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(1)

H

-'.1

t'\

E. \ \966

von

KARl\1AN INSTITUTE

FOR FLUID DYNAMICS

TECHNICAL NOTE 29

A STUDY OF THE BOW SHOCK INDUCED BY SECONDARY INJECTION INTO SUPERSONIC

AND HYPERSONIC' FLOWS

by

J .L. EVERS

(2)

TECHNICA~ NOTE 29

A STUDY OF THE BOW SHOCK INDUCED :BY SECONDARY INJECTION INTO SUPERSONIC

AND HYPERSONIC FLOWS

by

J.Lo EVERS

(3)

I II III

IV

TABLE OF CONTENTS Abstract • • • •

..

..

..

..

..

• • • • List of symbols List of figures • • e 0 • 0 0 0 0 • • • • • o 0 0 • 0 0 • • - . • • • • • :rNTRODUCTION

..

..

• • •

..

• • • THEORY o • •

..

..

..

o

..

..

..

.

.

..

• • • • • A. Blast wave analogy

B. Blast wave analogy

(first approximation) (second approKimation) C. Energy term in blast wave analogy • • EXPERIMENTS

..

• • • • • • • • • • • A. Apparatus .. .. 1. Facilities • .. 0 •

..

2. Models • 0 •

3.

Instrumentation B. Tests • • • • • o "

..

" • • "

..

• o o

..

o

..

10 Prelimnary tests" " 2. Secondary injection study Co Dispussion of results • "

..

• • " • •

..

• o •

..

o

..

• • • • • • • • • "

..

" " • • •

..

..

1. Center1ine stat ie pressure study 2. Sublimation tests . . . 0 3 .. Flow model. . . . • .. .. 4~ Shock shape • • • " . 0 ' . CONCLUSIONS . . . " • • • . " . References " • • • • • • • Figures • • • • • • •

..

• • • • • • • • • " • page i1 i1i v 1

5

5 7 8 11 11 11 11 12

13

13

14.

15

15

17

19

21

26

27

(4)

ABSTRACT

The flow pattern result1ng from perpend1cular 1njec-tion of a gas from a flat plate into free stream flows at Mach numbers rang1ng from 2.2 to

7

has been experimentally studied, with a primary interest in determ1n1ng the validity of the

assump~1on that the blast wave theory prediets the shape of the resulting bow shock wave. It has been found that by consider1ng the effect of origin shift, the shock shape can be predicted w1th considerable accurapy by the second order blast wave solut1ono

(5)

c

E J o n p p o q R R o R* R e t

u

u x

x*

Xl Y LIST OF SYMBOLS velocity of sound drag coefficient drag force

energy per unit length constant (see equation 1) mass flow rate

molecular weight statie pressure stagnation pressure dynamic he ad

radius of shock wave

characteristics length related to the energy of the explosion (see equation 2)

R dimensionless blast wave radius, R*

=

~

o

equivalent obstruct ion radius (see equation 21) time

velocit y of propagation of the line charge flow velocity

horizontal distance frorn shock origin dimensionless x-coordinate

horizontal origin shift vert ical origin shift

x

(6)

i p

1

specific heat ratio

boundary layer thickness at jet port with jet off constant (see equat10n 1)

constant (see equat10n 1) see equation 14

Subscripts

1njectant primary flow

free stream

(7)

Number 1 2

4

5 6 7 8 9 10 11 12 LIST OF FIGURES Title

Flat plate model

Centerline statie pressure tap loeations Shadowgraph of typieal shoek shape

Typieal eenterline statie pressure distribution Sublimation photographs

Centerline statie pressure survey Mco = 7 Centerline statie pressure survey Mco

=

7 Centerline statie pressure survey Mco

=

504

Centerline statie pressure survey Mco

=

504

Or1gin shift

Flow model

13 Horizontal origin shift

14 Maeh number effeet on horizontal origin shift 15 Vertieal orig1n shift

16

17

18

19

21 22 23

24

25

26

Dimensional bow shock shape Dimensional bow shock shape Dimensional bow shoek shape Dimensional bow shoek shape Dimensionless shoek shape Dimensionless shoek shape Dimensionless shoek shape Dimensionless shock shape Dimensionless shock shape Shock shape at Mco= 7~

504

Mco

=

7 Mco

=

7 &

504

M co

=

504

Mco

=

202

Mco

=

7 M co

=

7 Mco

=

504

Mco·

=

504

Mco

=

20 2

and

20 2

0

(8)
(9)

Io INTRODUCTION

In recent years the attitude control of rocket pro-pelled vehicles has received considerable attention due to the

increasing requirements tor more precise trajectories o

Aerody-namic surfaces are known to be inadequate as primary control

devices since they are effective only during the portion of the

flight when the vehi~le is moving at very high speeds o Control

techniques that accomplish a change in vehicle direction by

altering the direction of the rocket exhaust have been used

extensively in the form of jetavators~ jet vanes and pivoting

nozzles o However, these devices are all mechanical components

that must operate in the very high temperature region of the rocket exhaust and consequently the reliability of such tech~

niques has been marred by such failures as thermal deformation~

me1ting and blockage due to propellant particles o

The United Aircraft Corporation (1) introduced in

1952 a method of changing the direction of the thrust vector

of a rocket which required no moving mechanical componants in the rocket exhaust regiono The direction of the thrust vector

was altered by the injection of a secondary gas into the

ex-panding portion of the rocket nozzle o The side thrust resulting

from this technique, which has been termed secondary injection,

was found to be larger than that force which would re sult when

injecting the same maas flow through a rpcket vernier motor

exhausting perpendicular to the nocket axiso The ratio of the

force produced by secondary injection to that produced by the vernier motor is called the magnification factor, and this

factor has been used as an index for measuring the effectiveness

(10)

The absence of moving mechanical parts and a

magnifi-cation factor of approximately two (~) stimulated sufficient

interest to promote further study, unt1l at present the

practi-ca11~y of changing the thrust d~rection of a rocket engine by 1njecting a gas or liquid 1nto the nozzle is well established

(2H::l').

The side force produced by secondary 1njection has . . ,

been found to be a combination of the react10n force of the jet

resulting from the momentum force imparted to the nozzle wall

as the 1njectant flows from the port in the wall, and the

inter-action force which is a result of the shock envelope, induced

by the Jet obstructiono For instance, the higher pressure~

resulting from the flow being decelerated through the shock,

acting over the projected area of the shock envelope will tield

a force in the direction of the inJection stream and will add

to the reaction force of the jeto

Analytical attempts to mathematically ,predict the

magnitude of the aide force resulting from secondary injection

ha\te been made by several authors (~) (.5') (, E? ) 0 However, in

each of the theoretical studies listed here, an assumption was

made concerning the shape of the shock envelope resulting from

the jet issuing into the supersonic flow of the rocket exhaust

gases from the rocket wall o And in each case, the various

assumptions had to be made in the absence of experimental

evidence. Therefore, 1t would be of considerable intèr~st to

a study of this kind to know the shape of the shock induced by

secondary injection and to determine the validity and the range

(11)

This .• studp was made for the purpose of

studying the flow pattern produced by a sonic jet issuing from a flat _plate into supersonic and hypersonic streams, with a primary interest in determining the ability of the blast wa~e

theory to predict the shape of the bow shock under various secondary and primary flow conditions.

This investigation was ~arried out in partial ful-fillment of the requirements for the diploma of the von Karman Institute. It was done under the supervision of Professor

Jean J. Ginoux. Part of the financial support for the .work was provided by the European Office of Aerospace Research, Cont~act

(12)
(13)

II. THEORY

Ao Blast wave analogy (first approximation)

Taylor I S

Lr)

analysis of the intense spherical explo-sion has been extended to the plane and cylindrical cases by Sakurai (~ ). It has been found that the radius R of astrong

cylindrical shock wave produced by a sudden releaàe of energy per unit length E can be constructed in the form of a power series of the squares of the inverse of the shock Mach number

2

(~)

where C is the sound velocity of the undisturbed fluid and U is the velocity of propagation of the line chargee The distance from the line charge to the shock front is represented by

(1)

where R is the characteristic length related to the energy of o

the explosion and is expressed as

R o 1 E

?

=

(2 lTP ) co (2)

Jo and Àl are constants which have been computed numerically and are presented in the study by Sakurai

(

,

9

'

).

The first approximation of this theory is made by assuming that the product of \ times the square of .the 'inverse

C 2

of the shock MaQh number (U) is small compared to one which will eliminate all terms in the expansion except the first, yielding

(14)

Realizing that the shock velocity U is also the rata of change dR

of the shock radius with respect to time

di '

this quantity ~an be subst1tuted into aquat10n

3,

the variables can be separated and the expression can be integrated to yield

R R o / 2Ct IS R J

i

o 0

(4)

However, when the above expression is applied to a condition where the distürbance ;remains at rest and the flow moves at a

x

velocity of u~ the time term t can be replaced by - - while the

u uo>

velocity of sound C can be replaced by M<» resulting in an expres-sion for R as follows

x

Defi.Iling

R

as x* o

of the blast .wave x* x coordinate, M~ R* ....

(5)

R

and

R

as R* we get the non-dimensional form o

radius R* as a function of the non-dimensional

(15)

Bo Blast wave analogy (second approximation)

In the second approximation the power series expansion of equation (1) is again considered and in this case, one more term is retained in the expansion yielding

(f.) U 2(-2.) 2 B R

=

~

(C) 2

J

J 0 .. 1 + 1.1 U then by letting dR , dX

=

R o and dR

=

R dX o

and substituting these quantities into equation

(7)

we get

R/R J , R dX t

f

0 0 0

f

Cdt

~],/-J

À

J

~

=

0 0 X 0 1 (8)

which can now be integrated to yield

J

~

Ct À

J

l

R

=

~2Ctl

(1- o 1) R 0 R J "2 2R o 0 0

USing the same reasoning in applying this theQ~y to flow condi-tions where the disturbance is stationary and the flow moves at a velocity u~ as was outlined in the first order solution, we

x

can again replace Ct by M~ , and equation

(9)

oan be arranged in the following non-dimensional form

(16)

l

2x*

R*

=

1 (1-J 2M o "" ] 1 1 2" À J 2" 1 0 .!.ti) 2 M""

(10)

Co Energy term in blast-wave analogy

The energy term E in the expression for R (see

o

equation 2) has been defined in the blast-wave analogy as the energy per unit length that is suddendy rëleased to cause the resulting shock front. When this theory was applied to flow around blunt bodies in hypersonic flow by Lees and Kubota (10) the rate of energy imparted to the moving stream per unit time was assumed to be the product of the drag and the free stream

velocity,

d~

dt=

Du (11)

while the energy per unit length E could be obtained by divid1ng

d~

the rate of energy input

dt

by the free stream velocity u""'

which finally shows that the energy 1mparted by a blunt body

per unit length is simply the drag on the body

E

=

D (12)

Broadwell (~) applied this drag analogy to blast-wave

theory for the case of secondary injection by assuming that

the drag imparted to the free stream was equal to the momentum change that would occur by allowing the secondary flow to

accelerate to free stream velocity. Fluid which is injected perpendicular to the main flow enters the stream with zero

(17)

axial momentum and is accelerated to the free stream velocity thus imparting an effeative force on the primary stream equal to miu

co where mi is the mass flow rate of the secondary injectant. However, i t must be recalled that Erepresents the energy per

unit length in the case ofaxisymmetrical flow, whereas, in secondary injection flow the disturbance is confined to the space above the flat plateo Therefore, Broadwell reasoned that the energy E in seaondary injection is in faat producing half the effect and therefore should be equal to twice the drag force o

E

- =

D

=

2 i

(13)

Broadwell next generalized the preceding analysis ~o allow for volume addition to the flow by assuming "that heat is added to a portion 6f the primary flow at such a rate that the resulting

change in volume is equal to the added volume". This analysis{.

alters the energy term in the following way

E

=

211lIÎl i u co

(14)

where ( Yco-l) M?: n 1+ 2 T 1 co co oi (15) w = "2 +

-2(Yco -l)M2 n T i oco co

An attempt has also been made by Dahm (li) to derive the energy behind the blast-wave direatly from thermodynamic

cqnsiderations in order to avoid making any assumptions aon-cerning the magnitude of the drag resulting from the stream

(18)

of injectant. The work that is done on the primary fluid by the injectant is found by considering the secondary fluid to be

injected into an arbitrary volume, composed initially of primary fluid, then an arbitrary amount of adiabatic mixing of the two streams is assumed to occur and finally the mixture is assumed to expand from tnis in1tial state to free stream conditions. This ana1ysis results in an energy expression of the following form

(16)

where Y -1 1+ co 2

\

- M 2 co n T oi 1 1 00 w

=

2" + +

-Y coC Y 00-1 )Moo Yi-l Y M 2 n i T 00 co 0

The similarity between the results of Broadwell and Dahm is quite remarkable especially in view of the two tota11y different approaches to the problem.

, Using the above results of Dahm and substituting them into equation 2 we can now write ,the full expression for the characteristic length related to the strength of the explosion Ro' in terms of the mass flow rate of."-.1njectant mi' the Mach number of the free stream MooI and the molecular weights and the

stagnation temperatures of the primary and secondary streams.

R

(19)

l I l . EXPERIMENTS

A. Apparatu8

10 Facilities

The tests designed to study secondary inJeetion into hypersonic flows were eondueted in the VKI intermittent hypersonie wind tunnel H-l. This faeility which is described in detail in rëference 12, has a 12 cm x 12 em test seetion and is eapable of operating at Mach numbers ranging from

4

to

8.

This series of tests employed hypersonie flow at two different Mach numbers,

7

and

5.4.

All of the experimental data used in this report for flow at a free stream Maeh number of 2.2 was obtained from tests made by B. Gilman at the von Karman Institute in 1962 and

reported in referenee 13. Gilman conducted these tests in V;KI 1

supersonie tunnel S-l at a stagnation pressure of

4

atmosphere and at a total temperature of 29.4°C.

2. Models

The model tested at Maeh numbers of

5.4

and

7

is shown in fig. 1. It is a flat steel plate model with a sharp leading edge of approximately .02 millimeter in thickness and equipped with an injeetion port

3.25

millimeters in diameter whieh operates as a Bonie nozzle. Along the eenterline of the

model

18

statie pressure taps were loeated at positions shown in ftgo 20 A total pressure probe was fitted into the wallof

(20)

the inJection stagnation ehamber to allow a determination of the mass ~low from the sonie injection porto The injeetion stagnation chamber was suppl ied with air from a 14 atmosphere supply through eopper tubing which passed through the tunnel side wall and through the fl oor of the diffuser sect iono The

pressure in the injection stagnat ion chamber was maintained by a manually operated gl obe valveo

The models used by Gilman ,are described in detail in reference 13. It can be observed that the flat plate model is very similar in design to the one tested at hypersonic veloc1tieso The conical model, on the other hand, which gave a

Mach number of 1 0

86

al ong its surface, is not expected to yield

flow patterns ident1cal to those obtained on the flat plate models. However, i t is s t i l l felt that an order of m~gnitude

check could be made using this model in the origin shift study which will be desoribed under a future headingo

30

Instrumentat10n

The total temperature and total pressure of the tunnel were measur~d by probes plaeed i n the tunnel set tling chamber and referenced to ambient conditions.

The centerline statio pressure survey was aocomplished by the 18 pressure taps shown i n fig o 2 and conneoted to

v.riable reluotance differential transducers o

The injeotion chamber stagnation pressure was measured with Bourdon type gages.

(21)

The starting of the tunnel during each test was con~'

firmed by flow visualization which was prov1ded by the schlieren optical system. The shock shapes in the vertical plane were

obtained by shadowgraphs which were made by placing photographic film in front of' the optical glass view1ng ports. The film was allowed to intercept light which was generated by a spark from the discharge of a condenser at 15,000 voltso This light

ori-g1nat~ng at the spark, passed first to a flat mirror where the

direction is changed by reflection, then it was reflected from a parabolic mirror to yield parallel beams of light and finally

I

another flat mirror was used to direct these parallel rays through the tunnel test section to the photographic plate.

Bo Tests

10 Preliminary tests

---At the outset of this investigation i t was necessary

to determine the feasibility of such a test to be conducted

from the point of view of tunnel blockage, maximum allowable

injection rates, and the strength of the model support o

The shadowgraph method of shock determination was

also tested and found to give adequate detail for the deter-mination of the various shock patterns studied under the flow conditions.

Repeatability was also studied in this series of

preliminary tests and i t was found that the shock shape produaed by secondary inject~on, althQugh very unsteady in certain areas

(22)

especially at high injection rates, is quite repeatable from

test to testo The unsteady action is usually seen superimposed

on the basie shock envelope (see fig.

4)

and does not therefore

interfere with the determination of the dominant bow shoek wave.

The repeatability of the statie pressure survey however~ was

found to exhibit large variations particularly in the region

of the maln bow shock {see fig o

5)0

These variations were no

doubt caused by the large statie pressure gradients ln thls

region whi~h are moved to different loeations by a ehange in

injeetant flowo Therefore~ a small change in lnjeetant flow

eould move the high pressure reglon a very small distanee still

resulting in a rather large ehange in statie pressureo This

laek of repeatability, however~ was not considered to be fatal

to the statie pressure ·study sinee this information was af ter

all intended to be of a qualitative nature which might reveal

certain charaeteristics about the flow in the region of the

injeeted streamo

The prineipal part of this investigation was designed

to study the flow pattern resulting from the interaetion of a

sonie jet and primary flow at both. supersonic and hypersonic

veloeities with ~ secondary mass flow as the prlmary parameter.

Wi th this goal in mlnd the model was first teste,d in a stream

flowing at a Maeh number of

7

and the seeondary mass flow rate

was varied by altering the injeetion stagnation ehamber pressure

in five steps from 1.5 kg/em2 to

6

kg/em2 o Durlng eaeh of these

five runs the statie pressure data was obtained while a

(23)

at a free stream Mach number of

5&4,

except that in this case it was possible to vary the injectant stagnation pressure from

2 2

2 kg/cm to 13 kg/cm in eight steps, the possible range of this quantity being determined by requiringthat the shock envelope remainsentirely on the plate.

In an attempt to gather information that would aid in constructing a flow model for the interference region between the two streams, sublimation tests were cond~cted at both

hypersonic Mach numbers and for various injection rates (see figs. 6A, 6B and 6C) by first painting the model with marking blue and then coating i t with a thin uniform coating of

acenaphteneo ,The model was then placed into the tunnel and subjected to ~rimary flow at one of the Mach numbers listed

above with the desired secondary flow issuing from the injection port, until a~attern of dark and white areas appeared on the surface of the plate. Assuming constant plate temperature, the white spots represent areas of low surface friction such as separated regions, while black areas are known to be caused by high friction such as turbulent regions of flow, reattachment areas or ahy very high velocity regiono

c.

DiscussIDon of results

1. Centerline statie pressure study

---The statie pressure measured älong the centerline of the model is displayed graphically iQwthe form of Dondimensional pressure coefficients in figs.

7,

8,

9

and 10. The ffrst two curves we re plotted from data acquired at a free stream Mach

(24)

number of

7

with the seeondary injeetion stagnation ehamber pressure as a variable. It ean be seen that the pressure at the leading edge is higher than the statie pressure of the free streamo This ean be explained by realizing that unless the leading edge of the model is infinitely sharp the leading edge shock is slightly deta~hed allowing the higher pressure from the stagnation point to be felt .along the leading edge of the plateo In addition to this leading edge effect, in the

hypersonic flow regime the boundary layer which has a high rate of growth interacts with the inviscid flow field causing an additional increase in pressure at the leading edgeo Both of these ~ffects become less pronounced as the flow trave~s over more plate length and therefore the pressure approaches that of the free streamo The pressure coeffiaent can thus be seen to initially decrease as the distance 1s increased from the leading edgeo At some distance upstream of the injection port

the flow separates from the plate not being able to support the high pressure being fed back from the shock system and the statie pressure experiences a rise followed by a plateau which exists through most of the separated regiono Af ter the plateau

the pressure decreases, and then sharply increases to a maximum

val~e under the edge of the main bow shock and then decreases

again under the jet plume (figo

5)0

From the number of experi-mental points exhibitedon these curves i t is quite elear that the spacing of the statie taps on the present model was too large to prov1de an accurate picture of the statie pressure in the region from the end of the separation plateau to the injection porto However, an extensive study of surface pressure distribution with a sonic jet issuing trom a flat plate into flow ranging in Mach number from 2092 to

6

0

4

has been made by

(25)

,Cubbison, Ande~son and Ward ~~. The flat plate model tested in this study was equipped with a suffieient number of statie pressure taps to indieate a eonsistant pattern of pressure distribution along the eenterline of model similar to that

shown in fig.

50

The dotted lines in figs.

6

and

7

indieate the laek of experimental points, but the strong suspieion that a pressure pattern of this kind aetually exists.

The eenterline pressure aQquired at a:.free stream Maeh number of

504

(figs. 10 and 11) show that at this redueed Maeh number the extent of the separated region is considerably redueed. Therefore, the wide spaeing of the statie pressure

taps in this case did not deteet the separated plateau region, or the pressure deerease before the sharp rise to a maximum underneath the main shocko Therefore, this statie pressure data

eould only be used to show the eonststant aetion of the quantities that are deteetable from a study of the eurves. For instanee,

the point o( flow separation which is known to oecur at the first pressure rise, ean be observed to move upstream as the injectant mass flow rate is inereasedo The maximum statie

pressure rise under the main shock system also inereases with an inGrease in this mass flow rateo And finally the overexpansion

downstream of the injeetion port ean also be seen

inerease as the mass flow rate from the injeetant port is inereased.

20 Sublimation tests

A surfaee flow study uSing the sublimation teehnique was condueted for both hypersonie Maeh numbers and for various secondary flow rates. The full seale photographs shown' 1n

(26)

figs. 6A and 6B were made for the same injeetant rate at Mach numbers of

5.4

and

7.

Although the separated region which was originally of interest in this study is not elearly marked in these photographs due to the high sublimation of the aeenaphtene

at the leading edge which th~eatened to ~ase the enti~e pattern, before the separated region had time to appear, another inter-esting area just in front of the injection port and immediately beneath the main shock system is clearly shown. Recalling that the dark areas represent regions of high frietioni i t was

surprising to find these are as in a region which was originally believed to be entirely separated flow. By studying shadowgraph and sublimation tests made under the same flow conditions, i t has been determined that the out er centerline extremity of the white region surrounding the jet port corresponds to the position

of the intersection of the jet boundary and the jet shock o The next'Whüe region proceeding toward the leading edge has been found to be located slightly ahead of the intersection of the main bow shock and the separated flow reg1ono It is also believed that the position of this r egi on of luw surface friction

cor-responds t o that of the high statie pres~ure ridge observed in the centerline statie pressur e studies (figs o

7

and

8)

and also

noted by other investigat ors

(1

5

)

(

14)

(1

'

)

0

Howeveri due to the limited number of sublimation t est s made and the fact t hat the centerline statie pressure curves do not contain a sufficient number of experimental points, there is no conclusive evidence to this faet and it is therefore list ed here as a point to be

checked in further studies of this subjecto The upstream extr~ mity of the outermost black area corresponds to the position of the low pressure region between the separation plateau and

(27)

3.

Flow model

The main features of the flow pattern resulting from the interaction of the injection stream, the boundary layer and the hypersonic or supersonic free stream is illustrated schematically in fig. 12. This centerline view of the three dimensional flow reveals that the Jet expands from a sonic flow in the nozzle to a high Mach number and then experiences a

shock that decelerates the flow to a subsonic level. The obstruc-tion of this Jet plume to the main stream ~auses astrong bow shock wave ahead of the jet which decelerates a portion of the primary stream to a subsonic Mach number. The high pressure behind the bow shock is fed upstream through the subsonic region of the boundary layer causing extenstve separation of the boundary layer from the model surface. This separation which is accompanied by a swelling of the boundary layer results in a separation shock. All of the characteristics of the flow in this separated region have not been eonelusively determined but the experiment al evidence accumulated in this study sugges~at least three possible explanations of this phenomena which have been observed by the sublimation tests, the centerl ine statie pressure survey and the shadowgr~ph

pictures.

The first explanation to be presented is one suggested by Cubbison, Anderson and Ward (14),who have prop~sed- that the mass from both the Jet and the free stream create a pair, of eounterrotating vortiees with a stagnation region between the two, which would cause the region of high local statie pressure ahead of the Jet and the trailing off to lower values of the statie pressure in front and behind the stagnation point.

(28)

Also this explanation seems~to be consistent with the findings

in the sublimation tests, that is, two regions of high velocity

flow separated by a stagnation region.

Amiek and Hayes (15)have presented a model that eontains

an expansion of the air from the relatively high pressure of

the stagnation point between the main bow shock and the jet

shock to the separated region. This air is suggestëd to flow

from th1s high pressure region downward onto the plate and

radially outward along the surfaee of the plate inereasing in veloeity and losing statie pressure. Then when this flow meets the a1r in the separated plateau region i t is decelerated to

the lower velocity and higher statie pressure of this reg1on.

As this reverse flow proceeds outward i t turns toward the

downstream direction thus leaving the separated region and

making room for the mass of air which is continually being

supplied from the high pressure region deseribed abov ••

The final flow model to be presented follows the

classical ideas of boundary layer separation and reattachment

that have been shown to exist in two dimensional sho.k wave,

boundary layer interaotion. That is, the flow is separated by

the ~n pressure existing behind the shock which is fed back

through ths subsonic portion of the boundary layer and then

reattaohes just ahead of the jet plumea This action would

aocount for the additional pressure rise and the high skin

fr.wtion in this area. However, i t does not explain in obvious

ways the low pressure trough on each side of the so called

(29)

Finally the fluw from the Jets meets that of the primary flow along some contact surface, and both are

reaccel-erated around expansion corners to supersonic speeds 0 The

secondary flow is over expanded and must change its direction through a compression shock system downstream of the jet plurne.

4.

Shock shape

---A visual study of the ~low by schlieren and s~adów­

graph pictures has revealed that as the secondary mass flow

rate ±s increased,the jet plume (Jet shock and Jet boundaries)

inoreases in size and therefore moves the bow shock origin

I

upstreamo In addition, the extensive amount of flow separat10n

resulting from the injectant is accompanied by a large amount of swelling of the boundary layer which in effect changes the geometry of the flat plate, since the bow shock is npw sitting above the plate on the separated flow. This action of the flow again moves the origin of the bow shock, this time in the

vertical direction in amounts that vary with the injectant

flow rate.

The analytical studies of secondary injection which

were discussed in the introduction have not dealt with the

problem of an origin shifto Each has placed the origin of the

bow shock at the leading edge of the inJection port and has left i t there for all injection flow rates o The present

in-vestigation has shown that this assumption is not valid at least for the flow conditions dealt w1th in this study. In fact, by 19noring the phenomena of origin shift, the percent

variation from theory increases from

5%

to

26%

for the flow

(30)

No theoretical attempts at predicting the magnitd4e

of either oomponent of origin shift were m~de in this study,

but experimental information was gathered that will show the magnitude and the direction of variation in this quantity as various parameters àre Changed.

In experimentally studying the shift of the origin

in the horizontal direction (Xl) (see fig o 11) i t was believed

that this quantity would be in some way proportional to the size of the Jet plume, so the horizontal direction origin shift

(Xl) was non dimensionalized by dividing i t by a quantity whi~h

will be called the radius of ~he equivalent obstruction, R~.

e It was assumed that the Jet obstruction acts as a

blun~ nosed body which has a constant drag coefficient of 0.90.

Then as the mainstream flow ~xpands around the obstruction,it

will assume a size that will produce a drag equal to the drag D,

that ~he injeotant imparts to the primary flow.

1IR2 D

=

C q (_e)

D 00 2

The drag D is equal to the energy per unit length shown in equation 16

(31)

The x-d1rect1on or1~1n sh1ft

(X')

was d1v1ded by th1s equivalent obstruction radius and plotted as a function of the jet stagnation pressure ratio ('oi/Pi (fig. 13). For constant free Stream flow conditions i t was found that the ratio

X'/R

e

was a constant va1ue. An increase in Mach number, however, resulted in a decrease of the quantity

X'/R

(fig. ~4)0

e

Vertical origin shifts

(Y')

were also recorded and plotted as a nondimensional quantity by dividing the origin displacement by the boundary layer thickness that would exist at the injection port location without injection (ö). This swelling of the boundary layer

(Y'/ö)

is disp1ayed graphioa1ly as a function of the injectant stagnation pressure ratio

(Poi/P

I ) in figure 15.

Typical bow shocks are presented in ful1 scale dime~

sional form in figs. 16 through 19, a10ng with the shock shape predicted by the second order blast wave theory. One can observe that for a given Mach numner the peroent variation from the

theoretioa11y predicted shape increases as the 1njectant mass rate is increasedo For example, at Mach 7 the variation from theory was only 2.5% when the ~njectant stagnation pressure ratio was 236, however, as the injectant rate was increased by raising the jet stagnation pressurè ratio to 711, the variation from theory was found to be 9%. For the reduced

Mach number of 5.4 the variation from theory fol1owed the äame pattern. For 1nstance, at an injection stagnation pressure ratio of 57.6 the variation from theory was less than 105% and when the mass. flow rate of the 1njectant was increased by a

stagna-tion pressure ratio of 374, the variastagna-tion fr om theory of the shock shape 1ncreased to 9%.

(32)

At a free stream Mach number of 2.2 the variation from theory of the bow shock wave is quite pronounced at high injection rates. For instance, the variation at an indéctant stagnation pressure ratio of 189.5 was of the order of 25% while at the lower injectant pressure ratio of 18.1 the ~aria­

tion was reduced to 7%0 However, i t must be noted that the size

of the shocks at hypersonic tunnel speed had to be limited to approximately 50 mm at a distanoe behind the origin of 100 mm due to the limiting size of the flat plate and tunnel test section. On the other hand, all of the shock shape obtained by Gilman at a Maoh number of 2.2 were much l,~ger in size than those obtained during the hypersonic tests. For example, the smallest bow shock had a vertical dimension(of 80 mm at a distance of 100 mm qehind the origino The point of the shock size is raised here because as the injectant flow rate is increased beyond a certain limit, i t is expected that the

shock will no longer approach an axisymmetrical shape but will assume a shape that becomes more and more alliptical. Therefore, i t is be1ieved that a true comparison of the ability of the blast wave theory to predict shock shapes at various Mach number should be made between shock shapes of the same size.

The bow shock shapes obtained over a range of Mach numbers from 7 to 2.2 and inJectant pressure rat10s from 18.1 to 711 are presented, along with the first and second order

blast wave solut1on, in nondimensional form, in figs. 21 through 250 It should be noted that the dimenaionleas form. of the

theoretical curves are independent of free stream conditions and inJectant maas flow rate, therefore, all of the curves would be identical in s~~pe if the same graphical scales were used on each. However, the scales were varied for the range of

(33)

flow conditions in this ipvestigation since the experimental points at the lower ~ach number w~u~d have otherwise been cluttered into the region near the or~gin of the curves o

Figure 26 displays graphically the ability of the

blast wave analogy to predict shock shapes under three different free stream flow conditions o An attempt was made here to use

(34)

IV~ CONCLUSIONS

The follow1ng conclus1ons have been drawn from the 1nformat1on gathered during this 1nvestigat1on.

1. With1n the range of free stream parameters invest1gated, 1t

can be concluded that th~ second order solution of the blast

wave theory prediets with considerab~e_ aocuracy t4e s~ape of

the shock produced by a aonic jet issuing into a hypersonic

or superson10 stream.

-2. The first order solution does not predict with suff1cient

aocuracy the bow~shock produced by secondary injection.

3.

Aa the injectant rate 1ncreases,the abi11ty of the seoond

order blast wave theory to prediot the shook shape deoreases due to the break-up of the ax1symmetrioal shape.

4.

The essent1al features of the interaction flow model have

been established with the exception of the flow in the separated region.

5.

The effeot of origin shift on the shook shape cannot be

19nored in applying the blast wave theory~

6.

The origin of the blast wave is a funotion of the seoondary

(35)

REFERENCES

1. Amick, JoL.

&

Hays, P.B.: Interaction effects of side jets issuing from flat p1ates and cy1indera a1igned with a supersonic stream.

WADD TR 60-329, June 1960.

2. Berman, R.J.g Bow shock shape about a spherica1 nose. AIAA Jn1, vol. 3, n° 4, April 1965, pp. 778-780~

3. Broadwe11, JoE.: Ana1ysis of the f1uid mechanics of secondary injection for thrust vector control.

AIAA Jn1, vol. 1, n°

5,

May 1963, pp. 1067-1075.

4. Broadwe11, J.E.: Corre1at1on of rocket nozz1e gas injection data.

AI AA Jnl., vol. 1, n° 8, Aug. 1963, PP. 1911-1913.

5. Cubbison, R.W., Anderson, B.H.,. Ward, J •. L. g Surface

pressure distribut ions wi th a sonic jet normal t o adjacent flat surfaces at Mach 2.92 t o 6.4.

NASA TN D 580, Feb. 1961.

6. Dahm, T.J.g The deve10pment of an analogy to blast wave theory for the prediction of interaction forces

as~ociated with gaseous secondary injeat ion into a

supersonic stream.

(36)

7. Gilman, B.: An investigation of the interference effect of a high speed jet issuing norma11y into a supersonic stream.

TCEA Rep. 62-64, June 1962.

8. Green, C.J.

&

McCu1lough, F. Jr: Liquid inject10n thrust vector control.

Nav. Weps. Rep. 7744, NOTS TD 2711, US Naval Ordnance Test Station, China Lake, Cal., Jan, 19610

9.

Hausmann, G.F.: Thrust axis control of superson1c nozz1es by a1rjet shock 1nterferenceo

Un1ted A1rcraft Corp. Dept. Rep. R-63143-24, May 1952.

10. Hayman, L.O. Jr

&

McDearman, R.W.8 Jet effeots on oy11ndr1oal afterbodies hous1ng son1c and supersonic nozz1es wh1ch exhaust ag~t a supersonic stream at angles of attaok

f~om 900

to 180°. NASA TN D 1016, 1962.

11. Rsia, H.T.S., Se1fert, H.S.

&

Karamchet1, Kog Shocks induced by secondary injection.

Jn1 Spacecraft

&

Rockets, vol o 2, n° 1, Jan-Feb. 1965, PP. 67-72.

12. Karamcheti, K.

&

Heia, H.T.S.; Integral approach to an approx1mate analy.sis of thrust vector control by secondary inject1on.

(37)

130 Lees, Lo~ Inviseid hypersonie flow over blunt nosed slender

bodies o

I

Guggenheim Aeronautieal LaAo, Calteeh, Memo 31, Feb o 1956 0

14. Lees, Lo

&

Kubota, Tog Inviseid hypersonic flow over blunt nosed slender bodies o

Caltech, Guggenheim Aeronautioal Lab., Publ. 410, or Jnl Aeron o SOo, volo a4, n° 3, 1957, ppo 195-2020

15~ .Liepman, HoPog Interaetion effects of side jets with supe~ sonie streamsi experimental results and wInd tunnel

techniques o

Preprint of paper presen~ed at the joint meeting of

AGARD Wind Tunnel Panel and the Supersonic Tunnel

Association, Marseille, Franoe, Sept. 1959.

16~ Lin, SoCog Cylindr10al shock waves produced by instantaneous energy release.

Jnl Appl. PhYSics,volo 25, n° 1, Jan. 1954, pP054-57.

17. Love, E.S., Grtgs1ey, C.Eo, Lee, LeP.

&

Woodley, M.J.:

Experimental and theoretical studies ofaxisymmetrioal free jetso

NASA TR R-6, 19590

18. Love, E.S.: A reexamination of the use of simple conoepts

for predict1ng the shape and location of ~detached

shock waves .

(38)

19. McAu1ay, J.E.

&

Pau1i, A.J.: An investigation of jet induced thrust vector control.

NASA TM X-416, Dee. 1960.

20. Mager, A.: On the ~odè1 of the free shock separated turbulent boundary 1ayer.

Jn1 Aeron. Sc., v01023, Feb. 1956, PP. 181-184.

21. Mang1er, K.W.: The ea1eu1ation of the flow field between a b1unt body and the bow wave.

Colston Symp., Bristo1 1959, Paper n° 10, 1959.

22. Moecke1, W.E.: ApprD~imate method for predlcting form and loeation of detaehed shoek wave ahead of p1ane or axia11y symmetrie bodiés.

NACA TN 1921, June 1949.

23. Newton, JoFo

&

Spaid, F.W o : Interaetion of seoondary

injeetants and rocket exhausts for thrust vector control. ARS Jnl, Aug. 1962, PP. 1203-1211.

24. Osborne, W.K.

&

Crane, JoFoW.g Measurements of the sonie 1ine, bow shock wave shape and stand-off distanee for b1unt nosed bodies at M

=

6080

Royal Aircraft Est., TN Aero 2707, 1960.

25. Romeo, DoJo

&

Sterrett, JoR.:. Flow field for sonie jet exhausting counter to a hypers9nie mainstream. AIAA Jnl vol o 3, n° 3, Mareh 1965, pp. 544-546.

(39)

26. Romeo, DoJo

&

Sterret, JoR.g Exploratory mnvestigation of the effect of a forward-~acing jet on the bowshock of a blunt body in a Mach number 6 free stream. NASA TN D 1605, Feb. 1965.

27. Romeo, D.J.g Aerodynamic ~nteraction effects ahead of rectangulan Bonic jets exhausting perpendicularly from a flat plate into a Mach number 6 free stream. NASA TN D 1800, May 1963.

28. Walker, RoEo, Stone, AoRo

&

Shandor, M.~ Secondary gas injection in a conica1rocket nozzle.

AIAA Jnl, volo 1, n° 2, Feb o 1963.

290 Wu, J.Mo, Chapkis, RoL.

&

Mager, Ao8 Approximate ana1ysis

of thrust vector cont rol by fluid injection o ARS Jnl, vol o 31, n° 12, Dec o 19610

300 Korkeg1, RoHog The intermittent wind tunnel H-lo

TCEA TM 15, March 19630

310 Tay1or, Golo8 The formation of a blast wave by a very intense explosiono I g Theoreti cal discusslon o

Proc o Roy. Soc. (London) A 201, 1950, PP. 159-1740

32. Sakurai; Ag On the propagation and structure of the blast wave, I.

Jnl Phys. Soc o Japan, 8, 1953, ppo 662-669.

33. Sakurai, A08 On the propagation and structure of a blast

wave, Ilo

(40)
(41)

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(46)

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(57)

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(65)

A STUDY OF THE BOW SHOCK INDUCED BY SECONDARY INJECTION INTO SUPERSONIC AND HYPERSONIC FLOWS,

by J .L. Evers.

The flow pattern resulting from perpendicular

injection of a gas from a flat plate into free stream flows at Mach numbers ranging from 2.2

to

7

has been experimentally studied, with a

pr1mary interest in determ1ning the validity of the assumpt10n that the blast wave theory

predicts the shape of the resulting bow shock

wave. It has been found that by considering

V .K.I. TN 29

von Karman Institute for Fluid Dynamics,

1965.

A STUDY OF THE BOW SHOCK INDUCED BY SECONDARY INJECTION INTO SUPERSONIC AND HYPERSONIC FLOWS,

by J .L. Evers.

The flow pattern resulting from perpendicular

injection of a gas from a flat plate into free stream fiows at Mach numbers ranging from 2.2

to

7

has been experimentaily studied, with a

primary interest in determining the validity of the assumption that the blast wave theory

prediets the shape of the resulting bow shook

wave. It has been found that by considering

the effects of origin shift, the shock shape

can be predicted with considerabie accuracy by the second order blast wave soiution.

the effe cts of origin shift, the shock shape

can be predicted with considerable accuracy by the second order blast wave soiution.

(66)

A STUDY OF THE BOW SHOCK INDUCED BY SECONDARY INJECT!ON INTO SUPERSONIC AND HYPERSONIC FLOWS, by J .L. Evers.

The flow pattern resulting from perpendicular

injection of a gas from a flat plate into free

stream flows at Mach numbers ranging from 2.2

to

7

has been experimentally studied, with a primary interest in determining the validity of the assumption that the blast wave theory

predicts the shape of the resulting bow shock

wave. It has been found that by considering

V .K.I. TN 29

von Karman Institute for Fluid Dynamics,

1965.

A STUDY OF THE BOW SHOCK INDUCED BY SECONDARY INJECTION INTO SUPERSONIC AND HYPERSONIC FLOWS,

by J.L. Evers.

The flow pattern resulting from perpendicular

injection of a gas from a flat plate into free

stream flows at Mach'numbers ranging from 2.2

to

7

has been experimentally studied, with a primary interest in determining the validity of the assumption that the blast wave theory

prediets the shape of the resulting bow shock wave. It has been found that by considering

the effe cts of origin shift, the shock shape

can be predicted with considerable accuracy by the second order blast wave solution.

the effects of origin shift, the shock shape

can be predicted with considerable accuracy by the second order blast wave solution.

Cytaty

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