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.

scholarly journals Numerical Study of Turbulent Secondary Flows in Curved Ducts

1990 ◽  
Vol 112 (2) ◽  
pp. 205-211 ◽  
Author(s):  
N. Hur ◽  
S. Thangam ◽  
C. G. Speziale
Keyword(s):  
Experimental Data ◽  
Turbulent Flow ◽  
Secondary Flow ◽  
Cross Section ◽  
Numerical Study ◽  
Secondary Flows ◽  
Fully Developed Turbulent Flow ◽  
Volume Method ◽  
Curved Ducts ◽  
Good Agreement

The pressure driven, fully developed turbulent flow of an incompressible viscous fluid in curved ducts of square cross-section is studied numerically by making use of a finite volume method. A nonlinear K -1 model is used to represent the turbulence. The results for both straight and curved ducts are presented. For the case of fully developed turbulent flow in straight ducts, the secondary flow is characterized by an eight-vortex structure for which the computed flowfield is shown to be in good agreement with available experimental data. The introduction of moderate curvature is shown to cause a substantial increase in the strength of the secondary flow and to change the secondary flow pattern to either a double-vortex or a four-vortex configuration.

The influence of secondary flows induced by normal stress differences on the shear-induced migration of particles in concentrated suspensions

2008 ◽  
Vol 603 ◽  
pp. 207-243 ◽  
Author(s):  
ARUN RAMACHANDRAN ◽  
DAVID T. LEIGHTON
Keyword(s):  
Normal Stress ◽  
Secondary Flow ◽  
Cross Section ◽  
Concentration Distribution ◽  
Normal Stress Difference ◽  
Secondary Flows ◽  
Stress Difference ◽  
Second Normal Stress Difference ◽  
Normal Stress Differences ◽  
The Cross

It was first demonstrated experimentally by H. Giesekus in 1965 that the second normal stress difference in polymers can induce a secondary flow within the cross-section of a non-axisymmetric conduit. In this paper, we show through simulations that the same may be true for suspensions of rigid non-colloidal particles that are known to exhibit a strong negative second normal stress difference. Typically, the magnitudes of the transverse velocity components are small compared to the average axial velocity of the suspension; but the ratio of this transverse convective velocity to the shear-induced migration velocity is characterized by the shear-induced migration Péclet number χ which scales as B2/a2, B being the characteristic length scale of the cross-section and a being the particle radius. Since this Péclet number is kept high in suspension experiments (typically 100 to 2500), the influence of the weak circulation currents on the concentration profile can be very strong, a result that has not been appreciated in previous work. The principal effect of secondary flows on the concentration distribution as determined from simulations using the suspension balance model of Nott & Brady (J. Fluid Mech. vol. 275, 1994, p. 157) and the constitutive equations of Zarraga et al. (J. Rheol. vol. 44, 2000, p. 185) is three-fold. First, the steady-state particle concentration distribution is no longer independent of particle size; rather, it depends on the aspect ratio B/a. Secondly, the direction of the secondary flow is such that particles are swept out of regions of high streamsurface curvature, e.g. particle concentrations in corners reach a minimum rather than the local maximum predicted in the absence of such flows. Finally, the second normal stress differences lead to instabilities even in such simple geometries as plane-Poiseuille flow.

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.

A Numerical Study on the Generation Mechanism of Turbulence-Driven Secondary Flow in a Square Duct

1993 ◽  
Vol 115 (1) ◽  
pp. 172-175 ◽  
Author(s):  
Hyon Kook Myong
Keyword(s):  
Secondary Flow ◽  
Numerical Study ◽  
Reynolds Shear Stress ◽  
Secondary Flows ◽  
Generation Mechanism ◽  
Streamwise Vorticity ◽  
Reynolds Stresses ◽  
Cross Sectional ◽  
Square Duct ◽  
Vorticity Transport

The generation mechanism of turbulence-driven secondary flows in a square duct is numerically investigated in the present study by using an anisotropic low-Reynolds-number k–ε turbulence model. Special attention is directed to the distributions of turbulence quantities, which are responsible for the secondary flow generation, such as the anisotropy of normal Reynolds stresses and the secondary Reynolds shear stress acting on the cross-sectional plane. The vorticity transport process is also discussed in detail, based on the numerical evaluation of the individual terms which appear in the streamwise vorticity transport equation.

Automated Diagonal Slice and View Solution for 3D Device Structure Analysis

2018 ◽  
Author(s):  
Sang Hoon Lee ◽  
Jeff Blackwood ◽  
Stacey Stone ◽  
Michael Schmidt ◽  
Mark Williamson ◽  
...  
Keyword(s):  
Cross Section ◽  
Focused Ion Beam ◽  
Ion Beam ◽  
Image Data ◽  
Planar Surface ◽  
Device Structure ◽  
Cross Sectional ◽  
Device Structures ◽  
The Cross ◽  
Planar Analysis

Abstract The cross-sectional and planar analysis of current generation 3D device structures can be analyzed using a single Focused Ion Beam (FIB) mill. This is achieved using a diagonal milling technique that exposes a multilayer planar surface as well as the cross-section. this provides image data allowing for an efficient method to monitor the fabrication process and find device design errors. This process saves tremendous sample-to-data time, decreasing it from days to hours while still providing precise defect and structure data.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

scholarly journals A Review of Numerical Simulations of Secondary Flows in River Bends

Water ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 884
Author(s):  
Rawaa Shaheed ◽  
Abdolmajid Mohammadian ◽  
Xiaohui Yan
Keyword(s):  
Numerical Modeling ◽  
Numerical Simulations ◽  
Secondary Flow ◽  
Cross Section ◽  
Turbulence Models ◽  
Main Flow ◽  
Secondary Flows ◽  
River Bends ◽  
River Cross Section ◽  
River Bend

River bends are one of the common elements in most natural rivers, and secondary flow is one of the most important flow features in the bends. The secondary flow is perpendicular to the main flow and has a helical path moving towards the outer bank at the upper part of the river cross-section, and towards the inner bank at the lower part of the river cross-section. The secondary flow causes a redistribution in the main flow. Accordingly, this redistribution and sediment transport by the secondary flow may lead to the formation of a typical pattern of river bend profile. It is important to study and understand the flow pattern in order to predict the profile and the position of the bend in the river. However, there are a lack of comprehensive reviews on the advances in numerical modeling of bend secondary flow in the literature. Therefore, this study comprehensively reviews the fundamentals of secondary flow, the governing equations and boundary conditions for numerical simulations, and previous numerical studies on river bend flows. Most importantly, it reviews various numerical simulation strategies and performance of various turbulence models in simulating the flow in river bends and concludes that the main problem is finding the appropriate model for each case of turbulent flow. The present review summarizes the recent advances in numerical modeling of secondary flow and points out the key challenges, which can provide useful information for future studies.

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.

The Cross Section of Expected Returns with MIDAS Betas

2011 ◽  
Vol 47 (1) ◽  
pp. 115-135 ◽  
Author(s):  
Mariano González ◽  
Juan Nave ◽  
Gonzalo Rubio
Keyword(s):  
Cross Section ◽  
Risk Premium ◽  
Market Risk ◽  
Ordinary Least Squares ◽  
Mixed Data ◽  
Expected Returns ◽  
Data Sampling ◽  
Cross Sectional ◽  
Market Risk Premium ◽  
The Cross

AbstractThis paper explores the cross-sectional variation of expected returns for a large cross section of industry and size/book-to-market portfolios. We employ mixed data sampling (MIDAS) to estimate a portfolio’s conditional beta with the market and with alternative risk factors and innovations to well-known macroeconomic variables. The market risk premium is positive and significant, and the result is robust to alternative asset pricing specifications and model misspecification. However, the traditional 2-pass ordinary least squares (OLS) cross-sectional regressions produce an estimate of the market risk premium that is negative, and significantly different from 0. Using alternative procedures, we compare both beta estimators. We conclude that beta estimates under MIDAS present lower mean absolute forecasting errors and generate better out-of-sample performance of the optimized portfolios relative to OLS betas.

An Analytical Method of Analyzing the Heat Conduction for the Unequal Cross-Section Straight Fin

2013 ◽  
Vol 365-366 ◽  
pp. 1211-1216
Author(s):  
Fan Zhang ◽  
Peng Yun Song
Keyword(s):  
Heat Conduction ◽  
Cross Section ◽  
Analytical Method ◽  
Thermal Analyses ◽  
Cross Sectional ◽  
Cross Section Area ◽  
Section Area ◽  
Calculation Results ◽  
The Cross ◽  
Analytical Expressions

The cross-section area of straight fin is often considered to be equal in the thermal analyses of straight fin, but sometimes it is unequalin actual situation. Taking a straight fin with two unequal cross-sectional areas as an example,an analytical method of heat conduction for unequal section straight fin is presented. The analytical expressions of temperature field and heat dissipating capacity about the fin,which has a smaller cross-section area near the fin base and a larger one, is obtained respectively. The calculation results of the unequal cross-section are fully consistent with the equal area one, so the method is proved right. The results show that the larger the cross section areanear the base,the better is the heat transfer, and the temperature at the base with larger cross-section area is lower than that with smaller cross-section area when the amount of heat is fixed.

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