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.

Slip-Flow Pressure Drop in Microchannels of General Cross Section

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
M. Bahrami ◽  
A. Tamayol ◽  
P. Taheri
Keyword(s):  
Boundary Condition ◽  
Pressure Drop ◽  
Cross Section ◽  
Slip Flow ◽  
Homogeneous Boundary Condition ◽  
Slip Boundary Condition ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Cross Sectional ◽  
Slip Boundary

In the present study, a compact analytical model is developed to determine the pressure drop of fully-developed, incompressible, and constant properties slip-flow through arbitrary cross section microchannels. An averaged first-order Maxwell slip boundary condition is considered. Introducing a relative velocity, the difference between the bulk flow and the boundary velocities, the axial momentum reduces to Poisson’s equation with homogeneous boundary condition. Square root of area is selected as the characteristic length scale. The model of Bahrami et al. (2006, “Pressure Drop of Laminar, Fully Developed Flow in Microchannels of Arbitrary Cross Section,” ASME J. Fluids Eng., 128, pp. 1036–1044), which was developed for no-slip boundary condition, is extended to cover the slip-flow regime in this study. The proposed model for pressure drop is a function of geometrical parameters of the channel: cross sectional area, perimeter, polar moment of inertia, and the Knudsen number. The model is successfully validated against existing numerical and experimental data collected from different sources in literature for several shapes, including circular, rectangular, trapezoidal, and double-trapezoidal cross sections and a variety of gases such as nitrogen, argon, and helium.

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.

Slip-Flow Pressure Drop in Microchannels of General Cross-Section

2008 ◽  
Author(s):  
A. Tamayol ◽  
M. Bahrami ◽  
P. Taheri
Keyword(s):  
Boundary Condition ◽  
Pressure Drop ◽  
Cross Section ◽  
Slip Flow ◽  
Homogeneous Boundary Condition ◽  
Slip Boundary Condition ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Cross Sectional ◽  
Slip Boundary

In the present study, a compact analytical model is developed to determine the pressure drop of fully-developed, incompressible, and constant properties slip-flow through arbitrary cross-section microchannels. An averaged first-order Maxwell slip boundary condition is considered. Introducing a relative velocity, the difference between the bulk flow and the boundary velocities, the axial momentum reduces to the Poisson’s equation with homogeneous boundary condition. Square root of area is selected as the characteristic length scale. Bahrami et al.’s model, which was developed no-slip boundary condition, is extended to cover the slip-flow regime in this study. The proposed model is a function of geometrical parameters of the channel: cross-sectional area, perimeter, polar moment of inertia and the Knudsen number. The model is successfully validated against existing numerical and experimental data from different sources in the literature for several shapes, including: circular, rectangular, trapezoidal, and double-trapezoidal cross-sections and a variety of gases such as: nitrogen, argon, and helium.

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.

Heat Transfer and Pressure Loss in a Two-Pass, Rectangular Channel Featuring a Reduced Cross-Sectional Area After the 180-Degree Tip Turn With Different Turning Vane Configurations

2020 ◽  
Author(s):  
Sulaiman M. Alsaleem ◽  
Lesley M. Wright ◽  
Je-Chin Han
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Aspect Ratio ◽  
Cross Section ◽  
Pressure Loss ◽  
Circular Cross Section ◽  
Sectional Area ◽  
Cross Sectional ◽  
Number Range

Abstract Serpentine, varying aspect ratio cooling passages, are typically used in cooling advanced gas turbine blades. These passages are usually connected by sharp, 180-deg bends. In the open literature, most of the internal cooling studies use a fixed cross-sectional area for multi-pass channels. Studies that use varying aspect ratio channels, along with a guide (turn) vane to direct the flow with turning, are scarce. In general, studies show that the incorporation of turning vanes in the bend region of a multi-pass channel keeps the heat transfer rate high while reducing pressure loss. Therefore, the current study investigates the effect of using different guide (turn) vane designs on both the detailed heat transfer distribution and pressure loss in a multi-pass channel with an aspect ratio of (4:1) in the entry passage and (2:1) in the second passage downstream of the vane (s). The first vane configuration is one solid-vane with a semi-circular cross-section connecting the two flow passages. The second configuration has three broken-vanes with a quarter-circular cross-section; two broken vanes are located downstream in the first passage (entering the turn), and one broken vane is upstream in the second passage (exiting the turn). For a Reynolds number range 15,000 to 45,000, detailed heat transfer distributions were obtained on all surfaces within the flow passages by using a transient liquid crystal method. The results show that the turning vane configurations have large effects on the heat transfer, in the turning bend and second passage, and the overall pressure drop. Results show that including the semi-circular vane in the turning region of a multi-pass channel enhanced the overall heat transfer by around 29% with a reduction in pressure loss by around 20%. Moreover, results show that the quarter-circular vane design provides higher overall averaged heat transfer enhancement than the semi-circular vane design by around 9% with penalty of higher pressure drop by 6%, which yields higher thermal performance by 7%, over the Reynolds number range.

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.

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 Asymptotic Behavior of Stable Structures Made of Beams

2021 ◽  
Author(s):  
Georges Griso ◽  
Larysa Khilkova ◽  
Julia Orlik ◽  
Olena Sivak
Keyword(s):  
Asymptotic Behavior ◽  
Cross Section ◽  
Cross Sections ◽  
Linear Elasticity ◽  
Circular Cross Section ◽  
Linear Elasticity Theory ◽  
Linear Elastic ◽  
The Cross ◽  
Small Rotation ◽  
Stable Structures

AbstractIn this paper, we study the asymptotic behavior of an $\varepsilon $ ε -periodic 3D stable structure made of beams of circular cross-section of radius $r$ r when the periodicity parameter $\varepsilon $ ε and the ratio ${r/\varepsilon }$ r / ε simultaneously tend to 0. The analysis is performed within the frame of linear elasticity theory and it is based on the known decomposition of the beam displacements into a beam centerline displacement, a small rotation of the cross-sections and a warping (the deformation of the cross-sections). This decomposition allows to obtain Korn type inequalities. We introduce two unfolding operators, one for the homogenization of the set of beam centerlines and another for the dimension reduction of the beams. The limit homogenized problem is still a linear elastic, second order PDE.

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.

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