Hard Materials ◽  
Composite Samples

SEM observation of a specimen cross section can provide important information for research and development as well as failure analysis. In most cases, surface observation alone cannot provide information concerning the cross sectional structure of granular materials, layered materials, fibrous materials, and powders. Preparing highly-polished cross sections of these materials is both a science and an art.Typically, a cross section is prepared using mechanical means like conventional mechanical polishing methods or a microtome. The sample is first embedded in a holder or device, and then polished to achieve a flat cross section. In some cases, a staining procedure is used to highlight a specific component of the sample. Such methods can be lengthy procedures that require a great deal of skill, and can introduce artifacts into soft materials, deform the material around voids, or compress layers of soft and hard materials in composite samples. Mechanical polishing can miss fine details such as the presence of hairline cracks, and present a challenge to water-soluble phases.

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