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AN INVESTIGA1.VON OF:TEJTEAO

AS A EANSOF THRUST VECTOR CONTROL

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Autcrn4tic4~il DOwngrzided at Do by R 52~o.".. 01\v/c Ye,~r lnlerý-as -Decia~sified on5.5.e 3 SS EDWARDS and G- H- PARKER

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DECLASSIFIEDLLMSD:263& I

COpY NO.A__OF COPIESSERIES

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AN INVESTIGATION OF THE JETEVATOR

AS A MEANS OF THRUST VECTOR CONTROL.?

I I~t,

S. S. EDWARDS O O.H. PARKER

-. , FEBRURARY 1958

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DECLASSIFIED L -LOCKHEED AIRCIATT CORPORATION I - SSIL' adSPACE SION

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q~~19iLASSFIED

FOREWORD

The authors wish to acknoWledge thc early

work done on this problem at the Naval Air

Missile Test Center, Point MuGu, California,

by W.A. Fiedler, inventor of the jetevator,

and to thank Clinton Sherburne for his able

assistance in the experimental phase of the

study.

This study was presented at the Fourth

U.S. Navy Symposium on Aeroballistics in No-

vember, 1957, under the title "An Anal.ytical

and Experimental Investigation of a Method of

Thrust Vector Control for Solid Rocket Motors".

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TABLE CF CONTI't4TS

Foreword ....... . .. ii

List of Figrs ...... .... . iv

Summar-y . . . . .

Introduction . . ............. * *.... I

Symbols ........................... . 3

Analysis . ........ ......

Experimental Results .............. 25

Conclusions . . . 36

References . ..... ......... 37

I'!

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FIGURES

Figure No, Page

L 1 Jetevator Assembly ... 2

2 Orientation of Jetevator in Cartesian Coordinate Systemand Spherical Coordinate System .. ........ .

3 Criteria for Establishing Strength of Shock Due to Flow

Separation .... . . . . . ................. 114

Model for the Analysis of Separated Flow Case 15

5 Schematic of Separated Flow Case with Definitions . 15

6 "Cold Flow" Jetevator Test Setup ........ 26

7 Schematic of "Cold Flow" Jetevator Test Setup . . 27

8 Comparison of Predicted Pressure Distribution withExperimental Data .. ........ . 30

9 Radial Distribution of Peak Pressures for Separated FlowCase . . . . . . . . .. . .... . . . . . . . . . . . . 31

10 Comparison of Loads Predicted by Analytical Study to

Experimental Data ... . . .......... . 31

11 Effect of Jetevator Hinge Location on the PressureDistribution along Nozzle and Jetevator Centerline - 33

12 Effect of Gap on Pressure Distribution along Nozzle andJetevator Centerline ...... ......... .... 34

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SUMMARY

The jetevator is designed to control the thrust vector of solitl

propellant rocket engines. The device is a semi-spherical shell

hinged to the rocket nozzle and rotated, at the command of a sensing"

unit, into the exhaust flow to produce a control force. Optimium

design of the system requires maximum effectiveness with a minimum

reduction in thrust.

This paper presents an analytical study of jetevators which

includes analysis of control effectiveness, thrust decrement, and

aerodynamic hinge moments for two flow conditions--unseparated flow

in the rocket nozzle and separated flow in the nozzle due to the

deflected jetevator. The factors affecting jetevator performanec jare discussed, and the results of experimental investigation of

these factors are presented and compared with predicted results.

, Ii

I V°

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if T ,fLASSIF1IE It ~ INTRODUCTION

It has become increasingly apparnnt that, for ball.inti- missilos, rolid

propellant rocket engines have a number of logistic advantnges over thoso

powered with liquid propellants. To capitalize upon thesre advantages, how-

ever, the problem of stabilizing the missile by means of thrust vector control

must be solved, Thrust control in the liquid engine geoncraly i-, acoomp~llshed

by gimbcalling the rocket engines. A sim;,]ar scheoe f,;r the solid propellant

engine does not seem practical at the present time; coniequently, other mean:.

of controlling the thrust vector must be used (Ref, 1). One method for ac-

complishing this i., with Jet vanes or aerodynamic sxlrfaces that nre immersed

in the rocket exhaust stream and which are actuated to deflect the rocket

thrust. A seemingly more attractive method for thrust vector control is with

a device called the Jetevator - a spherical ring hinged to the rocket motor

exhaust nozzle free to swing in and out of the exhaust stream in response to

a control servo (see Ref. 2). A photograph of Jetevators installed on the

four nozzles of a solid propellant engine is shown in Fig. 1.

Several advantages for Jetevator control'can be cited. First, for condi-

tions in which no control is required, the jetevator is retracted from the

exhaust flow. As a result, neither degradation of thrust nor thermal erosion

of the Jotevator materials occurs. Secondly, hinge moments and the moment of

inertia can be held to low values by utilizing jetevators of spherical curva-

ture.

Two problems exist in the development of jetevators. First, the obvious

difficulty of obtaining material that will withstand the extreme heat, Second-

ly, the problem of the aerodynamic design with the objective of arriving at

configurations having maximum effectiveness with compatible values of associated

thrust decrement. This paper is concerned, primarily, with the second of these

two problems.

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SYMBOLS

A,B Coefficients of linear terms in powers series expansion

Co9 Friction drag coefficient

JL Jetevator lateral load coefficient

Jb Jetevator axisl load coefficient

im Jetevator aerodynamic hinge moment

N Mach number

p Pressure

Dynamic pressure

IZ Jetevator radius

(A) Cartesian coordinates I(•,•) Spherical coordinates of jetevator with radius

5 Jetevator deflection angle

4 Nozzle expansion half angle

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ANALYSIS

Ine analysis is divided into two parts. In the first part, expres-

sions for lateral control effectiveness, thrust decrement, and aerodynamie

hinge moments are presented for the condition wherein flow separation in

the nozzle ahead of the deflected jetevator does not occur. The second

section presents a similar analysis for the separated flow case.

THE UNSEPAPATED FLOW CASE

Flow in the nozzle for this ease is considered to be symmetrical

about the ceaterline for all Jetevator deflections. Therefore, it is

necessary to consider only the load on thp Jetevator.

Coordinate System A syatem of rectangular and spherical coordinates as

shown in Fig. 2 is assumed. An element of area of the jetevator is

d S - d (P d E) (1)

where 12 is the jetevator radius. The component of the elemental force

on this area perpendicular to the Xz plane is

AL - ApP.%,Rt 75 ( sine dd0 (2)

where Ap is the pressure acting on the elemental area d5

Pressure It is presently not possible to write an exact expression that

will give the pressure distribution on the jetevator. Because of the con-

cavity of the inner face, it is considered that the pressure can be represented

by a linearized function of the flow deflection angle.

LOCKHEED AIRCRAFT CORPORATION LASSRI1 ES omd SPACE DIVISION

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Fig. 2 Orientation of Jetevator in Carteý-ian Coordinate System andSpherical Coordinate System

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where: p1 - static pressure at the nozzle face for zero •letevator

deflection,

p - pressure on the side of the deflected jetevator that is

exposed to the nozzle exhaust gas.

p m pressure on the back side of the jetevator.

By expanding in a power series, the pressure in terms of the flow deflec-

tion angle isI l'()The difference in pressure between the inside and back side at any point,

then, is (for linear terms only)P +

where

A

An estimate of the value of the constants A and B can be made by

considering a two-dimensional flow in the x plane (see Fig. 2). The

constant A, therefore, is the ratio of the static pressure behind the

shock wave that origi.nates at the intersection of the nozzle trailing

edge and the jetevator to the static pressure just ahead of this shock

wave. By applying two-dimensional shock wave theory, the increase in

pressure on the inside face of the jetevator due to curvature can be

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computed. A straight line approximation to the slope of this pressure

increase with ) io consistent with the linearization and determines the

value of the constant B . As stated previously the foregoing procedure

is approximately correct only for the L plane. Because of the concavity,

however, it in believed that the approximation is reasonable for points away

from this plane.

Lateral Force Substituting Eq. 4 into Eq. 2, the total force normal to

the xx plane is

-~~ COO.

L - 2R [A E (e. -0o )- x] ,, son , d 9 dcp

This equation can be integrated to obtain a lateral force coefficient of

effectiveness as

JiL." 'L --N[' + 1CIS .Z M A 0.2 '

+ s in-, 0s (

where

N -M ,o,(G. - 1) + B5,,(.-• (e,•)€••,•M-A Be.o-

74

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m cosQ

Upon examining Eq. 5, it can be seen that the lateral force co-

efficient, JA. , is a function of A ,and The

dependence upon b , of course, needs no discussion. The parameter e0essentially defines the position of the Jetevator hinge relative to

the nozzle face. The two pressure parameters, A and B , are functions

of the Mach number at the nozzle face and the ratio of specific heats

for the rocket gasj they are related to the nozzle design as well as

the jetevator design. The ratio -• is retained as a parameter to ac-

count for the fact that the pressure on the back side of the jetevator

is a function of ambient pressure as well as the missile base pressure

which is influenced by the speed.

Thrust Decrement With reference to Fig. 2 again, the component of the

elemental force on the area d5 (see Eq. 1) perpendicular to the 9 planeis

p~m ARzw nr'cpcot, e dc(6)

Upon substitution for , p from Eq. 4, the total force in the X direction

is

O*- A + B(e. -Q cos e d 0 a

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or

sin? j sincQ

-B C os 6). -5 1Q - 5 Iý~~,Q. [C ( sin) cJ

The last temi in Eq- 7 was expanded in powers of -i.n Q and integrated term

by term. TIerms uxp to and including the seventh power were retAined. From

Eq. 7, then, a coefficient of thrust decrement ca~n be defined as j

r1 OS~ (L~ z ZL)])

Mo 4. Aos 6

4-NO BoI as -&- M in e-)+ B COS')M +e 0-am I--"

CA. ( 3 G

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From a comparison of Eqs. 5 and 8, it can be determined that J, and J,_

are functions of the same parameters.

Aerodynamic Hinge Moment Since the jetevator is spherical, pressures upon the

surface exposed to the rocket exhaust result in a load that passes through the

hinge line and, theoretically, contribute no hinge moment. Moments about the

hinge will be caused, however, by the frictional drag of the exhaust gases upon

the inside face of the jetevator and also by pressures acting aloig the trail-

Ing edge surface. In this section only the frictional hinge moment is consid-

ered.

The moment of the frictional force on the element of area c. (Eq. I)

is

d M5, CDý 31MI c de 9 A 9 ii

10

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,LSD- 2630

where

is the dynande pressure at the nozzle face and

Coj is the friction drag coefficient based upon c and the

area of the jetevator face exposed to the exhaust stream.

The total frictional hinge moment is

,v5 2L0 J CDl 4P JQ ei

or

JL4 -'

The first term in Eq. 10 was expanded in powers of 5irvcp and terms up

to and including the seventh power were retained. After integrating term

by term the following expression is obtained.

w~ee- •-~-~ - K -,-.i.- 4-k o)

,4 = 5I-l co'S 9,1-K1

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THE SEPARATED FLOW CASE

Near the wall of the rocket nozzle, a gradient in velocity exists, and

the resulting shears in this region cause a boundary layer of some undetermined

thickness. Since a favo'able pressure gradient exists in the nozzle, this

layer would be expected to be quite thin. However, it is true that in the

subsonic portions of the boundary layer pressure pulses from downstream can

move up into the nozzle. Thus it is that the increase in pressure associated

with the deflected jetevator can be felt upstream and a boundary layer separa-

tion point can be established at some point in the nozzle ahead of the deflected

jetevator. The assumptions associated with the prediction of the pressures ex-

isting on the jetevator and upon the nozzle in the presence of a separated

boundary layer are discussed in the following section.

Pressutre Most experimental and analytical studies of shock-induced boundary

layer separation pertain to air and generally do not consider a favorable pres-.

sure gradient such as exists in a rocket ncz.zle (see Refs. 3 and 4). Neverthe-

less, the assumption is made herein that existing data regarding shock-induced

separation for air can be applied to rocket gases. More specifically, the

increase in pressure associated with flow separation at various Mach numbers

can be estimated by examining published data for air. Accordingly, pertinent

12

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parameters an determined from wind tunnel teote are plotted in Fig. 3.The data given in this figure indicate that the prensure jýmp across the

shock wave induced by the boundary layer separation is a function primiarily

of Mach number. The equivalent wedge formed by the separated flow varies

approximately between 140 and 16°,

Schematic sketches of the flow with boundary layer separation is shown

in Figs. 4 and 5. The most forward point within the nozzle at which the

boundary layer is separated is Point 2 in Fig. 5. The point (in the xV

plane) at which the surface of discontinuity (aossmed to be conical) between

the separated flow and unseparated flov intersects the jetevator is Point 4

in Fig. 5. For computational. purposes it is assumed that the pressure along

the surface of discontinuity can be taken as an average pressure, •AV '

between that behind the shock at Point 2 and the pressure p which would exist

at the face of the nozzle (for no Jetevators). This pressure, therefore, acts

on the nozzle as well as on part of the jetevator. For the pressure alonge the

jetevator behind Point 41 the Mach number M , and static pressure p , war, con-

sidered to define the flow ahead of the shock at Point 4, and the effects of

the turning of the flow from Point 4 to the jetevator trailing edge wn. com-

puted two-dimensionally as in the unseparated ease.

The separation pattern within the nozzle is difficult to determine

uniquely. For purposes of mathematical analysis, it war assumed that in

the side view the separation boundary in the nozzle is a straight line drawn

from the most forward point (Point 2 in Fig. 5) to the point at which the

jetevator aft edge intersects the nozzle lip (Point 1 in Fig. 5). Au pre-

viously mentioned, the surface of discontinuity defining the separated layer

was assiuned to be conical and was considered to subtend equw.l wedge angles

measured from the nozzle wall in any plane passing through the nozzle center-

line. With these boundary conditions) then, a procedure for estimating the

lateral and axial forces upon the nozzle and jetevator is given in the fol-

lowing paragraphs.

Lateral Force on the Nozzle With reference to Fig. 5, consider that a plane

parallel to the - -axis passes through Points 1 and 2. The parametric

equations for the intersection of this plane and the conical nozzle are

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SEPARATED REGION -

SEPARATED REGION -" DEFLECTEDSP.T R-- JETEVATOR ".I

JETEVATOR HINGE POINT N/O ES I

PLANE

Fig. 4 Model for the Analysis of Sepa-rated Flow Cese

yd

POINTN

dEEVTR INEPOINT /

.8POINTi»

11-

0INITIAL SHOCK-j -SHOCK

(DUE TO SEPARATION)

FLOW PO IN T Ql

JETEVATOR HINGE POINT-

Fig. 5 Schemnatic~ of Separated Flow Case with Definitions

15

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A. -

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-fl4- (2-3)

If we consider, then, only values of defined by Eq. 13, and equittion

for the corresponding v- as a function of . can be obtained as

(•- "X.,)&o,, (4 + h + (14)

The line defined by Eq. 14 is in t < plane and represents the pro•-

jection of the boundary-layer separation points in the nozzle upon the

x7 plane. Equation 14 is an ellipse.

It is assumed that a constant pressure P,'^v acts outward on the conical

nozzle within the boundaries of the separated flow region. In order tn find

the lifting pressure contributing to the load on the nozzle, the preosuref}L,

must be compared to the pressure that normally would exist in the separated

portion of the nozzle had separation not occurred. Accordingly, the incmr-

ument in pressure contributing to the load is

P,- (15)

where pf , static pressure at the nozzle exit area for

unseparated flow.

p.^=average pressure in the separated flow

region as influenced by the increase in pres-

sure caused by the shock wave associated with

the boundary layer separation.

Pr the normal unseparated flow pressures in the

nozzle averaged for the area of the nozzle

covered by separated flow.

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1niese outward preanurco are inclined forward by the angle 4 (nozzle ex-

pansion half-anigle) relative to the ' axino

To compute the lateral load on the nozzle, the pressure multiplied

by the cosine of the angle 4 is integrated over the separated area of the

nozzle projected to the Yr plane. This area (Region I in Fig. 5) is

bounded by the line given in Eq. 14 and the line parallel to the A axis

defined by'-Oand x - k€af.

The load, then, is

Li - ~ ceE dr

This equation can be integrated to obtain

Y. { -('.d + U:A

[) - (X4+ 1 + ivi + (16)

+ on

ii

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where Ke is the x-distance of the nozzle cone vertex

from the origin of the Xg, coordinate system

(Jetevator hiagu).

X, is the x-coordinate of the foremost point

of boundary layer separation in the nozzle

ahead of the jetevator.

X, is the x-coordinate of the intersection of

tih, jcevtator trailing edgn and the nozzle lip.

a+l~

!-

is the y-coordinate of the boundary layer

separation point.

is the y-coordinate of the jetevator trailing

edge and the nozzle lip.

I , .ti

For computing purposes, it is convenient to express Eq. 16 non-

dimensionally. Accordingly) therefore, if all lengths are divided by

q2Z (the jetevator radius), a coefficient of lateral effectiveness can

be defined as

18

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Lateral Force on the Jetevator To estimate the loads on the jetevator,

it is assumed first that the general level of the static pressure in Region

II of Fig. 5 is P-AV . As a first nontribution to the lateral force on the

jetevator, it was considered that a constant pressure equal to P3, acted

upon the total inner surface. Upon examining Eq. 5, the contribution of

this pressure to the lateral load coefficient is

I.

where in Eq. 5 is zeroJ

MZ (Az -~ ) (In Region III (Fig. 5) an increase in pressure above that in Region

II occurs first due to the shock wave at Point 4 and then to the effect of

the jetevator curvature in Region III. To compute the contribution of the

pressures in this region to the jetevator lateral load, Eq. 5 was altered

so that it would apply only for Region III. To accomplish this, the angle

C-),., in Eq. 5 is redefined as the angle measured from the tj axis to a line

drawn from the hinge point to Point 4 in Fig. 5. Correspondingly, the angle

Sis measured from this new e- . The pressure in Region III was determined

by assuming that the static pressure and Mach number ahead of the shock at

Point 4 was equal to the value that would exist at the nozzle face for zero

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Jetevatar deflection. Again, two-dimens~ional flow considerations were upted to

in Eq- 5 then the contribution of Recgion III is

' ~ 4 CS -L (Cos_____

Total lateral Load The total lateral load coefficient contributed by the three

I ~~regionls is 41 )(.,s..?

Axial Force on the Nozzle The pressure t&p given in Eq. 15 exerts an axial

force on the nozzle in the forward direction and tends to reduce the overall

thrust decrement. To compute this force let d5,be an element of cone area

and dis be the projection of this area on the Xx plane.

Then

where jS is the dirl~ction cosine associated with the outward normal to db

In the direction. From the equation for the conical nozzle

21

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The radial force on the conical portion of the nozzle is ,j pd

The axial component of this force is

For the boundary conditions of the separated flow region previously dis-

cussed

and

"5,

Let t "hen

-,-. [ - +X. + (21)D - on +

Equation 21 was integrated to obtain an axial force coefficient equal to

(I. I - -A.)

~~~~~~~~C • Yloj. + b, (-kti - "-A.) -- c i (tl. - 3•) • £ , ,)*C,• -7)I(

4. Hili- si -L "L I"

22

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where all linear coordinates are in terms of the jetevator radius an in

Eq. 15 and where

bt - yy t (M• % _(., h)•

Qtn

Axial Force on the Jetevator To estimate the axial force on the Jete-

vator, the parameters in Eq. 8 were modified in a manner analogous to the

modifications to Eq. 5 that were made to obtain the lateral forcee More

rpecifically

N-

(23)

where B in Eq. 8 is zero

N D L .= - M . ,,,-,( • -S )

4

23

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EXPERIMENTAL RESULTS

In developing the mathematical model for analysi. pu•pione•e, it wusapparent that kan, of the arsuiptionn would require (.•x]:rmnnta] 1nvurti-

gation. Several of the more important points requiring clarificntion were:

1, Prensure distribution on the deflected jctevator.

2. P-,e-ssure distribution and nature of the separated flowvI

region in the nozzle.

1 3. TMoe inflencc of nozzle and jetevator geoimetry on theSaxbove itclns.

Moreover, it war desirable, of course, to check the loads predicted by y

the analytical results with experimental values for a jetcvator under

actual operating conditions. It was consider-ed that uscful tests couldbe conducted on a model using air as the test medium, thereby n,.r.'atin. ; the,

material heatingt problems and the jetevator effectiveness computations. Ac-

t cordingly, therefore, a series of "cold-flow" tests were devised for purposcs

of obtaining pressure distribution data. These results are discussed herein

together with limited test results from actual rocket firings.

Description of the Tests The cold-flow jetevator tcsts were conduc.ted in the

engine test cells of the Ordnance Aerophysics Laborutory at Doingerfield, Pexti.

A photograph andI schemiatic drawi~ng: of' the test netupl are jeene in F~

and 7. The model consisted of a conical nozzle, a series oL semi -. •t(,vtt 8

-* J of various radii, and equipment for positioninL; the jetevator. The nozzle was.

designed for Mach number 3 at the exit plane. The exit diametuj' of the noz-

zle was 9.4 in and the total divergence, angle woas L'o The jctevatC r chord

w;as approximately 14 in. at the center line, ,ctevator position, .ith .tUli'Cei

to the nozzle exit, was controlled by means of an hydraulic actuator.

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The analytical investigation indicated that the effects of several

factors could be important in jetevator design. Hinge yosition rela-

* tive to the nozzle exit face, possible boundary layer control by means

of increased gap between the nozzle lip and jetevator, and thickness of

the nozzle trailing edge were considered to be of primary importance.

Means of examining the influence of these parameters were, therefore,

incorporated into the design. Removable fittings were provided as a

means of varying the hinge point axially. Details of the fittings are

shown in Fig. 6. The gap between the nozzle lip and the inner surface

of the jetevator could be varied by removing special rings fitted to thenozzle and also by using Jetevators of varying radii. Finally, the noz-

zle trailing edge thickness was varied by changing the special rings

mentioned above,

Data recorded during the test consisted, primarily, of pressures

from approximately 50 static orifices located in the jetevator and

nozzle. The jetevator remained in a fixed position while the data were

recorded to allow the use of gages and multi-manometers to measure pres-

sure. All tests were made at a supply air temperature of 500 0 F. Supply

pressures were 45 and 210 psia, as noted on the figures. The cel. pres-

sure was adjusted to give a ratio of supply pressure to cell pressure of

approximately 37.

Test Results Results from the cold-flow tests and from representative

pressure distribution data obtained by Aerojet-General Corp. during rocket

motor firings confirm, in general, the fundamental assuuptionr utilized in

2 the analysis. The comparison of pressure distribution data mcasured along

the surfaces of the nozzle and jetevator on the cold-flow model with as-

* sumed pressure distributions in the analytical model is summarizcd as follows:

1. Without some means of boundary layer control, separation

occurs in the nozzle ahead of the deflected Jetevator.

The deflection angle at which this separation starts is

approximately 120.

23} ~ ~LOCKHEED AIRCRAFT CORPORATIUN JA.O~i oftd!J SPAC DIIION

.. #.ULMSD- 2630

i-

P. Based on values of pressure ratiq across the shock, the

strength of the Fhoci wave Generated b.• the scparatecl

flow in the nozule is 2.% higher than predicied (see

. Fig. 3),

3. The boundary formed by the aetua) flow is such that corm-pression on the jutevator occurs along a length of the

chord rather than through a strong shock as assumed in

the analysis (see Fig, 8). This tends to move the area

of high loading downstream on the jetevator and causes

a higher axial load (thrust decrement) than predicted.

4. The pressure on the jetevator surface is maximum along

the centerline but decreases toward the hinge-point.

Figure 9 shows radial pressure distribution of the peak

pressure points on the jetevator and nozzle as compared

to assumed values. The difference in radial distribution

is not considered significant, however, since the lateral

load-per-unit area decreases as a function of the cosine

of the radial angle. jA comparison of predi cted lateral loads with loads measured during

* rocket motor firings also indicates that the analytical flow model is in

reasonable agreement with test data. Figure 1.0 shows curves of lateral.

load as a function of jetevator deflection for unsctparatcd and sesparated

flow cases as computed from Eqs. 5 and 20, respectively. Phese computa.

tions have been made for a particular nozz".e-jcetcvator sy::ie•m r.ith th,

dimensions listed on the fI'gore nud ,orresponds to a coul].ieurat±iJon tested'

by the Aerojet-Goencral. Cor. during a roc.et motor firing. The re!;ults,

of this test are aulwj, shown on the figure.

The effects of rhanger in geometry were detennined by oom]aricon o'f

pressure distributions. 'The pre-ssure dats were o.so integrated ovne the

nozzle and jetevatur to give .lateral and axinal loads for -uelected config-

urations. One of the ifl 't arq t ]L a Paine t'r:; in the analysi •, 1ir (- P.a'ation"

LOCKHEED AIRCRAFT CORPORATION t"lJIFI ILJ T IfL. r •'IS9ILES and SPACE DIVISION

LMSD- 2630

NOZZLE JETEVATOR

d6=25°

JETEVATOR r-69 j%(f) Wi

C V) .. PREDICTED BY--' SEPARATED FLOW CASE

.. .30 ---- EXPERIMENTAL DATATOTAL PRESSURE= 45 PSIA

.20 I0 I

.10,

.44W .O--8-- 1 - ,

-10 -8 -6 -4 -2 0 2 4 6i NOZZLE STATION, IN.

Fig. 8 Comparison of Predicted Pressure Distribution with ExperimentalData

30

LOCKHEED AIRCRAFT CORPORATION .,.,. Lt i ..... d SPACE DIVISION

4.7A SFII LMSD- 2130

W JETEVATORW-ETVWO DEFLECTION ANGLE,

Cn8 x25 DEG.M w0.24_

J EXPERIMENTAL DATA(n- PREDICTED

0

0.06- ___ RSSR AI

R~tdialNOZZLE

00 0 30 40 s0 60 70 80

ANGLEFROMMODEL TOP CENTERLINE, DEG.

Fig. 9 EdaDitiuonof Peak Pressures for~ Separated Flow Case

2000 ICONDITIONS:

NOZZLE EXPANSION RATIO r8:INOZZLE EXPANSION ANGLE ý300(TOTAL)

6 60 JETEVATOR RADIUS *7 16 IN. ____ ____

.4HINGE PARAMETER e, a7 50NOZZLE EXIT PRESSURE e6.3 PSIA

0MOTOR CHAMBER PRESSURE 500 PSIA UNISEF'ARATED? 1.25 I FLOW CASE

~ 100 ..-.-.-L--.--EXPERIMENTAL I

0.

F00

0 SEPARATEDFLOW CASE

04 8 12 16 20 24 28JETEVATOR DEFLECTION, DEG

Fig. 10 Comparison o f Load s Predic~ted by Analytical Study toExperimental Data

LOCKHEED AIRCRtAFT CORPORATION J S A and SPACE DIVISION

114,M)- 26 3a

of the jetevator hinre point with respect to the nozz'le exit plane.

Since the location of the hinge point detcniitnes the angle 0. (seeFig. 5) and the initial flow turning anrle from the nozzle to jet.-

vator, it was expected that the sepnrntlon characteristics in the

nozzle and the pressure distribution over the jetevator would be Qf-

fected by a change in hinge Voint position. In the tests, the hinge

point location was varied to give a 7° change in Oo and the resutltn

are shown in Fig. 11. An the flow-turning angle inercam.d (represent-

ing a decrease in 0. ), the point of separation moved upstream in the

nozzle and the pressures over the aft surface of the jetevator increased.

Since the phenomenon of flow separation in the nozzle is a result of

an adverse pressure gradient due to the initial flow turning angle at theSI •uncture of the nozzle and jetevator, an investiGation wnr, ma(de using the

Cap between the nozzle and jetevator as a means of boundary layer control.

By opening the gap, and thus venting the high pressure region to the low

back pressure, it was found that the flow boundary over the .etevator was

changed causing greater compression which in turn restilted in higher pros-

sures over the aft three-fourths of the jetevator. Figure 12 presents thecenter-line pressure distribution for a minimum nozzle-to-jetevator gap

clearance (indicated as "0" on the figure) and a gap of 0.20 in. Similar

increases in pressure were recorded at stations measured 30 , )45°, and 600

radially from the center-line. Later tects run on similar eonfigurntions

showed the optimum gap to be in the order of 0.30 in. These results have

not yet been confirmed in rocket motor firings due to the serious problem

of the hot gases which blow back through the gap. The gap effects are

particularly interesting inasmuch as rocket firing experience has indica-

ted that serious difficulties can be encountered with scpalling metal

essentially welding the jetevators to the nozzle if small gaps are main-

tained. On the other hand, if shielding shrouds have to be provided to

deflect blowby gas, a weight penalty is incurred.

The effect of nozzle trailing edge thickness on the pressure distri-

bution was also investigated. A comparison of the pressure data for a

nozzle with a sharp trailing edge at a jetevator deflection of 250 (see

SLOCKHEED AIRCRAFT CORPORATION M tind SPACE DIVISION

- ~L

I .... .... d d..

DEFLECTEDJETEVATOR

i~i!FLOW•. 6-200

JETEVATOR O0HINGE POINT-. 1

Sg5.40a. SYMBOL Oo DEG.

li•-•'° ---- 67 -30 --- 60 I

TOTAL PRESSURE =200 PSIA //

0) .0

Cl) -10 -8 -6 -4 -2 0 2 4 6waNOZZLE STATION9 IN.(:L

Fig- 11 Effect of Jetevator 11inge Location on the Pressure Distributionalong Nozzle and Jetevator Centerline

33

LOCKHEED AIRCRAFT CORPORATO t. r .U and SPACE DIVISION

- FDN LMSD-2630

°; •GN F.]DE NT1.A.L`. -[,

GAPDEFLECTED

NOZZLE JETEVATOR

FLOW 6 =220

JETEVATOR .°=60O

HINGE POINT

r_ ".o -- 0-- 1 1 -_ _- _ _ " _ I t

0I a I -. __ - -0

SY o 0L GPIN I iS TOTAL PRESSURE= 200 PSI I-J .0

"0 -0

S.10 _J

LU

i.!OZZLE STf- o,T I,0!,

Fig. 12 Effect o;' -Owi on Pressure D• •tribution along Nozzle andoiJetevator Centerline an

34A" ,A

LOCKHEED AIRCRAFT CORPORTO u&'..)EN11~ and SPACE DIVISION

U-,7D 26.3•o w

I26X0

Fig. 8) to the one with a thick trailing edge for the case ofi "0" gnp

clearance (see Fig. 12) shows:

1. Separation occurs at a more forward point in the nozzle.

2. The pressure rise occurs over a more forward portion of

the jetevator.

3. A lower peak pressure is obtained for the ca&a of the

sharp trailing edge.

Sufficient data on the effect of nozzle trailing edge thickness are not

available. The data to date indicate however, that it is desirable to design

the nozzle trailing edge as thin as can be tolerated by the ability of thematerial to withstand heating. In fact, in several rocket firings excessive

nozzle trailing edge thickness is considered to have contributed to serious

load reversals at small jetevator deflection angles and nonlinearity of con-

trol load as a function of jetevator angle.

I

35

LOCKHEED AIRCRAFT CORPORATION and SPACE DIVISION

AMSD- 2(30

CONCLUSIONS

The analysis presented has proved to be very useful not only in preliminarydesign investigations of Jetevators but also in studies of the stability and

control of missiles employing Jetevator control systems. It is believed that.

the most pertinent parameters have been included; however, it is recognized

that a number of assumptions related primarily to the problems of real gas

flows have been made. The most troublesome areas, of course, are the formula-

tion of an analytical expression for the pressure distribution on the Jetevator

and the specification of the flow separation boundaries and their effect upon

the pressure distribution. Conceivably, further examination of second order

expressions for the pressure distribution (see Eq. 4) and a more detailed

study of the effects of pressure gradient upon boundary layer separation will

improve the accuracy of analytical computations. However, only a limited number

of jetevator tests have been made to date, and much of the information required

to more accurately formulate the analytical framework will probably come in

future tests of the devices.

I.......

36

LOCKHEED AIRCRAFT CORPORATION -"'"-.fJD,"1tAL -. "" 'ISSILES .,d SPACE DIVISION

"II

L", U tem." .,

RE F EREI4CES

1. A. Leone, "Surrey of Methods for Deflecting Exhaust in Missile Control".

U. S. Ncval Air Rocket Test Statio.n Report No. 60, September 1955.Confidential.

2. W. A. Fiedler, "Thrust Direction Control by Jetevator", Progress

Summary Report No. 15, USNAMTC, Point Mugu, Calif., May 1956,

3, Roy H. Lange, "Present Status of Information Relative to the Prediction

of Shock-Induced Boundary-Layer Separation". NACA TN 3065, February 1954.

4. Eli Reshofho and Maurice Tuicker, "Effect of a Discontinuity on Turbulent

Boundary-Layer Thickness Parameters with Application to Shock-Induced

Separation", NACA TN 3454, May 1955.

5. R. A. Nilson, "Final Test Report-XM-36 Thrust Alignment Test". Aerojet-

General Corporation Test No. D-232-SA-1, September ).957. Confidential,

37

LOCKHEED AIRCRAFT CORPORtATION S and SPAC. DIVISION