The effect of compressibility on the speed of propagation of a vortex ring

1985 ◽  
Vol 397 (1812) ◽  
pp. 87-97 ◽  
Keyword(s):  
Vortex Ring ◽  
Cross Section ◽  
Sound Speed ◽  
Rigid Rotation ◽  
Compressible Fluids ◽  
Perfect Gas ◽  
Cross Sectional ◽  
The Core ◽  
Speed Of Propagation ◽  
Compressibility Effects

A circular vortex filament of radius R , cross sectional area π a 2 and circulation Г propagates steadily in an inviscid, calorically perfect gas. The flow outside the filament is assumed to be irrotational and isentropic. If it is further assumed that a/R ≪ 1, the cross section is approximately circular and the speed of propagation of the filament is shown to depend on the distribution of circulatory velocity v 0 and entropy s 0 within the core. If s 0 is constant and equal to its value in the isentropic exterior of the filament, the vortex ring is slowed down by compressibility effects, whatever the distribution of circulatory velocity. If the circulatory velocity corresponds to rigid rotation in the core cross section, the speed, U , of propagation is given by U = Γ/4π R [ln 8R/ a - ¼ - 5/12 M 2 + O ( M 4 )], where M is the Mach number Γ /2π ac ∞ and c ∞ is the sound speed far from the vortex ring. Numerical results for finite M are also given in this case. These results enable the cut-off theory of filament motion to be extended to compressible fluids.

The velocity of a vortex ring with a thin core of elliptical cross section

1980 ◽  
Vol 370 (1742) ◽  
pp. 407-415 ◽  
Keyword(s):  
Vortex Ring ◽  
Cross Section ◽  
Constant Angular Velocity ◽  
Mean Velocity ◽  
Dimensional Solution ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
The Core ◽  
Elliptical Core ◽  
Axis Of Symmetry

The motion of a circular vortex ring with a thin elliptical core is considered. The core is untwisted so that the vortex ring is axisymmetric and the vorticity in the core is proportional to distance from the axis of symmetry. The core rotates with a constant angular velocity comparable to the circulation frequency, as in Kirchoff’s two-dimensional solution. The velocity of the ring, suitably defined, is periodic and the average velocity is Γ/4π R [ln(16 R / a + b )-¼], where Γ is the circulation around the core, a and b are the semi-major and semi-minor axes of the core cross section and R is the radius of the ring. This mean velocity is smaller than the velocity of translation of a ring of the same radius and circulation but with a circular core of the same-cross-sectional area.

On steady vortex rings of small cross-section in an ideal fluid

1970 ◽  
Vol 316 (1524) ◽  
pp. 29-62 ◽  
Keyword(s):  
Cross Section ◽  
Propagation Speed ◽  
Vortex Rings ◽  
Uniform Density ◽  
Inviscid Fluid ◽  
Small Cross Section ◽  
Cross Sectional ◽  
The Core ◽  
Ring Radius ◽  
Explicit Formulae

This paper is concerned with vortex rings, in an unbounded inviscid fluid of uniform density, that move without change of form and with constant velocity when the fluid at infinity is at rest. The work is restricted to rings whose cross-sectional area is small relative to the square of a mean ring radius. An existence theorem is proved for distributions of vorticity in the core that are arbitrary, apart from the condition imposed by the equation of motion and certain smoothness requirements. The method of proof relies on the nearly plane, or two-dimensional, nature of the flow in the neighbourhood of a small cross-section, and leads to approximate but explicit formulae for the propagation speed and shape of the vortex rings in question.

scholarly journals Cross-Sectional Geometry and the Intermetallics Structure in a High Pressure Die Cast Mg-Al Alloy

2010 ◽  
Vol 638-642 ◽  
pp. 1579-1584 ◽  
Author(s):  
A.V. Nagasekhar ◽  
Carlos H. Cáceres ◽  
Mark Easton
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Al Alloy ◽  
Cross Sectional ◽  
The Core ◽  
Die Cast ◽  
Increased Strength ◽  
Scanning Electron

Specimens of rectangular and circular cross section of a Mg-9Al binary alloy have been tensile tested and the cross section of undeformed specimens examined using scanning electron microscopy. The rectangular cross sections showed three scales in the cellular intermetallics network: coarse at the core, fine at the surface and very fine at the corners, whereas the circular ones showed only two, coarse at the core and fine at the surface. The specimens of rectangular cross section exhibited higher yield strength in comparison to the circular ones. Possible reasons for the observed increased strength of the rectangular sections are discussed.

Core Variation in the Entrance Region Flow of Casson Fluid in an Annuli

2013 ◽  
Vol 391 ◽  
pp. 376-381 ◽  
Author(s):  
A. Kandasamy ◽  
Rekha G. Pai
Keyword(s):  
Differential Equation ◽  
Cross Section ◽  
Casson Fluid ◽  
Entrance Region ◽  
Mass Balance Equation ◽  
Cross Sectional ◽  
The Core ◽  
Region Flow ◽  
Boundary Layer Region ◽  
Layer Region

The entrance region flow of a Casson fluid in an annular cylinder has been investigated numerically without making prior assumptions on the form of velocity profile within the boundary layer region, which is determined by a cross sectional integration of the momentum differential equation for a given distance from the channel entrance. Using the macroscopic mass balance equation, the thickness of the core has been obtained at each cross section of entrance region of annuli for different values of Casson number and for various values of aspect ratio.

scholarly journals Numerical analysis of chemically foamed thick-walled PA66 GF30 moldings

2021 ◽  
Vol 351 ◽  
pp. 01018
Author(s):  
Natalia Konczal ◽  
Piotr Czyżewski ◽  
Bartosz Nowinka
Keyword(s):  
Computer Simulation ◽  
Numerical Analysis ◽  
Pore Size ◽  
Cross Section ◽  
Computer Simulations ◽  
Real Object ◽  
Pore Density ◽  
Cross Sectional ◽  
The Core ◽  
Blowing Agent

The paper presents a numerical analysis of thick-walled PA66 GF30 moldings with the addition of a chemical blowing agent with a content of 1-3 wt%, and the obtained results were compared with the real object. Computer simulations were performed using Moldex3D® software. Based on the numerical analysis, it was found that regardless of the dose of the blowing agent used, the largest pores were place in the core of the sample. Moreover, it was found that the size of the pores depends on their number in the cross-section of moldings. Compositions containing a higher cross-sectional pore density were characterized by smaller pore sizes. The results of the computer simulation also showed that increasing the blowing agent dose above 2 wt% does not significantly affect the size of the pores in the structure. The experimentally determined pore size of the composition containing 3 wt% chemical blowing agent slightly differs from the pore size obtained based on numerical analysis.

Flow Characteristics of Upward Two-Phase Flows in a Rod Bundle Geometry

2020 ◽  
Author(s):  
Xu Han ◽  
Xiuzhong Shen ◽  
Toshihiro Yamamoto ◽  
Ken Nakajima ◽  
Takashi Hibiki
Keyword(s):  
Cross Section ◽  
Void Fraction ◽  
Axial Position ◽  
Equivalent Diameter ◽  
Wall Region ◽  
Two Phase Flows ◽  
Two Phase ◽  
Cross Sectional ◽  
The Core ◽  
Rod Bundle

Abstract In the present paper, the local two-phase flow parameters were measured with a four-sensor optical probe in adiabatic upward air-water two-phase flows in a 6 × 6 vertical rod bundle with rod diameter of 10 mm, pitch of 16.7 mm, square channel box side length of 100 mm and hydraulic equivalent diameter (DH) of 18.7 mm. The local measurements were performed in an octant triangular region of the rod bundle cross-section at the axial position with height-to-diameter ratio (z/DH) of 149 under a total of 16 flow conditions. The local void fraction, interfacial area concentration (IAC), bubble diameter and bubble velocity were obtained in the four-sensor probe measurements. Both of the measured void fraction and IAC show their radial local distributions with the core-peaking and wall-peaking shapes which are closely linked with the superficial velocity of two phases. The distribution shapes tend to change from the core-peaking to the wall-peaking when the superficial liquid velocity (<jf>) increases and the superficial gas velocity (<jg>) decreases. The measured diameters of local bubbles keep the similar values in the measuring cross-section, increase when the <jg> increases and decrease when the <jf> increases. The bubbles behave with the velocities whose main flow direction component keeps a typical radial power-law (core-peaking) profile and whose cross-sectional velocity components show a significant trend of bubbles migrating from the center to the wall region of the channel box especially under high <jf> conditions. The area-averaged results of void fraction and IAC were obtained by a cross-sectional area-averaging scheme. The resultant area-averaged void fraction and IAC were used to check the void fraction predicting capability of two drift-flux correlations and the IAC prediction performance of two IAC correlations respectively. The applicability of these correlations to the rod bundle geometry was discussed and concluded finally in this paper.

Conjugate-flow theory for heterogeneous compressible fluids, with application to non-uniform suspensions of gas bubbles in liquids

1972 ◽  
Vol 54 (3) ◽  
pp. 545-563 ◽  
Author(s):  
T. Brooke Benjamin
Keyword(s):  
Cross Section ◽  
Gas Bubbles ◽  
Arbitrary Cross Section ◽  
Compressible Fluids ◽  
Lagrangian Description ◽  
Pressure Force ◽  
Primary Flow ◽  
Cross Sectional ◽  
Dissipative Flow ◽  
Conjugate Flows

Conjugate flows have been defined generally as flows uniform in the direction of streaming that separately satisfy the relevant hydrodynamical equations, so allowing a transition from one flow to its conjugate to be consistent with mass and energy conservation. In previous studies of various examples, certain general principles have been found to apply to conjugate flows: in particular, one in a pair of such flows is subcritical (subsonic) and the other supercritical (supersonic), the former having greater flow force (i.e. momentum flux plus pressure force). In this paper these principles are confirmed in another field of application, for which the theory of conjugate flows takes a novel course.The theoretical model defined in § 2 consists of a straight duct of arbitrary cross-section filled with a perfect fluid whose constitutive properties vary with cross-sectional position, and whose primary, prescribed flow is axial with a velocity distribution that may be non-uniform. In § 3 the possibility of a conjugate flow in the same duct is investigated, and its principal properties relative to those of the primary flow are deduced from certain simple inequalities between integrals over the cross-section. A Lagrangian description of the conjugate flow is essential, but the properties in question are established without the necessity of determining this flow explicitly. At the end of § 3, a modification of the model is discussed accounting for dissipative, flow-force conserving transitions (shocks). The application of the theory to flows of non-uniform suspensions of gas bubbles is considered in § 4.

The Optimum Design for Core Section of Power Transformer when Cooling Oil Pans Are Added or Not

2010 ◽  
Vol 439-440 ◽  
pp. 309-314
Author(s):  
Sha Zhao ◽  
Yuan Biao Zhang ◽  
Qian Wan ◽  
Zhi Min Jiang
Keyword(s):  
Linear Programming ◽  
Cross Section ◽  
Programming Model ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Non Linear Programming ◽  
The Core ◽  
Core Section ◽  
Core Column

In terms of the design of the Core Section, aiming at the half of the core circumcircle, for the case of the Core Section without the Cooling Oil Pan, this paper firstly establishes a non-linear programming model taking the objective function that the geometric cross-sectional area of the column core is the largest. Then, on the basis of analyzing the case of Cross Section with the Cooling Oil Pans another non-linear programming model is estabished to make the geometric cross-sectional area of the core column be the largest and the adjacent area of the two parts divided by the Cooling Oil Pans be equal as much as possible. And, the series of the section and the width and thickness of the silicon steel sheets at all levels are fixed while the effective cross-section of the core column is maximum. At last, to the two instances, this paper analyses the effects of the addition of the Cooling Oil Pans on the design for Cross Section.

Mass Determination by Direct Measurement of Electron Scattering

1975 ◽  
Vol 33 ◽  
pp. 240-241
Author(s):  
M. K. Lamvik ◽  
A. V. Crewe
Keyword(s):  
Cross Section ◽  
Electron Scattering ◽  
Mass Density ◽  
Variable Mass ◽  
Scattering Cross Section ◽  
Mass Determination ◽  
Number Density ◽  
Cross Sectional ◽  
Thin Slice ◽  
Scattering Cross

If a molecule or atom of material has molecular weight A, the number density of such units is given by n=Nρ/A, where N is Avogadro's number and ρ is the mass density of the material. The amount of scattering from each unit can be written by assigning an imaginary cross-sectional area σ to each unit. If the current I0 is incident on a thin slice of material of thickness z and the current I remains unscattered, then the scattering cross-section σ is defined by I=IOnσz. For a specimen that is not thin, the definition must be applied to each imaginary thin slice and the result I/I0 =exp(-nσz) is obtained by integrating over the whole thickness. It is useful to separate the variable mass-thickness w=ρz from the other factors to yield I/I0 =exp(-sw), where s=Nσ/A is the scattering cross-section per unit mass.

A tilting high temperature gas reaction chamber for the JEM 7A T.E.M.

1978 ◽  
Vol 36 (1) ◽  
pp. 70-71
Author(s):  
Brian L. Rhoades
Keyword(s):  
Cross Section ◽  
Reaction Chamber ◽  
Objective Lens ◽  
Reduced Cross Section ◽  
Cross Sectional ◽  
Structural Investigations ◽  
Transmission Electron ◽  
Dynamic Experiments ◽  
Successful Design ◽  
Thermocouple Junction

A gas reaction chamber has been designed and constructed for the JEM 7A transmission electron microscope which is based on a notably successful design by Hashimoto et. al. but which provides specimen tilting facilities of ± 15° aboutany axis in the plane of the specimen.It has been difficult to provide tilting facilities on environmental chambers for 100 kV microscopes owing to the fundamental lack of available space within the objective lens and the scope of structural investigations possible during dynamic experiments has been limited with previous specimen chambers not possessing this facility.A cross sectional diagram of the specimen chamber is shown in figure 1. The specimen is placed on a platinum ribbon which is mounted on a mica ring of the type shown in figure 2. The ribbon is heated by direct current, and a thermocouple junction spot welded to the section of the ribbon of reduced cross section enables temperature measurement at the point where localised heating occurs.

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