scholarly journals Pinch-off of non-axisymmetric vortex rings

2014 ◽  
Vol 740 ◽  
pp. 61-96 ◽  
Author(s):  
Clara O’Farrell ◽  
John O. Dabiri
Keyword(s):  
Aspect Ratio ◽  
Vortex Rings ◽  
Equivalent Diameter ◽  
Local Curvature ◽  
Cross Sectional ◽  
Piston Cylinder ◽  
Circular Arcs ◽  
Axisymmetric Vortex ◽  
Formation Number ◽  
Nozzle Geometries

AbstractThe formation and pinch-off of non-axisymmetric vortex rings is considered experimentally. Vortex rings are generated using a non-circular piston–cylinder arrangement, and the resulting velocity fields are measured using digital particle image velocimetry. Three different nozzle geometries are considered: an elliptical nozzle with an aspect ratio of two, an elliptical nozzle with an aspect ratio of four and an oval nozzle constructed from tangent circular arcs. The formation of vortices from the three nozzles is analysed by means of the vorticity and circulation, as well as by investigation of the Lagrangian coherent structures in the flow. The results indicate that, in all three nozzles, the maximum circulation the vortex can attain is determined by the equivalent diameter of the nozzle: the diameter of a circular nozzle of identical cross-sectional area. In addition, the time at which the vortex rings pinch off is found to be constant along the nozzle contours, and independent of relative variations in the local curvature. A formation number for this class of vortex rings is defined based on the equivalent diameter of the nozzle, and the formation number for vortex rings of the three geometries considered is found to lie in the range of 3–4. The implications of the relative shape and local curvature independence of the formation number on the study and modelling of naturally occurring vortex rings such as those that appear in biological flows is discussed.

scholarly journals Circulation and formation number of laminar vortex rings

1998 ◽  
Vol 376 ◽  
pp. 297-318 ◽  
Author(s):  
MOSHE ROSENFELD ◽  
EDMOND RAMBOD ◽  
MORTEZA GHARIB
Keyword(s):  
Velocity Profile ◽  
Time Scale ◽  
Vortex Generator ◽  
Formation Time ◽  
Vortex Rings ◽  
Axisymmetric Vortex ◽  
Parabolic Velocity Profile ◽  
Formation Number ◽  
Experimental Findings ◽  
Good Agreement

The formation time scale of axisymmetric vortex rings is studied numerically for relatively long discharge times. Experimental findings on the existence and universality of a formation time scale, referred to as the ‘formation number’, are confirmed. The formation number is indicative of the time at which a vortex ring acquires its maximal circulation. For vortex rings generated by impulsive motion of a piston, the formation number was found to be approximately four, in very good agreement with experimental results. Numerical extensions of the experimental study to other cases, including cases with thick shear layers, show that the scaled circulation of the pinched-off vortex is relatively insensitive to the details of the formation process, such as the velocity programme, velocity profile, vortex generator geometry and the Reynolds number. This finding might also indicate that the properly scaled circulation of steady vortex rings varies very little. The formation number does depend on the velocity profile. Non-impulsive velocity programmes slightly increase the formation number, while non-uniform velocity profiles may decrease it significantly. In the case of a parabolic velocity profile of the discharged flow, for example, the formation number decreases by a factor as large as four. These findings indicate that a major source of the experimentally found small variations in the formation number is the different evolution of the velocity profile of the discharged flow.

A universal time scale for vortex ring formation

1998 ◽  
Vol 360 ◽  
pp. 121-140 ◽  
Author(s):  
MORTEZA GHARIB ◽  
EDMOND RAMBOD ◽  
KARIM SHARIFF
Keyword(s):  
Vortex Ring ◽  
Vortex Rings ◽  
Water Tank ◽  
Single Vortex ◽  
Piston Cylinder ◽  
Vortex Ring Formation ◽  
Image Velocimetry ◽  
Wide Range ◽  
Formation Number ◽  
Piston Stroke

The formation of vortex rings generated through impulsively started jets is studied experimentally. Utilizing a piston/cylinder arrangement in a water tank, the velocity and vorticity fields of vortex rings are obtained using digital particle image velocimetry (DPIV) for a wide range of piston stroke to diameter (L/D) ratios. The results indicate that the flow field generated by large L/D consists of a leading vortex ring followed by a trailing jet. The vorticity field of the leading vortex ring formed is disconnected from that of the trailing jet. On the other hand, flow fields generated by small stroke ratios show only a single vortex ring. The transition between these two distinct states is observed to occur at a stroke ratio of approximately 4, which, in this paper, is referred to as the ‘formation number’. In all cases, the maximum circulation that a vortex ring can attain during its formation is reached at this non-dimensional time or formation number. The universality of this number was tested by generating vortex rings with different jet exit diameters and boundaries, as well as with various non-impulsive piston velocities. It is shown that the ‘formation number’ lies in the range of 3.6–4.5 for a broad range of flow conditions. An explanation is provided for the existence of the formation number based on the Kelvin–Benjamin variational principle for steady axis-touching vortex rings. It is shown that based on the measured impulse, circulation and energy of the observed vortex rings, the Kelvin–Benjamin principle correctly predicts the range of observed formation numbers.

scholarly journals Nested contour dynamics models for axisymmetric vortex rings and vortex wakes

2014 ◽  
Vol 748 ◽  
pp. 521-548 ◽  
Author(s):  
Clara O’Farrell ◽  
John O. Dabiri
Keyword(s):  
Vortex Formation ◽  
Computational Cost ◽  
Small Region ◽  
Two Dimensions ◽  
Vortex Rings ◽  
Contour Dynamics ◽  
Piston Cylinder ◽  
Axisymmetric Vortex ◽  
Contour Models ◽  
Perturbation Size

AbstractInviscid models for vortex rings and dipoles are constructed using nested patches of vorticity. These models constitute more realistic approximations to experimental vortex rings and dipoles than the single-contour models of Norbury and Pierrehumbert, and nested contour dynamics algorithms allow their simulation with low computational cost. In two dimensions, nested-contour models for the analytical Lamb dipole are constructed. In the axisymmetric case, a family of models for vortex rings generated by a piston–cylinder apparatus at different stroke ratios is constructed from experimental data. The perturbation response of this family is considered by the introduction of a small region of vorticity at the rear of the vortex, which mimics the addition of circulation to a growing vortex ring by a feeding shear layer. Model vortex rings are found to either accept the additional circulation or shed vorticity into a tail, depending on the perturbation size. A change in the behaviour of the model vortex rings is identified at a stroke ratio of three, when it is found that the maximum relative perturbation size vortex rings can accept becomes approximately constant. We hypothesise that this change in response is related to pinch-off, and that pinch-off might be understood and predicted based on the perturbation responses of model vortex rings. In particular, we suggest that a perturbation response-based framework can be useful in understanding vortex formation in biological flows.

Quantitative Analyses of Morphological Variation of Cross-Sectional Tracheids of Hinoki (Chamaecyparis obtusa Endl.) Near Knot by Image Processing

Holzforschung ◽  
2002 ◽  
Vol 56 (3) ◽  
pp. 239-243
Author(s):  
J. Liu ◽  
X. M. Diao ◽  
T. Furuno
Keyword(s):  
Aspect Ratio ◽  
Narrow Range ◽  
Ring Width ◽  
Chamaecyparis Obtusa ◽  
Wall Thickening ◽  
Equivalent Diameter ◽  
Cross Sectional ◽  
Annual Ring Width ◽  
Circularity Index ◽  
Quantitative Analyses

Summary Eight transverse sections of hinoki (Chamaecyparis obtusa Endl.) were analyzed along the grain near a knot by circularity index (CI), aspect ratio and equivalent diameter. The specimens were divided into two groups, one above and one below the knot, and their distances from the knot were 0 mm (the nearest), 12 mm, 24 mm, and 36 mm, respectively. Another sample was also selected from knot-free wood for reference along the same grain. A gradual decrease in the aspect ratio of tracheids demonstrated that both boundaries and lumina tended to have small differences in length and width as they approached the knot along the grain. CIs of lumina nearest to the knot indicated astonishingly high values with a narrow range from hexagon to ellipse, compared with the others ranging from rectangle, via hexagon, to ellipse. In other words, lumina showed a tendency to become round near the knot. In addition, the equivalent diameters of lumina tended to decrease when approaching the knot, implying that cell wall thickening of tracheids occur near the knot. It should be noted that the above variations in tracheids accompanied changes in grain orientation and annual ring width, especially the sharp transformation nearest to the knot.

scholarly journals A model for vortex ring formation in a starting buoyant plume

2000 ◽  
Vol 416 ◽  
pp. 173-185 ◽  
Author(s):  
MICHAEL SHUSSER ◽  
MORTEZA GHARIB
Keyword(s):  
Vortex Ring ◽  
Time Scale ◽  
Ring Formation ◽  
Vortex Rings ◽  
Uniform Density ◽  
Dimensionless Time ◽  
Buoyant Plume ◽  
Piston Cylinder ◽  
Vortex Ring Formation ◽  
Formation Number

Vortex ring formation in a starting axisymmetric buoyant plume is considered. A model describing the process is proposed and a physical explanation based on the Kelvin–Benjamin variational principle for steady vortex rings is provided. It is shown that Lundgren et al.'s (1992) time scale, the ratio of the velocity of a buoyant plume after it has travelled one diameter to its diameter, is equivalent to the time scale (formation time) proposed by Gharib et al. (1998) for uniform-density vortex rings generated with a piston/cylinder arrangement. It is also shown that, similarly to piston-generated vortex rings (Gharib et al. 1998), the buoyant vortex ring pinches off from the plume when the latter can no longer provide the energy required for steady vortex ring existence. The dimensionless time of the pinch-off (the formation number) can be reasonably well predicted by assuming that at pinch-of the vortex ring propagation velocity exceeds the plume velocity. The predictions of the model are compared with available experimental results.

Gender determination of caucasoid hair using image analysis

1993 ◽  
Vol 51 ◽  
pp. 216-217
Author(s):  
T.B. Ball ◽  
W.M. Hess
Keyword(s):  
Image Analysis ◽  
Cross Sections ◽  
Scalp Hair ◽  
The Body ◽  
Equivalent Diameter ◽  
Cross Sectional ◽  
Hair Samples ◽  
Length Width ◽  
Morphological Differences

It has been demonstrated that cross sections of bundles of hair can be effectively studied using image analysis. These studies can help to elucidate morphological differences of hair from one region of the body to another. The purpose of the present investigation was to use image analysis to determine whether morphological differences could be demonstrated between male and female human Caucasian terminal scalp hair.Hair samples were taken from the back of the head from 18 caucasoid males and 13 caucasoid females (Figs. 1-2). Bundles of 50 hairs were processed for cross-sectional examination and then analyzed using Prism Image Analysis software on a Macintosh llci computer. Twenty morphological parameters of size and shape were evaluated for each hair cross-section. The size parameters evaluated were area, convex area, perimeter, convex perimeter, length, breadth, fiber length, width, equivalent diameter, and inscribed radius. The shape parameters considered were formfactor, roundness, convexity, solidity, compactness, aspect ratio, elongation, curl, and fractal dimension.

Modification of MnS inclusion by tellurium in 38MnVS6 micro-alloyed steel

2020 ◽  
Vol 117 (6) ◽  
pp. 615
Author(s):  
Ping Shen ◽  
Lei Zhou ◽  
Qiankun Yang ◽  
Zhiqi Zeng ◽  
Kenan Ai ◽  
...  
Keyword(s):  
Fatigue Life ◽  
Aspect Ratio ◽  
Strong Influence ◽  
Experimental Results ◽  
Alloyed Steel ◽  
Equivalent Diameter ◽  
Small Aspect Ratio ◽  
Steel Quality ◽  
Eds Analysis ◽  
Micro Alloyed Steel

In 38MnVS6 steel, the morphology of sulfide inclusion has a strong influence on the fatigue life and machinability of the steel. In most cases, the MnS inclusions show strip morphology after rolling, which significantly affects the steel quality. Usually, the MnS inclusion with a spherical morphology is the best morphology for the steel quality. In the present work, tellurium was applied to 38MnVS6 micro-alloyed steel to control the MnS inclusion. Trace tellurium was added into 38MnVS6 steel and the effect of Te on the morphology, composition, size and distribution of MnS inclusions were investigated. Experimental results show that with the increase of Te content, the equivalent diameter and the aspect ratio of inclusion decrease strikingly, and the number of inclusions with small aspect ratio increases. The inclusions are dissociated and spherized. The SEM-EDS analysis indicates that the trace Te mainly dissolves in MnS inclusion. Once the MnS is saturated with Te, MnTe starts to generate and wraps MnS. The critical Te/S value for the formation of MnTe in the 38MnV6 steel is determined to be approximately 0.075. With the increase of Te/S ratio, the aspect ratio of MnS inclusion decreases and gradually reaches a constant level. The Te/S value in the 38MnVS6 steel corresponding to the change of aspect ratio from decreasing to constant ranges from 0.096 to 0.255. This is most likely to be caused by the saturation of Te in the MnS inclusion. After adding Te in the steel, rod-like MnS inclusion is modified to small inclusion and the smaller the MnS inclusion, the lower the aspect ratio.

Application of Image Analysis System for Study of Activated Sludge Flocs

1986 ◽  
Vol 21 (1) ◽  
pp. 130-140 ◽  
Author(s):  
Da-hong Li ◽  
J. J. Ganczarczyk
Keyword(s):  
Image Analysis ◽  
Activated Sludge ◽  
Statistical Processing ◽  
Equivalent Diameter ◽  
Image Analysis System ◽  
Sectional Area ◽  
Cross Sectional ◽  
Computerized Image Analysis ◽  
Sludge Flocs ◽  
Analysis System

Abstract The computerized image analysis system has been successfully used for determination and statistical processing of the following geometric characteristics of activated sludge flocs: longest dimension, breadth, equivalent diameter, cross-sectional area, perimeter, elongation, and circularity. These parameters could be effectively and precisely determined by the system applied. In addition, the studied method, as compared to direct microscope observation and photography floc-sizing methods, was found to be more accurate, less time-consuming, and less dependent on the investigators.

scholarly journals Formation number of confined vortex rings

2018 ◽  
Vol 3 (9) ◽  
Author(s):  
I. Danaila ◽  
F. Luddens ◽  
F. Kaplanski ◽  
A. Papoutsakis ◽  
S. S. Sazhin
Keyword(s):  
Vortex Rings ◽  
Formation Number

Numerical Simulation of Flow and Heat Transfer in Rectangular Channel With Different Aspect Ratios

2016 ◽  
Author(s):  
Liu Wenhua ◽  
Mo Yang ◽  
Li Ling ◽  
Qiao Liang ◽  
Yuwen Zhang
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Characteristic Length ◽  
Rectangular Channel ◽  
Equivalent Diameter ◽  
Correction Coefficient ◽  
Corner Region ◽  
Flow And Heat Transfer ◽  
Aspect Ratios

Turbulent flow and heat transfer in rectangular channel has an important significance in engineering. Conventional approach to caculate Nusselt number of rectangular channel approximately is to take the equivalent diameter as the characteristic length and use the classic circular channel turbulent heat transfer coefficient correlations. However, under these conditions, the caculation error of Nusselt number can reach to 14% and thus this approach can not substantially describe the variation of Nusselt number of rectangular cross-sections with different aspect ratios. Therefore, caculation by using equivalent diameter as the characteristic length in classic experiment formula needs to be corrected. Seven groups of rectangular channel models with different aspect ratios have been studied numerically in this paper. By using standard turbulence model, the flow and heat transfer law of air with varing properties has been studied in 4 different sets of conditions in Reynolds number. The simulation and experimental results are in good agreement. The simulation results show that with the increase of aspect ratio, the cross-sectional average Nusselt number increased, Nusselt number of circumferential wall distributed more evenly and the difference between the infinite plate channel and square channel went up to 25%. The effects of corner region and long\short sides on heat transfer have also been investigated in this paper. Results show that in rectangular channel, heat transfer in corner region is significantly weaker than it in other region. With the increase of aspect ratio, effect on the long side of heat transfer of the short side is gradually reduced, and then eventually eliminates completely in the infinite flat place. Based on the studies above, correction coefficient for rectangular channels with different aspect ratios has been proposed in this paper and the accuracy of the correction coefficient has been varified by numerical simulations. This can reflect the variation of Nusselt number under different aspect ratios more effectively and thus has current significance for project to calculate Nusselt number of heat transfer in rectangular channel.

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