a base drag reduction experiment on the x-33 linear

NASA/TM-1999-206575

A Base Drag Reduction Experimenton the X-33 Linear Aerospike SR-71 Experiment (LASRE) Flight Program

Stephen A. Whitmore and Timothy R. MoesDryden Flight Research CenterEdwards, California

March 1999

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NASA/TM-1999-206575

A Base Drag Reduction Experimenton the X-33 Linear Aerospike SR-71 Experiment (LASRE) Flight Program

Stephen A. Whitmore and Timothy R. MoesDryden Flight Research CenterEdwards, California

March 1999

National Aeronautics andSpace Administration

Dryden Flight Research CenterEdwards, California 93523-0273

NOTICE

Use of trade names or names of manufacturers in this document does not constitute an official endorsementof such products or manufacturers, either expressed or implied, by the National Aeronautics andSpace Administration.

Available from the following:

NASA Center for AeroSpace Information (CASI) National Technical Information Service (NTIS)7121 Standard Drive 5285 Port Royal RoadHanover, MD 21076-1320 Springfield, VA 22161-2171(301) 621-0390 (703) 487-4650

Acknowledgments

The authors thank the SR-71 crew for allowing access to the aircraft during a high-pressure time near theend of the program. The authors also acknowledge the expert assistance of Dale Hilliard andJerry S. Reedy of Kaye and Associates in applying the gritted paint to the flight experiment.

d

A BASE DRAG REDUCTION EXPERIMENT ON THE X-33 LINEAR AEROSPIKE SR-71 EXPERIMENT (LASRE) FLIGHT PROGRAM

Stephen A. Whitmore,* Timothy R. Moes†

NASA Dryden Flight Research CenterEdwards, California

area of gap between reflection plane anA

e

a

Abstract

Drag reduction tests were conducted on the LASRX-33 flight experiment. The LASRE experiment is flight test of a roughly 20-percent scale model of aX-33 forebody with a single aerospike engine at the reThe experiment apparatus is mounted on top of SR-71 aircraft. This paper suggests a method reducing base drag by adding surface roughness althe forebody. Calculations show a potential for badrag reductions of 8 to 14 percent. Flight resucorroborate the base drag reduction, with actureductions of 15 percent in the high-subsonic fligregime. An unexpected result of this experiment is thdrag benefits were shown to persist well into thsupersonic flight regime. Flight results show no overnet drag reduction. Applied surface roughness cauforebody pressures to rise and offset base dreductions. Apparently the grit displaced streamlinoutward, causing forebody compression. Results of LASRE drag experiments are inconclusive and mowork is needed. Clearly, however, the forebody gapplication works as a viable drag reduction tool.

Nomenclature

total base area for LASRE model, ft2

projected area of LASRE boat tail base onto y-z plane, ft2

projected area of engine plug base ontoy-z plane, ft2

projected area of engine fence onto y-z plane, ft2

Abase

Aboat

Aeng base

Afence

1American Institute of Ae

*Vehicle Aerodynamics Group Leader, Senior Member, AIAA.†Aerospace Engineer, Member, AIAA.

Copyright 1999 by the American Institute of Aeronautics anAstronautics, Inc. No copyright is asserted in the United States unTitle 17, U.S. Code. The U.S. Government has a royalty-free liceto exercise all rights under the copyright claimed herein for Govemental purposes. All other rights are reserved by the copyright own

a
d
dernsern-er.

E/anar.anforongseltsal

htate

allsesragesthererit

model, ft2

wetted area of forebody surface grit, ft2

linear acceleration vector, measured at instrument package, ft/sec2

projected area of engine ramp onto y-z plane, ft2

LASRE forebody wetted area, ft2

reference span

base drag coefficient, referenced to basarea

predicted base drag coefficient, referenced to base area

predicted base drag coefficient, incompressible flow conditions, referenced to base area

forebody pressure drag coefficient, referenced to base area

total viscous forebody drag coefficient, referenced to base area

total pressure drag coefficient for the LASRE model, referenced to base are

LASRE parasite drag coefficient, referenced to base area

zero-lift drag coefficient of the LASRE model, from balance, referenced to base area

predicted zero-lift drag coefficient of theLASRE model, referenced to base are

zero-lift drag coefficient of the LASRE model, from pressures, referenced to base area

gap

Agrit

Ameas

Aramp

Awet

Bref

CDbase

C̃DbaseM∞[ ]

C̃Dbase

o( )

CD fore

CD fore

visc( )

CDp

CDparabase

CD0

C̃D0

CD0

p( )

ronautics and Astronautics

e

forebody skin friction drag coefficient, referenced to base area

skin friction coefficient for rough flat plate, referenced to

skin friction coefficient for smooth flat plate, referenced to

pressure coefficient

integrated surface pressure coefficient

integrated engine base pressure coefficient

integrated boat tail pressure coefficient

integrated lower engine fence pressure coefficient

integrated forebody pressure coefficient

pressure coefficient measured at i’th pressure port

integrated left-nozzle ramp pressure coefficient

integrated right-nozzle ramp pressure coefficient

true force vector acting on LASRE model, lbf

friction force acting between reflection plane and model, lbf

raw force vector measured by LASRE model balance, lbf

i

port index

L

length, ft

mass of the LASRE model, excluding reflection plane, slugs

divergence drag rise Mach number

freestream Mach number

N

number of ports used in integration

base pressure, lb/ft

2

psia absolute pressure, lb/in

2

psid differential pressure, lb/in

2

freestream static pressure, lb/ft

2

weighting function for surface pressure measurement

Reynold’s number based on length

offset from SR-71 instrument package tomodel center of gravity, ft

sps samples-per-second

planform reference area

reflection exit velocity, at base of model,ft/sec

freestream velocity, ft/sec

x longitudinal coordinate, ft, in.

y lateral coordinate, ft

z vertical coordinate, ft

increment in total viscous forebody dragcoefficient caused by added forebody roughness, referenced to base area

base drag reduction caused by added forebody roughness, referenced to basarea

equivalent sand-grain roughness of surface extrusions, in.

weighting function scale factor

local flow density, at reflection plane exitat base of model, slug/ft

3

freestream flow density, slug/ft 3

vehicle angular velocity vector, rad/sec

vehicle angular acceleration vector, rad/sec

2

slope of model surface along x-y direction at i’th port

slope of model surface along x-z direction at i’th port

cf base

c f L

rough( )

Awet

c f L

sm( )

Awet

Cp

Cp

Cpbase

Cpboat

Cp fence

Cpfore

Cpi

Cpleft

Cpright

Faero

F f Ram

Fraw

mmodel

Mdiv

M∞

pbase

p∞

qi

ReL

Rmodel

Sref

Vbase

V∞

∆CD fore

visc( )

∆CDbase

κs

ν i

ρbase

ρ∞

ω

ω̇

∂x∂y------

i

∂x∂z------

i

2American Institute of Aeronautics and Astronautics

e

heheforforipsvedne

.ee

sngals,uterwh.the

1

Introduction

Current proposed shapes for reusable single-stage-to-orbit vehicles like the Lockheed Martin X-33 andVentureStar

™

reusable launch vehicle have extremelylarge base areas when compared to previous hypersonicvehicle designs.

1

The comparatively large base areas forthe X-33 and VentureStar™ are a consequence of thelifting-body shape of the vehicle, and the need to fit therectangular linear aerospike engines into the baseregion. As a result, base drag—especially in thetransonic flight regime—is expected to be quite large.Alternatively, the need for a low-drag profile for theascent phase of the flight has resulted in a relativelyclean, low-camber forebody shape for the X-33.Consequently, at low angles of attack one would expectthe forebody drag of the X-33 to be relatively low; andthat base drag would dominate the vehicle dragcharacteristics.

The unique configuration of the X-33, with its largebase area and relatively low forebody drag, offers thepotential for a high payoff in base drag reduction. Thispaper presents results of a base drag-reduction test,conducted on the X-33 Linear Aerospike SR-71Experiment (LASRE).

2

This flight experiment attemptedto reduce base drag by increasing forebody surfaceroughness. This report presents results of theexperiment, and compares the resulting low angle-of-attack drag numbers to the X-33 wind tunnel data base.Effects of the aerospike rocket firing on the base dragcharacteristics are not addressed.

Use of trade names or names of manufacturers in thisdocument does not constitute an official endorsement ofsuch products or manufacturers, either expressed orimplied, by the National Aeronautics and SpaceAdministration.

Background on the LASRE Flight Experiment

The LASRE experiment is a flight test of a roughly

20-percent half-span scale model of an X-33 forebodywith a single aerospike rocket engine at the rear. Asshown in figure 1, the entire test model is mounted ontop of an SR-71 aircraft. It was intended that LASREflight test data would be used to define the aerospikeengine performance under realistic flight conditions andto determine plume interactions with the base andengine cowl areas. NASA Dryden recently concluded

testing of the LASRE without having actually fired throcket engine in flight.

The model is mounted onto the aircraft so that tlateral axis is aligned parallel to the normal axis of tSR-71. This alignment causes the angle of sideslip the SR-71 aircraft to be equivalent to angle of attack the LASRE model. Thus, with a zero-angle-of-sideslflight condition for the SR-71 aircraft, the model iessentially flying at zero angle of attack. To achiebetter flow quality, a reflection plane was mountebetween the SR-71 and the model. The reflection plashields the model from the SR-71 flow field.

Model mold lines are constructed from a 30-indiameter cylinder which is swept away from thlongitudinal axis by an angle of 20°. At the nosetip, thcylinder is faired smoothly with a 15-in. radiuhemisphere. Figure 2 shows a three-view line drawiof the model and documents the primary geometriccomponents—the forebody, boat tail, nozzle rampbase plug, and engine fences. Figure 3 compares omold-lines of the LASRE to a 20-percent scale top-vieof the X-33. Comparisons show a fairly close matcTable 1 compares some vital geometric properties of LASRE model to those of the X-33.™VentureStar is a registered trademark of Lockheed Martin, Inc.,

Mountain View, California.

Reflection plane

LASRE model

980550

Figure 1. The LASRE pod mounted on top of the SR-7aircraft.


ars,at

aesithse,

taofrd

onseargdeorreondpe

oadesonby

ce

Figure 2. The LASRE test model.

Figure 3. A comparison of the LASRE outer mold lineswith the X-33.

Instrumentation and Processing ofthe Onboard Measurements

In order to measure performance of the LineAerospike engine under a variety of flight conditionthe model was mounted to the SR-71 with a pylon thwas instrumented with 8 load cells oriented to allowsix-degree-of-freedom measurement of the total forcand moments. The model was also instrumented wsurface pressure ports on the forebody, boat tail, baengine ramps, and the lower engine fence.

Other onboard instrumentation included the airdameasurements—Mach number, airspeed, angle attack, angle of sideslip, and altitude—from the onboaairdata system of the SR-71, and vehicle acceleratiand angular rates from strapdown sensors located nthe vehicle center of gravity. All onboard analoinstrumentation were sampled using 12-bit pulse comodulation (PCM) and telemetered to the ground fpostflight analysis. The airdata parameters wetelemetered and recorded at 50 samples-per-sec(sps). Onboard accelerometer and rate-gyroscoreadings were telemetered and recorded at 200 sps.

Force Balance Data Measurements

The force balance measurements consisted of 8 lcells, oriented to give outputs proportional to the forcacting along the axial, vertical, and lateral directions the balance (fig. 4). A calibration tensor measured Lockheed Martin (Palmdale, California) prior todelivering the LASRE experiment to NASA Dryden

Front view Rear view

Left side view

Top view

Boat tail TPS

Right engine nozzle ramp

Left engine nozzle ramp

Engine nozzle base plug

Engine thrusters

Forebody

Engine nozzle fence

z

y

980551

57.8 in.

30 in.

20°

10.25 in.

25.5 in.

140 in.165 in.

x

x

z

y

980552

LASRE mold lines

X-33 mold lines

Table 1. Comparison of the LASRE and X-33 referendimensions.2

Symbol Description X-33 LASRE

Planform reference area

1608 ft2 32.15 ft2

Reference length 63.2 ft 13.12 ft

Reference span (60 percent of )

36.6 ft 3.75 ft

Wetted area (excluding base)

5120 ft2 101.62 ft2

Base area 466.9 ft2 12.04 ft2

Note: LASRE reference data are for a half-span vehicle.

Sref

Lref

BrefLref

Awet

Abase


dheta, isarorftthesheREtlyted

ureps,. A

ndtsedted

neAningthe

ereSP)ringncesors;adehlyer.SP

ureerenslsonsentsed

htle

was used to relate the output readings to the true forcesand moments acting on the balance. The balance wasnot re-calibrated during the course of this flightprogram.

Raw force-balance data were sampled at 50 sps, andthese were low-pass filtered using a second-orderButterworth digital filter3 to remove noise caused bystructural vibrations and aerodynamic turbulence. Filterlatency was accounted for by time-skewing the dataafter filtering. The filtered data were corrected for zero-offsets using preflight and postflight zero-tare data. Thezero-readings were taken for each load cell by averagingone minute of data each, from both preflight andpostflight. The calibration tensor was then used tocompute the axial, normal, and side loads, and pitch,roll, and yaw moments acting at the balance.

To determine the true aerodynamic forces acting onthe model, it is necessary to remove the centrifugal forceand vehicle accelerations acting at the model center ofgravity. These corrections were computed using thestrapdown instruments onboard the SR-71 aircraft. Thevector equations for the force transformations are

(1)

In equation 1, is the mass of the model, (thepart of the total experiment mounted above the

reflection plane), is the vector of correcteaerodynamic loads acting on the model, is tforce vector calculated from the uncorrected load da

is the measured linear acceleration vector, the angular rate of the vehicle, is the angulacceleration of the vehicle, and is the vectdistance from the location of the SR-71 aircraaccelerometer package to the center of gravity of model. The center of gravity of the LASRE model lie39.025 ft aft, 7.408 ft above, and 2.708 ft inboard of tSR-71 accelerometer package. For the SR-71 LASexperiment, angular acceleration was not direcmeasured; instead angular acceleration was compuby numerically differentiating the angular rate vector.4

Surface Pressure Measurements

Pressure instrumentation consisted of flush presstaps distributed on the forebody, boat tail, engine ramengine base plug, thruster cowling, and engine fencestotal of 95 ports were distributed on the forebody aboat tail. Locations of the forebody and boat tail porare shown in figure 5. In addition 58 ports were locatin the engine base area, with 20 pressure ports locaon the left engine ramp, 22 ports on the right engiramp, and 16 ports on the engine base plug. additional 2 pressure ports were located on the trailedge of the lower engine fence. Figure 6 shows locations of the engine pressure ports.

Forebody, boat-tail, and nozzle surface pressures wsensed using electronically scanned pressure (Emodules. Because of pressure ranges expected duaerospike engine hot-fire tests, engine ramp and fepressures were sensed using ±50 psid pressure senall other surface pressure measurements were musing ±10 ESPs. All ESPs were referenced to a higaccurate 0-38 psia 20-bit digital pressure transducThe reference pressure was added to the differential Ereadings to determine the absolute local pressreading. Temperature environments of the ESP wcontrolled using heater blankets. Zero-shift correctiousing preflight and postflight tare readings were aperformed. To reduce the effects of structural vibratioand aerodynamic turbulence, pressure measuremwere digitally filtered. All pressure data were measurat 50 sps.

Flight Test Maneuvers

Acceleration data from subsonic to supersonic fligconditions were used in this analysis. Initially, levealtitude accelerations were flown for envelop

Top mountingflange

Lateralload

Axialload

Supportstructure

Bottom mounting flange (to model)

Mounting pylon (to SR-71)

Load cell balance

Top mounting flange

Verticalload

Verticalload

980553

Figure 4. Schematic of the LASRE force balance.

Faero Fraw mmodel{ ⋅–=

Ameas ω ω Rmodel ω̇ Rmodel×+××[ ]+[ ] }

mmodel

FaeroFraw

Ameas ωω̇

Rmodel


d

REnedur,

tiesheeionsnt.ta

del

r

h

g a

on

tal

ise

the

ag

is

g-

expansion and flutter clearance. Once the flightenvelope clearance was obtained, a more fuel-efficientdipsy maneuver was used to accelerate through the largetransonic drag rise. The dipsy maneuver began at28,000 ft and Mach 0.9. The pilot put the aircraft into aslight dive to help get through the transonic drag riseand then leveled the aircraft at approximately Mach 1.07and an altitude of 25,000 ft, which was the minimumaltitude cleared for transonic flight. The aircraftcontinued to accelerate at an altitude of 25,000 ft until itobtained an equivalent airspeed of 450 kn, at whichpoint the pilot initiated a constant equivalent airspeedclimb to the desired Mach number. Structural loadrestrictions on the LASRE experiment required that theangle of sideslip—equivalent to angle of attack in themodel axis—be restricted to less than two degrees.Because of this restriction, all of the drag data obtainedare essentially for the zero-lift flight condition— .

Figure 6. Layout of LASRE engine nozzle plug anramp pressure port.

Baseline Drag Measurements on theLASRE Model Configuration

Baseline drag measurements on the clean LASconfiguration will be presented first. The cleaconfiguration is defined as the model without addforebody surface roughness. Data derived from fotypical flight maneuvers performed during flights 4647, 48, and 49 are used to illustrate the drag properof the model. These baseline drag data verify tresolution, repeatability, and accuracy of thmeasurements; and substantiate the earlier assertthat base drag is the dominating drag-force componeIn the remainder of this paper, all drag coefficient dawill be referenced to the base area of the LASRE moas presented in table 1.

Overall Model Drag Measurements

Figure 7 shows the overall drag coefficient, , fo

the clean LASRE model plotted as a function of Mac

number. Repeatability of the data are excellent, havin

total scatter band of less than 0.015. For comparis

purposes wind-tunnel derived values for the X-33 to

are also plotted. The very large transonic drag r

observed on the flight data does not show up on

wind tunnel predictions. Reasons for the transonic dr

difference are not definite at this point; however, it

possible that this difference is an effect of the stin

mount used to support the X-33 wind tunnel model.

z,in.

80

60

40

20

0

– 40 – 20 0y, in.

0 80x, in.

100 120 140 160

980554

20 40 60

20 40– 20

y,in.

z,in.

80

60

40

20

0

– 20

40

20

0

– 20

– 40

Aft facing boat tail area

Engine nozzle

Engine fence

Top view, looking down

Side view, looking inboard

Front view,looking aft

Engine fence

Figure 5. Port locations on LASRE forebody andboat tail.

CD0

30 in.Upper engine fence

980555

Lef

t th

rust

ers

Rig

ht th

rusters

Lower engine fence

2.125 in.

2.125 in.3

2.25 in.

7.25 in.

6.50 in.2.75 in. 2.75 in.

3.25 in.

6.50 in.

3.00 in.

2.00 in.91 1

2

243

5

3

4

10

11

12

791113

15

20

3.00 in.

5.50 in.8.50 in.

Engine base

Right rampLeft ramp

1.75 in.

6.50 in.

13

14

15

16

9.5 in.

5

6

7

8

171921

22

y

z

68101211975

10864

14161820

1

1

2

3

4

1

2

3

4

2

19171513

18161412

10.25 in.

3.50 in.

25.5 in.0.75 in.

CD0

CD0


otalcales,eatedntasred

thee

reheal

e

nrunnceee,

recalise of

Figure 7. Baseline LASRE total zero-lift dragcoefficient.

Individual Components of the Overall Model Drag Coefficient

The shape of the LASRE curve as a function ofMach number can be better understood by examiningthe individual drag-force components acting on themodel. Since the LASRE model has no camber andnominally flies at zero local angle of attack, induceddrag-due-to-lift is considered to be negligible. Thusthere are 3 remaining drag components which must beconsidered as important:

1. Base and boat tail drag,

2. Forebody pressure-profile drag, and

3. Viscous drag from forebody skin-friction andresidual parasite drag.

Effects of each component on the total LASRE drag arenow presented.

Surface Pressure Integration

Forebody, boat tail, and nozzle base drag coefficientsare computed by numerically integrating the pressuremeasurements along the surface of the body. The

pressure port distribution on the LASRE model is ndense enough to allow a full three-dimensiongeometric integration of the pressures. If a geometrigrid were used to numerically integrate the pressurthe uneven port spacing would give far too much arweighting to the ports located in the sparsely popularegions. Instead, for a given geometrical compone(such as the forebody surface) the surface integral wmechanized as a weighted average of the measupressures.

(2)

Instead of weighting pressures by their local area, weighting function applied in equation 2 is thprojection of the local surface onto the y-z plane,

(3)

Equation 3 weights more heavily ports that aaligned more perpendicular to the drag axis. Tnumerical integration was performed for 6 geometriccomponents on the model:

1. the model forebody, aft to 140 in. behind thnosetip,

2. the engine nozzle left ramp,

3. the engine nozzle right ramp,

4. the engine nozzle base plug,

5. the LASRE model boat tail, and

6. the lower engine fence.

In equation 3, is an arbitrary weighting functioscale factor which was assigned to give better run-to-data consistency. For the base, ramp, boat tail, and feintegrations, the value of was always unity. For thforebody integration, ports along the model centerlinand on the flat side-fairings unity values for weassigned. Ports along the sides of the swept cylindriforebody were assigned values of = 1.5. Thweighting increment helped to account for thsparseness of ports along the swept cylindrical sidesthe forebody.

Zero-liftdrag

coefficient,*CD0

1.0

Mach numberrangeFlight

LASRE total drag coefficientfrom force balance

X-33 total drag coefficient, wind tunnel*Referenced to LASRE base area

0.78 to 1.540.70 to 1.520.68 to 1.620.62 to 1.78

46474849

.2– .2

0

.2

.4

.6

.8

.4 .6 .8 1.0 1.2Mach number

1.4 1.6 1.8 2.0 2.2

980556

CD0

Cp

qiCpi[ ]

i 1=

N

∑

qi[ ]i 1=

N

∑----------------------------=

qi

ν i

1∂x∂y------

i

2 ∂x∂z------

+i

2+

-------------------------------------------------=

ν i

ν i

ν i

ν i


ag

is

ed,

ag

ag

se

he

e

lity

foraheeichtanend apeoes

e as)uretois

heaft,ain. in.ry

or

ll

ls

ly,

the

the

ined

e

ces

Once the individual pressure coefficients of eachgeometrical component are determined, surfacepressure drag is calculated as the area-weighted averageof integrated pressure coefficients for individualgeometrical components,

(4)

The resulting base drag coefficient, = ,

and forebody pressure drag coefficient, = ,

are presented as a function of Mach number in figure 8.

For comparison purposes a fairing of the total drag

coefficient, derived from figure 7, is also presented. In

the subsonic flight regime base drag remains relatively

constant at approximately 0.38 until the divergence dr

rise Mach number, , of approximately 0.90

reached. After the divergence Mach number is reach

compressibility effects dominate and base dr

coefficient rises rapidly. Beyond Mach 1, base dr

drops off steadily. In the subsonic flight regime, ba

drag accounts for approximately 125 percent of t

overall model drag. Approximately 80 percent of th

transonic drag rise can be attributed to compressibi

effects on base drag.

Since base drag is higher than overall model drag subsonic flight conditions, one would expect substantial amount of forebody suction to occur. Tlower curve in figure 8 verifies this expectation. Thforebody drag coefficient is negative until the transondrag rise is encountered. Even in the transonic fligregime, forebody drag coefficient accounts for less th8 percent of the total model drag coefficient. Thstrength of forebody suction is likely a result of a cleaforebody shape for the LASRE. As mentionepreviously, the mold lines for the LASRE forebody are20° swept cylinder faired to flat sidepanels. This shaensures that a significant adverse pressure gradient dnot occur along the forebody.

This premise is illustrated in figure 9(a) where thforebody pressure distribution at Mach 0.70 is plotteda function of the vertical (z) and longitudinal (xcoordinates. Figure 9(b) shows locations of the pressports on the forebody. From the nosetip approximately 40 in. aft, the pressure gradient strongly favorable. Between 40 in. and 100 in. aft, tpressure gradient is almost flat; and beyond 100 in. the pressure gradient becomes strongly favorable agAlthough the surface pressure gradient between 40and 100 in. aft is approximately neutral, the boundalayer in this region is clearly turbulent5 and flowseparation is very unlikely. Pressure distributions fother Mach numbers have a similar profile.

Skin Friction and Parasite Drag Coefficients

Total drag coefficient, , is compared with overa

pressure drag coefficient, , in figure 10. Residua

between the two curves are also plotted. Obvious

residual data include measurement errors in both

force balance and surface pressure data; however,

residual data represent a crude measure of the comb

viscous6 drag forces acting on the model. As will b

shown in the next section, these viscous forebody for

CDpCPfore

= –

Aramp CpleftCp right

+

Aeng base C p base +

+ A boat C p boat

A fence C p fence

+ /

2

A

ramp

A

eng base A boat A fence + + +

CDbase–Cpbase

CDforeCpfore

.2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0

1.0

0

.4

– .2

.2

.8

.6

Dragcoefficient*

Mach number980557

Forebody pressure drag

Base pressure drag

Base + forebody, integrated pressures


Total drag fairing, force balance

*Referenced to LASRE base area

0.78 to 1.540.70 to 1.520.68 to 1.620.62 to 1.78

46474849

Figure 8. Comparison of the total LASRE dragcoefficient with the base and forebody pressure dragcoefficients.

Mdiv

CD0

CDp


he

as

o bye

isthe

thea

g

strongly influence the base drag. As a check on the

accuracy of this crude viscous drag measurement, an

estimate of the viscous forebody drag coefficient,

, is also calculated. For the LASRE model

has two principal components: (1) the forebody skin

friction drag and (2) the

ram drag

resulting from a 1-inch

gap between the lower side of the model and t

reflection plane. The ram drag is considered

equivalent to the

parasite

drag which forms on more

complex aircraft configurations.

The forebody skin friction coefficient (referenced tthe base area of the LASRE model) was evaluatednumerically solving the nonlinear equation for th

Schoenherr line

,

7

(5)

where, is the forebody Reynold’s number, the base area, and is the wetted area of forebody (table 1).

The parasite drag (referenced to the base area ofLASRE model) is calculated by performing

2.0

1.5

1.0

.5

0

– .5

– 1.00

980558

Forebodypressure

coefficient

Distance aft, x, in.50 100 150

Cp –> z = 1.50 in.Cp –> z = 2.90 in.Cp –> z = 9.20 in.Cp –> z = 12.70 in.Cp –> z = 15.60 in.Cp –> z = 21.90 in.Cp –> z = 35.00 in.Cp –> z = 46.00 in.Cp –> z = top row

Flight 46, M∞ = 0.70

(a) Forebody pressure distribution.

(b) Pressure ports on side view of forebody.

Figure 9. LASRE forebody pressure data, Flight 046,Mach 0.70.

z,in.

See legend on Fig. 9(a) for z-axis measurementsindicated by connected pressure points

60

40

20

0

0 20x, in.

40 60 80 100

980559

120 140 160

CD fore

visc( )CD fore

visc( )

xx

.2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0

1.0

0

.4

– .2

.2

.8

.6

Dragcoefficient*

Mach number980560

Integrated base + forebody drag coefficient

Total drag fairing, force balanceComputed viscous forebody drag coefficient

*Referenced to LASRE base area**Parasite residual, total drag, integrated pressures

Base + forebody, integrated pressures

**


0.78 to 1.540.70 to 1.520.68 to 1.620.62 to 1.78

46474849

1

cf base

AbaseAwet--------------⋅

----------------------------------------- =

4.1322 ReL cf base

AbaseAwet--------------⋅ ⋅log

ReL AbaseAwet

Figure 10. Comparison of the total LASRE dracoefficient with total pressure drag coefficient.


m

ties

t

es

rly

the

n

d

s

ted

is

re

one-dimensional momentum and force balance in theaxial direction

(6)

In equation 6, is the frontal projection area of thegap between the model and reflection plane, and is the skin friction force acting between the reflectionplane and the lower surface of the model. Normalizingby freestream dynamic pressure and LASRE base area,equation 6 becomes

(7)

Assuming that exit velocity is much smaller than entrance

velocity, , and defining

equation 7 reduces

to

(8)

As mentioned earlier, total viscous forebody dragcoefficient is the sum of the skin friction and parasitedrag coefficients (referenced to base area)

(9)

is also plotted on figure 10. The computedvalues show reasonable agreement when compared tothe residual data.

Comparison of the Drag Coefficients Computed Using the Two Methods

If calculated values for are added to integrated

pressure drag, , an estimate of total model drag

coefficient, , is generated independently of the

force balance measurements. The two independent drag

coefficient estimates are compared in figure 11.

Residuals between the two estimates, – , are

also plotted. The average difference between the two

estimates is approximately 0.015, and the maximu

deviation is 0.04. Because there are more uncertain

involved in deriving the estimate of , it is likely tha

pressure-derived total drag coefficient estimat

contribute a larger portion of the overall error—

especially in the transonic flight regime.

Development of a Drag Reduction Strategy

The data presented in figures 8 through 11 clea

support earlier assertions that base drag dominates

overall drag LASRE. For subsonic conditions Saltzma

1

and Hoerner

7

have demonstrated a well-define

correlation between and for vehicle

with a wide variety of shapes, sizes, and base-to-wet

area ratios. For two-dimensional shapes Hoerner

7

has

demonstrated that the subsonic correlation

approximated by the empirical formula

(10)

Agap ρ∞V∞2 ρbaseVbase

2–( ) =

2F f RamAgap p∞ pbase–( )–

AgapF f Ram

ρ∞V∞2 ρbaseVbase

2–( )12---ρ∞V∞

2------------------------------------------------------ =

2 F

f

Ram

12---

ρ

∞

V

∞

2

A

base

--------------------------------- A

base A gap --------------

p

∞ p

base

–

( )

12---

ρ

∞

V

∞

2

-------------------------------–

ρ∞V∞2 >> ρ base V base

2

CDparabase

F f RamAbaseρ∞V∞

22⁄( )⁄≡

CDparabase

Agap

Abase-------------- 1

12---CDbase

+=

CD fore

visc( )cf base

CDparabase

+=

CD fore

visc( )

CD fore

visc( )

CDpCD0

p( )

CD0CD0

p( )

CD0

p( )

.2 .4 .6 .8

CD0

1.0 1.2 1.4 1.6 1.8 2.0

1.0

0

.1

.4

– .2

– .1

.2

.8

.6Dragcoefficient*

Dragcoefficient*

Mach number980561

Residual

a) Total drag coefficient

b) Drag coefficient residual

Integrated pressures + viscous drag estimate


Total drag fairing, force balance*Referenced to LASRE base area

0.78 to 1.540.70 to 1.520.68 to 1.620.62 to 1.78

46474849

Figure 11. Comparison of total surface pressucoefficients.

CD fore

visc( )CDbase

CDbase

.135

CD fore

visc( )3

---------------------=


For three-dimensional shapes, the correlation formula is

(11)

Saltzman

1

has found that for large-scale reentry-classflight vehicles the two-dimensional equation is a moreaccurate representation of the flight data. Based on thisreasoning, equation 10 will be preferred in this analysis.

The reasons for the correlation predicted byequations 10 and 11 become more clear if one examinesflow visualizations images of the LASRE obtained in theNASA Dryden Flow-Visualization Facility.

8

Figure 12shows water-tunnel flow images taken from tests of a2.5-percent scale model of the LASRE/SR-71configuration. Although the Reynolds numbers for thewater tunnel tests (~1000) are significantly lower thanfor flight (~2–5

×

10

6

), nevertheless, the imagespresented serve as a good illustration of the LASRE baseflow characteristics in the absence of engine thrust. Theimages clearly show the external freestream flowpumping fluid away from the engine base. This pumpingeffect reduces base pressures significantly. The forebodyboundary layer arriving at the edge of the model acts asan insulating layer between the external flow and theseparated base area. This insulating layer reduces theeffectiveness of the pumping mechanism. Because thethickness of the forebody boundary layer is directlyrelated to the viscous forebody forces, the source of thecorrelation of equation 10 becomes evident.

CDbase

0.029

CD fore

visc( )---------------------=

980562

External slipstream

2-D vortex shedding

Separated flow at nozzle base

(a) Top view.


(b) Right side view.

Figure 12. Water tunnel flow visualization images for a 2.5-percent scale LASRE model.

980563

"Vacuum pump" effect

Reynold's number ~ 1000Flow velocity ~ 1.5 in./sec.

yent

bee

ed14.ws

ofess

g

The above discussion leads to a possible method forbase drag reduction by increasing the viscous dragacting on the forebody of the vehicle. This viscous dragincrease serves to increase boundary thickness andreduces the effectiveness of the vacuum-pump acting atthe base. If the boundary layer modification can beperformed without additional flow separation orexcessive streamline displacement along the forebody, itmay be possible in some instances to decrease the dragof the entire configuration.

Development of a Mathematical Model for the LASRE Drag Coefficient

To determine whether this concept is feasible or not, a

mathematical model of the LASRE base drag coefficient

must first be developed which has as a

parameter and accounts for flow compressibility. As

mentioned earlier, LASRE base drag data show that in

the subsonic flight regime base drag remains relatively

constant until the divergence Mach number of

approximately 0.90 is reached. After this point

compressibility effects dominate and base drag

coefficient rises rapidly. Beyond Mach 1, base drag

drops steadily. These trends suggest a base drag

compressibility function of the form

(12)

The elements of equation 12 are derived from equation10 with modifications for compressibility defined by theKarman-Tsien correction,

9

and rules of similarity fortransonic flow.

10

The base drag model of equation 12 iscompared against measured LASRE base drag data infigure 13. For such a simple model the agreement isreasonable. Also presented in figure 13 are base dragreduction increments that would be expected (based

on

the model of equation 12) if is increased b25 percent, 50 percent, 75 percent, and 100 percrespectively.

The mathematical model of equation 12 can extended to total drag coefficient by adding in thviscous and forebody pressure-drag terms

(13)

The analytical drag model of equation 13 is comparwith the measured LASRE base drag data in figure Again, for such a simple model the comparison shogood agreement.

Increasing the Forebody Viscous Drag by Increasing Surface Roughness

Clearly, one of the most convenient methods increasing the forebody viscous drag is to add roughn

CD fore

visc( )

M∞ Mdiv C ̃ D base M ∞ [ ]⇒< C ˜ D

base

o

( )

.135

C

D

fore

visc

( )

3

---------------------= =

M

div

M

∞

1 C ̃ D base M ∞ [ ]⇒<≤ =

C

˜

D

base

o

( )

1

M

div

2

–12---

C

˜

D

base

o

( )

1 1

M

div

2

––+

1

M

∞

2

–12---

C

˜

D

base

o

( )

1 1

M

∞

2

––+

------------------------------------------------------------------------------------------

1

M

∞

2 C ̃ D base

M ∞ [ ]⇒< =

2 1

M

div

2

–12---

C

˜

D

base

o

( )

1 1

M

div

2

––+

M

∞

2

--------------------------------------------------------------------------------------------------

CD fore

visc( )

1.0

.8

.6

.4

.2

.10

.05

0 1.2Mach number

.6

980564

Dragcoefficient*

Base drag

CDforeincrease, percent

2550

75100

Base drag, force balance flights 46 to 49Computed base drag, Hoerner correlation model, baseline*Referenced to LASRE base area

∆CDbase

.8 1.0 1.4 1.6 1.8

Predicted base drag reduction

C̃D0Cp fore

CD fore

visc( )C̃Dbase

M∞[ ]+ +=

Figure 13. Comparison of the LASRE base dracoefficient with base drag prediction.


onhe

ecet in

ce at

to the surface. Other methods such as using vortexgenerators to energize the boundary layer wouldprobably work more effectively, but their intrusivenessinto the flow precludes this method for application to thehypersonic re-entry vehicle problem. For the LASREdrag reduction experiment no. 24 Silicon Carbide(0.035 in.) grit was glued to the skin using a spray-onadhesive and the surface was sealed using a high-tensilestrength white enamel paint. The resulting surface,depicted in figure 15, had an equivalent sand-grainroughness that varied between approximately 0.02 in.and 0.05 in. In an attempt to avoid inducing additionalflow separation at the boat tail or along the forebody,only the flat sides of the LASRE model were gritted. Thegrit, depicted in figure 16, covered an area of 32.4 ft

2 —

approximately 1/3 of the forebody wetted area.

Surface Roughness Calculations

In order to predict effectiveness of the surface grit in

reducing base drag, calculations of the increment

in were performed using the method of Mills

and Hang.

11, 12

For a smooth flat plate of length

L

, the

averaged skin friction coefficient is related to Reynolds

number according to the empirical formula

(14)

Figure 15. Close-up of LASRE grit application.

Figure 16. LASRE forebody surface grit.

When the surface of the plate is roughened, skin frictiincreases considerably. For a fully rough plate tempirical formula,

(15)

is a good approximation. In equation 15, , is thequivalent sand-grain roughness of the surfaextrusions. Using equations 14 and 15, the incremenviscous forebody drag caused by added roughness is

(16)

In equation 16, is the wetted area of the surfagrit, and

L

is the length of the gritted area measured

1.0

CD0

.8

.6

.4

.6 .8 1.0 1.2Mach number

1.4 1.6

980565

1.8.2

Total drag fairing, force balance, flights 46 to 49Computed drag, Hoerner correlation model, baseline*Referenced to LASRE base area

CD fore

visc( )

cf L

sm( ) 0.0740

ReL[ ] 1 5⁄----------------------≈

Pressure port

κs ~ 0.02 in. –> 0.05 in.

980566

Gritted area

980567

Gritted surface area ~ 32.4 sq. ft., 1/3 of forebody area

cf L

rough( )2.635 0.618loge

Lκs-----+=

2.57–

κs

∆CD fore

visc( )cf L

rough( )cf L

sm( )–

Agrit

Abase--------------=

Agrit

Figure 14. Comparison of the total LASRE dragcoefficient with total drag prediction.


of

sly

ag

b)

d to

cal

=

g

es

g.

dtheresritrtwn

the centroid. Based on an estimated range of surfaceroughness from 0.02 in. to 0.05 in., the calculatedincrease in ranges from 18 percent to 30 percentover the range of Mach and Reynolds numbersencountered during the LASRE flights.

Flight Test Results for theForebody Grit Experiment

Unfortunately, the drag reduction experimentoccurred so late in the LASRE program that only oneflight test was conducted prior to the cancellation of theprogram. As a result, it was not possible to verify theflight-to-flight repeatability of the experiment. Figure 17summarizes the flight results. The grit application didnot reduce the total drag of the configuration.Nonetheless, because the base drag was reduced, resultsof the experiment are encouraging.

Figure 17. Effect of LASRE forebody grit: summary ofdrag components.

Base drag data are shown in greater detail in

figure 18. Figure 18(a) shows the base drag coefficient

plotted as a function of Mach number. Forebody grit

reduces base drag by a peak of 15 percent in the high-

subsonic flight regime. Furthermore, drag reduction

benefits persist beyond Mach 1.4—well into the

supersonic flight regime. Because base drag

supersonic projectiles had never been previou

correlated to , the supersonic base dr

reduction was a significant positive result. Figure 18(

shows the measured base drag reduction compare

the base drag reduction predicted using the analyti

model (equations 12, 14, 15, and 16) assuming

{0.02 in., 0.05 in., and 0.10 in.}. Measured dra

reduction shows excellent agreement with rang

predicted by the analytical model.

(a) Base drag.

(b) Drag reduction increment.

Figure 18. Effect of forebody grit on LASRE base dra

Overall drag of the configuration was not reducebecause the forebody grit modifications caused forebody pressures to rise. The forebody pressualong the top and cylindrical sides of the model with gand without grit are compared in figure 19(a). The polocations for the pressures being compared are sho

CD fore

visc( )

.5 .6 .7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.5

1.0

0

.4

– .2

.2

.8

.6

Dragcoefficient

Base drag

Forebody drag

Skin friction drag increment

Total drag

Mach number980568

Flight

46 to 49 CD0 fairing, without grit

51 balance CD0, with grit

46 to 49 CDbase fairing, without grit

51 CDbase, with grit

46 to 49 CDfore fairing, without grit

51 CDfore, with grit

Skin friction increment, due to grit

CD fore

visc( )

κs

1.51.41.31.21.11.0.9.8.7.6.5

.9

.8

.7

.6

.5

.4

.3

CDbase*

Mach number 980569

Base drag coefficientsFlights 46 to 49, without gritFlight 51, with grit*Coefficients referenced

to LASRE base area

1.51.41.31.21.11.0.9.8.7.6.5

.06

.05

.04

.03

.02

.010

∆CDbase

Mach number980570

Flight data

Base drag reduction incrementPredicted, κs = 0.02 in.

Predicted, κs = 0.05 in.

Predicted, κs = 0.10 in.

Measured flight 51 with grit


of ofceipilldsanns

grit

dt.g

and thess.ceag

ceeakhe

henictorag

eagdyag,erestsn,

reea

th

yes

er,e

in figure 19(b). These pressure data, obtained fromflight 46 (no grit) and flight 51 (with grit) at Mach 0.7,are plotted as a function of the longitudinal distance aftof the nosetip. Notice that although the pressuredistribution along the model centerline was basicallyunchanged, the pressures on the sides of the forebodyare generally higher for the grit-on data. This forebodypressure rise is further demonstrated by comparing theintegrated forebody pressure drag coefficients infigure 17. When combined with added skin-drag causedby the surface roughness, the forebody pressure riseoffsets the benefits gained by the base drag reduction.

(a) Forebody pressure distribution.

(b) Forebody pressure ports, side view.

Figure 19. Comparison of the forebody pressuredistributions with and without grit.

The flight results suggest that the total drag modelequation 13 must be changed to include a possibilityincreasing forebody pressure drag with surfaroughness modifications. It is likely that the relationshof forebody pressure drag to viscous forebody drag wbe configuration dependent. Clearly, more work neeto be performed before more definite conclusions creached. It is also clear, however, that for configuratiowhere base drag is a dominating factor, the forebody method is a potentially useful drag reduction tool.

Summary and Concluding Remarks

A drag reduction experiment was conducteon the X-33 Linear Aerospike SR-71 ExperimenThe flight experiment performed baseline drameasurements on a clean experiment configuration, then attempted to reduce the base drag by increasingforebody skin friction using added surface roughnePreflight calculations showed that proposed surfaroughness modifications would result in base drreductions of 8 to 14 percent.

Flight results verified the effectiveness of the surfaroughness technique for reducing base drag. The pbase drag reduction was approximately 15 percent. Tbase drag reduction also persisted well into tsupersonic flight regime. Since base drag of supersoprojectiles had never been previously correlated viscous forebody drag, the sizable supersonic base dreduction was a significant positive result.

Unfortunately, flight test results for the rough-surfacconfiguration did not demonstrate an overall net drreduction. The surface grit caused a rise in forebopressures. Coupled with increased forebody skin-drthe forebody pressure rise offset benefits that wgained by base drag reduction. Because the flight tedid not demonstrate an overall net drag reductioresults of the drag reduction experiment ainconclusive. It is clear; however, that with somrefinement, the forebody grit method provides potentially useful drag reduction tool.

References

1

Saltzman, Edwin J., Charles K. Wang, and KenneW. Iliff,

Flight-Determined Subsonic Lift and DragCharacteristics of Seven Lifting-Body and Wing-BodReentry Vehicle Configurations With Truncated Bas

,AIAA Paper 99-0383, January 1999.

2

Corda, Stephen, David P. Lux, Edward T. Schneidand Robert R. Meyer, Jr., “Blackbird Puts LASRE to thTest,”

Aerospace America

, February 1998, pp. 25–29.

50

Forebodypressure

coefficient

Distance aft, x, in.0 100 150

2

1

0

– 1

M∞ ~ 0.70

Flight 46,without grit

Top rowLeft side portsRight side ports

Flight 51,with grit

Top rowLeft side portsRight side ports

980571

60 80 100 120 140 1600 20 40x, in.

z,in.

60

40

20

0

980572

Top rowSide ports


,

y

3,

3Otnes, Robert K. and Lauren D. Enochsen, DigitalTime Series Analysis, John Wiley & Sons, New York,1972, pp. 237–239.

4Haering, Edward A., Jr. and Stephen A. Whitmore,FORTRAN Program for Analyzing Ground-BasedRadar Data: Usage and Derivations, Version 6.2,NASA TP-3430, August 1995.

5Frieberger, W. F., ed., The International Dictionaryof Applied Mathematics, D. Van Nostrand andCompany, Inc., Princeton NJ, 1960, pp. 828, 829.

6Hoerner, Sighard F., Fluid-Dynamic Drag, Self-Published Work, Library of Congress Cardno. 64-19666, Washington, D.C., 1965, pp. 3-19, 3-20,15-4, 16-5.

7Schlicting, Hermann, Boundary-Layer Theory, 7thed., translated by Dr. J. Kestin, McGraw-Hill PublishingCo., New York, 1979, pp. 641, 642.

8Del Frate, John H., NASA Dryden Flow VisualizationFacility, NASA TM-4631, May 1995.

9Freiberger, W. F., Ed., International Dictionary ofApplied Mathematics, D. Van Nostrand Company Inc.Princeton, NJ, 1960, p. 506.

10Kaplan, Carl, On Similarity Rules for TransonicFlows, NACA TN-1527, Washington D.C., Januar1948, pp. 8–10.

11Mills, Anthony, F. and Xu Hang, On the SkinFriction Coefficient for a fully Rough Flat Plate,J. Fluids Engineering, vol. 105, September 198pp. 364–365.

12Mills, Anthony F., Heat Transfer, Richard D. Irwin,Inc., Homewood, IL, 1992, pp. 282–328.

16

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NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18298-102

A Base Drag Reduction Experiment on the X-33 Linear Aerospike SR-71Experiment (LASRE) Flight Program

WU 242-33-02-00-23-00-T15

Stephen A. Whitmore and Timothy R. Moes

NASA Dryden Flight Research CenterP.O. Box 273Edwards, California 93523-0273

H-2333

National Aeronautics and Space AdministrationWashington, DC 20546-0001 NASA/TM-1999-206575

Drag reduction tests were conducted on the LASRE/ X-33 flight experiment. The LASRE experiment is aflight test of a roughly 20-percent scale model of an X-33 forebody with a single aerospike engine at the rear.The experiment apparatus is mounted on top of an SR-71 aircraft. This paper suggests a method for reducingbase drag by adding surface roughness along the forebody. Calculations show a potential for base dragreductions of 8 to 14 percent. Flight results corroborate the base drag reduction, with actual reductions of15 percent in the high-subsonic flight regime. An unexpected result of this experiment is that drag benefits wereshown to persist well into the supersonic flight regime. Flight results show no overall net drag reduction.Applied surface roughness causes forebody pressures to rise and offset base drag reductions. Apparently thegrit displaced streamlines outward, causing forebody compression. Results of the LASRE drag experiments areinconclusive and more work is needed. Clearly, however, the forebody grit application works as a viable dragreduction tool.

Aerospike engine, Base drag, Skin friction

A03

22

Unclassified Unclassified Unclassified Unlimited

March 1999 Technical Memorandum

Presented at the 37th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 11–14, 1999 as AIAA-99-0277.

Unclassified—UnlimitedSubject Category 05

a base drag reduction experiment on the x-33 linear

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