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T Cain

Gas Dynamics Ltd.,2 Clockhouse Road, Farnborough, GU14 !"

#am$shire, U%

tcain&gasdynamics.co.uk

ABSTRACT

Intake design for supersonic engines, in common with other engineering design problems, is application

dependent and the true challenges are in meeting performance targets over the required Mach and

Reynolds number ranges while complying with the multitude of constraints imposed by the aircraft/missile

and its mission. The fundamentals and limitations of efficient ram compression are well understood and

since !"!, #TI$, RT% and !&R!#& provide free public access to a large database of intake

e'periments conducted in the ()*+s to ()+s, the designer should be aware of problems encountered and

the fi'es applied during previous testing of isolated intakes. The outline of this lecture is a brief tour of

some historic supersonic intakes discussing the features that enable the intake to meet its requirements

and applying some reverse engineering to deduce how the designers appear to have approached the

problem. The tour is combined with an introduction to tailoring compressive flow fields by e'ploitation of

one and two dimensional flow elements.

1 INTRODUCTION

'here is an established (ormat (or lectures, books and re)ie*s concerning intakes, *ith a large section

allocated to ta+onomy, distinguishing ty$es by the number and location on the aircra(t-missile the degree

o( e+ternal and internal com$ression *hether they are based on t*o dimensional $lane (lo*s,

a+isymmetric (lo*s, or are three dimensional and *hether they are out*ard turning or in*ard turning.

'he (unction and design o( the su$ersonic di((user is then dealt *ith be(ore a discussion o( the subsonic

di((user. /ethods o( accounting (or, and controlling boundary layers are necessarily included.

'his lecture a$$roaches the sub0ect (rom a di((erent $ers$ecti)e, here *e are less concerned *ith intakes

in general, and (ar more concerned *ith the details o( selected intakes. 'he di((erence in a$$roach re(lects

a di((erence in $hiloso$hy, and teaching styles. think it is easier to e+tra$olate and e+$and (rom a

detailed small study, than to imagine or rein)ent *hat has not been re)ealed in a general o)er)ie*. hould

a less (ocused a$$roach be $re(erred, there are good re(erences that are (ree to do*nload. Re(erence 31 is

a (ine e+am$le, summarising *hat *as kno*n about intakes in 1564, *hich is $ractically e)erything

kno*n about them today. t is not that *ork done a(ter that time is redundant, but since the ground *ork

*as com$lete, later intake studies tend to be either learning e+ercises (or the indi)iduals in)ol)ed, or are

(ocussed on an a$$lication and remain un$ublished (or commercial and-or military reasons.

Fortunately *ith the ela$se o( time and the retirement o( aircra(t and missiles, the sensiti)ity o( the a$$lied

design *ork reduces, and some details enter the $ublic domain. Consistent *ith the $ers$ecti)e outlined

abo)e, this lecture takes ad)antage o( the in(ormation a)ailable on historic intakes and dra*s conclusions

regarding the design a$$roach taken. 7( $articular interest are the (eatures that enable the intake to

(unction o)er the range o( /ach numbers and the angles o( attack to *hich it *as sub0ected. 'here is

considerable risk that some o( these conclusions are erroneous but the conse8uences o( a misinter$retation

are small, the aim is not to recreate the system, but to e+$lore the design dri)ers and the res$onse to them.

( ha)e dra*n the *rong conclusions, a$ologise to the designers (or misre$resenting their creations, but

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at least should still ha)e succeeded in introducing the $roblems to be addressed and the elements that are

the keys to the solution.

2 TROMMSDORFF RAMJETS

2.1 Mach 4+amjet !"#ee$ %&i'ht $(in' ))2

'rommsdor((9s ram0et $o*ered $ro0ectiles made the *orld9s (irst su$ersonic air:breathing (lights. ;bout

26< o( the e+$erimental 1=cm diameter > series, (igure 1, *ere (ired (rom a gun *ith mu??le )elocities o(

about 1

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e8uations that describe such (lo*s *ere (ormulated and $ublished by 'aylor and /acoll *ith re(erence to

Busemann.

'here is a limit to internal contraction abo)e *hich an intake *ill not start, and instead (lo* *ill s$ill

around the co*l *ith the amount entering the engine sim$ly set by choked (lo* through the intake throatas determined by stagnation conditions do*nstream o( a normal shock standing in (ront o( the co*l. 'his

limit, no* kno*n as the %antro*it? limit, *as (irst de(ined by 7s*atitsch in the study he made (or

'rommsdor((. ; translation o( his re$ort is a)ailable as re(erence 3@ and it also contains the $roo( o( the

result (or *hich he is best kno*n shocks o( a multi shock di((user should ha)e e8ual strength (or

ma+imum $ressure reco)ery. 7ne does not need a mathematical $roo( to understand this result, it is due to

the (act that entro$y rise increases ra$idly *ith the tem$erature ratio across a shock and i( t*o shocks

*ithin a se8uence did not ha)e the same tem$erature ratio the entro$y gain o)er the stronger shock *ill

out*eigh the decreased rise on the *eaker shock *hen the (lo* is com$ressed to the same /ach number.

Figure 2: Oswatitsch's optimal multi-shock intake parameters as a function of flight Machnumber

7s*atitsch9s o$timal intake ram$ angles are most easily (ound using his $rocedure, *hich starts *ith the

/ach number u$stream o( the terminal normal shock. U$stream obli8ue shocks all ha)e this normal

com$onent o( /ach number and one can determine a corres$onding (reestream /ach number by sim$ly

ste$$ing u$stream through the chosen number o( shocks. Results (rom this calculation are $resented in

(igure 2. 'here are three $oints to note (rom the (igure ;t /ach numbers abo)e three, $ressure ratio

across each shock is relati)ely high and in most cases *ould be su((icient to se$arate the boundary layer

total de(lection o( the t*o and three ram$ intakes is )ery high and unless the de(lections are in o$$osite

sense *hich im$lies internal com$ression, the co*l *ill be at a stee$ angle im$lying high drag successi)e

de(lections increase in magnitude, some*hat like C@ in (igure 1 and unlike >4.

7s*atitsch e+$erimented *ith a biconic intake at /ach 2.5 3@, e+$loring and de(ining su$er and

subcritical o$eration Estarted and unstarted in today9s $arlance, bu?? Ethe noise (rom (lo* $ulsation during

unstable subcritical o$eration, subsonic di((user losses, and the e((ect o( boundary layer bleed and angle

o( attack. Concerns o)er sel(:starting, co*l drag, and (lo* stability, immediately relegated his shock

strength o$timisation to the role o( guidance. From the beginning, the choice o( intake ram$ angles (or a

ram0et *as kno*n to be in(luenced by much more than 0ust shock losses.

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0123456789

1011

M

pressureratio

1 shock

2 shock

3 shock

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.05

10

15

20

25

30

35

4045

50

M

totaldeflection,

deg

1 shock

2 shock

3 shock

2 raps

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0468

1012141618202224

M

deflec

tion,

deg

2nd shock

1st shock

3 raps

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.04

6

8

1012

14

16

18

20

22

M

deflec

tion,

deg

3rd shock

2nd shock

1st shock

Ramjet Intakes

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2. The E4 intake %&"# %ie&$

'o e+$lore the design dri)ers and the resulting >4 intake, (igure 1 is assumed dra*n to scale and the

su$ersonic di((user (lo* calculated using the /ethod o( Characteristics E/7C. 'he calculation is

rotational Eallo*s (or the )ariation in entro$y throughout the (lo* (ield and assumes a+ial symmetry.

Figure 3: MOC solutions for the E4 19.5/30.5biconic intake

Blue lines in (igure @ de(ine the biconic sur(ace and the co*l li$. Red lines are the calculated shocks, the

one (rom the leading edge being straight and the one originating at the cone 0unction is cur)ed as it$ro$agates through the conical (lo* o)er the u$stream cone. 'he green line traces the streamline that

interce$ts the co*l li$. 'he light blue lines are the characteristic mesh )ia *hich the (lo*(ield solution has

been de)elo$ed. 'hese characteristics are /ach lines *ithin the (lo*, running both to the le(t and right o(

a streamline at the local /ach angle. 'he right runners are directed in*ards, to*ards the centreline, in this

solution and the le(t runners are $ro$agating out*ards, as are the shocks. 'he com$atibility relations that

hold at the intersection o( the le(t and right runners enable the (lo*(ield to be de(ined in a ste$*ise $rocess

that com$letes in less than a second on a mediocre $ersonal com$uter.

ote that in this solution *e are not yet concerned *ith the internal (lo* and the interaction *ith the co*l.

'he characteristics ha)e been de)elo$ed as i( the co*l *as not $resent. ;t the mu??le )elocity EMH2.52

the t*o shocks merge abo)e the li$ and their interaction has no e((ect on the ca$tured (lo*. /id:

acceleration EMH@.= the shock interaction generates an e+$ansion (an that enters the intake. 'he tri$le$oint de(ined by the intersecting cone shocks and the resulting strong shock, sets a limit to the amount o(

e+ternal com$ression that can be obtained. Ahen the de(lection is too high, such that the (lo* is subsonic

behind the strong shock, its $osition *ill de$end on do*nstream conditions and the (lo*(ield generally

becomes unstable. Charts that de(ine limits to e+ternal com$ression set by the tri$le $oint beha)iour, are

$resented in re(erence 1.

;t the $eak /ach number o( 4.2=, (lo* that has $assed through the single shock is entering the intake.

'his is normally regarded as )ery undesirable because the stagnation $ressure o( the (lo* on the strong

shock side o( the sli$ line Ethe streamline emanating (rom the tri$le $oint is much less than that o( the

(lo* that has $assed through t*o shocks. Ahether this truly is a $roblem is de$endent on *hat back

$ressure is being a$$lied to the intake Eby the combustor *hen it is in this state. ( this is in e+cess o( the

the lo*est stagnation $ressure then one is reliant on mi+ing bet*een the t*o streams, *ithin the isolator,

. . . . . . . . . .

.

.

.

.

.

.

.

. . . . . . . . . .

.

.

.

.

.

.

.

M=2.92

M=3.5

M=4.25

Ramjet Intakes

5 - 4 RTO-EN-AVT-185

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in order (or the higher entro$y air to $ass. 'he back $ressure must al*ays be less than that obtainable by

stagnating the mi+ed (lo* and ho* this is calculated is demonstrated in the ne+t section, be(ore returning

to a discussion o( the >4 intake design.

2.4 Steam th(st an$ ,e-ta t" sh"ck &"sses

/ost su$ersonic di((users $roduce non uni(orm (lo*s, either as a result o( skin (riction creating boundary

layers, or non uni(orm com$ression such as that $roduced by a conical com$ression sur(ace. 'he >4 intake

at /ach 4.2= is a rather e+treme e+am$le, *ith non:uni(ormity inherent in the com$ression on the (irst

cone Ealthough the straight shock guarantees uni(orm entro$y increase, the streamlines near the sur(ace

ha)e been sub0ect to isentro$ic com$ression *ithin the shock layer as they are turned to be asym$totically

$arallel *ith the sur(ace, a resulting cur)ed shock leading to the second cone, and most signi(icantly the

single strong shock to the (lo* abo)e the sli$ line.

Iarious methods ha)e been suggested to account (or the non:uni(ormities on di((user $er(ormance, but

only one is rigorous, and not reliant on em$irical correction. Ayatt 34 is credited *ith a$$lying basic

thermodynamics to the intake $roblem and (irst arguing that the e8ui)alent one dimensional (lo* is that

*ith the same stream thrust, mass (lo*, and total enthal$y as the integrated non:uni(orm (lo*. 'he

some*hat mystical Je+tra to shock lossesK *hich are so o(ten modelled em$irically are re)ealed and

8uanti(ied by this method.

Figure 4: Supersonic diffuser control volume

Consider the control )olume o( (igure 4, the conser)ation o( mass, a+ial momentum and energy re8uire,

< u

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'he $re:entry (orce -p has a $ositi)e in(luence on -(but the sum o(-p and-w*ill al*ays be in the

direction o(-wand has a minimum )alue set by the drag re8uired (or isentro$ic com$ression to the same

contraction ratio. n the case dra*n -pincludes the a+ial (orce (rom 0ust inside the co*l li$, but the

e+ternal com$onent is e8ui)alent to the intakes $re:entry Eor additi)e drag. hould one *onder *here

$re:entry drag acts on the air(rame, it is an e+cess in-w.

Ahen s$eci(ic heat is constant, e8uations 1 to @ reduce to the 8uadratic,

1 u1u4 co*l a$$ears to turn the (lo*

back (rom a$$ro+imately 2 Elocal streamline angle to .@, and the internal shock remained

attached o)er the (light /ach number range. 'he co*l9s contribution to a+ial stream thrust Edue to

the (inite length bet*een li$ and control )olume out(lo* boundary, (igure 4 *as calculated using

the $ressure do*nstream o( this internal shock, and included *ithin-p.

'he isolator a$$ears to be choked Ethe condition set by e8uation = at M

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assumed that the $ressure on the inside o( the co*l is that gi)en by a strong obli8ue shock

Esubsonic do*nstream rather than the *eak obli8ue shock, then the stream thrust is su((icient (or

the intake to o$erate su$er critically at /ach 2.52.

'he turbulent boundary layer on the s$ike *as modelled using the momentum integral e8uationand the (lat $late relationshi$s bet*een momentum Reynolds number and local skin (riction

coe((icient and edge /ach number and sha$e (actor. 'he re(erence tem$erature method accounts

(or com$ressibility. 'he techni8ue has $ro)ed itsel( to be su((iciently accurate *hen a$$lied to

many di((erent internal and e+ternal (lo*s modelled by the author, des$ite the $resence o( large

$ressure gradients under *hich (lat $late closure might reasonably be challenged.

Figure 5: Calculated E4 intake performance

re entry drag coe((icient Ebased on co*l area, mass ca$ture ratio and li$ /ach number are $resented in

(igure =. 'he signi(icance o( li$ /ach number has 0ust been discussed, but note the discontinuous dro$ as

the sli$ line intersects the li$ and the noise Erandom com$onent in the li$ /ach number $lot at (light

/ach numbers greater than @.=. n the $resent calculation the discontinuity in entro$y at the sli$ line hasbeen allo*ed to numerically di((use through the (lo*, in a non:$hysical *ay, that can only be e+cused on

the basis that it is com$utationally con)enient and has no bearing on the key lessons to be dra*n (rom the

>4 study.

'he increase in mass ca$ture E!

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4 $ressure cur)es as it accelerates is due to the

in(luence o( the tri$le $oint, and at high M+the s*allo*ing o( (lo* abo)e the sli$ line. But *e shall no*

see that this should ha)e had no in(luence on the $ro0ectiles $er(ormance.

2.0 ack !ess(e an$ c

ntakes can only be understood in relation to the engine they are designed to (eed. 'he 8uantity cMde(ined

by,

cM=

pc!nt

mc36

neatly e+$resses the relationshi$ bet*een the mass (lo*, mc, e+hausting through the no??le throat Earea!nt and the combustor stagnation $ressurepc.

Calculation o( cM is a $roblem o( e8uilibrium chemistry, and Gordon and /cBride9s Chemical >8uilibrium

;nalysis EC>; $rogram 3=, *hich is *idely used and (ree to do*nload, greatly sim$li(ies this task.

Recognising that the mass lea)ing the combustor is the ca$tured air mass $lus the (uel in a $ro$ortion

described by the (uel air ratio,fa, e8uation 6 may be *ritten as,

pc

q4 the )alue *as R greater than R can be increased, rising to RH1 is lo*er than the intake is ca$able o(

deli)ering. 'he intake is said to be running su$er critically and in this mode the terminal shock does not sit

*ithin (lo* determined by the su$ersonic solution o( e8uation 4 Ei( it did, conditions do*nstream sim$ly

corres$ond to the subsonic solution but mo)es do*nstream in the di)erging subsonic di((user to *here

the /ach number is higher and the shock losses *ill be 0ust that re8uired (or the stagnation $ressure to

satis(y e8uation .

Building on the (undamental studies at Braunsch*eig and Gottingen, 'rommsdor( added $erha$s the most

im$ortant (actor that must enter the design com$romise and that is that the manner in *hich mass ca$ture

)aries *ith /ach number as the ram0et accelerates should be tailored to maintain e((iciency. De(ining the

o$timum mass ca$ture characteristic is made $ossible by simulation o( the (light. 'otal (uel burn to

achie)e a gi)en state, is one metric by *hich the cou$led $roblem o( thrust re8uirement $re:entry drag

co*l drag $ressure reco)ery angle o( attack re8uirements and e)en structural *eight im$lications can

be 0udged and subse8uently o$timised.

2.3 ess"ns $a#n %"m the E4 st($5

;lthough created in a time *hen there *as little $rior art, the intake (or 'rommsdor(9s >4 is remarkably

so$histicated, and ser)es to illustrate the (ollo*ing design (eatures

/ass ca$ture characteristics are tailored by a$$ro$riate $ositioning o( the co*l li$ relati)e to the

cone ti$ and biconic 0unction

'he degree o( turning is set by the lo*est (light /ach number, and in $articular by the manner in

*hich the (lo* interacts *ith the co*l li$

ressure reco)ery at high /ach number *as com$romised by the $re)ious t*o constraints *ith no

e((ect on system $er(ormance, because back $ressure is determined by the engine and this *as

su((iciently lo*.

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ROS RO6CE T7OR AND ODIN

.1 &""$h"(n$

Bloodhound is a British sur(ace to air missile that entered ser)ice in 15= as the /k 1, to be su$erseded bythe more ca$able /k 2 in 156@. 'he 1

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Figure 8: MOC solutions for the Thor BT3 24/31biconic, the circle marks the cowl lip position

. Is"&at" c(8at(e

'he isolator, also kno*n as the intake throat, is a section o( near constant area that links the su$ersonic

and subsonic di((users. ;t ma+imum back $ressure, the isolator contains the terminal shock system that

con)erts the su$ersonic root o( e8uation 4 to the subsonic root. 'hese roots are related by identical mass

(lo*, energy and stream thrust and there(ore they are connected in $recisely the same *ay as the

conditions u$stream and do*nstream o( a normal shock. o matter ho* com$licated the isolator

(lo*(ield, the u$stream and do*nstream states are essentially linked by the Rankine #ugoniot relations.

7nly *all (orces and heat trans(er can alter this relationshi$ and a small decrease in stream thrust due to

skin (riction is una)oidable, but clearly minimised i( the isolator is ke$t short. Losses due to *all $ressure(orces are more di((icult to estimate e+ce$t in the tri)ial Ebut not uncommon (or scram0ets case in *hich

*all $ressure (orces do not ha)e a com$onent in the direction o( the inlet-outlet momentum balance.

Bloodhound9s short, high:cur)ature isolator is ty$ical o( intakes designed (or /ach 2 to @. uch intakes

normally e+hibit a region o( stable subcritical o$eration *hen tested in isolation, but it *ould be )ery

sur$rising i( any ram0et intake *as allo*ed to o$erate this *ay *hen cou$led to a combustor. ;llo*ing air

mass (lo* and $ressure to be cou$led to (uel (lo* and combustion *ould sim$ly be in)iting instability.

'here(ore *e should e+$ect a su$ersonic-transonic (lo* *ithin the cur)ed isolator and *all $ressure

(orces to $lay an im$ortant role. Aall (orce is re8uired to increase the a+ial stream thrust (rom -(cosO

Ee8uation 2 to-(as the (lo* is turned hori?ontal, i( the $otential $ressure reco)ery at the co*l $lane is to

be realised a(ter the turn. 7ne could imagine *ith a su((iciently large turn radius the di((erence bet*een

sur(ace $ressures on the s$ike and co*l induced by the centri(ugal acceleration o( the air (lo* *ouldresult in $recisely the re8uired thrust. #o*e)er in order to minimise the e+ternal drag the designer *ill try

to turn the (lo* as tightly as $ossible *ithout signi(icantly com$romising the $ressure reco)ery. 'he

em$irical rule that the radius o( cur)ature should be a minimum o( (our throat heights 3 has limitations

and a $hysical basis that are re)ealed by the (ollo*ing analysis.

M=2.0 M=2.5

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Fi'(e 9 A m"$e& t" $etemine the c(8at(e at #hich an is"&at" ch"kes

Consider the (lo* entering the isolator at /ach numberMiand corres$onding randtl /eyer angle 1i in

(igure 5. ( at the entrance both the co*l and s$ike are gi)en a small de(lection POH:1ithrough a *eak

shock Ered line and e+$ansion Eblue line res$ecti)ely, then the (lo* near the co*l *ill be at /ach 1, the

minimum allo*able i( the decou$ling (unction o( the isolator is to be maintained, and the (lo* near the

s$ike *ill be at a /ach number corres$onding to 21i. Do*nstream o( the intersection o( the shock and

e+$ansion, in the region *here the (lo* has encountered both, the /ach number is returned to Mibut the

streamline angle has been reduced by 21i. 'his $rocess takes a distance set by the ga$ height, h, and the

a)erage $ro$agation rate o( the trailing edge o( the e+$ansion (an. ince the shock and (an trailing edge

meet close to the s$ike sur(ace, the trailing edge $ro$agates most o( the *ay at the /ach angle (orMiandthe shock e+$ansion $rocess takes a distance o( a$$ro+imately hMi

21 to com$lete. 'he streamline

angle has changed by 21io)er this distance and the radius o( cur)ature r is there(ore,

r

h

Mi21

2i

3

'his (unction is consistent *ith the J(our throat heightsK rule o( thumb *hen the entrance (lo* /ach

number is 1.@ *hich is ty$ical (or intakes designed (or (light at /ach 2 to @ E(igure 5. ote the (unctions

strong sensiti)ity at lo* /ach number has im$lications (or o$eration at angle o( attack, because the e+tra

com$ression on the *ind*ard side can easily lead to subcritical o$eration i( the combination o( isolator

cur)ature and nominalMiare too close to the limit (or ?ero angle o( attack.

.4 S(:s"nic $i%%(se

; (lo* straightener is a sur$rising (eature to see in a ram0et engine, $articularly one that *ould a$$ear to

be unnecessary gi)en that it is $laced 0ust u$stream o( a colander (lame holder, as re)ealed in the

sectioned 'hor engine o( (igure . 7ne might ha)e e+$ected that the head loss across the (lame holder,

needed to dri)e the (uel-air mi+ing and stabilise the (lame, *ould ha)e been su((icient to encourage (lo*

uni(ormity. Fuel is introduced )ia the radial s$ray bar )isible 0ust do*nstream o( the honeycomb (lo*

straightener, and the (uel air mi+ture must $ass through the s8uare cut outs in the conical (lame holder.

Flame stabilisation is achie)ed by lea)ing the tab (ormed by cutting three sides o( the s8uare hole, bent

internally and hanging (rom the do*nstream (orth side: a rather beauti(ul $iece o( $ractical engineering.

ndeed, the straightener *as only introduced as a (i+ to the $roblem encountered during bloodhound9s

h

r2Qi

Qi

QH

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acce$tance trials. ;s the engine *as throttled (or cruise, the intake o$erated dee$ in its su$ercritical

regime *ith a strong terminal shock sitting in the subsonic di((user. 'his resulted in (lo* se$aration and a

narro* high )elocity stream, disru$ting the distribution o( (uel *ithin the air.

'he (lo* straightener sol)ed the $roblem by )irtue o( ha)ing a head loss that is $ro$ortional to localdynamic $ressure a narro* high )elocity stream results in a high $ressure dro$ and this (eeds u$stream to

reduce the si?e o( the se$aration and *iden the stream. 'hat is ho* (lo* straighteners Ealso kno*n as

aerodynamic grids *ork, but its (unction in 'hor had t*o additional attributes. 'he (irst *as that its

$resence resulted in the intake running closer to critical in cruise and thus reducing the strength o( the

terminal shock, ho*e)er during acceleration *hen the intake *as o$erating critically it did not ha)e a

strong ad)erse e((ect because in that state, the /ach number Eand dynamic head at the straightener *as

)ery lo*. 'he second attribute is associated *ith a rather cunning integration o( the $ilot (lame air su$$ly

into the base o( the straightener. 'he annular ga$ at the inner diameter o( the straightener (eeds air to a

centrally located $ilot (lame and the $ro$ortion that $asses to the $ilot increases *ith the head loss at the

straightener. 'his allo*ed the cruise (uel re8uirement to be (ed to the $ilot, allo*ing stable combustion

*ithin a $rimary stream $rior to mi+ing *ith the secondary stream in the main combustor.

t *ould be remiss not to mention that the main concern o( subsonic di((user design is $re)enting

boundary layer se$aration in the ad)erse $ressure gradient, and that kee$ing di((usion rates e8ui)alent to

that *ithin a @ to = hal( angle cone has $ro)ed e((ecti)e. 'his is a $roblem common to many

a$$lications o( (luid mechanics and the e)idence (or this result is $resented in te+tbooks such as that by

/assey 35. 'he bloodhound e+$erience adds to the story, by reminding us that the di((user must also

$ro)ide an acce$table le)el o( uni(ormity to the combustor *hen the intake is o$erating su$ercritically,

and that *hen the back $ressure a$$lied by the combustor is lo*, it may be $ossible to e+$loit the e+cess

$ressure that an intake can $ro)ide to hel$ o$timise the air(lo* *ithin the combustor.

./ Sea$at

eadart is a much smaller sur(ace to air missile than Bloodhound, ha)ing been designed to be stored

)ertically bet*een decks o( the Royal a)y 'y$e 42 destroyers. t is boosted to /ach 2Ehere *e assume

2.1 and can accelerate to /ach @ but the (light /ach number is a (unction o( total tem$erature Ean

air(rame limit and thus de$ends on altitude 36. eadart9s intake is an isentro$ic s$ike integrated *ith the

missile (orebody. ; central air trans(er duct (eeds the 7din engine at the rear. 'he central schematic in

(igure 1< sho*s the s$ike is $art o( a large central body that contains the *arhead and this dual (unction

combined *ith the need to create missile )olume allo*ed a long isolator *ith limited turning to be

combined *ith a subsonic di((user o( lo* di)ergence rate. 'he lo*er right (igure is the combustor )ie*ed

through the no??le, sho*ing an in)erted (lame holder in com$arison to that o( 'hor. 'he main air(lo*

$asses (rom the central air trans(er duct through the colander *hich generates longitudinal )ortices. Fuel is

in0ected through radial s$ray bars near the trans(er duct e+it. 'he $ilot ?ones are hidden behind the small

out*ard (acing tabs at the base o( the colander. 'he multi$le small holes in the combustor liner $ro)idecooling air *hich, like the $ilot air is dra*n (rom the outer edge o( the trans(er duct.

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Fi'(e 1; Sea$at. e%t han$ !h"t"'a!h c"!ie$ %"m )iki!e$ia."'< i'ht han$ !h"t"'a!hs #ee taken

at the =em:&e m(se(m< U=.

.0 Sea$at intake %&"#%ie&$

/easurements made (rom $hotogra$hs re)eal the intake has much in common *ith 'hor9s, ha)ing a 24

(ore cone and a co*l li$ $ositioned along the ray that is )ery close to the bo* shock angle at /ach 2.=.

lacing the (ocus o( a randtl /eyer (an at the co*l li$ and turning the (lo* to 24 there, de)elo$s the

isentro$ic turn bringing the sur(ace angle to @@. 'he resulting contour, (igure 11, matches that measured

(rom $hotogra$hs. 'hus the design a$$ears to be another te+tbook e+am$le, *ith the design /ach number

chosen mid range, and both the shock and (an (ocused on li$ at that /ach number.

Figure 11: MOC solutions for the Seadart 24/33isentropic spike, the circle marks the cowl lipposition

;n incom$lete /7C solution (or /ach 2.1 is sho*n on the le(t hand side o( (igure 11. 'he le(t running

characteristic originating at the end o( the turn has o)ertaken the one originating at the start. Ahere)er a

characteristic catches another o( the same (amily it merges to (orm a *eak shock *hich $ro$agates at the

mean o( the u$stream and do*nstream /ach angles, that is, it bisects the characteristics on *hich it *as

(ormed. ;*ay (rom its origin, as the shock gro*s in strength, the shock angle is best determined directly

(rom the Rankine #ugoniot relations, *hile ensuring com$atibility *ith the do*nstream (lo* (ield. ;ne+am$le o( this is gi)en later. For current $ur$oses, the solution is le(t incom$lete as it $ro)ides a

M=2.1 M=2.5 M=2.9

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re)ealing $hysical $icture o( the com$ression $rocess abo)e an isentro$ic s$ike *hen o$erated belo*

design /ach number. 'he right hand (igure (or /ach 2.5, sho*s the (lo* (ield at abo)e design /ach

number, and no such com$lication occurs.

;t /ach 2.1 the calculated mass ca$ture is =N, and the (lo* at the li$ is at 24 and /ach 1.25 *hile the/ach number at the sur(ace is closer to 1.24. Sudging (rom (igure 5 the radius o( cur)ature should be

bet*een (our and (i)e throat heights to maintain su$ersonic (lo*, and this is at least consistent *ith the

e+ternal )ie*s o( the intake. 'hus on the e)idence a)ailable there is little to distinguish the 'hor and

eadart intakes at lo* /ach number or suggest an im$ro)ed angle o( attack ca$ability. Further /7C

analysis indicates that belo* /ach 2.< the intake runs *ith the isolator either choked or subsonic,

de$ending on back $ressure. 'his is due $rimarily to the high degree o( e+ternal turning and is a $hase all

ram0ets must $ass through during boost. 'he tandem eadart booster attachment is designed to allo*

through (lo* and ignition during boost Ethe ignitor breech is in the 4 o9clock $osition in the combustor

$hotogra$h o( (igure 1ARIAE ?EOMETR6 AND EEDS

4.1 Int"$(cti"n

'he intakes e+amined abo)e are all (i+ed geometry su$$lying engines *ith (i+ed no??le throat areas. onehad boundary layer bleeds, $rimarily because they didn9t need them. ;lthough skin (riction *as taken into

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account in the calculation o( stream thrust and >4 intake $er(ormance, no ad0ustment *as made to account

(or boundary layer dis$lacement thickness in any o( the (lo*(ield calculations. 'his neglect *as based on

con)enience and a desire not to introduce unnecessary com$lications. #o*e)er, in $ractice com$lications

are o(ten una)oidable and )arious measures and ingenious de)ices ha)e been de)ised that allo* intakes to

(unction o)er large /ach number ranges and at relati)ely lo* Reynolds numbers. 'he ;; #y$ersonicResearch >ngine, the B;C-UD Concorde and the Lockheed R:1 *ill ser)e as an introduction to this

as$ect o( intake design.

4.2 NASA 75!es"nic eseach en'ine

'he #y$ersonic Research >ngine E#R> $ro0ect to design, de)elo$, construct and (light test a high

$er(ormance ram0et-scram0et *as an e+ce$tionally *ell documented research $rogramme that $ro)ides a

rare E$erha$s uni8ue )ie* o( intake de)elo$ment (rom engine conce$t to trials re)ie*. Recommended

reading (or this $ur$ose are the $ro0ect re)ie* by ;ndre*s and /acklay 31

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by an intake that increases both ca$ture area and contraction ratio as /ach number increases, as *ill be

e)ident (rom the Concorde and R:1 discussion. 'he #R> intake-engine cou$ling *as unusual and more

intimate the ga$ bet*een the co*l and s$ike do*nstream o( the throat *as the scram0et engine, *hile that

u$stream *as the intake, and both geometry )ary as the s$ike translates.

For the #R> intake to ha)e (ull ca$ture (rom /ach 6 to and simultaneously increase contraction, the u$

slo$ing throat *as an elegant solution that also allo*ed the intake to meet the re8uirement that it be closed

during the acceleration $hase o( the test (light. 'he s$ike *as sim$ly e+tended until the throat area *as

almost ?ero *hich occurred near the co*l li$. 7ne disad)antage o( an u$ slo$ing throat is high co*l drag

as the engine co*l has to gro* to accommodate the gro*ing s$ike Eand its matching internal contour.

Ahile the #R> is sometimes $ortrayed as a na)e design that (ailed to recognise the signi(icance o( co*l

drag, ma+imising net thrust by minimising co*l drag *as not a $ro0ect re8uirement. 'he ob0ecti)e *as to

demonstrate good internal $er(ormance in a $od that could be tested on the V:1= 31

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o( the unde(lected shock $osition reducing the stroke re8uired (or the s$ike. 'his had the disad)antage that

the throat angle Eu$:slo$e had to be increased to meet the s$eci(ied throat area )ariation bet*een /ach 6

and .

'he third ste$ in the $rocess is to identi(y the le(t running characteristic that intersects the shock at thene* /ach li$ $osition, as it (orms the u$stream boundary o( the (lo* through the ne+t turn. 'he (lo*

do*nstream o( this characteristic, calculated in ste$ 2, *ill no longer be )alid. ; randtl /eyer (an is

centred on the li$ and traced back to (ind the ne* sur(ace, continuing the turn until the re8uired e+ternal

contraction is reached.

'he (lo* o)er this contour at /ach 4 is sho*n on the right side o( (igure 1@. 'he regions o( in(luence o(

the t*o turns are made e)ident by the bunching o( the le(t running characteristics at the to$ o( the mesh.

'he second turn has not in(luenced the s$ill at /ach 4 since the leading Eu$stream characteristic (rom this

turn intersects the li$ in the /ach 4 $osition. 'hus con(irming the strategy o( setting /ach 4 ca$ture ratio

by the degree o( the (irst turn. 'he second turn does in(luence /ach 4 s$ill *ith the li$ in the /ach

$osition and this $ro)ed to be )ery im$ortant. 'he intake could not be started *ith the li$ in the (or*ard

$osition because the internal contraction *as *ell abo)e the limit established by 7s*atitsch Eand later

%antro*it?. 'o start the intake, the s$ike *as e+tended to reduce internal contraction, and then retracted

to the running $osition once the intake had started. ; ma0or obstacle to the design *as that the ratio o(

ca$ture area to throat area *as not monotonic and at /ach 4 it $eaked bet*een the starting and running

$ositions. >ndea)ouring to kee$ the $eak belo* a )alue o( 6, *hich *as regarded as a sa(e *orking limit,

*as a serious challenge that *as ne)er 8uite satis(ied. 'he $hase: ' intake, 0ust described, had a $eak

ca$ture:to:throat ratio o( 6.1 at /ach 4, and its starting $ro)ed unreliable and )ery sensiti)e to *all

tem$erature Ea boundary layer e((ect. /ost o( the other contours e+amined by the Lockheed engineers

had much higher $eaks, and intake '9s lo*er )alue is due, in $art, to the second (ocus.

4.4 C"nc"$e

; turbo0et $laces di((erent demands on an intake than those o( a ram0et, as noted in the $re)ious section.

But i( a ram0et *ere to be $art o( a combined cycle $ro$ulsion system, and-or *as re8uired (or an

a$$lication *here the mass o( (uel used *as su((icient to (a)our engine e((iciency o)er structural *eight

sa)ing, then some o( the so$histicated (eatures o( turbo0et intakes *ould likely be ado$ted (or the ram0et.

'he Concorde intake has set a )ery high standard, ha)ing high $er(ormance, being robust in o$eration,

mechanically sim$le, and ha)ing an uncom$licated control system that *as dormant (or most o( the (light.

o it *ould make a )ery good case study, (or anyone endea)ouring to meet similar re8uirements.

Figure 14: Concorde and its nacelle, courtesy of A. Pingstone and Wikipedia.org

Be(ore Concorde9s (irst (light on the 2nd/arch 1565, and eight years be(ore it entered ser)ice in Sanuary156, Rettie and Le*is described the design and de)elo$ment o( the su$ersonic trans$ort9s intake at the

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1

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;lthough the design *as (ocussed on cruise the intake must also satis(y the engine demands during take

o((, subsonic cruise and acceleration. 'he dum$ door contains a s$ring loaded (la$ that o$ens in*ards to

$ro)ide e+tra air during take:o(( and (urther a(t on the nacelle there is another s$ring loaded (la$ that

admits outside air to the engine bay *hen sub atmos$heric. During subsonic cruise, $ressure reco)ery in

the bleed slot is su((icient that all the cooling air including that (or the no??le is su$$lied by the bleed. nsubsonic (light the ram$ angle W2 is set to a$$ro+imately 2 and increased $rogressi)ely during

acceleration abo)e /ach 1.@, as illustrated in (igure 16b o( re(erence 314.

4./ Temina& sh"ck sten'th

ressure reco)ery at /ach 2 *as 5=N *ith X1N o( the loss attributable to the subsonic di((usion,

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a 6N stream tube contraction to accelerate the (lo* (rom /ach

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the internal contour o( the co*l. 'he s$ike is retracted as /ach number increases *hich simultaneously

increases ca$ture area and decreases throat area, thereby increasing stream tube contraction. 'he s$ike

boundary layer is e+tracted through a slotted sur(ace near ma+imum diameter and $asses through the

centre:body su$$ort struts to be )ented o)erboard. 'he co*l boundary layer is bled through a ram scoo$

kno*n as the Jshock tra$K, $asses through the engine com$artment to $ro)ide cooling and then into thee0ector no??le, shielding the no??le (rom the a(terburner e+haust and contributing to thrust. 'he (or*ard

by$ass is an acti)ely controlled e+traction o( air (rom the subsonic di((user through JdoorsK on the co*l

sur(ace located in bet*een the mice. 'he (or*ard by$ass air is )ented through the most u$stream lou)res

on the nacelle, )isible in (igure 16, *hile the do*nstream lou)res are those (or the s$ike bleed. 'he thrust-

drag $enalty o( (or*ard by$ass *as considerably greater than that o( the shock tra$ air or the manually

controlled a(t by$ass. 'o reduce the (lo* through the (or*ard by$ass the $ilot could select one o( three a(t

by$ass o$en $ositions 1=N, =

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unless the 4forward bypass5 doors were about to open up, or you took corrective action by shifting the aft

bypass doors closed6.Ae can in(er (rom this correcti)e action that high back $ressure *as not the source

o( instability because E1 the intake control system *ould ha)e sensed high $ressure 0ust do*nstream o(

the shock tra$ and o$ened the (or*ard by$ass and E2 i( the se$aration *as due to e+cess air Ehigh back

$ressure, closing the a(t by$ass *ould be certain to trigger the unstart. 'his highlights the additional(unction o( the (or*ard by$ass, both by$ass regulate air(lo* to match intake to engine Ealbeit one is

automatic, but the (or*ard by$ass is also an essential bleed *ithin the subsonic di((user, and at

intermediate s$ike $ositions it needed to be ke$t slightly o$en e)en *ith the intake running su$ercritically.

4. Mi-e$ c"m!essi"n #ith sh"ck "n sh"(&$e

Figure 18: MOC solution for M=3.2 and comparison with measured cowl pressures fromBlausey et al [26], noting at M=3.2 the minimum dynamic pressure is 310KEAS [25]. The lowestfigure compares calculated duct cross sectional area distribution with that from Bangert et al

[28] for the spike in the forward position.

0.9 1.0 1.1 1.2 1.3 1.4 1.5

0.860.88

0.90

0.92

0.94

0.96

0.98

1.00

%-#c

0%-#

c

0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.65

10

15

20

25

30

35

%-#c

p%p#

1

p02%p010.845

p02%p010.830

p02%p010.785

M"

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.400.410.420.430.440.450.460.470.480.49

%-#c

$#

3%$#

c

M" contour

$ctual

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Co*l drag is reduced by turning the (lo* to a+ial as ra$idly as $ossible. By using a relati)ely slender 1@

hal( angle cone 32, and an internal li$ angle that a$$ears to be ?ero, the ca$tured (lo* may be turned

back to near a+ial immediately by the co*l shock. But this is only the (irst stage o( com$ression. ;t /ach

@.2 the /ach number do*nstream o( the internal co*l shock )aries (rom 2.=6 at the co*l to 2.@= at the

s$ike and to obtain the $ressure reco)ery o(

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the author. 'he duct area distribution a(ter an

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detachment (rom the Rankine:#ugoniot shock relations Eblack line. ote the )ery large increase in

ca$ture area (rom

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/ CONCUSIONS

;$$lied intake design is a great aerodynamic challenge, (rom determining the s$eci(ications that enable it

to best match the engine and aircra(t-missile, right to u$ the (inal stages in *hich (ine tuning is

accom$lished to com$ensate (or things that didn9t go 8uite to $lan. Creating a geometry that directs (lo*e+actly *here one *ants it and in the state it needs to be, is made the more satis(ying by the (act that an

analytically based subtle change to a contour can ha)e a large e((ect in a com$ressi)e decelerating (lo*.

#o*e)er, esoteric intake studies are less re*arding than those *ith a$$lication the basic design

techni8ues are *ell kno*n, and there already e+ists large, (reely a)ailable, databases o( *ind tunnel

e+$eriments on generic intakes. t is ho$ed that by (ocussing this lecture on some historic intakes, and

highlighting the (eatures that think *ere critical to their o$eration the subtle beauty o( these de)ices and

the true accom$lishment o( their designers can be a$$reciated.

0 REFERENCES

31 ';FF ;' S#U:;L, 1564,8andbook of supersonic aerodynamics, section (9 #ucts, no::les and

diffusers, ;IA> re$ort 14, Iol. 6, a)ailable (rom D'C as ;D61@" >G>, 1561,! survey of ramL re$ort @=4, a)ailable (rom U% ational ;rchi)es as ;I; 6=-2;RC# ';FF, 1566, 8R& pro., 156,!nalyses of e'perimental results of the inlet for the nasa

hypersonic research engine aerothermodynamic integration model,;;:'/V:@@6=

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314 R>''> ., and L>A A., 156, #esign and #evelopment of an !ir Intake for a "upersonic

Transport !ircraft, ;;; S. o( ;ircra(t, Iol. =, o. 6, $$ =1@:=21

31= F#>R ., 156, Tests at Mach (.)(B on an air intake proposed for $oncord, ational Gas 'urbine

>stablishment, Re$ort o. R.25/; D., and #;R D., 152,-easibility study of inlet shock stability system

of E-;(7, ;;:CR:1@4=54

32 S7#7 #., and /7'7"; >., 15@,Cocal flow measurements at the inlet spike tip of a Mach F

supersonic cruise airplane, ;;:'D:65

32 B;G>R' L., F>L'Z >., G7DB" L. and /LL>R L., 151,!erodynamic and !coustic 3ehavior

of a E-;(7 Inlet at "tatic $onditions, ;;:CR:16@1redicted >erformance of a Thrust;&nhanced "R;( !ircraft with an &'ternal

>ayload, ;;:'/:1

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3@2 LUD> R and FL;#>R'" R., 15=, Gse of a shock;trap bleed to improve pressure recovery of

fi'ed; and variable;capture;area internal contraction inletsH Mach number 7.+ to F.+, ;C;:R/:

>=D24

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Ramjet Intakes