Vortex Rings

By: D. G. Akhmetov

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Hardcover | 3 November 2009

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168 Pages

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24.13 x 16.51 x 1.91

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Vortex flow is one of the fundamental types of fluid and gas motion. These flows are the most spectacular in the form of concentrated vortices, characterized by the localization of vorticity (curl of velocity) in bounded regions of a space, beyond which the vorticity is either absent or rapidly falls down to zero. Concentrated vortices are often observed in nature, exemplified by atmospheric cyclones, whirlwinds and tornados, oceanic vortices, whirlpools on a water s- face, and ring vortices caused by explosive outburst of volcanoes. In technical - vices concentrated vortices form when flow separates from sharp edges of flying vehicles and ships. Among these are vortices flowing off the ends of airplane wings, and intentionally generated vortices for intensification of burning in c- bustion chambers, vortices in cyclonic devices used for mixing or separation of impurities in fluids and gases. One such remarkable and frequent type of conc- trated vortices is a vortex ring which constitutes a vortex tube closed into a t- oidal ring moving in a surrounding fluid like an isolated body out of contact with solid boundaries of the flow region if such boundaries exist. Formation and motion of vortex rings are important part of the dynamics of a continuum medium and have been studied for more than a century.

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Introduction	p. 1
Theoretical Models of Vortex Rings	p. 5
Vortex Rings	p. 5
Equations of Motion. Vorticity, Circulation, and Stream Function	p. 7
Vorticity Distribution and Velocity Field of a Vortex Ring	p. 9
Integral Characteristics of a Vortex Ring	p. 11
Circular Line Vortex of Zero Cross-Section	p. 14
Vortex Ring with Finite Cross-Section (Lamb's Model)	p. 16
Hill's Spherical Vortex	p. 21
Family of Steady Vortex Rings	p. 22
Translational Velocity of a Vortex Ring	p. 30
Hydrodynamic Structure of a Vortex Ring	p. 33
Experimental Procedure	p. 33
Hot-Wire Anemometry: Method for Measuring Two-Dimensional Velocity Field	p. 35
Estimations of Measurement Accuracy of Two-Dimensional Velocity Field with Hot-Wire Probes	p. 42
Velocity Field of Vortex Ring	p. 49
Stream Function and Structure of Stream Lines	p. 50
Vorticity Distribution. Vortex Core. Circulation	p. 51
Dynamic Characteristics of a Vortex Ring	p. 55
Other Investigations of Vortex Ring Structure	p. 60
Comments on Experimental Methods of Studying Velocity Flow Field	p. 63
Structure and Parameters of a Family of Vortex Rings Formed on Outflow of a Submerged Jet	p. 67
Experimental Procedure	p. 68
Criteria Determining Vortex Ring Formation Process	p. 71
Basic Properties of Vortex Rings	p. 72
Vortex Ring Parameters as Functions of Jet Length	p. 73
Dependence of Vortex Ring Parameters on the Jet Reynolds Number	p. 78
Dependence of Vortex Ring Parameters on the Nozzle Angle of Taper	p. 85
Comparison between Some Conclusions from Theoretical Models of Vortex Rings and Experiment	p. 85
Vortex Ring Formation	p. 89
Vortex Ring Generation by Impulsive Motion of a Circular Disc	p. 89
Vortex Ring Formation on Outflow of a Submerged Jet	p. 91
Motion of Turbulent Vortex Rings	p. 105
Statement of the Problem	p. 106
Laws of Motion of a Turbulent Vortex Ring	p. 108
Structure of a Turbulent Vortex Ring	p. 113
Practical Implementation of Vortex Rings: Extinction of Fires at Gushing Gas and Oil Wells	p. 121
Origination and Characteristics of Powerful Gas and Oil Gushers	p. 121
Combustion of Gas and Oil Gushers. Conditions of Stabilization and Flame-Out	p. 123
Determination of Flow Rate of Burning Underexpanded Gas Gushers	p. 123
Physical Grounds for Extinguishing of a Diffusion Plume by an Air Vortex Ring	p. 130
Principles of Scale Modeling and Calculation of Amount of Fire Extinguishing Agents	p. 139
Extinguishing of Real Well Fires by a Vortex Ring	p. 140
References	p. 143
Index	p. 151
Table of Contents provided by Ingram. All Rights Reserved.

Vortex Rings

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