Vortex Rings (eBook)

Abstract 5
Nomenclature 8
Greek Symbols 9
Introduction 10
1 Theoretical Models of Vortex Rings 13
1.1 Vortex Rings 13
1.2 Equations of Motion. Vorticity, Circulation, and Stream Function 15
1.3 Vorticity Distribution and Velocity Field of a Vortex Ring 17
1.4 Integral Characteristics of a Vortex Ring 19
1.5 Circular Line Vortex of Zero Cross-Section 22
1.6 Vortex Ring with Finite Cross-Section (Lamb’s Model) 24
1.7 Hill’s Spherical Vortex 29
1.8 Family of Steady Vortex Rings 30
1.9 Translational Velocity of a Vortex Ring 38
2 Hydrodynamic Structure of a Vortex Ring 41
2.1 Experimental Procedure 41
2.2 Hot-Wire Anemometry: Method for Measuring Two- Dimensional Velocity Field 43
2.3 Estimations of Measurement Accuracy of Two-Dimensional Velocity Field with Hot- Wire Probes 50
2.4 Velocity Field of Vortex Ring 57
2.5 Stream Function and Structure of Stream Lines 58
2.6 Vorticity Distribution. Vortex Core. Circulation 59
2.7 Dynamic Characteristics of a Vortex Ring 63
2.8 Other Investigations of Vortex Ring Structure 68
2.9 Comments on Experimental Methods of Studying Velocity Flow Field 71
3 Structure and Parameters of a Family of Vortex Rings Formed on Outflow of a Submerged Jet 74
3.1 Experimental Procedure 75
3.2 Criteria Determining Vortex Ring Formation Process 78
3.3 Basic Properties of Vortex Rings 79
3.4 Vortex Ring Parameters as Functions of Jet Length 80
3.5 Dependence of Vortex Ring Parameters on the Jet Reynolds Number 85
3.6 Dependence of Vortex Ring Parameters on the Nozzle Angle of Taper 92
3.7 Comparison between Some Conclusions from Theoretical Models of Vortex Rings and Experiment 92
4 Vortex Ring Formation 95
4.1 Vortex Ring Generation by Impulsive Motion of a Circular Disc 95
4.2 Vortex Ring Formation on Outflow of a Submerged Jet 97
5 Motion of Turbulent Vortex Rings 110
5.1 Statement of the Problem 111
5.2 Laws of Motion of a Turbulent Vortex Ring 113
5.3 Structure of a Turbulent Vortex Ring 118
6 Practical Implementation of Vortex Rings: Extinction of Fires at Gushing Gas and Oil Wells 125
6.1 Origination and Characteristics of Powerful Gas and Oil Gushers 125
6.2 Combustion of Gas and Oil Gushers. Conditions of Stabilization and Flame- Out 127
6.3 Determination of Flow Rate of Burning Underexpanded Gas Gushers 127
6.4 Physical Grounds for Extinguishing of a Diffusion Plume by an Air Vortex Ring 134
6.5 Principles of Scale Modeling and Calculation of Amount of Fire Extinguishing Agents 143
6.6 Extinguishing of Real Well Fires by a Vortex Ring 144
References 147
Index 154