Fundamentals of Cavitation

by FRANC, JEAN-PIERRE; MICHEL, JEAN-MARIE

• ISBN13: 9781402022326
• ISBN10: 1402022328
• Format: Hardcover
• Copyright: 2004-07-01
• Publisher: Kluwer Academic Pub

Summary

Why are propeller blades of speedboats strongly eroded? Why does a syringe have to be filled slowly in order to avoid the formation of a vapour cavity near the piston? Why does a pump for watering the garden not work efficiently if it is placed too high above the ground water level? These questions, and many others taken from day to day experience, refer to situations which apparently have no connection between them, except for the fact that the motion of a liquid in part of the system plays an essential role.Cavitation science is that part of liquid physics which addresses the motion of liquids near -or beyond- the limit of vaporization. Generally, vaporization occurs if liquid velocities are large, causing pressure to decrease below a critical value at which the liquid continuum is broken at one or several points. Vapor cavities appear there and various unexpected effects follow for the system such as noise, lower performance, vibrations, wall erosion For a long time, it was believed that cavitation phenomena should be avoided entirely because of the generally negative character of their consequences. However, over the years it appeared that such a constraint could be costly, though not necessarily justified on scientific grounds. A limited development of cavitation - if carefully defined and controlled - can be allowed. This promotes the development of high speed hydrodynamics and hydraulics. The present book is aimed at providing a comprehensive presentation of cavitation phenomena in liquid flows. It is further backed up by the experience, both experimental and theoretical, of the authors whose expertise has been internationally recognized. A special effort is made to place the various methods of investigation in strong relation with the fundamental physics of cavitation, enabling the reader to treat specific problems independently. Furthermore, it is hoped that a better knowledge of the cavitation phenomenon will allow engineers to create systems using it positively. Examples in the literature show the feasibility of this approach.

Table of Contents

Foreword	xiii
Dr. Hiroharu Kato
Preface	xv
Symbols	xix
Introduction -- The main features of cavitating flows	1	(14)
The physical phenomenon	1	(4)
Definition	1	(1)
Vapor pressure	2	(2)
The main forms of vapor cavities	4	(1)
Cavitation in real liquid flows	5	(2)
Cavitation regimes	5	(1)
Typical situations favorable to cavitation	5	(1)
The main effects of cavitation in hydraulics	6	(1)
Specific features of cavitating flow	7	(3)
Pressure and pressure gradient	7	(1)
Liquid-vapor interfaces	8	(2)
Thermal effects	10	(1)
Some typical orders of magnitude	10	(1)
Non-dimensional parameters	10	(3)
Cavitation number σv	10	(1)
Cavitation number at inception, σvi	11	(1)
Relative underpressure of a cavity, σc	12	(1)
Some historical aspects	13	(2)
References	14	(1)
Nuclei and cavitation	15	(20)
Introduction	15	(2)
Liquid tension	15	(1)
Cavitation nuclei	15	(2)
Equilibrium of a nucleus	17	(4)
Equilibrium condition [Blake 1949]	17	(1)
Stability and critical pressure of a nucleus	18	(2)
Nucleus evolution in a low pressure region	20	(1)
Heat and mass diffusion	21	(6)
The thermal behavior of the gas content	21	(2)
Gas diffusion and nucleus stability	23	(4)
Nucleus population	27	(8)
Measurement methods	27	(3)
Conditions for inception of bubble cavitation	30	(2)
References	32	(3)
The dynamics of spherical bubbles	35	(22)
Basic equations	35	(3)
Introduction	35	(1)
Assumptions	35	(1)
Boundary and initial conditions	36	(1)
Rayleigh-Plesset equation	36	(1)
Interpretation of the Rayleigh-Plesset equation in terms of energy balance	37	(1)
The collapse of a vapor bubble	38	(4)
Assumptions	38	(1)
The interface velocity	38	(2)
The pressure field	40	(1)
Remark on the effect of surface tension	41	(1)
The explosion of a nucleus	42	(4)
The interface velocity	42	(1)
The equilibrium case (p∞ = p∞0)	43	(1)
The case of nucleus growth (p∞ < p∞0)	43	(1)
Dynamic criterion	44	(1)
Remark on two particular cases	45	(1)
The effect of viscosity	46	(1)
Linear oscillations of a bubble	46	(1)
Effect of viscosity on explosion or collapse of bubbles	46	(1)
Non-linear oscillations of a bubble	47	(1)
Scaling considerations	48	(5)
Non-dimensional form of the Rayleigh-Plesset equation	48	(1)
Characteristic time scales of the Rayleigh-Plesset equation	49	(1)
Qualitative discussion of the Rayleigh-Plesset equation	50	(1)
Case of a transient bubble near a foil	51	(2)
Stability of the spherical interface	53	(4)
References	55	(2)
Bubbles in a non-symmetrical environment	57	(20)
Introduction	57	(1)
Motion of a spherical bubble in a liquid at rest	57	(3)
Translation of a solid sphere in a liquid at rest	57	(1)
Translation with simultaneous volume variations	58	(1)
Application to bubbles	59	(1)
Non-spherical bubble evolution	60	(7)
Principle of Plesset-Chapman numerical modeling	60	(1)
Some general results	61	(3)
Blake's analytical approach	64	(3)
The path of a spherical bubble	67	(10)
References	71	(1)
Appendix to section 4.3.3	72	(5)
Further insights into bubble physics	77	(20)
The effect of compressibility	77	(6)
Tait's equation of state	77	(1)
Basic equations	78	(1)
The quasi acoustic solution [Herring 1941 & Trilling 1952]	79	(1)
The Gilmore approach (1952)	80	(3)
Bubble noise	83	(3)
Basic equations	83	(1)
Weak bubble oscillations	84	(1)
Noise of a collapsing bubble	85	(1)
Some thermal aspects	86	(6)
The idea of thermal delay	86	(3)
Brennen's analysis (1973)	89	(3)
A typical numerical solution	92	(5)
References	95	(1)
Appendix to section 5.1.3	96	(1)
Supercavitation	97	(34)
Physical aspects of supercavities	98	(7)
Cavity pressure	98	(1)
Cavity detachment	98	(3)
Cavity closure	101	(1)
Cavity length	102	(3)
Supercavity flow modeling using steady potential flow theory	105	(5)
The main parameters	105	(1)
Equations and boundary conditions	106	(1)
Cavity closure models	107	(1)
Overview of calculation techniques	108	(2)
Typical results	110	(5)
Infinite cavity behind a flat plate in an infinite flow field	110	(1)
Finite cavity behind a symmetrical body in an infinite flow field	111	(1)
Finite cavity behind a circular arc in an infinite flow field	112	(1)
Variation of lift and drag coefficients with cavity underpressure	113	(1)
Effect of submersion depth on the slope of the curve CL(α)	114	(1)
Axisymmetric cavities	115	(9)
The Garabedian asymptotic solution for steady supercavities	115	(1)
Momentum balance and drag	116	(1)
Approximate, analytic solution for steady supercavities	117	(4)
Unsteady axisymmetric supercavities	121	(3)
Specific problems	124	(7)
Unsteady 2D supercavities	124	(1)
Compressible effects in supercavitating flows	125	(1)
References	126	(3)
Appendix: singular behavior at detachment	129	(2)
Partial cavities	131	(38)
Partial cavities on two-dimensional foils	131	(7)
Main patterns	131	(2)
Cavity closure	133	(1)
Cavity length	134	(1)
Three-dimensional effects due to an inclination of the closure line	135	(2)
Multiple shedding on 2D hydrofoils	137	(1)
Partial cavities in internal flows	138	(2)
The cloud cavitation instability	140	(5)
Conditions for the onset of the cloud cavitation instability	140	(1)
Global behavior	141	(2)
Pulsation frequency	143	(1)
Jet thickness	144	(1)
Wakes of partial cavities	145	(8)
Mean pressure distribution	145	(1)
Production of vapor bubbles	146	(1)
Pressure fluctuations	147	(1)
Wall pressure pulses at cavity closure	148	(2)
Scaling of pulse spectra	150	(2)
Main features of the noise emitted by partial cavities	152	(1)
Thermal effects in partial cavitation	153	(6)
The Stepanoff B-factor	153	(1)
The entrainment method	154	(5)
System instability	159	(2)
Partial cavity flow modeling	161	(8)
References	162	(3)
Appendix: sonic velocity in a liquid / vapor mixture with phase change	165	(4)
Bubbles and cavities on two-dimensional foils	169	(24)
Attached cavitation	169	(10)
Cavitation inception on a circular cylinder	169	(3)
Cavity patterns on a two-dimensional foil	172	(2)
Boundary layer features on a slender foil	174	(2)
The connection between laminar separation and detachment	176	(3)
Traveling bubble cavitation	179	(7)
The effect of water quality and nuclei seeding	179	(3)
Scaling law for developed bubble cavitation	182	(2)
Saturation	184	(2)
Interaction between bubbles and cavities	186	(3)
Effect of exploding bubbles on a cavity	186	(1)
Critical nuclei concentration for transition between attached cavitation and traveling bubble cavitation	187	(1)
The prediction of cavitation patterns	188	(1)
Roughness and cavitation inception	189	(4)
References	191	(2)
Ventilated supercavities	193	(30)
Two-dimensional ventilated cavities	193	(16)
Ventilated hydrofoils	193	(1)
The main parameters	194	(2)
Cavity length	196	(3)
Air flowrate and cavity pressure	199	(3)
Pulsation regimes	202	(3)
Pulsation frequency	205	(1)
Concerning the pulsation mechanism	206	(3)
Axisymmetric ventilated supercavities	209	(5)
Different regimes of ventilated cavities	209	(1)
Gas evacuation by toroidal vortices	210	(1)
Deformation of the cavity axis by gravity	210	(1)
Gas evacuation by two hollow tube vortices	211	(3)
Analysis of pulsating ventilated cavities	214	(9)
Basic equations	214	(3)
Analysis of the pressure fluctuation equation	217	(1)
Comparison with experiments	218	(2)
References	220	(3)
Vortex cavitation	223	(24)
Theoretical results	223	(8)
Basic vorticity theorems	223	(1)
The main effects of cavitation on rotational flows	224	(2)
Axisymmetric cavitating vortex	226	(1)
Toroidal cavitating vortex	227	(4)
The non-cavitating tip vortex	231	(8)
Tip vortex formation	231	(1)
Vortex models in viscous fluids	232	(2)
Tip vortex structure	234	(5)
Cavitation in a tip vortex	239	(8)
Scaling laws for cavitation inception	239	(1)
Correlation of cavitation data with the lift coefficient	240	(2)
Effect of nuclei content	242	(2)
Effect of confinement	244	(1)
References	245	(2)
Shear cavitation	247	(18)
Jet cavitation	248	(4)
Some experimental results	248	(3)
Some elements of analysis of jet cavitation	251	(1)
Wake cavitation	252	(13)
Cavitation inception in the wake of circular discs	252	(1)
Modeling of wake cavitation inception	253	(3)
Cavitation in the wake of a two-dimensional wedge	256	(6)
References	262	(3)
Cavitation erosion	265	(28)
Empirical methods	266	(1)
Some global results	267	(2)
Influence of flow velocity	267	(1)
Time evolution of mass loss rate	267	(1)
Miscellaneous comments	268	(1)
Basic hydrodynamic mechanisms of energy concentration	269	(2)
Collapse and rebound of a spherical bubble	269	(1)
Microjet	269	(1)
Collective collapse	270	(1)
Cavitating vortices	270	(1)
Aggressiveness of a cavitating flow	271	(11)
Aggressiveness of a collapsing bubble	271	(2)
Pitting tests	273	(2)
Force measurements	275	(3)
Scaling laws for flow aggressiveness	278	(2)
Asymptotic behavior of pitting rate at high velocities	280	(2)
Insight into the material response	282	(11)
Interaction between the liquid flow and a solid wall	282	(1)
Cavitation erosion and strain rate	283	(1)
Correlation of volume loss with impact energy	284	(1)
Phenomenological model for mass loss prediction	285	(4)
References	289	(4)
Index	293