August 2015

NASA/TM–2015-218790

Transonic Investigation of Two-Dimensional 

Nozzles Designed for Supersonic Cruise

Francis J. Capone and Karen A. Deere

Langley Research Center, Hampton, Virginia
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Langley Research Center 

Hampton, Virginia 23681-2199

August 2015

NASA/TM–2015-218790

Transonic Investigation of Two-Dimensional 

Nozzles Designed for Supersonic Cruise

Francis J. Capone and Karen A. Deere

Langley Research Center, Hampton, Virginia
Available from: 

NASA STI Program / Mail Stop 148 

NASA Langley Research Center 

Hampton, VA 23681-2199 

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i 

Table of Contents 

Abstract ..................................................................................................................................... 1 

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

Introduction ............................................................................................................................... 2 

Symbols and Abbreviations ...................................................................................................... 3 

Nozzle Designs ......................................................................................................................... 6 

 Nozzle Sizing Criteria ......................................................................................................... 6 

 External Flap and Sidewall Geometry ................................................................................ 7 

 Nozzle Configurations Tested ............................................................................................. 8 

Experimental Procedures .......................................................................................................... 8 

 Wind Tunnel and Tests ....................................................................................................... 8 

 Air Simulation System ........................................................................................................ 9 

 Instrumentation ................................................................................................................... 9 

Calibration and Data Reduction Procedures ........................................................................... 10 

 Calibration Procedure ....................................................................................................... 10 

 Data Reduction ................................................................................................................. 10 

 Data Repeatability ............................................................................................................ 12 

Computational Flow Server .................................................................................................... 12 

 Governing Equations ........................................................................................................ 12 

 Turbulence Modeling ........................................................................................................ 13

 Boundary Conditions ........................................................................................................ 13 

 Performance Calculation ................................................................................................... 13 

 Computational Procedure .................................................................................................. 14 

Presentation of Results ............................................................................................................ 15 

 Summary Data .................................................................................................................. 15 

 Basic Data ......................................................................................................................... 15 

Discussion of Results .............................................................................................................. 16 

 Basic Nozzle Aeropropulsive Performance ...................................................................... 16 

 Experimental/Prediction Comparisons ............................................................................. 16 

 Nozzle N1 ...................................................................................................................... 16 

 Nozzle N3 ...................................................................................................................... 17 

 Effect of Nozzle Boattail Curvature ................................................................................. 17 

 Effect of Nozzle Flap Length ............................................................................................ 18 

 Effect of Sidewall Boattail Angle ..................................................................................... 18 

Effect of Sidewall Boattail Curvature ............................................................................... 19 

 Effect of Sidewall Height .................................................................................................. 19 

Conclusions ............................................................................................................................. 20 

Appendix A – Flap and Sidewall External Coordinates and Location of Pressure Orifices .. 21 

Appendix B – Data Repeatability ........................................................................................... 22

Appendix C – Static Data ....................................................................................................... 23
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Appendix D – Aeropropulsive Performance Data .................................................................. 24

Appendix E – Integrated Pressure Drag Data ......................................................................... 25

Appendix F - Integrated Pressure Drag Data at Scheduled NPR ............................................ 26

Appendix G – Jet Effects Drag Data ....................................................................................... 27

Appendix H – External Pressure Distributions ....................................................................... 28 

References ............................................................................................................................... 29 

Table 1. Reference dimensions ............................................................................................... 31 

Figures ..................................................................................................................................... 32 

Appendix A Figures ................................................................................................................ 74 

Appendix B Figures ................................................................................................................ 88 

Appendix C Figures .............................................................................................................. 118 

Appendix D Figures .............................................................................................................. 132 

Appendix E Figures .............................................................................................................. 188 

Appendix F Figures ............................................................................................................... 224 

Appendix G Figures .............................................................................................................. 242 

Appendix H Figures .............................................................................................................. 256 
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Abstract

An experimental and computational investigation has been conducted to 

determine the off-design uninstalled drag characteristics of a two-dimensional 

convergent-divergent nozzle designed for a supersonic cruise civil transport. 

The overall objectives were to: (1) determine the effects of nozzle external flap 

curvature and sidewall boattail variations on boattail drag; (2) develop an 

experimental data base for 2D nozzles with long divergent flaps and small

boattail angles and (3) provide data for correlating computational fluid 

dynamic predictions of nozzle boattail drag. The experimental investigation was 

conducted in the Langley 16-Foot Transonic Tunnel at Mach numbers from 

0.80 to 1.20 at nozzle pressure ratios up to 9. Three-dimensional simulations of 

nozzle performance were obtained with the computational fluid dynamics code 

PAB3D using turbulence closure and nonlinear Reynolds stress modeling. The 

results of this investigation indicate that excellent correlation between 

experimental and predicted results was obtained for the nozzle with a moderate 

amount of boattail curvature. The nozzle with an external flap having a sharp 

shoulder (no curvature) had the lowest nozzle pressure drag. At a Mach number 

of 1.2, sidewall pressure drag doubled as sidewall boattail angle was increased 

from 4° to 8°. Reducing the height of the sidewall caused large decreases in 

both the sidewall and flap pressure drags.

Summary

An experimental and computational investigation has been conducted to determine the offdesign uninstalled drag characteristics of a two-dimensional convergent-divergent nozzle 

designed for a supersonic cruise civil transport. The overall objectives were to: (1) determine the 

effects of nozzle external flap curvature and sidewall boattail variations on boattail drag; (2) 

develop an experimental data base for 2D nozzles with long divergent flaps and small boattail 

angles and (3) provide data for correlating computational fluid dynamics (CFD) predictions of 

nozzle boattail drag. The experimental investigation was conducted in the Langley 16-Foot 

Transonic Tunnel at Mach numbers from 0.80 to 1.20 at nozzle pressure ratios up to 9. Threedimensional simulations of nozzle performance were obtained with the computational fluid 

dynamics code PAB3D using turbulence closure and nonlinear Reynolds stress modeling. The 

results of this investigation indicate that excellent correlation between experimental and 

predicted results was obtained for the nozzle with a moderate amount of boattail curvature. The 

nozzle with an external flap having a sharp shoulder (no curvature) had the lowest nozzle 

pressure drag. At a Mach number of 1.2, sidewall pressure drag doubled as sidewall boattail 

angle was increased from 4° to 8°. Reducing the height of the sidewall caused large decreases in 

both the sidewall and flap pressure drag forces.

Excellent correlation between experimental and CFD results were obtained for the nozzle 

with an external flap having a moderate amount of boattail curvature at the shoulder at all Mach 

numbers tested. At a Mach number of 1.20, agreement between the experimental and predicted 

pressures was excellent for the nozzle having a sharp corner on the external flap. The nozzle with 

an external flap having a sharp shoulder (no curvature) had the lowest nozzle pressure drag. Even 

though this nozzle had the greatest expansion of flow about the nozzle shoulder, it exhibited 
2

more favorable pressure recovery characteristics when compared to the other three nozzles 

tested. At a Mach number of 1.2, sidewall pressure drag doubled as sidewall boattail angle was 

increased from 4° to 8°. Reducing the height of the sidewall caused large decreases in both the 

sidewall and flap pressure drag forces.

Introduction

The National Aeronautics and Space Administration sponsored a joint High-Speed 

Research Program with US airframe and propulsion companies to provide the critical high-risk 

technologies for a Mach 2.4, 300 passenger aircraft shown in (ref. 1). An artist concept of this 

aircraft is shown in figure 1(a). One task the NASA-industry team faced was what type of 

exhaust nozzle would be best suited for the High Speed Civil Transport (HSCT) propulsion 

system. The technical challenges addressed as part of the task involved developing a large nozzle 

with high aerodynamic efficiency, low noise, low weight and long life. Trade studies conducted 

during this program indicated that a very large two-dimensional convergent-divergent nozzle (2-

D C-D) would be best suited to meet the very stringent noise requirements of the HSR program 

(fig. 1(b)). Additionally, a number of investigations conducted at both static (no external flow) 

and forward speeds have verified the performance characteristics of 2-D C-D nozzles (refs. 2 to 

5).

The engine cycle chosen for the HSCT propulsion system was a mixed-flow turbofan. 

Although this cycle did have a moderate bypass ratio, a mixer-ejector type nozzle would be 

necessary to reduce engine noise at off-design conditions. One of the nozzle concepts 

considered, shown in figure 1(c), would employ a multi-lobe ejector that would entrain outside 

free-stream air at take-off conditions through bypass doors integrated with the nozzle. This 

arrangement will also help fill the nozzle at over expanded conditions. During transonic and 

supersonic cruise conditions, these doors would be closed since external air entrainment would 

not be necessary for noise abatement. Static performance of two multi-lobed mixer nozzles 

considered for the HSCT propulsion system is presented in reference 6.

A major problem in designing an exhaust system for a supersonic cruise vehicle is that the 

geometric shape must change as flight conditions vary. The nozzle exit area ratio has to be varied 

continuously to maintain high performance at all flight conditions from takeoff to supersonic 

cruise. Nozzle performance cannot be comprised at supersonic conditions since payload capacity 

is highly sensitive to nozzle efficiency. For example, a 1-percent decrease in nozzle performance 

has been estimated to be equivalent to about an 8-percent loss in payload for this class of aircraft 

(ref. 7).

The nozzle operates with the largest area ratio at supersonic cruise. In order to reduce flow 

angularity losses (flow not exiting parallel to nozzle center line), the divergent flap half-angle 

and thus, length, are set to provide maximum internal performance at the supersonic design point 

for a fully expanded area ratio. As seen in the schematic in figure 1(c), the nozzle would have 

very long divergent flaps and the nozzle boattail angle would essentially be at 0° at supersonic 

cruise conditions. At the subsonic/transonic cruise condition, the nozzle would operate at a much 

lower area ratio. At this condition, it is necessary to minimize nozzle boattail drag that results 

from not only the nozzle boattail angle but also the curvature at the start of the boattail.

The nozzle boattail drag can be a significant part of the overall drag at subsonic speeds. 

Several studies were also conducted that addressed installed nozzle boattail drag issues. These 
3

studies suggested that nozzle boattail drag could be as much as 25 to 40 percent of the subsonic 

cruise drag (ref. 8) for the HSCT aircraft. Since limited experimental data existed for this class of 

nozzles, an experimental and computational program was initiated at NASA-Langley to 

determine the uninstalled drag characteristics of this nozzle concept. The overall objectives were 

to: (1) determine the effects of nozzle external flap curvature and sidewall boattail variations on 

boattail drag; (2) develop an experimental data base for 2D nozzles with long divergent flaps and 

small boattail angles and (3) provide data for correlating CFD predictions of nozzle boattail drag.

The experimental investigation was conducted in the Langley 16-Foot Transonic Tunnel at 

Mach numbers from 0.80 to 1.20 at nozzle pressure ratios up to 9. Three-dimensional 

simulations of nozzle performance were obtained with the computational fluid dynamics code 

PAB3D using turbulence closure and nonlinear Reynolds stress modeling.

Symbols and Abbreviations

All model forces and moments are referred to the stability axis system with the model 

moment reference center located at model station 35.39. A discussion of the data-reduction 

procedure and definitions of forces and propulsion relationships used herein are discussed in 

reference 9. Table 1 contains a listing of all reference dimensions.

Ae nozzle exit area, in2

Ai internal area at metric break, in2

Amax maximum model cross-sectional area, in2

Aref reference area, in2

At measured nozzle throat area, in2

Ae /At nozzle area ratio for ideally expanded flow

bref reference span, in.

CD,f nozzle skin friction drag coefficient

CD,n measured nozzle drag coefficient

CD,p integrated nozzle pressure drag coefficient, CD,p,f + CD,p,s

CD,pf integrated nozzle pressure drag plus estimated friction drag, CD,p + CD,f

CD,p,f integrated nozzle flap pressure drag coefficient (for both upper and lower flaps)

CD,p,s integrated nozzle sidewall pressure drag coefficient (for both sidewalls)

CF computed thrust coefficient

CF,I ideal thrust coefficient

CA,p,f integrated nozzle flap pressure axial force coefficient (both upper and lower flaps)

CA,p,s integrated nozzle sidewall pressure axial force coefficient (both upper and lower flaps)

C(F-Dn) thrust-minus-nozzle drag force coefficient
4

CL,p,f integrated nozzle flap pressure lift coefficient (both upper and lower flaps)

CL,p,s integrated nozzle sidewall pressure lift coefficient (both upper and lower flaps)

CN,p,f integrated nozzle flap pressure normal force coefficient (both upper and lower flaps)

CN,p,s integrated nozzle sidewall pressure normal force coefficient (upper and lower flaps)

Cp,f nozzle flap pressure coefficient, (pf – po)/qo

Cp,s nozzle sidewall pressure coefficient, (ps – po)/qo

cref reference length, in.

ΔCD increment in drag coefficient between measured and integrated nozzle pressure drag,

CD,n - CD,pf

ΔCD,p jet effects parameter, (CD,p)NPR – (CD,p)Jet off

C-D convergent-divergent

CFD computational fluid dynamics

D total center body-nozzle drag, lbf

Df center body friction drag, lbf

Dn nozzle drag, lbf

EFD experimental fluid dynamics

F nozzle flap

F thrust along stability axis, lbf

FA axial force, lbf

(F-Dn)/Fi aeropropulsive parameter (thrust-minus-nozzle drag ratio)

F/Fi static thrust ratio

FA axial force, lbf

FA,bal total axial force measured by force balance, lbf

FA,mom momentum tare axial force due to bellows, lbf

Fflux CFD determined surface flux force, lbs

Ffriction CFD determined surface friction force, lbs

Fi ideal isentropic gross thrust, lbf

Fj measured thrust along the body axis, lbf

FN measured jet normal force, lbf
5

Fpressure CFD determined surface pressure force, lbs

Ft,b total body force vector, lbs

g gravitational constant, 32.174 ft/sec

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

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

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

HSCT high-speed civil transport

HSR High Speed Research program

La,f circular arc portion of nozzle flap (see fig. 3), in.

La,s circular arc portion of sidewall (see fig. 4), in.

Lf length of flap (see fig.3), in.

Ln length of nozzle (see fig.3), in.

Ls length of sidewall flap (see fig. 4), in.

M free-stream Mach number

MS model station, in.

N nozzle

N unit normal vector

NPR nozzle pressure ratio, pt,j/pa or pt,j/po

p surface static pressure, psi 

pf flap external static pressure, psi 

pi average internal static pressure, psi 

p0 free-stream static pressure, psi

ps sidewall external static pressure, psi 

pt,j average jet total pressure, psi

q0 free-stream dynamic pressure, psi

R specific gas constant, 1716 ft/sec °R

rf flap radius of curvature (see fig. 3), in.
6

rf,max maximum flap radius of curvature (see fig. 3), in.

rs sidewall radius of curvature (see fig. 4), in.

rs,max maximum sidewall radius of curvature (see fig. 4), in.

S sidewall

Tt,j average jet total temperature, °R

U velocity vector, ft/sec

wf flap width, 5.492 in. (see fig. 2)

wi ideal weight-flow rate, lbf/sec

wp measured weight-flow rate, lbf/sec

wp/wi discharge coefficient

x axial distance from MS 50.90 (see fig. 3), in.

y vertical distance (see fig. 3), in.

ya,f vertical distance to the terminal point of the flap circular arc (see fig. 3), in.

z lateral distance (see fig.4), in.

za,s vertical distance to the terminal point of the sidewall circular arc (see fig. 4), in.

ze sidewall trailing edge thickness (see fig.4), in.

2-D two-dimensional

α angle of attack, deg

βf flap boattail angle, deg

βs sidewall boattail angle, deg

ρ density, slugs/ft3

Nozzle Designs

Nozzle Sizing Criteria

For the experimental portion of this study, the 2-D C-D nozzle was sized for testing on one 

of the existing single-engine, propulsion simulation systems with a rectangular body at the 

Langley 16-Foot Transonic Tunnel (ref. 10). The system chosen has a maximum height of 6.20 

inches and a maximum width of 6.80 inches that results in the nozzle having an aspect ratio of 

1.10 (width to height). However, some of the full-scale nozzle concepts being considered for the 

HSCT vehicle, like the ones shown in figure 1, had aspect ratios of about 1.05. To account for 

the difference in nozzle aspect ratio, the height of the model 2-D C-D nozzle was chosen for 

scaling purposes, since this parameter should better represent nozzle boattail closure. This 
7

resulted in an 8.2-percent scale model of one of the Mach 2.4 passenger aircraft being studied in 

the HSR program. This aircraft was about 320 ft long with a reference area of 7200 ft2 and a 

reference chord of 1032.28 in. Using this model scale, an appropriate reference area was 

obtained to nondimensionalize nozzle drag in order to produce meaningful drag coefficients in 

terms of airplane drag counts (one drag count = 0.0001 in drag coefficient).

The two-dimensional convergent-divergent nozzle is a nonaxisymmetric exhaust system in 

which a symmetric contraction and expansion process takes place internally in the vertical plane. 

Basic nozzle components consist of upper and lower convergent and divergent flaps to regulate 

the contraction and expansion process and flat nozzle sidewalls to contain the flow laterally. The 

flap inner-surface (on full-scale hardware) can be varied or altered by actuators so that (1) the 

engine power setting (throat area) can be changed by varying the throat height and (2) the 

expansion surface angle (flat surface downstream of the throat) can be varied for optimum 

expansion of the exhaust flow. The overall nozzle geometry of the subscale 2-D C-D nozzle 

model is shown in figure 2 with a typical flap and sidewall setup. The overall length of the 

nozzle was 13.14 inches. The full-scale nozzle shown in figure 1(b) would be about 8 ft by 8 ft 

by 20 ft long.

All nozzles were tested with sidewalls. The height of the sidewall was fixed to a distance 

such that the nozzle internal flaps would not unport with the nozzle in the supersonic cruise 

position. In this position the boattail angle of the external flaps would be less than 4°. The 

sidewall cross sectional shape and maximum thickness were dictated by structural and actuation 

requirements for the full-scale nozzle.

External Flap and Sidewall Geometry

The geometric parameters used to define the nozzle external flap shape are shown in figure 

3. The two geometric parameters varied during the test were nozzle external flap length Lf and 

flap radius of curvature rf. These two parameters were nondimensionalized by the nozzle height 

hm and maximum radius of curvature rf,max. The baseline external flap had a length of 8.432 

inches. A shorter flap length of 6.739 inches was also tested. Note that the overall length of the 

nozzle, which is representative of the full-scale nozzle, was not changed when nozzle flap length 

was varied. Nozzles with boattail curvature parameters rf /rf,max from 0 to 1 were tested. A nozzle 

with no curvature would probably be the simplest to build since this flap would have a simple 

hinge joint. If curvature were required, some type of a sliding mechanism at the hinge joint (fig. 

1) would be necessary. The term La,f represents the portion of the nozzle flap that is a circular arc. 

Nozzle flap F1 was considered the baseline flap for this investigation since pretest predictions 

indicated that a nozzle with this flap external geometry would have the lowest drag. The external 

coordinates and location of the pressure orifices on the nozzle flaps are presented in Appendix A.

The various parameters used to define the sidewall external shape are shown in figure 4. 

Sidewall boattail angle βs and radius of curvature rs were the two geometric parameters that 

varied during the test. The sidewall height at the nozzle exit was 5.946 in. (see fig. 2) for 

sidewalls S1 to S7. An additional sidewall S8 was provided to determine the effect of sidewall 

height. The height of this sidewall was varied to follow the external contour of nozzle flap N1. A 

sketch of the nozzle flap and sidewall geometry is shown in figure 5, which also lists the 

summary of nozzle configurations tested. Sidewall S1 was chosen to be the baseline sidewall for 

this investigation. This sidewall should have the lowest drag of all the full height sidewalls tested 

because it had the lowest boattail angle. For a full-scale nozzle, the sidewall needs to be wide 
8

enough to house the actuation system for the nozzle and provide structural integrity for the 

overall nozzle. Thus, sidewalls with larger boattail angles were provided to assess any drag 

penalty that might occur if such sidewalls were required for the full-scale nozzle. The external 

coordinates and location of the pressure orifices on the sidewalls are presented in Appendix A.

Nozzle Configurations Tested

A summary of all the nozzles tested is provided in figure 5. Nozzle configurations in which 

the external flap geometry was varied are presented in figure 6. The flap radius of curvature 

parameter was varied from 0 to 1.0 for nozzles N1, N2, N3, and N4 with the baseline flap length 

being held constant. The flap boattail angle βf varied from 11.72° to 23.44° for these 

configurations. Flap radius of curvature rf /rf,max was also varied for the nozzles with the shorter 

flap length as indicated by nozzles N13 and N14, all of which were tested with sidewall S1. 

Nozzles N11 and N12 were tested with flaps F1 and F2 with the reduced height sidewall to 

determine whether a drag penalty may occur for the full height sidewalls. Photographs of nozzles 

N1 and N11 are presented in figure 7 to show the different sidewall heights.

The nozzle configurations used to investigate sidewall boattail angle βs and radius of 

curvature rs are shown in figure 8. Sidewall boattail angle was varied from 4° to 8° for nozzles 

N1, N5 and N6 with rs/rs,max = 0. The sidewall radius of curvature parameter rs/rs,max was varied 

from 0 to 0.4 for nozzles N5, N7, and N9 with the boattail angle at 6°, and from 0 to 1.0 for 

nozzles N6, N8, and N10 with the boattail angle at 8°.

All nozzles tested had the same internal geometry, because one of the objectives of this 

investigation was to only vary the external nozzle flap contour. Thus, any changes to external 

nozzle performance such as nozzle drag, should only be attributed to external flow effects over 

the nozzle flaps. The nozzles had a nominal throat height ht of 2.02 inches, an exit height he of 

2.70 inches and an area ratio Ae/At of 1.34 (fig. 2). The corresponding nozzle design pressure 

ratio was 5.0, which is where the flow in the nozzle is fully expanded and peak nozzle 

performance is generally expected. Static performance for each of the nozzles can be found in 

Appendix C. A comparison of all the nozzles static performance presented in figure 9 showed 

excellent agreement between all nozzles with differences of less than one-half percent in the 

static thrust ratio at any given pressure ratio. The maximum static pressure ratio reached was 

about 4.5 due to facility flow limitations.

Experimental Procedures

Wind Tunnel and Tests

The Langley 16-Foot Transonic Tunnel was a single-return atmospheric wind tunnel with a 

slotted octagonal test section and continuous air exchange. The wind tunnel had variable 

airspeeds up to a Mach number of 1.25 with test-section plenum suction used for speeds above a 

Mach number of 1.05. A complete description of this facility and operating characteristics can be 

found in reference 11.

This investigation was conducted at Mach numbers from 0.80 to 1.20. Nozzle pressure 

ratio was varied from jet-off up to 9, depending on Mach number. All nozzle configurations were 

tested at an angle of attack of 0°. Unit Reynolds number per foot varied from 3.8 x 106 to 4.2 x 

106. All tests were conducted with a 0.10 in. wide boundary-layer trip consisting of a strip of No. 
9

120 silicon carbide grit sparsely distributed in a thin film of lacquer located 1.00 in. from the tip 

of the forebody nose.

Air Simulation System

The nozzles were tested on an isolated, two-dimensional propulsion air-powered simulation 

system that was mounted in the wind tunnel by a sting/strut support system as shown in figure 

10. A photograph showing this installation with nozzle N1 is presented in figure 11. The 

propulsion simulation system was composed of three major sections: a nose-forebody, a 

centerbody, and the nozzle. The nose-forebody section up to station 26.50 was nonmetric; that is, 

it was not attached to the strain-gage force balance. The centerbody section was made up of the 

low-pressure plenum, instrumentation section and transition section. The centerbody section 

from station 26.50 to 50.90 was rectangular in cross-section with rounded corners and had a 

constant width and height of 6.80 in. and 6.20 in., respectively. All sections downstream of 

station 26.50 were metric and mounted on the force balance. A flexible Teflon strip inserted into 

a circumferentially machined groove between the nose-forebody and low-pressure plenum 

impeded flow into or out of the internal cavity.

An external high-pressure air system provided a continuous flow of clean, dry air at a 

controlled temperature of about 540 ̊R in the nozzles. This high-pressure air was brought through 

the support strut by six tubes that connect to a high-pressure plenum chamber. As shown in 

figure 10, the air was then discharged perpendicularly into the model low-pressure plenum 

through eight multi-holed sonic nozzles equally spaced around the high-pressure plenum. This 

method was designed to minimize any forces imposed by the transfer of axial momentum as the 

air passed from the nonmetric high-pressure plenum to the metric (mounted on the force balance) 

low-pressure plenum. Two-flexible metal bellows were used as seals and served to compensate 

for axial forces caused by pressurization. 

The air was then passed from the model low-pressure plenum, through a choke plate, an 

instrumentation section and a transition section that provided a smooth flow path for the airflow 

from the round low-pressure plenum to the rectangular nozzle entrance. All nozzle 

configurations were attached to the transition section at model station 50.90.

Instrumentation

The Langley 1631B six-component strain-gauge balance was used to measure forces and 

moments on the model downstream of station 26.50. The balance limits for this balance were 

±600 lbs normal force, ±800 lbs axial force and ±4,000 inch-pounds pitching moment. Flow 

conditions in the nozzle were determined from ten area-weighted total pressure probes and one 

total temperature probe located at station 45.65 in the instrumentation section, aft of the choke 

plate. Nozzle total pressure was determined from the average of these measurements. Weight 

flow of the high-pressure air supplied to the exhaust nozzle was measured by a critical flow 

venturi (ref. 12). Eight internal static pressures, measured at the metric break, were used to 

account for pressure forces at this location. All the pressures noted above were measured with 

individual pressure transducers.

The nozzle flaps were extensively instrumented with pressure taps because one of the 

primary objectives of this investigation was to provide data for correlating CFD predictions of 

nozzle boattail drag. The nozzle upper and lower flaps were each instrumented with two rows of 

pressure taps with 25 taps per row. On the upper flap, one row was located on the flap centerline 
10

and the other was located outboard near the sidewall. On the lower flap, one row was also 

located on the flap centerline and the other was located midway between the flap centerline and 

the outer edge of the flap. For each nozzle, one sidewall was instrumented with two rows of 

pressure taps with 20 taps per row. These pressures were measured with electronically scanning 

pressure devices. The locations of each pressure tap on all flaps and sidewalls were determined 

from actual measurements after the pressure taps were installed and are accurate to within 

±0.005 inches. These locations are presented in detail in Appendix A.

Calibration and Data Reduction Procedures

Calibration Procedure. The force balance measures the combined forces and moments 

due to nozzle gross thrust and the external flow field of that portion of the model aft of MS 26.5 

inches. Force and moment interactions exist between the bellows-flow transfer system (fig. 10) 

and the force balance. Consequently, single and combined loadings of normal force, axial force 

and pitching moment were made with and without the jets operating with Stratford calibration 

nozzles (ref. 10). The calibrations performed with the jets operating give a more realistic effect 

of pressurizing the bellows than simply capping off the nozzles and pressurizing the flow system. 

Thus, in addition to the usual balance-interaction corrections applied to the force balance under 

combined loads, another set of corrections was applied to account for the combined loading 

effect of the balance with the bellows system. These calibrations were performed over a range of 

expected normal forces and pitching moments. The balance data were then corrected in a manner 

similar to that discussed in references 9 and 10.

Data Reduction. All data were recorded simultaneously on magnetic tape. Approximately 

50 frames of data, taken at a rate of 10 frames per second, were taken for each data point; 

average values were used in data reduction computations. The average value of jet total pressure 

was also used in all computations. As stated in the Nozzle Design section, the nozzles were 

scaled to an equivalent 8.2-percent HSCT airplane so that appropriate reference dimensions 

could be used subsequently to non-dimensionalize drag in order to produce meaningful drag 

coefficients in terms of airplane drag coefficients. Thus, all aerodynamic coefficients were 

referenced to an equivalent reference area of 6824.4 in2 and chord of 84.337 in.

The axial force measured by the force balance must be corrected for both a pressure-area 

tare force acting on the model and for momentum tare forces caused by flow in the bellows in 

order to achieve desired axial-force terms. The internal pressure force on the model was obtained 

by multiplying the difference between the average internal pressure and free-stream pressure by 

the affected projected area normal to the model axis. The momentum tare force was determined 

from calibrations using the aforementioned Stratford calibration nozzles prior to the wind tunnel 

investigation.

At wind-on conditions, thrust-minus nozzle drag was obtained from equation 1

(1)

where the first term FA,bal includes all pressure and viscous forces (internal and external on the 

afterbody and nozzle and thrust system). The second term accounts for the interior pressure 

forces acting at the metric break. The internal pressure at any given set of test conditions was 

uniform throughout the inside of the model, thus indicating no cavity flow. The tare force FA,mom

is a momentum tare correction with the jet operating and is a function of the average bellows 
11

internal pressure that varies with the internal chamber pressure in the supply pipe just ahead of 

the sonic nozzles (fig. 10). Although the bellows were designed to eliminate pressure and 

momentum tares, small bellows tares still exist with the jet operating. These tares result from a 

small pressure difference between the ends of the bellows when internal velocities are high and 

from small differences in the forward and aft bellows spring constants when the bellows are 

pressurized. The last term Df is the friction drag of the centerbody section from stations 26.50 to 

50.90.

The adjusted forces and moments measured by the force balance are transferred from the 

body axis of the metric portion of the model to the stability axis. The attitude of the nonmetric 

forebody relative to gravity was determined from a calibrated attitude indicator located in the 

model nose. The angle of attack, α, which is the angle between the centerbody/nozzle centerline 

and the relative wind, was determined by applying terms for centerbody deflection (caused when 

the model and balance bend under aerodynamic load) and a tunnel flow angularity term to the 

angle measured by the attitude indicator. The flow angularity correction was 0.1 ̊, which is the 

average angle measured at the centerline of the 16-Foot Transonic Tunnel (ref. 11).

Thrust-removed (nozzle) forces and moments were obtained by subtracting the 

components of thrust in axial force, normal force, and pitching moment from the measured total 

(aerodynamic plus thrust) forces and moments. These thrust components at forward speed were 

determined from measured static data and were a function of free-stream and dynamic pressure. 

Total nozzle drag coefficient (including pressure and viscous forces) from balance measurements 

for only the nozzle (portion of model aft of model station 50.90) is then

€

CD,n = C(F−Dn ) + CF (2)

Nozzle flap and sidewall pressure drag coefficients were determined by integration of 

pressures over the respective surfaces in the body axis. Integrated axial (equation 3) and normal 

(equation 4) pressure force coefficients for the upper and lower flap of the nozzle are simply

(3)

(4)

and then converted to the stability axis

(5)

Sidewall pressure drag coefficient would be obtained in a similar fashion

(6)

Nozzle discharge coefficient wp/wi is the ratio of measured weight flow to ideal weight 

flow, where ideal weight flow is based on average jet total pressure pt,j, jet total temperature Tt,j, 

and the measured nozzle throat area At for each individual nozzle tested. Nozzle discharge 

coefficient is then a measure of the ability of a nozzle to pass weight flow and is reduced by any 

momentum and vena contracta losses (effective throat area less than measured throat area). 

Using the measured weight flow, ideal thrust of the nozzle can be computed from equation 7.
12

€

Fi = wp

RTt, j

g

2

2γ

γ −1

$

%

&

'

(

) 1− 1

NPR

$

%

& '

(

)

γ −1

γ

$

%

&

'

(

) *

+

,

,

-

.

/

/

0

1

2

3

2

4

5

2

6

2

1

2

$

%

& '

(

)

(7)

Ideal thrust is then used to compute basic propulsion performance ratios such as static thrust ratio 

F/Fi.

Data Repeatability. Data for this investigation was acquired within a single wind tunnel 

entry of the model. Short-term repeatability has been quantified in terms of a 95% confidence 

level for nozzle N1. Examples of short-term repeatability of integrated pressure drag values are 

shown in figure 12 for nozzle N1 flap and sidewall pressure drag coefficients, respectively, at a 

Mach number of 0.90 for seven NPR sweeps. Four of the NPR sweeps were performed at the 

beginning of the test and the other three were taken at the end of the test period. These figures 

show the residuals of the integrated pressure drag values defined as the difference in the 

individual measured data points from the estimated mean of the group of repeated NPR sweeps. 

The estimated mean was the average of the grouped data based on a piecewise, 3rd order 

polynomial fit of the individual NPR sweeps. Also shown with the dashed lines, are the bounds 

of the 95% confidence interval as a function of NPR. In general, the residuals are small over the 

NPR range tested. The basic data in graphical form can be found in Appendix B.

Computational Flow Solver

Governing Equations

The PAB3D computer code solves the three-dimensional, Reynolds-averaged NavierStokes (RANS) equations and uses one of several turbulence models for closure of the RANS 

equations. The governing equations are written in generalized coordinates and in conservative 

form. In an effort to decrease computational resources, simplified, thin-layer Navier-Stokes 

equations are implemented into PAB3D. This approximation neglects derivatives in the viscous 

terms streamwise and parallel to the surface, since they are typically negligible in comparison to 

the derivatives normal to the surface. Extensive details of PAB3D are found in references 13 and 

14.

The flow solver was written with three numerical schemes: the flux vector scheme of van 

Leer (ref. 15), the flux difference-splitting scheme of Roe (ref. 16), and a modified Roe scheme 

used primarily for space marching solutions. These schemes implement the finite volume 

principle to balance the fluxes across grid cells and the upwind biased scheme of van Leer or 

Roe to determine fluxes at the cell interfaces. Only the inviscid terms of the flux vectors are split 

and upwind differenced, while the diffusion terms of the Navier-Stokes equations are centrally 

differenced. The details and applications of these methods are given in references 13 and 14.

For this study and other typical three-dimensional simulations, the solutions are computed 

with the van Leer and Roe schemes. Each iteration to a steady state in the three-dimensional 

computational domain includes a forward and backward relaxation sweep in the streamwise 

direction, while implicitly updating each cross plane.
13

Turbulence Modeling

Turbulence modeling is required to predict solutions for many flow fields. The PAB3D 

code can perform several turbulence simulations by implementing either a 1- or 2-equation 

turbulence model with either a linear or nonlinear Reynolds stress model. For this study, the 2-

equation, viscous model was chosen because this model has proven reliable in predicting 

propulsive flows with mixing, separated flow regions, and jet shear layers. The nonlinear 

Reynolds stress model of Girimaji (ref. 17) was implemented to capture anisotropic flow features 

that are not resolved with the standard, linear stress-strain relationships. A modified Jones and 

Launder form (ref. 18) of the damping function was utilized to treat the singularity at the wall. A 

high Reynolds number model with no damping function was implemented in the free stream 

blocks.

Boundary Conditions

The PAB3D code allows for several boundary conditions at the inflow, outflow, free 

stream, and wall and centerline boundaries. Nozzle total temperature and total pressure with a 

normal fluid flow angle was used for the jet inflow boundary conditions. A jet total temperature 

of 528.67°R was used for all jet calculations. Riemann invariants along characteristics were used 

as inflow and free stream boundary conditions. A constant pressure boundary condition for 

subsonic outflow was used far downstream as an outflow boundary condition. A no-slip 

adiabatic wall boundary condition was implemented on solid surfaces to obtain viscous 

solutions.

Performance Calculation

The PAB3D code contains a performance module (ref. 19) that utilizes the momentum

theorem applied to a user-defined control volume to calculate nozzle or aerodynamic 

performance. Quantities such as lift, drag, thrust, moments, heat transfer and skin friction may be 

computed for many complex geometric configurations and multi-stream flows. Each quantity is 

updated throughout the solution development to monitor convergence.

Along flow-through sections of the control volume, mass and momentum fluxes, as well as 

pressure forces are integrated over cell with equations 8 and 9.

€

wp =∑(ρU ⋅ N)ΔA (8)

€

Fflux = ρU(U⋅ N) + p − p ∑[ ( o )N]ΔA (9)

where DA is the cell face area and N is the cell face unit vector.

Along solid surfaces of the control volume, skin friction and pressure forces are 

calculated. Surface pressure force Fpressure is determined by multiplying cell static pressure by cell 

face area using equation 10.

€

Fpressure = p − p ∑[( o )N]ΔA (10)

The cell surface static pressure is calculated by extrapolating the cell centered static pressure to 

the surface where the velocity is assumed to be zero.
14

The skin friction force Ffriction is calculated with only the velocity gradients tangential to the 

surface contributing to the velocity term of the viscous stress tensor. A two point difference 

method was used to determine the velocity gradients; one zero-magnitude velocity vector at the 

surface and a second at the cell center. Sutherland’s formula (ref. 20) was used to calculate the 

dynamic viscosity term at the surface by extrapolating the static temperature at a local cell center 

to the surface and using a reference viscosity and temperature condition. The total body force 

vector Ft,b is defined in equation 11.

€

Ft,b = Fflux + Fpressure + Ffriction (11)

Computational Procedure

PAB3D was used to predict solutions for nozzles N1 and N3 at Mach numbers 0.90 and 

1.20 with a nozzle pressure ratio of 5, which was the design pressure ratio. 

The computational mesh was fully three-dimensional with 9+3 blocks defining the internal 

nozzle, and 9+3 blocks representing the free stream domain. The far field was located 10 body 

lengths upstream and downstream of the aerodynamic nose and nozzle exit, respectively. The 

upper and lower lateral far field boundary was located 6 body lengths above and below the 

aerodynamic body. The boundary layer was defined for a law-of-the-wall coordinate y+ of 0.5 

on the fine mesh spacing for adequate modeling of the boundary layer flow.

The base grid is a quarter plane representation of the experimental model with 1.57 million 

grid points in 12 blocks. A cut 222 grid is generated by using a database reduction scheme that 

eliminates every other grid point in the i, j, and k directions. This cuts each grid dimension by 2, 

which decreases the grid count to 207,437 and substantially reduces the memory required to run 

the flow solver. The cut grid can also be sequenced in each direction for improved convergence 

rates and for grid assessment. For example, the flow solver uses alternating points in the i 

direction and every point in the j and k directions in a 211 sequence. Generally, a user would 

begin sequencing on the cut 222 grid. A pattern of 222, 221, 211, and then 111, or no sequencing 

might be used to assess solution behavior as more points are utilized in a particular direction. 

The solution is developed until convergence requirements are met at each level. Once the 

solution is converged on the cut 222 grid, the solution may be extrapolated to the base grid and 

sequencing may again be utilized.

For example, a converged solution was developed within 16.4 hours on a cut grid for 

nozzle N1 at M = 0.9 and NPR = 5. However, the solution was extrapolated and converged on 

the base level to quantify the effect of grid density. Nozzle drag coefficient decreased a mere 

0.00002 in another 30 hours of computer time. Therefore, the remaining solutions were

computed using sequencing only on the cut grid since the aforementioned solution was 

minimally dependent on doubling the grid density beyond the cut 222 level. This technique 

allowed for quicker solution times due to the substantially smaller memory requirement of the 

cut grid. Figure 13 presents typical convergence histories for Nozzle 3, and although not shown, 

similar results were obtained for Nozzle 1. The spikes in the residual history for Nozzle N3 at M

= 0.9 and NPR = 5 exhibit locations of solution extrapolation to a finer grid level. Accordingly, 

small adjustments in drag coefficient, Cd, were observed at these locations, also. The solution 

converged at the 222 grid level after 6500 iterations, with no further change in drag coefficient as 

the residual continued to decrease. Drag coefficient increased a mere 1.2 percent from the 422 

grid level to the 222 grid level.
15

Presentation of Results

Summary Data

The effect of Mach number on nozzle aeropropulsive performance parameters for nozzle 

N1 is presented in figure 14. Comparative and summary results from this investigation are 

presented graphically in figures 15 to 36. The comparisons show the correlation between the 

experimental and predicted results, as well as showing the effects of varying nozzle geometric 

parameters on the nozzle integrated pressure drags and pressure distributions at the design nozzle 

pressure ratio of 5.0. Although the discussion of results at this pressure ratio would generally be 

applicable to other pressure ratios, the relative difference between comparisons may vary.

Basic Data

All the experimental results from this investigation are presented in graphical form in 

Appendices D to H. Basic nozzle performance parameters for each nozzle are presented in 

Appendix D. Appendix E presents the effects of varying nozzle geometric parameters on the 

nozzle integrated pressure drag. The effects of varying nozzle geometric parameters on the 

nozzle integrated pressure drag values at the scheduled NPR are presented in Appendix F. Jeteffects parameter for each nozzle are presented in Appendix G. Appendix H presents the external 

pressure distributions for each nozzle.

An examination of the force and pressure data plots for an individual nozzle will show that 

at times, the force data plot may not contain as many data points as the experimental pressure 

data plot. During this investigation, pressure fluctuations were observed in the critical flow 

venturi. At times, these fluctuations would produce a sinusoidal type variation in nozzle 

discharge coefficient as nozzle pressure ratio was varied. Normally, there would be no variation 

of discharge coefficient with nozzle pressure ratio as long as the nozzle has choked flow. There 

are two valves in the air system for jet testing in the 16-Foot Transonic Tunnel that are used to 

vary mass flow and set nozzle pressure to the exhaust nozzles. One valve regulates pressure in 

the air line and the other is used as a throttling valve. The pressure fluctuations were caused by 

the pressure-regulating valve in the air system and subsequent operator problems associated with 

trying to set nozzle pressure ratio when these fluctuations occurred. In the past, this system has 

proven to be very successful in providing a very stable source of air to the exhaust nozzles. 

Unfortunately, repairs to the pressure-regulating valve could not be made in a timely manner and 

a decision was made to continue the test. After the test was completed, all discharge coefficient 

measurements for each of the nozzles were carefully examined. Any data point that had a value 

of discharge coefficient that was ±0.015 different from the average was deleted from the data 

listing for the particular nozzle in question. Thus, the force data listings will not contain as many 

data points as the experimental pressure data listings. These pressure fluctuations should have no 

effect on the external pressure measurements.
16

Discussion of Results

Basic Nozzle Aeropropulsive Performance

Typical nozzle aeropropulsive characteristics for nozzle N1 are presented as a function of 

nozzle pressure ratio, NPR, for each of the Mach numbers tested in figure 14. Figure 14(a) 

presents the aeropropulsive parameter (F-Dn)/Fi and nozzle discharge coefficient wp/wi. As 

expected because of increased drag, the aeropropulsive parameter decreases with increasing 

Mach number. Nozzle discharge coefficient is a measure of the ability of the nozzle to pass mass 

flow and is reduced from a theoretical value of 1.0 by boundary-layer thickness and non-uniform 

flow at the nozzle throat. Since nozzle discharge coefficient is a function only of internal nozzle 

geometry, it is independent of both Mach number and nozzle pressure ratio when the nozzle is

choked. In addition, changes in nozzle geometry that occur downstream of the nozzle throat 

(supersonic exhaust) usually do not affect nozzle discharge coefficient characteristics. Thrust 

minus nozzle drag coefficient C(F-Dn) and nozzle drag coefficient CD,n determined from the force 

balance measurements are present in figure 14(b). In general, the variation of nozzle drag 

coefficient with nozzle pressure ratio for a particular nozzle is similar to that of axisymmetric 

nozzles particularly at zero degrees angle of attack. Nozzle drag decreases with initial jet 

operation because there is a reduction in the external flow expansion required at the nozzle exit 

as the exhaust flow fills the nozzle base region. This reduced expansion generally results in 

higher pressures on the nozzle boattail regions. Figure 14(c) presents the pressure integrated 

nozzle flap drag CD,p,f, sidewall drag CD,p,s, and total pressure drag CD,p. Measured nozzle drag 

coefficient CD,n, nozzle pressure drag plus estimated friction drag coefficient CD,pf, and 

incremental drag coefficient DCD are shown in figure 14(d). Ideally, the incremental drag 

coefficient should be equal to zero. However, the greatest differences seen are at jet-off 

conditions (NPR ~ 1.0) and result because of inaccuracies in measuring jet-off drag with the 

force balance. Typically, measured jet-off drag is about 2 to 3 percent of the maximum rated 

balance axial force where the balance has been sized to measure thrust.

Similar results for the other 13 nozzles that were tested as part of this investigation can be 

found in the Appendix D.

Experimental/Prediction Comparisons

Nozzle N1. A comparison between experimental and predicted pressures on flap F1 for 

nozzle N1 are presented in figure 15 at Mach numbers of 0.90 and 1.20 at the design nozzle 

pressure ratio of 5.0. At the design pressure ratio, the flow is expected to be fully expanded and 

peak nozzle internal performance usually occurs. The boattail radius of curvature parameter 

rf/ rf,max was 0.40 for this flap and the sidewall was S1. Pressure distributions are compared along 

the flap centerline, at the flap mid station, and at the flap outboard station. At M = 0.90, the CFD 

computations tend to overpredict the expansion about the shoulder of the flap but do accurately 

predict the pressure recovery along the flap. Data indicates excellent agreement between 

predicted and experimental pressure data at M = 1.20 at NPR = 5. In addition, the pressure 

distributions across the flap are nearly identical, indicating that nearly uniform flow exists across 

the flap. The full height sidewalls tend to act like fences in inhibiting any communication 

between the sidewall and flap flows. The effects of reducing sidewall height will be discussed 

later in this section of the report.
17

The experimental and predicted nozzle pressure drag coefficients are presented in figure 16 

for nozzle N1 at NPR = 5.0. Shown in this figure are the flap, sidewall, and nozzle pressure drag

coefficient values where nozzle pressure drag coefficient is simply the sum of the sidewall and 

flap pressure drag coefficient values. As would be expected from the excellent correlation of 

pressures, the predicted drag coefficient values are in excellent agreement with experimental 

drag coefficient values at M = 0.9 and within 0.3 of a drag count (one drag count equals 0.0001 

drag coefficient) of the experimental drag coefficient value at M = 1.2.

A comparison of experimental and predicted nozzle total drag coefficients is also presented 

in figure 16 where the nozzle total drag coefficient includes skin friction. Skin friction drag 

coefficient for the prediction is computed within the performance module of the PAB3D code. 

The skin friction drag coefficient CD,f is determined using the Frankl-Voishel skin friction 

coefficient as part of the wind tunnel standard data reduction system (ref. 9). The measured drag 

coefficient is obtained from the force data measurements. As was the case for the pressure drag 

coefficients, excellent agreement exits. The total drag coefficients agree to within one-half drag 

count (0.00005) at M = 0.90 and one drag count (0.0001) at M = 1.20.

Nozzle N3. Experimental and predicted pressure distribution comparisons for nozzle N3 are 

shown in figure 17. The boattail radius of curvature parameter was 0 for this flap, which meant it 

had a sharp corner at the start of the boattail. As can be seen, the agreement between the 

experimental and predicted pressures was not as good as was the case for nozzle N1 at M = 0.90.

Consequently, there is a poorer correlation of flap pressure drag coefficient and nozzle total drag 

coefficient values (fig. 18). PAB3D predicts more flow expansion around the sharp corner than 

experimental data, which results in higher predicted drag. Another possible reason for this poor 

agreement of predicted and experimental data at M = 0.90 may be associated with treatment of 

the corner flow. Treatment of the corner flow is critical computationally at speeds less than Mach 

number 1. However, at M = 1.20, where geometrically matching the corner is not as important, 

agreement between the experimental and predicted pressures was similar to nozzle N1.

Effect of Nozzle Boattail Curvature

The effects of varying nozzle flap boattail radius of curvature on nozzle, flap, and sidewall 

pressure drag coefficient values are presented in figure 19 at the design nozzle pressure ratio of 

5.0. These nozzles all had the baseline flap length Lf/hm = 1.4 and were tested with sidewall S1. 

Although discussion of results at this pressure ratio would generally be applicable to other 

pressure ratios, the relative difference between comparisons may vary. Similar results at the 

scheduled nozzle pressure ratio can be found in Appendix F. Figure 19 also illustrates the typical 

breakdown of pressure drag between the nozzle flaps and the sidewalls. Generally, varying flap 

geometry had little or no effect on sidewall pressure drag. The breakdown of the pressure drag

coefficient values is similar for the other nozzle configurations tested.

The lowest nozzle pressure drag was obtained on nozzle N3 with flap F3 that had no radius 

of curvature (fig. 19). This was an unexpected result because previous experience has shown that 

axisymmetric nozzles with a sharp shoulder generally have higher drag (ref. 8). Similar results 

were found for 2-D C-D nozzles in reference 22 and 23. However, these nozzles generally had 

shorter external flaps and because they were designed for use with subsonic cruise vehicles. In 

order to try to understand this result, one can examine the pressure distributions on these nozzles.

Pressure distributions along the centerline row of the top flap for nozzles N1, N2, N3, and 

N4 are presented at M = 0.90 and 1.20 at NPR = 5 in figure 20. What is shown is that even 
18

though nozzle N3 with no curvature had the greatest expansion of flow about the nozzle 

shoulder, it exhibited more favorable pressure recovery characteristics when compared to the 

other three nozzles. Similar results were found for the pressure distributions along both the mid 

and outboard pressure rows (not shown).

The effects of varying nozzle flap boattail radius of curvature for nozzles with flap lengths 

of Lf/hm = 1.1 are presented in figures 21 and 22. These nozzles were also tested with sidewall 

S1. Figure 21 shows flap pressure drag coefficient for the two nozzles tested with the smaller 

flap lengths. Except at M = 1.20, these two nozzles followed similar trends as the nozzles with 

the longer flap lengths. At M = 0.90 and 0.95, nozzle pressure drag decreased as the flap radius 

of curvature parameter was increased from 0.1 to 0.4.

Effect of Nozzle Flap Length

The effects of varying the nozzle flap length for flaps having a radius of curvature of 0.1 

are shown in figures 23 and 24 and for those with a radius of curvature of 0.4 are illustrated in 

figures 25 and 26. Both nozzles (nozzles N13 and N14) with the shorter nozzle flap had higher 

total nozzle pressure drag at all the Mach numbers tested, except for N13 at M = 1.20. This was 

due primarily to these nozzles having steeper boattail angles than the nozzles with the longer 

flaps (nozzles N1 and N2). An examination of the pressure distributions in either figure 24 or 26 

generally shows that the nozzles with the shorter flaps have poorer pressure recovery 

characteristics than those with the longer flaps. It is interesting to note that at M = 0.80 to 0.95, 

the increment in pressure drag due to the change in flap length is about the same for the nozzles 

having the two different radii of curvature.

Similar results at the scheduled nozzle pressure ratio can be found in Appendix F.

Effect of Sidewall Boattail Angle

The effects of varying sidewall boattail angle on nozzle, flap, and sidewall pressure drag

coefficients are summarized in figure 27. There are no definite trends to changing sidewall 

boattail angle. For example, at M = 0.80 and 0.90, nozzle N6 with sidewall S3 having βs = 8° 

had the lowest sidewall pressure drag coefficient whereas, just the opposite was true at M = 1.20. 

At M = 0.90 (fig. 28), it is interesting to note that although sidewall S3 exhibited greater 

expansion of the flow about the boattail than sidewall S1, it exhibited somewhat better recovery 

and lower pressure drag. Figure 28 also shows that the flow across the sidewall is somewhat nonuniform in nature since expansion outboard about the boattail is greater for all the sidewalls than 

at the center of the sidewall. However, flow recovers to about the same pressure coefficient 

levels at both locations.

At M = 1.20, sidewall pressure drag for nozzle N6 with sidewall S4 was doubled that of 

nozzle N1 with sidewall S1 as sidewall drag increased from .000017 to .000035 (fig. 27). 

Examination of the pressure distributions of figure 28 at this Mach number reveals markedly 

different flow characteristics across the sidewall. Along the center of the sidewall, the flow is 

rather benign and shows relatively little differences as βs increased from 4° to 6°. Outboard on 

the sidewall, there is a rapid expansion of the flow about the shoulder for each of the boattail 

angles tested. The data indicates possible flow separation for the sidewalls with 6° and 8° 

boattail angles. Although the full-scale nozzle was designed to have a sidewall with 4° boattail

angle, it became evident as the HSR program progressed that sidewalls with boattail angles 
19

greater than 4° would probably be needed for both structural requirements and to house nozzle 

actuation hardware. This could pose a problem at supersonic cruise where the potential now 

exists for greater values of sidewall pressure drag to occur because of sidewall boattail angles 

would be greater than 4°.

Only at M = 0.95, did changing boattail angle appreciably affect flap pressure drag (fig. 

27). Flap pressure drag coefficient increased 0.00011 as boattail angle increased from 4° to 6°, 

which was twice as large as the increase in sidewall pressure drag. This is a somewhat surprising 

result in that one would not expect such a strong effect of varying sidewall geometry on flap 

performance. This is because the full height sidewalls tend to act like fences and isolate the 

sidewall flow from the flow over the flap.

Similar results at the scheduled nozzle pressure ratio can be found in Appendix F.

Effect of Sidewall Boattail Curvature

Several sidewalls were tested with varying amounts of curvature with both 6° and 8° 

sidewall boattail angles. Some typical results for nozzles N5, N7, and N9 with βs = 6° are 

presented in figures 29 and 30 and for nozzles N6, N8, and N10 with βs = 8° in figures 31 and 

32. Sidewall pressure drag decreased by 0.00014 as the sidewall radius of curvature rs /rs,max

was increased from 0 to 1.0 at M = 1.20. This could prove to be significant if sidewalls with 

boattail angles greater than 4° are needed as discussed previously. Sidewalls with full curvature 

would be feasible for the full-scale aircraft since the sidewalls would be fixed.

Similar results at the scheduled nozzle pressure ratio can be found in the Appendix F.

Effect of Sidewall Height

The height of the sidewall was fixed so that the nozzle internal flaps would not unport 

when the nozzle was in the supersonic cruise position. This type sidewall was selected to prevent 

impingement of any unwanted lateral nozzle exhaust on adjacent aircraft surfaces. As such, these 

sidewalls are very large panels that account for about 60-percent of the nozzle skin friction drag. 

Since these sidewalls could be also large unsupported panels, there could be an additional 

structural weight penalty associated with using them. To assess what drag penalties might occur 

with the full height sidewalls, some tests were performed with reduced height or cutback 

sidewalls. The height of the cutback sidewall S8 was contoured to match the external shape of 

flap F1. Sidewall S8 was then tested with flaps F1 and F2 to form nozzles N11 and N12 

respectively (fig. 6).

Nozzle, flap and sidewall pressure drag coefficients for nozzle N1 and N11 are presented in 

figures 33. Significant reductions in both sidewall and flap pressure drag were obtained for the 

cutoff sidewall over the entire Mach number test range. For example, at M = 0.90, there was a 

0.00012 reduction in nozzle pressure drag coefficient CD,p and a 0.00023 reduction in CD,p at 

M = 1.20. This drag reduction for the cutoff sidewall would be equivalent to at least a 0.00092 

reduction in drag coefficient for the HSCT vehicle with four engines. This does not include an 

additional, albeit small reduction in skin-friction drag.

The flow characteristics over the nozzle flap are different for the two sidewalls as shown in 

figure 34. With the reduced height sidewall, the flow along the sidewall tends to accelerate 

around the corner onto the flap where it can become three-dimensional. The full height sidewalls 
20

tend to act like fences that inhibit communication between the sidewall and flap flows, which 

results in the flow over the flap being more uniform. This is typical flow behavior for nozzles 

similar to nozzle N11, which has been found both experimentally (refs. 5 and 23) and 

computationally (ref. 24).

Similar results were also obtained for nozzle N12; however, the reduction in pressure drag 

was smaller than that noted for nozzle N11. (See figures 35 and 36.) Similar results at the 

scheduled nozzle pressure ratio can be found in Appendix F.

Conclusions

An experimental and computational investigation has been conducted to determine the offdesign uninstalled drag characteristics of a two-dimensional convergent-divergent nozzle 

designed for a supersonic cruise civil transport. The overall objectives were to: (1) determine the 

effects of nozzle external flap curvature and sidewall boattail variations; (2) develop an 

experimental data base for 2D nozzles with long divergent flaps and small boattail angles and (3) 

provide data for correlating computational predictions of nozzle boattail drag. The experimental 

investigation was conducted in the Langley 16-Foot Transonic Tunnel at Mach numbers from 

0.80 to 1.20 at nozzle pressure ratios up to 9. Three-dimensional simulations of nozzle 

performance were obtained with the computational fluid dynamics code PAB3D using 

turbulence closure and nonlinear Reynolds stress modeling. Based on the discussion of results in 

this paper, the following conclusions are made:

1. Excellent correlation between experimental and CFD results were obtained for the nozzle 

with an external flap having a moderate amount of boattail curvature at the shoulder at all 

Mach numbers tested. At a Mach number of 1.20, agreement between the experimental and 

predicted pressures was excellent for the nozzle having a sharp corner on the external flap.

2. The nozzle with an external flap having a sharp shoulder (no curvature) had the lowest 

nozzle pressure drag. Even though this nozzle had the greatest expansion of flow about the 

nozzle shoulder, it exhibited more favorable pressure recovery characteristics when 

compared to the other three nozzles tested.

3. At a Mach number of 1.2, sidewall pressure drag doubled as sidewall boattail angle was 

increased from 4° to 8°. 

4. Reducing the height of the sidewall caused large decreases in both the sidewall and flap 

pressure drags.

NASA Langley Research Center

Hampton, VA 23681-2199

July 2015
 21 

Appendix A

Flap and Sidewall External Coordinates and Location of Pressure Orifices

 This appendix presents the external coordinates of both the nozzle flaps and sidewalls. 

After installation, the locations of each pressure tap on all flaps and sidewalls were determined 

from actual measurements and are accurate to within ±0.005 inches. External coordinates for 

each nozzle flap and sidewall are presented in figures 37 to 50 as follows: 

Figure 

Flap F1 .................................................................................................................................... 37 

Flap F2 .................................................................................................................................... 38 

Flap F3 .................................................................................................................................... 39 

Flap F4 .................................................................................................................................... 40 

Flap F5 .................................................................................................................................... 41 

Flap F6 .................................................................................................................................... 42 

Sidewall S1 ............................................................................................................................. 43 

Sidewall S2 ............................................................................................................................. 44 

Sidewall S3 ............................................................................................................................. 45 

Sidewall S4 ............................................................................................................................. 46 

Sidewall S5 ............................................................................................................................. 47 

Sidewall S6 ............................................................................................................................. 48 

Sidewall S7 ............................................................................................................................. 49 

Sidewall S8 ............................................................................................................................. 50 
 22 

Appendix B

Data Repeatability

 This Appendix presents the repeat data from this investigation in figures 51 to 56 as 

follows: 

Figure 

Aeropropulsive performance data, nozzle N1 ........................................................................ 51 

External pressure data, N1 ...................................................................................................... 52 

Aeropropulsive performance data, nozzle N6 ........................................................................ 53 

External pressure data, N6 ...................................................................................................... 54 

Aeropropulsive performance data, nozzle N11 ...................................................................... 55 

External pressure data, N11 .................................................................................................... 56 
 23 

Appendix C

Static Data

 This appendix presents the static data for each nozzle as a function of nozzle pressure 

ratio, NPR. Included in each figure are the static performance parameter F/Fi

 and nozzle 

discharge coefficient wp/wi. The static data are presented in figures 57 to 70 as follows: 

Figure

Nozzle N1 ............................................................................................................................... 57 

Nozzle N2 ............................................................................................................................... 58 

Nozzle N3 ............................................................................................................................... 59 

Nozzle N4 ............................................................................................................................... 60 

Nozzle N5 ............................................................................................................................... 61 

Nozzle N6 ............................................................................................................................... 62 

Nozzle N7 ............................................................................................................................... 63 

Nozzle N8 ............................................................................................................................... 64 

Nozzle N9 ............................................................................................................................... 65 

Nozzle N10 ............................................................................................................................. 66 

Nozzle N11 ............................................................................................................................. 67 

Nozzle N12 ............................................................................................................................. 68 

Nozzle N13 ............................................................................................................................. 69 

Nozzle N14 ............................................................................................................................. 70 
 24 

Appendix D

Aeropropulsive Performance Data

 This Appendix presents the basic nozzle performance parameters for each nozzle as a 

function of nozzle pressure ratio, NPR, for each of the Mach numbers tested. Included in each 

figure are: (a) the aeropropulsive parameter (F-Dn)/Fi

 and nozzle discharge coefficient wp/wi; (b) 

thrust minus nozzle drag coefficient C(F-Dn) and measured nozzle drag coefficient CD,n; (c) nozzle 

pressure drag coefficient CD,p, flap pressure drag coefficient CD,p,f, and sidewall pressure drag 

coefficient CD,p,s; and (d) nozzle pressure drag plus nozzle friction drag coefficient CD,pf, and 

incremental drag coefficient ΔCD. The aeropropulsive performance data are presented in figures 

71 to 84 as follows: 

Figure

Nozzle N1 ............................................................................................................................... 71 

Nozzle N2 ............................................................................................................................... 72 

Nozzle N3 ............................................................................................................................... 73 

Nozzle N4 ............................................................................................................................... 74 

Nozzle N5 ............................................................................................................................... 75 

Nozzle N6 ............................................................................................................................... 76 

Nozzle N7 ............................................................................................................................... 77 

Nozzle N8 ............................................................................................................................... 78 

Nozzle N9 ............................................................................................................................... 79 

Nozzle N10 ............................................................................................................................. 80 

Nozzle N11 ............................................................................................................................. 81 

Nozzle N12 ............................................................................................................................. 82 

Nozzle N13 ............................................................................................................................. 83 

Nozzle N14 ............................................................................................................................. 84 
 25 

Appendix E

Integrated Pressure Drag Data

 This appendix presents the effects of varying nozzle geometric parameters on the nozzle 

integrated pressure drags as a function of NPR. Included on each figure is: (a) integrated nozzle 

pressure drag coefficient, CD,p; (b) integrated nozzle pressure drag plus estimated friction drag 

coefficient, CD,pf; and (c) integrated nozzle sidewall pressure drag coefficient (for both sidewalls) 

CD,p,s. The integrated pressure drag coefficient data are presented in figures 85 to 93 as follows: 

Figure

Effect of: 

Flap radius of curvature for nozzles N1, N2, N3, N4 with Lf /hm = 1.4 ................................ 85 

Flap radius of curvature for nozzles N13, N14 with Lf /hm = 1.1 .......................................... 86 

Flap length for nozzles N2, N14 with rf /rf,max = 0.1 .............................................................. 87 

Flap length for nozzles N1, N13 with rf /rf,max = 0.4 .............................................................. 88 

Sidewall boattail angle for nozzles N1, N5, N6 ................................................................... 89 

Sidewall radius of curvature for nozzles N5, N7, N9 with βs = 6° ...................................... 90 

Sidewall radius of curvature for nozzles N6, N8, N10 with βs = 8° .................................... 91 

Reduced sidewall height for nozzles N1, N11 ..................................................................... 92 

Reduced sidewall height for nozzles N2, N12 ..................................................................... 93 
 26 

Appendix F

Integrated Pressure Drag At Scheduled NPR

 This appendix presents the effects of varying nozzle geometric parameters on the 

nozzle integrated pressure drags at the scheduled NPR. Scheduled nozzle pressure ratio is the 

pressure ratio that the nozzle operates at for a particular Mach number and is dependent on the 

engine cycle design. Included on part one of each figure are: (a) integrated nozzle pressure drag 

coefficient, CD,p; (b) integrated nozzle pressure drag plus estimated friction drag coefficient, CD,pf;

and (c) integrated nozzle sidewall pressure drag coefficient (for both sidewalls) CD,p,s. Another 

part of the figure presents the corresponding pressure data. The integrated pressure drag 

coefficient data at scheduled pressure ratio are presented in figures 94 to 111 as follows: 

Figure

Effect of: 

Flap radius of curvature for nozzles N1, N2, N3, N4, pressure drag coefficients ............. 94 

Flap radius of curvature for nozzles N1, N2, N3, N4, pressure coefficients ..................... 95 

Flap radius of curvature for nozzles N13, N14, pressure drag coefficients ...................... 96 

Flap radius of curvature for nozzles N13, N14, pressure coefficients .............................. 97 

Flap length for nozzles N2, N14, pressure drag coefficients ............................................ 98 

Flap length for nozzles N2, N14, pressure coefficients .................................................... 99 

Flap length for nozzles N1, N13, pressure drag coefficients .......................................... 100 

Flap length for nozzles N1, N13, pressure coefficients .................................................. 101 

Sidewall boattail angle for nozzles N1, N5, N6, pressure drag coefficients ................... 102

Sidewall boattail angle for nozzles N1, N5, N6, pressure coefficients ........................... 103 

Sidewall radius of curvature for nozzles N5, N7, N9, pressure drag coefficients ........... 104

Sidewall radius of curvature for nozzles N5, N7, N9, pressure coefficients ................... 105 

Sidewall radius of curvature for nozzles N6, N8, N10, pressure drag coefficients ......... 106

Sidewall radius of curvature for nozzles N6, N8, N10, pressure coefficients ................. 107 

Reduced sidewall height for nozzles N1, N11, pressure drag coefficients ..................... 108 

Reduced sidewall height for nozzles N1, N11, pressure coefficients ............................. 109 

Reduced sidewall height for nozzles N2, N12, pressure drag coefficients ..................... 110

Reduced sidewall height for nozzles N2, N12, pressure coefficients ............................. 111 
 27 

Appendix G

Jet Effects Drag Data

This Appendix presents the jet-effects parameter ΔCD,p for each nozzle at both the design 

and scheduled pressure ratio NPR for each of the Mach numbers tested. The jet-effects parameter 

ΔCD,p data are presented for each nozzle in figures 112 to 125 as follows: 

Figure

Nozzle N1 ............................................................................................................................. 112 

Nozzle N2 ............................................................................................................................. 113 

Nozzle N3 ............................................................................................................................. 114 

Nozzle N4 ............................................................................................................................. 115 

Nozzle N5 ............................................................................................................................. 116 

Nozzle N6 ............................................................................................................................. 117 

Nozzle N7 ............................................................................................................................. 118 

Nozzle N8 ............................................................................................................................. 119 

Nozzle N9 ............................................................................................................................. 120 

Nozzle N10 ........................................................................................................................... 121 

Nozzle N11 ........................................................................................................................... 122 

Nozzle N12 ........................................................................................................................... 123 

Nozzle N13 ........................................................................................................................... 124 

Nozzle N14 ........................................................................................................................... 125 
 28 

Appendix H

External Pressure Distributions

This appendix presents the external pressure distributions for each nozzle. Pressure 

distributions measured along the top and bottom of the nozzle flaps as well as those on the 

nozzle sidewall are shown for each Mach number tested and are presented at four of the nozzle 

pressure ratios tested from jet-off (NPR = 1) to either NPR = 5 or 6.6 depending on Mach 

number in figures 126 to 139 as follows: 

Figure

Nozzle N1 ............................................................................................................................. 126 

Nozzle N2 ............................................................................................................................. 127 

Nozzle N3 ............................................................................................................................. 128 

Nozzle N4 ............................................................................................................................. 129 

Nozzle N5 ............................................................................................................................. 130 

Nozzle N6 ............................................................................................................................. 131 

Nozzle N7 ............................................................................................................................. 132 

Nozzle N8 ............................................................................................................................. 133 

Nozzle N9 ............................................................................................................................. 134 

Nozzle N10 ........................................................................................................................... 135 

Nozzle N11 ........................................................................................................................... 136 

Nozzle N12 ........................................................................................................................... 137 

Nozzle N13 ........................................................................................................................... 138 

Nozzle N14 ........................................................................................................................... 139 
 29 

References

1. Wilhite, Allan W.; and Shaw, Robert J.: An Overview of NASA's High Speed Research 

Program. 20th ICAS Congress, Paper112, August 2000. 

2. Capone, Francis J.: Static Performance of Five Twin-Engine Nonaxisymmetric Nozzles With 

Vectoring and Reversing Capability. NASA TP-1224, 1978. 

3. Capone, Francis J.; and Reubush, David E.: Effects of Varying Podded Nacelle-Nozzle 

Installations on Transonic Aeropropulsive Characteristics of a Supersonic Fighter Aircraft. 

NASA TP-2120, 1983. 

4. Leavitt, Laurence D.: Summary of Nonaxisymmetric Nozzle Internal Performance From the 

NASA Langley Static Test Facility. AIAA-85-1347, July 1985. 

5. Yetter, Jeffrey A.; and Leavitt, Laurence D.: Effects of Sidewall Geometry on the Installed 

Performance of Nonaxisymmetric Convergent-Divergent Nozzles. NASA TP 1771, 1980. 

6. Re, Richard J.; and Ingraldi, Anthony M.: Static Performance of Non-Axisymmetric 

Mixer/Ejector Nozzles With Hardwall and Acoustic Shrouds. NASA CDTM-10014, 1997. 

7. Stitt, Leonard E.: Exhaust Nozzles for Propulsion Systems with Emphasis on Supersonic 

Cruise Aircraft. NASA RP-1235, May 1990. 

8. Wallace, Hoyt; et al: Isolated and Installed Nozzle Boattail Drag Studies. NASA/CP-1999-

209691/VOL1/PT1. December 1999. 

9. Mercer, Charles E.; Berrier, Bobby L.; Capone, Francis J.; and Grayston, Alan M.: Data

Reduction Formulas for the Langley 16-Foot Transonic Tunnel: NASA Langley Research 

Center. NASA TM-107646, 1992. 

10. Staff of Propulsion Aerodynamics Branch: A User's Guide To the Langley 16-Foot Transonic 

Tunnel Complex, Revision 1. NASA TM-102750, rev. 1, 1990. (Supersedes NASA TM831865, Kathryn H. Peddrew, compiler.) 

11. Capone, Francis J.; Bangert, Linda S.; Asbury, Scott C.; Mills, Charles T.; and Bare, E. Ann: 

The NASA Langley 16-Foot Transonic Tunnel - Historical Overview, Facility Description, 

Calibration, Flow Characteristics, Test Capabilities. NASA TP-3521, 1995. 

12. Berrier, Bobby L.; Leavitt, Laurence D.; and Bangert, Linda S.: Operating Characteristics of 

the Multiple Critical Venturi System and Secondary Calibration Nozzles used for WeightFlow Measurements in the Langley 16-Foot Transonic Tunnel. NASA TM-86405, 1985. 

13. Abdol-Hamid, Khaled S.: Application of a Multiblock/Multizone Code (PAB3D) for the 

Three-Dimensional Navier-Stokes Equations. AIAA-91-2155, June 1991. 

14. Abdol-Hamid, Khaled S.: Implementation of Algebraic Stress Models in a General 3-D 

Navier-Stokes Method (PAB3D). NASA CR-4702. 1995. 

15. van Leer, B.: Flux-Vector Splitting for the Euler Equations. ICASE 1Report 82-30, 1982. 

16. Roe, P. L.: Characteristics Based Schemes for the Euler Equations. A Numerical Review of 

Fluid mechanics, 1986, pp. 337-365. 

17. Girimaji, S. S.: Fully-Explicit and Self-Consistent Algebraic Reynolds Stress Model. ICASE 

95-82, December 1995. 

18. Jones, W.P.; and Launder, B.E.: The Prediction of Laminarization with a Two-Equation 

Model of Turbulence. Int. J. Heat & Mass Trans., vol. 15, no. 2, Feb. 1972, pp. 301-314. 
 30 

19. Carlson, John R.: A Nozzle Internal Performance Prediction Method. NASA TP-3221, 1992. 

20. Ames Research Staff: Equations, Table and Charts for Compressible Flow. NACA Report 

1135, 1953. 

21. Pendergraft, Odis C. Jr.; Burley, James R. III.; and Bare, E. Ann: Parametric Study of 

Afterbody/Nozzle Drag on Twin Two-Dimensional Convergent Divergent Nozzles at Mach 

Numbers From 0.60 to 1.20. NASA TP 2640, 1986. 

22. Capone, Francis J.; Mason, Mary L.; and Leavitt, Laurence, D.: An Experimental 

Investigation of Thrust Vectoring Two-Dimensional Convergent-Divergent Nozzles Installed 

in a Twin-Engine Fighter Model at High Angles of Attack. NASA TM-4155, 1990. 

23. Compton, William B.: Comparison of Turbulence Models for Nozzle-Afterbody Flows With 

Propulsive Jets. NASA Technical Paper 3592, 1996. 
 31 

Table 1. Reference dimensions. 
 32 

(a). Conceptual HSCT airplane. 

(b). Comparison of full-scale nozzle to a man. 

Figure 1. Conceptual full-scale HSCT airplane exhaust nozzles. 
 33 

Supersonic Cruise (M = 2.4)

Centerbody

Divergent flap

Convergent flap

Reverser door

Subsonic Cruise (M = 0.9)

Fan/core mixer External flap

Sidewall

Takeoff

Ejector inlet doors

Ejector mixer

Figure 1. Sketches of full-scale nozzle concept at three flight conditions. (c). Sketches of full-scale nozzle concept at three flight conditions. 

Figure 1. Concluded 
 34 

Figure 2. Overall nozzle geometry. All linear dimensions in inches. 

2.017

13.136

MS 50.90

30°

1.91°

10.301

0.20 rad 2.703

5.946 6.200

5.494

2.835 0.654

6.800

0.654

5.492

Parameter

hm, in.

ht, in.

he, in

he /hm

At, in2

Ae, in2

Ae /At

Amax, in2

Ae /Amax

Value

6.200

2.017

2.703

0.436

14.846

11.079

1.34

40.064

0.36
 35 

Figure 3. Definition of nozzle flap geometric parameters. All linear dimensions in inches. 

Ln Lf

La,f x

y

ya,f

βf

rf , rf,max

hm/2

ht/2

he/2

Cylindrical Circular Arc Conical

Parameter F1 F2 F3 F4 F5 F6

0.4 0.1 0 1 0.4 0.1

16.38 12.88 11.72 23.44 20.30 15.97

1.4 1.4 1.4 1.4 1.1 1.1

13.136 13.136 13.136 13.136 13.136 13.136

8.423 8.423 8.423 8.423 6.739 6.739

4.856 1.548 0.0 8.423 3.904 1.245

2.401 2.925 3.100 1.353 2.401 2.925

43.059 69.421 83.835 21.179 28.142 45.254

17.224 6.942 0 21.179 11.257 4.525

Flap

Lf /hm

βf, deg 

rf /rf,max

Ln, in. 

Lf , in. 

La,f , in. 

ya,f , in. 

rf,max, in. 

rf , in. 
 36 

Figure 4. Definition of nozzle sidewall geometric parameters. All linear dimensions in inches. 

rs , rs,max

Ls

La,s βs

Ln

za,s

ze

x

z

Parameter S1 S2 S3 S4 S5 S6 S7 S8

4.0 6.0 8.0 6.0 8.0 6.0 8.0 4.0

0 0 0 0.1 0.1 0.4 1.0 0

13.136 13.136 13.136 13.136 13.136 13.136 13.136 13.136

9.055 6.024 4.505 6.630 4.960 7.357 9.055 9.055

0 0 0 1.208 0.906 4.209 9.055 0.000

0.654 0.654 0.654 0.590 0.590 0.433 0.020 0.654

0.020 0.020 0.020 0.020 0.020 0.102 0.020 0.020

259.96 115.53 104.34 115.65 65.10 100.73 65.10 260.09

0 0 0 11.565 6.510 40.292 65.102 0

Sidewall

s, deg 

rs /rs,max

Ln, in. 

Ls, in. 

La,s, in. 

za,s, in. 

rs,max, in. 

rs, in. 

ze, in. 
 37 

Figure 5. Summary of nozzle configurations tested. 

Nozzle

N3 F3 0 11.72 1.4 S1 4 0

N2 F2 0.1 12.88 1.4 S1 4 0

N1 F1 0.4 16.38 1.4 S1 4 0

N4 F4 1.0 24.44 1.4 S1 4 0

N14 F6 0.1 15.97 1.1 S1 4 0

N13 F5 0.4 20.30 1.1 S1 4 0

N5 F1 0.4 16.38 1.4 S2 6 0

N7 F1 0.4 16.38 1.4 S4 6 0.1

N9 F1 0.4 16.38 1.4 S6 6 0.4

N6 F1 0.4 16.38 1.4 S3 8 0

N8 F1 0.4 16.38 1.4 S5 8 0.1

N10 F1 0.4 16.38 1.4 S7 8 1.0

N12 F2 0.1 12.88 1.4 S8 4 0

N11 F1 0.4 16.38 1.4 S8 4 0

Nozzle Flap Nozzle Sidewall

Flap rf /rf,max Lf /hm rs

/rs,max

f, deg Sidewall s, deg 

Flap Sidewall
 38 

Figure 6. Sketches of nozzle configurations where the flap was varied. 

F2

Nozzle N2, r

f

/ rf,max = 0.1

F1

Nozzle N1, r

f

/ rf,max = 0.4

F3

Nozzle N3, r

f

/ rf,max = 0

Nozzles with L / h = 1.4, sidewall S1 f m

F4

Nozzle N4, r

f / rf,max = 1.0

F5

Nozzle N13, r

f / rf,max = 0.4

F6

Nozzle N14, r

f

/ rf,max = 0.1

Nozzles with Lf / hm = 1.1, sidewall S1

F1

Nozzle N11, r

f

/ rf,max = 0.4

F2

Nozzle N12, rf / rf,max = 0.1

Nozzles with Lf

/ h

m = 1.4, sidewall S8
 39 

Figure 7. Photographs of nozzles N1 and N11. 

Nozzle	N1 Nozzle	N11
 40 

Figure 8. Sketches of nozzle configurations where sidewall was varied. 

S1

Nozzle N1, βf = 4°

Nozzles with rs / rs,max = 0

S2

Nozzle N5, βf = 6°

S3

Nozzle N6, βf = 8°

S4

Nozzle N7, r

s

/ r

s,max

= 0.1

Nozzles with βf = 6°

S6

Nozzle N9, r

s / rs,max = 0.4

S7

Nozzle N10, r

s

/ r

s,max

= 1.0

S5

Nozzle N8, rs / rs,max = 0.1

Nozzles with βf = 8°
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

Figure 9. Static performance characteristics for all nozzles. 

41 

.5 

.6 

.7 

.8 

.9 

1.0 

F/Fi 

Nozzle 

N1 

N2 

N3 

N4 

N5 

N6 

N7 

N8 

N9 

N10 

N11 

N12 

N13 

N14 

Flap 

F1 

F2 

F3 

F4 

F1 

F1 

F1 

F1 

F1 

F1 

F1 

F2 

F6 

F5 

Lf /hm

1.4 

1.4 

1.4 

1.4 

1.4 

1.4 

1.4 

1.4 

1.4 

1.4 

1.4 

1.4 

1.1 

1.1 

rf /rf,max

0.4 

0.1 

0 

1.0 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.1 

0.4 

βf

, deg 

16.38 

12.88 

11.72 

23.48 

16.38 

16.38 

16.38 

16.38 

16.38 

16.38 

16.38 

16.38 

15.97 

20.30 

Sidewall 

S1 

S1 

S1 

S1 

S2 

S3 

S4 

S5 

S6 

S7 

S8 

S8 

S1 

S1 

rs /rs,max

0 

0 

0 

0 

0 

0 

0.1 

0.1 

0.4 

1.0 

0 

0 

0 

0 

βs

, deg 

4.0 

4.0 

4.0 

4.0 

6.0 

8.0 

6.0 

8.0 

6.0 

8.0 

4.0 

4.0 

4.0 

4.0 
5% thickness ratio parallel to

model centerline. 20.00 in. chord.

Airflow

8 equally spaced nozzles

exiting radially

6.00

2.0

Balance

Flexible seal

(metal bellows)

Support strut

MS 50.90

0.150 gap

Instrumentation

Choke plate

section

Transition

section

Nozzle Flaps

22.00

Tunnel

CL

High-pressure plenum

Total pressure rake Low-pressure plenum

45°

0.30c 0.40c 0.30c

MS 0.00 (Tunnel station 130.50 ft)

MS 26.5 MS 35.39

Thermocouple

MS 64.04

Airflow Nozzle Sidewall

Figure10. Propulsion simulation system with typical nozzle configuration installed. All linear dimensions are given in inches.

42
Figure 11. Model with nozzle N1 installed in the 16-Foot Transonic Tunnel.

43
0 1 2 3 4 5 6 7 

NPR 

0 

.0002 

.0004 

.0006 

CD,p,f 

Solid line is estimated mean value (curve fit) 

-.00005 

0 

.00005 

.00010 

∆CD,p,f 

Dashed line is 95% confidence interval 

0 1 2 3 4 5 6 7 

NPR 

0 

.0002 

.0004 

.0006 

CD,p,s 

Solid line is estimated mean value (curve fit) 

-.00005 

0 

.00005 

.00010 

∆CD,p,s 

Dashed line is 95% confidence interval 

Figure 12. Short term repeatability for flap and sidewall pressure drag 

coefficients for nozzle N1, M = 0.90. 

44 
45 

Figure 13. Residual and drag coefficient convergence history for nozzle N3. 

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

0

1

2

3

4

5

10-3

10-2

10-1

100

RMS

Cd

Nozzle N3 - Flap 3, Sidewall 1

βFL = 11.7° rc/rc,max = 0.0

βSW = 4.0° rc/rc,max = 0.0

PAB3D V13S - 3D grid

Girimaji ASM

444

422

222

442

M = 0.9, NPR = 5

Iterations

Aref(EFD)=6824.407 in2

Aref(CFD)=1 in2

CD

RMS 

Iteration

s 

M = 0.90, NPR = 5.0 

0 500 1000 1500 2000 2500 3000

5

6

7

8

9

10

10-4

10-3

10-2

10-1

100

RMS

Cd

Nozzle N3 - Flap 3, Sidewall 1

βFL = 11.7° rc/rc,max = 0.0

βSW = 4.0° rc/rc,max = 0.0

PAB3D V13S - 3D grid

Girimaji ASM 222

Aref(CFD)=1 in2

Aref(Exp)=6824.407 in2

M = 1.2, NPR = 5.0

CD

RMS 

M = 1.20, NPR = 5.0 

Iterations 
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 14. Aeropropulsive performance for nozzle N1 with flap F1 and sidewall S1. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 4.0°; rs /rs,max = 0. 

46 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 14. Continued. 

47 

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 14. Continued. 

48 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

M 

0.80 

0.90 

0.95 

1.20 

CD,p = CD,p,f + CD,p,s 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 14. Concluded. 

49 

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

CD,pf = CD,p + CD,f 

0 

.0005 

.0010 

.0015 

.0020 

.0025 

CD,n 

M 

0.80 

0.90 

0.95 

1.20 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 5 

Figure 15. Comparison of experimental to predicted flap pressures for 

nozzle N1. rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4. 

50 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap Pressure Row 

EFD Centerline 

EFD Mid 

EFD Outboard 

CFD Centerline 

CFD Mid 

CFD Outboard 

M = 0.90, NPR = 5 
Figure 16. Comparison of experimental to predicted nozzle drag coefficients

 for nozzle N1. rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; NPR = 5.0.

51

CFD

EFD

Sidewall Flap Nozzle Sidewall Flap Nozzle

M = 0.90 M = 1.20

CD,p

CFD

EFD - CD,p + CD,f

EFD - Balance Measurement

M = 0.90 M = 1.20

CD,n
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 5 

Figure 17. Comparison of experimental and predicted flap pressures for 

nozzle N3. rf /rf,max = 0; βf = 11.72°; Lf /hm = 1.4. 

52 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap Pressure Row 

EFD Centerline 

EFD Mid 

EFD Outboard 

CFD Centerline 

CFD Mid 

CFD Outboard 

M = 0.90, NPR = 5 
Figure 18. Comparison of experimental to predicted nozzle drag coefficients

 for nozzle N3. rf /rf,max = 0; βf = 11.72°; Lf /hm = 1.4; NPR = 5.0.

53

Sidewall Flap Nozzle Sidewall Flap Nozzle

M = 0.90 M = 1.20

CFD

EFD

CD,p

CFD

EFD - CD,p + CD,f

EFD - Balance Measurement

M = 0.90 M = 1.20

CD,n
Figure 19. Effect of flap radius of curvature on pressure drag coefficients for

 nozzles with sidewall S1 at design NPR.

M = 0.80

NPR = 5.0

M = 0.90

NPR = 5.0

M = 0.95

NPR = 5.0

M = 1.20

NPR = 5.0

CD,p,f

0.0004

0.0002

0

CD,p,s

-0.0002

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p

-0.0002

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

F1

F2 F3

F4 S1

Nozzle Flap rf /rf,max βf , deg Lf /hm Sidewall rs /rs,max βs , deg

N3

N2

N1

N4

F3

F2

F1

F4

0

0.1

0.4

1.0

11.72

12.88

16.38

23.48

1.4

1.4

1.4

1.4

S1

S1

S1

S1

0

0

0

0

4.0

4.0

4.0

4.0

54
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Nozzle 

N3 

N2 

N1 

N4 

Flap 

F3 

F2 

F1 

F4 

rf /rf,max

0 

0.1 

0.4 

1.0 

βf, deg 

11.72 

12.88 

16.38 

23.48 

Lf /hm

1.4 

1.4 

1.4 

1.4 

Sidewall 

S1 

S1 

S1 

S1 

rs /rs,max

0 

0 

0 

0 

βs, deg 

4.0 

4.0 

4.0 

4.0 

M = 0.80, NPR = 4.99 

Flap top center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 4.97 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 5.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 5.01 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.80, NPR = 4.99 

Flap top outboard row, z/wf /2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 4.97 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 5.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 5.01 

Figure 20. Effect of flap radius of curvature on upper flap pressure distributions for 

nozzles with sidewall S1 at design NPR. 

55 
Figure 21. Effect of flap radius of curvature on pressure drag coefficients

 for nozzles with sidewall S1 at design NPR.

56

M = 0.80

NPR = 5.0

M = 0.90

NPR = 5.0

M = 0.95

NPR = 5.0

M = 1.20

NPR = 5.0

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p,f

0.0004

0.0002

0

CD,p,s

CD,p

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

S1

F6

F5

Nozzle Flap rf /rf,max βf , deg Lf /hm Sidewall rs /rs,max βs , deg

N14

N13

F6

F5

0.1

0.4

15.97

20.30

1.1

1.1

S1

S1

0

0

4.0

4.0
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Nozzle 

N14 

N13 

Flap 

F6 

F5 

rf /rf,max

0.1 

0.4 

βf

, deg 

15.97 

20.30 

Lf /hm

1.1 

1.1 

Sidewall 

S1 

S1 

rs /rs,max

0 

0 

βs

, deg 

4.0 

4.0 

M = 0.80, NPR = 5.06 

Flap top center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 4.97 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 5.01 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 5.03 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.80, NPR = 5.06 

Flap top outboard row, z/wf /2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 4.97 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 5.01 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 5.03 

Figure 22. Effect of flap radius of curvature on upper flap pressure distributions for 

nozzles with sidewall S1 at design NPR. 

57 
Figure 23. Effect of flap length on pressure drag coefficients for nozzles with

 sidewall S1 at design NPR.

 58

M = 0.80

NPR = 5.0

M = 0.90

NPR = 5.0

M = 0.95

NPR = 5.0

M = 1.20

NPR = 5.0

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p,f

0.0004

0.0002

0

CD,p,s

CD,p

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

S1 F2 F6

Nozzle Flap rf /rf,max βf , deg Lf /hm Sidewall rs /rs,max βs , deg

N2

N14

F2

F6

0.1

0.1

12.88

15.97

1.4

1.1

S1

S1

0

0

4.0

4.0
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Nozzle 

N2 

N14 

Flap 

F2 

F6 

Lf /hm

1.4 

1.1 

βf

, deg 

12.88 

15.97 

rf /rf,max

0.1 

0.1 

Sidewall 

S1 

S1 

rs /rs,max

0 

0 

βs

, deg 

4.0 

4.0 

M = 0.80, NPR = 5.04 

Flap top center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 5.02 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 5.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 4.99 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.80, NPR = 5.04 

Flap top outboard row, z/wf /2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 5.02 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 5.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 4.99 

Figure 24. Effect of flap length on upper flap pressure distributions for nozzles with 

sidewall S1 at design NPR. 

59 
Figure 25. Effect of flap length on pressure drag coefficients for nozzles with

 sidewall S1 at design NPR.

 60

0.0004

0.0002

0

CD,p,s

M = 0.80

NPR = 5.0

M = 0.90

NPR = 5.0

M = 0.95

NPR = 5.0

M = 1.20

NPR = 5.0

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p,f

CD,p

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

F1

F5

S1

Nozzle Flap rf /rf,max βf , deg Lf /hm Sidewall rs /rs,max βs , deg

N1

N13

F1

F5

0.4

0.4

16.38

20.30

1.4

1.1

S1

S1

0

0

4.0

4.0
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Nozzle 

N1 

N13 

Flap 

F1 

F5 

Lf /hm

1.4 

1.1 

βf

, deg 

16.38 

20.30 

rf /rf,max

0.4 

0.4 

Sidewall 

S1 

S1 

rs /rs,max

0 

0 

βs

, deg 

4.0 

4.0 

M = 0.80, NPR = 5.02 

Flap top center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 4.97 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 5.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 5.04 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.80, NPR = 5.02 

Flap top outboard row, z/wf /2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 4.97 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 5.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 5.04 

Figure 26. Effect of flap length on upper flap pressure distributions for nozzles with 

sidewall S1 at design NPR. 

61 
Figure 27. Effect of sidewall boattail angle on pressure drag coefficients for

 nozzles with flap F1 at design nozzle pressure ratio.

 62

0.0004

0.0002

0

CD,p,s

 Nozzle Sidewall βs , deg rs /rs,max Flap Lf /hm rf /rf,max βf , deg

 N1 S1 4.0 0 F1 1.4 0.4 16.38

 N5 S2 6.0 0 F1 1.4 0.4 16.38

 N6 S3 8.0 0 F1 1.4 0.4 16.38

M = 0.80

NPR = 5.0

M = 0.90

NPR = 5.0

M = 0.95

NPR = 5.0

M = 1.20

NPR = 5.0

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p,f

CD,p

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

S1 S3

S2
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

Nozzle 

N1 

N5 

N6 

Sidewall 

S1 

S2 

S3 

βs

, deg 

4.0 

6.0 

8.0 

rs /rs,max

0 

0 

0 

Flap 

F1 

F1 

F1 

Lf /hm

1.4 

1.4 

1.4 

rf /rf,max

0.4 

0.4 

0.4 

βf

, deg 

16.38 

16.38 

16.38 

M = 0.80, NPR = 4.99 

Sidewall center row, y/hm /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.90, NPR = 5.01 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.95, NPR = 5.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 1.20, NPR = 5.01 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.80, NPR = 4.99 

Sidewall outboard row, y/hm /2 = 0.87 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.90, NPR = 5.01 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.95, NPR = 5.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 1.20, NPR = 5.01 

Figure 28. Effect of sidewall boattail angle on sidewall pressure distributions for nozzles 

with flap F1 at design NPR. 

63 
Figure 29. Effect of sidewall radius of curvature and base on pressure drag

 coefficients for nozzles with flap F1 at design NPR.

 64

0.0004

0.0002

0

CD,p,s

 Nozzle Sidewall rs /rs,max βs , deg Flap Lf /hm rf /rf,max βf , deg

 N5 S2 0 6.0 F1 1.4 0.4 16.38

 N7 S4 0.1 6.0 F1 1.4 0.4 16.38

 N9 S6 0.4 6.0 F1 1.4 0.4 16.38

M = 0.80

NPR = 5.0

M = 0.90

NPR = 5.0

M = 0.95

NPR = 5.0

M = 1.20

NPR = 5.0

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p,f

CD,p

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

S6

S4 S2
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

Nozzle 

N5 

N7 

N9 

Sidewall 

S2 

S4 

S6 

rs /rs,max

0 

0.1 

0.4 

βs

, deg 

6.0 

6.0 

6.0 

Flap 

F1 

F1 

F1 

Lf /hm

1.4 

1.4 

1.4 

rf /rf,max

0.4 

0.4 

0.4 

βf

, deg 

16.38 

16.38 

16.38 

M = 0.80, NPR = 4.99 

Sidewall center row, y/hm /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.90, NPR = 5.03 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.95, NPR = 5.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 1.20, NPR = 5.03 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.80, NPR = 4.99 

Sidewall outboard row, y/hm /2 = 0.87 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.90, NPR = 5.03 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.95, NPR = 5.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 1.20, NPR = 5.03 

Figure 30. Effect of sidewall radius of curvature and base on sidewall pressure 

distributions for nozzles with flap F1 at design NPR. 

65 
Figure 31. Effect of sidewall radius of curvature on pressure drag coefficients for

 nozzles with flap F1 at design NPR.

 66

0.0004

0.0002

0

CD,p,s

 Nozzle Sidewall rs /rs,max βs , deg Flap Lf /hm rf /rf,max βf , deg

 N6 S3 0 8.0 F1 1.4 0.4 16.38

 N8 S5 0.1 8.0 F1 1.4 0.4 16.38

 N10 S7 1.0 8.0 F1 1.4 0.4 16.38

M = 0.80

NPR = 5.0

M = 0.90

NPR = 5.0

M = 0.95

NPR = 5.0

M = 1.20

NPR = 5.0

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p,f

CD,p

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

S7

S3

S5
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

Nozzle 

N6 

N8 

N10 

Sidewall 

S3 

S5 

S7 

rs /rs,max

0 

0.1 

1.0 

βs

, deg 

8.0 

8.0 

8.0 

Flap 

F1 

F1 

F1 

Lf /hm

1.4 

1.4 

1.4 

rf /rf,max

0.4 

0.4 

0.4 

βf

, deg 

16.38 

16.38 

16.38 

M = 0.80, NPR = 5.01 

Sidewall center row, y/hm /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.90, NPR = 5.01 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.95, NPR = 5.05 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 1.20, NPR = 5.01 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.80, NPR = 5.01 

Sidewall outboard row, y/hm /2 = 0.87 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.90, NPR = 5.01 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.95, NPR = 5.05 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 1.20, NPR = 5.01 

Figure 32. Effect of sidewall radius of curvature on sidewall pressure distributions for 

nozzles with flap F1 at design NPR. 

67 
Figure 33. Effect of reduced sidewall height on pressure drag coefficients for

 nozzles with flap F1 at design NPR.

 68

0.0004

0.0002

0

CD,p,s

 Nozzle Sidewall βs , deg rs /rs,max Flap Lf /hm rf /rf,max βf , deg

 N1 S1 4.0 0 F1 1.4 0.4 16.38

 N11 S8 4.0 0 F1 1.4 0.4 16.38

M = 0.80

NPR = 5.0

M = 0.90

NPR = 5.0

M = 0.95

NPR = 5.0

M = 1.20

NPR = 5.0

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p,f

CD,p

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

F1 S8 S1
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Nozzle 

N1 

N11 

Sidewall 

S1 

S8 

βs

, deg 

4.0 

4.0 

rs /rs,max

0 

0 

Flap 

F1 

F1 

Lf /hm

1.4 

1.4 

rf /rf,max

0.4 

0.4 

βf

, deg 

16.38 

16.38 

M = 0.80, NPR = 4.97 

Flap top center row, z/wf /2 = 0 

S1 

F1 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 5.01 

S1 

F1 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 4.97 

S1 

F1 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 5.51 

S1 

F1 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.80, NPR = 4.97 

Flap top outboard row, z/wf /2 = 0.95 

S1 

F1 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 5.01 

S1 

F1 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 4.97 

S1 

F1 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 4.99 

S1 

F1 S8 

(a) Flap pressure distributions. 

Figure 34. Effect of reduced sidewall height on nozzle pressure distributions for nozzles 

with flap F1 at design NPR. 

69 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

Nozzle 

N1 

N11 

Sidewall 

S1 

S8 

βs

, deg 

4.0 

4.0 

rs /rs,max

0 

0 

Flap 

F1 

F1 

Lf /hm

1.4 

1.4 

rf /rf,max

0.4 

0.4 

βf

, deg 

16.38 

16.38 

M = 0.80, NPR = 4.97 

Sidewall center row, y/hm /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.90, NPR = 5.01 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.95, NPR = 4.26 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 1.20, NPR = 5.78 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.80, NPR = 4.24 

Sidewall outboard row, y/hm /2 = 0.87 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.90, NPR = 4.26 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.95, NPR = 4.97 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 1.20, NPR = 4.99 

(b) Sidewall pressure distributions. 

Figure 34. Concluded. 

70 
Figure 35. Effect of reduced sidewall height on pressure drag coefficients for

 nozzles with flap F2 at design NPR.

 71

M = 0.80

NPR = 5.0

M = 0.90

NPR = 5.0

M = 0.95

NPR = 5.0

M = 1.20

NPR = 5.0

CD,p,f

0.0004

0.0002

0

CD,p,s

-0.0002

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p

-0.0002

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

 Nozzle Sidewall βs , deg rs /rs,max Flap Lf /hm rf /rf,max βf , deg

 N2 S1 4.0 0 F2 1.4 0.1 12.88

 N12 S8 4.0 0 F2 1.4 0.1 12.88

S1

S8

F2
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Nozzle 

N2 

N12 

Sidewall 

S1 

S8 

βs

, deg 

4.0 

4.0 

rs /rs,max

0 

0 

Flap 

F2 

F2 

Lf /hm

1.4 

1.4 

rf /rf,max

0.1 

0.1 

βf

, deg 

12.88 

12.88 

M = 0.80, NPR = 3.53 

Flap top center row, z/wf /2 = 0 

S1 

F2 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 3.54 

S1 

F2 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 3.54 

S1 

F2 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 6.67 

S1 

F2 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.80, NPR = 3.53 

Flap top outboard row, z/wf /2 = 0.95 

S1 

F2 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 3.54 

S1 

F2 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 3.54 

S1 

F2 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 6.67 

S1 

F2 S8 

(a) Flap pressure distributions. 

Figure 36. Effect of reduced sidewall height on upper flap pressure distributions for nozzles 

with flap F2 at design NPR. 

72 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

Nozzle 

N2 

N12 

Sidewall 

S1 

S8 

βs

, deg 

4.0 

4.0 

rs /rs,max

0 

0 

Flap 

F2 

F2 

Lf /hm

1.4 

1.4 

rf /rf,max

0.1 

0.1 

βf

, deg 

12.88 

12.88 

M = 0.80, NPR = 3.53 

Sidewall center row, y/hm /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.90, NPR = 3.54 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.95, NPR = 3.54 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 1.20, NPR = 6.67 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.80, NPR = 3.53 

Sidewall outboard row, y/hm /2 = 0.87 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.90, NPR = 3.54 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.95, NPR = 3.54 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 1.20, NPR = 6.67 

(b) Sidewall pressure distributions at design NPR. 

Figure 36. Concluded. 

73 
74

Figure 37. Flap F1 external coordinates and location of pressure orifices.

1.000 0.000 0.000 0.000 0.000

1.000 0.231 CPF26 0.231 CPF1 0.225 CPF51 0.226 CPF76

1.000 0.296 CPF27 0.295 CPF2 0.288 CPF52 0.289 CPF77

1.000 0.327 CPF28 0.327 CPF3 0.322 CPF53 0.322 CPF78

1.000 0.359 CPF29 0.359 CPF4 0.354 CPF54 0.353 CPF79

1.000 0.366 CPF30 0.366 CPF5 0.361 CPF55 0.360 CPF80

1.000 0.375 CPF31 0.376 CPF6 0.370 CPF56 0.370 CPF81

0.998 0.391 CPF32 0.391 CPF7 0.386 CPF57 0.385 CPF82

0.993 0.423 CPF33 0.423 CPF8 0.418 CPF58 0.418 CPF83

0.985 0.456 CPF34 0.456 CPF9 0.450 CPF59 0.451 CPF84

0.973 0.488 CPF35 0.488 CPF10 0.483 CPF60 0.483 CPF85

0.958 0.520 CPF36 0.520 CPF11 0.515 CPF61 0.514 CPF86

0.939 0.552 CPF37 0.552 CPF12 0.546 CPF62 0.548 CPF87

0.918 0.584 CPF38 0.585 CPF13 0.580 CPF63 0.580 CPF88

0.892 0.616 CPF39 0.616 CPF14 0.612 CPF64 0.611 CPF89

0.863 0.648 CPF40 0.648 CPF15 0.644 CPF65 0.643 CPF90

0.831 0.680 CPF41 0.680 CPF16 0.676 CPF66 0.676 CPF91

0.795 0.712 CPF42 0.712 CPF17 0.709 CPF67 0.709 CPF92

0.755 0.744 CPF43 0.743 CPF18 0.742 CPF68 0.741 CPF93

0.716 0.775 CPF44 0.775 CPF19 0.773 CPF69 0.774 CPF94

0.675 0.808 CPF45 0.807 CPF20 0.806 CPF70 0.806 CPF95

0.634 0.841 CPF46 0.839 CPF21 0.839 CPF71 0.838 CPF96

0.595 0.872 CPF47 0.872 CPF22 0.872 CPF72 0.871 CPF97

0.556 0.904 CPF48 0.903 CPF23 0.905 CPF73 0.902 CPF98

0.516 0.936 CPF49 0.936 CPF24 0.938 CPF74 0.935 CPF99

0.476 0.968 CPF50 0.968 CPF25 0.969 CPF75 0.964 CPF100

0.436 1.000 1.000 1.000 1.000

Top

centerline

z/wf /2 = 0

y/hm/2 x/Ln orifice x/Ln x/Ln x/Ln orifice orifice orifice

Top

outboard

z/wf /2 = 0.95

Bottom

middle

z/wf /2 = 0.5

Bottom

centerline

z/wf /2 = 0

Ln

MS 50.90

Circular Arc Straight

x

ym /2

y

z/wf /2 = 0

z/ wf /2 = 0.5

z/wf /2 = 0.95

z/wf /2 = 0

y/hm/2
75

Figure 38. Flap F2 external coordinates and location of pressure orifices.

1.000 0.000 0.000 0.000 0.000

1.000 0.231 CPF26 0.231 CPF1 0.232 CPF51 0.229 CPF76

1.000 0.296 CPF27 0.295 CPF2 0.295 CPF52 0.295 CPF77

1.000 0.327 CPF28 0.327 CPF3 0.326 CPF53 0.327 CPF78

1.000 0.359 CPF29 0.359 CPF4 0.357 CPF54 0.358 CPF79

1.000 0.366 CPF30 0.366 CPF5 0.366 CPF55 0.365 CPF80

1.000 0.375 CPF31 0.376 CPF6 0.373 CPF56 0.375 CPF81

0.998 0.391 CPF32 0.391 CPF7 0.390 CPF57 0.390 CPF82

0.993 0.423 CPF33 0.423 CPF8 0.418 CPF58 0.420 CPF83

0.985 0.456 CPF34 0.456 CPF9 0.454 CPF59 0.456 CPF84

0.973 0.488 CPF35 0.488 CPF10 0.486 CPF60 0.485 CPF85

0.958 0.520 CPF36 0.520 CPF11 0.518 CPF61 0.519 CPF86

0.939 0.552 CPF37 0.552 CPF12 0.549 CPF62 0.550 CPF87

0.918 0.584 CPF38 0.585 CPF13 0.580 CPF63 0.583 CPF88

0.892 0.616 CPF39 0.616 CPF14 0.614 CPF64 0.614 CPF89

0.863 0.648 CPF40 0.648 CPF15 0.651 CPF65 0.647 CPF90

0.831 0.680 CPF41 0.680 CPF16 0.678 CPF66 0.679 CPF91

0.795 0.712 CPF42 0.712 CPF17 0.707 CPF67 0.712 CPF92

0.755 0.744 CPF43 0.743 CPF18 0.743 CPF68 0.743 CPF93

0.716 0.775 CPF44 0.775 CPF19 0.773 CPF69 0.777 CPF94

0.675 0.808 CPF45 0.807 CPF20 0.807 CPF70 0.807 CPF95

0.634 0.841 CPF46 0.839 CPF21 0.838 CPF71 0.840 CPF96

0.595 0.872 CPF47 0.872 CPF22 0.872 CPF72 0.873 CPF97

0.556 0.904 CPF48 0.903 CPF23 0.904 CPF73 0.904 CPF98

0.516 0.936 CPF49 0.936 CPF24 0.935 CPF74 0.936 CPF99

0.476 0.968 CPF50 0.968 CPF25 0.968 CPF75 0.968 CPF100

0.436 1.000 1.000 1.000 1.000

Top

centerline

z/wf /2 = 0

y/hm/2 x/Ln orifice x/Ln x/Ln x/Ln orifice orifice orifice

Top

outboard

z/wf /2 = 0.95

Bottom

middle

z/wf /2 = 0.5

Bottom

centerline

z/wf /2 = 0

y/hm/2
76

Figure 39. Flap F3 external coordinates and location of pressure orifices.

Top

centerline

z/wf /2 = 0

y/hm/2 x/Ln orifice x/Ln x/Ln x/Ln orifice orifice orifice

Top

outboard

z/wf /2 = 0.95

Bottom

middle

z/wf /2 = 0.5

Bottom

centerline

z/wf /2 = 0

1.000 0.000 0.000 0.000 0.000

1.000 0.231 CPF26 0.231 CPF1 0.225 CPF51 0.226 CPF76

1.000 0.296 CPF27 0.295 CPF2 0.288 CPF52 0.289 CPF77

1.000 0.327 CPF28 0.327 CPF3 0.322 CPF53 0.322 CPF78

0.992 0.366 CPF30 0.366 CPF5 0.361 CPF55 0.360 CPF80

0.985 0.375 CPF31 0.376 CPF6 0.370 CPF56 0.370 CPF81

0.970 0.391 CPF32 0.391 CPF7 0.386 CPF57 0.385 CPF82

0.942 0.423 CPF33 0.423 CPF8 0.418 CPF58 0.418 CPF83

0.914 0.456 CPF34 0.456 CPF9 0.450 CPF59 0.451 CPF84

0.887 0.488 CPF35 0.488 CPF10 0.483 CPF60 0.483 CPF85

0.858 0.520 CPF36 0.520 CPF11 0.515 CPF61 0.514 CPF86

0.829 0.552 CPF37 0.552 CPF12 0.546 CPF62 0.548 CPF87

0.801 0.584 CPF38 0.585 CPF13 0.580 CPF63 0.580 CPF88

0.773 0.616 CPF39 0.616 CPF14 0.612 CPF64 0.611 CPF89

0.745 0.648 CPF40 0.648 CPF15 0.644 CPF65 0.643 CPF90

0.717 0.680 CPF41 0.680 CPF16 0.676 CPF66 0.676 CPF91

0.690 0.712 CPF42 0.712 CPF17 0.709 CPF67 0.709 CPF92

0.662 0.744 CPF43 0.743 CPF18 0.742 CPF68 0.741 CPF93

0.633 0.775 CPF44 0.775 CPF19 0.773 CPF69 0.774 CPF94

0.604 0.808 CPF45 0.807 CPF20 0.806 CPF70 0.806 CPF95

0.576 0.841 CPF46 0.839 CPF21 0.839 CPF71 0.838 CPF96

0.549 0.872 CPF47 0.872 CPF22 0.872 CPF72 0.871 CPF97

0.520 0.904 CPF48 0.903 CPF23 0.905 CPF73 0.902 CPF98

0.492 0.936 CPF49 0.936 CPF24 0.938 CPF74 0.935 CPF99

0.463 0.968 CPF50 0.968 CPF25 0.969 CPF75 0.964 CPF100

0.436 1.000 1.000 1.000 1.000
77

Figure 40. Flap F4 external coordinates and location of pressure orifices.

1.000 0.000 0.000 0.000 0.000

1.000 0.231 CPF26 0.226 CPF1 0.229 CPF51 0.229 CPF76

1.000 0.295 CPF27 0.290 CPF2 0.293 CPF52 0.295 CPF77

1.000 0.326 CPF28 0.323 CPF3 0.326 CPF53 0.327 CPF78

1.000 0.359 CPF29 0.354 CPF4 0.358 CPF54 0.358 CPF79

1.000 0.364 CPF30 0.360 CPF5 0.365 CPF55 0.365 CPF80

1.000 0.374 CPF31 0.371 CPF6 0.374 CPF56 0.375 CPF81

0.999 0.387 CPF32 0.386 CPF7 0.390 CPF57 0.390 CPF82

0.995 0.423 CPF33 0.420 CPF8 0.421 CPF58 0.420 CPF83

0.988 0.456 CPF34 0.451 CPF9 0.457 CPF59 0.456 CPF84

0.979 0.486 CPF35 0.485 CPF10 0.486 CPF60 0.485 CPF85

0.966 0.520 CPF36 0.515 CPF11 0.520 CPF61 0.519 CPF86

0.952 0.550 CPF37 0.548 CPF12 0.550 CPF62 0.550 CPF87

0.933 0.583 CPF38 0.580 CPF13 0.583 CPF63 0.583 CPF88

0.913 0.616 CPF39 0.612 CPF14 0.616 CPF64 0.614 CPF89

0.889 0.648 CPF40 0.646 CPF15 0.647 CPF65 0.647 CPF90

0.862 0.681 CPF41 0.677 CPF16 0.678 CPF66 0.679 CPF91

0.832 0.714 CPF42 0.710 CPF17 0.715 CPF67 0.712 CPF92

0.803 0.744 CPF43 0.742 CPF18 0.744 CPF68 0.743 CPF93

0.768 0.776 CPF44 0.774 CPF19 0.776 CPF69 0.777 CPF94

0.731 0.807 CPF45 0.805 CPF20 0.808 CPF70 0.807 CPF95

0.685 0.843 CPF46 0.839 CPF21 0.841 CPF71 0.840 CPF96

0.643 0.873 CPF47 0.871 CPF22 0.874 CPF72 0.873 CPF97

0.596 0.905 CPF48 0.902 CPF23 0.904 CPF73 0.904 CPF98

0.545 0.937 CPF49 0.934 CPF24 0.936 CPF74 0.936 CPF99

0.499 0.965 CPF50 0.968 CPF25 0.968 CPF75 0.968 CPF100

0.436 1.000 1.000 1.000 1.000

Top

centerline

z/wf /2 = 0

y/hm/2 x/Ln orifice x/Ln x/Ln x/Ln orifice orifice orifice

Top

outboard

z/wf /2 = 0.95

Bottom

middle

z/wf /2 = 0.5

Bottom

centerline

z/wf /2 = 0

y/hm/2
78

Figure 41. Flap F5 external coordinates and location of pressure orifices

1.000 0.000 0.000 0.000 0.000

1.000 0.383 CPF26 0.384 CPF1 0.382 CPF51 0.385 CPF76

1.000 0.435 CPF27 0.435 CPF2 0.438 CPF52 0.435 CPF77

1.000 0.461 CPF28 0.460 CPF3 0.461 CPF53 0.461 CPF78

1.000 0.487 CPF29 0.487 CPF4 0.486 CPF54 0.484 CPF79

1.000 0.492 CPF30 0.492 CPF5 0.492 CPF55 0.490 CPF80

1.000 0.500 CPF31 0.499 CPF6 0.501 CPF56 0.501 CPF81

0.998 0.513 CPF32 0.513 CPF7 0.514 CPF57 0.514 CPF82

0.993 0.539 CPF33 0.539 CPF8 0.538 CPF58 0.538 CPF83

0.985 0.564 CPF34 0.563 CPF9 0.565 CPF59 0.565 CPF84

0.974 0.590 CPF35 0.589 CPF10 0.590 CPF60 0.591 CPF85

0.958 0.616 CPF36 0.615 CPF11 0.616 CPF61 0.617 CPF86

0.940 0.642 CPF37 0.641 CPF12 0.641 CPF62 0.642 CPF87

0.919 0.667 CPF38 0.667 CPF13 0.667 CPF63 0.667 CPF88

0.893 0.694 CPF39 0.692 CPF14 0.694 CPF64 0.695 CPF89

0.865 0.719 CPF40 0.718 CPF15 0.721 CPF65 0.720 CPF90

0.833 0.744 CPF41 0.744 CPF16 0.743 CPF66 0.746 CPF91

0.797 0.770 CPF42 0.768 CPF17 0.769 CPF67 0.771 CPF92

0.758 0.795 CPF43 0.794 CPF18 0.795 CPF68 0.794 CPF93

0.717 0.821 CPF44 0.820 CPF19 0.822 CPF69 0.822 CPF94

0.676 0.847 CPF45 0.845 CPF20 0.846 CPF70 0.848 CPF95

0.635 0.873 CPF46 0.871 CPF21 0.872 CPF71 0.873 CPF96

0.596 0.898 CPF47 0.897 CPF22 0.899 CPF72 0.899 CPF97

0.554 0.925 CPF48 0.923 CPF23 0.925 CPF73 0.924 CPF98

0.515 0.950 CPF49 0.948 CPF24 0.950 CPF74 0.950 CPF99

0.477 0.974 CPF50 0.974 CPF25 0.975 CPF75 0.976 CPF100

0.436 1.000 1.000 1.000 1.000

Top

centerline

z/wf /2 = 0

y/hm/2 x/Ln orifice x/Ln x/Ln x/Ln orifice orifice orifice

Top

outboard

z/wf /2 = 0.95

Bottom

middle

z/wf /2 = 0.5

Bottom

centerline

z/wf /2 = 0

y/hm/2
79

Figure 42. Flap F6 external coordinates and location of pressure orifices

1.000 0.000 0.000 0.000 0.000

1.000 0.385 CPF26 0.386 CPF1 0.386 CPF51 0.384 CPF76

1.000 0.435 CPF27 0.437 CPF2 0.438 CPF52 0.437 CPF77

1.000 0.463 CPF28 0.462 CPF3 0.462 CPF53 0.461 CPF78

1.000 0.487 CPF29 0.487 CPF4 0.489 CPF54 0.487 CPF79

1.000 0.492 CPF30 0.492 CPF5 0.495 CPF55 0.491 CPF80

0.999 0.501 CPF31 0.499 CPF6 0.502 CPF56 0.500 CPF81

0.996 0.513 CPF32 0.512 CPF7 0.514 CPF57 0.513 CPF82

0.984 0.537 CPF33 0.538 CPF8 0.542 CPF58 0.540 CPF83

0.964 0.563 CPF34 0.564 CPF9 0.566 CPF59 0.567 CPF84

0.934 0.589 CPF35 0.589 CPF10 0.591 CPF60 0.591 CPF85

0.903 0.615 CPF36 0.614 CPF11 0.619 CPF61 0.616 CPF86

0.872 0.641 CPF37 0.641 CPF12 0.644 CPF62 0.644 CPF87

0.839 0.668 CPF38 0.667 CPF13 0.668 CPF63 0.667 CPF88

0.810 0.692 CPF39 0.691 CPF14 0.694 CPF64 0.692 CPF89

0.778 0.718 CPF40 0.717 CPF15 0.719 CPF65 0.720 CPF90

0.747 0.743 CPF41 0.743 CPF16 0.746 CPF66 0.747 CPF91

0.716 0.769 CPF42 0.769 CPF17 0.768 CPF67 0.770 CPF92

0.686 0.794 CPF43 0.794 CPF18 0.798 CPF68 0.797 CPF93

0.654 0.820 CPF44 0.820 CPF19 0.823 CPF69 0.822 CPF94

0.622 0.847 CPF45 0.846 CPF20 0.846 CPF70 0.847 CPF95

0.592 0.872 CPF46 0.871 CPF21 0.873 CPF71 0.874 CPF96

0.561 0.897 CPF47 0.898 CPF22 0.898 CPF72 0.899 CPF97

0.529 0.924 CPF48 0.923 CPF23 0.927 CPF73 0.924 CPF98

0.497 0.950 CPF49 0.949 CPF24 0.948 CPF74 0.949 CPF99

0.467 0.975 CPF50 0.975 CPF25 0.973 CPF75 0.974 CPF100

0.436 1.000 1.000 1.000 1.000

Top

centerline

z/wf /2 = 0

y/hm/2 x/Ln orifice x/Ln x/Ln x/Ln orifice orifice orifice

Top

outboard

z/wf /2 = 0.95

Bottom

middle

z/wf /2 = 0.5

Bottom

centerline

z/wf /2 = 0

y/hm/2
80

Figure 43. Sidewall S1 external coordinates and location of pressure orifices

1.000 0.000 0.000

1.000 0.173 CPS1 0.173 CPS21

1.000 0.242 CPS2 0.241 CPS22

1.000 0.276 CPS3 0.276 CPS23

0.958 0.318 CPS5 0.316 CPS25

0.943 0.328 CPS6 0.328 CPS26

0.920 0.344 CPS7 0.345 CPS27

0.872 0.379 CPS8 0.380 CPS28

0.823 0.414 CPS9 0.413 CPS29

0.774 0.448 CPS10 0.448 CPS30

0.728 0.481 CPS11 0.482 CPS31

0.679 0.516 CPS12 0.518 CPS32

0.581 0.586 CPS13 0.585 CPS33

0.484 0.655 CPS14 0.654 CPS34

0.387 0.724 CPS15 0.723 CPS35

0.290 0.793 CPS16 0.792 CPS36

0.195 0.861 CPS17 0.862 CPS37

0.098 0.930 CPS18 0.931 CPS38

0.055 0.961 CPS19 0.964 CPS39

0.015 1.000 1.000

Centerline row

y/hm/2 = 0

z/zs,max x/Ln orifice x/Ln orifice

Outboard row

y/hm/2 = -0.87

y

Ln

MS 50.90

x

zs
81

Figure 44. Sidewall S2 external coordinates and location of pressure orifices.

1.000 0.000 0.000

1.000 0.450 CPS1 0.446 CPS21

1.000 0.496 CPS2 0.493 CPS22

1.000 0.517 CPS3 0.515 CPS23

0.965 0.543 CPS5 0.545 CPS24

0.948 0.551 CPS6 0.552 CPS25

0.923 0.563 CPS7 0.564 CPS26

0.875 0.585 CPS8 0.586 CPS27

0.825 0.609 CPS9 0.610 CPS28

0.775 0.633 CPS10 0.631 CPS29

0.729 0.655 CPS11 0.654 CPS30

0.682 0.677 CPS12 0.677 CPS31

0.583 0.724 CPS13 0.723 CPS32

0.489 0.768 CPS14 0.770 CPS33

0.391 0.815 CPS15 0.815 CPS34

0.294 0.861 CPS16 0.861 CPS35

0.201 0.905 CPS17 0.906 CPS36

0.102 0.952 CPS18 0.952 CPS37

0.054 0.974 CPS19 0.978 CPS38

0.015 1.000 1.000

Centerline row

y/hm/2 = 0

z/zs,max x/Ln orifice x/Ln orifice

Outboard row

y/hm/2 = -0.87

y

Ln

MS 50.90

x

zs
82

Figure 45. Sidewall S3 external coordinates and location of pressure orifices

1.000 0.000 0.000

1.000 0.590 CPS1 0.589 CPS21

1.000 0.624 CPS2 0.623 CPS22

1.000 0.640 CPS3 0.637 CPS23

0.957 0.661 CPS5 0.660 CPS25

0.910 0.678 CPS7 0.670 CPS27

0.866 0.693 CPS8 0.689 CPS28

0.827 0.707 CPS9 0.708 CPS29

0.774 0.726 CPS10 0.725 CPS30

0.726 0.743 CPS11 0.743 CPS31

0.675 0.761 CPS12 0.760 CPS32

0.580 0.795 CPS13 0.794 CPS33

0.485 0.828 CPS14 0.829 CPS34

0.386 0.863 CPS15 0.863 CPS35

0.291 0.897 CPS16 0.898 CPS36

0.193 0.932 CPS17 0.931 CPS37

0.093 0.967 CPS18 0.967 CPS38

0.049 0.983 CPS19 0.983 CPS39

0.015 1.000 1.000

Centerline row

y/hm/2 = 0

z/zs,max x/Ln orifice x/Ln orifice

Outboard row

y/hm/2 = -0.87

y

Ln

MS 50.90

x

zs
83

Figure 46. Sidewall S4 external coordinates and location of pressure orifices

1.000 0.000 0.000

1.000 0.396 CPS1 0.396 CPS21

1.000 0.445 CPS2 0.448 CPS22

1.000 0.470 CPS3 0.473 CPS23

1.000 0.495 CPS5 0.496 CPS25

0.989 0.508 CPS6 0.505 CPS26

0.978 0.521 CPS7 0.519 CPS27

0.943 0.546 CPS8 0.545 CPS28

0.904 0.571 CPS9 0.570 CPS29

0.853 0.596 CPS10 0.598 CPS30

0.799 0.622 CPS11 0.622 CPS31

0.746 0.646 CPS12 0.648 CPS32

0.638 0.698 CPS13 0.697 CPS33

0.532 0.748 CPS14 0.748 CPS34

0.426 0.798 CPS15 0.799 CPS35

0.319 0.849 CPS16 0.849 CPS36

0.212 0.899 CPS17 0.900 CPS37

0.100 0.952 CPS18 0.951 CPS38

0.052 0.975 CPS19 0.974 CPS39

0.015 1.000 1.000

Centerline row

y/hm/2 = 0

z/zs,max x/Ln orifice x/Ln orifice

Outboard row

y/hm/2 = -0.87

y

Ln

MS 50.90

x

zs
84

Figure 47. Sidewall S5 external coordinates and location of pressure orifices

1.000 0.000 0.000

1.000 0.540 CPS1 0.550 CPS21

1.000 0.584 CPS2 0.585 CPS22

1.000 0.604 CPS3 0.604 CPS23

1.000 0.623 CPS5 0.623 CPS25

0.989 0.630 CPS6 0.632 CPS26

0.969 0.641 CPS7 0.641 CPS27

0.940 0.660 CPS8 0.660 CPS28

0.901 0.679 CPS9 0.679 CPS29

0.856 0.697 CPS10 0.698 CPS30

0.800 0.717 CPS11 0.717 CPS31

0.750 0.734 CPS12 0.736 CPS32

0.646 0.771 CPS13 0.774 CPS33

0.535 0.811 CPS14 0.811 CPS34

0.427 0.849 CPS15 0.849 CPS35

0.320 0.887 CPS16 0.887 CPS36

0.211 0.925 CPS17 0.925 CPS37

0.105 0.963 CPS18 0.963 CPS38

0.053 0.981 CPS19 0.982 CPS39

0.015 1.000 1.000

Centerline row

y/hm/2 = 0

z/zs,max x/Ln orifice x/Ln orifice

Outboard row

y/hm/2 = -0.87

y

Ln

MS 50.90

x

zs
85

Figure 48. Sidewall S6 external coordinates and location of pressure orifices

1.000 0.000 0.000

1.000 0.327 CPS1 0.323 CPS21

1.000 0.384 CPS2 0.383 CPS22

1.000 0.410 CPS3 0.408 CPS23

1.000 0.440 CPS5 0.440 CPS25

0.999 0.453 CPS6 0.453 CPS26

0.998 0.465 CPS7 0.465 CPS27

0.990 0.495 CPS8 0.492 CPS28

0.977 0.523 CPS9 0.524 CPS29

0.959 0.552 CPS10 0.551 CPS30

0.936 0.580 CPS11 0.579 CPS31

0.908 0.608 CPS12 0.608 CPS32

0.818 0.664 CPS13 0.662 CPS33

0.709 0.721 CPS14 0.720 CPS34

0.590 0.776 CPS15 0.776 CPS35

0.476 0.833 CPS16 0.833 CPS36

0.359 0.888 CPS17 0.887 CPS37

0.237 0.945 CPS18 0.944 CPS38

0.180 0.971 CPS19 0.973 CPS39

0.113 1.000 1.000

Centerline row

y/hm/2 = 0

z/zs,max x/Ln orifice x/Ln orifice

Outboard row

y/hm/2 = -0.87

y

Ln

MS 50.90

x

zs
86

Figure 49. Sidewall S7 external coordinates and location of pressure orifices.

1.000 0.000 0.000

1.000 0.173 CPS1 0.173 CPS21

1.000 0.242 CPS2 0.242 CPS22

1.000 0.276 CPS3 0.276 CPS23

1.000 0.318 CPS5 0.318 CPS25

0.999 0.328 CPS6 0.328 CPS26

0.998 0.345 CPS7 0.345 CPS27

0.990 0.379 CPS8 0.379 CPS28

0.968 0.437 CPS9 0.413 CPS29

0.962 0.447 CPS10 0.449 CPS30

0.940 0.483 CPS11 0.483 CPS31

0.913 0.518 CPS12 0.520 CPS32

0.846 0.586 CPS13 0.585 CPS33

0.759 0.655 CPS14 0.655 CPS34

0.654 0.724 CPS15 0.724 CPS35

0.528 0.793 CPS16 0.793 CPS36

0.382 0.862 CPS17 0.862 CPS37

0.218 0.930 CPS18 0.932 CPS38

0.129 0.965 CPS19 0.966 CPS39

0.015 1.000 1.000

Centerline row

y/hm/2 = 0

z/zs,max x/Ln orifice x/Ln orifice

Outboard row

y/hm/2 = -0.87

zs

y

Ln

MS 50.90

x
87

Figure 50. Sidewall S8 external coordinates and location of pressure orifices. 

1.000 0.000 0.000

1.000 0.172 0.000 CPS1 0.173 -0.871 CPS21

1.000 0.240 0.000 CPS2 0.242 -0.871 CPS22

1.000 0.276 0.000 CPS3 0.278 -0.871 CPS23

0.957 0.318 0.000 CPS5 0.319 -0.871 CPS25

0.943 0.328 0.000 CPS6 0.327 -0.871 CPS26

0.919 0.345 0.000 CPS7 0.344 -0.871 CPS27

0.870 0.381 0.000 CPS8 0.383 -0.871 CPS28

0.821 0.415 0.000 CPS9 0.417 -0.871 CPS29

0.774 0.448 0.000 CPS10 0.449 -0.865 CPS30

0.724 0.484 0.000 CPS11 0.482 -0.839 CPS31

0.676 0.518 0.000 CPS12 0.516 -0.829 CPS32

0.580 0.587 0.000 CPS13 0.586 -0.787 CPS33

0.484 0.655 0.000 CPS14 0.654 -0.719 CPS34

0.387 0.725 0.000 CPS15 0.725 -0.639 CPS35

0.288 0.795 0.000 CPS16 0.793 -0.561 CPS36

0.195 0.861 0.000 CPS17 0.862 -0.468 CPS37

0.096 0.932 0.000 CPS18 0.935 -0.384 CPS38

0.056 0.960 0.000 CPS19 0.965 -0.339 CPS39

0.015 1.000 1.000

Centerline row

z/zs,max x/Ln orifice x/Ln orifice

Outboard row

y/hm/2 = 0 y/hm/2 = 0

zs

y

Ln

MS 50.90

x
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 51. Aeropropulsive performance data repeatability for nozzle N1. 

88 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

Symbols represent different runs.
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 51. Continued. 

89 

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 51. Continued. 

90 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 51. Concluded. 

91 

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

0 

.0005 

.0010 

.0015 

CD,n 
0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.54 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.58 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 1.06 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.02 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 4.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

(a) Flap top center row, z/wf /2 = 0. 

Figure 52. Nozzle N1 pressure coefficient repeatability from different runs. 

92 

Symbols represent different runs.
0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.54 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.58 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 1.06 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.02 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 4.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

(b) Flap top outboard row, z/wf /2 = 0.95 

Figure 52. Continued. 

93 
0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.54 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.58 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.02 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 4.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

(c) Flap bottom center row, z/wf /2 = 0. 

Figure 52. Continued. 

94 
0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.54 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.58 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 1.06 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.02 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 4.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

(d) Flap bottom middle row, z/wf /2 = 5. 

Figure 52. Continued. 

95 
0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.54 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.58 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 1.06 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.02 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 4.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

(e) Sidewall center row, y/hm /2 = 0. 

Figure 52. Continued. 

96 
0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.54 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.58 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 1.06 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.02 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 4.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

(f) Sidewall outboard row, y/hm /2 = -0.87. 

Figure 52. Concluded. 

97 
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 53. Aeropropulsive performance data repeatability for nozzle N6. 

98 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

Symbols represent different runs.
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 53. Continued. 

99 

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 53. Continued. 

100 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 53. Concluded. 

101 

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 
0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.01 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.66 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.51 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 1.09 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.02 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.99 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.99 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.99 

(a) Flap top center row, z/wf /2 = 0. 

Figure 54. Nozzle N6 pressure coefficient repeatability from different runs.

102 

Symbols represent different runs.
0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.01 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.66 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.51 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 1.09 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.02 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.99 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.99 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.99 

(b) Flap top outboard row, z/wf /2 = 0.95 

Figure 54. Continued. 

103 
0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.01 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.66 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.51 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 1.09 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.02 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.99 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.99 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.99 

(c) Flap bottom center row, z/wf /2 = 0. 

Figure 54. Continued. 

104 
0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.01 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.66 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.51 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 1.09 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.02 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.99 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.99 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.99 

(d) Flap bottom middle row, z/wf /2 = 5. 

Figure 54. Continued. 

105 
0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.01 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.66 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.51 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 1.09 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.02 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.99 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.99 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.99 

(e) Sidewall center row, y/hm /2 = 0. 

Figure 54. Continued. 

106 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.9 

-.6 

-.3 

0 

.3 

Cp,f 

NPR = 5.01 

-1.2 

-.9 

-.6 

-.3 

0 

.3 

Cp,f 

NPR = 3.66 

-1.2 

-.9 

-.6 

-.3 

0 

.3 

Cp,f 

NPR = 2.51 

-1.2 

-.9 

-.6 

-.3 

0 

.3 

Cp,f 

NPR = 1.09 

-1.2 

-.9 

-.6 

-.3 

0 

.3 

Cp,f 

NPR = 2.02 

-1.2 

-.9 

-.6 

-.3 

0 

.3 

Cp,f 

NPR = 3.00 

-1.2 

-.9 

-.6 

-.3 

0 

.3 

Cp,f 

NPR = 3.99 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.9 

-.6 

-.3 

0 

.3 

Cp,f 

NPR = 5.99 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.9 

-.6 

-.3 

0 

.3 

Cp,f 

NPR = 5.99 

(f) Sidewall outboard row, y/hm /2 = -0.87. 

Figure 54. Concluded. 

107 
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 55. Aeropropulsive performance data repeatability for nozzle N11.

108 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

Symbols represent different run numbers.
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 55. Continued. 

109 

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 55. Continued. 

110 

-.0005 

0 

.0005 

.0010 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 55. Concluded. 

111 

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 
0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.01 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.54 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.51 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 1.06 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.01 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 4.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

(a) Flap top center row, z/wf /2 = 0. 

Figure 56. Nozzle N11 pressure coefficient repeatability from different runs.

112 

Symbols represent different runs.
0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.01 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.54 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.51 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 1.06 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.01 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 4.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

(b) Flap top outboard row, z/wf /2 = 0.95 

Figure 56. Continued. 

113 
0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.01 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.54 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.51 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 1.06 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.01 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 4.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

(c) Flap bottom center row, z/wf /2 = 0. 

Figure 56. Continued. 

114 
0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.01 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.54 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.51 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 1.06 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.01 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 4.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

(d) Flap bottom middle row, z/wf /2 = 5. 

Figure 56. Continued. 

115 
0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.01 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.54 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.51 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 1.06 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.01 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 4.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

(e) Sidewall center row, y/hm /2 = 0. 

Figure 56. Continued. 

116 
0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 5.01 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.54 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.51 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 1.06 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 2.01 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 3.00 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 4.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.6 

-.4 

-.2 

0 

.2 

.4 

Cp,f 

NPR = 6.00 

(f) Sidewall outboard row, y/hm /2 = -0.87. 

Figure 56. Concluded. 

117 
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

Figure 57. Static performance for Nozzle N1 with flap F1 and sidewall S1. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs = 4.0°; rs /rs,max = 0. 

118 

.72 

.76 

.80 

.84 

.88 

.92 

.96 

1.00 

F/Fi 

Run 

300. 

301. 

310. 
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

Figure 58. Static performance for Nozzle N2 with flap F2 and sidewall S1. 

rf /rf,max = 0.1; βf = 12.88°; Lf /hm = 1.4; βs = 4.0°; rs /rs,max = 0. 

119 

.72 

.76 

.80 

.84 

.88 

.92 

.96 

1.00 

F/Fi 

Run 

303. 
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

Figure 59. Static performance for Nozzle N3 with flap F3 and sidewall S1. 

rf /rf,max = 0; βf = 11.72°; Lf /hm = 1.4; βs = 4.0°; rs /rs,max = 0. 

120 

.72 

.76 

.80 

.84 

.88 

.92 

.96 

1.00 

F/Fi 

Run 

308. 
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

Figure 60. Static performance for Nozzle N4 with flap F4 and sidewall S1. 

rf /rf,max = 1.0; βf = 23.44°; Lf /hm = 1.4; βs = 4.0°; rs /rs,max = 0. 

121 

.72 

.76 

.80 

.84 

.88 

.92 

.96 

1.00 

F/Fi 

Run 

313. 
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

Figure 61. Static performance for Nozzle N5 with flap F1 and sidewall S2. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs = 6.0°; rs /rs,max = 0. 

122 

.72 

.76 

.80 

.84 

.88 

.92 

.96 

1.00 

F/Fi 

Run 

302. 
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

Figure 62. Static performance for Nozzle N6 with flap F1 and sidewall S3. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs = 8.0°; rs /rs,max = 0. 

123 

.72 

.76 

.80 

.84 

.88 

.92 

.96 

1.00 

F/Fi 

Run 

304. 
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

Figure 63. Static performance for Nozzle N7 with flap F1 and sidewall S4. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs = 6.0°; rs /rs,max = 0.1. 

124 

.72 

.76 

.80 

.84 

.88 

.92 

.96 

1.00 

F/Fi 

Run 

305. 
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

Figure 64. Static performance for Nozzle N8 with flap F1 and sidewall S5. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs = 8.0°; rs /rs,max = 0.1. 

125 

.72 

.76 

.80 

.84 

.88 

.92 

.96 

1.00 

F/Fi 

Run 

306. 
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

Figure 65. Static performance for Nozzle N9 with flap F1 and sidewall S6. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs = 6.0°; rs /rs,max = 0.4. 

126 

.72 

.76 

.80 

.84 

.88 

.92 

.96 

1.00 

F/Fi 

Run 

314. 
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

Figure 66. Static performance for Nozzle N10 with flap F1 and sidewall S7. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 8.0°; rs

 /rs,max = 1.0. 

127 

.72 

.76 

.80 

.84 

.88 

.92 

.96 

1.00 

F/Fi 

Run 

315. 
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

Figure 67. Static performance for Nozzle N11 with flap F1 and sidewall S8. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs = 0°; rs /rs,max = 0. 

128 

.72 

.76 

.80 

.84 

.88 

.92 

.96 

1.00 

F/Fi 

Run 

307. 

310. 
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

Figure 68. Static performance for Nozzle N12 with flap F2 and sidewall S8. 

rf /rf,max = 0.1; βf = 12.88°; Lf /hm = 1.4; βs = 0°; rs /rs,max = 0. 

129 

.72 

.76 

.80 

.84 

.88 

.92 

.96 

1.00 

F/Fi 

Run 

309. 
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

Figure 69. Static performance for Nozzle N13 with flap F5 and sidewall S1. 

rf /rf,max = 0.4; βf = 20.30°; Lf /hm = 1.1; βs = 4.0°; rs /rs,max = 0. 

130 

.72 

.76 

.80 

.84 

.88 

.92 

.96 

1.00 

F/Fi 

Run 

311. 
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

Figure 70. Static performance for Nozzle N14 with flap F6 and sidewall S1. 

rf /rf,max = 0.1; βf = 15.97°; Lf /hm = 1.1; βs = 4.0°; rs /rs,max = 0. 

131 

.72 

.76 

.80 

.84 

.88 

.92 

.96 

1.00 

F/Fi 

Run 

312. 
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 71. Aeropropulsive performance for nozzle N1 with flap F1 and sidewall S1. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 4.0°; rs /rs,max = 0. 

132 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 71. Continued. 

133 

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 71. Continued. 

134 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

M 

0.80 

0.90 

0.95 

1.20 

CD,p = CD,p,f + CD,p,s 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 71. Concluded. 

135 

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

CD,pf = CD,p + CD,f 

0 

.0005 

.0010 

.0015 

.0020 

.0025 

CD,n 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 72. Aeropropulsive performance for nozzle N2 with flap F2 and sidewall S1. 

rf /rf,max = 0.1; βf = 12.88°; Lf /hm = 1.4; βs

 = 4.0°; rs /rs,max = 0. 

136

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 72. Continued. 

137 

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 72. Continued. 

138

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

M 

0.80 

0.90 

0.95 

1.20 

CD,p = CD,p,f + CD,p,s 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 72. Concluded. 

139 

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

CD,pf = CD,p + CD,f 

0 

.0005 

.0010 

.0015 

.0020 

.0025 

CD,n 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 73. Aeropropulsive performance for nozzle N3 with flap F3 and sidewall S1. 

rf /rf,max = 0; βf = 11.72°; Lf /hm = 1.4; βs

 = 4.0°; rs /rs,max = 0. 

140 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 73. Continued. 

141

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 73. Continued. 

142

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

M 

0.80 

0.90 

0.95 

1.20 

CD,p = CD,p,f + CD,p,s 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 73. Concluded. 

143

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

CD,pf = CD,p + CD,f 

0 

.0005 

.0010 

.0015 

.0020 

.0025 

CD,n 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 74. Aeropropulsive performance for nozzle N4 with flap F4 and sidewall S1. 

rf /rf,max = 1.0; βf = 23.44°; Lf /hm = 1.4; βs

 = 4.0°; rs /rs,max = 0. 

144 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 74. Continued. 

145

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 74. Continued. 

146 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

M 

0.80 

0.90 

0.95 

1.20 

CD,p = CD,p,f + CD,p,s 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 74. Concluded. 

147

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

CD,pf = CD,p + CD,f 

0 

.0005 

.0010 

.0015 

.0020 

.0025 

CD,n 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 75. Aeropropulsive performance for nozzle N5 with flap F1 and sidewall S2. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 6.0°; rs /rs,max = 0. 

148

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 75. Continued. 

149

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 75. Continued. 

150 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

M 

0.80 

0.90 

0.95 

1.20 

CD,p = CD,p,f + CD,p,s 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 75. Concluded. 

151

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

CD,pf = CD,p + CD,f 

0 

.0005 

.0010 

.0015 

.0020 

.0025 

CD,n 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 76. Aeropropulsive performance for nozzle N6 with flap F1 and sidewall S3. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 8.0°; rs /rs,max = 0. 

152 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 76. Continued. 

153

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 76. Continued. 

154 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

M 

0.80 

0.90 

0.95 

1.20 

CD,p = CD,p,f + CD,p,s 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 76. Concluded. 

155

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

CD,pf = CD,p + CD,f 

0 

.0005 

.0010 

.0015 

.0020 

.0025 

CD,n 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 77. Aeropropulsive performance for nozzle N7 with flap F1 and sidewall S4. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 6.0°; rs /rs,max = 0.1. 

156 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 77. Continued. 

157

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 77. Continued. 

158

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

M 

0.80 

0.90 

0.95 

1.20 

CD,p = CD,p,f + CD,p,s 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 77. Concluded. 

159

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

CD,pf = CD,p + CD,f 

0 

.0005 

.0010 

.0015 

.0020 

.0025 

CD,n 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 78. Aeropropulsive performance for nozzle N8 with flap F1 and sidewall S5. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 8.0°; rs /rs,max = 0.1. 

160 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 78. Continued. 

161

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 78. Continued. 

162

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

M 

0.80 

0.90 

0.95 

1.20 

CD,p = CD,p,f + CD,p,s 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 78. Concluded. 

163

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

CD,pf = CD,p + CD,f 

0 

.0005 

.0010 

.0015 

.0020 

.0025 

CD,n 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 79. Aeropropulsive performance for nozzle N9 with flap F1 and sidewall S6. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 6.0°; rs /rs,max = 0.4. 

164 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 79. Continued. 

165

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 79. Continued. 

166

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

M 

0.80 

0.90 

0.95 

1.20 

CD,p = CD,p,f + CD,p,s 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 79. Concluded. 

167 

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

CD,pf = CD,p + CD,f 

0 

.0005 

.0010 

.0015 

.0020 

.0025 

CD,n 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 80. Aeropropulsive performance for nozzle N10 with flap F1 and sidewall S7. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 8.0°; rs /rs,max = 1.0. 

168 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 80. Continued. 

169 

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 80. Continued. 

170

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

M 

0.80 

0.90 

0.95 

1.20 

CD,p = CD,p,f + CD,p,s 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 80. Concluded. 

171

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

CD,pf = CD,p + CD,f 

0 

.0005 

.0010 

.0015 

.0020 

.0025 

CD,n 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 81. Aeropropulsive performance for nozzle N11 with flap F1 and sidewall S8. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 4°; rs /rs,max = 0. 

172 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 81. Continued. 

173

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 81. Continued. 

174

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

M 

0.80 

0.90 

0.95 

1.20 

CD,p = CD,p,f + CD,p,s 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 81. Concluded. 

175

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

CD,pf = CD,p + CD,f 

0 

.0005 

.0010 

.0015 

.0020 

.0025 

CD,n 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 82. Aeropropulsive performance for nozzle N12 with flap F2 and sidewall S8. 

rf /rf,max = 0.1; βf = 12.88°; Lf /hm = 1.4; βs

 = 4°; rs /rs,max = 0. 

176 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 82. Continued. 

177

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 82. Continued. 

178 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

M 

0.80 

0.90 

0.95 

1.20 

CD,p = CD,p,f + CD,p,s 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 82. Concluded. 

179 

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

CD,pf = CD,p + CD,f 

0 

.0005 

.0010 

.0015 

.0020 

.0025 

CD,n 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 83. Aeropropulsive performance for nozzle N13 with flap F5 and sidewall S1. 

rf /rf,max = 0.4; βf = 20.30°; Lf /hm = 1.1; βs

 = 4.0°; rs /rs,max = 0. 

180 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 83. Continued. 

181 

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 83. Continued. 

182

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

M 

0.80 

0.90 

0.95 

1.20 

CD,p = CD,p,f + CD,p,s 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 83. Concluded. 

183 

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

CD,pf = CD,p + CD,f 

0 

.0005 

.0010 

.0015 

.0020 

.0025 

CD,n 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

.88 

.92 

.96 

1.00 

wp/wi 

(a) Variation of (F-Dn)/Fi and wp/wi. 

Figure 84. Aeropropulsive performance for nozzle N14 with flap F6 and sidewall S1. 

rf /rf,max = 0.1; βf = 15.97°; Lf /hm = 1.1; βs

 = 4.0°; rs /rs,max = 0. 

184 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

(F-Dn)/Fi 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0005 

.0010 

.0015 

.0020 

CD,n 

(b) Variation of C(F-Dn

)

 and CD,n. 

Figure 84. Continued. 

185 

-.010 

-.005 

0 

.005 

.010 

.015 

.020 

.025 

C(F-Dn

) 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) Variation of CD,p, CD,p,f , and CD,p,s. 

Figure 84. Continued. 

186

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

M 

0.80 

0.90 

0.95 

1.20 

CD,p = CD,p,f + CD,p,s 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0005 

0 

.0005 

.0010 

∆CD 

∆CD = CD,n - CD,pf 

(d) Variation of CD,n, CD,pf , and ∆CD. 

Figure 84. Concluded. 

187 

0 

.0005 

.0010 

.0015 

.0020 

CD,pf 

CD,pf = CD,p + CD,f 

0 

.0005 

.0010 

.0015 

.0020 

.0025 

CD,n 

M 

0.80 

0.90 

0.95 

1.20 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(a) M = 0.80. 

Figure 85. Effect of flap radius of curvature on pressure drag coefficients for 

nozzles with sidewall S1. βs

 = 4.0°; rs /rs,max = 0. 

188 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N3 

N2 

N1 

N4 

Flap 

F3 

F2 

F1 

F4 

rf /rf,max

0 

0.1 

0.4 

1.0 

βf

, deg 

11.72 

12.88 

16.38 

23.48 

Lf /hm

1.4 

1.4 

1.4 

1.4 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(b) M = 0.90. 

Figure 85. Continued. 

189 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N3 

N2 

N1 

N4 

Flap 

F3 

F2 

F1 

F4 

rf /rf,max

0 

0.1 

0.4 

1.0 

βf

, deg 

11.72 

12.88 

16.38 

23.48 

Lf /hm

1.4 

1.4 

1.4 

1.4 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) M = 0.95. 

Figure 85. Continued. 

190 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N3 

N2 

N1 

N4 

Flap 

F3 

F2 

F1 

F4 

rf /rf,max

0 

0.1 

0.4 

1.0 

βf

, deg 

11.72 

12.88 

16.38 

23.48 

Lf /hm

1.4 

1.4 

1.4 

1.4 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(d) M = 1.20. 

Figure 85. Concluded. 

191 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N3 

N2 

N1 

N4 

Flap 

F3 

F2 

F1 

F4 

rf /rf,max

0 

0.1 

0.4 

1.0 

βf

, deg 

11.72 

12.88 

16.38 

23.48 

Lf /hm

1.4 

1.4 

1.4 

1.4 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(a) M = 0.80. 

Figure 86. Effect of flap radius of curvature on pressure drag coefficients for 

nozzles with sidewall S1. βs

 = 4.0°; rs /rs,max = 0. 

192 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N14 

N13 

Flap 

F6 

F5 

rf /rf,max

0.1 

0.4 

βf

, deg 

15.97 

20.30 

Lf /hm

1.1 

1.1 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(b) M = 0.90. 

Figure 86. Continued. 

193 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N14 

N13 

Flap 

F6 

F5 

rf /rf,max

0.1 

0.4 

βf, deg 

15.97 

20.30 

Lf /hm

1.1 

1.1 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) M = 0.95. 

Figure 86. Continued. 

194 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N14 

N13 

Flap 

F6 

F5 

rf /rf,max

0.1 

0.4 

βf, deg 

15.97 

20.30 

Lf /hm

1.1 

1.1 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(d) M = 1.20. 

Figure 86. Concluded. 

195 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N14 

N13 

Flap 

F6 

F5 

rf /rf,max

0.1 

0.4 

βf

, deg 

15.97 

20.30 

Lf /hm

1.1 

1.1 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(a) M = 0.80. 

Figure 87. Effect of flap length on pressure drag coefficients for nozzles 

with sidewall S1. βs

 = 4.0°; rs /rs,max = 0. 

196 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N2 

N14 

Flap 

F2 

F6 

Lf /hm

1.4 

1.1 

βf

, deg 

12.88 

15.97 

rf /rf,max

0.1 

0.1 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(b) M = 0.90. 

Figure 87. Continued. 

197 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N2 

N14 

Flap 

F2 

F6 

Lf /hm

1.4 

1.1 

βf, deg 

12.88 

15.97 

rf /rf,max

0.1 

0.1 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) M = 0.95. 

Figure 87. Continued. 

198 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N2 

N14 

Flap 

F2 

F6 

Lf /hm

1.4 

1.1 

βf, deg 

12.88 

15.97 

rf /rf,max

0.1 

0.1 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(d) M = 1.20. 

Figure 87. Concluded. 

199 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N2 

N14 

Flap 

F2 

F6 

Lf /hm

1.4 

1.1 

βf

, deg 

12.88 

15.97 

rf /rf,max

0.1 

0.1 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(a) M = 0.80. 

Figure 88. Effect of flap length on pressure drag coefficients for nozzles 

with sidewall S1. βs

 = 4.0°; rs /rs,max = 0. 

200 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N1 

N13 

Flap 

F1 

F5 

Lf /hm

1.4 

1.1 

βf

, deg 

16.38 

20.30 

rf /rf,max

0.4 

0.4 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(b) M = 0.90. 

Figure 88. Continued. 

201 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N1 

N13 

Flap 

F1 

F5 

Lf /hm

1.4 

1.1 

βf, deg 

16.38 

20.30 

rf /rf,max

0.4 

0.4 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) M = 0.95. 

Figure 88. Continued. 

202 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N1 

N13 

Flap 

F1 

F5 

Lf /hm

1.4 

1.1 

βf, deg 

16.38 

20.30 

rf /rf,max

0.4 

0.4 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(d) M = 1.20. 

Figure 88. Concluded. 

203 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N1 

N13 

Flap 

F1 

F5 

Lf /hm

1.4 

1.1 

βf

, deg 

16.38 

20.30 

rf /rf,max

0.4 

0.4 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0001 

0 

.0001 

.0002 

CD,p,s 

(a) M = 0.80. 

Figure 89. Effect of sidewall boattail angle on pressure drag coefficients for nozzles 

with flap F1. rf /rf,max = 0.4; βf

 = 16.38°; Lf /hm = 1.4. 

204 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N1 

N5 

N6 

Sidewall 

S1 

S2 

S3 

βs

, deg 

4.0 

6.0 

8.0 

rs /rs,max

0 

0 

0 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(b) M = 0.90. 

Figure 89. Continued. 

205 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N1 

N5 

N6 

Sidewall 

S1 

S2 

S3 

βs

, deg 

4.0 

6.0 

8.0 

rs /rs,max

0 

0 

0 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) M = 0.95. 

Figure 89. Continued. 

206 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N1 

N5 

N6 

Sidewall 

S1 

S2 

S3 

βs

, deg 

4.0 

6.0 

8.0 

rs /rs,max

0 

0 

0 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(d) M = 1.20. 

Figure 89. Concluded. 

207 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N1 

N5 

N6 

Sidewall 

S1 

S2 

S3 

βs

, deg 

4.0 

6.0 

8.0 

rs /rs,max

0 

0 

0 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0001 

0 

.0001 

.0002 

CD,p,s 

(a) M = 0.80. 

Figure 90. Effect of sidewall radius of curvature on pressure drag coefficients for 

nozzles with flap F1. rf /rf,max = 0.4; βf

 = 16.38°; Lf /hm = 1.4. 

208 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N5 

N7 

N9 

Sidewall 

S2 

S4 

S6 

rs /rs,max

0 

0.1 

0.4 

βs, deg 

6.0 

6.0 

6.0 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(b) M = 0.90. 

Figure 90. Continued. 

209 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N5 

N7 

N9 

Sidewall 

S2 

S4 

S6 

rs /rs,max

0 

0.1 

0.4 

βs, deg 

6.0 

6.0 

6.0 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) M = 0.95. 

Figure 90. Continued. 

210 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N5 

N7 

N9 

Sidewall 

S2 

S4 

S6 

rs /rs,max

0 

0.1 

0.4 

βs, deg 

6.0 

6.0 

6.0 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(d) M = 1.20. 

Figure 90. Concluded. 

211 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N5 

N7 

N9 

Sidewall 

S2 

S4 

S6 

rs /rs,max

0 

0.1 

0.4 

βs, deg 

6.0 

6.0 

6.0 
0 1 2 3 4 5 6 7 8 9 

NPR 

-.0001 

0 

.0001 

.0002 

CD,p,s 

(a) M = 0.80. 

Figure 91. Effect of sidewall radius of curvature on pressure drag coefficients for 

nozzles with flap F1. rf /rf,max = 0.4; βf

 = 16.38°; Lf /hm = 1.4. 

212 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N6 

N8 

N10 

Sidewall 

S3 

S5 

S7 

rs /rs,max

0 

0.1 

1.0 

βs

, deg 

8.0 

8.0 

8.0 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(b) M = 0.90. 

Figure 91. Continued. 

213 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N6 

N8 

N10 

Sidewall 

S3 

S5 

S7 

rs /rs,max

0 

0.1 

1.0 

βs

, deg 

8.0 

8.0 

8.0 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) M = 0.95. 

Figure 91. Continued. 

214 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N6 

N8 

N10 

Sidewall 

S3 

S5 

S7 

rs /rs,max

0 

0.1 

1.0 

βs

, deg 

8.0 

8.0 

8.0 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(d) M = 1.20. 

Figure 91. Concluded. 

215 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N6 

N8 

N10 

Sidewall 

S3 

S5 

S7 

rs /rs,max

0 

0.1 

1.0 

βs

, deg 

8.0 

8.0 

8.0 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(a) M = 0.80. 

Figure 92. Effect of reduced sidewall height on pressure drag coefficients for nozzles 

with flap F1. rf /rf,max = 0.4; βf

 = 16.38°; Lf /hm = 1.4. 

216 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N1 

N11 

Sidewall 

S1 

S8 

βs

, deg 

4.0 

4.0 

rs /rs,max

0 

0 

S1 

F1 S8 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(b) M = 0.90. 

Figure 92. Continued. 

217 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N1 

N11 

Sidewall 

S1 

S8 

βs

, deg 

4.0 

4.0 

rs /rs,max

0 

0 

S1 

F1 S8 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) M = 0.95. 

Figure 92. Continued. 

218 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N1 

N11 

Sidewall 

S1 

S8 

βs

, deg 

4.0 

4.0 

rs /rs,max

0 

0 

S1 

F1 S8 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(d) M = 1.20. 

Figure 92. Concluded. 

219 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N1 

N11 

Sidewall 

S1 

S8 

βs

, deg 

4.0 

4.0 

rs /rs,max

0 

0 

S1 

F1 S8 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(a) M = 0.80. 

Figure 93. Effect of reduced sidewall height on pressure drag coefficients for nozzles 

with flap F2. rf /rf,max = 0.1; βf

 = 12.88°; Lf /hm = 1.4. 

220 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N2 

N12 

Sidewall 

S1 

S8 

βs

, deg 

4.0 

4.0 

rs /rs,max

0 

0 

S1 

F2 S8 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(b) M = 0.90. 

Figure 93. Continued. 

221 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p 

Nozzle 

N2 

N12 

Sidewall 

S1 

S8 

βs

, deg 

4.0 

4.0 

rs /rs,max

0 

0 

S1 

F2 S8 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(c) M = 0.95. 

Figure 93. Continued. 

222 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N2 

N12 

Sidewall 

S1 

S8 

βs

, deg 

4.0 

4.0 

rs /rs,max

0 

0 

S1 

F2 S8 
0 1 2 3 4 5 6 7 8 9 

NPR 

0 

.0001 

.0002 

.0003 

CD,p,s 

(d) M = 1.20. 

Figure 93. Concluded. 

223 

-.0005 

0 

.0005 

.0010 

.0015 

CD,p,f 

0 

.0005 

.0010 

.0015 

.0020 

CD,p 

Nozzle 

N2 

N12 

Sidewall 

S1 

S8 

βs

, deg 

4.0 

4.0 

rs /rs,max

0 

0 

S1 

F2 S8 
0.0004

0.0002

0

CD,p,s

Figure 94. Effect of flap radius of curvature on pressure drag coefficients

for nozzles with sidewall S1 at scheduled NPR.

224

M = 0.80

NPR = 3.54

M = 0.90

NPR = 3.54

M = 0.95

NPR = 3.54

M = 1.20

NPR = 6.6

CD,p,f

-0.0002

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p

-0.0002

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

F1

F2 F3

F4 S1

Nozzle Flap rf /rf,max βf , deg Lf /hm Sidewall rs /rs,max βs , deg

N3

N2

N1

N4

F3

F2

F1

F4

0

0.1

0.4

1.0

11.72

12.88

16.38

23.48

1.4

1.4

1.4

1.4

S1

S1

S1

S1

0

0

0

0

4.0

4.0

4.0

4.0
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Nozzle 

N3 

N2 

N1 

N4 

Flap 

F3 

F2 

F1 

F4 

rf /rf,max

0 

0.1 

0.4 

1.0 

βf, deg 

11.72 

12.88 

16.38 

23.48 

Lf /hm

1.4 

1.4 

1.4 

1.4 

Sidewall 

S1 

S1 

S1 

S1 

rs /rs,max

0 

0 

0 

0 

βs, deg 

4.0 

4.0 

4.0 

4.0 

M = 0.80, NPR = 3.52 

Flap top center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 3.55 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 3.53 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 6.62 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.80, NPR = 3.52 

Flap top outboard row, z/wf /2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 3.55 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 3.53 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 6.62 

Figure 95. Effect of flap radius of curvature on upper flap pressure distributions for nozzles with 

sidewall S1 at scheduled NPR. 

225 
Figure 96. Effect of flap radius of curvature on pressure drag coefficients

 for nozzles with sidewall S1 at scheduled NPR.

226

M = 0.80

NPR = 3.54

M = 0.90

NPR = 3.54

M = 0.95

NPR = 3.54

M = 1.20

NPR = 6.6

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p,f

0.0004

0.0002

0

CD,p,s

CD,p

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

S1

F6

F5

Nozzle Flap rf /rf,max βf , deg Lf /hm Sidewall rs /rs,max βs , deg

N14

N13

F6

F5

0

0.1

15.97

20.30

1.4

1.4

S1

S1

0

0

4.0

4.0
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Nozzle 

N14 

N13 

Flap 

F6 

F5 

rf /rf,max

0.1 

0.4 

βf

, deg 

15.97 

20.30 

Lf /hm

1.1 

1.1 

Sidewall 

S1 

S1 

rs /rs,max

0 

0 

βs

, deg 

4.0 

4.0 

M = 0.80, NPR = 3.54 

Flap top center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 3.55 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 3.50 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 6.55 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.80, NPR = 3.54 

Flap top outboard row, z/wf /2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 3.55 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 3.50 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 6.55 

Figure 97. Effect of flap radius of curvature on upper flap pressure distributions for nozzles with 

sidewall S1 at scheduled NPR. 

227 
Figure 98. Effect of flap length on pressure drag coefficients for nozzles

with sidewall S1 at scheduled pressure.

228

M = 0.80

NPR = 3.54

M = 0.90

NPR = 3.54

M = 0.95

NPR = 3.54

M = 1.20

NPR = 6.60

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p,f

0.0004

0.0002

0

CD,p,s

CD,p

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

S1 F2 F6

Nozzle Flap rf /rf,max βf , deg Lf /hm Sidewall rs /rs,max βs , deg

N2

N14

F2

F6

0.1

0.1

12.88

15.97

1.4

1.1

S1

S1

0

0

4.0

4.0
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Nozzle 

N2 

N14 

Flap 

F2 

F6 

Lf /hm

1.4 

1.1 

βf

, deg 

12.88 

15.97 

rf /rf,max

0.1 

0.1 

Sidewall 

S1 

S1 

rs /rs,max

0 

0 

βs

, deg 

4.0 

4.0 

M = 0.80, NPR = 3.54 

Flap top center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 3.54 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 3.52 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 6.64 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.80, NPR = 3.54 

Flap top outboard row, z/wf /2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 3.54 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 3.52 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 6.33 

Figure 99. Effect of flap length on upper flap pressure distributions for nozzles with 

sidewall S1 at scheduled NPR. 

229 
Figure 100. Effect of flap length on pressure drag coefficients for

 nozzles with sidewall S1 at scheduled pressure.

230

0.0004

0.0002

0

CD,p,s

M = 0.80

NPR = 3.54

M = 0.90

NPR = 3.54

M = 0.95

NPR = 3.54

M = 1.20

NPR = 6.6

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p,f

CD,p

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

F1

F5

S1

Nozzle Flap rf /rf,max βf , deg Lf /hm Sidewall rs /rs,max βs , deg

N1

N13

F1

F5

0.4

0.4

16.38

20.30

1.4

1.1

S1

S1

0

0

4.0

4.0
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Nozzle 

N1 

N13 

Flap 

F1 

F5 

Lf /hm

1.4 

1.1 

βf

, deg 

16.38 

20.30 

rf /rf,max

0.4 

0.4 

Sidewall 

S1 

S1 

rs /rs,max

0 

0 

βs

, deg 

4.0 

4.0 

M = 0.80, NPR = 3.52 

Flap top center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 4.22 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 3.51 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 6.53 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.80, NPR = 3.52 

Flap top outboard row, z/wf /2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 3.54 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 3.51 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 6.53 

Figure 101. Effect of flap length on upper flap pressure distributions for nozzles with 

sidewall S1 at scheduled NPR. 

231 
 Nozzle Sidewall βs , deg rs / rs,max Flap Lf

 / hm rf / rf,max βf , deg

 N1 S1 4.0 0 F1 1.4 0.4 16.38

 N5 S2 6.0 0 F1 1.4 0.4 16.38

 N6 S3 8.0 0 F1 1.4 0.4 16.38

M = 0.80

NPR = 3.54

M = 0.90

NPR = 3.54

M = 0.95

NPR = 3.54

M = 1.20

NPR = 6.6

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p,f

0.0004

0.0002

0

CD,p,s

CD,p

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

S1 S3

S2

Figure 102. Effect of sidewall boattail angle on pressure drag coefficients

 for nozzles with flap F1 at scheduled pressure ratio.

232
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

Nozzle 

N1 

N5 

N6 

Sidewall 

S1 

S2 

S3 

βs

, deg 

4.0 

6.0 

8.0 

rs /rs,max

0 

0 

0 

Flap 

F1 

F1 

F1 

Lf /hm

1.4 

1.4 

1.4 

rf /rf,max

0.4 

0.4 

0.4 

βf

, deg 

16.38 

16.38 

16.38 

M = 0.80, NPR = 3.53 

Sidewall center row, y/hm /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.90, NPR = 3.53 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.95, NPR = 3.55 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 1.20, NPR = 6.65 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.80, NPR = 3.53 

Sidewall outboard row, y/hm /2 = 0.87 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.90, NPR = 3.53 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.95, NPR = 3.55 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 1.20, NPR = 6.65 

Figure 103. Effect of sidewall boattail angle on sidewall pressure distributions for nozzles with 

flap F1 at scheduled NPR. 

233 
0.0004

0.0002

0

CD,p,s

 Nozzle Sidewall rs / rs,max βs , deg Flap Lf / hm rf / rf,max βf , deg

 N5 S2 0 6.0 F1 1.4 0.4 16.38

 N7 S4 0.1 6.0 F1 1.4 0.4 16.38

 N9 S6 0.4 6.0 F1 1.4 0.4 16.38

M = 0.80

NPR = 3.54

M = 0.90

NPR = 3.54

M = 0.95

NPR = 3.54

M = 1.20

NPR = 6.6

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p,f

CD,p

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

S6

S4 S2

Figure 104. Effect of sidewall radius of curvature and base on pressure drag

 coefficients for nozzles with flap F1 at scheduled pressure ratio.

234
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

Nozzle 

N5 

N7 

N9 

Sidewall 

S2 

S4 

S6 

rs /rs,max

0 

0.1 

0.4 

βs

, deg 

6.0 

6.0 

6.0 

Flap 

F1 

F1 

F1 

Lf /hm

1.4 

1.4 

1.4 

rf /rf,max

0.4 

0.4 

0.4 

βf

, deg 

16.38 

16.38 

16.38 

M = 0.80, NPR = 3.54 

Sidewall center row, y/hm /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.90, NPR = 3.57 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.95, NPR = 3.55 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 1.20, NPR = 6.66 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.80, NPR = 3.54 

Sidewall outboard row, y/hm /2 = 0.87 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.90, NPR = 3.57 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.95, NPR = 3.55 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 1.20, NPR = 6.66 

Figure 105. Effect of sidewall radius of curvature and base on sidewall pressure distributions for nozzles with. 

flap F1 at scheduled NPR. 

235 
0.0004

0.0002

0

CD,p,s

 Nozzle Sidewall rs / rs,max βs , deg Flap Lf / hm rf / rf,max βf , deg

 N6 S3 0 8.0 F1 1.4 0.4 16.38

 N8 S5 0.1 8.0 F1 1.4 0.4 16.38

 N10 S7 1.0 8.0 F1 1.4 0.4 16.38

M = 0.80

NPR = 3.54

M = 0.90

NPR = 3.54

M = 0.95

NPR = 3.54

M = 1.20

NPR = 6.6

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p,f

CD,p

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

S7

S3

S5

Figure 106. Effect of sidewall radius of curvature on pressure drag

coefficients for nozzles with flap F1 at scheduled pressure ratio.

236
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

Nozzle 

N6 

N8 

N10 

Sidewall 

S3 

S5 

S7 

rs /rs,max

0 

0.1 

1.0 

βs

, deg 

8.0 

8.0 

8.0 

Flap 

F1 

F1 

F1 

Lf /hm

1.4 

1.4 

1.4 

rf /rf,max

0.4 

0.4 

0.4 

βf

, deg 

16.38 

16.38 

16.38 

M = 0.80, NPR = 3.57 

Sidewall center row, y/hm /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.90, NPR = 3.51 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.95, NPR = 3.55 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 1.20, NPR = 6.64 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.80, NPR = 3.57 

Sidewall outboard row, y/hm /2 = 0.87 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.90, NPR = 3.51 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 0.95, NPR = 3.55 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,s 

M = 1.20, NPR = 6.64 

Figure 107. Effect of sidewall radius of curvature on sidewall pressure distributions for nozzles with 

flap F1 at scheduled NPR. 

237 
 Nozzle Sidewall βs , deg rs / rs,max Flap Lf

 / hm rf / rf,max βf , deg

 N1 S1 4.0 0 F1 1.4 0.4 16.38

 N11 S8 4.0 0 F1 1.4 0.4 16.38

M = 0.80

NPR = 3.54

M = 0.90

NPR = 3.54

M = 0.95

NPR = 3.54

M = 1.20

NPR = 6.6

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p,f

0.0004

0.0002

0

CD,p,s

CD,p

0.0014

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

F1 S8 S1

Figure 108. Effect of reduced sidewall height on pressure drag coefficients

 for nozzles with flap F1 at scheduled pressure ratio.

238
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Nozzle 

N1 

N11 

Sidewall 

S1 

S8 

βs, deg 

4.0 

4.0 

rs /rs,max

0 

0 

Flap 

F1 

F1 

Lf /hm

1.4 

1.4 

rf /rf,max

0.4 

0.4 

βf, deg 

16.38 

16.38 

M = 0.80, NPR = 3.53 

Flap top center row, z/wf /2 = 0 

S1 

F1 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 3.53 

S1 

F1 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 3.54 

S1 

F1 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 6.62 

S1 

F1 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.80, NPR = 3.53 

Flap top outboard row, z/wf /2 = 0.95 

S1 

F1 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 3.53 

S1 

F1 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 3.54 

S1 

F1 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 6.62 

S1 

F1 S8 

Figure 109. Effect of reduced sidewall height on nozzle pressure distributions 

for nozzles with flap F1 at scheduled NPR. 

239
M = 0.80

NPR = 3.54

M = 0.90

NPR = 3.54

M = 0.95

NPR = 3.54

M = 1.20

NPR = 6.6

CD,p,f

0.0004

0.0002

0

CD,p,s

-0.0002

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

CD,p

-0.0002

0.0012

0.0010

0.0008

0.0006

0.0004

0.0002

0

 Nozzle Sidewall βs , deg rs / rs,max Flap Lf / hm rf / rf,max βf , deg

 N2 S1 4.0 0 F2 1.4 0.1 12.88

 N12 S8 4.0 0 F2 1.4 0.1 12.88

S1

S8

F2

Figure 110. Effect of reduced sidewall height on pressure drag coefficients

 for nozzles with flap F2 at scheduled pressure ratio.

240
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Nozzle 

N2

N12 

Sidewall 

S1 

S8 

βs

, deg 

4.0 

4.0 

rs /rs,max

0 

0 

Flap 

F2 

F2 

Lf /hm

1.4 

1.4 

rf /rf,max

0.1 

0.1 

βf

, deg 

12.88 

12.88 

M = 0.80, NPR = 3.53 

Flap top center row, z/wf /2 = 0 

S1 

F2 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 3.54 

S1 

F2 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 3.54 

S1 

F2 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 6.67 

S1 

F2 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.80, NPR = 3.53 

Flap top outboard row, z/wf /2 = 0.95 

S1 

F2 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.90, NPR = 3.54 

S1 

F2 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 0.95, NPR = 3.54 

S1 

F2 S8 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

M = 1.20, NPR = 6.67 

S1 

F2 S8 

Figure 111. Effect of reduced sidewall height on nozzle pressure distributions 

for nozzles with flap F2 at scheduled NPR. 

241 
Figure 112. Incremental nozzle pressure drag for nozzle N1 with flap F1 and sidewall S1. 

rf / rf,max = 0.4; βf = 16.38°; Lf / hm = 1.4: βs = 4.0°; rs / rs,max = 0.

242

ΔCD,p

M = 0.80 M = 0.90 M = 0.95 M = 1.20

 NPR

 3.54 - Scheduled

 5.00 - Design

 6.60 - Scheduled

ΔCD,p = (CD,p)NPR - (CD,p)jet-off
Figure 113. Incremental nozzle pressure drag for nozzle N2 with flap F2 and sidewall S1. 

rf / rf,max = 0.1; βf = 12.88°; Lf / hm = 1.4: βs = 4.0°; rs / rs,max = 0.

243

ΔCD,p

M = 0.80 M = 0.90 M = 0.95 M = 1.20

 NPR

 3.54 - Scheduled

 5.00 - Design

 6.60 - Scheduled

ΔCD,p = (CD,p)NPR - (CD,p) jet-off
Figure 114. Incremental nozzle pressure drag for nozzle N3 with flap F3 and sidewall S1. 

rf / rf,max = 0; βf = 11.72°; Lf / hm = 1.4: βs = 4.0°; rs / rs,max = 0.

244

ΔCD,p

M = 0.80 M = 0.90 M = 0.95 M = 1.20

 NPR

 3.54 - Scheduled

 5.00 - Design

 6.60 - Scheduled

ΔCD,p = (CD,p)NPR - (CD,p)NPR, jet-off

ΔCD,p = (CD,p)NPR - (CD,p) jet-off
Figure 115. Incremental nozzle pressure drag for nozzle N4 with flap F4 and sidewall S1. 

rf / rf,max = 1.0; βf = 23.44°; Lf / hm = 1.4: βs = 4.0°; rs / rs,max = 0.

245

ΔCD,p

M = 0.80 M = 0.90 M = 0.95 M = 1.20

 NPR

 3.54 - Scheduled

 5.00 - Design

 6.60 - Scheduled

ΔCD,p = (CD,p)NPR - (CD,p)NPR, jet-off

ΔCD,p = (CD,p)NPR - (CD,p) jet-off
Figure 116. Incremental nozzle pressure drag for nozzle N5 with flap F1 and sidewall S2. 

rf / rf,max = 0.4; βf = 16.38°; Lf / hm = 1.4: βs = 6.0°; rs / rs,max = 0.

246

ΔCD,p

M = 0.80 M = 0.90 M = 0.95 M = 1.20

 NPR

 3.54 - Scheduled

 5.00 - Design

 6.60 - Scheduled

ΔCD,p = (CD,p)NPR - (CD,p)NPR, jet-off

ΔCD,p = (CD,p)NPR - (CD,p) jet-off
Figure 117. Incremental nozzle pressure drag for nozzle N6 with flap F1 and sidewall S3. 

rf / rf,max = 0.4; βf = 16.38°; Lf / hm = 1.4: βs = 8.0°; rs / rs,max = 0.

247

ΔCD,p

M = 0.80 M = 0.90 M = 0.95 M = 1.20

 NPR

 3.54 - Scheduled

 5.00 - Design

 6.60 - Scheduled

ΔCD,p = (CD,p)NPR - (CD,p)NPR, jet-off

ΔCD,p = (CD,p)NPR - (CD,p) jet-off
Figure 118. Incremental nozzle pressure drag for nozzle N7 with flap F1 and sidewall S4. 

rf / rf,max = 0.4; βf = 16.38°; Lf / hm = 1.4: βs = 6.0°; rs / rs,max = 0.1.

248

ΔCD,p

M = 0.80 M = 0.90 M = 0.95 M = 1.20

 NPR

 3.54 - Scheduled

 5.00 - Design

 6.60 - Scheduled

ΔCD,p = (CD,p)NPR - (CD,p)NPR, jet-off

ΔCD,p = (CD,p)NPR - (CD,p) jet-off
Figure 119. Incremental nozzle pressure drag for nozzle N8 with flap F1 and sidewall S5. 

rf / rf,max = 0.4; βf = 16.38°; Lf / hm = 1.4: βs = 8.0°; rs / rs,max = 0.1.

249

ΔCD,p

M = 0.80 M = 0.90 M = 0.95 M = 1.20

 NPR

 3.54 - Scheduled

 5.00 - Design

 6.60 - Scheduled

ΔCD,p = (CD,p)NPR - (CD,p)NPR, jet-off

ΔCD,p = (CD,p)NPR - (CD,p) jet-off
Figure 120. Incremental nozzle pressure drag for nozzle N9 with flap F1 and sidewall S6. 

rf / rf,max = 0.4; βf = 16.38°; Lf / hm = 1.4: βs = 6.0°; rs / rs,max = 0.4.

250

ΔCD,p

M = 0.80 M = 0.90 M = 0.95 M = 1.20

 NPR

 3.54 - Scheduled

 5.00 - Design

 6.60 - Scheduled

ΔCD,p = (CD,p)NPR - (CD,p)NPR, jet-off

ΔCD,p = (CD,p)NPR - (CD,p) jet-off
Figure 121. Incremental nozzle pressure drag for nozzle N10 with flap F1 and sidewall S7. 

rf / rf,max = 0.4; βf = 16.38°; Lf / hm = 1.4: βs = 8.0°; rs / rs,max = 1.0.

251

ΔCD,p

M = 0.80 M = 0.90 M = 0.95 M = 1.20

 NPR

 3.54 - Scheduled

 5.00 - Design

 6.60 - Scheduled

ΔCD,p = (CD,p)NPR - (CD,p)NPR, jet-off

ΔCD,p = (CD,p)NPR - (CD,p) jet-off
Figure 122. Incremental nozzle pressure drag for nozzle N11 with flap F1 and sidewall S8. 

rf / rf,max = 0.4; βf = 16.38°; Lf / hm = 1.4: βs = 4°; rs / rs,max = 1.0.

252

ΔCD,p

M = 0.80 M = 0.90 M = 0.95 M = 1.20

 NPR

 3.54 - Scheduled

 5.00 - Design

 6.60 - Scheduled

ΔCD,p = (CD,p)NPR - (CD,p)NPR, jet-off

ΔCD,p = (CD,p)NPR - (CD,p) jet-off
Figure 123. Incremental nozzle pressure drag for nozzle N12 with flap F2 and sidewall S8. 

rf / rf,max = 0.1; βf = 12.88°; Lf / hm = 1.4: βs = 4°; rs / rs,max = 1.0.

253

ΔCD,p

M = 0.80 M = 0.90 M = 0.95 M = 1.20

 NPR

 3.54 - Scheduled

 5.00 - Design

 6.60 - Scheduled

ΔCD,p = (CD,p)NPR - (CD,p)NPR, jet-off

ΔCD,p = (CD,p)NPR - (CD,p) jet-off
Figure 124. Incremental nozzle pressure drag for nozzle N13 with flap F5 and sidewall S1. 

rf / rf,max = 0.4; βf = 20.30°; Lf / hm = 1.1: βs = 4°; rs / rs,max = 1.0.

254

ΔCD,p

M = 0.80 M = 0.90 M = 0.95 M = 1.20

 NPR

 3.54 - Scheduled

 5.00 - Design

 6.60 - Scheduled

ΔCD,p = (CD,p)NPR - (CD,p)NPR, jet-off

ΔCD,p = (CD,p)NPR - (CD,p) jet-off
Figure 125. Incremental nozzle pressure drag for nozzle N14 with flap F6 and sidewall S1. 

rf / rf,max = 0.1; βf = 15.97°; Lf / hm = 1.1: βs = 4°; rs / rs,max = 1.0.

255

ΔCD,p

M = 0.80 M = 0.90 M = 0.95 M = 1.20

 NPR

 3.54 - Scheduled

 5.00 - Design

 6.60 - Scheduled

ΔCD,p = (CD,p)NPR - (CD,p)NPR, jet-off

ΔCD,p = (CD,p)NPR - (CD,p) jet-off
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.04 

2.02 

3.52 

4.98 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(a) M = 0.80. 

Figure 126. External pressure distributions for nozzle N1 with flap F1 and sidewall S1. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 4.0°; rs /rs,max = 0. 

256 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.06 

2.50 

3.52 

5.00 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(b) M = 0.90. 

Figure 126. Continued. 

257 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.08 

2.49 

3.55 

4.97 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(c) M = 0.95. 

Figure 126. Continued. 

258 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

0.90 

3.55 

5.00 

6.58 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(d) M = 1.20. 

Figure 126. Concluded. 

259 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.03 

1.98 

3.53 

5.01 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = 0.87 

(a) M = 0.80. 

Figure 127. External pressure distributions for nozzle N2 with flap F2 and sidewall S1. 

rf /rf,max = 0.1; βf = 12.88°; Lf /hm = 1.4; βs

 = 4.0°; rs /rs,max = 0. 

260 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.05 

2.48 

3.56 

5.03 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(b) M = 0.90. 

Figure 127. Continued. 

261 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.08 

2.52 

3.53 

5.01 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(c) M = 0.95. 

Figure 127. Continued. 

262 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

0.86 

3.56 

5.00 

6.66 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(d) M = 1.20. 

Figure 127. Concluded. 

263 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.02 

2.01 

3.53 

4.96 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = 0.87 

(a) M = 0.80. 

Figure 128. External pressure distributions for nozzle N3 with flap F3 and sidewall S1. 

rf /rf,max = 0; βf = 11.72°; Lf /hm = 1.4; βs

 = 4.0°; rs /rs,max = 0. 

264 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.04 

2.45 

3.53 

6.01 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = 0.87 

(b) M = 0.90. 

Figure 128. Continued. 

265 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.07 

2.48 

3.50 

5.03 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = 0.87 

(c) M = 0.95. 

Figure 128. Continued. 

266 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

0.87 

3.50 

5.06 

6.60 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(d) M = 1.20. 

Figure 128. Concluded. 

267 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.05 

2.02 

3.51 

5.03 

Flap top center row, z/wf / = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(a) M = 0.80. 

Figure 129. External pressure distributions for nozzle N4 with flap F4 and sidewall S1. 

rf /rf,max = 1.0; βf = 23.44°; Lf /hm = 1.4; βs

 = 4.0°; rs /rs,max = 0. 

268 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.07 

2.52 

3.60 

4.92 

Flap top center row, z/wf / = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(b) M = 0.90. 

Figure 129. Continued. 

269 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.07 

2.45 

3.54 

4.99 

Flap top center row, z/wf / = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(c) M = 0.95. 

Figure 129. Continued. 

270 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

0.88 

3.53 

5.00 

6.62 

Flap top center row, z/wf / = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(d) M = 1.20. 

Figure 129. Concluded. 

271 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.05 

1.99 

3.55 

5.00 

Flap top center row, z/wf / = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(a) M = 0.80. 

Figure 130. External pressure distributions for nozzle N5 with flap F1 and sidewall S2. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 6.0°; rs /rs,max = 0. 

272 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.08 

2.49 

3.55 

5.01 

Flap top center row, z/wf / = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = 0.87 

(b) M = 0.90. 

Figure 130. Continued. 

273 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.06 

2.51 

3.55 

5.00 

Flap top center row, z/wf / = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(c) M = 0.95. 

Figure 130. Continued. 

274 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

0.92 

3.51 

5.01 

6.70 

Flap top center row, z/wf / = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(d) M = 1.20. 

Figure 130. Concluded. 

275 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.06 

2.53 

3.51 

5.00 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(a) M = 0.80. 

Figure 131. External pressure distributions for nozzle N6 with flap F1 and sidewall S3. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 8.0°; rs /rs,max = 0. 

276 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.09 

2.49 

3.53 

5.02 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

 0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(b) M = 0.90. 

Figure 131. Continued. 

277 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.07 

2.52 

3.55 

5.02 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(c) M = 0.95. 

Figure 131. Continued. 

278 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

0.93 

3.54 

5.03 

6.68 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(d) M = 1.20. 

Figure 131. Concluded. 

279 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.05 

1.98 

3.50 

4.97 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(a) M = 0.80. 

Figure 132. External pressure distributions for nozzle N7 with flap F1 and sidewall S4. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 6.0°; rs /rs,max = 0.1. 

280 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.08 

2.42 

3.59 

5.10 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(b) M = 0.90. 

Figure 132. Continued. 

281 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.06 

2.47 

3.51 

4.97 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(c) M = 0.95. 

Figure 132. Continued. 

282 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

0.92 

3.51 

5.04 

6.64 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(d) M = 1.20. 

Figure 132. Concluded. 

283 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.06 

2.03 

3.54 

5.03 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(a) M = 0.80. 

Figure 133. External pressure distributions for nozzle N8 with flap F1 and sidewall S5. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 8.0°; rs /rs,max = 0.1. 

284 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.09 

2.49 

3.50 

5.01 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(b) M = 0.90. 

Figure 133. Continued. 

285 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.06 

2.48 

3.57 

5.07 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(c) M = 0.95. 

Figure 133. Continued. 

286 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

0.94 

3.57 

5.05 

6.64 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(d) M = 1.20. 

Figure 133. Concluded. 

287 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.05 

2.01 

3.56 

4.99 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(a) M = 0.80. 

Figure 134. External pressure distributions for nozzle N9 with flap F1 and sidewall S6. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 6.0°; rs /rs,max = 0.4. 

288 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.07 

2.49 

3.57 

4.99 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(b) M = 0.90. 

Figure 134. Continued. 

289 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.06 

2.54 

3.57 

5.03 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(c) M = 0.95. 

Figure 134. Continued. 

290 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

0.91 

3.54 

5.03 

6.65 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(d) M = 1.20. 

Figure 134. Concluded. 

291 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.06 

2.51 

3.67 

4.99 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(a) M = 0.80. 

Figure 135. External pressure distributions for nozzle N10 with flap F1 and sidewall S7. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 8.0°; rs /rs,max = 1.0. 

292 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.08 

2.51 

3.49 

4.99 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(b) M = 0.90. 

Figure 135. Continued. 

293 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.07 

2.51 

3.53 

5.05 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(c) M = 0.95. 

Figure 135. Continued. 

294 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

0.93 

3.55 

4.94 

6.59 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm / 2 = -0.87 

(d) M = 1.20. 

Figure 135. Concluded. 

295 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.04 

1.88 

3.53 

4.95 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row 

(a) M = 0.80. 

Figure 136. External pressure distributions for nozzle N11 with flap F1 and sidewall S8. 

rf /rf,max = 0.4; βf = 16.38°; Lf /hm = 1.4; βs

 = 4.0°; rs /rs,max = 0. 

296 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.06 

2.51 

3.54 

5.01 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row 

(b) M = 0.90. 

Figure 136. Continued. 

297 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.07 

2.53 

3.54 

4.98 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row 

(c) M = 0.95. 

Figure 136. Continued. 

298 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

0.91 

3.53 

4.99 

6.65 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row 

(d) M = 1.20. 

Figure 136. Concluded. 

299 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.02 

2.01 

3.54 

5.01 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row 

(a) M = 0.80. 

Figure 137. External pressure distributions for nozzle N12 with flap F2 and sidewall S8. 

rf /rf,max = 0.1; βf = 12.88°; Lf /hm = 1.4; βs

 = 4.0°; rs /rs,max = 0. 

300 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.04 

2.53 

3.53 

5.01 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row 

(b) M = 0.90. 

Figure 137. Continued. 

301 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.07 

2.54 

3.54 

4.99 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row 

(c) M = 0.95. 

Figure 137. Continued. 

302 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf / 2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf / 2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

0.85 

3.53 

5.02 

6.67 

Flap top center row, z/wf / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm / 2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row 

(d) M = 1.20. 

Figure 137. Concluded. 

303
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf /2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf /2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.05 

2.00 

3.53 

5.06 

Flap top center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm /2 = -0.87 

(a) M = 0.80. 

Figure 138. External pressure distributions for nozzle N13 with flap F5 and sidewall S1. 

rf /rf,max = 0.4; βf = 20.30°; Lf /hm = 1.1; βs

 = 4.0°; rs /rs,max = 0. 

304 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf /2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf /2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.06 

2.52 

3.57 

4.93 

Flap top center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm /2 = -0.87 

(b) M = 0.90. 

Figure 138. Continued. 

305 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf /2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf /2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.02 

2.55 

3.48 

5.04 

Flap top center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm /2 = -0.87 

(c) M = 0.95. 

Figure 138. Continued. 

306 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf /2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf /2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

0.86 

3.52 

5.09 

6.49 

Flap top center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm /2 = -0.87 

(d) M = 1.20. 

Figure 138. Concluded. 

307 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf /2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf /2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.04 

1.98 

3.55 

5.07 

Flap top center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm /2 = -0.87 

(a) M = 0.80. 

Figure 139. External pressure distributions for nozzle N14 with flap F6 and sidewall S1. 

rf /rf,max = 0.1; βf = 15.97°; Lf /hm = 1.1; βs

 = 4.0°; rs /rs,max = 0. 

308 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf /2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf /2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.06 

2.52 

3.52 

5.01 

Flap top center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm /2 = -0.87 

(b) M = 0.90. 

Figure 139. Continued. 

309 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf /2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf /2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

1.04 

2.53 

3.51 

4.99 

Flap top center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm /2 = -0.87 

(c) M = 0.95. 

Figure 139. Continued. 

310 
0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap bottom middle row, z/wf /2 = 0.5 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

Flap top outboard row, z/wf /2 = 0.95 

0 .2 .4 .6 .8 1.0 

x/Ln 

-1.2 

-.8 

-.4 

0 

.4 

Cp,f 

NPR 

0.87 

3.55 

4.98 

6.61 

Flap top center row, z/wf /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall center row, y/hm /2 = 0 

0 .2 .4 .6 .8 1.0 

x/Ln 

-.8 

-.4 

0 

.4 

Cp,s 

Sidewall outboard row, y/hm /2 = -0.87 

(d) M = 1.20. 

Figure 139. Concluded. 

311 
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Technical Memorandum

 4. TITLE AND SUBTITLE

Transonic Investigation of Two-Dimensional Nozzles Designed for 

Supersonic Cruise 

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 6. AUTHOR(S)

Capone, Francis J.; Deere, Karen A.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-2199

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National Aeronautics and Space Administration

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14. ABSTRACT

An experimental and computational investigation has been conducted to determine the offdesign uninstalled drag characteristics of a two-dimensional 

convergent-divergent nozzle designed for a supersonic cruise civil transport. The overall objectives were to: (1) determine the effects of nozzle external flap 

curvature and sidewall boattail variations on boattail drag; (2) develop an experimental data base for 2D nozzles with long divergent flaps and low boattail 

angles and (3) provide data for correlating computational fluid dynamic predictions of nozzle boattail drag. The experimental investigation was conducted in 

the Langley 16-Foot Transonic Tunnel at Mach numbers from 0.80 to 1.20 at nozzle pressure ratios up to 9. Three-dimensional simulations of nozzle 

performance were obtained with the computational fluid dynamics code PAB3D using turbulence closure and nonlinear Reynolds stress modeling. The results 

of this investigation indicate that excellent correlation between experimental and predicted results was obtained for the nozzle with a moderate amount of 

boattail curvature. The nozzle with an external flap having a sharp shoulder (no curvature) had the lowest nozzle pressure drag. At a Mach number of 1.2, 

sidewall pressure drag doubled as sidewall boattail angle was increased from 4° to 8°. Reducing the height of the sidewall caused large decreases in both the 

sidewall and flap pressure drags. 

15. SUBJECT TERMS

Boattails; Curvature; Flapping; Pressure drag

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319

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(757) 864-9658

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01- 08 - 2015