U.1 OEPMTMERT Of OOMHEKE li

AD-A02a 657

EFFECT OF THE CONSTRICTIVE AREA RATIO ON THE

ROCKET EXHAUST FLOW-FIELD IN THE LAUNCHER

TEXAS UNIVERSITY AT AUSTIN

PREPARED FOR

ARMY MISSILE COMMAND

FEBRUARY 1976

146098

THE UNIVERSITY OF TEXAS AT AUSTIN

EFFECT OF THE CONSTRICTIVE

AREA RATIO ON THE ROCKET EXHAUST

£* ' FLOW-FIELD IN THE LAUNCHER

«O. ^ > John J. Bertin, Gena M. Garms, and Ed S. Idar, III

O <

r D C

i

A

Aerospace Engineering Report 76001

This work was supported by

^ ) the U.S. Army Missile Command

through contract DAAH01-73-0-1016

«PRODUCED BY

NATIONAL TECHNICAL INFORMATION SERVICE '

U, S. jDCPAIITMENT OF COMMEIKE SPRINGFiaO. VA. 221S1

February 1976

Dcpanmcnt of Aerospace Engineering and Engineering Mechanics

pi: A'

.! ■ : ..iii^i*.

J

EFFECT OF THE CONSTRICTIVE AREA RATIO ON THE ROCKET EXHAUST FLOW-FIELD

IN THE LAUNCHER

by John J. Bert in, Gena M. Garms , and Ed S. Idar, III

Aerospace Engineering Report 76001

This work was supported by the U.S. Army Missile Command through Contract DAAH01-73-C-1016

n-

Department of Aerospace Engineering and Engineering Mechanics

The University of Texas at Austin February 1976

J

ACKNOWLEDGEMENTS

This analysis of flow field data for constrictive launch tubes was

supported by the U.S. Army Missile Command (Huntsville, Alabama) through

Contract DAAH01-73-C-1016. The authors acknowledge the considerable

efforts of Mr. David Booker and Dr. James L. Batson in providing informa-

tion about the relevant MICOM programs for which the University's tests

would provide meaningful support and for technical direction to the

University effort.

The authors would also like to thank Miss Bernadette Ashman and

Mrs. Pat Kleinert for cheerfully typing the numerous drafts of the manu-

script.

XA

f

TABLE OF CONTENTS

Pages

ACKNOWLEDGEMENTS i

IN1RODUCTION 1

NOMENCLATURE 5

EXPERIMENTAL PROGRAM 7 The Facility 7

Nozzle 8 Launch tubes 9

Data 10 Static-wall-pressure 11 Blow-by mass-flow-rate 11 Schlieren photographs 12

Test Program 13

DISCUSSION OF RESULTS 1U Launcher Configuration 2 15

Region 1: x > 0 15 0 ne Region 2: -6 r < x < 0 16 B ne ne Region 3: x < -6.5 r 16 B ne ne

Luimcher Configuration 3 20 Launcher Configuration 1 2U The Effect of Constrictive Area Ratio 2U

CONCLUDING REMARKS 2f

REFERENCES 27

TABLE 29

FIGURES 30

ii

INTRODUCTION

There are a variety of military rockets which are launched from vari-

able-area launch tubes. The change in cross section allows the rocket to

be initially constrained after ignition, while momentum is gained. The

flow of the high temperature and high pressure rocket exhaust gas is of

practical interest in the structural design of the launcher. Of special

concern is the possible generation of unbalanced forces on the rocket by

exhaust gases which are deflected upstream (i.e., blow-by flow) and which

could influence the trajectory, once the rocket is released from its con-

straints. Flow in the so-called "non-tipoff' launch tubes is particularly

conplex since these tubes have diameter changes so that the rocket flies

free of any tube support for a short distance as it emerges from the tube.

When the rocket exhausts directly into the small-diameter, aft tube,

the flow downstream of the nozzle exit is entirely supersonic and intersect-

ing, weak shock-waves occur. The resultant flow field is that for an undar-

expanded, supersonic jet exhausting into a constant-area tube having an in-

side diameter which is slightly larger than the nozzle exit. Fabri and

Siestrunck (Ref. 1) found that the flow field in the tube varied with in-

creasing rocket chamber pressure from mixed flow (subsonic and supersonic

flow exist in the tube) with flow separation in the tube to fully developed

supersonic flow throughout the tube (except, of course, in the viscous layers).

Batson (Ref. 2) found that the static wall-pressure distributions in a con-

stant-area tube which were obtained during a cold-gas test program were

qualitatively similar to those obtained when a stationary rocket was exhausted

into a constant-area tube. Batson and 3ertin (Ref. 3) examined the tube-wall

static-pressure distributions which were obtained when a rocket accelerated

through an instrumented tube. The static-wall-pressures from these dynamic

1

rocket firings were qualitatively similar to the corresponding data from the

static rocket firings of Ref. 2.

Significant blow-by flow was observed during an eight-flight test pro-

gram in which Rip-Zap con figuration? were launched from a sparsely instilment-

ed, non-tipoff launch tube. The constrictive launch tube, the launcher instru-

mentation, and the resultant data are described in Ref. U. However, because

of the paucity of test data, it was not possible to construct a flow model

from these data. After these firings, personnel from the University of Texas

at Austin entered the program. A more extensive instrumentation package for

the launcher was designed for use in a subsequent series of four flights.

Participation in the flight-test program by the University started with the

specification of instrumentation for these four flights. The instrumentation

package included static pressures, pitot pressures, and differential measure-

ments of diametrically opposed static wall-pressures. A primary objective

of this flight-test program was to obtain information which could be used to

define important parameters for the flow field in the launcher. Of special

interest was the identification of the source of blow-oy flow. Two launcher

geometries were included in the program. For one, the constrictive change in

geometiy was accomplished abruptly (i.e., a modified rectangular step); for

the other, the area change was more gradual (i.e., a 15° ramp). For both

configurations the cross-sectional area of the small-diameter, aft tube was

0.595 that of the forward tube. The flight-test data for this program have

been discussed in Refs. 5 and 6.

Because of the complexity of the flow in the launcher, additional data

were needed to construct a realistic flow model. To aid in the analysis of

the data from the Rip-Zap launch program, two additional test programs have

been conducted in which an underexpanded jet of unheated gas was exhausted

from a stationary nozzle into a constrictive launch tube. The programs were

conducted at the U.S. Army Missile Command and at the University of Texas at

Austin. The objectives ot the cold-gas tests conducted at the U.S. Army Missile

Command included the determination of the effect of reservoir pressure, nozzle-

exit-position, and constrictive geometry on the blow-by mass-flow rate and on

the static wall-pressure distribution in the launcher. The data from these tests

were discussed in Ref. 7. When the nozzle exhausted directly Into the small-

diameter, aft tube, there was no significant blow-by flow. When the nozzle ex-

hausted into the large-diameter, forward tube, significant blow-by flow was

generated. For many rest conditions, the blow-by flow in the annular region

between the rocket and the launcher wall was transonic.

The cold-gas test program conducted at the University of Texas was design-

ed to answer specific questions which arose during the analysis of the data from

the Rip-Zap flight-test program (Refs. 5 and 6). The objectives of the cold-

gas test program included the determination of the effect of vent ports located

just upstream of the constriction and the determination of the parameters which

govern the process by which flow downstream of the impingement shock is choked.

Design considerations required immediate answers to the questions about the ef-

fect of vent holes. Therefore, for this phase of the test programs, the

(quickly-built) launcher configuration simulated only a fraction of the length

of the small-diameter, aft tube (i.e., the aft tube was, therefore, in reality

a constrictive plug for the forward tube). However, the majority of the test

program used a complete-length (but approximate) 0.2-scale model of the Rip-

Zap launch tube. The geometry of the static nozzle which generated the re-

quired underexpanded, supersonic exhaust flow was the same for both phases of

the test program. The data from this experimental program were presented in

Ref. 8.

Experimental static-wall-pressure distributions were also obtained during

launchings of the Arrow configuration, which were conducted at the U.S. Army

Micsile Command Facility in Huntsville, Alabama. The cross-sectional area

of the aft tube was 0.718 that of the foivard tub« for the Arrow launch

tube. The pressure data indicated that there was not significant blow-by

flow for the Arrow configuration (Ref. 9). Thus, a comparison of the data

from the two flight-test programs demonstrates that the flow field in the

launcher depends on the ratio of the nozzle-exit radius:aft-tuLe radius:

forward-tube radius (as well as other parameters).

An experimental program has been conducted at the University of Texas

in which unheated clr was exhausted from an underexpanded nozzle into three

different constrictive launch tubes. The primary variable of the test pro-

gram was the diameter of the aft tube. Thus, for the present test-program,

the cross-sectional area of the aft tube was 0.668, 0.735, and 0.878 of the

area of the forward tube. The data for these three launcher configurations

are discussed in the present paper.

ne

aft

ate

ati »

atm

bb

cyl

■

ds

ex

for

HOHDICLATURE

A cross-sectional area

H Mach number

1 «ass-flow rate

P static pressure

Pt total pressure

P radius

R gas constant

T static temperature

Tt total tcroperature

u streamwise velocity

X axial coordinate

Y ratio of specific heats

0 density

9 half-angle of the conical nozzle

Subscripts

for the small-diameter, aft tube

at the exit plane of the aft tube

at the entrance plane (or initial station) of the aft tube

atmospheric conditions

for the blow-by flow

for the cylinder representing the external surface of the rocket

downstream of the strong impingement shock

for the flow exhausting through the nozzle

for the large-diameter, forward tube

n# for the nozzle exit-plane

us upstream of the strong impingement shock

for the reservoir chamber of the nozzle

EXPLRIMENT/vL PROGRAM

The objectives of the experimental program included the determination

of the parameters which govern the generation of & strong shock wave which

may occur when the exhaust flow impinges on the -./ail. Of special interest

was the detemination of the ratio of the radius of the aft the (r _ ) to

the radius of foivard tube (r, ) for which the flow was no longer choked

by the constriction. The variables of the test program included the total

pressure in the nozzle stagnation chamber, the nozzle-exit-plane position,

and the ratio r .^.^r (or» equivalently, the constrictive area ratio

aft for

The Facility

As shown in r':e sketch of Fig. 1, the cold-gas Rocket-Exhaus effects

Facility at the University of Texas at Austin consists of a high pleasure

supply system, a convergent-divergent nozzle (to simulate the rocket motor),

and an instrumented, variable-are a, launch tube. The instrumented tube could

be moved axially to vary the location of the nozzle-exit-plane relative to

the constriction and, thereby, to simulate (in a quasi-steady manner) the

flow-fields which result when the rocket accelerates through the launcher.

The assumption that the exhaust flow for the dynamic rocket launching is

quasi-steady is based on the fact that the velocity of the exhaust gas is

more than twenty times the velocity of the rocket as it leaves the launcher.

Photographs of the facility are presented in Fig. 2. The high pressure

supply line (or feed pipe) which supplies air to the nozzle appears near the

left center of the photograph of Fig. 2a. The launch tube is mounted on a

movable table so that Its location relative to the exit plane of the station-

ary nozzle is a parameter of the test program. For the present program the

nozzle axis and the launcher axis were colinear (although tipoff configurations

can be simulated with the current apparatus). Also shown are the launcher

instrumentation and the data monitoring systems. A close-up photograph of the

"simulated" rocket positioned relative to the launch tube is presented in

Fig. 2b. Note the pitot probe located in the annular region between the

"simulated" rocket and the launcher wall. The probe is located at the up-

stream end of the forward tube in order to provide a measure of the mass-flow

rate of the reverse, or blow-by, flow.

Nozzle. - A sketch of the convergent-divergent nozzle used in the present pro-

gram is presented in Fig. 3. For this nozzle, the fairing between the con-

vergent section and the conical divergent section was such that the throat

radius of curvature was relatively small. If the flow is assumed to accelerate

isentropically, the Mach number in the exit plane is 2.3U for the area ratio

of the nozzle. However, shock waves which intersect at the nozzle axis in

the vicinity of the nozzle-exit plane and which are evident in the schlieren

photograph of the exhaust flow indicate that the acceleration of the flow in

the conical divergent section was not an isentropic process. As suggested by

Cline (Ref. 10), a possible source of the obl..que shock wave is the discontin-

uity of the second derivative of the nozzle contour, A discussion of this

shock is given in Ref. 11. It is possible to minimize (or to eliminate) this

shock wave by increasing the radius of curvature or by contouring the throat

curvature just upstream of the tangency point. Because of the presence of

the shock waves, a series of tests were conducted in which pitot-pressure

rakes were used to probe the» flow from the nozzle-exit plane to four diamete.s

downstream of the nozzle as it exhausted into a straight tube. For the pre-

sent conical nozzle (i.e., 6 = 10°), the transverse distributions of the * ne

experimentally-determined total-pressure were in approximate agreement with

the theoretical solutions obtained using a numerical code which assumed that

the flow in the nozzle and that upstream of the weak, inpingeraent shock wave

was isentropic. For larger half-angle nozzles (i.e., 6 = 20°), there were

significant differences between the data (from the unreported tests) and the

theoretical solutions. Therefore, no effort was made to alter the nozzle ex-

haust characteristics for the present test progx'am.

Launch tubes. - The relevant dimensions of the three launch tubes are present-

ed in Fig. k together with a sketch of the launcher and its instrumentation.

The diameter of the aft tube was less than that of the forvard tube. Hence,

with the exit plane of the nozzle in the forward tube, the change in cross

section served to constrict the flow of the exhaust gases. The change in

geometry was acconplished by a rectangular step. The face of the step served

as the origin of x (or axial) coordinate system. The coordinate system was

such that x was positive for the aft tube and negative for the forward tube.

As has been discussed, these tests were conducted to determine the ratio

of A ft'-hf for which the flow was no longer choked by the constriction.

For the three launcher configurations of the present program, the cross-sec-

tional area of the aft tube was 0,668, 0.735, and 0.878 of the area of the

forward tube. The data from these configurations were intended to complement

the data from the 0.2-scale Rip-Zap launcher, whose area ratio was 0.595

(refer to Ref. 8). Therefore, a single nunbering system was used to identify

the four tubes used in the two programs. Tube no. 1 identifies the Rip-Zap

configuration (Ref. 8). Tubes 2 through •* represent the three configurations

of the present report. The constrictive area ratio, A _ :Af , increases with

the tube nuirber. The diauneter of the fonrard tube was the same for all four

tubes, i.e., 1.75 inches (t.U5 cm). Thus, the variation in the area ratio

was accomplished by varying the diameter of the aft tube. The specific values

are presented in the table of Fig. 4.

1(1

Experience with the analysis of the flight test data for the Arrow launcher

configuration, which had only six static-wall-pressure orifices (see Ref. 9),

indicated that six gages would suffice if considerable a priori insight into

the flow field was available. Thus, it was decided that the data from six

static-wall-pressure orifices would be sufficient to "verify" the character of

the flow field in the launcher. The use of the term "verify" presupposes that

the flow field models which were developed in the analyses of Refs. 5, 8, and

9 will exist for the present configuration and can be identified with the pres-

sure measurements from the six orifices. Three orifices were located in the

sraall-diaineter, aft tube and three in the large-diameter, forward tube. In

each tube, one gage was located near the internal end, another near the middle.,

and the third near the external end. The overall length was 33.000 in.

(83.820 cm.) for all three launcher configurations. The forward tube was nom-

inally 15.0 in. (38.1 cm.) and the aft tube was nominally 18.0 in. (US.7 cm.).

See Fig. H for details.

Data

The first step of the test procedure was to firmly position the launch

tube so that the zero reference station was at the desired distance from the

nozzle-exit plane. Furthermore, the axes of the nozzle and the launcher were

colinear. The stagnation pressure in the nozzle reservoi. and, therefore, the

mass-flow-rate of the unheated air was controlled using the control valve of

Fig. 1. The minimum value of stagnation pressure in the nozzle reservoir (ptl)

6 2 for which data were recorded was approximately 200 psia (1.38 x 10 N/m ). At

this value of p , the theoretical value (for isentropic flow) of the static

pressure in the nozzle-exit plane was approximately equal to the atmospheric

pressure. Through periodic adjustments of the control valve, the stagnation

pressure was increased to another value, held constant while the data were

11

c 9 recorded, and increased again up to a maximum of 1000 psia (6.90 x 10 N/m ).

Approximately 5 seconds were required to obtain the required data at a parti-

cular stagnation pressure. The experimental data obtained during a run in-

cluded the static-wall-pressure distribution, the stagnation pressure in the

nozzle reservoir, the total pressure of the reverse (or blow-by) flow in the

annular region, and (for certain tests) schlieren photographs.

Static-wall-pressure. - The locations and dimensions of the static-wall-pres-

sure orifices were discussed in the previous section. The static-wall-pressures

were measured using either bourdon-type dial gages or potentiometer-type trans-

ducers. The bourdon-type gages used had ranges of 0 to 30 psig, 0 to 60 psig,

-14.7 to 100 psig, -1U.7 to 50 psig, 0 to 200 psig, 0 to U5 psig, and 0 to

2000 psig. The pressure ranges for the transducers were 0 to 45 psig, 0 to

100 psia, 0 to 600 psia, 0 to 1000 psia, and 0 to 3000 psia. The output from

the dial-type gages were recorded photographically. The output from the trans-

ducers was recorded using either strip chart recorders or on an oscillograph

(See Fig. 2a). Because the number of orifices exceeded the number of gages

available, it was necessary to run more than once to obtain a conplete distri-

bution for a particular nozzle position.

Blow-by mass-flow-rate. - An estimate of the blcw-by mass-flow-rate was made

using the pressure data from the pitot probe located in the annular region be-

tween the "rocket" nozzle and the launch tube (see Fig. 2b). In order to

obtain numerical values, the variations of the local flow properties across

the annular region were neglected for the present calculations. Thus,

**> = "bbV^for - rcyl) (1)

For a perfect gas

and

17

'- ■ 4

"bb •'S* V^55» (3)

Since the blow-by flow was found to be subsonic, the static pressure at the

forward exit-plane of the launcher was atmospheric (which was verified by the

static-wall-pressure measurements from this region). The ratio Pvv/?*.>.>, was

used to calculate the blow-by Mach number (Ref. 12). If one assumes that the

flow was adiabatic from the reservoir, thro'j^jh the nozzle, and through the

flow reversal, the energy equation yields

Of primary interest is the fraction of the nozzle exhaust flow which was

reversed. The mass flow of the "rocket" nozzle exhaust is given by:

1

Thus, the dimensionless blow-by mass-flow-rate is:

2

Y+l \Y+l) (r )

For the geometry of the current test program, which used unheated air as the

test gas:

%= «+.1I1384 M 1^- ^- (7) "ex UJTbb Ptl

Schlieren photographs. - The facility has an all-lens schlieren system which

was used during certain runs to study the flow as it exhausted from the an-

13

nular region at the forward exit-plane of the launcher or from the vent ports.

Schlieren photographs were also taken of the nozzle exhaust flow (refer to

Fig. 3).

Test Program

As noted earlier, the variables of the test program included the total

pressure in the nozzle stagnation chanber, the nozzle-exit-plane position, and

the ratio r ^sr. . Data were obtained over the range of reservoir stagna-

tion pressure from 200 psia (1.38 x 106 N/m2) to 1000 psia (6.90 x 106 N/m2).

As can be seen in the run schedule presented in Table 1, the nozzle exhausted

directly into the small-diameter, aft tube for some tests, i.e., x = -fl.OO r . ' ' ' * ne ne

However, for the majority of the runs, the nozzle exhausted into the large-dia-

meter forward tube. The nozzle-exit positions investigated were such that

-19.25 r < x < +1.00 r . It should be noted that two or three runs were ne — ne — na

conducted for each rocket-nozzle location/launcher configuration indicated in

Table 1. In each case, the measurements from the repeat runs were in essential

agreement with each other. For launcher 2, A £. was 0.668 A- ; for the launcher

3, A _ was 0.735 k, ; and for launcher <+, \ _. was 0.878 A£ . aft for* aft for

DISCUSSION OF RESULTS «

The static-wall-pressure distributions obtained during the Rip-Zap

flight test program (for which A _= 0.S95 A- ) indicate that the exhaust

flow was choked by the constriction, a strong shock wave was generated when

the flow inpinged on the wall and the downstream flow was subsonic. The

large adverse pressure gradient produced by the s+rong shock wave caused a

significant fraction of the flow in the impinging shear layer to be turned

upstream (which is termed the reverse, or blow-by, flow). The static-wall-

pressure distributions obtained during the Arrow flight-test program (for

which A ... = 0.718 A, ) indicate that the exhaust flow remained supersonic, aft for ^

As a result, there was not significant blow-by flow. Using ecld-gas data ob-

tained in the university's Rocket-Exhaust Effects Facility, a flow model was

developed which described the choked flow in the launcher. Despite the

simplicity of the flow model, the theoretical pressures were in excellent

agreement with the cold-gas data for the 0.2-scale model tests and were in

fair agreement with the flight-test data. A sketch of the proposed flow model

is presented in Fig. 5. The relative dimensions of nozzle-exit radius (r ):

aft-tube radius (r .c^.):forward-tube radius (r_ ) are to scale. The axial di- art ror

mansions are not to scale. Thus, whereas the inpingement shock wave 5s sketch-

ed as a normal shock wave extending almost from wall to wall, oblique shock

waves associr.ted with the initial turning of the flow probably extended over

a longer distance than indicated in the sketch. The extent over which the

pressure rise occurred would be a measure of the interaction between the viscous

shear layer and the complex shock-wave structure. The essential features of the

flow model include: (1) the underexpanded flow in the nozzle exit plane (desig-

nated by the subscript ne), (2) the supersonic flow just upstream of the impinge-

ment shock wave (designated by the subscript us), (3) the subsonic flow just

1U

1!.

downstream of the strong impingement shock wave (designated by the subscript

ds), (U) the reverse, or blow-by, flow (i.e., that fluid in the viscous shear

layer which cannot overcome the adverse pressure gradient generated by the inter-

action between the impingement shock and the viscous flow), (5) the region at

the base of the step where some of the fluid which has passed through the shock

system stagnates, (6) the subsonic flow at the entrance of the small-diameter,

aft tube (designated by the subscript ati), and (7) the sonic flow at the exit

plane of the small-dianeter, aft tube (designated by the subscript ate).

Since the data for launcher configuration 2 (for which A _= 0.668 A- ) 6 aft or

indicate that the flow field was qualitatively similar to that (described

above) for the Rip-Zap configuration (i.e., launcher configuration 1), they

will be presented first. After discussing the data for launcher configurations

3 and 4, correlations indicating tha effect of the constrictive area ratio will

be presented.

Launcher Configuration 2

As was the case for launcher configuration 1 (i.e., the 0.2-scale Rip-Zap

launcher), the blow-by flow rates for launcher configuration 2 can be used to

define the range of nozzle exit positions for each of three cheu?acteristics re-

gions. The blow-by mass-flow-rate divided by the total flow through the nozzle

is presented as a function of the nozzle-exit position in Fig. 6 for p , s 950

6 2 psia (6.55 x 10 N/m ). Based on these data, the three characteristic regions

are as follows.

(1) Region 1: For x > 0, the downstream flow remained entirely supersonic

and the blow-by mass-flow-rate was negligible. Only that portion of the fluid

in the shear layer which could not overcome the relatively small adverse pressure

gradient associated with the weak, impingement shock wave was turned upstream.

If.

(2) Region 2: lor -6 r S x < 0, the mass-flow-rate varied rapiilly with

nozzle location. When x = -1.0 r , m.. was approximately 0.07 m . Foi-

-4.16 r <_ x <_ -2.35 r , m. . was approximately 0.05 m . This position-

dependent variation is believed to be similar to the puff of blow-by flow ob-

served during the Rip-Zap flight-test program (Ref. 6). For -6.U1 r ^_ x

< -4.16 r , the blow-by mass-flow-rate increased with distance from the face ne '

of the rectangular step.

(3) Region 3: When the exit plane was well into the forward tube, :'..e.,

x < -6.5 r , the flow downstream of the inpingement shock wave was choked ne ne f e,

by the constrictive change in cross section. The normal shock wave which was

generated when the exhaust flow inpinged on the wall caused a rapid increase

in pressure in the streamwise direction. This large, adverse pressure gradient

caused a considerable portion of the fluid in the viscous layer to be turned

upstream into the annular region. With the exception of the measurements ob-

tained when x was -15 r , the blow-by flow rate was essentially independent

of nozzle position at this value of the stagnation pressure, i.e.^ approximately

950 psia (6.55 x 10 N/m ). Whether the relatively low blow-by flow rates ob-

tained for x = -15.0 r were due to experimental error or to some unexplain- ne ne r T

ed flow mechanism is not known. However, the relatively large scatter in the

data and the fact that a similar phenomena was not observed for launcher con-

figuration 1 indicate experimental error.

Also presented In Fig. 6 are data from experimental programs where an un-

heated gas was exhausted into a constrictive launcher with A ^ = 0.595 Af

(i.e., the Rip-Zap configuration, or launcher configuration 1). For -5 r ~

x < 0, m,, increased with distance from the step for the 0.2-scale launcher

of Ref. 8 (based on the two locations tested) but decreased from the MICOM

configuration with th« rectangular-step (i.e., the launcher of Ref. 7). Note,

however, that the 0.38 scale launcher of Ref. 7 simulated only 4.19 r of the J ne

17

forvard tube, whereas the launcher of Ref. 8 simulated the entire length. A:-

a result, the forward tube was much shorter and the dimension of the annular

gap larger for the launcher of Ref. 7. Thus, in Ref. 8 the principal author

observed that "the viscous effects were significantly different for the two

rectangular-step configurations. Whether the differences in the viscous ef-

fects explains the apparent anomaly in the blow-by data of Fig. 6 is not known".

For -U r < x < 0, the blow-by flow rates decreased with distance from the ne — ne

step for launcher configuration 2, which supported the data of Ref. 7. Fur-

thermore, the blow-by flow rates were equal for the two Pip-Zap launchers

(i.e., those of Refs. 7 and 8) when x was approximately -2.4 r (which was ne ^r J ne

the only nozzle-exit location tested for launcher configuration 1 in the range

-Ur £x <0). Thus, the apparent discrepancy between the blow-by data

for the two launchers with A ft = 0.595 Af was not a discrepancy at all. In-

stead, with the additional insight provided by the data of the present tests,

it is believed that had more data been available for the configuration of

Ref. 8, the correlation between blow-by flow rate and nozzle-exit location

would have been the same for both Rip-Zap launchers.

The pressure distributions measured for configuration 2 with x = -2.35 r r 0 ne ne

are compared with the data for configuration 1 (i.e., the Rip-Zap configuration

of Ref. 8) in Fig. 7a. For p < »+37 psia (3.02 x 10 N/m ), the data were

qualitatively similar for the two configurations. At these relatively low

stagnation pressures, the theoretical value of the static pressure in the noz-

zle exit-plane (assuming isentropic flow in the nozzle) was "approximately" equal

to the atmospheric value. The exhaust flow apparently impinged on the face of

the step, producing the pressure increase evident at the base of the step. The

resultant pressure gradient from the internal end of the forward tube (i.e.,

x = 0) to the forward end of the launcher (i.e. , x = -26.6 r ) apparently was ne

not sufficient to produce a significant blow-by flow-rate.

18

For p >_ 506 psia (3.U9 x 10 N/m ), the pressure in the exit-plane of

the nozzle was so much greater than the atmospheric value that the exhaust flow

impinged on the wall as it expanded into the forward tube. Downstream of the

Impingement shock, the pressure increased, reaching a maximum at the base of

the step. Thus, the impinging exhaust flow encountered a large adverse pressure

gradient which caused a significant portion of the fluid to be turned upstream,

i.e., to be reversed. The mass-flow rate of the reverse, or blow-by, flow was

approximately 5 per cent of the mass-flow-rate through the nozzle (see Fig. 6).

The blow-by flow rate was sufficient to produce nonatmospheric values for the

static-wall-pressure measurements in the annular region between the rocket and

the wall of the forward tube. However, since the reverse flew was subsonic,

the static pressure at the forward end of the annular region was equal to the

atmospheric value. The experimental static pressures from the aft tube are

significantly less than the values obtained in tests where the flow in the aft-

tube was subsonic, e.g.. Fig. 7d. Thus, it is believed that the flow in the

aft tube was supersonic over the entire range of p .. for x = -2.35 r

The pressure measurements for x = -C+l r , -10.11 r , -15.00 r and r ne ne' ne' ne

-19.25 r are presented in Figs. 7b through 7e. For a given nozzle-exit lo-

cation, the pressure distribution changed character when the stagnation pressure

(or, equivalently, the mass-flow rate through the nozzle) was above a critical

value. The critical value was a function of nozzle-exit-position. As a re-

sult of the changes in the mass flow-rate» in the strength of the iinpinger»nt

shock, and in the fluid properties downstream of the impingement shock wave,

the flow was choko 1 by the constriction. A strong shock wave was generated

in the region where the exhaust flow impinged on thj wall. The fact that the

static pressure decreased as the flow passed through the constriction indicated

that the flow downstream of the impingement shock-wave was subsonic. Recall

that, if dA < 0, subsonic flow accelerates while supersonic flow decelerates.

19 The interaction between the strong shock wave and the viscous shear layer

created a large pressure gradient which caused a large fraction of the flow

to be turned upstream. Thus t the exhaust flows which produced the pressure

data presented in Figs. 7b-7e correspond to the flow model presented in

Fig. 5.

To substantiate the validity of the flow model for the choked flow of

Region 3, let us compare the experimental pressures of Figs. 7c-7e with the cor-

responding theoretical values. The theoretical values assume a one-dimen-

sional flow incorporating the phenomena of Fig. 5. The one-dimensional ex-

haust flow was assumed to accelerate isentropically from the sonic condi-

tions at the throat to the conditions just upstream of the shock. Since A,

* wcs 5.302A . M was 3.237 (see Ref. 12). Downstream of the normal shock-wave ' us

the theoretical Mach number CM. ) was 0.U626 and the theoretical static ores- os

sure (p^) was 0.2147 p . The theoretical value for the static pressure was

in reasonable agreement with the experimental values of Fig. 7e (the exper-

imental values were approximately 0.22 Ptli« The theoretical stagnation-pres-

sure downstream of a normal shock-wave (0.2676 p^,) was in reasonable agreement

with the pressures measured at the base of the rectangular step. Thus, CD there

was reasonable agreement between the experimental data and the theoretical

values Cfor the relatively crude approximations), C2) the location of the nor-

mal shock wave was fixed with respert to the nozzle exit-plane, and (3) the

choked flow-by flow rate was independent of nozzle-exit location. These three

observations support the conclusion (as illustrated in Fig. 5) that the fluid

which constituted the blow-by flow did not pass through ..he shock system.

The drop in pressure indicated that the flow accelerated through the con-

striction (and was, therefore, subsonic). The model for the resultant flow in

the aft tube appears to be that described by Shapiro (Ref. 13) as choking due

to friction. That the flow in the exit plane of the aft tvise was indeed sonic

was indicated by the static pressure measurements (see Fig. 7e). Assuming that

the fluid near the center of the launcher accelerated isentropically from "ds",

the static pressure at the sonic location would have been 0.5283 p ,,, or

O.iuiu p . This vadue for the theoretical static pressure at the sonic loca-

tion was essentially equal to the static-pressure Measurements frcm near the

exit plane of the aft tube.

Launcher Configuration 3

The constrictive area ratio, A ^/A, , for launcher configuration 3 was art *or

0.735. Thus, the constrictive area ratio was close to that for the Arrow

launch tube (which was 0-718). However, whereas no significant blow-by flow

was observed during the Arrow flight-test program, such was not the case wnen

unheated air was exhausted into launcher configuration 3. Parameters which

differed between the cold-gas simulation and the rocket launching included the

following.

(1) Constrictive area ratio: 0.718 for the Arrow launch tube, 0.735

for launcher configuration 3

(2) Constrictive geometiy: U0 ramp by the Arrow la-mci tube, rectangular

step for launcher configuration 3

(3) y: 1.18 for the Arrow rocket, 1.U0 for the University's cold-gas

facility

(U) Nozzle half-angle: 5° for the Arrow rocket, 10° for the rocket ex-

haust effects facility.

The nondiroensionalized blow-by mass-flow-rates are presented in Fig. 8

as a function of the nozzle-exit location for the highest value of the stag-

nation pressure at which data were obtained, i.e., p . r 950 psia (6.55 x 10

2 N/m ). As was the case for launcher configurations 1 and 2, a significant,

position-dependent blow-by flow occurred as the nozzle exit-plane entered the

forward tube. The nondimensionalized blow-by mass-flow-rates for launcher

configuration 3 are significantly less than the values for launcher configure -

21

tions 1 and 2 (refer to Fig. 6). The variation in the magnitude of the blow-

by flow as the nozzle moved from the step has been duscribed as a puff. For

-10.HI r < x < -6.41 r . i.e., when the nozzle exit-plane was in the mid- ne — ne '- ne' r

die of the forward tube, the blow-by flow rate was negligible. The lack of

measureable blow-by flow indicated that the impingement shock wave was weak and

that the flow downstream of the impingement shock and into the aft tube remain-

ed supersonic. These conclusions based on the blow-by measurements were sub-

stantiated by the i->tatic-wall-press>':,e measurements, which are presented in

Figs. 10b and 10c. Thus, for these two nozzle positions, the cold-gas data were

consistent with the Arrow flight-test data.

When the nozzle exit-plane was positioned further frcm the step, the blow-

by flow rate increased dramatically. For x < -15.00 r , the blow-by flow ' ^ ne — ne' J

rate was constant at a "relat.'.vely high" value. Thus, the exhaust flow had

apparently choked as it encountered the constriction. Since th^ exhaust flow

did not choke until the nozzle exit-plane was 15.00 r , or more, into the r ne*

forward tube, the reduction of the effective cross-section due to the growth

of the viscous boundary-layar contributed to the choking of the flow.

The nondimensionalized blow-by mass-flow-rates are presented in Fig. 9

as a function of the reservoir stagnation pressure (for all six nozzle-exit

locations). As noted previously, the Mach nunber in the exit plane would be

2.34 if the flow in the nozzle expanded isentrop'cally. Therefore, the flow

in the nozzle would be overexpanded for p <_ 200 psia (1.38 x 10 N/m ).

Data are not presented for the overexpanded nozzle flows, since they were not

relevant to the applications of the present study. For x = -1.00 r , the

nondimensionalized blow-by flow rate was constant for p . > 400 psia (2.76 x

10 N/m ). The exhaust flow impinged directly on the face of the constrictive

step producing a pressure gradient along the annular region between the rocket

and the launcher wall. The pressure drop from the face of the step to the

2?

atmospheric value at the forward (external) eno of the forvard tube was :;ulli-

cient to turvi approximately 5% of the exhaust flow upstream. For x = -2.3b v , rr J ne IK-

the nozzle exit-plane was far enough into the forward tube that the exhaust fK>w

impinged on the wall upstream of the step. The majority of the exhaust gases

passed through the "weak" impingement shock-wave system. The fraction of the

exhaust flow which did not have sufficient momentum to overcome the adverse

pressure gradient associated with the impingement shock wave was negligible for

'tl c o

p <_ 700 psia (4.83 x 10 N/m ). The nondimensionalized blow-by flow rate in-

creased with p . for p .. > 700 psia (4.83 x 10 N/m ). Although the mechanism

which generated the pressure-dependent blow-by flow for this nozzle-exit loca-

tion is not understood, the nondimensionalized static pressure recorded at the

orifice located in the wall just upstream of the step was also significantly

greater for p...., > 700 psia (4.83 x 10 N/m ). For x = -6.41 r or -10.41 r , 0 ^tl r ne ne ne

the blow-by mass-flow-rate was insignificant over the entire range of reservoir

pressures tested. As noted, the lack of significant blow-by flow was consistent

with the data from the Arrow flight-test program. However, for x <_ -15 r ,

a significant portion of the exhaust flow was turned upstream over the entire

range of reservoir stagnation pressure tested. As evident in the static-wall-

pressure distributions (refer to Figs. lOd and lOe), the impingement shock wave

was strong. The downstream flow vjas subsonic as indicated by the acceleration

of the flow through the constriction (i.e., the pressure decreased).

Based or previous flight-test data (.Ref. 6) and cold-gas data (Ref. 8),

the difference in the geometry of the constriction should not significantly

alter the flow in the launcher. It is possible, however, that the constrictive

geometry would affect the internal flow-field for launcher configurations where

the total reduction in the effective cross-section due to the boundary lay«r

3pd to the constriction first causes the flow to choke. Since the constrictive

area ratio was greater for launcher configuration 3 than for the Arrow config-

uration, the fact that the flow choked was surprising. However, the differences

in Y and the conical-nozzle half-angle would cause th* impingement shock structure

to be different. Rip-Zap flight-test data dramatically illustrated (Ref. 5) how

the exhaust flow characteristics and the resultant changes in the impingement

shock structure could produce radical changes in the internal flow field. Be-

cause the cold-gas flow choked only when the nozzle was far into the forward tube,

it is believed that the growth of the viscous boundary-layer significantly af-

fected the choking process.

The static-wall-pressure distributions obtained for launcher configuration

3 are presented in Fig. 10. It has been concluded that, for x > -10.Ul r , ne — ne

the exhaust flow remained supersonic as it passed the constriction and through

the aft tube. This conclusion is s\^>ported by the fact that the static pressure

increased as the flow passed through the constriction (since supersonic flow

decelerated for dA < 0). Thus, a pattern of weak shock waves reflecting across

the tube produced periodic increases in presfure along the tube. The shock-

induced pressure variations are evident in the pressure measui'ements of Figs.

10a-10c. For x = -2.35 r , the static wall-pressure measurements for the ne ne * r

orifice just downstream of the nozzle exit location were in reasonable agreement

with the theoretical pressure immediately downstream of the weak, impingement

shock-wave, which was 0.075 p ... The theoretical value was calculated assuming

that the underexpanded flow in th? nozzle exit-plane expanded to tho base pres-

sure, which was atmospheric, and was turned parallel to the wall by a weak

oblique shock wave. Viscous effects were neglected. Because of the location

of the nozzle-exit plane relative to the orifice locations for the other nozzle

positions, i.e.. Figs. 10b and 10c, the local peak pressure just downstream of

the impingement shock wave.

For x < -15.00 r , the combined constrictive effect of the boundary ne — ne' J

layer and of the change in cross section caused the flow to choke. The static"

wall-pressure distributions presented in Figs. lOd and lOe verify that the impinge-

?'t

ment shock wave was strong so that the downstream flow was subsonic. The exper-

imentally-determined pressures are in reasonable agreement with the theoretical

values for the one-dimensional flow model of Fig. 5.

Launcher Configuration U

The constrictive area ratio for launcher configuration 4 was 0.878. The

nondimensionalized blow-by mass-flow-rate measured when p . was approximately

6 2 950 psia (6.55 x 10 N/m ) is presented in Fig. 11 for all nozzle-exit locations

for which data were obtained. The blow-by flow rate was negligible for all exit

locations. Based on the data for the other launch tubes, the negligible blow-

by flow rates were expected.

The static-wall-pressure distributions, which are presented in Fig. 12,

show that the pressure increased (albeit slightly) as the supersonic flow de-

celerated through the constriction. No pressure greater than 0.06 p ., was mea-

sured. Note that the theoretical static pressure downstream of the weak inpinge-

ment shock wave for the forward tube was 0.07 p . Furthermorf;, static pressures

for orifices in the aft tube which were measuring during the Arrow flight test

program (Ref. 14) were measurably above the shock impingement value. Thus,

the experimental values presented in Fig. 12 were lower them expected. Because

there were only a limited number of orifices available it is possible that the

orifices recorded only the relatively low values which exist between the reflect-

ing shock waves. Since each test condition was repeated without significant

changes in the pressure data, the measured values are believed to be valid.

If the measured pressures are indeed low in comparison to the "theoretical"

flow models used to date, the flow mechanism unique to launcher configuration H

is not understood.

The Effect of Constrictive Area Ratio

Nondimensionalized blow-by mass-flow-rates are presented as a function of -

25

the constrictive area ratio for x = -2.35 r , -10.41 r . and -19.25 r in ne ne ne ne

Figs. 13, 14, and 15, respectively. Based on these data, the following con-

clusions are made.

(1) The stagnation pressure did not significantly affect the nondimensional-

ized blow-by mass-flow-rate for these two stagnation pressures. An exception

to this conclusion is evident in Fig. 13a. When A cJkc was 0.595 and x = 0 aft for ne

-2.35 r , the blow-by flow rate was very sensitive to the reservoir stagnation

6 2 pressure for values near 400 psia (.2.76 x 10 N/m ).

(2) The fraction of the exhaust flow which was turned upstream by the adverse

pressure gradient created by the strong impingement shock wfive generated when

the flow choked increased as the diameter of the aft tube decreased.

(3) The constrictive area ratio required to choke the flow was a funccion of

nozzle-exit location.

CONCLUDING REMARKS

Static wall-pressure distributions have been measured when an underexpanded

jet of unheated air was exhausted into a constrictive launch tube. The

corresponding blow-by rate was determinad using a pitot probe located in the

annular region between the simulated rocket and the launcher wall at the exit

plane of the forward tube. Based on these data, the following conclusions

are made:

(1) The stagnation pressure did not significantly affect the fraction of

the exhaust flow turned upstream for reservoir pressures in excess of U00 psia

(2.76 x 106 N/m2).

(2) The fraction of the exhaust flow which was turned upstream by the adverse

pressure gradient created by the strong impingement shock wave generated when

the flow choked increased as the diameter of the aft tube decreased.

(3) The constrirtive area ratio required to choke the flow was a function

of the nozzle-exit location.

It might also be noted that the data from these cold-gas simulations

were in essential agreement ■rith the data from flight-test programs.

26

REFERENCES

1. Fabri, J., and Siestrunck, R.: "Supersonic Air Ejectors", Advances in Applied Mechanics, Vol. V, Academic Press, Inc., New York, 1958, pp. 1-34.

2. Batson, J.L. : "A Study of the Flow Field Produced by an Axisymroetric Underexpanded Jet Exhausting into a Cylindrical Tube", Ph.D. Dissertation, December 1972, The University of Texas at Austin.

3. Batson, J.L., and Bertin, J.J.: "Experimental Study of Flow Field Pro- duced When an Underexpanded Rocket Exhausts into Cylinder Tube", AIAA Paper No. 73-1227, Presented at AIAA/SAE 9th Propulsion Conference, Las Vegas, November 1973.

4. . "Feasibility Flight Testing of Rocket Impelled Projectle (RIP)", Report Number 7-52100/3R-5, 1 May 1973, LTV Aerospace Corporation, Michigan Division.

5. Bertin, J.J. and Reiman, R.A.: "The Analysis of the Launch-Tube Flow- Field for Rip-Zap Firings", Aerospace Engineering Report 74005, October 1974, The University of Texas at Austin.

6. Bertin, J.J., and Batson, J.L.: "Experimenatlly Determined Rocket-Exhaust Flowfield in a Constrictive Tube Launcher", Journal of Spacecraft and Rockets, December 1975, Vol. 12, No. 12. "'"

7. Bertin, J.J., Horn, M.K., and Webber, T.L.: "Experimental Study of Flow Field Produced When an Underexpanded Jet Exhausts into a Constrictive Stepped Launch Tube", Aerospace Engineering Report 74002, January 1974, The University of Texas at Austin.

8. Bertin, J.J., Morris, R.R., Garms, G.M., Motal, M.R., and Faria, H.T.: "Experimental Study of an Underexpanded, Supersonic Nozzle Exhausting Into A Constrictive Launch Tube", Aerospace Engineering Report 75001, June 1975, The University of Texas at Austin.

9. Bertin, J.J., and Galanski, S.R.l "The Analysis of Launch Tube Flow-Field for Arrow Firings", Aerospace Engineering Report 75004, May 1975, The University of Texas at Austin.

10. Cline, M.C.: Private transmittal, July 3, 1974, University of California Los Alamos Scientific Laboratory, Los Alunos, New Mexico.

11. Back, L.H., and Cuffel, R.F.: "Detection of Oblique Shocks in a Conical Nozzle with a Circular-Arc Throat", AIAA Journal, December 1966, Vo: . 4, No. 12, pp. 2219-2221.

12. Ames Research Staff: "Equations, Tables, and Chaits for Compressible Flow", Report 1135, 1953, NACA.

27

28

13. Shapiro, A.H., The Dynamics and Thermodynamics of Coinpressible Fluid Flow, Ronald Press, 1953, New York.

14. Bertin, J.J., and Batson, J.L., "A Comparison of Cold-Gas Simulation end Rocket-Launch Data for Constrictive Launchers", to be published.

CO

§ o 4-» m <u

41 •a

tn CM • X X X 01 H

o o • \ X X X tn H

o o • X CO H

1

H 3 • X X X o H

1

H d' • X X 00

1

o in • X i

«1 4) H cl C *

tr\u • X X x ; 1

o o « X in i

(O H • X X

t o 0

• 1 X m i

in «

• X X X

1

o o • X X X H

I

o o • X X H +

* ' s* | Q)

fl ü § *

w CO d-

J

o •H

bo •H

c 8 a) •8 § ID

0)

14H

8 b0

.8

o •p

2

I n « 11 P* tu

I 8 6 3

o

04

s I

I 6

s . woo «

5

I •8

I

J« ^ ■p (0

^ •H -H •H Ü ro U.

w -t-» O <D

K-t l+H W

•H

■P

9 H (0

O ■5 to M "^ i

+-> IU « o A;

o » o • Q> oi n

•H •H > m +J n) co

rH bO 3

s 4,* u H +J ^ O fl > O o

(U S Ä X

/-v ■P 0) nj H

^w »P O UH

0 CO t^ (0 -H

äs O 0)

■p > O «H

£5

<N

0)

o

X)

0)

■8 2

i V 0) o

I 3 H O C o o

CN

bO

IM

(a) Schlieren photograph of the nozzle exhaust flow.

'/MM^m^m^m^^^

r ^.

mmssmz e =10

f .565(1.UU) .38(0.95) f

_ A I

.638(1.02)

Note: dimensions in inches (centimeters)

(b) Dimensions of the convereent-divergent nozzle.

Figure 3. - Characteristics of the convergent-divergent nozzle used during the cold-^as test program.

a,

Ou 0) ^

H A

§!o M «H , •M +-" b U « 0 00 in co ^ f4 ^ U> CO t^ u < ID r«» 00 •p « ^ • • •

S2 t O o o o « « ü <

(4 m m in P r^ t* r^

«4 ■ . . b H tH H ^ 'v >«. "«v

4-> m O * MH d- m «O « • • •

h H H H

b • O o> O» V CM r^ O

diar

oe

tub

e /c

m.)

r- ID 00 • • •

in a-

v. «v "«^ i o ^■ in

a§.s o 00 CO o o» o

« ntw • • 00 t» CD

en H rH H

b • O •H •H 4J « O * rH

ll^ H H o • • • rj 00 00

•H E m en CO

7« 0) <0 •

^ ^. >s. o (O m o rH (O

ffg^ o • O • JS^^ in m zr

H H rH

(4 »

■8

• CM P» d-

■j

0)

§

« O O

4-»

Xlb

o o o o o o

I I I

Q t^ a- H <o m « H I r-l CN

n «a

t a,

r-) CM co j m u> to w en w to to PU CU HM fr. dt (V)

c 0) in

8 a.

«

e u § m

r

M I o

s t i &

a) 0)

% A • W <-«

CO ■-( id c ß o M "H O b0 C 4)

(2 iti

« • U 01 0) .

W H C H 0 «

•H > •M •H 4) T3 £. C P o

0 T3

be

a E 'S

11 IP <^

0) (0 0) 3

g a* O X a b 4) w fl

to V

t (V Ä ^: v a p

e 0) MH 0) to O J= u y ff J: > O XI

■o V 0) 05 « •M

*■ «

E C CO h

0) O V < S CJ -H 0) t-g 1 DC

to

3 (Ö bC >

•H

0.14

0.12

0.10

0.08

'"bb m ex

0.06

0.04

0.02

■20

% Launcher configuration 1 (Ref. 7)

O Launcher confißuration 1 (Ref. 8)

^ Launcher configuration 2

iiiö

o

T—i—i—i—r j—]—i—i—i—r "i—i—i—r

O o

1 t

I 1

o.ool J I I I I I I I I |_J I I I I I -15 -10

J I I ^ I I L + 5

ne

ne

Figure 6. - The nondimensionalized blow-by mass-flow-rate as a function of nozgle 2 exit location for launcher configurations 1 and 2, p : 950 psia (6.55 x 10 N/m )

_ CM

c o

•H ^.

C o u

(1)

CN CSj CN CM ß B B B

— ^ "^ ^ 2 Z Z 2

-•s

o ID O

ID O H

a) o

US o

X X X X X

ID in

CN O ä CD

a-

3 m n)

■Ö CO

e -a .-

2 *

CN CO f) ^- (D

(0 (Tt 10 (0 •H «fH »H -H 01 01 (0 CO o. a ex a, t~ (D CN Ol n a) (>> •* m ID

ii ii ii

CT>

•P P +J ■»-' cu & a, cx

• ■♦►^

OM ü O

OD O OM GO <«• o#

Oö ü o

OMa o

^^ ft

o^j Da 8

cs CN

^ CM

-1 O CM

- «D

CN

as

O s&<$ a 0

ä Ol*3 -

-rH

c o

•H ^^* /-N ^^ ^^ ^^ 'tlCN CN <N CM CN

js e E E e e n ^ ^ ^ ^ ^ pa z ä ä ä

•H iD (D ID (D (D "♦j o o o o o C rH rH H H H

_o X X X X X

f< H o o* a) r- 3 *

-O ^H CN cö

^0M»l^ - CN

00 (D o a o M

CO

CM

_ d-

to

* (0

00

n) n)

co (0 to Pu (X Ot

"IP CN

P5 11 II

o

* o ro m

(TJ «

CO 0)

00 o

n) •P ■!-» +J +J +J

CX CX CX Q< (X

.jo o a O ><3

co CO

8 a.

0) x: m

P <

o o

D OM

o a otxi

-| (JO I

I

10

3- CN

O ■ ii o n an

ID H

O

CN •-t

O

oo o

3- o

o o

4)

*\u

in co

CN I

<0 .a

§ P 3

X> ••H

P

3

to to

2 c I

0)

? u

% p to

a> x; p

c o

•H P m o o

0) i 0) H N N O C

§

S gCM

a. c

g 2 ti 3 0) bO CO »H

B| 0^ P fl) O JS 0) o « g

tp 3 a) to

H

Ht2 i

• 0)

§3 3 XI bO O

•H

J,

T "T 1 1 1 » 1 f I

[ 00fl f o CM

•H CM CM CN CM ti E E E E CO \ ^ ^. >^

I U S* *i X X

t30 CD (D iO (D •H O O O O

1 Itl H H H H

j O X X X X

0

o

1 H O» t^ C^ _ U * O U) CM " d) • . . .

£ CM CO d- (D 0 N^' S_-' N.^ v-^ ß^ M

.3 fO IT) (0 (t) flj -H »iH .H -H

•» rA (0 (0 01 01 CO tt

CM CM CM CM CN c e B e E E O ^ ^ "v '•^ "^

•H 2 as Z 2 SB _

<0lO (O ID «D «D g o o o o o 3 H H H H f»

.rl X X X X X

« ^ s CO c 9 2 St» * . • • . •

H CM CO in «o ^ ^. w w w s-/ 4) js tj nj m TJ fl

XJ »H «H -H «H »H C M M m w w p & ex a. a, Oi

o

al

h ^

o 10

oo

04

to oo m H o d- 3; oo * ^- 4

CM m d- t»- o>

oi oo CM a> * d- «o o o d- ■<o o>

n n n ii

•P 4-> ■P ■»-> a* a. ft a.

• ■ ► ^

<* n II II II II

oo CM

CM

o CM

ID

CN

00

_ d-

CD Ö C3> txj

rn D

DO <t>

^» l^ 0) o tu

0 0

o a) ■M « Q

+j +J 4J ♦J +J ft ft ft ft ft o a o > < J «

*><

o o

%.

^

CM

a) c

ID I

- o

X fc 0) c

ui =i R

•rl

C 0 u

£ 2

g o a OC i O D ^ ft o o

t ■g. o CO

•e«,

< o a44

i T^Tfl

CM i

CO I

I

00 I

CM

ID

o CM

I

CM I

3 bO

•H

00 CM CM

O CM

ID r-l 9 oo

o o o o

J ■p ft

CN CM CNJ CM <N e £ e e e ^. >^ ^^ ^> v. 2: z 2; z ss

CD (O iO (D (D O O O O O

ODKXl

at«

00 GO o

CO rH oo t-

ro oo (D

n> n) n) •H -H «H

CO CO CO a a &

HJ to •H co n

CM 00 in CM 00 r- ;t in oo ro CM ^- in ID o> it ii ii ii n

H >H H H H 4J 4J fi p «J

„ o, &. a. ex a.

• ■^►^ ■M _r ^ c C (0 « o

co <g o -M

H bO

id

oaföö otta

a föC ■ *

CDC>0 CD <p<m*

ODCXXl QOKl

0 D K>

o Co<

CK«

00 - CM

CM CM CM CM e e e e ■ d- ^ "s ^^ ^v "^ CM z z » 35 K

co <D CD ID IO o O O O o o H H .H rH rH CM

X X X X X

CD CO cn .H •-) CD 00 in 00 H CD ' •H

H CM CO m CD ^7 (t3 (0 fj (T3 (0

•H «H •H "H 'H (0 10 CO CO CO a, o. p, o< Ou

* r» d- iH oo co CD cD ^ m CM ro m t» o>

CN

oo

II II it II II - * H H -H «H H 4J 4-> V 4-* 4J

O. CX Cu (X O- _

o a o > < ■

•> bO 00 -rH

If« • c

I4H 0

0-6.2 « « ä Q H 3

. N

CO 0) c

o

I

0) II

xc

CM

CO

00 CM CM

o <N

CD CM 00 O

.SB i"

i

00

CM rH

I

CD

I

O CM

CN I

s a 4-" c O U

a;

liO •H

o o o

J a.

-i 1 r

8a>

-(a>

(ID

m>o

CM O CM s

c o

bO

SO § O

CM CM (N CN CM g e e e e "»v >^ ^ >^ ^ SB 95 SE 2 2

vD IO ID «O ^O O O O O O

o CO

CM CO CO

(O CN • • d- »o

IT) ID IT» id •H •H •^ •H •H H M M co M CO

a, O. a a. cx « r- t-- iß CM 00 +-• in J- ui t» o IT) m d- in lO a> T)

n M n II n •M C r-l -H H H H 0) •M +J ■P ■P +-" CO a a. a CX a 8 O D 0< >

i

IM

CD CM

d- CN

O CM

U>

CN

00

ff _ *

ksL

D T3 CM c a)

b 3 C

o •H o P

■H • C m O -H U

1 <» i O 1 B 1

xlu ii • « r-- c

1 I CM

1 v-* a

co 1

•3- 1

> 00

1

CN

1

VO

o CM

I

■a- CM I

CN .-I

00 o 4-

o o o

J 4-»

e O ^ '-N

»H CM <N PEE rfl "^ ^ b SS 2 3 OOUD (O

•H O O MH H H ß o x X 0 u 0)

x:

CM CM CN e e E ^ "^ ^v 2 2 2

U3 'X) lO o o o H H H

en o

CO

CM CO CO «3 N—* »—' >«-' >—' v^'

3 0 10 (0 (0 H Irt •H •H •H •H •H

^1 CO CO n (0 CO (X a a. a a.

(Ö r- 00 m CM CM •P m * J- a» in

•3 « s m <£) ai

ii II II 11 n

c —i r-i ^1 rH r-

a) •p +J +J •P +

(0 c a. a. a, a | • ■ ♦ »> 4

GCDC

a»

^

<3

<

§ P

I s o (M

10

00

& »4-1 O

10 p m a

CM CM CM CM CM e e e e e •v "«^ "^ ^ v» 2 2 2 2 2

<D CD CD ID (O o o o o o

n m u> ui O) CM (T 00 CO

CS CM d- «D

(0 (0 f0 n) f0 •H -H -H «-« «H w co w w co (X Cb CU (X cu

a> (O CD CM co r* CM CM o o> CM m * r- o»

II It II II ll

CM en

oo CM

CM

o CM

CO

CN

00

- d"

a. ex a. a. a. o aOC> <

_ CM

CO

XI b

CM I

CO I

I

0) c

b IT) CM • ■

ai •a i

i 0) D c II H

U 0) C c 0

X a

.-v 1

<o • N-^

g 3

1^-,

•Tsh

1%

co co I a

x: S-DO Od

•4r

<

00 I

CM

I

CO

o CM

I

J- CM I

CM

O

CM O CM

CO H

CM

■ O

oja

o o

o o o

m ex

0.00

ne

ne

Figure 8. - The nondimensionalized blow-by mass-flow-rate äs a function of nozzle exit location for launcher configuration 3, p . Z 950 psia (6.55 x 106 N/m2). tl

CM

CD H

O O

u")

H

(O

D

o c

0) 0)

x0^

T^-L i-1

o o >

o

s o

o o o

o o

o o o o

<9

OQ

o o 0

00 o o

AB*

o o o

4i

a o o

«i

*

o

o o

(0

m

ft

0 •H

IT)

I M

0) 0)

g 0)

4-»

0

§

O

MH

IP I m

i m

■«I s|

o c •H O w o

e a)

c c

0) ^ fi

a. y m u

bO ft

i—i—i—r i—r^T

CM (N (N H a e 6 B

■»s v. ^ •^ '^ Z 55 K Z Z

0 (£ (C <o to o O o o o H ■-I H H H

X X X X a c~- o OT O) t» in H f> Ol in • • • « « CM m CO d- ID

N—' *^ *-^ N_> s^

0) (0 (0 n) m •H •H •H •r) •H

CO (0 W (0 CO ft ft ft ft ft CM oo o> CO CM t*- IT. d- CM in m d" in t~ en H II it N ii

H H H H H +J ■H ■P 4J •P

O. ft ft ft ft

CO

o

O D o< 0

ui ■ 4

i—i—i—i—i—i—r < » DO

<&><&

<& no

CO m £ o t 0)

ocoo

CM

o CM

o CM

o H

o

J L o o

■a

I

CM CO

3- CM

lO

00

0) C

*\u

in CO

CM

I

II

0) c

i

H I

CM I

O §

J ft

8 B I

| l m w

u

■p

•3 v i

a) N N • O CO C . e tJ o

§ V» m §g M

CO «H

E I a o u u

p-8 s § CO to

^ e V-i o 0 '♦H

U Q) .JU c

4» -P

0) o

1 «H

O Ä

b H (0

bO'O •H U.

1

i—r T—i—i—i—i—r—i—r

CM CM CM CM CM E e B e e

"N. ^. "*«. ^S, "Si 2; Ä z a SB

IA 10 (O (O (O O O O O O

X X n CM d- j- CM d- ro t^ c^ in • • ■ • • CM CO CO a-

(0 n> rti (0 m •H •H •H •H •H M (0 (0 M CO a a a. & a.

CM H H <D in m oo j- oo ^ co j- in a» o* ii ii II n II

H H H H H V +J ■»-' +J +J

Q, (x a, <x a.

O G 0< >

i—i—i—i—r m

GO

CM CO

00

00

M M

s o

a) J= a. m

Sft! J I L-_J I L J L JLiUJ I

Is

0) $ c ■V

h 0) 3

rH C d- •H • ■P ID c

o 1 o II 1

V • c O

X -H

»-v ? A 3 *-* M

CM 00 * o to CM CO * o CO CM CM CM H ^H o o o • • • • • • • o o o o o

cj H

a.

O o o o

I o

T—r T—i—\—i—r—r tt)

as

^-^ "e ̂ Ä

e 2

o H

O H

o rH

ID O .-1

ID O

X X X X X

CO IS H •->

CO j- *—/ 10

•rH m ft

(0 •H (0 &

id •rH n

10 •H 0)

10 •H to

CM 5 LO

00 ID

en

ii II II II n

H H .-i +-•

0 D 0<3 >

CM o (N

m>

OD

§ « e a o

a.

i

J I \ I I i I I I

OM

O D <W>

V o

CM H

O

00 o

D OO

CM CO

CN

ID

« • c •o

b s M c d- •S • •p o c

oo

0) i

o u 1

c II X u ■

0) o c -H

X o 2

'-s 3 o bO

s^ Ü

CD 1

I

cv I

o o o

J ex

i—i—i—i—i—r—r

dtr CM

<N CM CM CM CM a E e E E N. "^ ^ "Si 'N.

Z z 2 ■ ■ ID 10 lO (O ID

O o o o O •-i •H H H •-i

X X X X X

00 ^5 d- ID f* t^ co r- CM

CM CO 3- ID \-y

HJ m (0 « <0 •H •rH •H •H •H (0 W CO m en O. a a (X a

(«• 00 lO <T> O) in o m 00 (N ro m ID CT> ii n II II II

H H H rH •H ■P P •H •H ■P

O. a O. a a

O D0<3 > CHp

Ä" T—i—i—i—r

□ O

DO

o

«p

J L I 1 I I \ L ? o «O CM

CM

3- CM

ID

V .C

— o

i •g □ o

I

CM

o CM

o

ID H

O

j J I m»

CD

x\u

o o in -t

l

II

0) c

2 3 «JO

7

ID

3-

7

00 o o

o o

loT

m-MM U<M

i—i—i—I—r -i—i—i—\—i—i—i—r

BDO CM CM CM CM

E E E E E ^. •^ •v •v ^ z Z z Z * 0OO>

(O (O (O to to o o o o o r-i ^t rH ^H r-i

X X X X a * n c» H rH in r-i I* oo 10

CM •

ID

« « (0 « • •H •H ^-t •H •H

CO n (0 0) (0 CX a a a a

CD CO o r- 00

ft in * O) m J- m (O a>

II II n n n rH ^H H H H V ♦J P •P fi

a O. (X a o.

O D 0<1 >

o »a o

1

J I L ao CM

J I I I I I I 1 L CM

O CM

(O CM 00 o

. _S5u

CN

CM

U>

m CM

* •

| 00

1 -1

-I'V 1

1

• o o •-t

t 3

00

5 1

■ ■ t —

o. Ü

t m ? 1

1

CM

O o c

ojo.

0.04-

0.02-

V m ex

0.00 -20

ne

ne

Figure 11. - The nondiroensionalized blow-by mass-flow-rate as a function of nozzle-exit location for launcher configuration 4, p . : 950 psia (6.55 x 10 N/m )

i—r i—i—i—i—i—i—i—i—r

CN CN CM CN CM E e E E E

■V. -^ ^ x, •s. 55 z SB a Z

ID o UD UD (D O o O o O r4 rH rH H H

X X X X X 00 CM o o CO 00 U1 en CD U3

—' CM CO

w J- ID

(ö n) fO tJ T) •^^ -H T-l -H .rH (0 (0 (0 (0 (0 a, P, o. a, a,

•H (D d" O O t^ U> (D H ID CN C) Irt P- <J)

CO

II II II II II

H H H H H ■P -M -H •P •♦-•

Oi a. cx a, a.

O D 0<1 >

J L 00 CN CN

T—^—r

oao

o -

o

OD0O

J I L ■ III L hs pa <^

CN CO

-J- CM

lO

00

GO I

ID

CN I

o CM

(D rH

O

CN CO O

3- O

o o

0' Vi : i 10 in

g O. I

r-l

^ 3 I U

•H

•1-' ■v

*-> m

ai x: v

c o

c o

•H +J

ni O 0 H

♦' e c 'S u 0) |

in I a'

CO -H • N CM N •

O J 1) 1 c c c x\u II •o 0

i m -P c r0

X

P bO ^ « TH (0 w u.. w

gure

»■>.

-

The

eff

ect

cf

rese

rvo

ir p

re

dis

trib

uti

on

obta

ined

fo

r l

aun

cher

co

n

J Ou

i—i—i—i—i—i—r T—i—i—i—i—r"i—r a»

CM e e

an

CM CN E

CM e

ID o o

^1

ID 03

3 o

X X X X X

a o 00 00

CM

CM CO 00 ID

10 m CO a

(0 •H m w a (0

O CN LT)

o IT)

o CO

- a a o.

O D 0< >

on

oa»

§ n w

fa «

aw>

^§QW>' J L J I I I I J__J L iQiiM

CM

iß

01 g

00

0) I

X fa ii

0) c

X

s c

•H +-• c o o

CM

bo •H

CO I

U3

CM

CM 00 J- o 10 CM CO d- § CO CN CM. CM •-i rH o o • • • • • • •

O o o o o o

1 H o o o

^^"" - i r i i i T r ■ ■■ T —"I ■ 1 I 1 1

- »-» ^ /->» <-s ^-,

<N CM W CN CN ■ ■ ■ ■ ■ •s. >. ■>. «v «v z a a 2: ä

m

-

(O (O iO (D ID O O O O O H H H H H

X X X X X

O CO t^ rt f* d- rH r~ r» m

0»

- IN CO CO ^ «o N^ \-/ «—> '-Z V-'

-

- (T) IT) io rd 10

•H 'r4 1-1 •H »H B « ■ a « a o. o. a, a -

- r- O «O CM CM ^ »o d- oo in <o 3- m «D en

ii n n ii n

a» - .-! H ,-( H H

V 4-" 4-» +J +J o. a a cx o. o«

-■ O D 0< > -

- m m 8

OGMO"

-

Ü

t 1

-

1 1

oiac«>"

1 1 1 i 1 1 1 1 1 1 1 '^TlinBn

a- CM

00

- <o

CO

0) c 8

U o -H M

J- i: • t) O i) -I

« X . £ II »

b CN 00

1 0) c

M

X

§ ^ JO O .H

ID •-<

I

_ CM

00

CM O CM

ID

o

CM

O

CO o o

o o

H

00

CM F

CM S e

55 S5

CM

S5

O (A

O H

ID o ^1

10 o H

(0 o H

X X X X X

o 00 o

CM 00 in

CO a- ID

10 •H n a.

•H 01

a»

0)

10 •H 0)

10

a,

CO 1 in in

CM CM in en

II II n II n H 4-»

P. P.

O D 0<J 0

i—r" Ott

o»

880

00»

awi>

OD0Ct>

CM

»nn»n

CM

(O

00 XI

i 3 c c

U o c o o a

o in

i i

X s ii •

CM

b 0)

xC |

00 -^«k bT 1 •o •H

N-/ U,

I

CM I

CM CO

O CM

«3 H

O

CM H

O

00 o o

O I o

H a.

Til 1 1 1 I I - r i i r i- 1 1 I 1 om

u

*""*. ^"N ^ ^^ rf-\ CM CM CM CM CM

B B B B B ^. ^ ^v "^ -^ 2 2; 2 X 2

(£> (O (d (O (O o o o o o H H 1-4 H H

-^

l-

283 psia (1.96 x

372 psia (2.57 x

466 psia (3.22

x

724 psia (5.00 x

943 psia (6.51 x

0(» J

l-

ii n n ii ii

H H H rH H ^ «i 4J +i +1

O* O» Ot Ot Oi

O D 0<3> m A

l- OD<» 1

u J

L i (0 m 8 ODO0 |

L ü —1

U

M 0)

|

1 <

-j

P* -s^O] -L 1 1 1 1 1 i 1 J 1 1 1 1 i nan nn J

CM

- CM

iS - - o

•o V

T) « 3

uc ^ m § CM O

Ol 1 H

1 • CM

II rH

xc i ÖÜ

•rH '-« U.

CM H

1

CM I

CM CO CM CM

o CM • o 0

.16

0.12

He?

00 o o

o o

0.10

0.08

—r O

T r

V m

0.06

ex 0.04

m ex

0.02

0.00 L-n-1—4 »-o—'—&- 0.0

0.10,

0.0(-

o.oe-

"bb o.oi-

0.6 0.8 1.0

"aft

for

(a) p_ . U00 psia (2.76 x 106 N/m2)

O

T r

o.o:-

o. od- 71—1 1— 0.0 0.6

J—Qi 0.8

Aaft/Afor

UO

(b) ptl : 950 psia C6.55 x 106 N/m2)

Figure 13. - The effect of constrictive area ratio on the blow-by mass- flow-rate, XM = - 2.35 r . ne ne

"bb

ex

- ~r- O I 1 r-

-

0.12 —

o -

0.08 - -

O.OU — -\

o.no —17 i i l r» . i.. r\i

m ex

aft' for ta) ptl = 100 psia (2.76 x 10 N/nT)

I T O

1 T" I -

0.12

- o

■

0.08 — -

0.0»* - A

0.00 -W-»- 1 —Le_ _4_ -e*- 0.0 0.6 0.8

aft for

l.C

Cb) ptl s 950 psia (6.55 x 106 N/m2)

Figure 14. - The effect of the constrictive area ratio on the blow-by mass- flow-rate, x . = - 10.«a r ne ne

\ jb

ex

O.lßr

0.12-

o.oe-

0.0^-

i—5 r

o. od— u-i — 0.0 0.6

i r

0.8

aft for

-1—e1- 1.0

(a) ptl = «+00 psia (2.76 x 106 N/m2)

\b

ex

■T" 6 1 1 T~

0.

-

o -

0.0{ o ;

0.01 - -

O.Of ^_I . • 1 -I n\

aft for

1.0

(b) p_ : 950 psia (6.55 x 106 N/m2)

Figure 15. - The effect of the constrictive area ratio on the blow-by mass- flow-rate, x ne 19.25 r . ne