HYPERSONIC AERODYNAMICS Prepared by Mohammad Fazlur Rahman Asst.
Professor (AERO) B. S. Abdur Rahman University This document
contains the basic information regarding the subject matter
HypersonicAerodynamics.Theeffortismadetohelpthestudents
gettingexposuretothesubjectaswellasunderstandthebasicand
fundamental behaviour of the fluid when the flow takes place at
very high speed in the hypersonic regime. It must be noted that
this document in no
waycanavoidtheuseoftextbooks.Forthedetailedanddeep
understandingofthesubjectmatterstudentsmustreferthetextbooks.
WhileprovidinginformationthesyllabusoftheB.S.AbdurRahman University
has been targeted. Introduction to Hypersonic Aerodynamics Notes on
Hypersonic Aerodynamics prepared by Asst. Professor MohammadPage 1
Contents Motivation
...............................................................................................................................
2 Introduction
............................................................................................................................
6 Some historical facts
.......................................................................................................
8 Comparison of Supersonic and Hypersonic Vehicles
.......................................... 16 Types of hypersonic
vehicles
.....................................................................................
28 Hypersonic Atmosphere
...................................................................................................
35 Definition of Hypersonic Flow
....................................................................................
35 Hypersonic flow characteristics
.................................................................................
36 Thin Shock Layers
...........................................................................................................
36 Entropy Layer
..................................................................................................................
37 Viscous Interaction
..........................................................................................................
38 High Temperature Flow
...................................................................................................
40 Low Density
Flow............................................................................................................
43 Recapitulation
..................................................................................................................
48 Extra thinking
..................................................................................................................
49 Hypersonic Studies
..........................................................................................................
50 Summary
............................................................................................................................
52 Notes on Hypersonic Aerodynamics prepared by Asst. Professor
MohammadPage 2 Motivation
Travellingandreachingsomewhereasfastaspossibleistheveryfascinatingideaforany
one.Evenforthecargotransportation,wenormallyliketomakethecargosreachtoits
destinationsassoonaspossible.Andthishasledtodiscovernewtechnologiesandinvent
newconceptvehiclescontinuouslywhichcantravelwithveryhighspeed.Highspeedhas
beenfascinatingthehumankindsincethebeginningthatshowsprinters100mrunis
inspiredandpeopletakeanyavailablemeanstoimprovetheexistingrecordevenbythe
fraction of seconds. No doubt speed thrills.
Whenwetalkaboutspeed,inthecaseoftravelingontheground,wenormallygoforhigh
speedsuptonotmorethan0.3Machnumber.Whenwetravelinthesky,weevenliketo
cross the sonic barrier and would like to go for supersonic speeds.
But thats more than 100 years old story. Now we are in the space
age and we talk about space travels and supersonic doesnt charm the
space scientists any more. Now we talk about the hypersonic speeds.
Travellinginthespacewithsupersonicspeedsgivelittlecharmandeventheslowest
traveling spacecraft is very near to hypersonic speeds. Speed of
moon going round the Earth is 1023 m/s!!! Taking the low
temperature there in the space, this speed will be more than
even5M.soanormalspeedinthespacegoesinthehypersonicrange.Takingthecaseof
EarthsrevolutionaroundSun;itrevolveswithanaveragespeedof30,000m/s.Students
shouldfindthemoreaccurateresultsbytakingtheorbittobeellipticalandrealisethe
veracity of the figures. (Note: The average distance of moon from
earth is3.85 108 m and assuming moon completes its revolution
around the earth 27.32 days on the average, average speed of the
moon around the Earth is 1023 m/s.) Humanity is seeking great hope
in the space science and it is said the future of the humanity
liesinthespace.Ifthesciencefictionistobebelieved,spacetravelandinterplanetary
transportation is going to be a reality sooner or later. Space is
so wide apart that distances are
measuredinlightyears,notinkilometerormiles.Insuchasituation,onlythevehicles
travellingwithhypersonicspeedsisgoingtohelpus.Soinoneworditcanbesaidthat
hypersonicvehiclesisthefutureoftransportationandstudyingthehypersonicspeedinthe
aerospace science is a necessity. Hypersonic is not only related
with the space travel. Even in the case of aircraft it is tried to
make some vehicle which can travel at the hypersonic
speeds.Hypersonic vehicle travelling Notes on Hypersonic
Aerodynamics prepared by Asst. Professor MohammadPage 3
intheskycanmakeaquicktransportationforthehumanbeingaswellascargo.Sointhe
aeronautics also, hypersonic speed vehicles make important
subject.In1913theLondonnewspaperTheDailyMailofferedaprizeof10,000to"theaviator
who shall first cross the Atlantic in an aeroplane in flight from
any point in the United States
ofAmerica,CanadaorNewfoundlandandanypointinGreatBritainorIreland"in72
continuous hours".
Ajetlinertakesmorethan13hours40minutestocrossoverPacificrouteandreachfrom
Kuala Lumpur to Heathrow. A supersonic passenger aircraft which
used to take only half the
timetakenbyitscontemporaryjetlinersinitsregularflights,frequentlyflewinthe
transatlantic route form London and Paris to New York and
Washington and Barbados. Speed
hasbeenthrillingandattractingthehumankindsincethebeginningandraceisstillon.
Peoplehavenotrestedandnowstartingfromlowsubsonicspeedandgoingthroughhigh
supersonic speeds, now the era of hypersonic has begun. A
hypersonic plane will hardly take nearabout 2 hours to go to
Heathrowfrom KualaLumpur. A hypersonic vehicle whichcan travel Mach
7 to 12 can take man from New York to Tokyo in less than two hours.
Notes on Hypersonic Aerodynamics prepared by Asst. Professor
MohammadPage 4 Concorde taking off Distance between Kuala Lumpur,
Malaysia to Heathrow, London Notes on Hypersonic Aerodynamics
prepared by Asst. Professor MohammadPage 5 Notes on Hypersonic
Aerodynamics prepared by Asst. Professor MohammadPage 6
Introduction Now we are already know that humanity is opting for
higher and higher speed which not only gives thrilling effect
rather it also helps in the growth of humanity in so many ways. We
are living in the space age so hypersonic is the only option we
must go for. We have already seen
thateventhesimplespeedassociatedwiththespacecraftarehavinghypersonicspeed
associated with it. So hypersonic speed and objects associated with
the hypersonic speed are
goingtobetheprimeareaofconcerninthenextfutureofhumanity.Questionis;whatis
hypersonic speed? What is the definition of it?
Whenwestudythedynamics,baseduponthevariousrangesofspeedswecanclassifythe
study of motion in following ways: Sl. No. RangeDescription 1. Low
subsonic speed
Inthisregionobjecttravellingwithverylowsubsonicspeeds
arestudiedinwhichcompressibilityeffectisneglectedand
viscosityisthemaincriteriawhichisconsideredasitaffects
mostoftheflowphenomenaspeciallytheappearanceof boundary layer. This
ranges from 0.0 to 0.3 M 2. High subsonic speed In this region,
though speed is still subsonic, it is high enough
tocausethecompressibilityeffectandhenceitmustbe
consideredwhileanalysingtheflow.Viscosityoftheflow
graduallystartlosingeffectinthisregion.Thisnormally ranges from 0.3
M to 0.85 M. 3. Transition speed In this region flow over any body
is partly sub sonic and partly supersonic extra care has to be
taken while analysing the flow.
Theflowbehavesinboththeway,subsonicandsupersonic. This type of
behavior normally starts at 0.8 M and sustains till 1.2 M. After
the upper limit flow becomes fully supersonic. 4. Supersonic speed
In this region flow speed is more than 1.0 M and flow is mostly
characterisedbycompressibilityandappearanceofshocks
whicharecompressionwavesinnature.Duetotheexistence
ofshocksflowbecomesdiscontinuousandsuddenrisein
temperature,pressure,densityandentropyisfeltintheflow. Hypersonic
Aerodynamics (Introduction to Hypersonic Aerodynamics) Notes on
Hypersonic Aerodynamics prepared by Asst. Professor MohammadPage 7
Sl. No. RangeDescription
Shockeffectissoprominentinthisregionthatflowcan actually be taken
as inviscid for all practical purposes. 4. Hypersonic speed In this
region even the supersonicconcepts are not very much
applicable.Thisregionischaracterisedbythespecific
phenomenawhichtakeplaceatveryhighspeedswhichisthe main topic of
discussion of the following session. What is hypersonic speed and
at which Mach number the vehicle can be said to be travelling at
hypersonic speed? A very interesting and intriguing type of
question it is. P. L. Roe made a comment in his lecture at Von
Karman Institute, Belgium; January, 1970:
Almosteveryonehastheirowndefinitionofthetermhypersonic.Ifweretoconductsomethinglikean
opinion poll among thosepresent,and askedeveryoneto namea Mach
number above which theflow a gas should properly be described as
hypersonic, there would be a majority of answers round about five
or six, but it would be quite possible for someone to advocate, and
defend, numbers as small as three or as high as 12.Before we
actually get into the deep discussion for proper comprehension of
hypersonic and
itsbehaviour,letusknowalittleaboutthehistoricalfactsassociatedwiththehypersonic
speeds and event. Notes on Hypersonic Aerodynamics prepared by
Asst. Professor MohammadPage 8 Some historical facts
OnFebruary24,1949rocketV2/WACCorporalwaslaunchedfromtheWhiteSand
Proving Ground test range. This rocket was brought from Germany
after the WWII and it was an attempt to demonstrate the use of use
of multistage rocket to achieve high speed and high
velocity.ThiseventwaspartofabigprogrammelabeledBumperbytheU.S.Army.Till
then all the previous rockets launched either in America or in
Europe had utilised the single
stage.V2itselfwasasinglestagerocketandWACCorporalwasaddedtoittoprovidean
extra stage. V2 took the flight to 100 miles of altitude and
attained the velocity of 3,500 mph,
atthispointWACCorporalwasignitedandtheslenderupperstage(WACCorporal)
accelerated to maximum velocity of 5150 mph and reached an altitude
244 miles. This broke the earlier record of 130 miles set by V2
rocket alone. After reaching the peak altitude, WAC Corporal noses
over and careers back into the atmosphere at about 5000 mph.In
doing so, it became the first object of human origin to achieve
hypersonic flight. It was the first time any vehicle has flown at a
speed five times faster than the speed of sound. An interesting
part of
thisstoryis,despitethepenplottercharteditscoursebackontheearth,andtheWAC
Corporal was never found back in the desert. However the charred
electric switch and part of the tail section were found later after
almost one year in April, 1950. V2/WAC Corporal lift off on
February 24, 1949, the first object of human origin to achieve
hypersonic flight. Notes on Hypersonic Aerodynamics prepared by
Asst. Professor MohammadPage 9
Anothereventoftheinterestinthepresentdiscussiontookplaceinasmallvillagecalled
SmelookaintheTrenovdistrict,SaratovregionofRussia.OnApril12,1961astrange
looking object landed just now under the canopy of parachute. The
surface of the capsule is charred by high temperature and it
contained three windows covered with heat resisting glass. Inside
the capsule is Flight Major Yuri Gagarin who has went in space by
sitting on the top
ofarocketandjustnowreturnedwhilehavingafreefallintheearthsatmosphere.Yuri
GagarinwentinspaceinhisspaceshipcalledVostokIandenteredintotheorbittogo
around the earth. The orbit of this space has minimum distance from
earth atperigeeequal
to175kmandmaximumdistancefromtheearthatitsapogeehas302km.Itenteredinto
theatmospherebyfiringtheretro-rocketaftergoingroundtheearthintheorbitwith
specification mentioned above. During re-entry the capsule entered
into the atmosphere with
aspeedinexcessof25timesthespeedofsound.YuriGagarinbecamethefirstmanin
history to experience the hypersonic flight. Entire flight of the
Yuri Gagarin from takeoff to
landingtookalmost108min.Theseprecious108min.madeamangoinspace,goaround
the earth and come back on earth. Vostok I, in which Russian Major
Yuri Gagarin became the first human to fly at hypersonic speed,
during the world first manned, orbital flight, April 12, 1961.
Notes on Hypersonic Aerodynamics prepared by Asst. Professor
MohammadPage 10 Some pictures of interest: V2 Rocket Model Big
Bertha Rocket Model V2 firing Notes on Hypersonic Aerodynamics
prepared by Asst. Professor MohammadPage 11 Vostok 1 Notes on
Hypersonic Aerodynamics prepared by Asst. Professor MohammadPage 12
Vostok 1 Capsule (Schematic view) Notes on Hypersonic Aerodynamics
prepared by Asst. Professor MohammadPage 13 Vostok 1 Capsule (The
recovered one) Notes on Hypersonic Aerodynamics prepared by Asst.
Professor MohammadPage 14
Latertheyear1961becamethebumperyearforthehypersonicflights.OnMay5,AlanB.
Shepherdbecomesthesecondmaninthespace.HetakesasuborbitalflightoverAtlantic
Ocean reaching an altitude of 115.7 miles, entering the atmosphere
at a speed above Mach 5.
ThenonJune23,U.S.AirForcetestpilotMajorRobertWhitefliestheX-15airplaneat
Mach 5.3. This record was bettered by White on November 9, by
flying the X-15 at Mach 6. Air Force Major Joe Eagle with X-15 X-15
Notes on Hypersonic Aerodynamics prepared by Asst. Professor
MohammadPage 15 In the military application, many vehicles like
rockets, missiles and the space shuttle during re-entry travel at
very high speed in the hypersonic range. The urge for the high
speed travel can be understood by this fact that starting from the
Write Brothers flyer which flew 35 mph
atsealevelin1903,wealreadyhaveaircraftwhichflewat400mphat30,000ft.during
theWWIIandthentransitioningto1200mphsupersonicflightsat60,000ft.altitudein
the 1960. Not to forget the flights of experimental X-15 at the
hypersonic speed. On August 23,1963X-15flewat
Mach7atanaltitudeof354,200 ft.Thisraceofflyinghigherand
higherspeedwascappedwiththeeventofspaceshuttlere-entrywithMach25intothe
Earthsatmospherefrom200milelowearthorbit.Ifweplotthegraphagainstthetime
linethenweshallfindthatthespeedaswellasaltitudebothhaveincreasedexponentially
over the time in the last 100 years. Above were the examples of
manned vehicles in the civilian uses. Taking into account of the
militaryapplicationsandmissilesandrocketsfurtherconfirmsthepassionofhumankind
towardshighspeed.IntercontinentalballisticmissilesweredesignedtoflyatMach25
during1950s.When
thesafetyconcernisnotthereandsafelandingisnotexpected,speed
limitautomaticallybecomeshighforthevehicle.Intheraceofhighspeedformanned
mission,historiceventofApollospacecraftleadstherace,foritssuccessfulreturningthe
men from Moon while reentering at Mach 36 in 1969 followed by the
Mach 25 Mercury, Gemini and Vostok manned orbital space missions of
1960s. FlightatthisendofspectrumiscalledHypersonic
Flightsandtheaerodynamicsandgas dynamics characteristics of such
flights are classified as Hypersonic Aerodynamics.
Onceitstartedthereisnoendtoitandeffortsaremadetoreachhigherandhigherspeed
which will enable the interplanetary travel a reality one dayIN
SHAA ALLAH. Notes on Hypersonic Aerodynamics prepared by Asst.
Professor MohammadPage 16 Comparison of Supersonic and Hypersonic
Vehicles Hypersonic aerodynamics is different from the more
conventional and experienced regime of
supersonicaerodynamics.Toknowdetailsofthesedifferences,wemustwaittillwe
comprehend and the terms and basic ideas of hypersonic
aerodynamics. Some features which are related to vehicle shape and
other features can be discussed here.
PicturebelowshowsasupersonicairplaneLockheedF104.Thisaircraftisdesignedfor
sustainedsupersonicflightatMach2.Itsbodyandoutershapeemploysagooddesign
basedupontheprinciplesofsupersonicaerodynamicdesign.Asharp
needlelikenoseand
slenderfuselage,verythinwingsandtailsurfaceswithsharpleadingedgeswith3.36
percent of thickness to chord ratio and aspect ratio as low as
equal to 2.45 for the straight wing itself. All these are efforts
to make the wave drag as low as possible as we know that in
thesupersonicrangeofflightsurfacefrictiondragissupersededbythewavedragwhich
becomeverymuchprominentduetoappearanceofsupersonicwaves.A3viewfigureof
LockheedF104isgivenbelowforthebettercomprehensionofthesupersonicdesignshape
of the aircraft. Lockheed F104 Notes on Hypersonic Aerodynamics
prepared by Asst. Professor MohammadPage 17 3View design of
Lockheed F104
Thedesignofsupersonicvehiclewasatemptingreplicaforthehypersonicvehiclesalso
duringtheearlydesignofhypersonicvehiclesin1953.ThatswhyRobertCarmanand
HubertDrakeofNACAdesignedtheirhypersonicplanewithsharpnoseasseenbelow.
Supersonicdesigninfluenceisclearlyevidentinthedesignitself.Atthattimeideaof
hypersonic aerodynamics was in its infancy stage. Drake-Carman
hypersonic aircraft (Proposed in 1953) Notes on Hypersonic
Aerodynamics prepared by Asst. Professor MohammadPage 18 Just seven
years later a new spacecraft X20A Dynasoar was designed with
complete contrast and a completely different look has emerged.
X-20A Dyna Soar Space Orbital X-20A Dynasoar with its powerful
engine Notes on Hypersonic Aerodynamics prepared by Asst. Professor
MohammadPage 19 X-20A Dynasoar utilises a sharply swept delta wing
with blunt, rounded leading edge and
ratherthickfuselage.Fuselagewasplacedonthetopofthewingsothatentireunder
surfaceofthevehiclewasflat.Itwasdesignedtobeanexperimentalaircraftforrocket
powerd flight at Mach 20. Eclipsed by the Mercury, Gemini and
Apollo manned space-flight, Notes on Hypersonic Aerodynamics
prepared by Asst. Professor MohammadPage 20 X-20 project was
cancelled in 1963 without production of any single vehicle.
Nonetheless the design features were uniquely hypersonic and were
later contained in the design of space shuttle. Space Shuttle Notes
on Hypersonic Aerodynamics prepared by Asst. Professor MohammadPage
21 Space Shuttle in Action Notes on Hypersonic Aerodynamics
prepared by Asst. Professor MohammadPage 22 Space Shuttle Block
Components
Sowefindthathypersonicvehicledesignsarequitedifferentfromthesupersonicvehicle
designs.Theimmediatequestionwhichcomesinourmindis,ishypersonicaerodynamics
alsodifferentformthesupersonicaerodynamics?TheanswerisYES.
Belowisthepicture of hypersonic vehicle which, was designed to
return the humans from the Moon and enter the Earths atmosphere at
extreme hypersonic speed of Mach 36. Artistic view of Apollo space
craft re-entry Notes on Hypersonic Aerodynamics prepared by Asst.
Professor MohammadPage 23 Artistic View of Apollo re-entry Notes on
Hypersonic Aerodynamics prepared by Asst. Professor MohammadPage 24
ThemainproblemapartfromAerodynamics,aerospacevehicledesignisgoingtofaceis
extremeamountofpropulsiveforcerequiredtopropelthevehicletohypersonicspeed.
ThisideaswasfirstseriouslyexaminedbytheU.S.AirForceintheearly1960sandthe
combinationofair-breathingandrocketpropulsionwasintendedtopowerthevehicle.
WorkonearlyaerospacevehiclewascancelledinOctober1963,mainlyduetothedesign
requirement exceeding the state of art at that time. The idea was
resurrected in the mid-1980s by both NASA and Department of Defense
as well as by the aerospace companies in England and Germany.
Current thinking of manned aerospace plane are shown in the picture
below.
Artists impression of hypersonic aerospace vehicles Notes on
Hypersonic Aerodynamics prepared by Asst. Professor MohammadPage 25
These trans-atmospheric aerospace planes will relyheavily on
thesupersonic combustion
RAMjet(SCRAMJet)engineforthepropulsion.Whatdistinguishesthehypersonic
transportandaerospaceplaneconceptsfromtheconventionalsubsonicandsupersonic
airplane design philosophy? It is a great area of interest
Forthesupersonicandsubsonicaircraft,thecomponentsforprovidinglift(thewing),
propulsion (the engine and nacelles) and the volume (the fuselage)
are not strongly coupled to each other. They are separate and
distinct components and easily identifiable while looking at
theairplane.Moreovertheyallareaerodynamicbodiesseparatelywhicharecombined
togetherwithamoderateinteractionwhichaffectstheircombinedperformancemildly.
Modern hypersonic aircraft has entirely opposite aerodynamics.
Notes on Hypersonic Aerodynamics prepared by Asst. Professor
MohammadPage 26 IHSTDV (Indian Hypersonic Technology Demonstration
Vehicle) Notes on Hypersonic Aerodynamics prepared by Asst.
Professor MohammadPage 27 Someofthehypersonicaircraftare shown
above in the pictures. They give clear idea about the mixed
components involvedinthedesign.Theentire
undersurfaceofthevehicleisthepart oftheSCRAMJetengine.Initial
compressiontakesplacethroughthe bowshockfromthenoseofthe
aircraft.Furthercompressionand supersoniccombustiontakesplace
inside a series of modules near the rear of the aircraft and then
the expansion of the burned gases is partially realised through
nozzle
intheenginemodulebutmainlyoverthebottomrearsurfaceoftheaircraftwhichis
sculpturedtoanozzlelikeshape.Hencethepropulsionmechanismisintimatelyintegrated
over the air-frame.
Moreover,mostoftheliftisproducedbythehighpressurecreatedbehindthebowshock
which,isexertedovertherelativelyflatundersurfaceofthevehicle,sothelarge,distinct
wingsarenotnecessaryfortheproductionofthehighlift.Alsohighliftcoefficientisnot
required to lift the plane because high velocity will take care of
the net lift generation for this
typeofvehicles.Alsothefuelfortheairbreathingenginetobeusedinthehypersonic
aircraftwilllikelytobeLiquidH2(LH)whichoccupiesalargevolumeowingtoitslow
molecularweightandhencedensity.Alltheseconsiderationscombineinahypersonic
vehicle in such a fashion that the components to generate lift,
propulsion, and volume are not Notes on Hypersonic Aerodynamics
prepared by Asst. Professor MohammadPage 28 separate from each
other; rather they are closely integrated in the same overall
lifting shape in direct contrast to conventional subsonic and
supersonic vehicle design.
Sohypersonicisphysicallydifferentfromthesupersonicanditisgoingtodictatethe
forthcoming age of humanity which can be easily termed as Space Age
Types of hypersonic vehicles
Bylookingintomissionrequirementsthehypersonicvehiclescanbeclassifiedinvarious
categories. Some of the missions are designed for high deceleration
in the outer atmosphere during re-entry. Hence, those flight
vehicles experience longer flight duration at high angle of attacks
due to which, blunt nosed configuration are generally preferred for
such aircrafts. On the contrary, some missions are centered on low
flight duration with major deceleration
shouldtakeplaceclosertoearthsurface;hencethesevehicleshavesharpnoseandlow
angleofattackflights.Reentryflightpathofhypersonicvehicleisthusgovernedbythe
parameterscalledasballisticparameterandliftingparameter.Theseparametersare
obtained by applying momentum conservation equation in the
direction of the flight path
andnormaltoit.Velocity-altitudemapoftheflightisthusmadefromtheknowledgeof
these governing flight parameters, weight and surface area.
Ballistic parameter is considered for non-lifting reentry flights
like flight path of Apollo capsule, however lifting parameter is
considered for lifting reentry trajectories like that of space
shuttle. Therefore hypersonic flight vehicles are classified in
four different types based on the design constraints imposed from
mission specifications.
1.Re-entryVehicle(RV):Thesevehiclesaretypicallylaunchedusingrocket
propulsionsystem.Re-entryofthesevehiclesiscontrolledbycontrolsurfaces.Large
angleofattackflightofbluntnosedconfigurationsistheneedoftheseflights.Space
shuttle(US),BURAN(Russian),HOPE(Japan)andHERMES(European)aresome
examples of these kind vehicles.
2.CruiseandAccelerationVehicle(CAV):Inthesetypes,highspeedismore
important and slender configurations with low angle of attack
flights are main features of
theseflights.Thesevehiclesarepreparedforhighheatingloadswithablativecooling
system. Air breathing propulsion system of ramjet or scramjet type
is generally preferred for these vehicles. Sanger, which is a two
stage (TSTO) hypersonic vehicle, has first stage with air breathing
propulsion and second stage is propelled with rocket. Hence first
stage of Sanger falls in CAV category for which separation takes
place at Mach 7. Notes on Hypersonic Aerodynamics prepared by Asst.
Professor MohammadPage 29 3.Ascent and Reentry Vehicle (ARV): These
vehicles have opposite requirements for
theirdesignduetodualduty.Theirascentflightisdominatedbythefuelrequirement
andthereentryflightisdominatedbyaero-braking.Rocketorair-breathingpropulsion
canbepreferredfortheseflights.NASPorNationalAerospacePlaneofUS,Space
PlanebyJapanandHOTOLaresomeexampleofthesevehicles.Intercontinental
ballisticmissilesfallinthesamecategorywhichareusedinthebattlefieldduringwar
time. 4.Aero-assisted Orbital Transfer Vehicle (AOTV): Ionisation
and hence presence of plasma in the vicinity of the spacecraft is
the major concern of these vehicles. This new hypersonic vehicle
concept is the aero-assisted orbital transfer vehicle (AOTV) which
will be employed to transfer material and people between the space
shuttle in low
earthorbitcalledLEO(about300kmabovethesurfaceofearth)andsatellitein
geosynchronousorbits(35,000kmabovethesurfaceofearth).WhentheAOTVleaves
thegeosynchronousorbitandreturnstolowearthorbit,itwilldipintotheearths
atmosphereanduseaerodynamicdragtoreduceitsvelocity.Thusenablingrendezvous
with the space shuttle. AOTV will be the high-flying hypersonic
flying designed to fly at no less than Mach 30 and at an altitude
no less than 250,000 ft. altitude. Each of these four types of
vehicles face different flight challenges based upon their missions
andflightconfigurations.Thesechallengesformthetopicofresearchinthefieldof
hypersonic aerodynamics. Notes on Hypersonic Aerodynamics prepared
by Asst. Professor MohammadPage 30 Challenger and Buran Hope of
Japan and Hermes of Europe Notes on Hypersonic Aerodynamics
prepared by Asst. Professor MohammadPage 31 Sanger II NASP of NASA
Notes on Hypersonic Aerodynamics prepared by Asst. Professor
MohammadPage 32 NASP of NASA HOTOL Notes on Hypersonic Aerodynamics
prepared by Asst. Professor MohammadPage 33 HOTOL ICBM,
Intercontinental Ballistic Missile Notes on Hypersonic Aerodynamics
prepared by Asst. Professor MohammadPage 34 Cassini inter-planet
trajectory Notes on Hypersonic Aerodynamics prepared by Asst.
Professor MohammadPage 35 Hypersonic Atmosphere It is a new term we
aregetting introduced with, hypersonic atmosphere.What is it? A
good intriguing question. In all the other regime of speeds, we
normally associate the body and its speed with the regime. Like we
call subsonic speed, or supersonic speed. This speed may be the
speed of the object flying with the particular speed or it may be
the speed at which flow is passing over the body. But in both the
cases, we normally associate the speed with the speed regime. Why
talk about the atmosphere in the case of hypersonic?
Theanswerliesintheverydefinitionofthehypersonicitself.Definitionofflowregimeis
based on the Mach number of the flow. If Mach number is below unity
then the flow is called as subsonic. Sonic flowhas Mach number
exactlyequal to one howeverflow in the narrow
rangeofMachnumberbetween0.8-1.2iscalledastransonicflow.WhentheflowMach
number exceeds beyond 1 then flow is called as supersonic flow.
Definition of Hypersonic Flow
Forallthesethreeregimes,itisappropriatetotaketheMachnumberasthebasisof
definition of the flow regime, but in the case of hypersonic flow
regime it is not the specific
Machnumberwhichmakesaflowregimetobehypersonic,rathersomeofthecertain
physicalphenomenawhichstartexhibitingintheatmosphere,tellthattheflowisactually
hypersonic. And these certain physical phenomena start showing upon
as early as Mach 3 or
Mach4,butinaverybeginningmanner.TheygraduallygrowwithMachnumberand
becomefullydevelopedatnearaboutMach10orMach12.Sobylookingatthedefinition
two things are clear right now. 1.There is not fixed Mach or sharp
boundary of Mach number which will make the flow
hypersonicononesideandnon-hypersonicontheotherside.So,asperthethumbrules,
when flow speed exceeds five times the sound speed, we start
treating it as hypersonic flow.
Howeverhypersonicflowhascertaincharacteristicswhich,whenexperiencedintheflow,
should then only be termed as hypersonic. So the thumb rule is just
a thumb rule as it is said to be, and there is not great change in
the flow regime and flow behaviour takes place when
theflowMachnumberchangesfrom4.99to5.01likewhatweseeinthecaseflowgoing
from subsonic at Mach 0.99 to supersonic Mach 1.01. Notes on
Hypersonic Aerodynamics prepared by Asst. Professor MohammadPage 36
2.Itisalsoclearthatitisthecharacteristicoftheatmospherewhichdefinesand
hypersonicnatureoftheflowratherthantheMachnumberoftheflow.Hencetherecomes
the term hypersonic atmosphere in use. Hypersonic flow
characteristics
Theatmosphericcharacteristicswhichdefinethehypersonicflowregimearementioned
below. Thin Shock Layers The region between the shock and the body
(flight vehicle) is known as shock layer. The
picturebelowgivestheideaabouttheshocklayerregioninthecaseofanobliqueshock
appearinginthecaseofflowovera wedge with some wedge angle. For the
samewedgeangleasthefreestream Machnumberisincreasedthewave angles
becomes smallergradually then thereisverythinregionavailable
betweenthesolidboundaryandthe shock wave for the after stream flow
to
takeplaces.Sothesameflowwhichbeforetheshockwastakingplaceinamorewideand
openregion,isnowforcedtoflowinacomparativelynarrowregionaftertheshock.This
decrement of thewave angle with the increasingMach number is also
evident from the relation.When theflowMachnumber isveryhighinthe
hypersonicregion,the thicknessoftheshock layercomesdown
drasticallyandthis phenomenonisalso markedbythehigh
densityoftheflowin thethinshocklayer region.Thisisrequired
tocompensatethedecrementinarea,sothatcontinuitycanbemaintainedasthelawof
Notes on Hypersonic Aerodynamics prepared by Asst. Professor
MohammadPage 37
conservationofmasscannotbeviolatedinanycase.Forexampleweintheabovecaseof
flow over a wedge of 200 half wedge angle when the Mach number is
of the order of 20 to 25,
theweaveanglebecomessomewhat220.Ifthewedgeangleissmallerlike150thewave
angle becomes very close to 180. This is correct for the
calorically perfect gases which have constant specific heat
capacities. This interpretation of thinness of shock layer for
calorically perfect gas, is also applicable for the thermally
perfect gas and chemically reacting gas, although their specific
heat capacities may not remainconstant at that level.As a matter of
fact inthe case of chemicallyreacting gaseous flow when the
temperature is very high, this thin region can be expected to be
further thin. So this is a basic characteristic of the hypersonic
flow that the shock layer is very thin and shock lies very close to
the solid body surface.
Whenthethinshocklayersbecomesthinenoughtobecomparablewiththethickboundary
layer growing over the solid surface, the situation becomes little
bit complicated, because the
thinshocklayerstartsinteractingwiththethickboundarylayer.Thisproblembecomes
importantforthelowReynoldsnumberflow.However,whentheReynoldsnumberishigh,
the flow in the shock layer is practically inviscid, the thinness
of the shock layer becomesa
theoreticaladvantage,andageneralanalyticalapproachcalledthinshock-layertheory
becomesapplicable.Thisthinkshocklayertheorybecomesahandytoolandisfrequently
usedinthehypersonicaerodynamicsforapproximatecalculations.Thistheorywas
postulatedbytheIsaacNewtonin1687;weshallstudythistheoryinmuchdetailsalittle
later. Entropy Layer When we have a conical leading edge, the shock
remains attached with the body and strength
oftheshockremainsalmostsameforaconsiderablelength.Inthecaseofhypersonic
vehicles,wenormallyhavebluntleadingedgeforwewantadetachedshockhere.This
detached shock varies in its strength form normal shock at the
leading edge to strong oblique
shockandthenweakobliqueshockandthenfinallyaMachwave.Wealsoknowthatthe
Notes on Hypersonic Aerodynamics prepared by Asst. Professor
MohammadPage 38 entropy change in the flow depends upon the
strength of the shock. Stronger the shock, larger
willbethechangeintheentropy.Alsotheshocklayerforthestrongershocknearthenose
will be very thin, with a small shock detachment distance, d. So
the entropy gradient will be
verylargeintheregionnearnose,i.e.largeentropychangewilltakeplaceinaveryshort
region.Nowastheshockstrengthdecreasesdownstreamflow,alayerofentropyvariation
getsformeddownstreamoftheshockanditiscalledentropylayer.Thisstrongentropy
layer flows downstream and wets the body for a large distance from
nose. Now the boundary
laterwhichgrowsnearthesurface,growsinsidetheentropylayerandisaffectedbyit.
Boundary layer is essentially a region of
non-zerovorticityduetohighviscous effectavailableintheregion.Since
entropylayerisalsoaregionofstrong vorticityaccordingtotheCroccos
theoremfromclassicalcompressible flow;thisinteractionbetweenthetwo
regionsisalsocalledasvorticity interaction.Thepresenceofentropy
layercausesanalyticalprobleminthe
standardboundarylayercalculationonthesurface,becausethereisnotcertainideanow
aboutwhatwillbeproperconditionattheouteredgeoftheboundarylayer.Thisentropy
layer is essentially a property of hypersonic flow which also takes
part in its definition. Viscous Interaction
Weknowthatformationofboundarylayertakesplacenearthesolidsurfaceduetonoslip
conditionintheviscousfluidflow.Nowletusrefertotheabovefigureagainandconsider
theboundarylayerflowovertheflatplateinthehypersonicregime.Highvelocity
hypersonicflowcontainshugeamountofkineticenergy,butinsidetheboundarylayer,
owingtotheeffectofviscosity,thefluidhastocometorestinthelayeradjacenttothe
surfaceandmustincreasegraduallytoattainthefinalflowspeed.Sowithintheboundary
layer,thelostkineticenergyistransformedintointernalenergyofthegas.Thiseffectis
called viscous dissipation. We already know from the ideas we
gathered during early classes of heat transfer that; increased
internal energy actually increases the temperature of the gas. A
typical temperature profile in the boundary layer in the hypersonic
regime has been shown in the figure below. Notes on Hypersonic
Aerodynamics prepared by Asst. Professor MohammadPage 39
Itisverymuchevidentthatvelocityvariationisalmostsameasinanormalhighspeed
boundary layer profile but temperature variation is a little bit
typical here. Near the boundary temperature increases and becomes
even larger than the flow temperature. This is due to the
transformationofhighkineticenergyintointernalenergyofthegas.Nowthisincreased
temperaturedoestwoworks.Firstlythisincrementoftemperatureinturn,affectsthe
viscosity and increases it (we know this by the knowledge of the
effect of temperature on the viscosity of gases). This increased
viscosity affects the growth of boundary layer and there is
arapidincreaseintheboundarylayerthickness.Inadditiontoit;becausethepressure
remainsconstantintheboundarylayerinthedirectionnormaltosurface(weknowthis
throughourknowledgeduringtreatmentofforcedconvectionoveraflatplateinboundary
layertheory),theincreaseintemperature ,resultsindecreaseindensity
throughthe equationofstate = ,where
isthespecificgasconstant.Soinordertopassthe required mass through
the boundary layer, at decreased density, the boundary layer
thickness
mustbelarger.Soagrowthinboundarylayerthicknessisexpected.Bothofthese
phenomenacombinetomaketheboundarylayerthicknessgrowfasterthanthatatthelow
speed flows. Indeed, over a flat plate, boundary layer thickness
grows essentially as below:
2
SoastheMachnumberincreases,boundarylayerthicknessincreasestooanditincrease
accordingtothesquarecurve.Soitwillbecomelargeinthehypersonicregimeandthe
reason is that explained above. Notes on Hypersonic Aerodynamics
prepared by Asst. Professor MohammadPage 40
Thisthickboundarylayerinhypersonicflowcanexertamajordisplacementeffectonthe
outerinviscidflowregion.Thiswillcauseabodytoappearmuchthickerthanitreallyis.
Now due to this extreme thickness of the boundary layer flow, outer
inviscid flow is greatly
changed,andthechangeintheinviscidflowinturnfeedbacktoaffectthegrowthofthe
boundarylayer.Thismajorinteractionbetweentheouterinviscidflowandtheboundary
layer iscalledviscous interaction which takesplace in a loop. This
viscous interaction can have important effect on the surface layer
pressure distribution, hence lift, drag and stability of the
hypersonic vehicle, all are affected by it. Moreover, skin friction
and heat transfer are also increased by the viscous interaction.
Thefigurebelowillustratestheeffectof
viscousinteractiononthepressurevariation on the surface of a sharp
right circular cone at zero degree angle of attack. In the absence
of viscousinteractionpressurewillbe constant
throughout the length but it varies
duetointeractionofboundarylayerwiththe outer flow which practically
remains inviscid. It is clear that the effect of viscous
interaction isgreaternearthenoseareaanditseffect
diminishesfurtherdownstreamandfardownstreamitapproachesthevalueequaltothe
inviscid value.
(Note:Theboundarylayerattimecanbecomesothickthattheshocklayercompletelymergedwithinitand
then shock layer must be treated fully viscous and in this case
theconventional boundary layer analysis is not valid.) High
Temperature Flow We have already discussed about the high
temperature generation within the boundary layer
inahypersonicflowduetoviscousdissipation.ButdowerealisehowHIGHthis
temperature might be which is generated due to hypersonic speed?
Actually this temperature sometimes can be so high that it can
excite the vibrational energy inside the molecules, and to cause
dissociation and even ionization within the gas. If the surface of
the hypersonic vehicle
isprotectedbyanablativeheatshield,theproductofablationarealsopresentinthe
boundarylayer,givingrisetocomplexhydrocarbonchemicalreactions.Sowhetherbeit
dissociationandionizationorthehydrocarbonchemicalreaction,onbothaccounts,surface
Notes on Hypersonic Aerodynamics prepared by Asst. Professor
MohammadPage 41
ofahypersonicvehiclewillbewettedbyachemicallyreactingboundarylayer.Thisisthe
caseofboundarylayerinthehypersonicflow.Sothechemicalequilibriumhastobe
accountedwhiledoingtheseestimations.Thishappenssobecause,forthehypersonicflow,
not only the boundary layer will be chemically reacting, rather
entire shock layer too can be dominated by the chemically reacting
flows. Boundarylayerisnottheonlyregionofhigh
temperatureflowoverahypersonicvehicle.At the nose where blunt shape
is given to detach the shockandprotectthestructurefromexcessive
temperature,thebowshockhasanatureof
normalshock.Thisstrongnormalshockatvery
highMachnumbercangenerateveryhigh
temperaturebehindtheshock.Thisveryhigh
temperaturesometimescanbegoodenoughto
causethemoleculardissociationoftheglowing gas. This gives rise to a
complex situation that at theseelevatedtemperaturetheconceptof
caloricallyperfectgasdoesntremainvalidand hence assumptions of
constant thermodynamic properties gives unrealistic estimations.
Hence
itbecomesessentialtotakeintoaccountthetemperaturedependenceofspecificheatsand
theirratioasfunctionoftemperatureforrational estimates.
TakingthecaseofApollosreentryatMach36,
temperaturebehindtheshockandintheboundary layer can be estimated to
be near about 11,000 K by considering the chemically reacting gas
flow at that hightemperature.Takingconstant willgivevery high value
which is unrealistic. Thegraphbelowillustratestheideaabouthow
unrealistic the temperature estimation can become at very high
reentry vehicle velocity if we assume the gas to be calorically
perfect. Notes on Hypersonic Aerodynamics prepared by Asst.
Professor MohammadPage 42 Thedependenceof thermodynamicpropertieson
temperaturemainlycomesfrom microscopic changes in the fluid
duetoincreaseininternal energyofthefluidbythevirtue
oflossofkineticenergy. Increasedinternalenergyleads
initiallytovibrationalexcitation followedbydissociationand
finallyionizationaccordingto theextentofincreaseininternal
energy.Thiscausesthespecific heats
and
tobecomefunctionoftemperature.Sotheratioofspecificheats =
alsobecomesafunctionoftemperature.Forairthiseffectbecomesimportantabovea
temperature of 800 K. As per the order of magnitude estimate,
vibrational excitation of air takes place at around 800 K. Oxygen
dissociation starts at around 2000 K and completes at 4000 K. At
around 4000 K
nitrogendissociationcommencesandcompletesat9000K.Ionizationofthishigh
temperature air or mixture of gases starts from 9000 K temperature.
Hence the initial air with
atmosphericcompositionbecomesplasmaafter9000K.Asaresultofallthesereactions,
hypersonicvehiclegetsengulfedbyreactingboundarylayerandhightemperatureplasma.
Therefore treatment of air or any fluid flowing with hypersonic
speed over any configuration should be done properly by
incorporating all the microscopic changes which essentially leads
tochangeinthermodynamicpropertieswithtemperature.Thisdependenceishighlynon-linear,henceanalysisorpredictionofflowfieldbecomestougherinthisflowregime.
Thereforetwotypesofassumptionsaregenerallymadeabouttheflowconditionsforhigh
temperaturefluidasequilibriumflowandnon-equilibriumflow.Ifthemicroscopicchanges
or reactions are at faster rate than the movement of the fluid,
then it is treated as equilibrium flow otherwise it is treated
asnon-equilibrium flow which is difficult toanalyze. All these
difficultiesarecollectivelytermedashightemperatureeffectandarealsofrequently
referred as real gas effects although there are technical reasons
to discourage the use of this term for this effect. Notes on
Hypersonic Aerodynamics prepared by Asst. Professor MohammadPage 43
Someconsequencesofpresenceofhightemperaturereactingfluidorplasmainthevicinity
of the flight vehicle include, influence on aerodynamic parameters,
aerodynamic heating
andcommunicationblock-out.Flightparameterslikepitch,roll,drag,lift,deflectionof
control surfaces get largely deviated from their usual estimate
ofcalorically perfect gas. Presence of hot fluid near the cold
vehicle surface induces heat transfer not only through
convectionbutalsothroughradiation.Communicationwaveswhicharenecessarilyradio
wavesgetabsorbedbyfreeelectronsformedfromionizationofatmosphericfluid.This
phenomenoniscalledascommunicationblock-outwhereonboardandground
communication gets terminated. Low Density Flow
Inanormalenvironmentwhichwenormally
encounterinourdailylives,aircontainsmillionsof
particleswhicharecontinuouslyinrandommotion.
Asingleparticletravelstosomedistancetillit
collideswithanotherparticleandthenitsdirection
getschanged.Thesecollisionsarepractically100%
elasticsothereisnolossofenergy.Thedistance
moleculetravelbeforetheycollide,isnotalways
constantratheritvariesfromcollisiontocollision,
butontheaveragetheytraveladistancebetween two collisions which we
call as mean free path and is denoted by . So by definition, mean
free path is thedistancemoleculesofagastravelonthe
averagebetweenany twocollisions.At standardsealevelcondition, = .
m.Itispractically
averysmalldistance.Thisimpliesthatwhensomeonemovesat
thesealevelcondition,thenumberofimpactsofairparticleson his body
will be so large and continuous that individual impact of
theparticleswillbehardlyfeltbythebody.Thiswillfeellikea continuous
medium and the flow of medium too can be treated as continuous and
this concept of accepting the flow to be continuous in the airflow
in the technology, is called continuum. Most aerodynamic problems
are dealt with by assuming this concept to be very much valid.
Notes on Hypersonic Aerodynamics prepared by Asst. Professor
MohammadPage 44 Now as we move at higher and higher altitude the
possibility of the existence of huge number
ofparticlesinasmallspacekeepsdiminishingandparticleskeepgettingapartfromeach
otherandtheirmeanfreepathkeepsincreasinggradually.Atanaltitudeabout105km,the
mean free path of the air particles becomes as high as equal to 1
ft. Now if any one moves in
thisenvironmentthenthepossibilityofairparticlehittinghisbodywillbetoolowand
numberofparticleshittingperunitareawillalsobe
low.Sotheindividualhittingoftheparticlewillbe
feltandthenthemediumwillnolongerbefeltas continuous. It will feel
like an open region punctuated
byindividual,widelyspacedparticlesofmatter.
Undertheseconditions,theaerodynamicconcepts,
equations,andresultsbasedupontheassumptionof
continuumbeginstobreakdown;andwhenthis
happenswehavetoapproachaerodynamicsfroma different point of view,
using concepts from kinetic theory. This regime of aerodynamics is
called low-density flow. In most of the hypersonic applications low
density flow is involved specially at high altitudes flights. For
example, at about 95 km altitude, the flow in the nose region
cannot be treated as
continuum.Withthegradualincreaseinaltitude,assumptionofcontinuumflowbecomes
tenuous.Soanaltitudecanbereachedwheretheconventionalviscousflowno-slip
conditionbeginstofail.Soatlowdensities,theflowvelocityatthesurface,whichis
normallyassumedtobezeroduetofriction,takesonafinitevalue.Thisiscalledvelocity
slipcondition.Intheanalogousfashionthe,thegastemperatureonthesurface,whichis
normallythetemperatureofthesurfaceitself,nowbecomessomethingdifferent.Thisis
calledtemperatureslipconditionortemperaturejumpcondition.Ontheonsetofthese
Notes on Hypersonic Aerodynamics prepared by Asst. Professor
MohammadPage 45
slipeffect,governingequationstillassumingthecontinuumconceptoftheflow,canbe
utilisedwiththeproperconsiderationofvelocity-slipconditionandtemperature-slip
conditionsattheboundary.Howeverifthealtitudeincreasesfurther,therecomesapoint
where the continuum equation no longer remain valid and methods
fromkinetic theory must be used to predict the aerodynamic
behaviour of the flow. Finally, the air density can become so low
that only a few molecules impact the surface per unit time and
after the reflection they never collide with the incoming molecule.
Such regime is called asfree molecule flow. For
spaceshuttlethisfreemoleculeflowregimebeginsatabout150km.Soduringreentrythe
space shuttle faces a flight from a much rarified atmosphere to
denser atmosphere. This will
shiftfromfreemoleculeregime,whereindividualmoleculesimpactonthesurfaceis
important,tothetransitionregimewherenoslipconditionisimportanttofinallynormal
continuum regime where continuum of the flow becomes more
important.
Thesimilarityparameterwhichgovernstheseregimeoffreemolecule,transitionand
continuumregimesistheKnudsennumber.Knudsennumberisdefinedbytheratioof
meanfreepathoftheparticlestothecharacteristiclengthoftheflowproblem.By
definition =
.Theapplicabilityoftheflowregimeandtheirrespectivegoverning
equations which is controlled by the Knudsen number is shown in the
picture shown below. It is clear that for the < 0.2 the
continuum concept is very much valid and the continuum
Navier-Stokesequationsareverymuchapplicablethere.Howevertheslipconditionstarts
takingplaceasfortheKnudsennumberaslowas0.03.SoforlargervaluesofKnudsen
numberslipconditionstartstakingplaceandthismustbeaccountedforanyregime
with >
0.03.Thefreemoleculeflowbecomeeffectivethemomentmeanfreepath Notes
on Hypersonic Aerodynamics prepared by Asst. Professor MohammadPage
46 becomes comparable to the characteristic length i.e. =
or = 1 and then the range for
theapplicabilityofthefreemoleculeregimeextendstoinfinity.Sothetransitionregimeis
essentially contained within the range of Knudsen number 0.03 to 1
i.e. (0.03 < < 1).
NowitmustbenotedtherethatKnudsennumberactuallydependsupontwoparameters1.
Meanfreepath ()and2.Characteristiclength (
).Sobothhavetheirowneffect.Inthe space where mean free path is
very large, effectively any type of vehicle actually deals with the
free molecule regime. In the nearby space altitude where mean free
path is not very large,
theapplicabilityofthefreemoleculeregimewilldependupontheeffectivecharacteristic
length.VehicleswithlowcharacteristiclengthwillstillhavethehighKnudsennumber
effect. So the free molecule regime effect will still be applicable
there, however for the large
characteristiclengthvehicles,theregimemayhavechangedtocontinuumortransition
regime.Sothesetwoparameterscombinedlydeterminewhichwhattypeofequationsare
applicable in the flow regime.
Inthecaseofflowoveraflatplatenormallywetakethedistanceofthelocationfrom
leading edge as the characteristic length. So near the leading edge
where characteristic length is very small, the value of Knudsen
number may go equal to unity. Hence for any vehicle at any
altitude, the flow immediately at the leading edge is governed
bylow density flow. For most practical cases in the aerodynamics,
this leading edge region is very small and is usually ignored.
However for high altitude hypersonic vehicles, the proper treatment
of leading edge flow by low density flow methods is important.
Another point to be noted here is, in all the other hypersonic
characteristics we took the Mach
numberasbasisofdefinition.Likehightemperaturephenomenonorthinshocklayer
phenomenon, it is the Mach number which forms the basis and at
which we define that these
phenomenonbecomesignificantatsoandsoMachnumberwhichfallinthehypersonic
regime, but in thecase of low densityflow andfree molecule flow
this is not thecase.It is
basicallyKnudsennumberbasedphenomenonwhichbecomesimportantforanyMach
numberdependingupontheKnudsennumber.Soathighaltitudewheremeanfreepathis
very large, Knudsen number too will be large and hence a vehicle
even if it travels at Mach number, not in the hypersonic range; low
density flow methods treatment is necessary. Thats
whythisphenomenonthough,notrelatedtohypersonicMachnumber,stillimportantto
know because most of the hypersonic vehicles normally navigate in
the space where Knudsen number is very large and more or less flow
regime falls in the low density flow regime. Notes on Hypersonic
Aerodynamics prepared by Asst. Professor MohammadPage 47 On
concluding the low density regime part, up to the altitude of 90 km
from Earths surface,
whereKnudsennumberremainsbelow0.2,theapplicabilityofthecontinuumassumption
remains intact. However applicability of no slip condition and no
temperature jump condition
becomesapplicableatthevalueaslowas0.3.Abovethisaltitudetill150kmfromthe
surface of the Earth, density becomes very low and the assumption
of no-slip condition starts losing its validity. So the transition
range lies within 0.03 to 1.0 where continuum assumption can be
applied with the no slip condition correction. Beyond this altitude
of 150 km, density of the atmosphere become so low that a need for
change in governing equations arise in this
regime.Hencekinetictheoryofgasesfindsitsapplicationforhypersonicflightsatsuch
altitudes. Notes on Hypersonic Aerodynamics prepared by Asst.
Professor MohammadPage 48 Recapitulation So to recall and collect
all the ideas we gathered about hypersonic regime, hypersonic flow
is the flow where all or some of the specific phenomenon become
more important as the Mach number is increased to high values.
These phenomenon are (just repeating): 1.Thin shock layer 2.Entropy
layer 3.Viscous interaction 4.High temperature flow 5.Low density
flow.
Thefigurebelowsummarisestheentirediscussionofhypersonicspecificphenomenonina
nutshell. Notes on Hypersonic Aerodynamics prepared by Asst.
Professor MohammadPage 49 Extra thinking One question may arise
this time in mind that, are these specific phenomenon available
only
inthehypersonicregime?Arethesephenomenanotapplicabletotheotherflowregimes?
The answer is, YES. These phenomena are actually available even for
the low speed regime,
buttheirsignificanceisnotthere.Likeweknowandunderstandthatflowbecomes
compressible beyond the Mach 0.3. And gradually becomes more and
more compressible and
bythetimeitbecomeshighsubsonicregime,wedontcountviscositythatimportantand
compressibilitybecomesmoreimportantforus.Thefactis,alltheseeffectsof
compressibility and viscosity are available in every regime, but
depending upon their relative significance, we treat them important
or non-important in the various flow regimes. So at low speed the
effect of viscosity is more important than compressibility and as
the speed increases
gradually,effectofcompressibilitykeepsbecomingmoreimportantandeffectofviscosity
keeps becoming less and less important relatively. Similar kind of
concept is applicable in the
caseofhypersonicphenomenaalso.Theseeffectsareavailableinalmosteveryregimebut
their significance is very low as their effect on the behaviour of
flow is insignificant. So they
areignoredinthenon-hypersonicflowregimes.Inthehypersonicregimes,these
phenomenon become highly effective and their treatment becomes very
much important. So they are not ignored here, rather they are used
in the definition of hypersonic aerodynamics. Notes on Hypersonic
Aerodynamics prepared by Asst. Professor MohammadPage 50 Hypersonic
Studies
Hypersonicaerodynamicscanbedividedinthreeblocksandtheycomprisethreedifferent
sub regions of the fluid flow mechanics. These are: 1.Inviscid flow
2.Viscous flow 3.High temperature flow Inviscid Flow:In the
inviscid flow we normally analyse the dynamiceffects of largeMach
number and any viscous effect is intentionally ignored for the time
being. In this section we analyse the flowat verylarge Mach number
andtry to observe what happens when the free
streamMachnumberbecomeslarge,andhowthisinfluencestheaerodynamictheoriesat
highMachnumber.Inthis;compressibilityisthemaintopicwediscuss,andthen
compressibleflowphenomenalikeshocksandexpansionfansbecomemoreimportant.The
studiescanbefurtherdividedintolocalsurfaceinclinationmethodsandflowfield
consideration method. The other typical aspects followed in each
method is listed below:
Localsurfaceinclinationmethod:Newtonianflowmethod,Tangentwedgemethod,
Tangent cone method, shock-expansion method
Flow-fieldconsideration:Machnumberindependence,hypersonicsimilarity,Blast-wave
theory, Thin-shock layer theory, Method of characteristics, the
blunt-body problem, Modern computational approach (Eulers
equations).
ViscousFlow:HerethecombinedeffectofthehighMachnumberandfiniteReynolds
numberisexamined.Fluiddynamiceffectofhypersonicflowwithfrictionandthermal
conduction is the main issue in this section, but high temperature
effect is excluded here for the time being. This normally deals
with the flow in the very vicinity of the solid surface and
treatmentofboundarylayerinthehypersonicregimeisdoneinthissection.Thetechnical
aspects which are dealt with in this regime are as follows:
Basicaspects,Hypersonicboundarylayertheory,Hypersonictransition,Hypersonic
turbulentboundarylayer,ReferenceenthalpyandotherApproximateengineeringmethods,
Strongandweakviscousinteractions,Moderncomputationalmethod(Navier-Stock
equations)
Hightemperatureflow:Itthissection,importantaspectsofthehightemperaturegas
dynamicsisdiscussed.Chemicallyreactinggasesinthevicinityofthevehiclearethemain
Notes on Hypersonic Aerodynamics prepared by Asst. Professor
MohammadPage 51 issue of discussion and also how they affect the
viscous and inviscid flow are discussed. High
temperaturenormallycausesdissociationandionizationofthefluidmolecules.Itcanalso
cause the exothermic chemical reaction if some hydrocarbon are
available in the near vicinity
ofthefluidflow.Sobasicallyhightemperatureflowsectionstudiesachemicallyreacting
flow which may containplasma instead of neutral gases. High
temperatureflow finds many
applicationinthefieldsadditionaltohypersonicflows,suchascombustionprocess,
explosion, plasmas, high energy lasers etc. The basic aspects dealt
with in this section are:
BasicphysicalchemistryincludingStatisticalThermodynamicandKineticTheory,
Chemicallyreactinginviscidflow(equilibriumandnon-equilibrium),Chemicallyreacting
viscous flow (equilibrium and non-equilibrium), Catalytic wall
effects, Shock layer radiation. Notes on Hypersonic Aerodynamics
prepared by Asst. Professor MohammadPage 52 Summary
Beforeweactuallygoaheadletussummarisethehypersonicphenomena;thephenomena
whicharecharacteristicsofahypersonicregime.Thewholestorycanbetoldbytheflow
chart given below.