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.

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 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.

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

scholarly journals The frequency of Kozai–Lidov disc oscillation driven giant outbursts in Be/X-ray binaries

2019 ◽  
Vol 489 (2) ◽  
pp. 1797-1804 ◽  
Author(s):  
Rebecca G Martin ◽  
Alessia Franchini
Keyword(s):  
Orbital Period ◽  
Time Scale ◽  
Orbital Plane ◽  
Material Flows ◽  
X Ray ◽  
System Parameters ◽  
Be Star ◽  
Chaotic Nature ◽  
X Ray Binaries ◽  
Good Agreement

ABSTRACT Giant outbursts of Be/X-ray binaries may occur when a Be-star disc undergoes strong eccentricity growth due to the Kozai–Lidov (KL) mechanism. The KL effect acts on a disc that is highly inclined to the binary orbital plane provided that the disc aspect ratio is sufficiently small. The eccentric disc overflows its Roche lobe and material flows from the Be star disc over to the companion neutron star causing X-ray activity. With N-body simulations and steady state decretion disc models we explore system parameters for which a disc in the Be/X-ray binary 4U 0115+634 is KL unstable and the resulting time-scale for the oscillations. We find good agreement between predictions of the model and the observed giant outburst time-scale provided that the disc is not completely destroyed by the outburst. This allows the outer disc to be replenished between outbursts and a sufficiently short KL oscillation time-scale. An initially eccentric disc has a shorter KL oscillation time-scale compared to an initially circular orbit disc. We suggest that the chaotic nature of the outbursts is caused by the sensitivity of the mechanism to the distribution of material within the disc. The outbursts continue provided that the Be star supplies material that is sufficiently misaligned to the binary orbital plane. We generalize our results to Be/X-ray binaries with varying orbital period and find that if the Be star disc is flared, it is more likely to be unstable to KL oscillations in a smaller orbital period binary, in agreement with observations.

Disorientations in dislocation structures: Formation and spatial correlation

2002 ◽  
Vol 17 (9) ◽  
pp. 2433-2441 ◽  
Author(s):  
Wolfgang Pantleon
Keyword(s):  
Plastic Deformation ◽  
Spatial Correlation ◽  
Distribution Functions ◽  
Scaling Behavior ◽  
Dislocation Dynamics ◽  
Slip Systems ◽  
Experimental Findings ◽  
Good Agreement

During plastic deformation, dislocation boundaries are formed and orientation differences across them arise. Two different causes lead to the formation of two kinds of deformation-induced boundaries: a statistical trapping of dislocations in incidental dislocation boundaries and a difference in the activation of slip systems on both sides of geometrically necessary boundaries. On the basis of these mechanisms, the occurrence of disorientations across both types of dislocation boundaries is modeled by dislocation dynamics. The resulting evolution of the disorientation angles with strain is in good agreement with experimental observations. The theoretically obtained distribution functions for the disorientation angles describe the experimental findings well and explain their scaling behavior. The model also predicts correlations between disorientations in neighboring boundaries, and evidence for their existence is presented.

Simulation of Sphere’s Motion Induced by Shock Waves

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Dan Igra ◽  
Ozer Igra ◽  
Lazhar Houas ◽  
Georges Jourdan
Keyword(s):  
Shock Waves ◽  
Drag Coefficient ◽  
Drag Force ◽  
Stationary Flow ◽  
Experimental Results ◽  
Experimental Findings ◽  
Sphere Drag ◽  
Simulation Scheme ◽  
Good Agreement

Simulations of experimental results appearing in Jourdan et al. (2007, “Drag Coefficient of a Sphere in a Non-Stationary Flow: New Results,”Proc. R. Soc. London, Ser. A, 463, pp. 3323–3345) regarding acceleration of a sphere by the postshock flow were conducted in order to find the contribution of the various parameters affecting the sphere drag force. Based on the good agreement found between present simulations and experimental findings, it is concluded that the proposed simulation scheme could safely be used for evaluating the sphere’s motion in the postshock flow.

On Wall Effects in Cavity Flows

1984 ◽  
Vol 28 (01) ◽  
pp. 70-75
Author(s):  
C. C. Hsu
Keyword(s):  
Numerical Results ◽  
Cavity Flows ◽  
Two Dimensional ◽  
Wall Effects ◽  
Free Jet ◽  
Theoretical Predictions ◽  
Experimental Findings ◽  
Good Agreement

Simple wall correction rules for two-dimensional and nearly two-dimensional cavity flows in closed or free jet water tunnels, based on existing linearized analyses, are made. Numerical results calculated from these expressions are compared with existing experimental findings. The present theoretical predictions are, in general, in good agreement with data.

Relaxations at GaN (1010) and (110) Surfaces

1996 ◽  
Vol 449 ◽  
Author(s):  
Alessio Filipetti ◽  
Manuela Menchi ◽  
Andrea Bosin ◽  
Giancarlo Cappellini
Keyword(s):  
Bond Length ◽  
Rotation Angle ◽  
Surface Structures ◽  
Small Energy ◽  
Zinc Blende ◽  
Length Contraction ◽  
Experimental Findings ◽  
Formation Energies ◽  
Surface Bond ◽  
Good Agreement

ABSTRACTWe present an ab-initio calculation of GaN wurtzite (1010) and zinc-blende (110) surface structures and formation energies. Our method employs ultrasoft pseudopotentials and plane-wave basis. These features enable us to obtain accurate results using small energy cut-off and large supercells. The (110) surface shows a Ga-N surface dimer rotation of ∼ 14°, i.e. about one half that of the ordinary III–V non-nitride compounds, and a 5% contraction of the surface bond-length (more than the double that occurring in GaAs). For the (1010) surface, a layer rotation angle of about 11° and a bond-length contraction of 6% has been found. Zinc-blende GaAs (110) and wurtzite ZnO (1010) surfaces have been studied as well, for the sake of comparison. GaAs results are in good agreement with the experimental findings. For ZnO a large bond contraction and a rotation angle of around 11% result. Thus, our findings place GaN closer in behaviour to the highly ionic II–VI compounds than to the non-nitride III–V semiconductors.

The transient start of supersonic jets

2007 ◽  
Vol 578 ◽  
pp. 331-369 ◽  
Author(s):  
MATEI I. RADULESCU ◽  
CHUNG K. LAW
Keyword(s):  
Numerical Simulations ◽  
Ambient Air ◽  
Hydrogen Gas ◽  
Shock Interactions ◽  
Round Jets ◽  
Reactive Gases ◽  
Acoustic Instabilities ◽  
Diffusive Fluxes ◽  
Experimental Findings ◽  
Good Agreement

This study investigates the initial transient hydrodynamic evolution of highly under-expanded slit and round jets. A closed-form analytic similarity solution is derived for the temporal evolution of temperature, pressure and density at the jet head for vanishing diffusive fluxes, generalizing a previous model of Chekmarev using Chernyi's boundary-layer method for hypersonic flows. Two-dimensional numerical simulations were also performed to investigate the flow field during the initial stages over distances of ~ 1000 orifice radii. The parameters used in the simulations correspond to the release of pressurized hydrogen gas into ambient air, with pressure ratios varying between approximately 100 and 1000. The simulations confirm the similarity laws derived theoretically and indicate that the head of the jet is laminar at early stages, while complex acoustic instabilities are established at the sides of the jet, involving shock interactions within the vortex rings, in good agreement with previous experimental findings. Very good agreement is found between the present model, the numerical simulations and previous experimental results obtained for both slit and round jets during the transient establishment of the jet. Criteria for Rayleigh–Taylor instability of the decelerating density gradients at the jet head are also derived, as well as the formulation of a model addressing the ignition of unsteady expanding diffusive layers formed during the sudden release of reactive gases.

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