Shock Wave Science and Technology Reference Library. Volume 1. Multiphase Flows I

371 Pages·5.944 MB·English

ShockWaveScienceandTechnologyReferenceLibrary
ThenewSpringercollection,ShockWaveScienceandTechnologyReferenceLibrary,con-
ceived in the style of the famous Handbuch der Physik, has as its principal motivation to
assemble authoritative, state-of-the-art, archival reference articles by leading scientists and
engineersinthefieldofshockwaveresearchanditsapplications.Anumberedandbounded
collection,thisreferencelibrarywillconsistofspecificallycommissionedvolumeswithin-
ternationallyrenownedexpertsaseditorsandcontributingauthors.Eachvolumeconsistsof
asmallcollectionofextensive,topicalandindependentsurveysandreviews.Typicalarticles
startatanelementarylevelthatisaccessibletonon-specialistsandbeginners.Themainpart
of the articles deals with the most recent advances in the field with focus on experiment,
instrumentation,theory,andmodeling.Finally,prospectsandopportunitiesfornewdevelop-
mentsareexamined.Lastbutnotleast,theauthorsofferexpertadviceandcautionsthatare
valuableforboththenoviceandthewell-seasonedspecialist.
ShockWaveScienceandTechnologyReferenceLibrary
CollectionEditors
HansGro¨nig
HansGro¨nigisProfessoremeritusattheShockWaveLaboratoryofRWTH
AachenUniversity,Germany.HeobtainedhisDr.rer.nat.degreeinMe-
chanicalEngineeringandthenworkedaspostdoctoralfellowatGALCIT,
Pasadena, for one year. For more than 50 years he has been engaged in
manyaspectsofmainlyexperimentalshockwaveresearchincludinghy-
personics,gaseousanddustdetonations.Forabout10yearshewasEditor-
in-ChiefofthejournalShockWaves.
YasuyukiHorie
ProfessorYasuyuki(Yuki)Horieisinternationallyrecognizedforhiscon-
tributionsinhigh-pressureshockcompressionofsolidsandenergeticmate-
rialsmodeling.Heisaco-chiefeditoroftheSpringerseriesonShockWave
andHighPressurePhenomenaandtheShockWaveScienceandTechnol-
ogyReferenceLibrary,andaLiaisoneditorofthejournalShockWaves.
HeisaFellowoftheAmericanPhysicalSociety,andSecretaryoftheIn-
ternationalInstituteofShockWaveResearch.Hiscurrentinterestsinclude
fundamentalunderstandingof(a)theimpactsensitivityofenergeticsolids
and its relation to microstructure attributes such as particle size distribu-
tionandinterfacemorphology,and(b)heterogeneousandnonequilibrium
effectsinshockcompressionofsolidsatthemesoscale.
KazuyoshiTakayama
ProfessorKazuyoshiTakayamaobtainedhisdoctoraldegreefromTohoku
Universityin1970andwasthenappointedlecturerattheInstituteofHigh
SpeedMechanics,TohokuUniversity,promotedtoassociateprofessorin
1975 and to professor in 1986. He was appointed director of the Shock
WaveResearchCenterattheInstituteofHighSpeedMechanicsin1988.
TheInstituteofHighSpeedMechanicswasrestructuredastheInstituteof
FluidSciencein1989.Heretiredin2004andbecameemeritusprofessor
ofTohokuUniversity.In1990helaunchedShockWaves,aninternational
journal,takingontheroleofmanagingeditorandin2002becameeditor-
in-chief. He was elected president of the Japan Society for Aeronautical
andSpaceSciencesforoneyearin2000andwaschairmanoftheJapanese
SocietyofShockWaveResearchin2000.Hewasappointedpresidentof
theInternationalShockWaveInstitutein2005.Hisresearchinterestsrange
fromfundamentalshockwavestudiestotheinterdisciplinaryapplication
ofshockwaveresearch.
M. E. H. van Dongen (Ed.)
Shock Wave
Science and Technology
Reference Library, Vol. 1
Multiphase Flows I
With188Figures,6inColorand11Tables
MarinusE.H.vanDongen
EindhovenUniversityofTechnology
DepartmentofAppliedPhysics
Eindhoven,TheNetherlands
Email:[e-mail]
MarinusE.H.vanDongen
ProfessorMarinus(Rini)vanDongenisaphysicistwhohasbeenactivein
researchandeducationinfluiddynamics,physicalgasdynamics,physical
transportphenomena,wavesinporousmedia,waveswithphasetransition,
nucleationandcondensationinrealgasesandinbio-fluiddynamics.Heis
amemberoftheJ.M.Burgerscentrum,ResearchSchoolforFluidMechan-
ics.HehasbeenaffiliatedwithEindhovenUniversityofTechnologyand
part-timewithTwenteUniversity,DepartmentofMechanicalEngineering.
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ISBN-13978-3-540-35845-9SpringerBerlinHeidelbergNewYork
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Preface
Shock waves in multi-phase media refer to a rich variety of phenomena of
interest to physicists, chemists, mechanical engineers, fluid dynamicists and
aeronauticalengineers.Today,newapplicationsinbiomedicalengineeringare
being explored. For the description of shocks in multi-phase media, elements
from thermodynamics and thermal physics, mechanics and fluid mechanics
havetobecombinedwithelementsfromappliedmathematics.Tostudyshocks
inmulti-phasemediauseofdedicatedandsophisticatedexperimentalfacilities
isrequiredwhiletheseexperimentalstudiesprovidenewinsightsintothestate
of matter, ranging from micro-bubbles in distilled water to yield stresses and
plastic deformation in porous materials.
This book contains chapters on shocks and expansion waves in complex
liquids with bubble clouds and single bubbles, shock waves in superfluid he-
lium,shockwavesrelatedtophasetransitionandshocksinteractingwithsolid
foams,textilesandporousandgranularmaterials.Differentauthorswillfocus
onbiomedicalapplications.Someofthesearewidelyusedinmedicalpractice,
such as extracorporeal shock wave lithotripsy (ESWL), applied successfully
to the non-invasive disintegration of kidney stones.
The book opens with a section on shock waves in bubbly liquids (van
Wijngaarden). The reader will be directly confronted with the peculiar wave
properties of such a bubbly liquid, its different wave speeds and its strong
dispersion.Itwillbeshownthatshocksinbubblyliquidsareformedasaresult
ofacompetitionofnon-linearsteepeningeffectsandofdispersion,sothatsuch
shocksareessentiallydifferentfromsinglephaseshocks.Thestructureofthese
shocksinbubblyliquidswillbeaddressedinphysicalandmathematicaldetail.
Free bubbles, subjected to shock wave loading, start to collapse, thereby
loosing their symmetry (Tomita). Liquid microjets are formed with speeds of
hundreds of meters per second, colliding on the bubble wall and giving rise
to high values of pressures and tensile stresses. When such a bubble collapses
near a solid wall, the microjet may cause cracks or pits, depending on geom-
etry, wave amplitude and wave form. Collapsing bubbles may also generate
secondary shocks, interfering with other bubbles attached to a solid wall and
VI Preface
thereby causing wall damage. A peculiar phenomenon, also associated with
bubblecollapseissonoluminescence,thegenerationofahighpowerlightpulse
of extremely short duration.
Strong pulse-shaped shocks in water, reflecting from a free interface, will
lead to strong rarefaction waves and possibly to strong cavitation effects
(Kedrinskii). Such experiments have led to the characterisation of even pure
waterasamulti-phasemediumconsistingofasmallvolumefractionofmicro-
bubbles,withdiametersrangingfromthenanoscaletothemicroscaleandwith
concentrations on the order of 105−106 cm−3. This has direct consequences
for the dynamic strength of a liquid subjected to strong tensile stress waves.
The initial stages of disintegration of liquids and of solids are discussed and
compared.Anextensivesurveyisgivenofrecentdevelopmentsintheapplica-
tionofshockwavesinmedicalpractice(Kedrinskii,Tomita),withadiscussion
of the physical principles involved.
Shocks in cryogenic liquids, in particular shocks in superfluid HeII, have
peculiarproperties(Murakami)thatcanbeunderstoodonthebasisofatwo-
fluid model. In this model, HeII consists of a superfluid component with zero
viscosity and a normal component with relative concentrations depending on
temperature. The concepts of the two-fluid model and their consequences for
wavepropagationingeneralandforshockwavesinparticularareoutlined.It
is shown that two different types of shock waves exist: a normal compression
shock (with peculiar properties) and an entropy shock or a thermal shock
wave. Experimental facilities are described that enable one to observe such
shocks and to study their characteristics.
Waves in wet vapours and in wet carrier gas–vapour mixtures are charac-
terisedbytheinterplayofdifferentrelaxationprocesses,associatedwithtrans-
fer of momentum, heat, and mass between the droplet cloud and gas/vapour
(Guha).Thelatterprocessreferstophasetransition,whichhasimportanten-
ergetic consequences due to the relatively large value of the latent heat. The
relaxation processes strongly affect the structure of shock waves. Different
types of partly and fully dispersed shocks are distinguished. Their proper-
ties and structure are described in detail and the overall jump conditions are
specified.
When dry steam or a humid carrier gas is subjected to a fast isentropic
expansion,itispossiblethatthegas/vapourisbroughttoahighlysupersatu-
ratedstate.Thisleadstostrongproductionofthesmalleststabledropletspos-
sible,aprocesscalledhomogeneousnucleation.Thedropletsgrowuntilanew
phaseequilibriumisattained.Again,itisthelatentheatthatleadstoimpor-
tantconsequencesfortheflowfield(Delale,SchnerrandvanDongen).Sucha
situationismetinconvergent–divergentnozzles,orLavalnozzles,inunsteady
expansionwaves andinsteadysonicorsupersonicflowsaroundasharpedge,
the so-called Prandtl–Meyer corner flows. In steady flow, the amount of la-
tentheatthatcanbe“absorbed”bytheflowislimited.Thisleadstothermal
choking and to the formation of condensation-induced shocks and, in slender
Preface VII
nozzles, to condensation-induced oscillations. Results of asymptotic analysis
and of numerical modelling are compared with experimental observations.
Shock compression in a gas/vapour does not easily lead to the formation
of a liquid. This is because shock compression is accompanied by a temper-
ature increase (shocks in HeII form a possible exception), which brings the
gas/vapour further away from vapour–liquid equilibrium. Still, if the spe-
cific heat is sufficiently large, the temperature increase may be significantly
reduced, such that anomalous gas dynamic behaviour occurs with the lique-
faction shock as the most spectacular example (Meier). The theoretical back-
groundisexplainedandinterestingobservationsaredescribedforliquefaction
shocks, wave splitting and of vortical instabilities, with a discussion of open
questions that still remain.
The last chapter starts with a description of shock waves interacting with
perforated rigid sheets, with textile materials, with flexible foams, for dif-
ferent shock strengths and for different inclinations (Skews). From carefully
designed experiments a clear physical picture is obtained of the nature and
the importance of the different processes involved. Special attention is given
to peak pressure amplification that is observed for porous slabs adjacent to a
solid wall, subjected to shock wave compression.
When describing wave propagation in porous media, two different com-
pression wave modes have to be distinguished (Smeulders and van Dongen).
This is predicted by linear theory,which yields important information on dis-
persionanddamping,impedancesandamplituderatiosandtheimportanceof
boundaryconditions.Differentnon-lineartheoreticalmodelswillbediscussed.
Results are compared with shock wave reflection experiments with rigid and
flexible porous materials.
While the first examples of shock interactions with porous materials deal
with shock waves of moderate strengths, the last contribution to this book
(Golub and Mirova) covers compaction, plastic deformation, and destruc-
tion of granules caused by the interaction of a porous material with very
strong shocks (1–10 GPa). Attention is given to modelling of such interac-
tions, thereby reducing as much as possible its full physical complexity.
When studying shock waves in multi-phase media, one meets phenomena
on largely different length and time scales, but strongly coupled. Thermal
effects, entangled quantised vortices, cavitation and collapse, periodic for-
mation of shocks, wave splitting, anomalous thermodynamic behaviour,
interfering relaxation processes and the constructive interference of small dis-
cretesphericalshockstoglobalshocksareencountered.Thisbooknecessarily
only captures a limited part of these and related phenomena. Nevertheless,
thecontributionstothisbookwillserveasanoverviewandasanintroduction
to the fascinating world of discontinuous transport phenomena.
M.E.H. van Dongen
Contents
Part I Shock Waves in Complex Liquids
1 Shock Waves in Bubbly Liquids
Leen van Wijngaarden............................................ 3
1.1 Introduction ............................................... 3
1.2 Elements of Bubble Dynamics................................ 3
1.3 Nonlinear Compressive Waves................................ 9
1.4 Mechanisms Opposing Steepening of Compressive Waves ........ 11
1.4.1 Viscous Stresses..................................... 11
1.4.2 Dispersion.......................................... 11
1.4.3 Relaxation ......................................... 12
1.5 Strong Shock Waves ........................................ 14
1.6 Shock Waves of Moderate and Weak Strength.................. 17
1.7 Solitons in bubbly flows ..................................... 28
References ...................................................... 31
2 Interaction of a Shock Wave with a Single Bubble
Yukio Tomita.................................................... 35
2.1 Introduction ............................................... 35
2.2 Violent Bubble Collapse and Liquid Jet Formation ............. 37
2.3 Shock Wave–Bubble Interaction near Boundaries ............... 48
2.4 Bubble Collapse Induces High Temperature and
Sonoluminescence .......................................... 59
References ...................................................... 63
3 Shock Induced Cavitation
Valery K. Kedrinskii ............................................. 67
3.1 Introduction ............................................... 67
3.2 Real Liquid State (Nucleation Problems) ...................... 68
3.3 Bubble Clusters ............................................ 72
3.3.1 Formation Mechanisms............................... 72
3.3.2 Mathematical Model of Cavitating Liquid .............. 73
X Contents
3.3.3 Comparison with Experiments ........................ 75
3.3.4 Dynamic Strength of Liquid .......................... 76
3.3.5 Tensile Stress Relaxation (Cavitation in a Vertically
Accelerated Tube)................................... 77
3.4 Methods of Hydrodynamic Pulse Tubes and Experimental
Technique ................................................. 80
3.4.1 Hydrodynamic Tube of Rarefaction.................... 80
3.4.2 Hydrodynamic Shock Tube, Pulse X-Ray Method
and Resolution of Cavitation Zone Dynamics ........... 80
3.4.3 “Frozen” Profile of Mass Velocities in a Cavitation Zone.. 83
3.5 Comparison of the Initial Stages of Disintegration of Solids
and Liquids................................................ 85
3.5.1 Liquids ............................................ 85
3.5.2 Solids.............................................. 88
3.6 Shock Waves, Bubbles, and Biomedical Problems............... 89
3.6.1 General Questions and Statements..................... 89
3.6.2 Some Results on Modeling of ESWL Applications ....... 92
References ...................................................... 95
4 Shocks in Cryogenic Liquids
Masahide Murakami.............................................. 99
4.1 Cryogenic Fluids and Superfluid Liquid Helium ................ 99
4.1.1 Cryogenic Fluids ....................................100
4.1.2 Superfluid Liquid Helium (He II)......................102
4.2 Shock Waves in He II .......................................112
4.2.1 Compression Shock Wave ............................112
4.2.2 Thermal Shock Wave ................................116
4.2.3 Superfluid Shock Tube Facility........................122
References ......................................................130
Part II Shock Waves and Phase Transition
5 Shock Waves in Fluids with Interphase Transport
of Mass, Momentum and Energy (Vapour–Droplet Mixtures
and Solid-Particle-Laden Gases)
Abhijit Guha ....................................................135
5.1 Introduction ...............................................135
5.2 Relaxation Gas Dynamics for Pure Vapour–Droplet Mixtures
and Detailed Structure of Shock Waves........................137
5.2.1 Relaxation Phenomena...............................137
5.2.2 Gas Dynamics ......................................143
5.2.3 Detailed Structue of Shock Waves ....................148