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
ddernsern-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
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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.
3American Institute of Aeronautics and Astronautics
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
4American Institute of Aeronautics and Astronautics
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
5American Institute of Aeronautics and Astronautics
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
6American Institute of Aeronautics and Astronautics
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
7American Institute of Aeronautics and Astronautics
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ag
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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
Mach numberrangeFlight
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
8American Institute of Aeronautics and Astronautics
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
**
Mach numberrangeFlight
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.
9American Institute of Aeronautics and Astronautics
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
Mach numberrangeFlight
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
---------------------=
10American Institute of Aeronautics and Astronautics
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.
11American Institute of Aeronautics and Astronautics
(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.
12American Institute of Aeronautics and Astronautics
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.
13American Institute of Aeronautics and Astronautics
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
14American Institute of Aeronautics and Astronautics
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
15American Institute of Aeronautics and Astronautics
,
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
American Institute of Aeronautics and Astronautics
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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
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