NASA Technical Memorandum 4719

Static Internal Performance of a TwoDimensional Convergent-Divergent Nozzle

With External Shelf

Milton Lamb, John G. Taylor, and Mark C. Frassinelli

September 1996

NASA Technical Memorandum 4719

Static Internal Performance of a TwoDimensional Convergent-Divergent Nozzle

With External Shelf

Milton Lamb and John G. Taylor

Langley Research Center • Hampton, Virginia

Mark C. Frassinelli

Air Force Wright Research and Development Center •

Wright-Patterson Air Force Base, Ohio

National Aeronautics and Space Administration

Langley Research Center • Hampton, Virginia 23681-0001

September 1996
Acknowledgments

The research presented in this report is the result of the cooperative

effort of General Electric Aircraft Engines and Langley Research

Center. The design and development of the nozzle concept were accomplished by General Electric Aircraft Engines. The test was conducted by the staff of the former Propulsion Aerodynamic Branch at

Langley Research Center.

Available eleclronically at the following URL address: http://techreports.larc.nasa.gov/ltrs/ltrs.html

Printed copies available from the following:

NASA Center for AeroSpace Information

800 Elkridge Landing Road

Linthicum Heights, MD 21090-2934

(301) 621-0390

National Technical Information Service (NTIS)

5285 Port Royal Road

Springfield, VA 22161-2171

(703) 487-4650
Contents

Summary .......................................................................... 1

Introduction ....................................................................... 1

Symbols .......................................................................... 2

Apparatus and Methods .............................................................. 2

Static Test Facility ................................................................. 2

Single-Engine Propulsion Simulation System ........................................... 3

Model Description ................................................................. 3

Instrumentation ................................................................... 4

Data Reduction ................................................................... 4

Presentation of Results ............................................................... 5

Results and Discussion ............................................................... 5

Pressure Data ..................................................................... 5

Performance Data ................................................................. 6

Shelf Surface Oil Flow Visualization .................................................. 6

Conclusions ....................................................................... 7

References ........................................................................ 7

Tables ............................................................................ 9

Figures .......................................................................... 54

ooo

Iil

Summary

An investigation was conducted in the static test

facility of the Langley 16-Foot Transonic Tunnel to

determine the internal performance of a two-dimensional

convergent-divergent (2-D C-D) nozzle. The nozzle

design was tested with dry and afterburning throat areas

which represent different power settings and three expansion ratios (subsonic cruise, subsonic acceleration, and

supersonic cruise).

For each configuration, three trailing-edge geometries were tested. The baseline geometry had a straight

trailing edge. Two different shaping techniques were

applied to the baseline nozzle design to reduce radar

observables: the scarfed design and the sawtooth design.

A flat plate extended downstream of the lower divergent

flap trailing edge parallel to the model centerline to form

a shelflike expansion surface. This shelf was designed to

shield the plume from ground observation (infrared radiation (IR) signature suppression). The shelf represents

the part of the aircraft structure that might be present in

an installed configuration. These configurations were

tested at nozzle pressure ratios (NPR) from 2.0 to 12.0.

Results indicated that discharge coefficient and peak

resultant thrust ratio were not significantly affected by

the addition of the shelf or by changes to the upper divergent flap and shelf geometry. Discharge coefficient for

these 2-D C-D shelf nozzles was lower than typical 2-D

C-D nozzles due to the sharp corner at the nozzle geometric throat. Resultant pitch vector angles were typically nonzero and varied with increasing NPR. In

addition to nozzle internal asymmetry, the shelf significantly affected the pitch vector angle by producing a surface on which the shock-cell pressure variation could act.

Only the asymmetrical scarfed nozzle produced resultant

yaw thrust vector angles.

Introduction

Aircraft survivability has always been an important

consideration in the airplane design process. In World

War I, the issue of survivability was primarily concerned

with the avoidance of visual detection by patrolling aircraft or ground observers. With the introduction of

ground-based radar in World War II, aircraft became vulnerable to long-range detection and tracking that allowed

adversaries to concentrate forces to intercept them along

their route. Once intercepted, precise maneuvering was

required at close range to shoot down the enemy with

machine guns. During the Vietnam War and more recent

conflicts in the Middle East, the combat environment

included new weapons such as heat-seeking and radarguided air-to-air and surface-to-air missiles capable of

targeting and destroying aircraft beyond visual range.

Advances in sensors and microprocessors will continue

to increase the risk of high-threat environments in the

future. Thus, advanced aircraft designs will require visible, infrared, and radar cross-section (RCS) signature

shaping and reduction techniques to increase aircraft survivability. (See ref. 1.) Technologies to reduce observables are currently being incorporated into the design

of the aircraft structure as well as into the propulsion

system.

The capabilities that are necessary to reduce observables require careful integration of the propulsion system

into an aircraft because inlets and nozzles are typically

large contributors to the overall aircraft infrared and RCS

signature. Infrared signature suppression techniques

include cooling of the exhaust plume and hot engine and

aircraft components as well as shielding of these hot

parts from view. The RCS signature shaping techniques

include internal and external shaping of leading and trailing edges and elimination of 90 ° angles between adjacent

surfaces. Incorporating technologies that reduce observables can affect nozzle performance as a result of more

complex internal and external geometry. (See ref. 2.) To

produce acceptable levels of survivability and performance, a compromise must be reached between aircraft

aerodynamics and signature-suppression designs. These

concerns are addressed in this paper for the design of a

two-dimensional convergent-divergent (2-D C-D) nozzle

with a flat plate (herein called a shelf) extending downstream of the lower divergent flap trailing edge.

An investigation has been conducted in the static test

facility of the Langley 16-Foot Transonic Tunnel to

determine the internal performance of this 2-D C-D shelf

nozzle design. The nozzle design was tested with dry and

afterburning throat areas which represent different power

settings and three expansion ratios (subsonic cruise, subsonic acceleration, and supersonic cruise). For each of

theses configurations, three trailing-edge geometries

were tested. The baseline geometry had a straight trailing

edge. Two different shaping techniques were applied to

the baseline nozzle design to reduce radar observables,

henceforth called the scarfed design and the sawtooth

design. A flat plate (shelf) extended downstream of the

lower divergent flap trailing edge parallel to the model

centerline. This shelf was designed to shield the plume

from ground observation (IR signature shaping). The

shelf also simulated installation of the nozzles on an aircraft surface. These configurations were tested at nozzle

pressure ratios (NPR) from 2.0 to 12.0.

The results of this investigation are presented as nozzle internal performance data (discharge coefficient,

internal thrust ratio, resultant thrust ratio, resultant pitch

thrust vector angle, and resultant yaw thrust vector angle)

and internal static pressure ratio data on the divergent
flapsandshelf.Surfaceoil flow visualizationphotographsof theshelfarealsopresentedtogainaqualitative

understandingof theflowphenomena.

Symbols

All forces and resultant vector angles are referenced

to the model body axis (measured from the model centerline). A detailed discussion of the data reduction, calibration procedures, and propulsion relations used in this

report is presented in references 3 and 4.

A,B,C,D

A e

Ae/A t

At

F

Fi

Fu

G

Fs

g

he

ht

L flap

Lshelf

NPR

(NPR) d

P

Pa

Pt,j

P/Ptd

Rj

r,,j

W

represent model stations and dimensions in

figures 3-6, in.

nozzle exit area, in 2

nozzle expansion ratio

nozzle throat area, in 2

measured thrust along body axis, positive in

upstream direction, lbf

ideal isentropic gross thrust,

w,4 U,J+ 27/_7-J ] 459.67)fl _ (_pR)_J, lb f

measured normal force, lbf

resultant gross thrust, _/F 2 + F 2 + FS2 , lbf

measured side force, lbf

acceleration due to gravity, 32.174 ft/sec 2

exit height of nozzle (see fig. 3), in.

throat height of nozzle (see fig. 3(a)), in.

reference length of upper and lower divergent flaps (see fig. 2), 4.000 in.

reference length of shelf (see fig. 2),

6.600 in.

nozzle pressure ratio, Pt, j

Pa

design nozzle pressure ratio (NPR for fully

isentropic expanded flow at nozzle exit)

local static pressure, psi

ambient pressure, psi

jet total pressure, psi

static pressure ratio

gas constant for air, 1716 ft2/sec2-°R

jet total temperature, °R

width of nozzle at throat (see fig. 2),

4.000 in.

wi ideal weight-flow rate,

_.XZL_

_ ( 2 "_O'-U / Tg lbf/sec

/ttPt'J_ ''_ ) 4-Rj(TI,j + 459.67) '

Wp measured weight-flow rate, lbf/sec

x distance along nozzle surface for tap locations (positive downstream), in.

y spanwise distance for tap locations (positive

to right, see fig. 5), in.

ctl divergence angle for lower divergent flap

(see fig. 3), deg

°tu divergence angle for upper divergent flap

(see fig. 3), deg

13 convergence angle for convergent flaps

(see figs. 3(a) and 4), deg

2' ratio of specific heats for air, 1.3997

_Sp resultant pitch thrust-vector angle,

tan-17' deg

8y resultant yaw thrust vector angle,

tan- 1Fs

-_-, deg

8v, p geometric pitch thrust vector angle,

measured from model centerline (positive

angle produces positive normal force),

0.5(o_ u + tx/), deg

0 cutback angle on upper convergent flap

(see fig. 6), deg

Abbreviations:

A/B afterburner

2-D two-dimensional

Config configuration

C-D convergent-divergent

IR infrared radiation

MS model station, in.

RCS radar cross section

Apparatus and Methods

Static Test Facility

This investigation was conducted in the static test

facility of the Langley 16-Foot Transonic Tunnel. Tests

were performed in a large room with high-pressure air

directed through a single-engine propulsion simulation

system and exhausted to the atmosphere. The static test

facility uses the same clean, dry-air supply as the 16-Foot

2
TransonicTunnel(ref.3)andasimilaraircontrolsystem

thatfeaturesaheatexchangertomaintainaconstant jet

flow stagnationtemperature(approximatelyroomtemperature).Thestatictestfacilityhasbeeninstrumental in

thedevelopment of innovativenonaxisymmetric nozzle

conceptsthroughthedetailedevaluationof nozzleinternalperformance. (Seerefs.5and6.)

Single-Engine Propulsion Simulation System

During this investigation, nozzle configurations

were tested on the single-engine, air-powered jet simulation system. Figure 1 shows a schematic of the propulsion simulation system with the 2-D instrumentation

section and a typical test nozzle. An external high-pressure air system provided a continuous flow of clean, dry

air at a controlled temperature of about 540°R as jet total

pressure was varied up to approximately 175 psi in the

nozzle. High-pressure air was directed through a dollymounted support strut containing six tubes which connect to a high-pressure plenum chamber. As indicated in

figure 1, the air was then discharged perpendicularly into

the low-pressure plenum through eight multiple-hole

nozzles equally spaced around the high-pressure plenum.

This arrangement was designed to minimize the forces

imposed by the transfer of axial momentum as the air

passes from the nonmetric high-pressure plenum to the

metric low-pressure plenum (mounted to the force balance). Two flexible metal bellows were used as seals and

compensated for axial forces caused by pressurization.

The air then passed from the low-pressure plenum

through a transition section, choke plate and instrumentation section. The transition section provided a smooth

flow path from the circular cross-section low-pressure

plenum to the rectangular cross-section choke plate,

instrumentation section, and nozzle. The nozzle model

was attached at model station 41.845.

Model Description

The basic design parameters for the present nozzle

were power settings, expansion ratios, and trailing-edge

designs. Throat areas were chosen to represent dry

and afterburner (A/B) power settings. Three expansion

ratios (same for both dry and A/B configurations) were

selected to represent subsonic cruise (AelAt= 1.100),

subsonic acceleration (AeJAt= 1.750), and supersonic

cruise (AelA t = 2.500) operating modes. Typically

2-D C-D nozzles have divergent flaps that are equal in

length, but for the present investigation an extension

(shelf) was added to the lower divergent flap to provide

IR shielding from below. (See fig. 2.) Three trailing-edge

geometries were investigated. The baseline configurations (fig. 2(a)) had trailing edges that were normal to the

airflow and internal surfaces that are at right angles to

each other. The other two planform geometries (scarfed

and sawtooth) were designed to have the same throat

areas and expansion ratios.

The scarfed configurations (fig. 2(b)) had trailing

edges (upper divergent flap and shelf) that were swept

(scarfed) 30 ° to the sidewall normal. The sawtooth configurations (fig. 2(c)) had double scarfed surfaces (swept

45 °) extending from the vertical centerline which

resulted in a sawtooth appearance. The internal surface

of the upper divergent flap consisted of two planar surfaces extending from the vertical centerline.

The throat areas were rectangular as shown in figure 2. The lengths of the flap (Lflap = 4.000 in.) and shelf

(Lshelf=6.600in.) were constant among the three

designs and represented the average lengths for the

scarfed and sawtooth configurations. For the baseline

and scarfed configurations, these lengths were measured

along the surface at the vertical centerline. For the

sawtooth configurations, the lengths were measured at

(ylw)12 = -0.500. (See fig. 2(c).) These dimensions provided configurations that had constant planform areas at

each expansion ratio.

Typically, exit area or expansion ratio of 2-D C-D

nozzles is varied by changing the waterline location of

the trailing edge of both upper and lower divergent flaps.

Thus the divergent flap surfaces remain symmetric about

the nozzle centerline, which results in a change in A e,

whereas the geometric pitch vector angle 5v, p remains

zero. However for the present investigation, the lower

divergent flap and shelf remained stationary and the

expansion ratio was varied by moving only the upper

divergent flap trailing edge. (See fig. 3.) This geometry

produced nozzle asymmetry about the nozzle centerline,

which results in nonzero geometric pitch thrust vector

angles for all configurations tested. This angle 5v, p is in

figures 3(b)-3(d) and table 1 and is the average of the

upper and lower divergent flap divergence angles o_u

and a 1.

The design parameters that are common to all configurations are shown in figure 3(a). All test configurations were attached to the 2-D instrumentation section at

MS A (41.845) as shown in figures 1 and 3(a). A summary of the test configurations is provided in table 1. The

width of all nozzles at the throat was 4.000 in. Thus

changing from a dry power to A/B power configuration

required an increase in throat height (ht) from 1.000 to

1.200 in. The changes in throat height resulted in changes

in the convergence angle (_) as shown in figure 3(a).

Note that MS B has shifted downstream slightly for the

A/B configurations. The nozzle geometric throat (minimum internal cross-sectional area) occurred at the juncture of the convergent and divergent flaps. This juncture

formed a sharp corner. All dry power configurations used

3
thesameconvergent flapgeometrywhichwassymmetricalabouthemodelcenterlinebetweenMSA (41.845)

andMSB (44.296).Likewiseall A/B configurations

used the same convergent flap geometry as shown in

figure 3(a).

As mentioned previously, the lengths of the divergent flaps were a constant 4.000 in., and these lengths

were measured along the surfaces of the flaps. Changing

from a dry power to A/B power configuration resulted

in an increase in divergence angle (ctl) on the lower

divergent surface and a slight reduction in the length

between MS B and MS C. Therefore as shown in

figures 3(b)-3(d), slight overall differences in length

existed for dry and A/B configurations (MS D) as shown

in figures 3(b)-3(d). Figures 3(b)-3(d) also show the

parameters that pertain to a particular type of nozzle.

Details of the individual parts (including pressure tap

locations) are given in figures 4-9. The sidewalls for

baseline configurations 1-6 were mirror images as

shown in figure 9(a). The sidewalls for scarfed configurations 7-12 were different as shown in figure 9(b). The

sidewalls for sawtooth configurations 13-18 were mirror

images as shown in figure 9(c).

To help understand the flow physics, static pressure

taps were utilized on the nozzle lower divergent flap and

shelf for all configurations and on the upper divergent

flap for the sawtooth configurations. The dry power

configurations had 9 static pressure taps on the lower

divergent flap, whereas the A/B power configurations

had 27 taps as shown in figure 5. These taps were

arranged in three rows, one along the flap centerline and

the other two on either side of the centerline halfway to

the sidewall. The sawtooth configurations had a row of

9 taps on the upper divergent flap ((y/w)/2 = -0.500) as

shown in figure 7(c). The baseline nozzle shelf had 7 taps

placed along the shelf centerline. (See fig. 8(a).) The

scarfed nozzle shelf had 21 taps in three rows, one row

along the centerline and one on either side halfway to the

edge. (See fig. 8(b).) The sawtooth nozzle shelf had a

row of 7 taps at (ylw)/2 = -0.500 as shown in figure 8(c).

Instrumentation

An internally mounted six-component strain-gage

balance was used to measure the forces and moments on

the model downstream of MS 20.500. (See fig. 1.) Jet

total pressure was measured at a fixed station in the

instrumentation section by a four-probe rake through the

upper surface, a three-probe rake through the side, and a

two-probe rake through the corner. Jet total temperature

was measured with a thermocouple positioned in the

instrumentation section upstream of the nozzle. The

weight-flow rate of the high-pressure air supplied to the

nozzle was determined by calibrating weight flow as a

4

function of pressure and temperature measurements in

the high-pressure plenum (located on top of the support

strut) with standard axisymmetric nozzles of known discharge coefficient in place of the test nozzle. Static pressures were measured with individual transducers.

Data Reduction

All data were recorded on magnetic tape. Each data

point is an average of 50 frames of data, acquired at a

rate of 10 frames/sec. Data were recorded in ascending

order of NPR.

The basic nozzle internal performance parameters

presented are internal thrust ratio FIF i, resultant thrust

ratio Fr/Fi, discharge coefficient wp/w i, and resultant

pitch and yaw vector angles _p and _y. All data are referenced to the model centerline with the exception of

resultant gross thrust F r. A detailed discussion of the data

reduction methodology is presented in reference 4.

The internal thrust ratio F/F i is the ratio of the measured thrust along the body axis to the ideal isentropic

gross thrust. Ideal thrust F i is computed from the measured weight-flow rate Wp, jet total pressure Pt, j, and

jet total temperature Tt, j by assuming isentropic expansion through the nozzle. (See definition of Fi in the

section "Symbols.") Nozzle thrust F along the body axis

was obtained from the balance axial-force measurement

with corrections for model weight tares, balance interactions, and bellow tares. Although the bellows arrangement in the propulsion simulation system was designed

to eliminate any pressure and momentum interactions

with the balance, small bellows tares on all balance components still existed. These tares resulted from a small

pressure difference between the ends of the bellows at

high internal velocities and from small differences in the

forward and aft bellows spring constants during bellows

pressurization. The bellows tares were determined by

testing standard axisymmetric calibration nozzles with

known performance over a range of loadings expected

during the test. These calibration data were used to correct balance force measurements to obtain final forces

and moments. (See ref. 4.)

The internal thrust ratio F/F i provides a measure of

the nozzle efficiency in directing the exhaust flow in the

axial direction. Axial thrust F is decreased by deflecting

the thrust vector away from the axial direction. Axial

thrust F and thus internal thrust ratio F/F i are reduced by

actual losses in nozzle efficiency or by thrust vectoring.

The resultant thrust ratio FrlF i is the resultant gross

thrust F r normalized by the ideal thrust F i. Resultant

thrust is computed from corrected values of axial-,

normal-, and side-force balance measurements. By definition, differences between FIF i and Fr/F i occur when

the exhaust flow is directed (vectored) away from the
axialdirection.DecreasesinresultantthrustFr are due to

actual losses in nozzle efficiency and turning losses, not

to geometric losses as discussed for F.

Nozzle discharge coefficient Wp/W i is the ratio of

measured weight-flow rate to ideal weight-flow rate,

where the ideal weight-flow rate is computed from measurements of jet total temperature, jet total pressure, and

measured nozzle throat area (the minimum internal

cross-sectional flow area in the nozzle). The nozzle discharge coefficient reflects the nozzle efficiency in passing weight flow. This performance parameter is reduced

by momentum and vena contracta losses; this results in a

decrease in the effective flow (throat) area. (See ref. 7.)

Resultant thrust vector angles _p and 8y are effective

angles at which the thrust-vectoring mechanism turns the

exhaust flow from the axial direction. As indicated in

the section "Symbols," determination of these angles

requires the measurements of axial, normal, and side

forces on the model.

In addition to force and pressure data, surface oil

flow visualization photographs were obtained to qualitatively gain a better understanding of the flow phenomena. A mixture of fine black grit particles and oil was

spread on the upper surface of the shelf. The nozzle pressure ratio was held at the desired test conditions for

approximately 5 min or until all excess oil was blown out

of the nozzle and the oil flow patterns were fully developed. At this point, the high-pressure air was quickly

reduced to atmospheric pressure so that the flow patterns

were not disturbed. The oil flow patterns were closely

observed during this process with a video camera to

insure that patterns did not change from those observed

at the test NPR. No changes in oil flow patterns were

observed during the reduction in NPR from test conditions to jet off.

Presentation of Results

A configuration summary is provided in table 1,

which describes the different nozzle designs, power settings, and expansion ratios of each configuration tested

in this investigation. In addition, the design nozzle pressure ratio (NPR) d for fully expanded flow (based on

expansion ratio Ae/At) and the geometric pitch vector

angle are provided. Tabulated nozzle performance data

for all configurations are presented in tables 2-4, and the

internal static pressure ratio data at all test conditions are

presented in tables 5-10. Plots of internal static pressure

ratios are presented in figure 10 at selected NPR's for all

configurations. Internal performance data are presented

in figures 11, 12, and 13 for the baseline, scarfed, and

sawtooth configurations, respectively. These plots also

show the effect of expansion ratio. Comparison plots for

power settings are presented in figures 14, 15, and 16

for the baseline, scarfed, and sawtooth configurations,

respectively. Comparison plots for RCS modifications

are shown in figures 17 and 18 for the dry power and

A/B power configurations, respectively. Also, surface oil

flow visualization photographs are presented in figure 19

to aid the researcher in the understanding of the flow

phenomena.

Results and Discussion

Pressure Data

Static pressure ratio data along the lower divergent

flap and shelf surfaces are presented in figure 10 as a

function of NPR. Data are presented on the nozzle centerline for the baseline and scarfed configurations and at

a spanwise location of (y/w)/2 = -0.500 for the sawtooth

configurations. A decision was made to more densely

instrument the lower divergent flap of the A/B configurations than the flap for the dry configurations. This decision was based on the likelihood that if flow separation

were shown not to occur on the A/B configurations, separation would also be absent on the dry configurations,

which have smaller convergence and divergence angles.

Because of the limited pressure instrumentation on even

the A/B flap, it could not be determined if the flow

was attached. As shown in figures 10(b), 10(d), and

10(f), the first tap (Ae/A t = 1.100) downstream of the

throat (x/Lfla p = 0.10) may be in a separation bubble. At

low values of NPR, internal shocks are evident. These

shocks are characteristic of highly overexpanded nozzle

flows and are likely followed by regions of shockinduced separated flow. As NPR is increased and overexpansion of the nozzle is reduced, these shocks move to

the nozzle exit. Based on the limited instrumentation, the

dry power configurations appear to show the same

trends. (See figs. 10(a), 10(c), and 10(e).) Additionally,

the configurations with AelAt= 1.100 experienced an

additional internal shock, evidenced by the pressure rise

near the nozzle exit. This shock was likely an impingement of a shock emanating from the downstream end of

the throat separation bubble. The impingement occurs for

these configurations because the upper flap divergence

angle is reduced to obtain the low expansion ratio. (See

fig. 3(a).)

However, a change in the static pressure distribution

almost always occurred along the shelf as NPR

increased. Typically, the size (axial extent) of the shock

cells in a supersonic jet increases with increasing NPR.

These shock cells indicate the expansion and compression cycles that the exhaust flow undergoes as it adjusts

to ambient pressure and are illustrated in the flow visualization photographs discussed later in the paper. The

shock cells are evident by the cycling static pressure distributions seen in figure 10. Static pressures on the shelf
surfacegreaterthanPa exert a negative normal force on

the nozzle, whereas static pressures on the shelf less than

ambient pressure exert a positive normal force on the

nozzle. The integrated effect of these shelf loads, as well

as similar loads on the divergent flaps, is to influence the

magnitude of the thrust vector angles.

Performance Data

The performance data (nozzle internal thrust ratio

F/F i, resultant thrust ratio F, JF i, discharge coefficient

Wp/W i, resultant pitch thrust vector angle 8p, and resultant

yaw thrust vector angle By) are presented as functions of

NPR in figures 11-18. The data in figures 11, 12, and 13

show the effect of expansion ratio for the baseline,

scarfed, and sawtooth configurations, respectively. Comparison plots for power settings are presented in figures 14, 15, and 16 for the baseline, scarfed, and sawtooth configurations, respectively. Comparison plots for

RCS modifications are shown in figures 17 and 18 for

the dry and A/B power configurations, respectively.

In general, the discharge coefficients for the three

shelf nozzle designs (figs. 11-13) were lower than levels

typically measured on a 2-D C-D nozzle by approximately 2 percent. (See refs. 7-12.) The lower level of

weight-flow efficiency was probably due to the sharp

throat corner formed between the convergent and divergent flaps. Sharp throats have been shown to cause

separation bubbles immediately downstream; this results

in a reduced effective throat area. A separation bubble is

indicated by the pressure distribution in figure 10, particularly for A/B configurations with Ae/A t = 1.100, where a

sharp pressure rise occurs between the first two pressure

taps. As reported in reference 7, a 2-D C-D nozzle with a

zero radius (sharp) throat generated a reduced discharge

coefficient. In general, increases in expansion ratio

produced no significant change in discharge coefficient,

the exception being for the baseline configurations with

Ae/At= 1.100. (See figs. ll(a) and ll(b).) The effects

were attributed to the more pronounced separation bubble indicated by the pressure distributions. (See fig. 10.)

A larger throat area would be more efficient, which is

generally shown in the discharge coefficient data of

figures 14-16. In general, RCS modifications (figs. 17

and 18) had no effect on discharge coefficient except for

the baseline configurations with AelAt= 1.100 as discussed earlier.

The internal thrust ratio FIF i curves are typical of

2-D, C-D nozzles. All C-D nozzles have the same basic

thrust curves consisting of internal normal shock flow

regime, oblique shock flow regime, and underexpanded

flow regime. The first two regimes (normal shock regime

at NPR < 3 and oblique shock regime at NPR > 3) can be

seen in the data for the configurations with Ae[A t = 2.500

(figs. 11-13), but because (NPR)d (table 1) is above the

NPR range, the underexpanded regime is not seen.

Increasing the expansion ratio shifts the curves to the

right as expected. The resultant thrust ratio FrlF i curves

are similar to the internal performance curves--a result

of the relatively low levels of thrust vectoring. Peak

resultant thrust ratio levels were less than 1.00 due to

flow angularity, skin friction, and shock losses. However, despite the additional surface area of the shelf,

these levels were comparable peak values typical of 2-D

C-D nozzles without shelves. (See refs. 8-12.) The thrust

ratio curves are quite similar for the dry and A/B configurations. (See figs. 14-16.) The data in figures 17 and 18

tend to show that RCS modifications have very little

effect on peak thrust ratio.

The baseline and sawtooth designs were symmetric

about a vertical cut along the nozzle centerline; therefore

zero values of resultant yaw vector angles 8y were

expected and are generally shown for those configurations. (See figs. 11-13.) As expected, the asymmetrical

scarfed nozzle produced nonzero 8y values. (See fig. 12.)

Resultant pitch thrust vector angles 8p were typically

nonzero and varied with NPR. Nozzle divergent flap

geometry (nonzero By, p (table 1)) and the influence of

the shelf on the shock-cell pressure variations contributed to these varying pitch thrust vector angles. These

nonzero normal forces (Sp) and side forces (By) would

require an exhaustive investigation of any concept considered for integration into a flight vehicle. The vehicle

would have to be able to trim these propulsion-induced

longitudinal and lateral forces and moments. Since the

engines would probably be used in pairs, the nonzero

side force would be balanced out by the second engine.

The trend for dry and A/B configurations is quite similar

as shown in figures 14-16.

Shelf Surface Oil Flow Visualization

Oil flow visualization photographs are presented in

figure 19 to illustrate the complex flow patterns on the

shelf surface. As previously described, a mixture of fine

black grit particles and oil was used to depict flow

patterns along the shelf surface. Flow patterns were

closely observed with a video camera to ensure that they

were fully developed and did not change as the jet

was turned off. No changes in oil flow patterns were

observed as NPR was reduced from test conditions to jet

off. Flow visualization data were obtained only on

the dry power configurations with AelA t = 1.100

(Config 1, 7, and 13) at NPR near peak Fr/F i.

All three photographs show what appears to be

under-expanded flow although the nozzles are nominally

at design or overexpanded conditions. The pressure distributions indicate high pressure at the exit plane as a
resultof thecompressionshockgeneratedbythegeometryforAJAt = 1.100, as discussed in the pressure discussion. All three nozzle designs--baseline, scarfed, and

sawtooth----exhibited flow expansion and recompression

along the shelf surface as shown in figure 19. Flow on

either side of the centerline expanded away from the

centerline just downstream of the nozzle exit plane and

then recompressed back toward the centerline farther

downstream. Another expansion process was evident

downstream of the recompression. The size of these

regions of expansion and compression is dependent upon

NPR, and they dictate the static pressure distributions

along the shelf. These variations in static pressure

resulted in variations in 5p with NPR (as shown in the

force data) because normal force was generated on the

shelf by static pressure greater or less than Pa"

The scarfed nozzle configuration 7 shown in figure 19(b) also exhibited a compression plane on the shelf

that appeared to be parallel to the scarf angle of the upper

divergent flap and shelf trailing edge. In addition, the

flow on the left side of the shelf (looking upstream)

appeared to expand farther away from the nozzle centerline than flow on the right side. These phenomena were a

result of nozzle geometry which expanded flow to the

left side of the nozzle as well as out the shelf. However,

flow at the trailing edge of the scarfed shelf recompressed to travel parallel to the nozzle centerline.

Similar trends appeared for the sawtooth nozzle configuration 13, as shown in figure 19(c). The oil flow photographs highlight the lines formed as the expansion and

compression waves impinged on the shelf surface.

Downstream of the nozzle exit, flow along the sides

expanded away from the centerline and recompressed

back toward the centerline further downstream. At the

trailing edge of the sawtooth nozzle shelf, the flow patterns were nearly parallel to the nozzle centerline. Weak

shock patterns again parallel to the trailing edge can be

seen on the shelf surface (one shock nearly intersects orifice 69, as shown).

Conclusions

An investigation was conducted in the static test

facility of the Langley 16-Foot Transonic Tunnel to

determine the internal performance of a two-dimensional

convergent-divergent nozzle. The nozzle design was

tested with dry and afterburning throat areas, which represent different power settings and three expansion

ratios. For each configuration, three trailing-edge geometries were tested. The baseline geometry had a straight

trailing edge. Two different shaping techniques were

applied to the baseline nozzle design to reduce radar

observables: the scarfed design and the sawtooth design.

A flat plate extended downstream of the lower divergent

flap trailing edge parallel to the model centerline to form

a shelflike expansion surface. This shelf was designed to

shield the plume from observation from the ground

(infrared radiation (IR) signature suppression). The shelf

represents part of the aircraft structure that might be

present in an installed configuration. These configurations were tested at nozzle pressure ratios from 2.0

to 12.0.

Results of this investigation indicated the following

conclusions:

1. Discharge coefficient and peak resultant thrust

ratio were not significantly affected by the addition of

the shelf and changes to the upper divergent flap

and shelf geometry. Discharge coefficients for these twodimensional convergent-divergent shelf nozzles lower

than typical two-dimensional convergent-divergent nozzles due to the sharp corner at the nozzle geometric

throat.

2. Resultant pitch vector angles were typically nonzero and varied with increasing nozzle pressure ratio. In

addition to nozzle internal asymmetry, the shelf significantly affected the pitch vector angle by producing a surface on which the shock-cell pressure variation could act.

Only the asymmetrical scarfed nozzle produced resultant

yaw thrust vector angles.

NASA Langley Research Center

Hampton, VA 23681-0001

April 4, 1996

References

t. Deitchman, Seymour J.: Military Power and the Advance of

Technology--General Purpose Military Forces for the 1980's

and Beyond. Westview Press, 1983.

2. Leavitt, Laurence D.; and Berrier, Bobby L.: Static Performance of Nozzles Designed for Low Infrared Radiation and

Radar Cross-Section Signatures. NASA TM-4689, 1995.

3. Staff of the Propulsion Aerodynamics Branch: A User's Guide

to the Langley 16-Foot Transonic Tunnel Complex--Revision

1. NASA TM-83186, 1990. (Supersedes NASA TM-83186.)

4. Mercer, Charles E.; Berrier, Bobby L.; Capone, Francis J.; and

Grayston, Alan M.: Data Reduction Formulas for the 16-Foot

Transonic Tunnel: NASA Langley Research Center Revision

2. NASA TM-107646, 1992. (Supersedes NASA TM-86319.)

5, Berrier, Bobby L.: Results From NASA Langley Experimental

Studies of Multiaxis Thrust Vectoring Nozzles. SAE Paper

881481, Oct. 1988.

6. Leavitt, Laurence D.: Summary of Nonaxisymmetric Nozzle

Internal Performance From the NASA Langley Static Test

Facility. AIAA-85-1347, July 1985.

7
7. Mason, Mary L.; Putnam, Lawrence E.; and Re, Richard J.:

The Effect of Throat Contouring on Two-Dimensional

Converging-Diverging Nozzles at Static Conditions. NASA

TP- 1704, 1980.

8. Mason, Mary L.; and Berrier, Bobby L.: Static Investigation of

Several Yaw Vectoring Concepts on Nonaxisymmetric Nozzles.

NASA TP-2432, 1985.

9. Hiley, E E.; Wallace, H. W.; and Booz, D. E.: Study of NonAxisymmetric Nozzles Installed in Advanced Fighter Aircraft.

AIAA-75-1316, Sept.--Oct. 1975.

10. Capone, E J.: Nonaxisymmetric Nozzle--It is for Real.

AIAA-79-1810, Aug. 1979.

11. Capone, Francis J.; and Berrier, Bobby L.: Investigation of

Axisymmetric and Nonaxisymmetric Nozzles Installed on a

O. lO-Scale F- 18 Prototype Airplane Model. NASA TP- 1638,

1980.

12. Taylor, John G.: Static Investigation of a Two-Dimensional

Convergent-Divergent Exhaust Nozzle With Multiaxis ThrustVectoring Capability. NASA TP-2973, 1990.
Table 1. Configuration Summary

Configuration Design Power Ae/A t (NPR)d _iv,p, deg

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

Baseline

Baseline

Baseline

Baseline

Baseline

Baseline

Scarfed

Scarfed

Scarfed

Scarfed

Scarfed

Scarfed

Sawtooth

Sawtooth

Sawtooth

Sawtooth

Sawtooth

Sawtooth

Dry

Dry

Dry

A/B

A/B

A/B

Dry

Dry

Dry

A/B

A/B

A/B

Dry

Dry

Dry

A/B

A/B

A/B

1.100

1.750

2.500

1.100

1.750

2.500

1.100

1.750

2.500

1.100

1.750

2.500

1.100

1.750

2.500

1.100

1.750

2.500

3.060

8.371

15.647

3.060

8.371

15.647

3.060

8.371

15.647

3.060

8.371

15.647

3.060

8.371

15.647

3.060

8.371

15.647

6.47

1.82

-3.74

7.80

2.30

-4.70

5.00

0.35

-5.21

6.33

0.83

-6.17

5.20

0.55

-5.02

6.53

1.03

-5.98

9
Table2. NozzleInternalPerformanceCharacteristics forBaselineConfigurations

(a) Drypowerconfigurations

NPR Wp/W i FIF i FrlF i 8p, deg _Sy,deg

Configuration 1; Ae/A t = 1. lO0

2.003

2.502

3.006

3.497

3.996

4.502

5.004

6.005

8.005

9.996

1.165

0.961

.961

.961

.961

.962

.962

.962

.963

.963

.963

.962

0.940

.959

.967

.971

.972

.971

.969

.964

.952

.945

.942

0.940

.959

.967

.971

.972

.971

.970

.964

.953

.952

1 .954

Configuration 2; Ae/A t = 1.750

-0.568

-.316

-.574

1.543

-.849

-1.106

-1.026

-.010

-.692

-7.078

-9.279

-0.208

-.117

.013

.017

-.006

-.002

-.018

.017

.027

-.213

-.278

1.999

2.999

3.999

5.003

5.996

6.998

8.000

8.503

9.011

9.497

9.995

10.572

0.968

.966

.966

.967

.968

.968

.968

.967

.967

.967

.967

.967

0.871

.907

.940

.961

.974

.980

.984

.986

.987

.987

.988

.988

0.872

.907

.940

.961

.974

.981

.985

.986

.987

.988

.988

.988

-1.510

1.085

-.034

1.360

-.705

-1.629

-1.828

-1.655

-1.414

-1.081

-.715

-.356

-0.078

-.054

-.125

-.089

-.048

.060

.068

.026

.049

.026

-.008

-.037

Configuration 3; Ae[A t = 2.500

2.001

3.003

4.002

5.006

6.004

6.997

7.995

9.000

9.998

10.793

10.994

0.964

.967

.967

.968

.968

.968

.968

.967

.968

.967

.967

0.896

.875

.912

.899

.917

.936

.951

.963

.971

.976

.977

0.896

.875

.913

.903

.921

.937

.954

.967

.976

.981

.982

-1.204

1.297

1.994

-5.785

-4.997

-3.370

--4.298

-5.136

-5.677

-5.730

-5.679

-0.541

-.122

-.025

-.115

-.008

.012

.048

.010

.039

.048

.027

10
Table2. Concluded

(b) A/Bpowerconfigurations

NPR WdW i F]F i Fr[F i _p, deg 5_, deg

Configuration 4; AelA t = 1.100

2.004

2.503

3.007

3.504

4.003

4.507

5.007

6.003

7.721

0.958

.957

.957

.957

.957

.958

.957

.958

.957

0.949

.964

.972

.975

.975

.974

.971

.966

.957

0.949

.964

.973

.975

.976

.974

.971

.966

.957

Configuration 5; AeJA t = 1.750

2.003

2.998

4.008

5.001

6.009

7.000

8.004

8.495

8.996

9.565

0.972

.972

.973

.973

.973

.973

.972

.972

.972

.971

2.000

3.002

3.998

5.007

5.997

7.002

8.005

9.007

9.982

0.963

.969

.970

.970

.970

.970

.970

.969

.968

0.890

.920

.943

.967

.978

.984

.989

.990

.991

.991

0.890

.920

.943

.967

.978

.985

.989

.990

.991

.991

Configuration 6; AelA t = 2.500

0.942

.866

.901

.920

.929

.935

.953

.966

.977

0.942

.866

.901

.918

.927

.931

.947

.958

.968

-0.151

.751

1.808

-.412

-1.655

-1.020

.054

1.977

-.435

-0.075

-.095

-.054

-.09 l

-.119

-.096

-.043

-.043

-.004

-0.206

1.946

-.813

1.386

-1.226

-2.013

-1.431

-.844

-.363

-.036

0.068

-.064

-.073

-.014

.008

.033

.038

.018

-.021

-.022

-0.108

1.514

-1.092

-3.845

-3.864

-5.717

-6.577

-7.533

-7.817

-0.248

-.093

-1.129

-.035

.046

-.003

.046

.106

.155

11
Table3. NozzleInternalPerformanceCharacteristics forScarfedConfigurations

(a)Drypowerconfigurations

NPR wJw i F/F i FrlF i 8p, deg by, deg

Configuration 7; Ae/A t = 1.100

2.001

2.504

3.001

3.497

4.003

4.508

5.007

6.002

6.998

8.001

9.007

10.006

10.939

0.970

.969

.968

.969

.969

.969

.970

.970

.970

.970

.970

.970

.969

0.914

.935

.954

.966

.974

.977

.978

.978

.975

.973

.972

.969

.968

0.914

.935

.954

.966

.974

.978

.980

.980

.979

.977

.976

.974

.973

-0.526

-.251

.375

-.057

-.825

-.142

.406

.505

1.608

1.481

.317

-1.115

-2.742

Configuration 8; Ae/A t = 1.750

0.316

-.048

-.169

.390

1.523

2.346

3.014

3.896

4.539

4.988

5.186

5.318

5.362

2.001

3.005

4.009

5.000

5.999

7.001

7.998

8.493

9.001

9.493

10.001

11.080

0.971

.969

.969

.969

.970

.969

.969

.969

.969

.969

.969

.968

0.866

.911

.923

.945

.961

.972

.980

.982

.985

.986

.987

.989

0.866

.911

.923

.947

.962

.973

.980

.983

.986

.987

.988

.990

-1.127

-.222

-.718

1.316

-.586

-2.134

-2.423

-2.456

-2.412

-2.328

-2.172

-1.565

0.931

.998

-1.216

-2.384

-1.469

.386

.403

.724

1.021

1.239

1.452

1.790

Configuration 9; AelA t = 2.500

1.998

2.998

3.999

4.997

6.002

6.997

8.009

9.013

10.008

11.474

0.962

.967

.968

.968

.968

.968

.968

.967

.968

.966

0.940

.870

.879

.910

.912

.918

.934

.947

.956

.967

0.940

.870

.883

.912

.917

.922

.938

.952

.963

.975

-1.121

.759

-3.894

-2.564

-4.779

-4.918

-4.919

-5.635

-6.504

-7.169

0.335

.560

-4.143

-2.010

-2.841

-2.726

-2.529

-2.207

-1.619

-.815

12
Table3. Concluded

(b) A/Bpowerconfigurations

NPR Wp/W i F/F i Fr/F i _p, deg 8_ deg

Configuration l O; At/A t = I. lO0

2.005

2.499

2.998

3.496

3.999

4.501

5.010

5.995

8.010

9.848

0.970

.971

.971

.971

.971

.972

.972

.972

.971

.970

0.927

.946

.962

.971

.976

.978

.978

.977

.972

.968

Configuration 11; At/A t

0.927

.946

.962

.971

.976

.979

.980

.980

.976

.973

= 1.750

-0.068

.060

.668

-.371

-.007

.884

1.022

1.592

-.265

-2.682

0.893

-.955

-.359

.552

1.678

2.515

3.116

4.021

4.900

5.156

1.999

3.001

3.993

4.991

5.981

6.994

7.965

8.498

8.991

9.485

0.972

.970

.971

.971

.971

.971

.971

.971

.970

.970

0.864

.916

.929

.951

.967

.977

.984

.986

.989

.990

0.864

.916

.931

.952

.967

.978

.986

.987

.990

.991

-0.336

-.471

.503

1.368

-1.444

-2.986

-3.119

-2.952

-2.616

-2.233

Configuration 12; At/A t = 2.500

2.074

.186

-3.138

-2.612

-1.492

-.349

.407

.757

1.029

1.246

2.003

3.006

3.999

5.000

6.002

7.006

7.987

9.009

10.030

0.964

.970

.970

.971

.971

.970

.970

.969

.968

0.947

.905

.869

.891

.914

.927

.938

.947

.956

0.947

.905

.876

.899

.919

.932

.945

.957

.968

-0.373

.238

-5.403

-3.500

-5.367

-5.584

-6.280

-7.760

-8.798

0.944

1.645

-4.972

-6.660

-2.512

-2.540

-2.692

-2.395

-I .755

13
Table4. NozzleInternalPerformanceCharacteristics forSawtoothConfigurations

(a)Drypowerconfigurations

NPR Wp/W i F/F i Fr/F i _ip, deg _y, deg

Configuration 13; Ae/A t = I. IO0

2.000

2.501

3.092

3.502

3.992

4.500

5.004

6.002

7.994

10.020

11.315

0.972

.970

.971

.971

.970

.972

.971

.972

.972

.971

.971

0.916

.941

.959

.969

.976

.977

.978

.977

.972

.965

.961

0.916

.941

.960

.969

.976

.977

.978

.977

.972

.966

.961

-0.933

-1.320

-1.247

-.741

-1.533

-.284

-.138

-.049

1.636

2.478

.853

0.592

-.139

-.145

-.088

-.103

-.065

-.023

.020

.116

.030

-.022

Configuration 14; Ae/A t = 1.750

2.000

3.007

3.999

5.011

6.002

7.017

8.008

8.414

9.000

10.000

11.205

0.970

.969

.969

.970

.970

.970

.970

.970

.970

.970

.969

0.866

.890

.930

.953

.968

.977

.982

.984

.986

.988

.989

0.866

.894

.931

.954

.968

.977

.983

.985

.987

.988

.989

-0.880

-5.224

-3.134

-2.554

-.798

-2.292

-3.118

-3.103

-2.658

-1.696

-.635

-0.216

-.218

-.031

-.086

-.047

-.007

.005

.040

.009

.016

-.044

2.003

3.006

3.996

6.003

8.008

9.000

10.013

11.851

Configuration 15; Ae]A t = 2.500

0.963

.969

.969

.970

.970

.969

.970

.968

0.945

.867

.886

.907

.939

.951

.959

.971

0.945

.867

.894

.917

.944

.957

.966

.980

-0.506

.481

-7.704

-8.659

-6.189

-6.628

-7.278

-7.866

-0.388

-.192

-.081

.053

.031

.044

.088

.174

14
NPR wp/w i

Table 4. Concluded

(b) A/B power configurations

F/Fi F,/Fi

Configuration 16; Ae/A t = 1.100

_p, deg _ deg

2.005

2.501

3.003

3.504

4.000

4.502

5.001

5.503

6.002

8.004

8.929

0.971

.969

.970

.970

.970

.971

.971

.971

.971

.969

.969

0.935

.955

.967

.974

.977

.977

.976

.975

.974

.967

.964

0.935

.955

.967

.975

.977

.977

.976

.975

.974

.969

.965

-0.363

-.254

.112

-.924

-.672

.231

.436

.595

.704

3.268

3.341

-0.086

-.208

-.085

-.099

-.047

-.002

.007

-.003

.036

.057

.048

Configuration 17; AelA t = 1.750

NPR Wp/W i FIF i Fr/F i _p, deg _r deg

1.999

3.007

3.997

4.998

6.002

0.971

.971

.971

.972

.971

0.849

.917

.932

.954

.970

0.853

.917

.933

.955

.970

-2.585

1.075

-2.450

-.802

-1.666

7.004

7.995

8.497

8.999

9.729

.971

.971

.97 I

.970

.970

.979

.986

.987

.989

.991

.980

.988

.988

.990

.992

-3.180

-3.701

-3.152

-2.559

-1.817

Configuration 18; AeIA t

1.996

3.001

3.999

4.999

5.997

7.000

7.999

8.998

10.017

10.119

0.965

.971

.971

.972

.971

.971

.970

.970

.969

.969

0.950

.858

.888

.896

.919

.931

.942

.952

.960

.961

= 2.500

0.950

.863

.896

.909

.928

.940

.950

.963

.973

.974

-0.053

-6.545

-7.645

-9.844

-8.227

-7.888

-7.598

-8.681

-9.393

-9.435

-5.188

-.080

.013

-.052

.014

.085

.072

.071

.085

.080

-0.184

-.099

.002

.015

.086

.110

.129

.222

.243

.284

15
Table5. NozzleInternalStaticPressureRatiosforDryPowerBaselineConfigurations

(a)Configuration1;Ae/A t = 1.100

P/Ptj for lower divergent flap at--

(y/w)12 = 0.500 for x/Lfla p of-- (y/w)/2 = 0.000 for x/Lfla p of-- (y/w)12 = -0.500 for x/Lfla p of--

NPR 0.500 0.500 0.700 0.900 0.500 0.700 0.900

0.291

.288

.286

.285

.284

.283

.283

.283

.283

.283

.284

0.700 0.900

0.358 0.449

.357 .305

.356 .304

.356 .303

.355 .303

.355 .302

.355 .302

.356 .302

.356 .302

.357 .302

.357 .301

0.288

.287

.286

.286

.285

.285

.285

.285

.284

.284

.283

0.362

.361

.360

.359

.359

.358

.358

.357

.358

.359

.359

0,457

.314

.308

.299

.296

.294

,293

.292

.292

.292

.292

0.291

.287

.286

.285

.284

.283

.283

.283

.282

.283

.283

0.359

.359

.359

.359

.358

.358

.358

.358

.358

.359

.358

2.003

2.502

3.006

3.497

3.996

4.502

5.004

6.005

8.005

9.996

11.165

0.450

.305

.305

.305

.305

.304

.305

.305

.305

.305

.306

P/Pt,j on shelf at (y/w)/2 = 0.000 for x/LshelfOf---

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985

2.003

2.502

3.006

3.497

3.996

4.502

5.004

6.005

8.005

9.996

11.165

0.558

.522

.453

.435

.436

.436

.437

.439

.441

.442

.442

0.513

.371

.335

.363

.276

.209

.203

.203

.203

.203

.203

0.507

.454

.239

.180

.150

.159

.165

.108

.087

.087

.087

0.506

.384

.469

.298

.200

.172

.154

.076

.044

.042

.042

0.505

.439

.294

.400

.308

.255

.184

.134

.089

.091

.084

0.504

.385

.292

.268

.292

.316

.263

.174

.111

.093

.086

0.501

.409

.403

.230

.220

.205

.223

.215

.145

.096

.086

16
Table5. Continued

(b) Configuration2;AelA t = 1.750

P]Pt,j for lower divergent flap at-

(y/w)/2 = 0.500 for x/Lfla p of-- (y/w)12 = 0.000 for x/Lfla p of--- (ylw)/2 = -0.500 for x/Lfla p of--

NPR 0.500 0.700 0.900 0.500 0.700 0.900 0.500 0.700 0.900

t .999 0.498 0.527 0.433 0.500 0.527 0.432

2.999

3.999

5.003

5.996

6.998

8.000

8.503

9.011

9.497

9.995

10.572

0.437

.220

.219

.219

.218

.218

.218

.218

.218

.218

.218

.218

.160

.159

.159

.159

.159

.159

.159

.159

.159

.159

.158

.285

.118

.118

.118

.117

.117

.117

.117

.116

.116

.116

.219

.218

.217

.216

.216

.215

.215

.215

.214

.213

.213

.163

.163

.162

.162

.162

.162

.162

.162

.161

.161

.161

.289

.137

.127

.124

.122

.120

.118

.117

.116

.116

.116

.220

.219

.218

.218

.217

.217

.217

.217

.217

.217

.217

0.497

.159

.158

.158

.158

.158

.158

.158

.158

.158

.158

.158

0.526

.281

.118

.118

.118

.118

.118

.118

.118

.117

.117

.117

P/Pt,j on shelf at (y/w)12 = 0.000 for x/Lshel f of--

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985

1.999

2.999

3.999

5.003

5.996

6.998

8.000

8.5O3

9.011

9.497

9.995

10,572

0.536

.367

.249

.167

.167

.167

.166

.166

.166

.165

.165

.165

0.514

.424

.315

.242

.137

.138

.138

.138

.138

.138

.138

.138

0.510

.316

.248

.346

.231

.110

.108

.108

.108

.108

.107

.107

0.511

.374

.265

.255

.298

.242

.105

.095

.092

.090

.089

.089

0.511

.327

.265

.139

.179

.224

.187

.152

.088

.062

.050

.047

0.510

.362

.292

.112

.121

.126

.152

.166

.160

.149

.111

.048

0.502

.313

.206

.216

.124

.112

.094

.102

.110

.120

.128

.127

17
Table5. Concluded

(c) Configuration3;AelA t = 2.500

P/Ptj for lower divergent flap at-

(y/w)/2 = 0.500 for x/Lfla p of-- (ylw)12 = 0.000 for x/Lfla p of--- (y/w)12 = -0.500 for x/Lfla p of--

NPR 0.500 0.700 0.900 0.500 0.700 0.900 0.500 0.700 0.900

2.001 0.484 0.528 0.478 0.486 0.531 0.474

3.003

4.002

5.006

6.004

6.997

7.995

9.000

9.998

10.793

10.994

0.484

.232

.109

.109

.109

.109

.109

.109

.109

.109

.109

.238

.196

.070

.067

.067

.066

.066

.066

.066

.066

.303

.193

.136

.082

.065

.063

.061

.060

.058

.056

.236

.Ill

.110

.110

.110

.109

.108

.108

.107

.105

.239

.206

.116

.067

.067

.066

.066

.066

.066

.066

.306

.212

.141

.071

.068

.066

.064

.062

.060

.060

.235

.110

.110

.109

.109

.109

.108

.108

.108

.108

0.489

.238

.195

.067

.065

.065

.065

.065

.065

.065

.065

0.531

.299

.192

.130

.071

.065

.064

.063

.062

.061

.060

P/Pt,j on shelf at (y/w)/2 = 0.000 for x/Lshel f of---

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985

2.001

3.003

4.002

5.006

6.004

6.997

7.995

9.000

9.998

10.793

10.994

0.531

.408

.212

.180

.149

.092

.091

.09 !

.091

.091

.090

0.510

.401

.232

.224

.188

.160

.071

.071

.071

.071

.070

0.508

.309

.263

.223

.242

.191

.150

.115

.054

.054

.054

0.508

.354

.259

.214

.169

.249

.199

.150

.125

.079

.075

0.507

.355

.284

.229

.145

.137

.227

.218

.179

.146

.137

0.506

.326

.237

.203

.134

.123

.111

.172

.206

.189

.183

0.501

.345

.251

.190

.220

.083

.084

.081

.115

.155

.161

18
Table6. NozzleInternalStaticPressureRatiosforA/BPowerBaselineConfigurations

(a) Configuration4;AelA t = 1.100

P[Pt,j for lower divergent flap at (ylw)12 = 0.500 for x/Lfla p of--

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

2.004

2.503

3.007

3.504

4.003

4.507

5.007

6.003

7.721

0.367

.366

.364

.362

.361

.361

.360

.360

.359

0.465

.464

.465

.465

.465

.465

.465

.465

.465

0.445

.444

.444

.444

.444

.444

.443

.443

.443

0.385

.385

.385

.385

.385

.385

.385

.385

.385

0.335

.334

.333

.333

.332

.332

.332

.332

,332

0.287

.286

.286

.285

.285

.285

.286

.285

.287

0.383

.382

.382

.382

.382

.383

.383

.383

.383

0.362

.362

.360

.359

.359

.359

.359

.359

.359

0.482

.346

.345

.345

.345

.345

.345

.344

.344

plpt,j for lower divergent flap at (y/w)/2 = 0.0130 for x/Lllap of--

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

2.004

2.503

3.007

3.504

4.003

4.507

5.007

6.003

7.721

0.359

.358

.356

.355

.354

.354

.354

.354

.353

0.464

.462

.461

.460

.459

.459

.458

.458

.457

0.448

.447

.447

.447

.447

.446

.446

.446

.446

0.392

.392

.392

.392

.391

.391

.391

.391

.391

0.332

.332

.332

.332

.332

,332

.333

.332

.333

0.285

,285

.285

.285

.285

.284

.284

.284

.284

0.389

.388

.387

.388

.388

.388

.388

.389

.390

0.368

.368

.368

.368

.368

.368

.369

.369

.369

0.487

.344

.343

.343

.343

.343

.342

.342

.343

19
Table6. Continued

(a) Concluded

P/Ptj for lower divergent flap at (y/w)/2 = -0.500 for x/Lfla p of---

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

2.004

2.503

3.007

3.504

4.003

4.507

5.007

6.003

7.721

0.350

.349

.348

.348

.347

.347

.347

.346

.345

0.473

.470

.469

.468

.467

.466

.465

.465

.464

0.441

.44 i

.441

.441

.441

.441

.441

.442

.443

0.390

.389

.390

.392

.392

.392

.393

.393

.394

0.334

.334

.334

.333

.331

.330

.329

.328

.327

0.289

.288

.287

.286

.286

.286

.285

.285

.285

0.380

.380

.379

.379

.379

.379

.379

.380

.381

0.365

.365

.364

.364

.364

.364

.364

.364

.365

0.478

.345

.345

.344

.344

.344

.344

.344

.345

P/Pt,j on shelf at (y/w)/2 = 0.000 for xlLshelfOf--

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985

2.004

2.503

3.007

3.504

4.003

4.507

5.007

6.003

7.721

0.577

.544

.441

.431

.428

.426

.425

.424

.423

0.514

.379

.415

.323

.253

.248

.249

.249

.250

0.508

.423

.228

.226

.214

.170

.138

.110

.110

0.507

.416

.311

.197

.131

.102

.103

.076

.053

0.506

.379

.425

.306

.328

.211

.168

.120

.066

0.505

.421

.281

.352

.310

.302

.228

.137

•104

0.498

.387

.286

.256

.272

.293

.266

.203

.132

2O
Table6. Continued

(b) Configuration5;Ae/A t = 1.750

P/Pt,j for lower divergent flap at (y/w)2 = 0.500 for x/Lfla p of--

NPR 0.100 0.200 0,300 0.400 0.500 0.600 0.700 0.800 0.900

2.003

2.998

4.008

5.001

6,009

7.000

8.004

8.495

8.996

9.565

0.316

.315

.313

.312

.312

.311

.311

.311

.311

.310

0.308

.308

.308

.308

.308

.308

.307

.308

.307

.307

0.238

.238

.238

.238

.238

.238

.238

.239

.239

.239

0.369

.180

.180

.180

.180

.180

.180

.180

.180

.180

0.390

.228

.228

.227

.227

.227

.226

.226

.226

.226

0.453

.203

.203

.204

.204

.204

.204

.204

.204

.204

0.514

.180

.180

.180

.180

.180

.179

.179

.179

.179

0.534

.287

.159

.159

.159

.158

.158

.158

.158

.158

0.549

.307

.140

.140

.140

.140

.140

.140

.140

.140

NPR

2.003

2,998

4.008

5.001

6,009

7,000

8,004

8.495

8.996

9.565

P[Pt,j for lower divergent flap at (y/w)/2 = 0,000 for x/Lfla p of__

0. !00 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

0.311

.309

.308

.308

.308

.308

.307

.307

.307

.307

0.313

.310

.309

.309

.308

.308

.308

.308

.308

.308

0.245

.241

.240

.237

.236

.236

.236

.236

.236

.235

0.369

.180

.180

.180

.180

.179

.179

.179

.179

.178

0.391

.219

.218

.217

.217

.217

.217

.216

.216

.216

0.455

.201

.202

.201

.200

.199

.199

.200

.200

.200

0.513

.185

.185

.185

.185

.184

.184

.184

.185

.185

0.537

.291

.163

.163

.163

.162

.162

.162

.162

.162

0.556

.310

.141

.142

.142

.142

.142

.142

.142

.142

21
Table6. Continued

(b) Concluded

P/Pt,j for lower divergent flap at (ylw)/2 = -0.500 for x/Lttap of----

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

2.003

2.998

4.008

5.001

6.009

7.000

8.004

8.495

8.996

9.565

0.307

.307

.307

.306

.305

.305

.305

.304

.304

.304

0.310

.309

.308

.308

.307

.307

.307

.307

.307

.307

0.241

.241

.241

.240

.240

.240

.240

.240

.240

.240

0.371

.181

.181

.180

,180

.180

.180

.180

.180

.180

0.388

.226

.226

.225

.225

.224

.224

.224

.224

.224

0.450

.205

.206

.205

.205

.205

.205

.205

.205

.205

0.510

.180

.180

.180

.180

,179

.179

,179

.179

.179

0.534

.289

,158

.158

.158

.158

.158

.158

.158

.158

0.550

.307

.140

.140

.140

.140

.140

.140

.140

.140

P/Pt,j on shelf at (y/w)12 = 0.000 for x/Lshel f of--

NPR 0.076 0.227 0.379 0.530 0,682 0.833 0.985

2.003

2.998

4.008

5.001

6.009

7.000

8.004

8.495

8.996

9.565

0.552

.421

.216

.165

.165

.164

.165

.165

.165

.165

0.513

.471

.350

.221

.123

.122

.122

.122

.123

.123

0,508

.306

.318

.318

.214

.135

.133

.133

.133

.133

0.508

.306

.196

.310

.279

.242

.117

.108

.103

.101

0.507

.387

.163

.186

.226

.186

,161

.119

.077

.07t

0.506

.294

.279

.110

.155

.189

.140

.120

.105

.085

0.499

.370

.312

.134

.124

.121

.144

.151

.142

.111

22
Table6. Continued

(c) Configuration6;AJAt = 2.500

P/Pt,j for lower divergent flap at (y/w)2 = 0.500 for x/Lfla p of--

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

2.000

3.002

3.998

5.007

5.997

7.002

8.005

9.007

9.982

0.333

.316

.313

.312

.311

.311

.311

.310

.310

0.354

.305

.305

.305

.305

.305

.305

.305

.305

0.548

.235

.235

.235

.235

.235

.235

.235

.235

0.555

.178

.178

.178

.178

.178

.178

.178

.178

0.515

.148

.135

.135

.135

.135

.135

.135

.135

0.497

.247

.110

.105

.105

.106

.106

.106

.106

0.499

.249

.200

.085

.085

.085

.085

.085

.085

0.509

.252

.202

.133

.070

.070

.070

.070

.070

0.549

.264

.205

.144

.058

.058

.059

.059

.059

NPR 0.100

2.000 0.325

3.002 .308

3.998 .307

5.007 .307

5.997 .307

7.002 .307

8.005 .306

9.007 .306

9.982 .306

p_t,j_rlowerdivergentflapat_lw)12=O.OOO_rx/LflapOf--

0.2_ 0.3_ 0.400 0.5_ 0._0 0.7_ 0.800 0.9_

0.360

.306

.305

.305

.304

.304

.304

.304

.304

0.545

.237

.236

.233

.232

.232

.232

.232

.231

0.556

.176

.177

.177

.176

.176

.175

.175

.175

0.516

.253

.135

.135

.135

.135

.135

.135

.135

0.499

.267

.107

.107

.107

.107

.107

.107

.106

0.499

.264

.187

.086

.086

.086

.086

.086

.086

0.511

.262

.187

.153

.071

.071

.071

.071

.071

0.559

.270

.190

.156

.059

.059

.059

.059

.059

23
Table6. Concluded

(c) Concluded

plpt,j for lower divergent flap at (ylw)/2 = --0.500 for x/Lfla p of---

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

2.000

3.002

3.998

5.007

5.997

7.002

8.005

9.007

9.982

0.322

.305

.305

.304

.303

.303

.303

.302

.302

0.355

.304

.303

.303

.303

.302

.302

.302

.302

O.548

.237

.237

.236

.236

.236

.236

.235

.235

0.556

.177

.177

.177

.177

.177

.177

.177

.177

0.516

.154

.134

.134

.134

.135

.135

.134

.134

0.503

.250

.107

.107

.107

.107

.107

.106

•106

0.499

•250

.127

.084

•084

.084

.084

•084

.084

0.509

.253

.168

.113

.069

.069

.069

.069

.069

0.552

.263

.180

.141

.058

.058

.058

.058

.058

P/Pt,j on shelf at (y/w)/2 = 0.000 for x/Lshel f of---

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985

2.000 0.510 0.508 0.507 0.507 0.507

3.002

3.998

5.007

5.997

7.002

8.005

9.007

9.982

0.555

.312

.220

.184

.130

.069

.069

.069

.069

.372

.285

.226

.197

.138

.072

.063

.062

.375

.289

.242

.223

.220

.141

.112

.090

.358

.277

.200

.186

.242

.211

.140

.112

.344

.229

.223

.153

.125

.248

.204

.139

.335

.319

.220

.134

.104

.111

.206

.203

0.500

.337

.248

.179

.183

.104

.109

.090

.148

24
Table7. NozzleInternalStaticPressureRatiosforDryPowerScarfedConfigurations

(a)Configuration7;Ae/A t = 1.100

plPt J for lower divergent flap at-

(y/w)/2 = 0.500 for x/Lfla p of---- (ylw)/2 = 0.000 for x/Lfla p of--- (y/w)/2 = -0.500 for x/Lfla p of__

NPR 0.500 0.700 0.900 0.500 0.700 0.900 0.500 0.700 0.900

2.001 0.420 0.504 0.260 0.427 0.523 0.263

2.504

3.001

3.497

4.003

4.508

5.007

6.002

6.998

8.001

9.007

10.006

10.939

0.261

.261

.261

.261

.261

.261

.261

.260

.260

.260

.260

.261

.261

.272

.272

.272

.271

.271

.271

.270

.270

.270

.270

.270

.270

.331

.227

.227

.227

.226

.226

.226

.226

.226

.226

.226

.225

.259

.259

.259

.259

.259

.259

.259

.259

.259

.259

.259

.259

.230

.225

.220

.215

.210

.206

.199

.193

.189

.186

.184

.182

.390

.243

.239

.236

.230

.227

.225

.224

.224

.224

.224

.224

.262

.262

.261

.261

.260

.260

.260

.260

.260

.260

.260

.260

0.470

.189

.189

.189

.189

.189

.189

.189

.188

.188

.188

.188

.189

0.548

.373

.331

.229

.227

.226

.226

.226

.226

.226

.226

.226

.226

P/Ptj on shelf at (y/w)/2 = 0.500 for x/Lshel f of__

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985 1.061

2.00 l 0.514 0.505 0.505 0.504 0.505

2.504

3.001

3.497

4.003

4.508

5.007

6.002

6.998

8.001

9.007

10.006

10.939

0.561

.457

.329

.254

.254

.254

.253

.253

.253

.254

.254

.254

.254

.383

.358

.426

.298

.222

.222

.221

.221

.220

.220

.220

.220

.400

.333

.223

.260

.255

.246

.175

.135

.135

.135

.135

.135

.406

.367

.289

.181

.240

.186

.101

.087

.076

.053

.051

.051

.407

.319

.361

.259

.149

.190

.146

.120

.080

.069

.062

.055

.409

.365

.285

.332

.230

.214

.198

.121

.102

.075

.049

.043

0.502

.400

.324

.256

.261

.280

.213

.193

.166

.111

.094

.084

.080

0.501

.402

.354

.298

.211

.253

.253

.204

.181

.123

.098

.089

.105

25
Table7. Continued

(a)Concluded

P/Ptj on shelf at (ylw)12 = 0.000 for x/LshelfOf---

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985

2.001

2.504

3.001

3.497

4.003

4.508

5.007

6.002

6.998

8.001

9.007

0.006

0.939

0.554

.446

.415

.256

.252

.252

.252

.252

.252

.253

.253

.253

.253

0.519

.410

.361

.418

.389

.312

.216

.210

.209

.209

.209

.209

.209

0.510

.417

.291

.235

.244

.289

.248

.166

.130

.119

.118

.118

.118

0.510

.409

.390

.218

.201

.164

.150

.130

.119

.087

.068

.061

.060

0.505

.407

.332

.405

.180

.169

.172

.108

.060

.059

.058

.046

.038

0.505

.41 i

.330

.292

.354

.266

.187

.156

.125

.074

.068

.050

.075

0.500

.396

.342

.248

.263

.296

.237

.234

.182

.128

.109

.098

.088

P/Pt,j on shelf at (y/w)/2 = -0.500 for xlLshelfOf--

NPR 0.076 0.227 0.379 0.530 0.682 0.833

2.001

2.504

3.001

3.497

4.003

4.508

5.007

6.002

6.998

8.001

9.007

10.006

10.939

0.543

.481

.431

.371

.326

.317

.298

.277

.275

.274

.275

.275

.275

0.512

.395

.326

.356

.346

.300

.190

.176

.167

.156

.153

.153

.153

0.520

.429

.358

.231

.241

.274

.245

.164

.089

.086

.080

.077

.076

0.507

.397

.357

.268

.226

.148

.149

.179

.153

.068

.052

.046

.044

0.507

.403

.361

.339

.222

.225

.203

.103

.111

.117

.084

.065

.063

0.503

.407

.300

.326

.338

.193

.192

.187

.084

.073

.070

.068

.065

26
Table7. Continued

(b) Configuration8;Ae/A t = 1.750

P/Pt,j for lower divergent flap at-

(y/w)/2 = 0.500 for x/Lfla p of-- (y/w)2 = 0.000 for x/Lfla p of--- (y/w)/2 = -0.500 for x/Lfla p of----

NPR 0.900 0.900 0.500 0.700 0.900

2.001

3.005

4.009

5.000

5.999

7.001

7.998

8.493

9.001

9.493

10.001

11.080

0.500 0.700

0.458 0.515

.201 .279

.201 .146

.201 .146

.201 .145

.201 .145

.201 .145

.201 .145

.201 .145

.201 .145

.201 .145

.201 .145

0.532

.359

.202

.105

.104

.104

.104

.104

.104

.104

.104

.104

0.500 0.700

0.441 0.517

.242 .269

.183 .144

.182 .144

.181 .144

.181 .144

.181 .144

.181 .143

.181 .143

.181 .143

.181 .143

.181 .143

0.532

.310

.127

.115

.112

.110

.108

.107

.106

.105

.103

.102

0.413

.258

.109

.109

.109

.109

.109

.109

.109

.109

.108

.108

0.514

.268

.134

.134

.134

.134

.134

.134

.134

.133

.133

.133

0.535

.299

.174

.106

.106

.106

.105

.105

.105

.105

.105

.105

P/Ptj on shelfat _/w)12 = 0.500for_LshelfOf--

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985 1.061

2.001

3.005

4.009

5.000

5.999

7.001

7.998

8.493

9.001

9.493

10.001

11.080

0.529

.443

.230

.113

.113

.113

.113

.113

.113

.113

.113

.113

0.504

.321

.284

.246

.106

.105

.105

.105

.105

.105

.105

.105

O.504

.376

.254

.294

.218

.129

.086

.085

.085

.085

.085

.085

0.506

.315

.265

.200

.274

.224

.167

.099

.091

.084

.077

.064

0.505

.335

.292

.189

.147

.195

.202

.193

.166

.139

.124

.079

0.505

.351

.260

.174

.108

.109

.140

.159

.168

.160

.135

.100

0.502

.340

.227

.179

.198

.116

.087

.094

.106

.114

.122

.108

0.501

.346

.244

.262

.155

.132

.086

.084

.088

.098

.107

.111

27
Table7. Continued

(b) Concluded

P/Pt,j on shelf at (y/w)/2 = 0.000 for x/L shelf of--

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985

2.001

3.005

4.009

5.000

5.999

7.001

7.998

8.493

9.001

9.493

10.001

11.080

0.521

.393

.238

.111

.111

.111

.111

.111

.111

.111

.111

.111

0.510

.359

.393

.257

.129

.112

.112

.112

.112

.112

.112

.112

0.509

.342

.217

.339

.256

.133

.112

.099

.095

.094

.093

.093

0.509

.353

.344

.220

.278

.243

.175

.096

.093

.090

.084

.072

0.505

.355

.233

.126

.180

.214

.210

.200

.181

.113

.091

.065

0.504

.325

.254

.169

.123

.134

.155

.161

.161

.165

.161

.092

0.500

.334

.239

.219

.154

.119

.107

.105

.109

.115

.120

.131

P[Ptj on shelf at (y/w)/2 = -0.500 for xlL shelf of--

NPR 0.076 0.227 0.379 0.530 0.682 0.833

2.001

3.005

4.009

5.000

5.999

7.001

7.998

8.493

9.001

9.493

10.001

11.080

0.528

.359

.320

.181

.163

.134

.124

.123

.123

.123

.123

.122

0.509

.373

.293

.232

.194

.168

.119

.112

.105

.099

.093

.082

0.515

.340

.249

.279

.206

.148

.133

.126

.122

.118

.116

.111

0.506

.336

.257

.253

.186

.179

.146

.125

.098

.093

.089

.081

0.504

.346

.234

.138

.231

.170

.131

.129

.128

.128

.119

.066

0.502

.333

.245

.185

.122

.174

.178

.152

.131

.111

.102

.095

28
Table7. Continued

(c) Configuration9;Ae/A t = 2.500

P/Ptj for lower divergent flap at--

1.998

2.998

3.999

4.997

6.002

6.997

8.009

9.013

10.008

11.474

(y/w)/2 = 0.500 for x/Lfla p of-- (y/w)/2 = 0.000 for x/Lfla p of-- (y/w)12 = -0.500 for x/Lfla p of--

NPR 0.500 0.700 0.900 0.500 0.700 0.900 0.500 0.700 0.900

0.497 0.500 0.544 0.495 0.497 0.541 0.492

.256

.108

.109

.109

.109

.109

.109

.109

.109

.260

.198

.157

.067

.067

.067

.067

.067

.067

.299

.196

•154

.095

.045

.045

.045

.045

.045

.262

.110

.110

.110

.110

.110

.110

.110

.110

.260

.169

.123

.067

.067

.067

.067

.067

.067

.299

.190

.135

.103

.054

.053

.052

.051

.050

.240

.110

.110

.110

.110

.110

.109

•109

.109

0.498

.245

.158

.066

.066

.066

.066

.066

.066

.066

0.539

.305

.267

.118

.084

.045

.045

.045

.045

.045

P/Pt,j on shelf at (y/w)/2 = 0.500 for x/L shelf of--

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985 1.061

1.998

2.998

3.999

4.997

6.002

6.997

8.009

9.013

10.008

11.474

0.535

.368

.210

.162

.145

.082

.082

.082

.082

.082

0.503

.384

.246

.196

.187

.162

.062

.062

.062

.062

0.505

.363

.277

.213

.149

.223

.165

.108

.069

.049

0.507

.341

.257

.214

.161

.144

.201

.167

.105

.069

0.505

.328

.296

.234

.164

.103

.122

.170

.182

.103

0.506

.336

.257

.184

.199

.100

.099

.100

.125

.149

0.503

.338

.238

.184

.190

.162

.077

.079

.081

.110

0.501

.335

.279

.218

.146

.188

.110

.071

.077

.082

29
Table 7. Concluded

(c) Concluded

P/Pt,j on shelf at (y/w)/2 = 0.000 for x/L shelf of--

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985

1.998

2.998

3.999

4.997

6.002

6.997

8.009

9.013

10.008

11.474

0.523

.357

.247

.158

.108

.106

.078

.074

.074

.074

0.510

.388

.297

.246

.177

.081

.102

.096

.073

.060

0.509

.362

.382

.234

.254

.280

.117

.078

.080

.072

0.511

.344

.216

.190

.198

.167

.277

.161

.066

.066

0.506

.331

.271

.313

.139

.114

.128

.241

.194

.072

0.506

.338

.247

.164

.189

.130

.087

.096

.158

.222

0.501

.335

.245

.176

.177

.118

•109

.068

.070

.130

P]Ptj on shelf at (y/w)/2 = -0.500 for x/L shelf of--

NPR 0.076 0.227 0.379 0.530 0.682 0.833

1.998

2.998

3.999

4.997

6.002

6.997

8.009

9.013

10.008

11.474

0.528

.391

.272

.219

.231

.081

.076

.074

.072

.067

0.507

.384

.260

.213

.174

.155

.148

.136

.123

.101

0.518

.376

.269

.208

.172

.153

.135

.118

.105

.092

0.506

.351

.253

.203

.168

• 144

.131

.116

.104

.090

0.506

.338

.254

.204

.168

,143

.125

.116

.105

.091

0.503

.341

.252

.200

.167

,143

.124

.110

.102

.092

3O
Table8. NozzleInternalStaticPressureRatiosforA/BPowerScarfedConfigurations

(a) Configuration10;Ae/A t = 1.100

P]Pt,j for lower divergent flap at (ylw)12 = 0.500 for x/Lflap of--

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

2.005

2.499

2.998

3.496

3.999

4.501

5.010

5.995

8.010

9.848

0.348

.347

.345

.344

.343

.342

.342

.341

.341

.340

0.412

.412

.412

.412

.412

.411

.412

.411

.412

.412

0.406

.406

.406

.406

.406

.406

.406

.406

.406

.406

0.355

.355

.355

.354

.354

.354

.354

.355

.355

.356

0.301

.301

.301

.300

.300

.300

.300

.301

.301

.302

0.300

.260

.260

.259

.259

.259

.259

.258

.258

.258

0.431

.223

.222

.222

.222

.221

.221

.221

.220

.221

0.467

.267

.266

.266

.265

.264

.264

.263

.263

.262

0.516

.348

.250

.250

.249

.249

.249

.249

.248

.246

P]Pt,j for lower divergent flap at (y/w)12 = 0.000 for x/Lftap of----

NPR

2.005

2.499

2.998

3.496

3.999

4.501

5.010

5.995

8.010

9.848

0.100

0.329

.329

.327

.326

.325

.325

.325

.325

.324

.324

0.200

0.390

.388

.387

.386

.386

.385

.384

.384

.384

.384

0.300

0.380

.381

.381

.380

.380

.379

.379

.378

.378

.378

0.400

0.348

.348

.348

.347

.346

.346

.346

.345

.345

.345

0.500

0.304

.304

.304

.304

.304

.304

.304

.304

.303

.303

0.600

0.291

.264

.263

.263

.262

.262

.261

.260

.260

.261

0.700

0.442

.226

.225

.225

.225

.224

.224

.224

.224

.225

0.800

0.497

.328

.194

.194

.193

.193

.193

.192

.191

.191

0.900

0.552

.368

.284

.249

.248

.248

.247

.247

.247

.247

31
Table8. Continued

(a) Continued

P/Ptd for lower divergent flap at (ylw)/2 = --0.500 for x/Lfla p of---

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

2.005

2.499

2.998

3.496

3.999

4.501

5.010

5.995

8.010

9.848

0.309

.309

.309

.308

.308

.307

.307

.306

.305

.305

0.345

.345

.344

.344

.343

.343

.342

.342

.342

.342

0.363

.363

.362

.361

.361

.360

.360

.36O

.360

.359

0.343

.342

.342

.342

.342

.341

.341

.341

.341

.341

0.304

.304

.305

.305

.304

.304

.304

.303

.303

.303

0.360

.264

.264

.263

.263

.262

.262

.262

.263

.263

0.471

.229

.229

.229

.229

.229

.229

.228

.228

.228

0.525

.217

.201

.200

.200

.200

.200

.200

.200

.199

0.559

.365

.307

.181

.176

.176

.176

.175

.175

.175

P/Pt,j on shelf at (y/w)/2 = 0.500 for x/L shelf of--

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985 1.061

2.005

2.499

2.998

3.496

3.999

4.501

5.010

5.995

8.010

9.848

0.583

.445

.337

.313

.313

.312

.312

.312

.312

.312

0.520

.448

.410

.460

.258

.256

.256

.256

.255

.255

0.505

.396

.250

.249

.298

.297

.231

.169

.165

.165

0.506

.400

.348

.203

.195

.144

.135

.119

.073

.064

0.505

.398

.364

.320

.179

.207

.182

.105

.076

.053

0.505

.420

.304

.355

.300

.231

.187

.144

.068

.052

0.501

.397

.362

.245

.318

.255

.238

.194

.123

.075

0.500

.404

.340

.241

.286

.267

.229

.195

.139

.108

32
Table8. Continued

(a) Concluded

NPR

2.005

2.499

2.998

3.496

3.999

4.501

5.010

5.995

8.010

9.848

0.076

0.570

.418

.409

.326

.314

.309

.308

.308

.308

.309

plptd on shelf at

0.227 0.379

0.515 0.511

(y/w)/2 = 0.000 for x/L shelf of--

0.530 0.682 0.833

0.509 0.506 0.502

.393

.373

.319

.179

.150

.113

.083

.068

.046

.421

.317

.393

.327

.190

.210

.133

.091

.067

.459

.400

.450

.353

.282

.277

.267

.266

.266

.399

.297

.264

.298

.325

.262

.149

.140

.140

.429

.355

.207

.174

.158

.167

.157

.079

.074

0.985

0.499

.390

.316

.250

.329

.295

.240

.215

.109

.096

plptd on shelf at (y/w)/2 = -0.500 for x/L shelf of--

NPR 0.076 0.227 0.379 0.530 0.682 0.833

2.005

2.499

2.998

3.496

3.999

4.501

5.010

5.995

8.010

9.848

0.564

.525

.452

.383

.364

.362

.353

.327

.324

.324

0.514

.435

.378

.411

.321

.229

.223

.215

.186

.182

0.521

.407

.319

.264

.303

.336

.275

.119

.112

.099

0.506

.423

.318

.204

.166

.173

.191

.223

.062

.060

0.512

.390

.399

.290

.255

.150

.118

.128

.120

.046

0.501

.410

.311

.389

.235

.219

.210

.089

.078

.073

33
Table8. Continued

(b) Configuration 11 ; Ae/A t = 1.750

P]Pt,j for lower divergent flap at (y/w)/2 = 0.500 for x/Lflap of--

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

1.999

3.001

3.993

4.991

5.981

6.994

7.965

8.498

8.991

9.485

0.315

.314

.311

.310

.310

.309

.309

.309

.309

.309

0.306

.306

.306

.306

.305

.305

.305

.305

.305

.305

0.240

.240

.241

.240

.240

.240

.240

.240

.240

.240

0.375

.181

.181

.181

.181

.180

.180

.180

.180

.180

0.400

.147

.138

.137

.137

.136

.136

.136

.136

.136

0.470

.269

.182

.183

.183

.183

.183

.183

.184

.184

0.529

.298

.161

.160

.160

.160

.160

.160

.160

.160

0.542

.309

.143

.143

.143

.143

.143

.143

.143

.142

0.559

.325

.123

.123

.123

.123

.123

.123

.123

.123

P/Ptj for lower divergent flap at (y/w)/2 = 0.000 for xlLtlap of---

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

1.999

3.001

3.993

4.991

5.981

6.994

7.965

8.498

8.991

9.485

0.310

.309

.308

.308

.308

.308

.308

.308

.307

.307

0.312

.310

.309

.308

.308

.308

.308

.308

.308

.308

0.238

.239

.239

.239

.239

.239

.239

.239

.239

.239

0.384

.181

.181

.181

.180

.180

.180

.179

.179

.179

0.398

.192

.138

.138

.138

.137

.137

.137

.137

.137

0.442

.255

.153

.151

.148

.145

.143

.142

•140

.139

0.500

.277

.157

.156

.156

.156

.156

.156

.155

.155

0.536

.297

.140

.140

•140

.140

.140

.140

.140

.140

0.559

.311

.122

.122

.122

.122

.122

.122

.122

.122

34
Table8. Continued

(b) Continued

NPR

1.999

3.001

3.993

4.991

5.981

6.994

7.965

8.498

8.991

9.485

0.100

0.306

.308

.307

.306

.305

.305

.304

.304

.304

.304

0.200

0.310

.310

.309

.308

.308

.307

.307

.307

.307

.307

P]Pt,j for lower divergent flap at (ylw)/2 = -0.500 for x/Lfla p of---

0.300 0.400 0.500 0.600 0.700

0.241 0.382 0.393 0.434 0.484

.240 .181

.239 .181

.239 .181

.239 .181

.240 .181

.239 .181

.239 .181

.239 .181

.239 .181

.136

.137

.137

.137

.137

.137

.137

.137

.136

.223

.108

.108

.108

.108

.108

.108

.108

.108

.256

.119

.100

.098

.096

.095

.094

.O94

.093

0.800

0.522

.335

.177

.127

.127

.127

.127

.126

.126

.126

0.900

0.543

.387

.175

.124

.119

.119

.119

.119

.119

.119

P/Pt,j on shelf at (ylw)12 = 0.500 for x/L shelf of--

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985 1.061

1.999

3.001

3.993

4.991

5.981

6.994

7.965

8.498

8.991

9.485

0.552

.384

.270

.146

.146

.146

.146

.146

.146

.146

0.512

.390

.315

.207

.106

.106

.106

.106

.106

.106

0.506

.351

.251

.283

.203

.111

.092

.090

.089

.089

0.506

.348

.271

.251

.255

.213

.113

.104

.097

.091

0.506

.330

.250

.168

.198

.224

.210

.166

.103

.095

0.505

.348

.296

.181

.134

.157

.180

.176

.157

.125

0.502

.334

.254

.165

.121

.093

.117

.136

.151

.148

0.501

.324

.234

.173

.164

.093

.093

.104

.121

.135

35
Table8. Continued

(b) Concluded

P/Pt,j on shelf at (ylw)12 = 0.000 for x/L shelf of--

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985

1.999

3.001

3.993

4.991

5.981

6.994

7.965

8.498

8.991

9.485

0.545

.385

.258

.140

.140

.140

.140

.140

.140

.140

0.514

.401

.360

.178

.119

.110

• 109

.109

•109

.109

0.511

.309

.272

.330

.202

.110

.096

.091

.089

.088

0.509

.371

.193

.289

.288

.221

.117

.107

.101

.095

0.507

.316

.320

.161

.238

.246

.220

.166

.099

.089

0.504

.360

.276

.104

.145

.182

.193

.189

.181

.170

0.501

.334

.257

.214

,151

.117

.139

.150

.159

.156

P/Pt,j on shelf at (y/w)2 = -0.500 for x/L shelf of--

NPR 0.076 0.227 0.379 0.530 0.682 0.833

1.999

3.001

3.993

4.991

5.981

6.994

7.965

8.498

8.991

9.485

0.547

.370

.277

.213

.197

.178

.164

.161

.160

.159

0.516

.353

.314

.208

.173

.152

.139

.132

.127

.121

0.518

.339

.261

.242

.165

.135

.116

.109

.102

.097

0.507

.358

.241

.236

.210

.155

.136

.133

.111

.087

0.511

.324

.266

.184

.230

.206

.147

.127

.108

•100

0.502

.355

.294

.164

.133

.190

.184

.168

,140

.123

36
Table8. Continued

(c) Configuration12,AJAt = 2.500

NPR

2.003

3.006

3.999

5.000

6.002

7.006

7.987

9.009

10.030

O. 100

0.330

.312

.311

.310

.310

.309

.309

.309

.308

P]Pt,j for lower divergent flap at (y/w)12 = 0.500 for x/Lfla p of--

0.200

0.353

.303

.303

.303

.303

.303

.303

.303

.303

0.300

0.555

.237

.236

.236

.236

.236

.236

.236

.236

0.400

0.556

.183

.178

.178

.178

.178

.178

.178

.178

0.500

0.517

.157

.135

.135

.135

.135

.135

.134

.134

0.600

0.500

.266

.147

.105

.105

.105

.106

.106

.106

0.700

0.504

.280

.200

.085

.085

.085

.085

.085

.085

0.800

0.520

.325

.201

.070

.070

.070

.070

.070

.069

0.900

0.563

.382

.199

.112

.058

.058

.058

.058

.056

P/Pt,j for lower divergent flap at (ylw)12 = 0.000 for x/Lfla p of---

NPR

2.003

3.006

3.999

5.000

6.002

7.006

7.987

9.009

10.030

0.100 0.200

0.325

.306

.305

.305

.306

.306

.305

.305

.305

0.358

.305

.305

.304

.303

.303

.303

.303

.303

0.300

0.554

.240

.235

.234

.234

.234

.234

.234

.234

0.400

0.559

.193

.177

.177

.176

.176

.176

.175

.175

0.500 0.600 0.700 0.800 0.900

0.516

.166

.135

.135

.134

.134

.134

.134

.134

0.502

.275

.107

.107

.107

.107

.107

.106

.106

0.504

.283

.168

.086

.086

.086

.086

.086

.085

0.518

.313

.169

.071

.071

.071

.071

.07 I

.070

0.563

.363

.175

.060

.059

.059

.059

.059

.059

37
Table8. Continued

(c) Continued

P/Pt,j for lower divergent flap at (y/w)/2 = -0.500 for x/Lfla p of---

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

2.003

3.006

3.999

5.000

6.002

7.006

7.987

9.009

10.030

0.318

.302

.302

.301

.301

.301

.301

.301

.301

0.354

.303

.302

.302

.302

.301

.301

.301

.301

0.554

.242

.237

.236

.236

.236

.235

.235

.235

0.556

.193

.177

.177

.177

.177

.177

.177

.177

0.516

.159

.134

.134

.134

.134

.134

.134

.134

0.500

.272

.105

.105

• 106

.106

.106

•106

•106

0.501

.280

.084

.084

.084

.084

.084

•084

•084

0.513

.310

.160

.068

.069

.069

.069

.069

.069

0.552

.353

.206

.106

.058

.058

.058

.058

.058

P/Pt,j on shelf at (y/w)/2 = 0.500 for x/Lshel f of----

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985 1.061

2.003

3.006

3.999

5.000

6.002

7.006

7.987

9.009

10.030

0.557

.451

.215

.125

.133

.070

.070

.070

.070

0•505

.356

.250

.182

.208

.142

.064

.049

.049

0.503

.333

.272

.292

.191

.194

.147

.081

.075

0.505

.363

.274

.210

.170

.160

.190

.154

.089

0.505

.319

.252

.161

.154

.133

.141

.189

.161

0.504

.353

.298

.268

.153

.117

.107

.136

.117

0.501

.330

.229

.230

.218

.132

.079

.071

.121

0.500

.330

.239

.185

.201

.148

.107

.096

.081

38
Table8. Concluded

(c) Concluded

P/Pt,j on shelf at (ylw)12 = 0.000 for x/Lshel f of--

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985

2.003

3.006

3.999

5.000

6.002

7.006

7.987

9.009

10.030

0.542

.448

.224

.116

.132

.068

.068

.068

.067

0.504

.358

.336

.296

.186

.140

.075

.049

.048

0.509

.324

.254

.269

.240

.197

.135

.102

.070

0.508

.372

.308

.218

.211

.218

.235

.116

.093

0.505

.322

.227

.175

.150

.135

.182

.230

.155

0.502

.348

.305

.190

.132

.118

.082

.130

.210

0.499

.327

.232

.208

.198

.126

.092

.060

.093

P/Ptj on shelf at (y/w)/2 = -0.500 for x/Lshel f of---

NPR 0.076 0.227 0.379 0.530 0.682 0.833

2.003

3.006

3.999

5.000

6.002

7.006

7.987

9.009

10.030

0.553

.444

.336

.257

.116

.104

.098

.095

.085

0.508

.349

.281

.219

.194

.149

.127

.101

.083

0.518

.371

.261

.211

.184

.159

.137

.119

.101

0.505

.358

.269

.206

.172

.150

.132

.118

.107

0.510

.335

.258

.206

.170

.146

.128

.117

.107

0.501

.347

.254

.203

.167

.143

.124

.111

•106

39
Table9. NozzleInternalStaticPressureRatiosforDryPowerSawtoothConfigurations

(a)Configuration13;Ae/A t = 1.100

P/Pt,j for upper divergent flap at (y/w)2 = -0.500 for x/Lfla p of----

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

2.000

2.501

3.092

3.502

3.992

4.500

5.004

6.002

7.994

10.020

11.315

0.502

.502

.501

.501

.500

.500

.500

.501

.501

.501

.500

0.370

.370

.370

.370

.370

.370

.370

.371

.372

.372

.373

0.251

.252

.252

.252

.252

.252

.252

.251

.251

.251

.252

0.323

.321

.320

.319

.318

.317

.316

.316

.314

.314

.313

0.315

.314

.313

.312

.312

.312

.312

.312

.311

.311

.311

0.293

.293

.293

.293

.293

.293

.292

.292

.292

.293

.293

0.407

.262

.261

.261

.260

.260

.260

.260

.259

.259

.259

0.486

.250

.251

.252

.252

.253

.253

.253

.253

.253

.253

0.504

.372

.213

.213

.212

.212

.211

.211

.210

.210

.211

P/Ptj for lower divergent flap at-

(y/w)/2 = 0.500 for x/Lfla p of-- (y/w)12 = 0.000 for x/Lfla p of-- (y/w)/2 = -0.500 for x/Lfla p of--

NPR 0.500 0.700 0.900 0.500 0.700 0.900 0.500 0.700 0.900

0.410 0.503 0.259 0.417 0.474 0.269 2.000

2.501

3.092

3.502

3.992

4.500

5.004

6.002

7.994

10.020

11.315

0.264

.265

.265

.265

.265

.265

.264

.264

.264

.264

.265

.258

.257

.255

.254

.252

.250

.245

.237

.229

.224

.415

.249

.248

.248

.247

.247

.246

.246

.245

.246

.259

.259

.259

.259

.258

.258

.258

.258

.258

.258

.258

.257

.257

.256

.255

.254

.253

.252

.251

.251

.408

.245

.242

.238

.232

.230

.229

.228

.227

.227

.269

.268

.268

.267

.267

.267

.267

.266

.267

.267

0.415

.261

.259

.257

.255

.253

.250

.246

.236

.227

.221

0.479

.415

.253

.251

.251

.250

.250

.250

.250

.250

.250

40
Table9. Continued

(a) Concluded

NPR

2.000

2.501

3.092

3.502

3.992

4.500

5.004

6.002

7.994

10.020

11.315

0.076

0.554

.470

.464

.339

.300

.275

.264

.261

.262

.264

.264

P/Pt,j on shelf at

0.227 0.379

0.522 0.518

(y/w)/2 = -0.500 for x/Lshel f of---

0.530 0.682 0.833

0.506 0.506 0.506

.407

.355

.353

.237

.199

.209

.128

.059

.045

.048

.411

.321

.316

.297

.281

.213

.207

.141

.061

.049

.384

.325

.373

.313

.300

.203

.175

.151

.151

.151

.435

.343

.234

.244

.256

.214

.204

.094

.090

.090

.392

.348

.270

.236

.205

.134

.106

.084

.038

.038

0.985

0.498

.395

.323

.259

.241

.246

.215

.234

.180

.105

.083

41
Table9. Continued

(b) Configuration14;Ae/A t = 1,750

P[Pt,j for upper divergent flap at (y/w)/2 = -0.500 for x]Lfla p of---

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

0.363

.364

.362

.361

.360

.359

.359

.359

.359

.359

.359

2.000

3.007

3.999

5.011

6.002

7.017

8.008

8.414

9.000

10.000

11.205

0.301

.301

.302

.301

.302

.302

.302

.302

.302

.302

.302

0.443

.210

.211

.211

.211

.210

.210

.210

.210

.210

.210

0.442

.146

.146

.146

.146

.146

.146

.146

.146

.146

.146

0.442

.176

.175

.175

.174

.174

.173

.173

.173

.172

.171

0.446

.165

.165

.165

.165

.164

.164

.164

.164

.164

.164

0.454

.148

.142

.141

.141

.141

.140

.141

.141

.141

.141

0.464

.269

.130

.128

.129

.129

.129

,129

.129

.129

.129

0.476

.362

.222

.112

.105

.105

.105

.105

.105

.105

.104

P/Pt,j for lower divergent flap at-

(y/w)/2 = 0.500 for x/Lfla p of-- (y/w)/2 = 0.000 for x/Lfla p of-- (y/w)2 = -0.500 for x/Lfla p of--

NPR 0.500 0.700 0.900 0.500 0.700 0.900 0.500 0.700 0.900

2.000 0.515 0.525 0.454 0.512 0.523 0.423

3.007

3.999

5.011

6.002

7.017

8.008

8.414

9.000

10.000

11.205

0.419

.179

.180

.180

.180

.180

.179

.179

.179

.179

.179

.242 .315

.140 .206

.140 .108

,140 .108

.140 .108

.140 .108

.140 .108

.139 .108

.139 .108

.139 .108

.187

.187

.187

.187

.187

.187

.187

.186

.186

.186

.272

.135

.135

.135

.135

.134

.134

.134

.134

.134

.296

.220

.109

.107

.104

.103

.102

.101

.099

.097

.180

,180

.180

.180

.179

.179

.179

.179

.179

.179

0.516

.264

,137

.138

.138

.138

.138

.138

.138

.138

.138

0.527

.309

.195

.108

.108

.108

.108

.108

.108

.108

.108

42
Table9. Continued

(b) Concluded

P/Ptj on shelf at (y/w)/2 = -0.500 for x/Lshel f of--

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985

2.000

3.007

3.999

5.011

6.002

7.017

8.008

8.414

9.000

10.000

11.205

0.521

.381

.307

.169

.145

.123

.119

.118

.118

.118

.i18

0.508 0.515

.341

.250

.260

.171

.152

.143

.138

.124

.101

.092

.356

.259

.234

.257

.135

.116

.109

.103

.093

.087

0.505

.353

.306

.205

.264

.215

.151

.139

.097

.085

.072

0.504

.339

.223

.173

.134

.210

.198

.159

.132

.111

.070

0.504

.339

.257

.192

.122

.104

.156

.161

.165

.125

.092

0.497

.334

.262

.248

.145

.119

.092

.105

.107

.114

.109

43
Table 9. Concluded

(c) Configuration 15; Ae/A t = 2.500

P/Pt,j for upper divergent flap at (y/w)/2 = -0.500 for x/Ltlap of--

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

2.003

3.006

3.996

6.003

8.008

9.000

10.013

11.851

0.490

.202

.202

.200

.199

.199

.198

.199

0.488

.200

.199

.199

.198

.198

•198

.198

0.487

.303

.150

.150

.150

.150

.150

.150

0.486

.313

.111

.110

.110

.110

.110

.110

0.486

.312

.093

.083

.083

.083

.083

.083

0.486

.312

.176

.066

.066

.066

.066

.066

0.489

.315

.247

.095

.094

.094

.094

.094

0.491

.316

.321

.091

.092

.092

.092

.092

0.490

.319

.253

.149

.076

.076

.076

.076

P/Pt,j for lower divergent flap at-

(y/w)/2 = 0.500 for x/Lna p of--- (y/w)2 = 0.000 for x/Lltap of---- (y/w)/2 = -0.500 for x/Lfla p of---

NPR 0.500 0.700 0.900 0.500 0.700 0.900 0.500 0.700 0.900

2.003 0.498 0.535 0•492 0.498 0•538 0•492

3.006

3.996

6.003

8.008

9.000

10.013

11.851

0.492

.248

.109

.110

.I10

.110

.110

.109

.252

.181

.O67

.067

.067

.067

.067

.295

.229

.106

.045

.045

.045

.045

.270

.110

.110

.110

.110

.110

.110

.265

.201

.067

.067

.067

.067

.067

.299

.221

.115

.053

.052

.051

.050

.249

.110

.110

.110

•109

.109

.109

0.496

.252

.181

.067

.067

.067

.067

.067

0.538

.295

.231

.108

.046

.046

.046

.046

NPR

2.003

3.006

3.996

6.003

8.008

9.000

10•013

11.851

P]Ptj on shelf at (y/w)/2 = -0.500 for x[Lshel f of----

0.076

0.524

.371

.277

.207

.102

.102

.101

.096

0.227

0.507

.377

.277

.184

.129

.116

.099

.082

0.379

0.515

.371

.260

.170

.134

.116

.100

.079

0.530

0.504

.358

.255

.168

.130

.123

.104

.081

0.682

0.504

.347

.254

•170

.132

.112

.107

.091

0.833

0.504

.339

.252

.173

.113

.108

.100

.094

0.985

0.496

.330

.250

.165

.122

.105

.093

.089

44
Table10.NozzleInternalStaticPressureRatiosforA/BPowerSawtoothConfigurations

(a) Configuration16;Ae/A t = 1.100

P[Pt,j for upper divergent flap at (ylw)/2 = -0.500 for x/Lfla p of--

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

2.005

2.501

3.003

3.504

4.000

4.502

5.001

5.503

6.002

8.004

8.929

0.531

.529

.529

.528

.528

.527

.527

.527

.527

.527

.527

0.431

.430

.430

.430

.430

.430

.430

.431

.431

.431

.432

0.313

.313

.314

.313

.313

.313

.313

.313

.313

.313

.313

0.226

.225

.225

.225

.225

.225

.225

.225

.225

.225

.224

0,334

.332

.330

.329

.328

.327

.326

.325

.325

.324

.323

0.323

.323

.323

.323

.323

.322

.322

.322

.322

.322

.322

0.337

.297

.296

.296

.295

.295

,294

.294

.294

.293

.293

0.500

.291

.292

.293

.293

.293

.293

.293

.293

.293

.293

0.515

.331

.256

.255

.254

.254

.254

.253

.253

.253

.253

NPR

2.005

2.501

3.003

3.504

4.000

4.502

5.001

5.503

6.002

8.004

8.929

P/Pt,j for lower divergent flap at (y/w)/2 = 0.500 for x/Lna p of---

0.100 0.200 0,300 0.400 0.500 0.600 0,700 0.800 0.900

0.339

.338

.337

.335

.335

.334

.334

.333

.333

.332

.332

0.392

.392

.391

.391

.391

.391

.390

.390

.390

.390

.390

0.393

.393

.393

.393

.394

.394

.394

.394

.394

.394

.394

0.359

.358

.358

.358

.358

.358

.358

.358

.358

.358

.358

0,312

.312

.311

.311

.311

.311

.310

.310

.310

.310

.310

0.267

.267

.267

.267

.267

.267

.267

.267

.267

.267

.267

0.430

.230

.230

.230

.229

.229

.229

.229

.228

.228

.228

0.464

.348

.199

.199

.198

.198

.198

.198

.198

.197

.197

0.508

.399

.282

.253

.252

.251

.251

.251

.251

.250

.250

45
Table10.Continued

(a) Continued

P/Pt,j for lower divergent flap at (ylw)12 = 0.000 for x/Lfla p of---

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

2.005

2.501

3.003

3.504

4.000

4.502

5.001

5.503

6.002

8.004

8.929

0.341

.340

.338

.337

.337

.337

.337

.337

.337

.336

.336

0.415

.413

.412

.411

,411

.410

.410

.409

.409

.408

.408

0.396

.394

.391

.390

.390

.389

.389

.389

.388

.388

.388

0.349

.349

.349

.349

.348

.348

.347

.347

.347

.346

.347

0.305

.304

.304

.304

.304

.304

.304

.304

.304

.304

.304

0,359

.264

.264

.264

.263

.263

.262

.262

.262

.261

.261

0.438

.226

.225

.225

.225

.225

.224

.224

.224

.224

.224

0.453

.357

.258

.256

.254

.251

.249

.248

.246

.237

.234

0.484

.408

.265

.265

.265

.265

.265

.264

.264

.264

.264

P/Pt,j for lower divergent flap at (y/w)/2 = -0.500 for x/Lfla p of--

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

2.005

2.501

3.003

3.504

4.000

4.502

5.001

5.503

6.002

8.004

8.929

0.327

.327

.327

.326

.325

.324

.324

.324

.324

.323

.323

0,397

.396

.395

.394

.394

.393

.393

.392

.392

.391

.391

0.402

.400

.399

.399

.398

.398

.398

.397

.397

.397

.397

0.360

.359

.359

.358

.358

.358

.358

.358

.358

.358

.358

0.310

.310

.310

.310

.310

.309

.309

.309

.309

.309

.309

0.269

.269

.268

.268

.268

.268

.267

.267

.267

.267

.267

0.428

.227

.227

.227

.227

.227

.227

.227

.227

.227

.227

0,459

.352

.197

.198

.198

.198

,198

.197

.197

.197

.197

0.501

,398

.297

.257

.256

.256

.256

,256

.255

.255

.255

46
Table 10. Continued

(a) Concluded

P/Pt,j on shelf at (y/w)12 = 0.000 for x/Lshel f of--

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985

2.005

2.501

3.003

3.504

4.000

4.502

5.001

5.503

6.002

8.004

8.929

0.563

.486

.462

.373

.346

.325

.313

.308

.304

.303

.304

0.522

.445

.367

.422

.337

.248

.232

.219

.207

.188

.184

0.509

.408

.281

.236

.251

.259

.248

.254

.127

.110

.107

0.506

.432

.331

.246

.184

.137

.123

.127

.132

.056

.051

0.506

.396

.403

.320

.205

.235

.211

.105

.082

.068

.056

0.504

.423

.271

.373

.342

.222

.204

.223

.217

.077

.042

0.496

.395

.331

.247

.288

.259

.256

.235

.225

.144

.110

47
Table10.Continued

(b) Configuration17;AelAt = 1.750

P[Pt,j for upper divergent flap at (y/w)/2 = --0.500 for x/Lfla p of---

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

1.999

3.007

3.997

4.998

6.002

7.004

7.995

8.497

8.999

9.729

0.341

.340

.338

.336

.335

,335

.335

.335

.335

.335

0,326

.325

.325

.326

.326

.326

.326

.326

.327

.327

0.247

.248

.248

.248

.248

.248

.248

,248

.248

.248

0.343

.182

.182

.182

.181

.181

.181

.181

.181

.181

0.499

.293

.135

.135

.135

.135

.134

.134

.134

.134

0.498

.294

.110

.110

.110

,110

.110

.110

.110

.110

0.500

.300

.153

.152

.152

.151

.151

.151

.151

.150

0.522

.307

.164

.149

.150

.150

.151

.151

.151

.151

0.504

.310

.225

.126

.122

.122

.122

.122

.122

.122

P/Pt,j for lower divergent flap at (y/w)/2 = 0.500 for x/Lftap of--

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

1.999

3.007

3.997

4.998

6.002

7.004

7.995

8.497

8.999

9.729

0.316

.315

.313

.312

.312

.311

.311

.310

.310

.310

0.306

.306

.305

.305

.305

.305

,305

.305

.305

.305

0.323

.237

.237

.237

.237

.237

.237

.237

.237

.237

0.406

.179

.179

.179

,179

.179

.179

.179

.179

.179

0.407

.145

.137

.137

.137

.136

.136

.136

.136

.136

0.416

,251

.162

.162

.162

.162

.162

.162

.162

.162

0.432

.273

.154

.153

.153

.153

.153

.153

.153

.153

0.452

,290

.139

.139

.139

.139

.139

.139

.139

.139

0.474

.310

.189

.126

.126

.125

.125

.125

.125

.125

48
Table10.Continued

(b) Continued

P/Pt,j for lower divergent flap at (y/w)12 = 0.000 for x/Lftap of--

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

1.999

3.007

3.997

4.998

6.002

7.004

7.995

8.497

8.999

9.729

0.309

.308

.308

.308

.308

.308

.307

.307

.307

.307

0.310

.309

.308

.308

.307

.307

.307

.307

.307

.307

0.245

.240

.239

.237

.236

.236

.236

.236

.236

.236

0.382

.179

.180

.179

.179

.179

.179

.178

.178

.178

0.390

.146

,143

.141

.140

.139

.139

.139

.138

.138

0.412

.183

.169

.169

.169

.168

.168

.167

.167

.167

0.452

.284

.149

.149

.148

.148

.148

.148

.148

.147

0.485

.295

.131

.131

,131

.131

.131

.131

.131

.131

0.514

.326

.229

.116

.116

.116

.115

.115

.115

.115

P/Pt,j for lower divergent flap at (y/w)/2 = -0.500 for x/Lfla p of--

NPR 0.100 0.200 0.300 0,400 0.500 0.600 0.700 0.800 0.900

1.999

3.007

3.997

4.998

6.002

7.004

7,995

8,497

8.999

9.729

0.306

.306

.306

.305

.304

.304

.303

.303

.303

.303

0.311

.310

.309

.309

.309

.309

.308

.308

.308

.308

0.241

.241

.241

.240

.240

.240

.240

.240

.240

.240

0.371

.182

.181

.181

.181

.181

.181

.181

.181

.181

0.505

.152

.137

.137

.138

.138

.137

.137

.137

.137

0.495

.257

.160

.160

.159

.159

.158

.158

.158

.158

0.496

.275

.148

.148

.148

.148

.148

.148

.148

.148

0.504

.290

.135

.135

.135

.135

.135

.135

.135

.135

0.511

.306

.196

.124

.124

.123

.123

.123

.123

.123

49
Table10.Continued

(b) Concluded

P/Ptd on shelf at (y/w)2 = 0.000 for x/LshelfOf---

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985

1.999

3.007

3.997

4.998

6.002

7.004

7.995

8.497

8.999

9.729

0.514

.370

.276

.203

.175

.154

.151

.151

.151

.151

0.509

.373

.312

.205

.165

.142

.123

.115

.107

.098

0.504

.364

.275

.336

.177

.156

.107

.099

.093

.085

0.504

.340

.239

.174

.304

.150

.125

.118

.112

.108

0.504

.331

.312

.173

.141

.227

.201

.142

.111

.093

0.503

.343

.235

.152

.153

.128

• 164

.166

.157

.119

0.500

.332

.242

.201

.138

.107

.124

.139

.130

.126

50
Table10.Continued

(c) Configuration18;AetA t = 2.500

P/Pt,j for upper divergent flap at (y/w)/2 = -0.500 for x]Lfla p of__

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

1.996

3.001

3.999

4.999

5.997

7.000

7.999

8.998

10.017

10.119

0.496

.157

.157

.156

.156

.156

.156

.156

.156

.155

0.493

.182

.182

.181

.181

.181

.181

.181

.181

.181

0.493

.165

.153

.153

.153

.153

.153

.153

.153

.153

0.493

.231

.124

.124

.123

.123

.123

.123

.123

.123

0.492

.258

.128

.095

.095

.095

.095

.095

.095

.095

0.492

.331

.185

.079

.079

.079

.079

.079

.079

.079

0.494

.351

.252

.103

.132

.064

.064

.064

.064

.064

0.495

.365

.311

.165

.136

.110

.057

.057

.057

.057

0.494

.341

.243

.253

.149

.124

.105

.091

.052

.048

plpt J for lower divergent flap at (ylw)/2 = 0.500 for x/Lfla p of___

NPR 0.300 0.400 0.500 0.600 0.700 0.800 0.900

1.996

3.001

3.999

4.999

5.997

7.000

7.999

8.998

10.017

10.119

0.100 0.200

0.331 0.356

.312 .304

.310 .303

.310 .303

.310 .303

.310 .303

.309 .303

.309 .303

.309 .303

.309 .303

0.564

.236

.237

.236

.236

.236

.236

.236

.236

.236

0.553

.177

.178

.178

.178

.178

.178

.178

.178

.178

0.515

.245

.135

.135

.135

.135

.135

.135

.135

.135

0.499

.267

.110

.105

.106

.106

.106

.106

.106

.106

0.503

.309

.195

.085

.085

.085

.085

.085

.085

.085

0.514

.330

.203

.153

.070

.070

.070

.070

.070

.070

0.549

.380

.227

157

.108

.059

.059

.059

.058

.058

51
Table10.Continued

(c) Continued

P/Pt,j for lower divergent flap at (y/w)/2 = 0.000 for x/Lfla p of---

NPR 0.100 0,200 0,300 0.400 0.500 0.600 0.700 0.800 0.900

1.996

3.001

3.999

4.999

5.997

7.000

7.999

8.998

10.017

10.119

0.325

.308

.307

.308

.308

.307

.307

.307

.307

.307

0.361

.306

.305

.305

.305

.304

.304

.305

.305

.305

0.560

.237

.235

.233

.232

.232

.231

.231

.231

.231

0.555

.176

.176

.176

.176

.176

.175

.175

.175

.175

0.516

.284

.135

.135

.135

.135

.134

.134

.134

.134

0.503

.289

.191

.107

.107

,107

.107

.106

.106

.106

0.504

.296

.212

.092

.086

.086

.086

.085

.085

.085

0.516

.307

.216

.164

.071

.071

.071

.071

.070

.070

0.560

.326

.225

•166

.126

.059

.059

.059

.059

.059

plpt,j for lower divergent flap at (y/w)/2 = -0.500 for x/Lfla p of--

NPR 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

1.996

3.001

3.999

4.999

5.997

7.000

7.999

8.998

10.017

10.119

0.322

.306

.305

.304

.304

.304

.303

.303

.303

.303

0.356

.304

.303

.303

.302

.302

.302

.302

.302

.302

0.564

.238

.237

.237

.236

.236

.236

.236

.236

.236

0.554

.178

.178

.177

.177

.177

.177

.177

.177

.177

0.516

.224

.134

.135

.135

.135

.135

.134

.134

.134

0.503

.265

.107

.107

.107

.106

.106

.106

.106

.106

0.503

.314

.189

.084

.084

.084

.084

.084

.084

.084

0.513

.336

.197

.146

.069

.069

.069

.069

.069

,069

0.551

.391

.228

,151

.106

.058

.058

.058

.058

.058

52
Table 10. Concluded

(c) Concluded

P/Ptj on shelf at (y/w)/2 = 0.000 for xlLshet f of--

NPR 0.076 0.227 0.379 0.530 0.682 0.833 0.985

1.996

3.001

3.999

4.999

5.997

7.000

7.999

8.998

10.017

10.119

0.545

.370

.300

.222

.139

.100

.095

.090

.086

.085

0.511

.353

.285

.255

.198

.184

.128

.101

.085

.083

0.505

.338

.279

.236

.155

.160

.130

.117

.106

.105

0.507

.337

.248

.202

.173

.130

.143

.118

.102

.101

0.507

.335

.273

.216

.168

.137

.120

.119

.112

.119

0.506

.333

.245

.192

.172

.135

.115

.111

.107

.107

0.498

.331

.251

.202

.171

.144

.122

.105

.096

.098

53
54

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oo

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c_i

o

Q_ L

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0 ,i.._

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LT_
!

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c_

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55
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56
I

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b_

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- -_7-

II

00

c_

_J

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57
III I

II

!i

C.

u

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'r-0

0

u

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>. 0

_2

.g

e_

¢..,

.__

e.-

-d

IN

e-,

t,...,

"8

e-,

58
ii I

V

\

0

_t

II

- ?=

E

Cz

cJ

C_

0

'E

o

.c

c_

c_

CL

0

0

"E

o

_0

0 _/'_I/3 o o o

r_ _0 O0 0 0 0

0 _"_ _"_ o o o

0 _'_ _'_3 o o o

e'3 O0 O0 0 0

r_ e'q O0 0 _D O0

_ _ _ o o o

_ _ _ o o o

__-

0

E

=

-=

=

0

L_

59
\

0

e_

e_

0

._

'E _

0

r_

_J

_J

e_

r_

tO

IJ

0

_ _"_ _ o o o

_ o6,_c_ 06

_ u"_ _ o o o

eC OO -q" ,d" _ rC

ie'_ C,I O O_ _D OO

_ V'_ _ o o o

eC OO _d" _O CD rc

_,":,':__

_C) v'_ _ o o o

O_ _D C4 _',I oO CD

O

o_

o

_L

-j

.,._

O
_J

e.

0

-r.

0

b5

b5

C_

0 u"_ _r_ o o o

e_'_oo oo b_ _ oo

_£ o6 _ic_ _6 vi

i_, _'_ u'_ o o o

x,O ,_"_ _'3 o o o

O_ 0", _ _ " O0 t'q

_ _ _- _ ,r, _,

,m

o

(1,)

o

_, t_ _ V3 _'_ o o 0

.o

E

61
4.000

1

f

Config A B 13

Dry 0.500 2.451 17.67

A/B .600 2.485 20.00

3.750 l

.250 rad.

Horizontal centerline

Figure 4. Details of lower convergent flaps. Linear dimensions are in inches.

62
I

,411i

.

-FI

i

i

I

.--¢ -¢ 4- I I I T T T ? ? ? t t I I I t t t I l I

L,.4"

IITI4IIIII

II

f

K_

"_._

¢-0

-r-0

bt

om

-gEo0

e-0

63
4.000

A

B

C

D

A

B

C

D

oo

Dry power

Config ! ,7,13 Config 2,8,14

0.500

2.419

2.451

!.818

20.00 °

-5.76 °

0.500

2.495

2.451

2.297

20.00 °

3.54 °

Config 3,9,15

0.500

2.487

2.451

2.702

20.00 °

14.66 °

Dry power

Config 4,10,16 Config 5,11,17 Config 6,12,18

0.600

2.378

2.485

!.712

17.67 °

-7.00 °

0.600

2.494

2.485

2.312

17.67 °

4.00 °

0.600

2.481

2.485

2.790

17.67 °

18.00 °

.500

_'_ _¢_----. 120 rad.

3.750

B

1 I _(

Horizontal centerline

Figure 6. Details of upper convergent flaps. Linear dimensions are in inches.

64
.d

r

f |

C_

C_

A_

I.d

C_

fC_

0_

/

C_

f

c_

c_

,-I

C_

c_$

¢)

¢)

°_

.E

.<

¢)

E_

C)

65
.<

0

N _

0

C_

y

C_

C_

O0

I

66
0

O0_00_O_

o

II

0

C_

II

C_

\

\

\

¢.j

o _. @i _

<0

.__, TC_

C_

C_

II

6?
J

_ t"-

C_

II

4r_

lJI

0

If

cpI

C_

II

f

_ pr

o._

II

,J

C_

C_

¢)

o_

..=E

¢)

Q)

_S

m

r"

¢) O

°_

[._

68
| o+o

r

Ii

I

ITI

I

II

II

II I I

It

T_T

1

I ' I

I

I

t

II

f -4 +- t t I I I t

• Ii I I 0

\

,I

e- C0

69
°

_

H

",i\

/

/

/

/

/

\?

I"I

°IIIiITII

\

\

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H

c#:

',O

I"-

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0

I#"i

00

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"-" i.E

70
m

1.750

.500

.020

I

Id 6.419

(a) Baseline sidewalls; fight and left are identical.

Figure 9. Details of sidewalls. Linear dimensions are in inches.

fl

71
\

\Y

0

o_

TlJ

-5i

@°_

¢- @

O

72
T

!.750

_"--.250 rad.

I

.500

45 °

.500

F" 4.843

020 trailingedge thickness

7.500

!<

Centerline

6.419 f|

1.200

(c) Sidewalls for sawtooth configurations; right and left are identical.

Figure 9. Concluded.

73
P/Pt, j

P/Pt,j

P/Pt, j

,6

,5

.4

.3

.2

,1

0

A e/A t = 1.100

iiiiili !!! iiiiiiiiii!! l i iiiiii!ii' ii iiiiii iiii

"'i"'+": ...... r "_,'"r'" "'T"_"_ ...... i"" ;--" -'1 .... _--':'"

_....i...,.!..i.._H...__.i i .!..i..i..i.._r..t_.i..t.

::i:::i::i::::::::::::::::::::::::::::i:::i:: ::::::i:::i::

...., ...... i_!!,!!i: _

..i--.i-.i... i--i---F---i.-i_..'.-iq.-i--_7--_..- ii_iiit!iiiii!i!i!iliiiii_ iiiiiii!!i!!!iii!ii!il;

-.i---,_--i--i---i ....._-.+...4--_.-i .....i.._.......

: . - _ .L._..

_--_---i--&_--N._-- --_-_4--_--

_ ..... _i..__:___!

'!_i .... !_ !.... ,__; - '_ _! ..... i! ':

O

[]

A

_x

r_

¢3

.6

.5

.4

.3

.2

.1

0

Ae/A t = 1.750

4 .... i-. !-.i.--:---i.-l---i---i-..!..-Ii i .i.... i-_-..i..

....._--_--,.--_ .....i--,---::---i--!---ti--i--_ !..4..-!.-

-4---_..... '.--.4-.-'- --÷--i-.÷-'--i-. i_-i---'.-;-4- -;--

.£i:--_;:iX__: ,+-i.- ';_:_-:-___$T'___::i!!_

O

[]

A

tx

t3

n

x/L flap x./L shelf

O

[]

(>

A

t_

r_

(a) Dry power baseline configurations.

Figure 10. Static pressure ratio distributions along surface where Lshet f = 6.600 in.

NPR

2.003

3.006

3.996

6,005

8.005

9.996

1 !.165

NPR

1.999

2.999

3,999

5.996

8.000

9.995

10.572

NPR

2.001

3.003

4.002

6.004

7.995

9.998

10.994

74
PlPt,j

plPt,j

P/Pt,j

.6

.2

.I

0

Ae/A t = 1,100

:_i_i!!i !!,_7_i :!_i_!!i!!,_:i_i_i!_. _:_i_!!_

: ! : , i : i i i : i

..+.x ._......;-.:- ; .1-.._-i--[---I--!--'F-!--',-!-'+'-!-

A e/A t = 1.750

i:ii!!!!!!tiliti!!!:!!! i!!!!!! !!_!!_::i:@_.+i---i-

.5 .-i.-i--i.... :.._4 ....._--4.--/-._......... i.....

::i:::!::i:: ::i::!:::i..... i -v-T-¢)-i -..'-_...... _--?--r--

.4 i , , i , , i , , i , : i i

.3 i-_;_ _-i.i---/---i-+-!.....!---i...... i:m-i--

.6

.5

.4

.3

.2

A e/A t = 2.500

•!ii+ i.... '--!--!--il::i:::i::!::!:i:$:i::: ::_:::_::i: "!i_ :;:t r-_--_--:---. • , ,

!i!iii!!i!!i!!!i!!i

:::::::::::::::::::::::::

..;.-i..i...i-.-_---i'l"-i-.;.4--..i._ _.:,--

. !...?..!_.,..!..!...!..... _..!.._...... !...?..!..;..!.._...!..

.l

0 iP! .... _':! .... ,:__-:,......., _: ...... !::_"

0 .2 .4 .6 .8 1.0 0 .2 .4 .6

x/L flap x/L shelf

(b) A/B power baseline configurations.

-i-i--_+i-! ........... ::---:: -I-i-i--i ::i_ :::::::::::::::::::::::::::::i:::i:: ::iiiiiiii!!!

..... _ _T :_'/'_--: _t"i_ _:_;:.

-+--I-F: - - ........

:::::::::::::::::::::::::::::::::::::: ::::_::i::: "*"

-_-----_ ..... _...... _....i-_-::--, i_-.i--::i::i:::!::

.-;_-!.J.. i-._--!--._ ....!...¢_ _I:I_.-_-iZi_E

-iTf:i....i--t-?"_-l_,!:;-_-,_c_,.t_-

'__i©_:i__ __ iii_<,

--i iii::!_,_._ i-+-i!i!!_:::i_a=___!_ _ _:i::_"

..:._L ....._._ :,:..i..___.l..:._.._..'.--_ ....._..

--!_,_ _-._---_ ...... i--i--i--- --i---Vi ...... i--!---i--

.8 1.0

Figure 10. Continued.

O

[]

O

A

Ix

O

[]

O

A

Ix

r_

O

[]

<>

A

h,

Eh

NPR

2.004

3.007

4.003

6.003

7.721

NPR

2.003

2.998

4.008

6.009

8.004

9.565

NPR

2,000

3.002

3.998

5.997

8.005

9.982

75
P/P t,j

P/Pt,j

P/Pt,j

.6

.5

.4

.3

.2

.1

0

Ae/A t = 1.100

-._---':--i.... i-._--.i..... ':-.-!-.-;: ...... ':.-._-4.t--i .....

Z_ i_Iiiili IIIIIIII_S _i:,::::i:::i::

•-_---_--_....... _--._.... _ -_.-_..... !lt_ --i--i---i--

.6

,5

.4

.3

.2

.1

0

A e/A t = 1.750

--i---i! ......i-i! !-i--!--:!---_--!i,--i ..... iiii!iii!i!!illiiiii

-.i---:4 ......L-!-..---!-4...LA.... i-.._..,,_,,_I.:..:--._-.

..... _-.......... _--.;-.l--._-A--_--...a-.U._..... i.4.

iiii!_i_!!iitiiffiii _,.._..iiii_ !iiii,_:i!_iii

.. ........ _........ , .-..-_--_..... __..>....

.A-.-F.-I--i 4 ..... ;1 ' '_ .....I _-.-'..i--'...i..'---i-.

-._.--L._.-..-.:--._L..'_:_:::::il_i--:- _-_,F.,_ _-.: .....

-A-.-:..i.._t..D-:..i _ :_.4._ _(,..).J..... :-._..-;..

:::::::::::::::::::::::::::::::: ::i::: ::iii:_::::J:::!:

.5

.4

.3

.2

.1

0

0

A e/A t = 2.500

::i:::!:: ::t: i i lii + I i::2i-k!-i--i--

ii?_!_ T'17:?i:U?!?2_:_! _:

;. _.; _ i "[..... [ ......;..... :";,_.:,_ , ..... :"" _i_ii:fiiiiiiiii:iii_ iii_iiiii, ii_iiiiiiii

--_-----_ ...... _--_--._ ..... _-;-.i--'-.i.--: _--i_l_:i::;

'"_+" ..... ..... _.....'-__+_!_, i!i '!i!i

.2 .4 .6 .8 1.0

--'--+--_,_ --_..... _--.+\-!I_-- --,'/_.-i ....D-'.--i--

'_::l!_it--i--.-_.,-.._ ....*-+

--i---!.+-,---_--i---!--l---i---i--_ ....i---i-- I-;-i---i-

'!-t_.....!-T:!-r,_ ....!--:_....!-i--_-

0 .2 .4 .6 .8 1.0

x/L flap x/L shelf

(C) Dry power scarfed configurations.

Figure 10. Continued.

O

[]

<>

A

t,,

th

n

O

[]

<>

A

Ix

[3

O

[]

<>

A

Ix

th

[3

NPR

2.001

3.001

4.003

6.002

8.001

10.006

10.939

NPR

2.001

3.005

4.009

5.999

7.998

10.001

11.080

NPR

1.998

2.998

3.999

6.002

8.009

10.008

11.474

76
P/Pt, j

P/Pt,j

P/Pt, j

A e/A t = 1.100

.6 ..i-...:-4..... ;-i---;.... ;-+-.i..... _--:---i .... i-._.4-.

.5'::i:::L::i ::_:: :i:::i::l:::i::i::i:::_::i :::i::_::: _iiii

.4: i::i::!!: _ :i!!! !!i!!i !:!:}!i}!i!!! :::_::_:::_::

i i -___-

.3 ! ; ; : _ _ ' _ ...L -i--

.2 , : , , , , , ,

})i)}ii)il}) )}i)}ii::k ::i:3i::::i::i:i::+i:::i::

A e/A t = 1.750

., ii!i_iiiiiiiii_i_ iiiiiliii!iil _iiiii2)_,,_:i:

..I....'.--..:.....i--'---i.-i-::t:.:7._ ...... _---_--

.4 !i_!I! ii ii ! l;i;_I!i_.i!i!!! i.ii.i! i t

,--i--_-i--t_,,--i-/-i ...... i-i i"_'_'_-"_i"i"i

--, ...... , .... ,-I , , , '

.l !---i-i-h-+--i-n-;-&........... '!_i

A e/A t = 2.500

.6 .... !........ b_.,$i---i--_ _" t" ..... i---!--i .... !:.O'i

.5 ' /: i|i _(. ,=-_: _ : : '

-i-i-i .... L !-@.t. i @!-[-iHi" "!.... i- i" !-' :_::i:i://:i !::i:r:_:i:i::lqi:!:I:!:7!::

.4 21i2_i_(_:.ii{!iii: i_i:ii:!i:"ii!:iil::iii"iii_"-:iii

o ::i:::!::i::: ::i:::::!:::::;::::i:::i:::i:: ::::::!:::i::

0 .2 .4 .6 .8 1.0

x/L flap x./L shelf

(d) A/B power scarfed configurations.

Figure 10. Continued.

O

[]

o

A

r_

o

[]

o

A

tx

O

[]

o

A

b.

[5

NPR

2.005

2.998

3.999

5.995

8.010

9.848

NPR

1.999

3.001

3.993

5.981

7.965

9.485

NPR

2.003

3.006

3.999

6.002

7.987

10.030

77
P/Pt, j

P/Pt, j

P/Pt, j

.6

.5

.4

.3

.2

.1

0

At/A t = 1.100

;_!;;;_::i:; i;;i_;_;_;i _;i

i i ! I ! : ! i : i i : i i • i

,6

.5

.4

.3

.2

.1

0

A e/A t = 1.750

iT+iti,+l+.............. ....

--+:--i--_--÷--i'-_---,+--t-.-?+4-.+--i---,'--i--i---' -_--_---_--

!!i!!iiii!ii:!!i'!!?!!iiiiliii!!ii:_!!i!!i!!!;!!i!ii:ili_!iiii

(iiiiiiiiiii '+'+...."_+' _ _+_---+--_--

"-':"_" r |" +'"+ +i + i""_"'; .... ,_.L.+;..

'?--i-?--,7-+---N---_++--_.........+.....i,><$:'-+-- i : ',

+++i i+l +i ii1 ;i;;illlii_

-!.%..!-.

.... ,,Wi_--: +--

+;+;+;+;++;I;;+;;++;:!:+ :+i;;i::i::+ ;+i;:i;;+++ / +++,,+'.++::

+-£-.'---i-.' --+--+---i.....!!!!!i!!i!! L : ._ ..l...-..i-A. !!i!!!i!!i! I!.i--'-..i.. i!!!!!!i!

...+..._ +..+__.+.. +..+.._.%..+.__+...+_.

+...... ........

"_i i++i ....i+++i+++_+i ..... i+ii +-i+

•+:+++++;i;+++i++++++i+++i++!+i+_T_t_+i +++++++!

.4 '+"i"++ -++++"+-l++ +'+..... ii '+ .... +"+-'+- ..+..._...+...i+..+.__...+_. +++..+..+.....+...+..+..1.+ .._.....

7........... +_+r,'_ !++-:--,--:---r+7--,--r-.---! +-22i,22 iP2;;

--7+++;- -+..... p.._+..+_.

.-i. 2..._..... _. +:...;.... :. :._r..... _.__'.y...,.._+.._...

....._----4----+...... '..+O_L-:._O++_.+...:..+_.. ;

.I

..+...+..+.. +..+_...'+....-..+..:7: _ :_ ....

-+_-..:-++_ .... i-._---_.... _--.:........ -.;'I_.,_ -+++_ +--I--+ ....+I+-++_--+--+ ...._i_i!+!

0_ +i+7..... _-i ....... 7:"7 7 + _

0 .2 .4 .6 .8 1.0

x/L flap

A efA t = 2.500

..._ ...... +...... _.............. ;..+.++..._...; ...... .;+

.-!+++?..!..... !..,...+_.... .-..! +_ --!---_---i-+--!-._---!-

_:_+_ +7+T _/_._ l+.+.:_,_2....+:. _ -._..,.-+..-:.++:-..,+

--J...... !--. _'--i---_ ..... "..;_.7...+..'.?'7++i.. _. +++Z_,

'+'...... ++7+71++....

I ++'++ I

.++.--I-.+.+.+-.!+.-N--+++ :+:::l::i...+::+_

..i._.L..:. _

.._+:.i+:i ............

--++-+i-+-

,-++++-+-+ .....+......+-+-+l+j-+ +-•+++++ ...... ++:--+-I-+ ....+++i+ _...... I-+---+---+--. _.....

0 .2 .4 .6 .8 1.0

x/L shelf

(e) Dry power sawtooth configurations.

Figure 10. Continued.

O

[]

<>

A

tx

_3

O

[]

<>

A

t_

t7

r7

O

[]

A

t_

r7

NPR

2.000

3.092

3.992

6.002

7.994

10.020

11.315

NPR

2.000

3.007

3.999

6.002

8.008

10.000

11.205

NPR

2.003

3.006

3.996

6.003

8.008

10.013

11.851

78
P/Pt,j

P/Pt,j

P/Pt,j

.6

.4

.3

.2

A e/A t = 1.100

. _-.-;......... _.......i-._ _-+i,-i--

iii iiiiiit!! :iiTili! 7iiii i

ii_ ::L+:L: __+1+_!....i.+-i--

_- ,-_ ................ .. :--.!_.

:' ..I..L.'......'..I..-".... :...-',...!....._..-L._._

'i -_---i-"

-.._-,-_........:-Nt:%-i-+:--i---_--/_---i<,

--_--i-+---_---_ .....i.-.._._i-_--i--:-i-.+--!--

::i:::i::iq::_ ?ii!i ii:.i_i--i--_c

--i---i--i ...... i--i---i.-l---i-- :..... i---:--_--l_--_---!--

-._--!--_......!...,..._.... ,_--'--_-,,, .-_---_--_.... _..?.._..

.6

.5

.2

.1

0

Ae/A t = 1.750

.._.._.:,. _!/..._ ..... .:..... i.-._-_L_-i--i.-._..

.....i...... ii-! .....!-i-: '!? _ !_!

..... _-...'... .:..l.-.i.-_ ......... ':---_ -i--I--i--i- 4--

--_---;--_ ..... _--_---_ ...._--_--+-'--_---;--_ ..... _-i---_ -

-_0_ _'? _i-2_'.'_-."-' _--_--_;_

:iiLii iiiiiiii i7 iiiii!i ii Q! i ii i:: iiii:ii7

--!---?-! .... !--v--!--,-?- !--?--,- ":"'!"! ..... ! "+'-!'"

-._&-4--i--i-+-_--!---i--i-+!--_---i--

:::!-.-_-_::i:::_ _Ei__

_!-:;7.K_ITTY _ ...... {Sii " r :

.._.i.._._i_ ./,-..!_ .-;.-i---_..

l--i--:--i--_--_.--_---_42 ..+--:,.-i-.---5---L4-.: ......:..i.-.:--

'i-ii"i-iiIi-i'_.:I:i:::i::]::l::i::i:::i::

.6

A elA t = 2.500

-i-.-i.-i '.-i-.:' i._..i--._..-i ....i-._-.i-.l .;.!--i.-.

--_.--i--_ .-+ ! -!--!--i- 'i-!i..... iO-!-

.4 . i "i _.i:!: i L i i _ I:i::i :i,::::]i:]i2]L]

"__q'_'_%:':Z'""_:"

. . . . I;l%,t_li

0 !!_ ..... !.... :"..... ?:_' 'i-; .......... i:

0 .2 .4 .6 .8 1.0

x/L flap

--i------,--t--,-_ ......t......_.......... _-_i:[iii]

..... F-] ._ ......... " ...... ;;4.;.;.- L_

--i---7--:: .....i-.;-.-T::-'J--i-- --v--_--v-, "....... -v-_---..--

.._..+.._ ..... _...:..._..,..+.._..-... ::::::::::::::::::::::::::

' i ' I , . I , I ,

--_-_-!!! ......"-i--_l-f-i_ ....!ii :i7

...... •"__.."_- _ ......:---_.-- __--r.i.._.--_-. --b--L.i .... v-*--_.... ! :- '_ . .- i. -'.--_---" -i _I ...._i--r_- _i_

']'"FT_XF'7[_":!T '1"',! " :

_i _: _-_z_A_

-.v.-.',,,':.....:-.!---.,,,."--!_"_ :--.v_-_-!-y-

•-!_::]:::r4_:l__ _-__q.'_

--iI_.--_ _i--:-"_-.i---,--_--i--_---r -i---i--i.-.,.--i--i---i -_

"'""!"7 ..... V'!-? ...... 7"':".' "'7-: ........ T'",,"V0 .2 .4 .6 .8

xiL shelf

(f) A/B power sawtooth configurations.

Figure 10. Concluded.

1.0

o

[]

o

A

l',.

O

[]

o

A

ix

r',,

O

[]

o

A

ix

F_

NPR

2.005

3.003

4.000

6.002

8.004

8.929

NPR

1.999

3.007

3.997

6.002

7.995

9.729

NPR

1.996

3.001

3.999

5.997

7.999

10.119

79
a/a t (NPR)a

Wp/Wi

8/F,

1.00 i i ! i i : I i i : : : T : : : , • ; :

..... :'-'7 .... _--_- *---[- -_---r---:

96I-.i...i i.. !_..:__..._:..._.i.... i.7? P_-_ : _-_...... "!P

.92 : : : r : : : _ : : :

'!"T- ..... :_7 '1 '_?"_' I'?"_-P I"!"T_c'_'"7T "

.84 '__)"-i!i--t ii '_, .... )!if-.-! _-I--_ ...... ).-

1.00

.96

F/F i .92

.88

,84

---,--_--, .... ..--.,-,..... _.-i---'.... i-_-..i.... i-..i--_..

3 5 7 9 11 13

NPR

O !. 100 3.060

[] 1.750 8.371

2.500 15.647

8 ! : ! ; ! i i : i I ! I i I ! i !

" _--P_+-I', ...... !-!'.'- .... P_-!-t-_ -;--! t ?--!--P

4 ;ii';i i!: i!;ili;i!il

_p,_,deg -4 TP_]Ii ! ! ! ! i ';+ ' '__"_ ........ _................. :T'_z : l: ,, : [ ! :

.....

z?r ......tz :.

-12 :: i ! , : T?T .... !-T!TTY:: .... i-TY

: : : : i : ! ! i i [ i : i ' ! : !

?-_" ........ .....__ ...... !P? .... __ITTPI ...... FPI

7TT ...... !"_ ..... y"__ ..... r--i---!-- :----_--y-! ..... : -: --r

-16 i i i . : : : i i i i I ' i : . i i :

By, deg

12 ..i-.-i _-...... .:_..i_._.._..... ':---[-;i .i..;.i. i[

...... : : I : ; :

_ ! _ ! ---i.... "--!-= ..... _......... :---_............

4 _, _', i i i : i i : :_ i : i

0 : ' _" "_"K'*'_:'_:_:_tr_ri'_'_'! i !

......__,..._ i .T..i ___"_ :_

-4 i ' i i ' i i : i i : i i ' i i ' i

--,---:---i ...... ;--:---i .... i-.2.-i ...... :---:--.i ..... i .-:..i .... :..i...: ....

3 5 7 9 11 13

NPR

(a) Dry power.

Figure 11. Effect of expansion ratio on internal performance characteristics of baseline configurations.

80
Wp/W i

F/F i

1.oo_i_::___i_ 1i_i_::

.96 !__ ,_--_-----u_ ! _ _ t ! : i

....... %-i....:-i-i1.00

.96

.92

.88

.84

iii!iiiiii_ ----i---it--:_-i--i-[i--:" _ _ i--!S_!_ iiiii'-ii_ _]_i-!--- !ii !!!_::ii ii

,!!!!!!!!!!! I!!!!!!!! !!!!!!!!!!! !!!I!!!

i iiii!: iiiiiiiiiiiiiiiiiiiiiiiiiiiiiii!iiiiiiiiiiiiii:iiill 'ST8p, deg

Ae/A t (NPR)d

1.00

.96

.92

.88

.84 _ .-!--.p-

!!!!!i!! li!!!!!!t!i-i !!!!1!!!!!

3 5 7 9 11 13

NPR

By, deg

(b) A/B power.

O 1.100 3.060

[] 1.750 8.371

<> 2.500 15.647

Figure 11. Concluded.

.... _....................... _._._....._.--_-._... i-..;--;

4 :! _ I : ! : I : ! _ I : ! ! : : : 1 ; ; _

- _-+-!-t_--+-i---t-_-i_---I--__-_t!__ .... _ -_--

0 !_'i ._" : i [.)i .l_i i i i i

-4

.--_--i..-i--,---i----i---,--i---i--_ .....i_i_! .....il _i ....

'!--V," ........__......_ "_......r7! 7_'_,.....TI !

-12 --i-.+-i .....;.-.i--i ......i.-+-!.....;--;--; ....;.4.!.....:,-.i.i12

-4

-8

-.i-.-!-..i... ......... i : : : "i '[ i'": :' , • ....................

_i_i _i__i_'_!_!_ _i_: _:__i__i

1 3 5 7 9 11 13

NPR

81
Ae/A t (NPR)d

wp/w i

F/F i

1.00

.96

.92

1.00

t-i.--i--_.....i--_--i--].-i---i--i---I---_±_3-!.--i.--_..

.84, ii!!_i_ii_i i,i tii!i}i!!ii iii! !ii ii!:i ili !i!ii_iliii! iii

.92

I 3 5 7 9 11 13

NPR

_p, deg

_y, deg

-4

-8

-12

-16

© 1.100 3.060

[] 1,750 8.371

2.500 15,647

--?--!--?.....!--?--!..... !---!--_......_--_--_.... i---_-_..... _-.-;.-._-

"i-!, _..... !-!---!....... !-i...... :'--_---_.... _-..i.._..... i--._-.._.

'T !_ 1_ T!t ?_- ..'---_-_--!-i-*-i-_--i---I.-+--i---_---

--_.-.!_.!-..,-.-!.._--.! .....!---?-_---,.-._--!..-! ..... _..._.._..'__..._..._..

....? li iliiilfii

."-i-i-.l. :,-: i...... i...i--i--.l..__.._..._ ..I ._i...i.. i. I .i... i. _i..

_ _ : _ i ,' : i i_ 'i-_ ..... _i '_

12

0

-4

-8

iiiiiiiiiiiill iiiiiiilllIiiiiiiiiiiiii!iiiii!iiii i iiiiii!iiiill iiiiiiiiiiil

...... i.... t---...... _---'--! ..... _---'---, ....i-.-_--_ ........ i..._..

--:-.... '.... !.._..-i.... ."...;.. ,L.... : .... : :

3 5 7 9 11 13

NPR

(a) Dry power.

Figure 12. Effect of expansion ratio on internal performance characteristics of scarfed configurations.

82
Wp/W i

6_

F/F i

ilil iii L iii ii _i

i ! ! _ ' ' i : i_i --

.96 :_:1 : I _!1! i I i ! ! I ! !

: : : : . , : .........

.92 'fi-_ ..... i_i ..... ]T] ...... !ii ..... i]i _ii

1.00

.96

.92

.88

.84

..!...i...i..t..!..!.-.!.-.

-+-i---i--

4--.i.._-..

::::,::i::: :::i::

...._2_ i i .l....... i...i.....i-.

" ] I ! i ', : : ', : : :

::i:i::i :!:i::i:i:: ::i: ::i:: :!:i: ::::i::_:

_p, deg -4

-8

-12

-16

12

1.00

.96

.92

.88

.84

---H---I--_

1

ili liii!ii ii!!i iiti i!i::

3 5 7 9 11 13

NPR

By, deg

(b) A/B power.

Figure 12. Concluded.

Ae/A t (NPR)d

O 1.100 3.060

[] 1.750 8.371

2.500 15.647

! ! ! ! : : I : ', ! i : ! ! : : : : i

-_-.._.---,.-.i-._d-.t i..... !-I-+!..... '..... _--f--, i-_-_

?. .._ .................. ,..._--_.--; ...... _--4-_ ...... :- _--+--

-!"-:F--!-r7"TI '7TT"VV7TT!7 '] ..... TT V

..............; --,--_-_ : _ _i__'_I <2--Hf--i-i ..........................1fi ..... i

_!._.;..i.__ ...... !.i._ ..... _....... _-i-- I-i-;4 ::i:i:!:iii:___/::i:::i:: i:i_-i-_t£::i::i i:i:ii:::ii

::!:::i::_::t::-h!---i-t__ _i-!i.....i!!

--!.--i---!--I---i--+--i--t--!---i--i--I---!--i-

I I I i I : : : I i : : I ; :

i_--fl ..... i..... I.. !....... --i---H--i--_ i..... ii--

",,i ........... i ii:,"PII..... r__...... i..

i14111!ii]]i_£i]i14111 JZ_2_Iil]il]i_iiiiii!iiiii14111, i_!iiiiii_..

.i..-i.-.i ... _:.-i..-i ..... i--i.d ...... i.-i---i ...... !-.-i-! -I---:,---:--i -_

8 : i ' ' i : ' i ' : i ' _ i ', I ' i i

..._ ..... i..... i._ ......... i...:_4..._ .-_q..... _..... !-

;::i:i_::;;,:_... :.:i:::i--i ....._--i---L_+-i--,4i--i--

° -i--i____-i-i---J-_f i!]

.4::iI::!i:: _,_:i 4: ti+i "

-8:i:::i:l,, !i:i _ )),,.ii iiii iii., ii,..i

1 3 5 7 9 11 13

NPR

83
A e/A t (NPR)d

1.00

Wp/W i

1.00

1.00

.96

F/F i .92

.88

.84

; : : I : : : I ! [ : I : i : " ' ; ' ; :

!-..+:___.!--_.-i-_.!-..i4-.l-.__i .....+._...!.- :::i:_::::::::::::::::::::: ===============================

_ i5!: :133ri! 33_i5!!33i 51ii13!i3

--i--i---!--:::::::::::::::::::::::::: ::-T-::!:::i::: ::i::ii: !::!::-i::

1 3 5 7 9 11 13

NPR

0

_p, deg -4

-8

_iy, deg

0 1.100 3.060

[] 1.750 8.371

O 2.500 15.647

- i-i ..'..I...i..i..! ..... L..L._ .I...L.L..L..L.i..i..L..I..£.._..',..

"4"-'i-''i'-'1---t"4---t ..... 4-'-i---', ...... l:'-_---t .... t---_--_ ..... ',- -; .._- 4 ::il ::!i :,iil:iil::i!li::i

:::::::::::::::::::::::::i::_ *+ .....,+i.+ .....+--i--*--_. __::i:<: .......... '................

_<k_"-+i....i i i-l-+4i+i_i ...... _+_

......it ....._....,_--,-_--_--_--t_...... !_+

-12 'i........ t.....+ t"i .....i.....i i!t ':!i .....!ii

12

-._i:il-, _.--:--_i :i::i:::_:_:!::_ ...... +"_:::i::i:::::_::_.._,--_.... _---:... ___

, 7: T..... !d] ..... ]!T .... r-!-: .... v--_---z--v--!---r--

,-._...... _..... L-6..:..... "..... =...... :...... _.... i.. :.._ ...... :

4 ili i:i i:i i:i _:_ _:i o:::::::::::::::::

-41 ili! ii

-8

1 3 5 7 9 11 13

NPR

(a) Dry power.

Figure 13. Effect of expansion ratio on internal performance characteristics of sawtooth configurations.

84
Wp/W i

F/F i

.96 " ' ....

_i!i!iiii!i___:iiii ii. iii'ii!'iii'i!i ii i iiii!iiiii

0

1.00 iiiiiiiii_iii[.._.._i_, _

.96 -i--i-i,_ __ __

.88

.84 :: i

-_I--!---L---I,---I -_L---

F ;_i__ii!!i!_i!!i!!t!_i! !!i!

/.-i-._..I..i..._..:: ....::.-_-.-_..t-.i--:.--_ ......::---i.-.i..

_p, deg -4

-8

-12

-16

12

1.00

.96

.92

i)i_:;! ......i!_.....iii::::i::i_:

.84 .

I 3 5 7 9 11 13

NPR

(b) A/B power.

_y, deg

4

-4

-8

Figure 13. Concluded.

Ae/A t (NPR)d

O 1.100 3.060

[] 1.750 8.371

2.500 15.647

.._..._...-..... '........... _.._...... -..!. _.... :..... :...... :...... _..

.-4...... i..... i........... i_ ..... _-!....... !-- i..... - .... !

'!--_i .... i-_--ivi-!i ..... _-!-i--_7-!_---i_i

"::X_L; _ L_":_ _ _3 ..... :i!

_!i___7i'':'_-_' ..... _'...

..i-d3i -i..-i-..i.--i ...---_--_......_.i..._....._...i..._..t i-.._--i..

:::::i:::i :::_...... _..___i!i iri ii.....!_i!

1 3 5 7 9 11 13

NPR

85
Power

O Dry

[] A/B

Wp/W i

F/F i

1.00

.96

.92

.88

.84

1.00

.96

.92

.88

.84

:::::::::::::::::::::::::::::::::::::::::::::::::::::::

,:i,,},,i,,,,,,i,,i,,i,,i,,i,,,i,,i i,,i, ii,,i,,,, i,i,,,t ii,

1 3 5 7 9 11 13

NPR

_ip, deg

_y, deg

-4

-8

-12

-16

.-.i..-_.--_- '<_ii_i_i ..... _.._...;.... _..._..._.... _...__._.... ..... i-.-i-.i ii_::i:::!::i ..... l i...i...L_

!: !l!:!.:,!ili!ill iiii! i

•i.....i...............i-i---[ ......_--!---i-t--,.---!-_i ......i---<i _-

12

-4

-8

(a) AelA t = 1.100; (NPR)d = 3.060.

Figure 14. Effect of power setting on internal performance characteristics of baseline configurations.

86
Power

0 Dry

[] A/B

wp/w i

Fr_

F/F i

1.00

,.oo

.96 ..... ':

i::i:::_:::i ::'_:_I:i::!:i:::i::i::: :::_!::i:::i t:i++ ifi:::!:::i:: .9_,i,_,,+,i. ....... i... i...... i--_

88i_'ii_it_i_i_ Ii_i !i_i_i::,_i_!_i_

.84 ii iii ii iiiiii ii iii ii ...:...[..3..... ]...!_.[..

1.00

.96'i'i+_...... i-+i+++i-._i--i---,-t--+---i---i--t-i---+--i--

.92

.84::i:::i:::!::i:::!::: ::i:::i::i::: ::+i::: :::+::i:: :::i:: :i::

1 3 5 7 9 11 13

NPR

8p, deg

4

0

-4

-8

-12

-16

12

4

_y, deg

0

.-_---i.-._--' ........+_.-.i-.-i ................................... iii iii iii _i.-.b....-

'+_":i....1 _--_---_ --i---_---_--_i ......iii+i.....•.......... i'.i ,'........ iiii

++..: ...... +--+-r-+--_----+--_--....:+_ii+; -+_-i---i-- i--i---; ...... _-+-;--_...... i.--i---i ..... ; i--i ..... _ !---!--- .-!-.__-.i.-i_-,---i--i---_-t_-i--_ .....!--.

•i-.-,-+.,!-.4..._....+--,--_.

--3..... _.... ;..-i -_..... _..-i.--!--+--_ ............. i........ !--.;---i I ::[ ........ t .....

.._..;.-._. ..... ;- ,-.4 ..... _...;-+-',---,---+--._+-+.... +---; -+ ..... :---+--++- .i...i...i+.l.i..i .....t.....i..i....i.....q.....i..i...l..i IA.

+i '+ t+-iff--H-i---i-H--i-:,---ii-ff!-H -ff!---i

- !--!-i ..... !-!-- ! +d---b! .... ?-!--!- .... !-i-!-- ":-b--?-

't-i-i ......i--!i....t-i-i ......N i....i-t? -?-i---i-

--!++-! ......i-+-i....i-.._--_ ......Hi ....i!i ....._++__

---_--!---! ...... _-i--! ....!!--i......_!--f....i i+-'-i-i i-

-4

-8

--_..-+---i ....i..+.-i....i..-!.--i_-,---i--i---! .....i---i--_---i+--i ---!--,

i...... it..... i.. +i....i:,ii.......... ii,i... i:

..... !ti.....!...i...!.... i_...... i i! i i!

:"_'"__ ..L.L..::...... !-.-+..... _ i+-.:.-.!

iiiiii_[iiiii+-t--_- ',----+,.-;-4-- ii iii_iii ---:++-:--_ ...... i--i-i.....!.... i--

,+!+, .....+++, ...... i,,+ '+il ii_ii''iiiiill,:,ill ..... +--+...... _---_-+-i ...... i--+i--!--

iiiiii+iiii+i' ';:; ......++"+ iiii_iiiiiill iii iiiiiiill +iiiii/ill

3 5 7 9 11 13

NPR

(b) AelA t --- 1.750; (NPR) d = 8.371.

Figure 14. Continued.

87
Power

© Dry

[] A/B

Wp/W i

Fr/Fi

F/F i

..2.4..:.....!.._...- ...........................................

--*--_--* ..... !---:-.-_ ...... _-.-_--4...... ;-._...; ..... !--i--_ ..... &-i-..L..

: : : , : : : : : .... , ,

1.00

.88 .+.i._f!.i.+_ ___ _..... ' _,i:

.84 'ii! ..... i ii .... ii: '1!i i _i i i"! .....i

1.00

.96

.92

.88

.84

_p, deg -4

-8

-12

-16

12

iii!ili!:: iiiiii!tiii iii!i iii!it iii f!iii

3 5 7 9 I1 13

NPR

_y, deg

-4

-8

i i ! : :

'?!? .... !i

'-i -!-? ..... !-- ".'-

: i i i i

T -: 'r ..... V T

_ t.cje : :":

_q "7 "5 ..... _"]"

_ !7 .... ."-"_'

"'T":'"r .... F"T

]i:: ii

_"'!'"? .... iT

?! _ --!-.?-

........ ,--.---. ......... ....._...!..?..,

-i---i--_......++-- ......!--+-_..... _-+--,:--

.-!...!..! .... +.._..._.._..._...:..+.._ ..+__ ..:..._

.-!...!.._ ...... _..!...? ................. _...! ....

'_"!"_ ....... Y7i -÷ ............. ' 7! .....

'!-!_ ....... ?!-! ..................... i"!--:-"

.-_---_ -_....... -..!...!.._ .......... _ _- !-.--. !

-i"!_ ......,-:i_ ................. _i :_

iil ̧!fill iii i ilill iiiiiiiiilliiiiiiiiiilliiiiilli i ilillilill

i i : i i : ill : ! : : i ' i i :

"..... _.... ! ...... !..... _---i--+-., .-+-.4 ....... !- -i ..... :- i...'-

i " i i ' i i r i i ' i i ' i i i

.J__ ' ' " i ! i _. ! ! !T.i, !"WI : :

::i:i:iiii:: ii! iiilii i!iiiii!:.iiiiiiiii!iii!

3 5 7 9 11 13

NPR

(c) AelA t = 2.500; (NPR)d = 15.647.

Figure 14. Concluded.

88
Power

O Dry

[] A/B

wp/w i

Fr_

F/F i

1.00

1.00

_ ? ? ?!iii::?iSi!ili?I:i!ilill _iilii_i:iiiii

.96

.92

.88 ...................

84:iiiiiii?liill iiili?!:il ili?i iiii?iiii

1.00

.96

.92

.88

.84

-4._) 4. ......,i..i...i...,--i---i-._ . i ........... '-;--i-..i._.....i.-_-4.i....._..

",:T_ ..... __': ......!-__ ...... _7 7T7-Y_ [?i?

'?ii .....??-i......?i! ......!?i ......??i .....???

3 5 7 9 11 13

NPR

_p, deg

_y, deg

! : ! ! : : i : : ! i i ' i i i ! : :

..?..!..._-..... !...!.--!......,...!...,...... !..! ,-!...... !..?. !..... ?..!..?.

--'-.-_--+--_--._-.:.-..!--,--_---_--! --+--i---!--t--!..+--! 'i'"i7

-.-i..-i---i ...... L-L.J...... _-.-L.i--.' ..... 4 _i_ _, ::,:_!i-!..... !7!.... _:ii

--i---i---!-.r-i-----i.-_--i---i--i -..i .i---i--,-.i--._-+--,.-i--

--_---_---t- ..... _--+--t ..... _---'.---_ .... _---i---:- --

0 .._.._.].._..-i -i-i.-.l-.-;-_ ...L: i...l..L.i..

..-;-.i--'.--u.i-._-i 4-.i.i.-i-..i..+--i--i--_;iii_iii

-4 ............... i i I _i ! .-.i.--i..i...... ::..i.5,...

_--i---i---_--l---_--i---=,--4.-i---i--_---l---i--i---i-+-i-

..+..i.+.t..._..i...{.__t..4...!..M...!..,....!..r_.-.r-.: _.-_.- _..._

-81...... ;I;_...... _..... 14,i;_.4_._ili:.i

-,.--i..-i ...... L_--.i.-J--.L--_ ...... !...i.--; ....._---_.-_ .....+-._..-:.--

-12 --_.--;---_ .....;-.-i..-i-- -_..-;--.i ....._--i.--i.- .i---;-.i ...._---i-.4--

12

-4

-8

(a) Ae/A t = 1.100; (NPR) d = 3.060.

Figure 15. Effect of power setting on internal performance characteristics of scarfed configurations.

89
Power

O Dry

D A/B

vplw i

F/F i

1.00

.96

.92

1.00

.96

.92

.88

.84

1.00

.96

.92

.88

.84

"'!_i!i...... _>?!i _i!!i!i!i_+ii-_i>_i_i_

-!!i....

8p, deg

8iii ii!iiil ii.:i_.:;i'.;;_ "_-'--_i_i • iii ii:-i>:_i

iii i>>i!<iiiii i:i:! ;ii

4 .i...j...i. - _,i i:,ii:,__,_ _,

o_>_:_!_:-_ _©_>i_i :_

-4i! i:iiiiiiiiiiii i!!ii!!ii-

.... i.il-iii_-i_--->!_

" _ i-! .....:'"!'":'"_ --__--? ...... " _-"

' , _ _ , t _ i _ i i !

._ " _-)ii!-i-iiii_ ]_i, "_i_!!.ii!! -16 '!-TT

_!7_i_ ;_> ____i<_i_i_i_i<_ •

1 3 5 7 9 11 13

NPR

tJy, deg

12

i | i ill i i | i T i i i !

i-__>_i_>i .--__?!i>_i:_ _!_>_i_ _>?i>!

_i->i<i-iiiii-tii-iiiiiiii-_ii-liiii!i->i iiiiiii2_4_-_ _i>i!ii

ili iii iii iil iil ii::

0

-4 _ t

-8

1 3 5 7 9 11 13

NPR

(b) AelA t = 1.750; (NPR)d = 8.371.

Figure 15. Continued.

9O
Power

0 Dry

[] A/B

Vp/W i

6_

1+iii ',i+iiii .96

.92

.-4-.-;--+_--|---i--_+--+ ...... i--4--4 ...... _--?--! ...... !--?-!--- ?!-?-"

.96 ....i---i---i-t--ii-t--l-!-+i--:: .....7¢-r '_,: !-7

19828 ii ii_!! _ _iIi iiii iil itiiiii ii iiiil ii i il

!+:!N_i- t14+;'!-!4' ..... _.....'.........i1.00

F/F i .92

.88

,84 '_+i+_ .... i_+ ...... !!_, ...... ii-! ...... :/7_ ..... _i_

1 3 5 7 9 11 13

NPR

8 %--i--+i--',--+---i--+ .......... ...... i-.-+-.-+....................... ii! i!!

...7..t...?..I...N.T..t --_--- i- --p-..,-- -i ---7- +:---.--- 1--+: ---.'--V-'I"""!'"_

d

---,--+,---+-. ..... ,, ..... + .... ,,-------..+,"_++t+P+-ri?-P

4 iiiiiii_ili:il%ii:Liiii!ili_iiliiiiiiiiiii_ki_ii:i:iiil

o +_ +_..+.I+.++%ii+i ....+il.....i+i

<Sp,deg -4 ._.!...j.++_.... i_:.-._'_:_iii.+---i--

-!iNH}!"+it!-'+"i-i-i%ii'"!ii ++i!

-12

.....i'.+.i.._..i_.J.._ ..._......;.....:,+..I-..+ ....... I......_-i-

_,6::i+:: +::i+::_+ :+_++: _++_i++_i+:i_::+::_i:+i:::_+::++:i _++_ +:+i _

5y, deg

12

0

-4

-8

++....... ++r+iiiiiiiiii '+++

...:.+j +5 ..... !.._.--! ..... :-.-L-: ..... :..-i.++'--

_..i.--:.--i ..... _--'---v-. .-:---i-% ..... !.+-i---!...... L+4--+ .... +-.-i- _ -

i i ill i i i i ' i

i+!++

+i++ ++i++l+_+i+_ _++_+++++ +++;+++++ +++t +++?+++

1 3 5 7 9 11 13

NPR

(c) Ae/A t = 2.500; (NPR) d = 15.647.

Figure 15. Concluded.

91
Power

0 Dry

[] A/B

Vp/W i

Fr_

F/F i

1.00

,.0o::::::::::::::::::::::::::::::::::::::::::::::::::: i::

.96 .... t ' ' "

:_;i_iiiiiiii!i _iiiiiiiilii iti_ilfi_iii

.92 --J--_--!,:: ..... i--i---i ......i---i--i'' ']''|'"'i_''_--i--i .... i---i--i ....._---i---i--

-_ ..... 5-+-, ..... "_..... * ..... _--_ ...... _ _---_ .... _ _--_ ..... *.-_-.*--

.88 .-i.-+---i -+-i--_--++ ......i---+--i---l--i +.!_t.....i.....l-!---i--!

+++..... H_+_++:+ :i:i::i:+:;::::i:+: :+::i: .84 . . "r! +i

1.00

.96

+92

.88

.84

--i---+.++i--[--+--i---+--++-+---+--i .....i--i+--:, ......+---i--i .....;--+-+++-

ii_¢i_!iiii! ii_l ii!!i i!_il! iii!I!! iil_i !!!i!

--.i---i-.-i.. : ...... !: ---+--+:- +--r--_-++--: ..... _ +..._++ +.+:-.._ ..... :...... __+

l 3 5 7 9 11 ,3

NPR

_Sp, deg

_y, deg

-4

-8

-12

-,6

: ! : _ : : : : i : i : : : : : : : :

i_:!iiiiiii:i! iii_i

++i...i-+il..+.-+..!..+..+...+..+..l.._i+.i..l+.+..i.. +......+..+!-

:-i--i--_tl--i.............. +-I---i-++--i .....++?+_--+_-

:::::::::::::::::::::::::::: ::!::i::!:: =+=!: :::::::::::::::::::::::::

.-;.-i+.-i..,..-i.-.i.+.+ : : ........ +, ! .. 3 --< ..... _---I---_ -_---_--.I-.._-.-:.--_ • - +--l-.-_--

--i---!--_ ......_--i---i ......+--+."--+ ... +-.i..+.-

'+i?i .....??+ .....77-i......i-?+......+i-+.....i---Pi....

12

0

-4

+8

i:_+: i!I+::i::i:::i:: :i+_::i::!::i:::::+i::!:::i:: [ +I_.::i:::!.:!:::[::i::_!:

-'---i---"..... +---i+--_ .... -.'---++-÷..... i.-_...... +--+.-!..... -.-++.!.. :+i ii i++ ,+i ,!i +

!i222_!i!,!!!i!i!!!!_ i!_!i! _!!!i

+[..... ;. +2 + '+' ' t ' .:+'+'.' ."v: ,-, . :

:::::::::::::::::::::::::::::::::::ii_

i + i i I i ¢

3 5 7 9 11 13

NPR

(a) Ae/A t = 1.100; (NPR)d = 3.060.

Figure 16. Effect of power setting on internal performance characteristics of sawtooth configurations.

92
Power

0 Dry

[] A/B

Vp/W i

Fr /F i

F/F i

|.00 : : , : : _ ' : : ! I ! ! ! ! i I :

.....i+;-i___:)i-_--;.... !--i! ..... -F- r-!-!-! ......!--!-+-- ........

.96

...................... i......_...... _..... !..... i-!-i ..... i-!---i-

.92 iiiiiiiiiiii iiiiiiiiiii i;iiiii!iiiii"iiilii;iiii'_'Tii ................ ....iTi _

1.00

.96 ::::::::::::::::::::::: ::::::::::::::::::::::::::::::

.88 4 ..... i.-.!.-i 4.--i.. i+::..i-4.-14.-.i ............ i.-.

......i.......+-q ......i4.......... !--i....._......-

.84 jD_ ...... i-::i ..... _.i+_ ...... _it .... i +i_+..... +:,+i_+

1 3 5 7 9 11 13

NPR

8p, deg

By, deg

8 .-J.4-.-[.... i...!.... '+..J_..I.+._..!._.Li i+..Li L.

-8 _ i i i ; i i i i ' i i i ' i i ! ' ! i !

71!ii_+-_--+-- i;i : : : -i--t-i......i--i---i......iq---i.....i--i---i -_

"+7-! ...... 7Tt ..... !-_! ..... ::!i .... 71 7

-12 i i ! i : ! : : i : i ! : : : i : :

--!--'t---:+.... _--!---!......!"'-!"! ...... !"!""! ......!"'-!"1 " -!""!"+'!'"

iiiiiiiiii-__-_......__++_......"!-+_......_+::.....! _?

-16 + i "PI i ......+++i ...... !+i-i ......+:ii ...... iii

12

4

-4

-8

;ii

!i++ ++i+++i++!+ !++i++ +i+!++ii+ ++iiii+ !i++I ++!

1 3 5 7 9 11 t3

NPR

(b) AelA t = 1.750; (NPR) d = 8.371.

Figure 16. Continued.

93
Power

© Dry

[] A/B

Wp/W i

F/F i

,.oo::Li::i:::::Li::H::i:::i::i:::l::i::i:::i:: ::H::h::Li::i::

iii5iiiliil_i_i_iiiii iiil>;iiilili

.92 ............

1.00 ..i...i...i..]..i.._..i..i..i...i.._l.i..i...i ...... i---_-+i..... _--.i-!

.96 i'--i"i'"! i i i...... t it_'i"i ; ..... [ i:i .... i:i .... ' ' ';i'

9,:ii!iiifi i ii iiil >!> i ii t ?:iiiit !> !i:i:

.88

.84 '!ii ...._>ii! i!i-+ i:i iliiiii

'.00

.96

.92

.88

.84

8p, deg

; : : : : i + i : ; ; : :

---L+b--:- ..... L-.i..-i ..... i.--i--_ ..... i....... , , ,

:::::::::::::::::::::::::::::::: ::i:+:::h :+::H::i:::+::i::

3 5 7 9 ,1 13

NPR

By, deg

4i:::_:.i::,::+::F:+:i:::l:::!:--::_:::F+!::::

'? i! ............ ;............................................... ) : I : : : : : : l: : :

"'?"!'" i...... !"_+"!'" ;"!'"!"': ..... ?"!'"! ..... !"'?"!"', "'?"!'"i""

t..-..._....; ..... !--+..! ........ _..÷ ..... ?.._ .......... _ ....... : ..... ;..

0 i_ -'_

:::h::i::::i::i:::::i:::H::: :;:i::!:::::i::i::i::: ::i:::i:::i::

-!-) -_ ...... ; i .... _--+i.._ ...... i-J--4 .... b--;-q .... ':--.i t..

i i L : : : : : : : : : : ..

- 12 -+:---,-.;...... _--,-+-+.... +..-;-.4...... i...i.-.;+.

.:...;...L ..... L.'.+ _....+ i...L..: ..... -..i.._i .....t" i...:.£ .... 2...i...'..

""::"":""_.... i--i--i--l--+--i::---F--i ..... t ..... i ........... ::... -16 i i : , : i i : i : : i : : i i : ; :

12

•.- !....,-+!--i--.i--t-i---!-.i-.-:---i--i-++i--Li-+.+ .....i..i.-.i..

- + _ : ..... D..I ......... %4--2 ...... L.b..i ...... L-.L._ ..... :.... L..

4 i : i i i i i : i i : i i i i i : ]

0 : gi,,,,_ rT_.. : ,.., : ,,f, : ,..t. i .,. : .. _ ,

'"+........ ""..... :+ili+! ..... i-_.... _ili........ 4::i::: :i:: ::i::!:::!::: ::i:::!::i:: :::i::: ::::!::::i:: ::L'.:::i:: ::::i::::i:::;i:::l:::i:: :::i::::i::i::i:::t:L :::i::

-8 _"-+r ' ' ..... 1 r-?-: ' ' .... " _!-,,+-Ii-+-+ ' ' • .......P--I-I.....i+-iI 3 5 7 9 11 13

NPR

(c) AJA t = 2.500; (NPR)d = 15.647.

Figure 16. Concluded.

94
wp/w i

F r/F i

RCS modifications

© Baseline

[] Scarfed

O Sawtooth

,96 : _-.r-. ,,6-.r,. 2"":'T : T : I : Z : I T r" i

• , . , ; ..... . ,

--i-i-_.....r-i---!--_--i--r-!......!-!--_......r--r-i....._-T::_

.92 ".-T--!..... _]i ......:,[] ......F]i ..... ii] ..... ][T

.96 'ii-"__.i._ ..i ......i...i..i-i__-:,i

.92 ..i.gti ..... i..2..i..... i...LJ .....:_.._......... _--i.... 4......i-

.88 : : : : : I : ! : I ', : :

.84:iiiiiiiiill ili:i!:il iiilii:i iliill ililliiiiiit ii:fill: ilill

1.00

_p, deg

4

By, deg

-4

-8

-12

-16

12

,-4.4.--._........ ::---i ..... _.--i---! ...... _-..-..-+--_--.--_--t---:---,---_--,

i!i!it!i!i

ii?i i i!i!ii iiiiii i iii: iiiiii:il i 2 .....i::i:i::i:i i..-:..-; .....i:_...L..:._. _ii!i:i:i i:!:i 2..i. iiiiii 2..

i i i [ i ; i i i : : : I : : ; I : ! i

_,_.9_i_q i!!iii!iii,iiiiiiii!-iiil °

--,---,.-,--,---,--,---,--,--',---,--,--,-,--,-, *t---:: ---_,--_--r_

'!T_-ITT-I ......i!i (_i_ ..... i '!-i /iii

.88 ....::.-.i.--::.--'.4-i.-:, ..... i.4..i_--L-_4.-i......i.-.i-.i.-.Li-.-:.-.-:_..

.84 "ii-! ....._ii ......':i! ......i!; ..... ii] ......]Ti

1 3 5 7 9 11 13

NPR

-4

-8

 i!iiiii iiii!iiiiiii iiiiii....,1

: i i : ! ' ' i i ; [ i ' ! _ ' i i ,

-+-i---i--

: _ ,,,,v,¢,,- :v : : v : ._;_.i..:_.. !-4-.-

: i • i

-ii}-:

1 3 5 7 9 11 13

NPR

(a) Ae/A t = 1.100; (NPR) d = 3.060.

Figure 17. Effect of RCS modifications on internal performance characteristics of dry power configurations.

95
Wp/W i

G_

F/F i

1.00

.96

.92

.88

.84

:+i+!ii!i' _ _ii!!i _iiii!iii+i _2_iii!i::

-+-i-Hi ....i--i---!---'--:---i ------' !--:--i-_ii---i....... i--i+-

5p, deg -4

-8

-12

-16

12

1.00 i i i I i : i

ii_i_ii_iii  ̧

96iiiiiiiiiii :if::

.92 i}:)i_ _:![:i "i--!'!_iii[ii._i_..

.84+ii

1 3

ii!-:.ii.iiiiiiil...i:.i.i..iii.:ii.i

5 7 9 11 13

NPR

_v, deg

-4

-8

(b) AeIA t = 1.750; (NPR)d = 8.371.

RCS modifications

© Baseline

[] Scarfed

Sawtooth

---i---!---! .... . .....

--i- ' . _31 .......i_ _..... i..._...i.. ' -- _---]...i_.

!i:_4:: _::i:i_::t_:_:: :_+it:i+_:

Figure 17. Continued.

..-...q ._.... _

'_i_-_-_-_ .....!-!---!......_---_--_ .....t-7ii_7 ?7

3 5 7 9 11 13

NPR
_lw i

6_

F/F i

;.._...i...i ..... i--i---:, ..... i--.!..i ....i--!.--i .--+.-.!-._-; _.-.!-..i '®iiiI!iiIiliI_ ..... i,i..... !..... iii

.96 "i _ _ I_ _ _ _ !

"?': : i : : : : I : ! : I : : : ' :

.._+..÷._._ .....;.._:...: ....:..._.._.-.-_-._ ........!..-: .... _-..i-._

•92 ii!ii iii iii ii iiiii iii ii ii iii iiiii iii iiiii iiiii iii iiiii_iii'_i-_ "'T":'"!"

_® -i---i---i--i .....i---i ....i---i--i ......i-%-t--i---i-i .....i---',-!-

.96 i ! ': ._:i i ]-.-!-.i.... i .: _._ ..... _.....i.- !_i__i_i_ _I_i_ _',?!_I? _

.92 !i!!_!!_?__i.!!!;!!!!i! I :!_i_l_i_i_i_

.88 __ i_ .-_-.._.--:: ....._.-.i-.-:+.I.-:,---_--i--i--_--.i--.:+.

--!-.-7-7.-,..-!-.+ -!

_ ?i ..... !_+ .... !! __-!__t!_!-t__+_

1.00

.96

.92

.88

.84

8p, deg

RCS modifications

© Baseline

I-'1 Scarfed

Sawtooth

+,,,,, i__!i!: _ ..... ii---_i!!i!iii_i!!!i!i: _i_!i_ ̧

:+i_+'I..... ....................... l:,.I::: ++_ -++-ii

•!!iliilii-iili!iliiMiil'!

1 3 5 7 9 11 13

NPR

By, deg

8 l..i......i..l--.i..::-.-i--+--i--.i---+ ......i--i---i.... i---i..i---l.::---i-.-i-.

4iiiii_ii!iiiii!iiiiiliiii_

o+_+!_++_+I+++I++_++

-8 --i-::-:_-----_--_+_---_ '"-_+ , ......i--i---:_ ......i--il.....i--'_-.-i -

"-!-!--i.....?-_-! ......!--!-_.....i-!---!....!?! .....!-! +i

•_--i--i ..... !-i--! ..... !--i-_....!-i--! ..... !-i!...._-i-i

.._-.-_.-.,:- ..... i-.-

.--i---i--, ....i--i---i ...... i---!--i ..... ,--i---i ..... !--4+...... i-i_-

-16 i !-P....i+! ...... ?ii ....?i! ..... !-ii..... ::ii

12

4

-4

-8

i--!---i--!--.

..2.._b.:...

i : + j :, :. i i ! :, li ! i

-d-.._+-i ...... L-:--4 ..... _---5--'_--- : : : : : : : : :

3 5 7 9 11 13

NPR

(c) AelA t = 2.500; (NPR) a = 15.647.

_-.-_..i--_ .....i.-.i._.......i--1-4--

+:+++!? ++++++++:+++i++:++

Figure 17. Concluded.

97
RCS modifications

© Baseline

[] Scarfed

Sawtooth

Wp/W i

8_

F/F i

q-_____-+i ......i--i--i -+

.96 --i--_,_ _ 31 ..... ' , .';..+i..... _...i-.2..

.--'--_---:--4---:---_--:---|..:.-.+.-.:.. .92 'Tii ..... iTi ..... ]-iT ; i i i : i i ! i

1.00

.96

.92

.88

.84

1.00

ii iiiiiiii!!tiiii!i, iiiiti iiii i!t ii iiili

" ' " I " : : I : : ; I : : : ! , ! [ .

•-,:--F--'--]---_-÷+F--_--F--i--u+--I---F-----i--_-F-F-F--t--+--i.--F-

-i--!-_--t---i--!+ +i +-i---i--!+-t-#--!---i--t---i---':-+i-+-t--i---i---_--

,!ff'i't'b! fft i-i f-t bi--i t-ff-bf-t--i-i--b

iii=iii!il il!!!it ii!iiii it!!ilii i!iit!iiii_i 'T-i+_ _, _ i i i i _ i i + _ _ ; _

.96 iiii iiii_]'_|_]_t_iii iit ii ii ilii

.92 +_i,lii, i!+.+!+,ili i++

7:" ::!f_Ti ...... _."_ ...... r-!-r:-_; _- -_-!-.."

--_--:-"r..... +'--_---: ...... !+"b-_...... ;-d--!" 2-!-b! ..... ":+-!--?-

.88 i+i+-i.....iii ......ifb! -i-i--i-f-i i-i......i+ff+i,

-.-!---;-+._ ....._.-_-.-+ .....+.4..++....._--i--._ ... +---i---+ ......+---;-- -_

".'+++!_ ...... i--"1 ..... 7!-_ ..... !..T _+..... .:...!..7._

-.4--._---_-1-.-_+.+:-..;.-.p-._---_+ 4++ _++-:---4-.._--_.-;.+4++.;...+..4...+...;.++

,84 i + + + i i i i i i i i i i + i + i

1 3 5 7 9 11 13

NPR

8p, deg

By, deg

-4

-8

-12

-16

i : i i i ! ! : [ T : i ! I i i : !

'?t_ .... !?! ...... !b'i ...... h!!++ti!+"l ! !!

-! + +- _++-_-.._--.:--+++: ..... :..._..:..:...: ..... :..=..: ..... :...;..:.. -+...... ,.....+++.....;+......... ,.....+-+T ..... ++i......+

•-i.....!i::h::!::tiiil::::::::::::::::::::::

=========================

-!'i-it--i!--it--!---i-i-fi-i--H--i---i--i-ti-i- i

r-i---+---i-l---+--i---d--!---+--+--l-+-i--i---++-

ii+iiii++ ilii+i+ii++++I+ +i+:iI!+i

12 : : ; i ; : i ; ; ; , ;

+!+i! ...... _....... _---+--_-'+--+--++-+-+

:_:_i_:_|_:_I:::_ .... _....._ +_...._.....-'++-_-

8 + i i : + + _ : + :

4 ilili__"+'"++"; ..... _-+i--i......i.+.+-'.-.

0 _t

-4

-•+ ;---i........ _--+-.

--_---i--,+-.-

-8

l 3

.-i : +i..

i_i :i: !i:

I i I I ' t I ' l

-_i:;,(",[ .'',.....i-"i---_--

; ; I i i ! !

---+-+_--i ...... _-..L_.-I.._-..;.---+

---L-: ........... i ....... t +...i.._: .... ...i..i...i+.._..!...i..-.'..... +:...i...L..

5 7 9 11 13

NPR

(a) Ae/A t = 1.100; (NPR)d = 3.060.

Figure 18. Effect of RCS modifications on internal performance characteristics of A/B power configurations.

98
Wp/w i

F/F i

1.00

.96

.92

.96

.84 _ _ _ '. _ _ _ _ : _ _ _ i _ i i i i

8p, deg -4

-8

-12

-16

1.00

_y, deg

RCS modifications

0 Baseline

[] Scarfed

Sawtooth

............ t..... i..... t!i.......... i..... t..... i!.........

--5---_---?--t---_--+--!---F-H---_--5--+--t--_---!--÷--!---?--!--_--+-i- t-

_...!._-..,...i..i...i.-t--x-!-! -.4.--i -_..

-_---i--÷-q---_--_---_ --_---i--_---_--<-.-]---i --b--V-_---_--_---_--_

'T__-l_:,i-ri!_ =""":__'_ "_ Tii .-i---;--i--l-.!..;--i---Li---i.-i ---,--_---,--,--,---,--, -_---,---,-

.... :,--i---i ....... i--i---i ....i---!--i ...... ]---!---i--:---!---!--i ....... :,-- !--':---

--+--i---_-- _-'.:---i ..................... _--_.... ÷ _---_...... ".. _-

..L..i..-..... i..:.. L.x..j...i..L..l..2..L.2..l-..i...L..i...I..i..±..

12

..:-.-;.._ ..... l !--4-.-i-- -i---_--_- -----_--+ -._-.-i..._ ........ ; --. 8 --;.-i...i .. i-i---i ....i..... i..--.-i--i---i--

..i..._..".....I "---i---_ i ' i i i 4-_,...... i....i-!---i---i ....._,..... i--_, ......!--_-ii ............ i.

--i-+..... i--i---i--r-i--i! ..... _!io '___--_-_-_-_,-_ __,c_::!::: ::!:::i:::!:

-4!i!'i!iiii!i!iiii .''' iiiiiii!!:i --4---:,--- ...... --.i---i........ _.....

iiii iiiii iiii

-8

1 3 5 7 9 11 13

(b) Ae/A t = 1.750; (NPR) d = 8.371.

Figure 18. Continued.

NPR

9{)
Wp/Wi

rr_

F/F i

1.00

iliii_i:ii_ ::. _il]i:ii";÷+ ..... _+:' .......:"......_.... +......+--t-i'_,++ .......-+.!

.96 !_ I_i ...... i!t

,--i---i--,:--I---i--i---!.-+--i---_--i -.-_--+--.i '---+--+--_ ....._-.-i.-s..

..+._+.._....._..++.+ ........._.......-.._.........___..:__: .....:_.._..._.

.92 ;i _, i : i ill i :.: i ! :

1.00 8p, deg

1.00 _ : : i _ _ :

.92

84

1 3

i i !" ! i !' : ; + i i _

--<---:--+..... +--++---P--t--+---+--+

'r.:::::....._ii .....i--+:'--i .....+---++-.+.-

--<---;+---: ...... :--.<+..+--...i._-_ ..... -_---i---_--

_;::"i iIiiii!:i :ii_:ii::iii:iiii_iiiiii

5 7 9 11 13

NPR

_y, deg

RCS modifications

© Baseline

[] Scarfed

Sawtooth

8 i i i I i : i I ! i ! I i : ! + ' ; _' ;

--:-..... +-.rl.+'--t---: .... <---+--:-..... .+--:---+...... b-._--q..... -+--+i---b-

_+i--i--l---i--i---+--÷--j---i--+---l---..:--j---+ ......+--+.....t--i.....+-

4 ,+:+P............. +...........i i+"...... :'+i' ......... i+i:.....l......... ii+"

r+;-_"!..--_'!i-..+"_i! ..... !!?--I..+-+--_ -

i' ,__ii!!iiiii!!i!i!i!iiiiii t!_i!! i!iiii!liiii,i !!

-._,-_--- .....i--i---i ....i---i--::------_--i---i .....i-+---i .....4-.!--+.-

-t6 '-i+_lt-tlt-?-+i--l-!?!-t-t_-+ ......+---+---i--

--.;--÷.-i.-.

--÷--b++:--

4 i.i

o

.._.._+...f..

-8 i_ iil

(c) Ae/A t = 2.500; (NPR)d = 15.647.

Figure 18. Concluded.

--i---i--i ......i-i---+......i--.i..i.....+..+-..+-

--+.--b-! ..... ÷--i---.:...... L--I---+' ..... J---b.2.

.--i---_--.!...... _--_---i...... i-+.:.-_...... I...L.._..

i i i i i : :i _ ' i ;

.-_..-i.--.....!!'+-: : ..... :--+..:i i Iiiz-.i.--_-. :

:-:-_ _ _ --_......_....i...i...i.. "..:..._'_...L' " '

:+i 2222..... 22......+..._.._..-_-.+..i ...... ......"++++......._-..

5 7 9 11 13

NPR

1 3

100
!!i!! _'

(a) Baseline configuration 1; NPR ---3.00.

Figure 19. Shelf surface oil flow visualization for dry power configurations. Ae]A t = 1.100.

101
(b) Scarfed configuration 7; NPR = 5.00.

Figure 19. Continued.

102
(c) Sawtoothconfiguration13;NPR=5.00.

Figure19.Concluded.

103
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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

September 1996 Technical Memorandum

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Static Internal Performance of a Two-Dimensional Convergent-Divergent

Nozzle With External Shelf WU 505-59-70-04

6. AUTHOR(S)

Milton Lamb, John G. Taylor, and Mark C. Frassinelli

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-0001

9. SPONSORING/MONITORING AGENCY NAME(S) ANDADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

8. PERFORMING ORGANIZATION

REPORT NUMBER

L-17478

10. SPONSORING/MONrTORING

AGENCY REPORT NUMBER

NASA TM-4719

11. SUPPLEMENTARYNOTES

Lamb and Taylor: Langley Research Center, Hampton, VA; Frassinelli: Detailed to NASA from Air Force Wright

Research and Development Center, Wright-Patterson Air Force Base, OH.

12a. DISTRIBUTION/AVAILABILITYSTATEMENT

Unclassified-Unlimited

Subject Category 02

Availability: NASA CASI (301) 621-0390

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

An investigation was conducted in the static test facility of the Langley 16-Foot Transonic Tunnel to determine the

internal performance of a two-dimensional convergent-divergent nozzle. The nozzle design was tested with dry and

afterburning throat areas, which represent different power settings and three expansion ratios. For each of these

configurations, three trailing-edge geometries were tested. The baseline geometry had a straight trailing edge. Two

different shaping techniques were applied to the baseline nozzle design to reduce radar observables: the scarfed

design and the sawtooth design. A fiat plate extended downstream of the lower divergent flap trailing edge parallel

to the model centerline to form a shelflike expansion surface. This shelf was designed to shield the plume from

ground observation (infrared radiation (IR) signature suppression). The shelf represents the part of the aircraft

structure that might be present in an installed configuration. These configurations were tested at nozzle pressure

ratios from 2.0 to 12.0.

14. SUBJECT TERMS

Two-dimensional; Convergent-divergent shelf nozzles; Static internal performance;

Pressure distributions

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Unclassified

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Unclassified

19. SECURITY CLASSIFICATION

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Unclassified

15. NUMBER OF PAGES

106

116. PRICE CODE

A06

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