Experimental investigation of annular and throttleable plug nuzzles

< ::0;; H

2

8

Q;!ï

. 1965

I I Bibliotheek TU Delft

Faculteit der Luchtvaart-en Ruimlevaarttecr' KluyvelWeg 1

2629 HS Delft

von

KARMAN

IN~rl-'ITUTE

FOR FLUID DYNAMICS

TECHNICAL NOTE 24

EXPERIMENTAL INVESTIGATION ON ANNULAR AND THROTTLEABLE PLUG NOZZLES

by G. ANGELINO and E. SACCHI ,RHODE-SAINT-GENESE, BELGIUM 1964

von KARMAN INSTITUTE FOR FLUID DYNAMICS

TECHNICAL NOTE 24

EXPERIMENTAL INVESTIGATION ON ANNULAR

AND THROTTLEABLE PLUG NOZZLES

by G. ANGELINO and E. SACCHI

Bibliotheek TU Delft

1964

Faculteit L & R c2297695

1111111111111

F 0 R E WOR D

The present investigation derives from the

coop-eration of the Centro Nazionale di Ricerca sulla Tecnologia della Propulsione e dei Materiali Relativi. Milano (Italy)

and the von Karman Institute for Fluid Dynamics _a

Rhode-Saint-Genèse (Belgium)0

The plug nozzle models were computed and fabricated

at the Centro Nazionale di Rice-rca sulla Tecnologia della

Propulsione e dei Materiali Relativi 0 The von Karman Institute

provided the basic test apparatus and tec,hnical assistance

during the experimentso

The authors wish to thank the Director of the

Centro Nazionale di Ricerca sulla Tecnologia della Propulsione

e dei Materiali Relativi. Professor Corrado· Casci and the

pirector of the von Karman Institute, Mr. Wo Fo Campbell who

ACKNOWLEDGMENT

The authors are grateful to the Olivetti SopoAo

(Ivrea) for the manufacture of the four close-tolerance models tested in this investigation_o

Chapter 1 0 1:':0 1110 IVQ Vo TABLE OF CONTENTS Tit1e Nomen c1ature Li st of Fi gure s INTRODUCTION

DESIGN TECHNIQUE FOR ANNULAR PLUG NOZZLES

THRUST OF AN ANNULAR PLUG NOZZLE

APPARATUS INSTRUMENTATION AND MODELS

RESULTS AND DISCUSSION

b Q Co

e 0 f Q

Ca1cu1ation of the thrust

Operation at off-design conditions Base pressure measurements

Truncated nozz1e performance Thrott1eab1e nozz1e performance

Base contribution to the tota1 thrust

CONCLUSIONS List of References i i i iv 1

4

8 12

16

16

19 21 23 23 25

26

27

ii

A

s

M P ~ P(n) V. x r

t

w tp

11

passage area surface Mach number pressure NOMENCLATURE

force acting on unit surface

sonic Mach number

axi.a~ coordinate

radia~ coordinate

trace of the throat in a meridian plane

plug length

basic plug length thrust

thrust coefficient. defined by Eqo (~5)

vacuum thrust

thrust contributed by the ~ateral surface of plug

drag

function of Y. defined by Eqo (17)

geometric expansion ratio

isentropic exponent

Mach angle

Prandt~-Meyer function. defined by Eq. (3)

throat inner wa~l inclination

i i i Sub scripts 0 stagnati on t throat e exit a ambient d design m mean value b base sub 0 subsonic Superscripts non-dimensional value

iv

LIST OF FIGURES

Figure

lo Three different solutions for a rocket propulsive .ystem.

20 Simple and annular plug nozzles developing the same thrust.

30 a)o Thrust coefficients of the engine of a supersonic

commercial plane having respectively a fixed and a

variable-ge?metry nozzle (cruising Mach number M=2.2).

b)o Mechanical and aerodynamic adaptability of a

conventional and of a plug nozzle.

40 Nomenclature

5.

Characteristic net and plug profile of nozzle No. 30

6.

Characteristic net and plug profil~ of nozzle No o 4.

7.

Vacuum thrust formation in a simple and annular plug nozzle g

8.

Test section of the experimental apparatus.

90

Meridian curves of plug nozzles computed by the method

of characteristicso

100 Plugs of nozzle No o 1. 2, 3 and 4 fixed on the wind

tunnel supporting stingo

110 Thrust format ion in an ann ufar plug noz zle.

12. Flow pattern in a plug nozzle at off design operation o

130 Effect of external flow in plug and conventional nozzleso

140 a) o Pressure di stributions along nozzle No. 1.

b) . Pressure di tributions along nozzle No. 2.

c). Pressure distributions along nozzle No. 30

d)o Pressure distributions along nozzle Noo 40

15 .

a)

.

b)o

C)

O

d

).

e ) 0

Thrust coefficients of nozzles No. 1. lTl and lT2 .

Thrust coefficients of nozzle No. 2.

Thrust coefficients of nozzles Noo 3, 3Tl and 3T2.

Thrust coefficients of nozzle No. 4.

17. 18. 19.

aL

b )0 c) 0

aL

b) 0 c) 0

alo

b) 0 c) 0

aL

b ) ~ c) 0 200 a) o b) 0 c) 0 d) 0 210 a) o

bL

c) 0 d) 0 22. &) 0 b) • c) 0 d)o

Schlieren picture of nozzle Noo 2: Pa/PO

=

000650

Schlieren pi cture of nozzle Noo 2: Pa/PO

=

0 00700

Schlieren pi cture of nozzle Noo 2g Pa/PO

=

0 01430

Schlieren picture of nozzle Noo 3: Pa/ PO

=

00073.

Schlieren picture of nozzle Noo ~: Pa/PO

=

0 0093.

Schlieren picture of nozzle Noo 3g Pa/PO

=

0 01550

Schlieren picture of nozzle Noo 4: Pa/PO

=

000200

Schlieren picture of nozzle Noo 4: Pa/ PO

=

00044 0

Schlieren picture of nozzle Noo 4: Pa/PO

=

000650

Pressure distributions along nozzles lTl and lT2 0 Pressure distributions along nozzles 3Tl and 3T2o

Pressure di stributions along nozzles 4Tl and 4T2o

Schlieren pi cture of nozzle lTlg Pa/PO = 000590

Schlieren picture of nozzle lTl: Pa/PO = 00122.

Schlieren picture of nozzle lT2: Pa/PO

=

002030

Schlieren picture of nozzle lT2: Pa/PO = 002500

Schlieren picture of nozzle 3Tl: Pa/PO

=

000720

Schlieren picture of nozzle 3Tl: Pa/PO = 0 00940

Schlieren picture of nozzle 3T2: Pa/PO

=

00055 0

Schlieren picture of nozzle 3T2: Pa/ PO

=

001890

Schlieren pict ure of nozzle 4Tl: Pa/PO

=

000170

Schlieren picture of nozzle 4Tl: Pa/ PO

=

00039.

Schlieren picture of nozz~e 4T2: Pa/ PO

=

0 0021.

Schlieren picture ~f nozzle 4T2: Pa/PO

=

a

o0430

230 Variat ion of noz zIe throat are a by me an s of an axi al

mot ion of the plug o

240 a)o Schlieren picture of nozzle 2Mlg Pa/PO

=

00047

throat area/design throat area

=

0 08430

b) o Schlieren picture of no~zle 2Ml: Pa/PO

=

00103

throat area/design throat area

=

008430

c)o Schlieren picture of nozzle 2M2g Pa/PO = 00044

throat area/design throat area = 00686 0

d)o Schlieren picture of nozzle 2M2: Pa/PO

=

0 0107

throat area/design throat area

=

0 0686 0

vi

250 a). Pressure distribution a10ng nozz1es 2M1 and 2M2o

blo Thrust coefficiente of nozz1es 2M1 ahd 2M2.

IQ INTRODUCTION

One of the reasons which make impractical the use of a single rocket engine in large space vehicles is the technical

difficulty encountered in manufacturing reliable large

combustion chambers and nozzles o The intrinsic mechanical

weakness of large convergent-divergent nozzles in the throat region derives directly from the effuser configuration

(Figo la)o

In order to overcome these difficulties the single-nozzle engine is in general replaced by a number of small

motors distributed on the base of the vehicle. as shown ~n

Figc lbo The reduction of the propulsion system volume and

weight for an unchanged total jet cross-section is represented by an annular nozzle similar to that shown in Fig. lCG

The selection of the propulsion system configuration affects the aerodynamic behavior of the vehicle. whose base pressure and drag depend on the interaction of the nozzle jets with the external flow and with the vehicle structure o

Similarly. for a simple plug nozzle there may be

substituted an annular nozzle of reduced length as shown in

Figo 2 a and b o The potential advantages of the plug-type

effusers are well known and depend chiefly on the nozzle

auto-adaptability to off-design operation Q To show the

practical implications of this characteristic of plug nozzles. let us consider a typical mission of a supersonic commeréial plane. similar to supersonic transports which are currently

being developedo For the same basic journey. two different

propulsion systems are analyzed~ having respectively a fixed

20

The design point of the fixed geometry effuser ~s

at minimum pressure ratio, in this way. operation in the

under-expanded regime, at which the nozzle behavior becomes

unpredictable. is avoidedo Conversely. the variable

geometry nozzle is "adapted" at all flying conditions. The

efficiency of the propulsion system air intake and the

temperature of the combustion products at the turbine inlet are

assumed constanto The computed thrust coefficients, defined

in Eqo (15), are shown in Figo 3a in which the altitude-range

diagram and the flight Mach number are also reportedo The

superiority of the variable geometry effuser is evidento

While in conventional nozzles the effuser geometry

is mechanieally modified to match different operating conditions, the plug nozzle adapts automatically to off-design ambient

pressure as shown in Figo 3b. in which pictures are given of

a conventional and of a plug nozzle in the underexpanded

field of operationo

The present investi~&tion was conducted primarily

to study the performance of annular plug effusers; an attempt

was made to evaluate the influence of the nozzle configuration

on the base drago All the experiments were conducted in the

absence of external flOW·; the validity of the results may be

extended to free flight conditions only in the cases in which the influence of the external flow on the propulsion system

A second part of this investigation deals with the

performance of throttleable annular plug nozzleso To perform

these tests, the movable plug of one of the models was

shifted in the axial direction, in this way causing a reduction

of the nozzle throat area and mass flowg The efficiency of the

modified nozzle was measuTed. for various plug axial positions

and working pressure ratioso

All the experimental data were obtained by means of pressure measurements and Schlieren flow visualizationo

Thrust and drag were obtained by numeri cal integration of the

Ilo DESIGN TECHNIQUE FOR ANNULAR PLUG NOZZLES

The necessary design data for an annular plug nozzle are the design exit Mach number and the ratio of the

base radius to the outer jet radiuso From the exit Mach

number Me the ,area and p,ressure ratios are readily calculatedg

.x..:...!

M 2) Y + 1 2 (1 + 2{y -1) A 1

E

2 e

J

e e:

=

At

=

-

M e y ₊ 1

(1)

Pa y (1 + Y - 1 M 2) y - 1

(-) =

₂ Pe d e (2 )

where the s'I,lbscript "e" refers to exit, "til to throat, IlO"

to stagnation conditions, and the subscript "d" characterizes the design values o The basic principles of plug nozzle design

are exposed extensively in Refo

[11

and [2J ' and are recalled

here brieflyo

Wi th reference to Fi go

4,

assume the flow is uniform

at the throat MA of the plug nozzleo At A an expansion fan

exists which locally follows the two-dimensional lawBo In

order to have uniform axial flow 'at the exit, the throat outer

wall is inclined at an angle ti) corresponding to the exit Mach

e

number M through the Prandtl-Meyer relation~

e

ti)

5 0

The inclination ~ of the throat inner wall with respect to the nozzle axis is given by the relation~

~

-

_We t-tan 2 _.= 1

-

r

.

_rit r

=

-~ +-w _r:.t t 1 r e + e tan 2

where re i s the jet exit radius and r is the distance of point M from the axi s of symmetryo

Eqo

(4)

represents the condition of the existence (4 )

of a minimum passage area in an axi-symmetric channel di rected toward the axis of symmetryo Under the following considerations i t wil l be assumed that the velocity vector at the throat is

I

inclined at a mean angle

IAk

g

=

~ + ₂ w e

Then. the nozzle exit and throat areas are given respectively byg

A _e

=

1I"(r _e 2 _ r _b 2)

in which r_b is the base radiuso

r At

=

11" 2 2

-

r e cos w m

The resulting geometri e expans~on ratio is~

A r 2

-

_rb-2

e e

E =

-

= cos w

At _r 2

-

_r 2 m

or. in non-dimensional term~~ = where r · may be cos W m ealeulated

r"

b

=

from the e quation:

*

r r = -_r ( 6 ) e (1 - .f 2 ) cos

J

1/2

~

-

rb wm r* = t

the traee of the throat in the meridian plane

R-

₌

_r i"

₌

1

-

r- _r

e e

cos w

m

(4),(5),(7) ( 8 )

..

From Eqs 0 and 1jJ

•

w m' r and

The nozzle length L ~s known from the design

L = re - r b

tan lJ

e

lJ _e being the exit Mae~ number o

s~n lJ e

=

(7 ) is~ ( 8 )

..

R. are eomputedo

exit Mach number:

1

M

e

When the prineipal geometrie elements are eomputed

as indieated. the plug profile is determined by the method of

e~araeteristies, whieh may be described in summary as follows o

With referenee to Figo

4

the flow conditions are supposed to

be known at the geometrie throat AM (for instanee. a slightly

supersonie. uniform flow may be assumed ~o exist at

cross-seetion AM

(3)

)

0 At A a corner expansion takes plaee.

des-cribed. in the vieinity of point A by the two-dimensional

A sufficient numb~r of elements are known to calculate the region AMG (MG being a characteristic line)ê

7.

In particular the flow properties are computed along the upper

boundary MG of the flow region AMGo Flow properties at G.

are in general slightly different from flow properties at A.

because the expansion fan does not occur in a plane but in an axial-symmetric fieldo

Detailed computations show that the flow at G is

slightly overexpanded with respect to point Ao

Now line AG may be prolonged to the axis as a straight, constant properties line along whicb the flow is

slightly over-expanded with respect to the design valueo

There are sufficient elements to compute. from the known

boundary conditions the whole ~egion GNM • by the method of

ch~racteristics in axial symmetryo The plug profile is the

flow line drawn from point Mo

In Figso 5 and 6 are shown the characteristic nets

and the plug profiles of two nozzles tested in this

8.

1110 THRUST OF AN ANNULAR PLUG NOZZLE

The conceptual difficulties of separating. in a

propulsion system the "thrust" from the "drag" are well known

{see. for instance. Refo [5J )0

. In ~n annular plug nozzle the uncertainty of this

sepa~ation is increased by the particular nozzle configuration.

To show this. consider a nozzle operating in the absence of

ext;ernal flow o In Figo 7 are represented a simple plug

nozzle, (base radius equal to zero) and an annular plug nozzle.

designed for the same exit Mach number and mass flow rateo

If both nozzles are perfect and the working gas is

inviscid, the flow leaving the two envelopes has the same

characteristics of velocity and pressure and the thrust is

the same in both cases; ora to be more precise. the vacuum

thrust defined respectively as~

=

.

,

where P(n) is the force acting on a unit surface perpendicular

. +

to un~t vector n ~ has the same valueg

For operation in vacuum, thrust T

V1 may be

effectively measured. while the actual thrust developed by the annular nozzle in similar operating conditions is not represented by T

V2 ' because i t is inclusive of the thrust

acting on the base, product of the mean base pressure times the base surface o For operation in vacuum the plug base contributes a positive thrust ori in other words_a is responsible for a negative drag, which,in fact ₈ has been measured in flight tests of actual space launchers

[6J

0

ConverselYe if statie operation in s t i l l air,

at

design pointe is considered. the force acting on the two

engines is given byg 2 lTr p 1 a

90

(11) 2 lTr p + e a -+ 2 2 Pb

Isf

p(n)dS

1-

(r - _{r b --)lTp} 2 e Pa a

(12)

where Pa and Pb are respectively the ambient and base pressure o

Since both engines have the same mass rate ~

2 2 _lTr b 2

(13)

lTT l

=

lTr e

-for statie operation in s t i l l _{air Pb <Pa} then, from Eqso ( 9)

to

(13).

100

the difference between Tl and T

2 being due to the base drag:

=

where

=

(14)

In statie tests, the thrust developed by a simple plug nozzle is larger than that of an annular nozzle, but the latter may be designed to cover the full main-section of the vehicle and, as a firs~ approximation. no further base drag for the vehicle is to be expected in flight o On the contrary a vehicle propelled by a simple plug nozzle would exhibita in flight. a base drag which was absent in statie tests o

As a conclusion it may be said that. for a conser-vative interpretation of experimental results, the thrust of an annular plug nozzle may be defined as T

2 of Eqo (12)0

When the nozzle is fitted to the vehicle. benefits are to be expected for the net force - thrust minus drag -acting on the vehicle itselfo

~nstead of computing and comparing _{thrusts a it is}

more eonvenient to introduce thrust coefficients defined as follows:

=

_POAt T

The ideal vacuum thrust coefficient related to

Eqo (9) is known from current computations:

=

=r

ç

_{lv -}

2J...,

[1

-1 Y -1 1/2

(

~)-YJ

J

+ PO

(15)

(16)

in which

r

=

If the design sonic Mach number V

*

is known. the

e

vacuum thrust coefficient is given by:

=

r ( y )

2 1/2 '" V '111' Pe y + 1 e+p"; e:

and. for operation with dry compressed air as in the present investigation

Y

=

1 .400

=

007396 V ~+

e e:

120

IVo APPARATUS INSTRUMENTATION AND MODELS

The basic test apparatus and instrumentation used in this study is the same described in Refo [2J and employed in a previous investigation on plug nozzleso Figo

8

shows the test section of the wind tunnel in which all the models were tested o

Dry, compressed a1r is admitted through a system of piping and controls into an annular chamber which directly feeds the nozzle annular throato The flow Mach number in the settling chamber is about 00060 From the throat. the flow

expands through the plug nozzle into a test chamber. the windows of which are made of transparent perspex, which

allows flow visualization by means of a schlieren systemo The air jet is then exhausted to the atmosphere through a fixed geometry diffuser wi th partial recovery of the kinetic energy of the jeto The desired pressure ratio (stagnation

to test chamber) is obtained by regulating the air inlet

conditions to the settling chambero A further possibility of adjusting the pressure ratio to the desired value is given by two vent valves connecting the test chamber with the

atmosphe re 0

A number of pressure taps were distributed along the plug meridian line and connected with a mercury multimano-meter allowing 30 simultaneous measurements of pressure ranging from 0 to 2 absolute atmosphereso Stagnationand test chamber pressure were measured through other pressure holeso

13Q

The flow pattern was visualized by means of a schlieren system. equipped with a spark light source and photographic recording facilities.

Models were manufactured according to design data computed by the method of characteristics as described in

Section 2Q Figure

9

shows. in a non-dimensional diagram. the

computed nozzle profilesQ

In Figso 10a). b). c) and d) are presented the actual plugs mounted on the wind tunnel supporting sting.

Three of them were annular plug nozzles designed for

an exit Mach number of 2.4~ A fourth nozzle was a simple

plug nozzle with a design exit Mach number of 3~0.

Af ter having been tested at design and off-design conditions. nozzles were modiried in order to obtain further

informati on about truncated and throttleable plug nozzles.

Three of them were successively shortened by

truncating the af ter section of the effuser. The throat area

of the foUrth nozzle was instead varied by means of an axial

mot ion of the plug.

The leading data of the models are summarized in

Refe-rence. number J. 2 3

4

Reference denomination lTl lT2 3Tl 3T2 4Tl 4T2 2Ml 2M2 TABLE I Basic NozzJ.e

De si gn . Mach Design jet Non dimensional

number diameter base radius

(mm) M D r· .. e e b 2.4 60 Oa5 204 60 006 2 .. 4 60 007 3.0 50 0 00 Modified Nozzles

Reference number ot Actual length divided

basic nozzle by basic nozzle length

L/LO 1 0.46 1 0.26 3 0.43 3 0.19 4 0.26 4 _0.14 2 1.00 2 1.00 Length (mm) LO 3600 28,,5 2101 6900 Throat area (mm2 ) At 2410 2079 1681 1859 I-' +:-•

Throat area divided by design throat area

1.00 1.00 1000 1.00 1.00 1.00 0.842 0.686

15.

For each nozzle, along a meridian line, wer~ .

distributed a number of pressure taps; namely: 11 in nozzle

Noo 1, 12 in nozzle ~oo 2, 10 in nozzle Noo 3 and 11 in nozzle

No.

40

Two pressure holes measured the base pressure in ánnular nozzles.

Since all nozzles had different jet cross-sectional area and mass rate i t was found necessary to use two different diffusers to obtain a satisfactory pressure recovery fOT the various nozzles and the various operating conditions.

16.

v.

RESULTS AND DISCUSSION a. Calculation of the thrust.

Since the experimental measurements did not include direct force measurements. the thrust was calculated indirectly from pressure distribution along the nozzle surface. With

reference to Fig. 11 the force acting on the rocket motor equipped with a plug nozzle is expressed. in the most general way. by:

-+

-1'

=

Assume that surface S is separated from surface S by point

c s

T. where the flow is sonico Along S the flow is everywhere

c

subsonic. along S everywhere supersonic; on S the atmospheric

5 a

pressure' acts (static tests); finally Sb is the boundary of a region of separated flow (detached wake flow)o The resultant of the elementary forces acting on surface (S + S ) is:

c s

=

J

(18)

T~e resultant forces acting on surfaces Sa and Sb are easily evaluated:

IJ

p (n) dS

I

=

T

=

-lTr e Pa 2 S a a

IJ

S ; (n) dS

I

=

Tb

=

lT r_{b Pb} 2 b (20)

Eqo (17), taking into account Eqso (18), (19) and (20) may

be ,.,ri tten ~

T

=

₌

Let us divide the vacuum thrust TV into two components.

respectively contributed by the subsonic and the supersonic portions of the nozzle:

f

....

TV

=

p(n)dS

=

T + T_VS S +S V sub 0 c s where: T _{V sub o}

₌

f

_s

_;

_{(n) dS}

_{I ;}

T

_vs

=

i

f

_{; (n) dS}

I

S c c

Eqs. (21) and (22) give:

17.

(21 )

(22 )

(23)

(24)

The measured pressure distribution along the plug and the

knowledge of atmospheric and base pressure allow the calculation

2 2

of T , (nr p ) and (nr_b Pb) . The thrust contributed by the

Y

s

e a

nozz e subsonic portion TV b • is not directly measuredo

su 0

lts value may be obtained fr om the following considerationso

If the nozzle flow is choked (ioeo i f the flow at the throat

is sonic) the pressure distribution on surface S is not

c

affected by changes in ambient pressure o In other words the

contribution of the subsonic portion of the nozzle is a

constant termwhich may be evaluated at a particular working

18.

At design operation we haveg

TV _su b 0

=

T V sUbo,d

=

the term T_VS d is computed from Eq. (23) by the pressure

•

distribution along the plug at the design point; the term TV d is the design vacuum thrust and may be obtained from

•

theoretical calculati onso Passing from thrusts to thrust coefficients. defined in Eqo (15). we have from EqsG (24)

an d (25) : Pa = C _{V sub} + C -0 VS Po 1Tr e At 2

in which Cv d is given by Eqo (16) and C_VS d is computed by

•

•

numerical integration according to the following equations (inviscid flow):

=

= L 21T

J

prdr o L =

l

_pdA

where the integrale of Eqso (28) and (29) are extended from (26)

(28)

the plug base to the throat and dA is the increment of the plug cross-secti onal area passing from abscissa x to abscissa

x + dx (x being the axis of symmetry directed as the nozzle thrust and. the origin of which is on the plug base)o The integrals of Eqso (28) and (29) do not include the base contribut ion 0

It must be pointed out that Cv sU~o ~s evaluated through Eqo (27) employing theoretical information (CV d)

•

190

and an experimental coefficient (C

VS

_•

d)' this procedure being

due to the fact that the nozzle thrust wa~ not direc~ly

measuredo Only ~n the case of an ideal behavior of the nozzle

at design point is the actual Cv b coincident with the one

su •

given by Eqo (27) 0 If the nozzle behavior a.t design point

is not ideal, Cv

enters Eqo (26) 0

b is affected by an error which in turn

su • .

Since Cv _{su •} b is independent of operating _.

conditions and is computed only once (at design point), any

such error present affects all thrust coefficients in the

same way~ the relative values of which remain substantiaIIy

corre ct Q

bo Operation at off-design condit i onso

One of the most interesting characteristics of

plug nozzlei is the high effici ency at off-design operatibno

It may be useful to recall the theoretical reasons for this

behavior, resorting, once again. to the method of

character-isticso As shown in Figo 12, if the ambient pressure is

higher than the design ambient pressureat the expansion

corner, the f l ow wil l turn an insufficient angle to make it

parallel to the axis of symmetryo The free boundary will

then be inclined toward the axis~

Consider the characteristic line AB, whose pressure

at point A is equal to the ambient pressureo The flow field

upstream of this l ine i s i dentical to that corresponding to

design conditionso For the computation of the flow field

1)0 the inclination of the velocity along the plug'is specified by the plug geometry. and

2). the pressure along the outer boundary of the jet must be equal to the ambient pressure of the surroundingso

For the case of no external flow this pressure may be taken as constanto

It may be worth noting that the expansion character-istics like lines a and b in Fig o 12 are reflected by the free boundary as compression waves which. when strikingthe plug walls,

produce a rather abrupt increase of pressureQ This pressure

increase causes an increase in thrust collected by the plugo

With respect to the nozzle operation in the underexpanded

range, the theoretical thrust performance is identical to that corresponding to design conditionsQ This can be easily

under-stood when one considers that at operation above the design point, the pressure distribution along the plug remains undisturbed o At the expansion corner the flow will turn an angle larger than necessary to provide an axial exit flow, so that the exhaust jet will be diverging from the axis. The method of characteristics is once again suitable to evaluate

theoretically this off-design operating modeo

Considering the overexpanded range of operation, if the assumption of no external flow is dropped~ the thrust

collected by the plug is strongly dependent on the interaction

of the two flows o With reference to Figo 13 a) the pressure

acting on the free jet boundary~ which is equal to ambient pressure in statie tests, drops below the atmospheric value due to the expansion of external flow past corner C (external flow is assumed supersonic)o An equilibrium configuration in

jet boundary will be reachedo The net result is a reduction of the pressure along the plug and a consequent thrust reduction

with respect to the no external flow case o However it must be

pointed out that this thrust reduction is not a peculiarity of

plug nozzles aloneo If the same vehicle is equipped with a

conventional adapted nozzle, the thrust of the engine is not

affected by external flow which instead causes a rear-body drag

that has a parallel influence on thrust reduction in plug

nozzles (see Figo 13b)o

The mixing of the two flows (external and internal)

whieh has been neglected 1n the foregoing considerations. is

likely to be responsible for further deviation of the free

flight thrust from statie thrusto

c. Base pressure measurementso

The nozzle thrust and the thrust eoeffieient depend.

through Eqso (24) and (26) on the plug base pressure o Final

results are reliable only if this pressure is not influeneed

by the experimental proeedure o Results were considered

aeeeptable and are reported in this paper only for tests in whieh

th~re was evidence from sehlieren photographs that the diffuser

behavior did not alter the base pressure; sueh is the case in

Figo 22 c).

The experimental pressure distributions along

complete nozzles are presented in Figs o 14 a)~ b)~ c) and d)o

The eontribution to total thrust of the plug surfaces (lateral

plugs base) is reported in Figso15 a), b). e). d). and e)

22.

(30)

where CVS 18 g1ven by Eq. (29).

The ~inal resu1ts are partia11y summarized 1n Table II.

TABLE II

N ozzle Design Ope rating Nozzle Ratio of

reference pre S8ure pre s sure thrust actual to

number ratio ratio coefficient i de al thrust

(Pa/PO}d CPa/PO) (CT) (T/T_id) 1 0.0684 0.061 10315 Oe 97 9 1 0.0684 0.085 1.255 0.974 1 0.0684 00192 1.127 14014 2 0.0684 0.068 1.278 0.965 2 0.0684 0.093 1.233 0.970 2 0.0684 0.174 1.101 0.969 3 0.0684 0.069 1.240 0.937 3 00 0684 0.090 1.187 0.930 3 0.0684 0.169 1.012 0.885 4 0.0272 0,025 1.460 10000 4 0.0272 0.065 1.365 1.020 4 00 0272 Oe135 1.232 1.030

Sch1ieren photographs showing the flow pattern at design and

230

d. Truncated nozzle performance ~

The calculation procedure for the thrust does not

-~hange if truncated plug nozzles are considered. Equations derived in Section 5 a) .. l.n particular Eqs. (24) and (26),

are still valido since the b.se surface is increased by

truncation and the resultant base pressure is higher than the

base pressure of the complete nozzle, the base contribution to

the total thrust becomes more significant. The results of

annular nozzle tests confirm what was known about the

performance of truncated simple nozzles, namely that the

total thrust is only slightly affected by truncation both

at design and off-desi gn operation 0 Truncation appears to be

a practical way to reduce the length of annular plug nozzleso

Pressure distributions and plug thrust coefficients

are reported in Figso 19 a), b), c) and 15 a), c). and e) .

The flow pattern is visualized in a number of schlieren pictures

(Figs. 20, 21, 22 ).

eG Throttleable nozzle performance 0

As a preli minary investigation about the possibility

of controlling the thrust intensity by means of throat area

variation, nozzle Noo 2 was ~ested in a modified arrangement

obtained from the basic configur~tion by mèans of an axial

motion of the plug with respect to the nozzle outer envelope,

as sh own in' Fi g. 230 In two di fferen t set s of te st s the

throat area was reduced, respectively. to 0.843 and to 0 0686

of the design throat area (nozzle reference denominationsg

24.

From a qualitative analysis i t ca? be said that the reduced-throat-area nozzles tend to behave like under-expanded nozzles also when operating at the design pressure ratio of the basic nozzle 0

The flow pattern becomes similar to that of the basic nozzle at the design point only for larger stagnation to ambient pressure ratios (corresponding to the

under-expansion range of basic nozzles). This is in agreement with

the simple observation that. due to the reduced maas flow. only for higher expansion ratios will the flow fill the

cross-sectional area of the basic nozzle at the design point o

In general the flow pattern includes non-isentropic regions with strong compression waves localized at particular points, which vanish when a sufficient pressure ratio is reached.

Some examples of flow visualization are given in Figo 240

Pressure distributions along the plug, and thrust coefficients,

are presented in gràphs of Fig. 25 a) and b) 0

The performance of the reduced-throat-area nozzles for statie operation is given below in Table 1110

TABLE 111

Reference De sign Operating Nozzle Ratio of Ratio of

denomination pre s sure pressure thrust actual to actual to

ratio ratio coeff'Ï- design ideal

cient throat area thrust

(Pa/PO)d (Pa/PO) (CT) _{(At/A td )} (T/T

id)

lMl 0.0684 0'.047 1.364 0.843 00987

lMl 00 0684 0.103 1.258 0 0843 1.004

lM2 0.0684 0 0044 1.341 0.686 0.962

Since, ~n these tests, the base pressure was influenced by the wind tunnel diffuser (as is clear from some of the schlieren photographs), the base contribution to

the total force developed by the nozzle was not computedo

The results reported in Table 111 do not include the base drag, which, i f taken into account, would somewhat reduce the actual nozzle thrusto

A summary of the experimental results obtained from

the various nozzles (basic, truncated and throttleable) is presented in Figo 26.

fo Base contribution to the total thrust.

The thrusts developed by the various nozzles have all been calculated according to Eq. (21) • with the

exception of that reported in Table l I l , and include the base drag, defined in Eqo (14)0 Recalling here the simplified analysis of Section 3 i t may be observed that, at design point, the jet produced by an annular nozzle is limited by a

cylindrical free boundarYi and its cross-section covers the

full cross-section of the vehicle which it propels. In addition

to the plug base drag already taken into account, no further base drags act on the vehicleo If a conventional nozzle is employed instead. the vehicle will experience in flight an

additional drag. acting on a surface nrb2 which is not covered by the jet cross-secti on o For this reaSon the results given in Table 11 are to be considered conservative for flight operation

if one neglects the interaction of external and internal flows.

The possible dependence of base pressure on nozzle Reynolds number

[7J

was not investigated in this study.

VI o CONCLUSIONS

As shown in Figo 26, the efficiency of the annular

plug nozzle was found to be close to unity even in the under-expanded field of operationo

Previous experiments on plug nozzles are confirmed. The possibility of designing the nozzle to cover the full cross-section of a rocket vehicle may have a favorable effect

on base drag in some flight regimes.

Reductions in weight and dimensions are to be

expected from the use of annular rather than simple plug-nozzles.

Variation of nozzle throat area by means of an axial motion of the plug would seem to be a practical way

to control the thrust intensityo The aerodynamic mechanism

of the nozzle adaptation to the varied throat area was found

similar to that shown by fixed geometry plug nozzles operating in the under-expanded regime.

Finally, the efficiency of annular nozzles appears to be affected only slightly by truncation of the nozzle

LIST OF REFERENCES

10 Berman SI K. and Crimp t F 0 Wo Jr 0, "Performan ce of Plug

Type Rocket Exhaust Nozzles". ARS Journal 31, p. 18-23 (1961)0

20 Angelinot GOi "Theoretical and Experimental Investigation

of the Design and Performance of a Plug-Type Nozzle", TCEA TN 120

3~ Oswatitsch, Kot "Ga!ldynamik" t Springer-Verlag, Wien, 1952a

40

Ferri. Ao, " Elementa of Aerodynamics of Supersonic Flows",

The Macmillan Company, New York (1949)0

50 Simonov, Lo A. _a "Advances in Aeronautical Sciences,

Vol~ 3", po 409, Pergamon Press, Oxford, 1962 .

60 Garcia, Fo So, "An Aerodynamic Analysis of Saturn I

Bloek 1 Flight Test Vehicles", NASA TN D-20020

Howarth, Lo editor, "Modern Developments in Fluid

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TET BOUNDARY IN STATIe TEST

0.7 0.6 ( ;a)

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