Liquid Sloshing Dynamics: Theory and Applications

by Raouf A. Ibrahim

• ISBN13: 9780521838856
• ISBN10: 0521838851
• Format: Hardcover
• Copyright: 2005-06-20
• Publisher: Cambridge University Press

Summary

The problem of liquid sloshing in moving or stationary containers remains of great concern to aerospace, civil, and nuclear engineers; physicists; designers of road tankers and ship tankers; and mathematicians. Beginning with the fundamentals of liquid sloshing theory, this book takes the reader systematically from basic theory to advanced analytical and experimental results in a self-contained and coherent format. The book is divided into four sections. Part I deals with the theory of linear liquid sloshing dynamics; Part II addresses the nonlinear theory of liquid sloshing dynamics, Faraday waves, and sloshing impacts; Part III presents the problem of linear and nonlinear interaction of liquid sloshing dynamics with elastic containers and supported structures; and Part IV considers the fluid dynamics in spinning containers and microgravity sloshing. This book will be invaluable to researchers and graduate students in mechanical and aeronautical engineering, designers of liquid containers, and applied mathematicians.

Table of Contents

Foreword	xii
Acknowledgment	xiv
Introduction	xvi
Part I Linear sloshing dynamics	1	(206)
Fluid field equations and modal analysis in rigid containers	3	(85)
Introduction	3	(2)
Fluid field equations	5	(4)
Variational formulation	9	(3)
Normal modes in an upright cylindrical container	12	(8)
Bare wall cylindrical tank	12	(4)
Cylindrical tank with ring baffles	16	(1)
Annular tank	17	(1)
Cylindrical quarter tank	18	(2)
Normal modes in a rectangular container	20	(3)
Normal modes in containers with variable depth	23	(57)
Canal with 45°-straight walls	23	(2)
Horizontal cylindrical and spherical containers	25	(21)
Prolate spheroidal tank	46	(7)
Oblate spheroidal tank	53	(3)
Conical container	56	(10)
Toroidal containers	66	(6)
Upright elliptic containers	72	(2)
Paraboloid container	74	(6)
Closing remarks	80	(8)
Appendix	81	(1)
Curvilinear coordinates	81	(1)
Cylindrical coordinates	82	(1)
Spherical coordinates	82	(1)
Prolate spheroidal coordinates	83	(1)
Oblate spheroidal coordinates	84	(1)
Bipolar coordinates (ξ, η, z)	84	(3)
Toroidal coordinates (η, ξ, φ)	87	(1)
Linear forced sloshing	88	(68)
Introduction	88	(1)
Upright cylindrical containers	89	(13)
Lateral excitation	90	(7)
Pitching excitation	97	(5)
Annular sectored tank	102	(13)
Lateral excitation	102	(4)
Pitching excitation	106	(3)
Roll excitation	109	(6)
90°-sector cylindrical tank	115	(12)
Lateral excitation	115	(4)
Pitching excitation	119	(2)
Roll excitation	121	(6)
Annular containers	127	(3)
Lateral excitation	127	(2)
Pitching excitation	129	(1)
Rectangular containers	130	(7)
Lateral excitation	130	(4)
Pitching excitation	134	(1)
Roll excitation	135	(2)
Spherical containers	137	(3)
Prolate and oblate spheroidal containers	140	(5)
Conical containers	145	(3)
Paraboloid containers	148	(3)
Sloshing of magnetic fluids	151	(3)
Closing remarks	154	(2)
Viscous damping and sloshing suppression devices	156	(51)
Introduction	156	(3)
Viscous damping in liquid containers	159	(8)
Damping in a circular cylindrical container	159	(6)
Damping in other containers	165	(2)
Free and forced oscillations of viscous fluids	167	(11)
Modal analysis of viscous fluids	167	(6)
Lateral excitation of viscous fluids	173	(5)
Suppression devices	178	(13)
Damping in a circular cylinder with baffles	179	(12)
Periodic boundary layers	191	(13)
Stokes boundary layer over an oscillating flat plate	191	(2)
Periodic boundary layers in cylindrical tanks	193	(5)
Effect of immersed rods	198	(6)
Closing remarks	204	(3)
Part II Nonlinear and parametric sloshing dynamics	207	(272)
Weakly nonlinear lateral sloshing	209	(87)
Introduction	209	(2)
Rotary sloshing	211	(30)
Experimental observations	211	(3)
Analysis of rotary sloshing	214	(27)
Random excitation	241	(12)
Background	241	(1)
Experimental observations and results	242	(1)
Stochastic analysis of earthquake excitation of liquid rigid tanks	243	(10)
Nonlinear phenomena in rectangular tanks	253	(10)
Background	253	(2)
Longitudinal standing waves	255	(8)
Conical tanks	263	(9)
Prolate spheroidal container	272	(6)
Spatial resonance	278	(2)
Nonlinear sloshing of magnetic fluids	280	(5)
Self-induced sloshing in nuclear reactors	285	(8)
Description of liquid dynamic problems in nuclear plants	285	(1)
Experimental results	286	(7)
Closing remarks	293	(3)
Appendix	294	(1)
Orthogonality and recurrence relations	294	(2)
Equivalent mechanical models	296	(42)
Introduction	296	(2)
Spring-mass-dashpot modeling	298	(9)
Lateral excitation of undamped models	300	(1)
Pitching excitation of undamped models	301	(1)
Model parameters for a circular upright cylinder	301	(3)
Model parameters for a rectangular tank	304	(3)
Pendulum modeling	307	(7)
Lateral excitation x = X0 sin Ωt, ψ = 0	309	(1)
Pitching excitation: Ψ = Ψ0 sin Ωt, x = 0	309	(1)
Mechanical parameters for a circular cylinder	310	(1)
Mechanical parameters for a rectangular tank	311	(1)
Spherical and oblate spheroidal containers	311	(3)
Remarks on linear modeling	314	(1)
Nonlinear modeling	314	(20)
Mechanical modeling of nonplanar sloshing	315	(5)
Dynamics of the spherical pendulum	320	(9)
Linear plus spherical pendulums	329	(5)
Closing remarks	334	(4)
Parametric sloshing: Faraday waves	338	(67)
Introduction	338	(3)
Linear theory of parametric sloshing	341	(3)
Nonlinear parametric sloshing of a single mode	344	(6)
Nonlinear modal competition	350	(6)
Autoparametric interaction in cylindrical tanks	356	(14)
Historical overview	356	(2)
Lagrangian formulation	358	(3)
Two-to-one internal resonance	361	(9)
Autoparametric interaction in rectangular tanks	370	(24)
Analytical modeling	370	(6)
Single mode excitation	376	(4)
One-to-one internal resonance	380	(9)
Experimental results	389	(5)
Random parametric excitation	394	(6)
Surface disintegration	400	(4)
Closing remarks	404	(1)
Dynamics of liquid sloshing impact	405	(74)
Introduction	405	(3)
Shock wave in a gas column analogy	408	(9)
Lateral excitation of a rectangular tank	417	(6)
Impact due to sudden acceleration	423	(2)
Modeling of hydrodynamic impact forces	425	(5)
Analytical approaches	430	(8)
Step-by-step integration method	430	(1)
Asymptotic approximation techniques	430	(1)
Nonsmooth coordinate transformation	430	(1)
Saw-tooth time-transformation (STTT) method	431	(3)
Lie group transformation	434	(4)
Structure interaction with sloshing impact	438	(17)
First mode parametric excitation	443	(5)
Second mode parametric excitation	448	(4)
Mixed mode parametric excitation	452	(3)
Numerical simulation of sloshing impact	455	(16)
Preliminaries	455	(6)
The volume-of-fluid (VOF) method	461	(2)
Sloshing impact in ship tankers	463	(8)
Sloshing in road tankers	471	(2)
Closing remarks	473	(6)
Appendix	475	(1)
Functions Ψii of equations (7.54)	475	(4)
Part III Sloshing -- structure interaction	479	(212)
Linear interaction with elastic containers	481	(57)
Introduction	481	(1)
Basic problem of hydroelastic dynamics	482	(7)
Kinematic relations	482	(4)
Hydroelastic interacting forces	486	(3)
Interaction with tank bottom	489	(12)
Interaction with elastic bottom	490	(11)
Interaction with tank walls	501	(19)
Interaction with bending modes	501	(11)
Interaction with breathing modes	512	(8)
Interaction with tank bottom and walls	520	(16)
Shell with membrane bottom	523	(8)
Shell with elastic plate bottom	531	(5)
Closing remarks	536	(2)
Nonlinear interaction under external and parametric excitations	538	(69)
Introduction	538	(3)
General equations of motion	541	(2)
Shells partially filled with liquid	543	(3)
Free vibration of shells partially filled with still fluid	543	(1)
Influence of liquid free surface oscillations	544	(1)
Forced vibration of shells partially filled with still fluid	545	(1)
Shells filled with liquid	546	(25)
Historical overview	546	(2)
Interaction with linear liquid sloshing	548	(2)
Free nonlinear multi-mode problem	550	(5)
Multiple internal resonances	555	(3)
Linear shell interaction with nonlinear liquid sloshing	558	(6)
Nonlinear sloshing interaction with linear elastic bottom	564	(7)
Nonlinear interaction with nonlinear sloshing	571	(7)
Governing equations of motion	571	(4)
Free nonlinear interaction	575	(2)
Forced autoparametric interaction	577	(1)
Interaction under parametric excitation	578	(10)
Historical overview	578	(2)
Parametric excitation of fundamental modes of a shell-liquid system	580	(1)
Liquid-filled shell	581	(7)
Nonlinear interaction with orthotropic shells	588	(13)
Nonlinear free vibration	588	(8)
Excitation of nonlinear sloshing interacting with linear orthotropic shells	596	(5)
Storage liquid tanks	601	(2)
Numerical techniques	603	(3)
Numerical simulation of liquid sloshing	603	(1)
Numerical simulation of sloshing-structure interaction	604	(2)
Closing remarks	606	(1)
Interaction with support structures and tuned sloshing absorbers	607	(84)
Introduction	607	(2)
Basic concept of linear vibration absorbers	609	(4)
Tuned liquid sloshing absorbers	613	(3)
Tuned liquid dampers	613	(2)
Liquid column vibration absorbers	615	(1)
Analytical modeling of liquid sloshing absorbers	616	(19)
Vertical ground harmonic excitation	620	(5)
Horizontal ground harmonic excitation	625	(10)
Random excitation	635	(24)
Horizontal and vertical random excitations	636	(13)
Vertical random excitation	649	(10)
Autoparametric sloshing absorber	659	(14)
Summed type internal resonance: r3 = r1 + r2, r3 = nv	663	(5)
Principal type internal resonance: r3 = 2r2, r3 = nv	668	(5)
Nonlinear sloshing absorber in a rectangular tank	673	(4)
Ship roll stabilization using liquid tanks	677	(12)
Ship in pure rolling motion	680	(2)
Influence of other ship motions	682	(7)
Closing remarks	689	(2)
Part IV Rotating fluid and low gravity sloshing	691	(142)
Dynamics of rotating fluids	693	(59)
Introduction	693	(3)
Fluid-filled spinning containers	696	(7)
Historical background	696	(1)
Fluid-filled spinning cylinder	697	(6)
Dynamics of partially filled spinning containers	703	(27)
Historical background	703	(5)
Inviscid fluid in partially filled upright cylinder	708	(9)
Free oscillations of spinning viscous liquid	717	(13)
Parametric excitation of a spinning liquid	730	(7)
Inertia waves in a rotating fluid	737	(2)
Periodic breakdown of free surface	739	(4)
Rotating liquids in microgravity	743	(8)
Nonrotating free surface shape	747	(1)
Rotating free surface shape	747	(1)
Time-dependent rotation and gravitational field	748	(3)
Closing remarks	751	(1)
Microgravity sloshing dynamics	752	(81)
Introduction	752	(1)
Kinetics and geometry of liquid free surface	753	(9)
Surface tension and Bond number	753	(2)
Static and dynamic contact-angle	755	(6)
Kinematics of spherical surface	761	(1)
Modal analysis	762	(8)
Modal analysis under microgravity	762	(2)
Modal analysis under zero gravity	764	(4)
Experimental modal analysis	768	(2)
Sloshing with slipping and anchored contact lines	770	(11)
Modal analysis	771	(10)
Forced excitation	781	(7)
Slipping contact-line	784	(2)
Anchored contact-line	786	(2)
G-jitter modeling and effects	788	(3)
Liquid handling	791	(2)
Capillary systems	793	(20)
Marangoni flow	793	(2)
Special forms	795	(1)
Static stability of liquid bridges	795	(2)
Dynamic stability of liquid bridges	797	(3)
Axial excitation of liquid bridges	800	(5)
Axial excitation of spinning liquid bridges	805	(8)
Thermocapillary convection	813	(11)
Thermocapillary instability of fluid flow	813	(5)
Thermocapillary instability of liquid bridges	818	(6)
Sloshing problems of cryogenics	824	(5)
Physical characteristics of superfluids	824	(1)
Sloshing of cryogenics	825	(4)
Hydroelastic oscillations	829	(1)
Closing remarks	830	(3)
Appendix	831	(1)
A1 Common dimensionless numbers	831	(2)
References	833	(107)
Index	940