On the stability of flow in an elliptic pipe which is nearly circular

1994 ◽  
Vol 281 ◽  
pp. 357-369 ◽  
Author(s):  
A. Davey ◽  
H. Salwen
Keyword(s):  
Cross Section ◽  
Specific Problem ◽  
Sectional Area ◽  
Leading Order ◽  
Straight Pipe ◽  
Cross Sectional ◽  
Double Eigenvalue ◽  
Circular Problem ◽  
Qualitative Structure ◽  
The Stability

In an earlier paper (Davey 1978) the first author investigated the linear stability of flow in a straight pipe whose cross-section was an ellipse, of small ellipticity e, by regarding the flow as a perturbation of Poiseuille flow in a circular pipe. That paper contained some serious errors which we correct herein. We show analytically that for the most important mode n = 1, for which the circular problem has a double eigenvalue c0 as the ‘swirl’ can be in either direction, the ellipticity splits the double eigenvalue into two separate eigenvalues c0 ± e2c12, to leading order, when the cross-sectional area of the pipe is kept fixed. The imaginary part of c12 is non-zero and so the ellipticity always makes the flow less stable. This specific problem is generic to a much wider class of fluid dynamical problems which are made less stable when the symmetry group of the dynamical system is reduced from S1 to Z2.In the Appendix, P. G. Drazin describes simply the qualitative structure of this problem, and other problems with the same symmetries, without technical detail.

scholarly journals Numerical simulation of cutting layer in internal corners milling

Mechanik ◽  
2019 ◽  
Vol 92 (7) ◽  
pp. 412-414
Author(s):  
Jan Burek ◽  
Rafał Flejszar ◽  
Barbara Jamuła
Keyword(s):  
Numerical Simulation ◽  
Numerical Model ◽  
Cross Section ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Cross Section Area ◽  
Section Area ◽  
The Cross ◽  
The Stability

The analytical and numerical model of the cross-section of the machined layer in the process of milling of concave rounding is presented. Simulation tests were carried out to determine the cross-sectional area of the cutting layer. A strategy has been developed that allows to increase the stability of the cross-section area of the cutting layer when the mill enters the inner corner area.

Optimization of High Concrete Retaining Wall Structure

2013 ◽  
Vol 357-360 ◽  
pp. 597-603
Author(s):  
Su Yang Gao ◽  
Yan Chen ◽  
Yao Feng Xie ◽  
Wen Dong Lei ◽  
Kai Yin
Keyword(s):  
Cross Section ◽  
Optimization Design ◽  
Retaining Wall ◽  
Cross Sectional Area ◽  
Wall Structure ◽  
Sectional Area ◽  
Cross Sectional ◽  
Structure Selection ◽  
Great Height ◽  
The Stability

The height of vertical pier retaining wall is relatively larger in regions with great height of water. As the retaining wall becomes higher, the cross-sectional area of ordinary gravity pier structure becomes larger and foundation strength needs to be larger, thus there are some restrictions for traditional structure form. This research focuses on new structure forms of high concrete retaining wall and its optimization design for piers in regions with great height of water. This study establishes a nonlinear constrained mathematical model of pier high retaining wall structures. The objective function is cross-sectional area of the pier retaining wall which is restricted by the stability, bearing capacity of foundation and strength of cross-section of retaining wall. This model is solved by fmincon function from Matlab and the results present an economically reasonable cross-section form. This new selection is greatly significant to improve the stability of high concrete retaining wall and reduce the project cost. The new structure is successfully used in a port of Huaihe River and it can be a solution to pier structure selection problem in regions with great height of water in the future.

Online Monitoring of Functional Electrical Properties in Aerosol Jet Printing Additive Manufacturing Process Using Shape-From-Shading Image Analysis

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Roozbeh (Ross) Salary ◽  
Jack P. Lombardi ◽  
Prahalad K. Rao ◽  
Mark D. Poliks
Keyword(s):  
Cross Section ◽  
Electrical Resistance ◽  
Online Monitoring ◽  
Shape From Shading ◽  
Sectional Area ◽  
Cross Sectional ◽  
Jet Printing ◽  
The Cross ◽  
Aerosol Jet Printing ◽  
Line Resistance

The goal of this research is online monitoring of functional electrical properties, e.g., resistance, of electronic devices made using aerosol jet printing (AJP) additive manufacturing (AM) process. In pursuit of this goal, the objective is to recover the cross-sectional profile of AJP-deposited electronic traces (called lines) through shape-from-shading (SfS) analysis of their online images. The aim is to use the SfS-derived cross-sectional profiles to predict the electrical resistance of the lines. An accurate characterization of the cross section is essential for monitoring the device resistance and other functional properties. For instance, as per Ohm’s law, the electrical resistance of a conductor is inversely proportional to its cross-sectional area (CSA). The central hypothesis is that the electrical resistance of an AJP-deposited line estimated online and in situ from its SfS-derived cross-sectional area is within 20% of its offline measurement. To test this hypothesis, silver nanoparticle lines were deposited using an Optomec AJ-300 printer at varying sheath gas flow rate (ShGFR) conditions. The four-point probes method, known as Kelvin sensing, was used to measure the resistance of the printed structures offline. Images of the lines were acquired online using a charge-coupled device (CCD) camera mounted coaxial to the deposition nozzle of the printer. To recover the cross-sectional profiles from the online images, three different SfS techniques were tested: Horn’s method, Pentland’s method, and Shah’s method. Optical profilometry was used to validate the SfS cross section estimates. Shah’s method was found to have the highest fidelity among the three SfS approaches tested. Line resistance was predicted as a function of ShGFR based on the SfS-estimates of line cross section using Shah’s method. The online SfS-derived line resistance was found to be within 20% of offline resistance measurements done using the Kelvin sensing technique.

scholarly journals Optimization of Geometric Parameters of Thermal Insulation of Pre-Insulated Double Pipes

Energies ◽  
2019 ◽  
Vol 12 (6) ◽  
pp. 1012 ◽  
Author(s):  
Dorota Krawczyk ◽  
Tomasz Teleszewski
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Cross Section ◽  
Thermal Insulation ◽  
Major Axis ◽  
Heat Losses ◽  
Sectional Area ◽  
Cross Sectional ◽  
Elliptical Shape ◽  
Half Axis

This paper presents the analysis of the heat conduction of pre-insulated double ducts and the optimization of the shape of thermal insulation by applying an elliptical shape. The shape of the cross-section of the thermal insulation is significantly affected by the thermal efficiency of double pre-insulated networks. The thickness of the insulation from the external side of the supply and return pipes affects the heat losses of the double pre-insulated pipes, while the distance between the supply and return pipes influences the heat flux exchanged between these ducts. An assumed elliptical shape with a ratio of the major axis to the minor half axis of an ellipse equaling 1.93 was compared to thermal circular insulation with the same cross-sectional area. All calculations were made using the boundary element method (BEM) using a proprietary computer program written in Fortran as part of the VIPSKILLS project.

scholarly journals HYDRAULICS AND SEDIMENTARY STABILITY OF COASTAL INLETS

1972 ◽  
Vol 1 (13) ◽  
pp. 38 ◽  
Author(s):  
M.P. O'Brien ◽  
R.G. Dean
Keyword(s):  
Cross Section ◽  
Stability Index ◽  
Hydraulic Loss ◽  
Cross Sectional ◽  
Equilibrium Relationship ◽  
Depositional Patterns ◽  
Storage Area ◽  
Loss Coefficients ◽  
The Stability ◽  
Coastal Inlets

A method is presented for investigating the stability of coastal inlets against closure due to transport and deposition of sand in the inlet cross-section. The method utilizes earlier contributions by: (1) Keulegan representing the hydraulics of inlets, (2) O'Brien which describes an equilibrium relationship between the cross-sectional area of an inlet and the bay tidal prism, and (3) Escoffier which relates to the stability of an inlet under changes in conditions which tend to close or enlarge an inlet. A "stability index" is defined which incorporates the buffer storage area available in the inlet cross-section, prior to the onset of closure and also includes the capability of the inlet to transport excess sand from its cross-section. In order to apply the method, geometric and hydraulic data representing the inlet are necessary; the minimum data required include a survey of the inlet throat cross-section and the lag between high (or low) water in the ocean and the following slack water in the inlet. In addition, it is necessary to conduct measurements or make assumptions concerning the minor and gradual hydraulic loss coefficients. Based on assumed depositional patterns in the inlet, the method is applied to five real inlets and the stability indices are presented.

Modelling the Acoustical and Airflow Performance of Simple Lined Ventilation Apertures

2005 ◽  
Vol 12 (4) ◽  
pp. 277-292 ◽  
Author(s):  
D J Oldham ◽  
Jian Kang ◽  
M W Brocklesby
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
High Aspect Ratio ◽  
Natural Ventilation ◽  
Ventilation System ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Ventilation Performance ◽  
Acoustic Treatment

The pressure differences that can be used to drive a natural ventilation system are very small and thus large apertures are required to allow sufficient air to enter and leave a building to ensure good air quality or thermal comfort. Large apertures are potential acoustic weak points on a façade and may require some form of acoustic treatment such as absorbent linings, in which case the ventilator is similar to a short section of lined duct. In ducts, the performance of absorbent linings increases with the length of lining and the ratio of the length of lined perimeter to the cross sectional area of the duct. Thus, for a duct of a given cross sectional area, a lining is more effective for a duct with a high aspect ratio than for a duct with a square cross section. However, the high aspect ratio cross section will result in greater flow resistance and impede the airflow performance. In this paper numerical methods are employed to investigate the effect of different configurations of a lined aperture on the acoustical and ventilation performance of the aperture in order to establish the optimum configurations.

Efficiencies for Partially Wetted Spine Fins: Uniform Cross Section, Conical, Concave Parabolic, and Convex Parabolic Spines

2013 ◽  
Vol 135 (8) ◽  
Author(s):  
Worachest Pirompugd ◽  
Somchai Wongwises
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Cross Section ◽  
Transfer Rate ◽  
Approximate Equation ◽  
Sectional Area ◽  
Cross Sectional ◽  
Fin Efficiency ◽  
Conduction Heat Transfer ◽  
Uniform Cross Section

In this study, efficiencies for partially wetted fins for the uniform cross section spine, conical spine, concave parabolic spine, and convex parabolic spine are presented using an analytical method. Depending on the set of boundary conditions, there are two methods for deriving the efficiencies of partially wet fins for each spine. The eight equations for fin efficiencies were investigated. Fin efficiency is a function of the length of the dry portion. Thus, the equations for calculating the length of the dry portion are also presented. The findings indicate that a larger cross-sectional fin results in a higher conduction heat transfer rate. Contrarily, the fin efficiency is lower. This is different from the longitudinal fin, for which the trend lines of heat transfer rate and fin efficiency are the same. This converse relationship is due to the effect of the ratio of the cross-sectional area to the surface area. Moreover, partially wet fin efficiencies decrease with increased relative humidity. For convenience, the approximate equation for efficiencies for partially wet fins, which is derived from the equations for fully wet and fully dry fin efficiencies, is also presented.

Normalization of force generated by canine airway smooth muscles

1991 ◽  
Vol 260 (6) ◽  
pp. L522-L529 ◽  
Author(s):  
H. Jiang ◽  
A. J. Halayko ◽  
K. Rao ◽  
P. Cunningham ◽  
N. L. Stephens
Keyword(s):  
Smooth Muscle ◽  
Cross Section ◽  
Cross Sections ◽  
Smooth Muscles ◽  
Muscle Cells ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Muscle Stress ◽  
Total Tissue

A variety of normalizations have been employed to compare maximal isometric force (Po) produced by smooth muscles at different locations and stages of maturation. Because these procedures have not always been based on rigorous principles, confusion has resulted. To obtain a less ambiguous index of force production, we measured in vitro Po from mongrel canine tracheal (TSM) and bronchial (BSM) smooth muscle with an electromagnetic lever and normalized it to force per unit cross-sectional area of whole tissue (tissue stress), to force per unit cross-sectional area of muscle in the cross section of total tissue (muscle stress), and to force per fractional unit of myosin in the tissue cross section (myosin stress). Proportion of myosin in cross-sectional area of tissue was deduced from data obtained by sodium dodecyl sulfate gel electrophoresis of crude muscle extracts. For TSM, tissue stress was 1.499 X 10(5) N/m2 +/- 0.1 (SE), whereas it was only 0.351 X 10(5) N/m2 +/- 0.05 (SE) for BSM, representing a 4.27-fold difference (P less than 0.01). There was a 1.60-fold difference (P less than 0.05) in muscle stress, which was correlated to the morphometric finding that 79 +/- 1.4% (SE) of the tracheal strip cross section was muscle, whereas only 30 +/- 1.0% (SE) of bronchial tissue was occupied by muscle. Average myosin content was the same in smooth muscle cells of TSM and BSM, indicating that total amount of myosin in tissue cross sections was essentially a function of proportional area of muscle cells in total tissue cross sections.(ABSTRACT TRUNCATED AT 250 WORDS)

Corrosion-Induced Concrete Cracking, Steel-Concrete Bond Loss, and Mechanical Degradation of Steel Bars

2014 ◽  
Vol 919-921 ◽  
pp. 1760-1770 ◽  
Author(s):  
Fu Jian Tang ◽  
Gen Da Chen ◽  
Wei Jian Yi
Keyword(s):  
Cross Section ◽  
Crack Width ◽  
Surface Profile ◽  
Concrete Surface ◽  
Cross Sectional Area ◽  
Mechanical Degradation ◽  
Sectional Area ◽  
Cross Sectional ◽  
Steel Bars ◽  
The Cross

This study experimentally investigated corrosion-induced deterioration in reinforced concrete (RC) structures: concrete cover cracking, steel-concrete bond loss, and mechanical degradation of corroded steel bars. Pullout and RC beam specimens were prepared, subjected to accelerated corrosion in a wet sand bath, and tested under loading. A 3D laser scan was employed to measure the surface profile of corroded steel bars and determine the corrosion effect on the distribution of residual cross section area. The crack width on the concrete surface was sampled randomly and analyzed statistically. Corrosion reduced the bond strength between steel bars and concrete, particularly in the form of corrosion-induced number and width of cracks. Both the yield and ultimate strengths depended upon the critical cross sectional area of steel bars, whereas the elongation changed with the cross section distribution over the length of the steel bars. Corrosion also changed the distribution of the cross sectional area of steel bars. The crack width on the concrete surface can be well represented by a normal distribution regardless of corrosion levels.

scholarly journals Nonuniform Internal Structure of Fibrin Fibers: Protein Density and Bond Density Strongly Decrease with Increasing Diameter

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Wei Li ◽  
Justin Sigley ◽  
Stephen R. Baker ◽  
Christine C. Helms ◽  
Mary T. Kinney ◽  
...  
Keyword(s):  
Light Intensity ◽  
Internal Structure ◽  
Cross Section ◽  
Fiber Diameter ◽  
Blood Clot ◽  
Sectional Area ◽  
Cross Sectional ◽  
Bond Density ◽  
Major Structural Component ◽  
Protein Density

The major structural component of a blood clot is a meshwork of fibrin fibers. It has long been thought that the internal structure of fibrin fibers is homogeneous; that is, the protein density and the bond density between protofibrils are uniform and do not depend on fiber diameter. We performed experiments to investigate the internal structure of fibrin fibers. We formed fibrin fibers with fluorescently labeled fibrinogen and determined the light intensity of a fiber,I, as a function of fiber diameter,D. The intensity and, thus, the total number of fibrin molecules in a cross-section scaled asD1.4. This means that the protein density (fibrin per cross-sectional area),ρp, is not homogeneous but instead strongly decreases with fiber diameter asD-0.6. Thinner fibers are denser than thicker fibers. We also determined Young’s modulus,Y, as a function of fiber diameter.Ydecreased strongly with increasingD;Yscaled asD-1.5. This implies that the bond density,ρb, also scales asD-1.5. Thinner fibers are stiffer than thicker fibers. Our data suggest that fibrin fibers have a dense, well-connected core and a sparse, loosely connected periphery. In contrast, electrospun fibrinogen fibers, used as a control, have a homogeneous cross-section.

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