National Aeronautics and Space Administration Langley Research Center • Hampton, Virginia 23681-0001 NASA Technical Memorandum 4673 Surface-Pressure and Flow-Visualization Data at Mach Number of 1.60 for Three 65° Delta Wings Varying in Leading-Edge Radius and Camber S. Naomi McMillin Langley Research Center • Hampton, Virginia James E. Byrd Lockheed Engineering & Sciences Company • Hampton, Virginia Devendra S. Parmar Old Dominion University • Norfolk, Virginia Gaudy M. Bezos-O’Connor and Dana K. Forrest Langley Research Center • Hampton, Virginia Susan Bowen Computer Sciences Corporation • Hampton, Virginia December 1996
Transcript
National Aeronautics and Space AdministrationLangley Research Center • Hampton, Virginia 23681-0001
NASA Technical Memorandum 4673
Surface-Pressure and Flow-Visualization Dataat Mach Number of 1.60 for Three 65° DeltaWings Varying in Leading-Edge Radius andCamberS. Naomi McMillinLangley Research Center • Hampton, Virginia
James E. ByrdLockheed Engineering & Sciences Company • Hampton, Virginia
Devendra S. ParmarOld Dominion University • Norfolk, Virginia
Gaudy M. Bezos-O’Connor and Dana K. ForrestLangley Research Center • Hampton, Virginia
Susan BowenComputer Sciences Corporation • Hampton, Virginia
December 1996
Printed copies available from the following:
NASA Center for AeroSpace Information National Technical Information Service (NTIS)800 Elkridge Landing Road 5285 Port Royal RoadLinthicum Heights, MD 21090-2934 Springfield, VA 22161-2171(301) 621-0390 (703) 487-4650
The use of trademarks or names of manufacturers in this report is foraccurate reporting and does not constitute an official endorsement,either expressed or implied, of such products or manufacturers by theNational Aeronautics and Space Administration.
Available electronically at the following URL address: http://techreports.larc.nasa.gov/ltrs/ltrs.html
An experimental investigation of the effect ofleading-edge radius, camber, Reynolds number, andboundary-layer state on the incipient separation of a deltawing at supersonic speeds was conducted at the LangleyUnitary Plan Wind Tunnel. The three delta wing modelsexamined had a 65° swept leading edge and varied incross-sectional shape: a sharp wedge, a 20:1 ellipse, anda 20:1 ellipse with a−9.75° circular camber imposedacross the span. The three wings were tested at a Machnumber (M) of 1.60 over a free-stream Reynolds number(R) range of 1× 106 to 5× 106 ft−1. The wings weretested with and without transition grit applied. Surface-pressure coefficient data were obtained, as well asflow-visualization data. The flow-visualization tech-niques employed were the vapor-screen, the painted-oil-flow, the injected-oil-flow, and the liquid-crystaltechniques. The surface-pressure coefficient data andflow-visualization data are electronically stored on aCD-ROM that accompanies this report.
The data indicated that by rounding the wing leadingedge or cambering the wing in the spanwise direction,the onset of leading-edge separation on a delta wing atsupersonic speeds can be raised to a higher angle ofattack than that observed on a sharp-edged delta wing.Specifically, a 20:1 elliptical cross section increased theangle of attack at which leading-edge separation beginsby about 2° over that observed on a sharp-edged deltawing. A cambered elliptical wing, which decreased thelocal angle of attack at the leading edge by 3.76°, effec-tively increased the angle of attack at which leading-edgeseparation begins by 1.5° over that observed on theuncambered elliptical wing.
The application of transition grit on the wing or anincrease inR increased the angle of attack at whichleading-edge separation began. Fixing transition orincreasing R causes the boundary-layer transition tooccur closer to the wing apex and leading edge of thewing. A turbulent boundary layer has more energy than alaminar boundary layer and will therefore allow the flowto remain attached at the wing leading edge at higherangles of attack than is possible with a laminar boundarylayer
Introduction
A standard configuration for supersonic wing designis that of a highly swept, thin delta wing at moderateangles of attack. Several researchers have experimentallyinvestigated and classified the leeside flow over slenderswept wings in supersonic flow. Stanbrook and Squire(ref. 1) originally classified separated and attached lee-side flow regimes by using the similarity parameters
Mach number normal to the leading edge (MN) and angleof attack normal to the leading edge (αN). Whitehead(ref. 2), Szodruch and Ganzer (ref. 3), Szodruch (ref. 4),Miller and Wood (ref. 5), Seshadri and Narayan (ref. 6),and Covell and Wesselmann (ref. 7) extended this workby redefining the separated- and the attached-flowregimes into smaller regimes containing more complexflow structures. The flow structures identified over theleeside of sharp-edged delta wings at supersonic speedsincluded attached flow, cross-flow shocks, separationbubbles, and a complex vortical system of primary andsecondary vortices (ref. 5). The boundaries between theexperimentally derived flow regimes have been identi-fied as functions ofMN andαN.
The aerodynamicist prefers not to be limited to a par-ticular type of flow so that an optimum design may makeuse of both attached and separated flows. The boundariesbetween separated- and attached-flow regimes are sensi-tive to changes in wing leading-edge radius, wing thick-ness, and Reynolds number (refs. 1, 4, 6, and 8). To takeadvantage of the sensitivity of the boundaries betweenflow regimes, it becomes necessary to understand theinfluence of geometrical and flow parameters on theincipient separation of a delta wing. Incipient separationis defined as the onset of flow separation at the leadingedge of the wing.
The present wind-tunnel investigation was con-ducted to establish a database to improve the understand-ing of incipient separation on delta wings at supersonicspeeds. The effects of leading-edge radius, camber,Reynolds number, and boundary-layer state on the incip-ient separation on a 65° delta wing atM = 1.60 weredetermined. The three delta wing models tested hada 65° swept leading edge and varied in cross-sectionalshape: a sharp wedge, a 20:1 ellipse, and a 20:1 ellipsewith a −9.75° circular camber imposed across the span.The three wings were tested in the Langley Unitary PlanWind Tunnel at anM of 1.60, anR range of 1× 106 to5 × 106 ft−1, a nominal angle of attack(αnom) range of0° to 9°, and an angle of sideslip (β) of 0°. The wingswere tested with and without transition grit applied.Extensive surface-pressure coefficient data wereobtained at twolongitudinal stations. Extensive flow-visualization data were obtained to better understand theflow phenomena associated with incipient separation.The flow-visualization techniques employed were thevapor-screen, the painted-oil-flow, the injected-oil-flow,and the liquid-crystal techniques.
Symbols
AOA angle of attack
b wing reference span, in.
2
bto wing span with wingtipsremoved, in.
CN normal force coefficient obtainedby integrating surface-pressurecoefficient data
Cp surface-pressure coefficient,(P − P∞)/q
CP# designation on CD-ROM to denotepressure orifice number
c wing root chord, in.
ESP electronic scanning pressure
M free-stream Mach number
MN component of Mach number normalto leading edge,
n refractive index of a material
P local static pressure, lb/ft2
P∞ free-stream static pressure, lb/ft2
q free-stream dynamic pressure, lb/ft2
R free-stream Reynolds number, ft−1
Rx local Reynolds number based ondistance from apex along centerlineof wing
r leading-edge radius, in.
rc radius of curvature, in.
S wing reference area, in2
s arc length, in.
Taw adiabatic wall temperature,°FTo stagnation temperature,°Ft wing thickness, in.
UPWT Langley Unitary Plan Wind Tunnel
x, y, z Cartesian coordinates where origin isat apex of wing, in.
α corrected angle of attack, deg
αac angle of attack as measured byaccelerometer, deg
αatt last angle of attack at which attachedflow was observed, deg
αknu pitch of model as set by knuckle, deg
αN angle of attack normal to leadingedge, deg,
αnom nominal angle of attack, deg
αsep angle of attack at which leading-edgeflow separation is first detected, deg
β sideslip angle, deg
γ display monitor parameter whichcontrols contrast and brightness ofdisplay
∆α change in angle of attack, deg
ζ z/local semispan
η y/local semispan
θc angle of spanwise camber, deg
θf angle of wind-tunnel flow, deg
Λ sweep angle, deg
φ roll angle, deg
Subscripts:
LE leading edge
l lower surface of wing
lam laminar
max maximum
min minimum
TE trailing edge
turb turbulent
u upper surface of wing
Tabulated Data Symbols:
ALPHA α, deg
CP Cp
ETA ηFLOW ANGLE θf, deg
MACH M
PHI φ, deg
PINF P∞, lb/ft2
Q q, lb/ft2
R/FT R, ft−1
X x, in.
Model Description
A conical 65° delta planform atM = 1.60 was chosenas the baseline geometry. The criteria used to select thebaseline wereMN andαN, which are shown in figure 1.As angle of attack increases, the 65° delta planformat M = 1.6 traverses the Stanbrook-Squire boundary(ref. 1) that delineates attached-flow and separated-flowregimes. The effects of wing leading-edge radius, wingleading-edge camber, Reynolds number, and boundarylayer (laminar or turbulent) on leading-edge flow separa-tion were expected to be most pronounced in the regionof the Stanbrook-Squire boundary.
M ΛLE 1 sin2α tan
2ΛLE+cos
tan 1– tan α cosΛLE⁄( )
3
The effect of wing leading-edge radius and wingcamber on leading-edge flow separation was examinedby varying the cross-sectional shape of the baselinegeometry. Details of the three models examined are infigure 2 and table 1. Appendix A contains the analyticalexpression for each of the cross-sectional shapes.Figure 3 shows the elliptical model installed in theLangley Unitary Plan Wind Tunnel (UPWT).
The baseline geometry was a 65° delta planformwith a ratio of centerline thickness to semispan of 0.10.Cross-sectional shape was varied to obtain three wingdesigns: a sharp wing, an elliptical wing, and a camberedwing. The sharp wing had a wedge-shaped cross section,which is shown in figure 2(a). For machining purposes,the sharp wing had a leading-edge radius of 0.003 in. Theelliptical wing, shown in figure 2(b), had a 20:1 ellipticalcross section, which yielded a leading-edge radius tolocal semispan ratio (r/(b/2)) of 0.0025 along the lengthof the leading edge. The elliptical geometry was used asa baseline cross section in examining the effect of cam-ber. A spanwise circular-arc camber was imposed on theelliptical cross section in the cross-flow plane to definethe cambered wing. The angle of camberθc is defined asthe spanwise camber angle at the wing leading edge. Thecambered model had anθc of −9.75° (fig. 2(c)).
It should be noted in figure 2 that the wingtips ofeach model could be removed. The left side (viewedupstream from the trailing edge of the model) of the plan-form shows the wingtips attached and the right sideshows the wingtips removed. The models were built withremovable wingtips for testing in another facility with asmaller test section than that of the UPWT. The wingtipswere attached for this investigation.
Each model was instrumented with pressure orificeson both the upper and the lower surfaces. The orificeswere arranged in two spanwise rows atx = 6 in. andx = 12 in. (measured from the apex along the centerline).The upper surface-pressure orifices were located on theright side (viewed upstream from the trailing edge of themodel) of the wing and the lower surface-pressure ori-fices were located on the left side of the wing. Each ori-fice on the elliptical and the cambered wings had an innerdiameter of 0.01 in. Each orifice on the sharp wing hadan inner diameter of 0.015 in. All tubing came out theback of the models as shown in the photographs infigure 3.
Tables 2, 3, and 4 contain thex and theη locationsof each pressure orifice, the CP# of each pressure orifice(the CP# is also used in the pressure-listing file on theCD-ROM), and the condition of the orifice. On the ellip-tical and the cambered wings, the pressure orifice loca-tions range fromη ≈ 0.10 to η ≈ 0.98 at bothx stationson the upper surface. However, because of the thinness
of the sharp wing at the leading edge, the upper surface-pressure orifice locations on the sharp wing range only toη = 0.820 for thex = 6 in. station and toη = 0.899 for thex = 12 in. station. On the lower surface, the pressure ori-fice locations range fromη = 0.200 to η ≈ 0.95 at bothx stations for the elliptical and the cambered wings. Forthe lower surface of the sharp wing, the pressure orificelocations range toη = 0.802 for thex = 6 in. station andη = 0.901 for thex = 12 in. station.
To minimize any effect of the model support systemon the flow over the upper surface of the delta wing, asting was constructed that attached to the trailing edge ofeach wing with two bolts. Figure 4 shows the details ofthe sting.
An electronic accelerometer measured angle ofattack during pressure data acquisition. The angle ofattack (AOA) sensor was placed in a housing that wasattached to the lower surface of the mounting pad of thesting. Thus, the AOA sensor was located directly behindthe trailing edge of the delta wing. Because of this loca-tion, the AOA sensor was not influenced by sting deflec-tions due to aerodynamic loading. The details of theAOA housing are shown in figure 5. Figure 3(b) showsthe assembly of the elliptical wing, sting, and AOA hous-ing components.
Wind-Tunnel Test Description
The wind-tunnel test program was conducted in testsection 1 of the UPWT atM = 1.60 over a range ofRfrom 1× 106 ft−1 to 5× 106 ft−1. All data were obtainedat stagnation temperature (To) of 125°F with the excep-tion of the liquid-crystal data. The liquid-crystal datawere obtained atTo = 120°F, 125°F, and 130°F. Thetest program was conducted under the following testconditions:
Reference 9 contains a detailed description of thewind tunnel and the operating conditions of the windtunnel.
Mach numberStagnation
pressure, psf To, °F R, ft−1
1.60 539 125 1× 106
1.60 1067 120 2× 106
1.60 1079 125 2× 106
1.60 1091 130 2× 106
1.60 1618 125 3× 106
1.60 2157 125 4× 106
1.60 2668 120 5× 106
1.60 2697 125 5× 106
1.60 2728 130 5× 106
4
The dew point was maintained sufficiently low dur-ing the pressure tests to prevent condensation in the tun-nel. However, atR= 5 × 106 ft−1, the dew point wasdifficult to control and it rose throughout the run. Even-tually, a fog appeared in the test section. To control thedew point, it became necessary to manually bleed in dryair. Figure 6 shows the effect of dew point on thesurface-pressure measurements for the cambered wing atR= 5 × 106 ft−1. Dew point was considered unacceptablewhen the generally accepted value (from unpublisheddata based on ref. 9) was not met and/or a fog appearedin the test section.
As discussed in reference 9, flow angularity existsinside the wind-tunnel test section and is illustrated infigure 7. To account for this flow angularity, the modelwas offset in pitch before data were acquired. This offsetis known as the flow angleθf where positive flow angu-larity means the flow is deflected upward. A detailed dis-cussion on the determination of the flow angle iscontained in appendix B. The angle of attack correctiondue to flow angularity was determined to be 0.4°. Thecorrected angle of attack is referred to asα.
To obtain pressure data, the model was set atφ = 0°and the angle of attack was measured with the AOA sen-sor located directly behind the trailing edge of the wing.The angle of attack measured with the AOA sensor isreferred to asαac and is shown in figure 7.
To acquire flow-visualization and liquid-crystaldata, the model was set atφ = 90°. Because the AOAsensor could not be used at this roll angle, the angle ofattack was set by using the beta angle system of the windtunnel. (The beta angle system sets the sideslip angle of amodel atφ = 0°.) This arrangement sets the pitch angle atthe tunnel end of the sting instead of at the base of themodel. Thus, sting deflections had to be accounted forwhen the angle of attack was set. Sting deflections weredetermined by comparingαac with a corresponding pitchangle measured at the knuckleαknu. The knuckle is thetunnel hardware in which the sting is installed and isshown in figure 7. Figure 8 shows an example plot ofαknu andαac, which were measured on the elliptical wingwithout grit atR= 1 × 106 ft−1. The line through the datapoints is a least squares fit and was used to determine thesting deflections. Sting deflections were also obtained atR= 2 × 106 and 5× 106 ft−1.
Transition grit was used to ensure fully turbulentflow over the model when the flow was attached at thewing leading edge. Boundary-layer transition strips ofNo. 40 (0.0181-in. diameter) sand grit were applied0.169 in. perpendicular to the leading edge of the deltawing on both the upper and the lower surfaces. The grit
was sprinkled on the wing in a strip that was 0.0625 in.wide. The grit size and location were selected by consult-ing unpublished data that were based on the methods andthe data in references 10 to 12.
Shown in figure 9 is the location of the grit withrespect to the pressure orifices for each of the three deltawings. The surface-pressure coefficients at the orifices inor near the strip of grit are affected by the presence of thegrit (fig. 10). The effect of the grit is more pronounced atthex = 6 in. station than at thex = 12 in. station. The ori-fices at thex = 6 in. station are spaced closer togetherthan at thex = 12in. station, which can be seen infigure9(c). Thus, the effect of the grit covers more of theorifices at thex = 6 in. station.
For the lower surface, the effect of grit is presentover the entire angle of attack range. However, for theupper surface, the effect of grit on the surface-pressuredistribution is present only at low angles of attack. Thisobservation can be explained by noting that for attached-flow cases at low angles of attack, the flow movesinboard from the wing leading edge to the transitionstrip. Whereas, for separated-flow cases at higher anglesof attack, the flow approaches the transition strip fromthe other direction as the flow separates at the leadingedge, reattaches inboard of the transition strip, andmoves outboard towards the transition strip as shown infigure 11 (from ref. 5).
Test Techniques
The five test techniques used during the test programwere surface-pressure measurements, vapor screens,painted oil flows, injected oil flows, and encapsulatedliquid crystals.
Surface-Pressure Measurements
Each model had surface-pressure orifices on theupper and the lower surface with the tubing exiting at therear of the model. The tubing was connected to the elec-tronic scanning pressure (ESP) system located outsidethe wind-tunnel test section. A valuable feature of thesystem is the ability to calibrate the ESP modules at any-time during the test. With this feature, changes in temper-ature or other environmental features can be taken intoconsideration.
The selection of ESP modules was based on theexpected maximum and minimum pressures on the deltawing over the angle of attack range of 0° to 9°. The fol-lowing is a table of the expected maximum and minimumpressures on the upper and the lower surface of the deltawing for M = 1.60 andTo = 125°F:
5
The expected maximum and minimum pressureswere obtained from the computational solutions forthe wind-tunnel model geometries atM = 1.60 andTo = 125°F. (See ref. 13.)
At the higher Reynolds numbers, the lower surfacewould likely experience pressures beyond the range of a5 psi module; so the 15 psi module was used. The uppersurface would likely experience pressures ranging fromvery low values up to 5 psi; therefore, the 5 psi modulewas selected. In some instances, the upper surface pres-sures exceeded the range of the 5 psi module—for exam-ple, when the wing was subjected to negative angles ofattack atR= 5 × 106 ft−1. These data were discarded.The 5 psi modules had an accuracy of±0.0025 psi andthe 15 psi module had an accuracy of±0.0075 psi.
When obtaining surface-pressure measurements, theangle of attack was set and the pressures were allowed tosettle before taking measurements. A study of the effectof settling time on the pressure measurements was per-formed. Figure 12 shows surface-pressure coefficientdata taken with a 2 min settling time and with a 7 minsettling time at three points. The measurements obtainedat the different settling times are the same within theaccuracy of the equipment. Based on these results, a set-tling time of 2 min was allowed between angle of attackchanges.
To obtain the pressure data, anα sweep from 0° to9° in 0.5° increments was performed. When warrantedby inspection of the on-line pressure plots, a secondαsweep was performed to obtain data over a selected rangein 0.25° increments. These twoα sweeps were used todetermine the repeatability of the pressure data. Fig-ure13 shows a plot of surface-pressure coefficients withα for both α sweeps. Figure 13 shows that the datarepeatability is satisfactory because the surface-pressurecoefficients obtained during the secondα sweep followthe trend of the surface-pressure coefficients from thefirst α sweep.
Vapor-Screen Technique
The vapor-screen technique provides qualitative dataon the flow field above the leeward surface of the model.Model preparation for the vapor-screen technique con-sisted of painting one coat of black paint onto the surfaceof the model. White dots were painted on the model sur-face centerline atx = 6 in. andx = 12 in. (the locations ofthe rows of pressure orifices). Once tunnel start-up wascomplete, water was added in the diffuser downstream ofthe test section until a uniform vapor was produced in thetest section.
A 4-W argon-ion laser, which emits a blue-greenlight, was used to create the light sheet across the tunneltest section. Usually, only 2 W of laser power were nec-essary to produce the desired vapor-screen image. A dualcylindrical lens was used to spread the laser beam. Thelens assembly was mounted on a support that could rotateand traverse vertically to the desired orientation. Once adesired orientation was reached, the laser was fixed inplace and the model was moved to obtain vapor-screenphotographs at variousx locations. Still photographswere obtained with 70-mm film and a camera inside thetest section. The relative locations of the model, lightsheet, and camera are shown in figure 14. Still photo-graphs were obtained at thex = 12 in. station only.
One undesirable characteristic of the vapor-screentechnique is the reflection of the light sheet off the sur-face of the model. The use of flat black paint on the sur-face of the model minimizes this reflection, but does noteliminate it. Another undesirable characteristic of thevapor-screen technique is that the quality of the vapor ismore difficult to control in the UPWT at lower Machnumbers such as 1.60. Constant visual monitoring of thevapor and subsequent adjustment of the water input isnecessary to ensure an evenly distributed vapor in the testsection.
Painted-Oil-Flow Technique
The painted-oil-flow technique provides qualitativedata on the flow characteristics of the surface of themodel. For the painted-oil-flow technique, the model waspainted with one coat of flat black zinc chromate primer.The model surface was then brushed with a mixture of90W oil and yellow fluorescent powder. During the tun-nel start-up period, the model was kept horizontal to pre-vent the oil from running. The model was rolled 90°(wings vertical) and was illuminated by four ultravioletlamps that were mounted on the sidewall door. With self-developing film, photographs of the painted oil flowswere taken through the window by a camera mounted
R, ft−1
Pl, max at(Cp)l,max= 0.25,
psi
Pl, max at(Cp)l,min = 0.05,(Cp)u,max= 0.05,
psi
Pl, max at(Cp)u,min = −0.45,
psi
1 × 106 1.276 0.9597 0.1701
2 × 106 2.553 1.921 0.3417
3 × 106 3.828 2.881 0.5118
4 × 106 5.103 3.840 0.6819
5 × 106 6.381 4.801 0.8535
6
outside the tunnel on the sidewall door. After the modelwas positioned, the oil-flow pattern stabilized in approxi-mately 3 to 4 min.
An undesirable characteristic of this technique wasthat only 3 or 4 angles of attack could be documentedbefore the oil had to be replaced. The number of anglesof attack that can be documented in one setup decreaseswith increasing Reynolds number.
Injected-Oil-Flow Technique
The injected-oil-flow technique also provides quali-tative data on the flow characteristics of the surface ofthe model. The injected-oil-flow technique differs fromthe painted-oil-flow technique in that the oil is injectedonto the surface through the pressure orifices. The injec-tion was accomplished by the pressure differencebetween the pressure inside the tunnel and the higheratmospheric pressure outside the tunnel. A peristalticpump was also used to inject the oil through the orifices.Each upper surface orifice tube was connected to a peri-staltic pump module located outside the test section. Theoil-flow rate was adjustable as a function of pump speedfor all the orifices simultaneously. The oil-flow rate foreach orifice was adjustable from 0 to approximately4 ml/min. The source of oil for each peristaltic pumpmodule was a common container of SAE 10 oil that wasmixed with fluorescent powder.
Maintaining constant flow rates between orificeswas difficult at times. The difficulty was caused by thefluorescent powder clogging the tubes. The oil and pow-der mixture had been stirred and filtered beforehand toeliminate large pieces of powder. However, the nonuni-form restrictions of each orifice and the associated tubinglength of 15 ft allowed small pieces of powder to accu-mulate and clog some of the tubes. The disparity betweenorifice flow rates was greater when the pressure differ-ence across the tubes was allowed to be the only motiveforce of the oil through the tubes. The peristaltic pumpprovided better uniformity in flow rate among orifices.
The model was prepared and illuminated in the samemanner as it was for the painted-oil-flow technique. Theoil flows were photographed with an instrumentationcamera that had a wide angle lens and 70-mm black andwhite film. A 30-sec exposure time was generally used.
The flow patterns took less than a minute to settleafter a change inα. When a more significant amount oftime was needed to obtain a desired change in flow con-ditions, the oil flow could be slowed by clamping thetubes and removing them from the container of oil andpowder mixture. However, after approximately 2 hr, thefluorescent powder caused the paint to flake. Never-theless, the injected-oil-flow technique allowed many
more data points to be obtained than could be obtainedwith the painted-oil-flow technique. In the painted-oil-flow technique, the oil wore off after 3 to 4 datapoints (10–20 min) were obtained. However, as the oil onthe model is being continually replaced in the injected-oil-flow technique, data points could be taken until thepaint started to flake.
Liquid-Crystal Technique
The liquid-crystal technique provides quantitativedata on the flow characteristics of the surface of themodel. This technique records the data visually withphotographs that capture the varying colors of the ther-mochromic liquid crystals. The thermochromic liquidcrystals used in this technique are materials that demon-strate color changes when their temperature is changed.Reference 14 discusses the properties of liquid crystalsand how these properties are exploited in measuring tem-perature. The color of a liquid crystal changes from blackto red to blue as the temperature is increased. As a resultof this feature, these liquid crystals have been usedwidely in thermometry and thermography of surfaces.
In their normal state of operation, these liquid crys-tals are in a viscous fluid state and flow under an appliedshear stress (ref. 15). Thus, the liquid crystals do not bindrigidly to the model surface that is exposed to a flow offluid (ref. 16). To avoid flowing when under shear stress,microdroplets of these liquid crystals are encapsulated inpolymer shells (ref. 14). A slurry of the capsules in awater and polymer solution produces a paint that can besprayed on the model surface with an air brush. When itdries on the model surface, the paint leaves a rigid film ofmicroencapsulated thermochromic liquid-crystal dropletsbound rigidly to the surface yet capable of responding tothe surface temperature (refs. 14 and 17). The density ofthe microencapsulated droplets is high enough so that adry film (approximately 50–100µm thick) will providethe necessary continuous spread of liquid crystals on thesurface. The color pattern on the surface provides infor-mation about the temperature distribution on the surfaceby referring to the calibration of the liquid crystals. Thecalibration is obtained with the methods in references 15and 17. The commercially available microencapsulatedliquid crystals generally cover a limited temperaturerange of≈9°F. This limited range allows one to choose aliquid crystal that is suitable for the desired operation.
To prepare the model for the installation of the liquidcrystals, the model surface was thoroughly cleaned withacetone and methanol. The model was then given a blackcoating compatible with the encapsulated liquid crystals.The black coating (approximately 10µm) was depositedon the model surface by spraying a flat black paint withan air brush. Unlike many lacquer-based flat black
7
paints, the black paint used for this test was water solubleand absorbed the light incident on its surface. Thisabsorption meets the necessary condition that theobserved reflected light is from the liquid-crystal layerand not from the black coating itself. The paint, being agood thermal insulator, also provides an adequate ther-mal insulation layer between the liquid crystal and themodel surface. After the black coating has completelydried, the encapsulated thermochromic liquid crystal isspray painted on the black coated model to provide a dryuniform film that is approximately 50µm thick.
In the present experiment, the upper surface of themodel was divided into two parts at the centerline. Eachside was coated with liquid crystals of different operatingranges of temperature. To gather as much information aspossible with these two ranges of temperature, data wereobtained with threeTo: 120°F, 125°F, and 130°F. Thetemperature range of the liquid crystals was selectedbased on theTaw for a flat plate atM = 1.60. (Seeref. 18.) The following is a table of theTaw at each tem-perature for both a laminar and a turbulent boundarylayer:
Based on these values, the right side (viewingupstream from the trailing edge of the model) was coatedwith liquid crystals that had an operating range of 86°Fto 95°F. The left side was coated with liquid crystals thathad an operating range of 95°F to 104°F.
To obtain photographs of the liquid-crystal data, themodel was rolled 90° (wingtips vertical) with angle ofattack set by using the beta angle system of the wind tun-nel. The model was illuminated by white light lampsmounted on the sidewall door. The light reflected normalto the model surface was recorded by still photographs.An instrumentation camera with a wide angle lens wasmounted outside the tunnel on the sidewall door. Colorphotographs were obtained with 70-mm color film. Datawere obtained for theαnom range of 0° to 9° in 0.5°increments. After an angle of attack change, the changein liquid-crystal color due to changes in surface tempera-ture was virtually instantaneous.
The advantage of using the liquid-crystal techniqueis the ability to gain both qualitative and quantitative dataover the entire surface of the model. A possible source ofconcern in this technique is the interplay of temperatureon the lower and the upper surfaces because of conduc-
tion of heat through the model. Although the black paintapplied on the model is an insulator, it probably does noteliminate the heat transfer completely. One disadvantageof the liquid-crystal technique was that the coating wouldstart to flake away from the model after being in the flowstream for 2 to 4 hr. This problem, however, could proba-bly be avoided by using a sturdier oil-based paint.
Results and Discussion
An experimental investigation of incipient separa-tion on supersonic delta wings was conducted. Three 65°delta wing models were tested in UPWT atM = 1.60over anR range of 1× 106 ft−1 to 5× 106 ft−1 with andwithout transition grit applied to the surface of the mod-els. The three delta wing models had a 65° swept leadingedge and varied in cross-sectional shape: a sharp wedge,a 20:1 ellipse, and a 20:1 ellipse with a−9.75° circularcamber imposed across the span. Surface-pressure coef-ficient, liquid-crystal, and flow-visualization data wereobtained for each model. Table 5 summarizes the differ-ent data obtained for each configuration. Theαnomobtained is also listed in table 5. Presented in tables 6to 11 are indexes of the angles of attack at which datawere obtained during each test technique. The angle ofattack data in tables 6 to 11 have been corrected forwind-tunnel flow angularity and sting deflections.
All experimental data obtained from the wind-tunneltest program are on a CD-ROM. The flow-visualizationdata are stored on the CD-ROM in digital images.Appendix C contains a detailed description of the processused to convert the film negatives or prints to digitalimages. Appendix C also contains a description of thedirectory structure and the file formats on the CD-ROM,as well as information on public domain software avail-able to examine the data. The surface-pressure coeffi-cient data are also stored on the CD-ROM in an ASCIIfile. The surface-pressure coefficient data have beensummarized and are plotted in appendix D.
Representative results obtained from the experimen-tal investigation are presented here. The discussion isdivided into four sections. The first section discusses theeffect of angle of attack on the development of flowstructures observed over the leeside of the delta wingmodels. The second section discusses the effect of longi-tudinal position on the development of the flow on thedelta wing model. The third and the fourth sections dis-cuss the effect of Reynolds number and transition grit onthe leeside flow of the delta wing models. Surface-pressure coefficient data are presented for all threewings. However, the majority of the flow-visualizationdata presented here are for the elliptical wing model.
To, °F Taw,lam, °F Taw,turb, °F
120 90.6 96.4
125 95.3 101.2
130 100.0 106.0
8
Effect of Angle of Attack
Upper surface-pressure coefficient data.The effectof angle of attack on the surface-pressure coefficientdistribution (hereafter referred to as pressure distribu-tion) on the upper surface for each wing without gritat x = 12 in.,M = 1.60, andR= 2 × 106 ft−1 is presentedin figure 15. Forα < 2.22° on the elliptical wing (seefig. 15(b)), the pressure distribution is smooth to theleading edge. This pressure distribution is typical for anattached-flow condition at the wing leading edge. How-ever, forα ≥ 2.22°, inflections in the pressure distribu-tion over the elliptical wing occur near the leading edge.These inflections are indicative of flow separation at thewing leading edge (referred to hereafter as leading-edgeseparation). Asα increases, the inflections develop into apressure coefficient distribution typical of a vortex ema-nating from the wing leading edge (referred to hereafteras leading-edge vortex).
At the onset of leading-edge separation, a separationbubble forms at the wing leading edge. A separation bub-ble emanating from the wing leading edge (referred tohereafter as a separation bubble) has been defined (refs. 5and 19) as a leading-edge vortex whose core lies veryclose to the wing surface so that the reattachment of theinduced flow onto the wing surface coincides with theinboard edge of the vortex. As angle of attack increases,the core of the vortical structure lifts off the surface andthe reattachment line of the induced flow then occursslightly inboard of the vortex. Figure 11 (from ref. 5)shows the basic leading-edge vortex characteristics.
As discussed in reference 5, when the energy of theflow normal to the leading edge is not sufficient to nego-tiate the expansion at the leading edge, the flow will sep-arate at the leading edge and form a region of rotationalflow referred to as the primary vortex. The pressure dis-tribution associated with a leading-edge vortex is charac-terized by a sudden change in the surface-pressurecoefficient that occurs over a small range ofη with thelower pressures occurring outboard. This characteristiccorresponds to the region where the vortex-induced flowreattaches inboard of the vortex. On the inboard side ofthis reattachment point there is streamwise flow. On theoutboard side of the reattachment point, there is outboardspanwise flow, which can induce surface velocities thatcan decrease the surface pressure relative to the attached-flow pressure distribution (fig. 11).
Figure 16 presents the surface-pressure coefficientdistribution for each wing without grit at common nomi-nal angles of attack forx = 12 in., M = 1.60, andR= 2 × 106 ft−1. All three configurations develop aleading-edge vortex as angle of attack increases, which is
shown in figures 15 and 16. The data in figure 16 showthat wing cross-sectional shape affects the vortexstrength as indicated by the sudden change in pressurecoefficient near the inboard edge of the vortex. The sharpwing data in figure 16 show a greater increase in pressurecoefficient occurring over a smaller range ofη than theelliptical and the cambered wings forαnom= 8°. Thisgreater increase in pressure indicates a stronger vortexthan that observed for the elliptical and the camberedwings. Of the three wings, the cambered wing has thesmallest change in pressure coefficient over the largestrange ofη. Thus, wing leading-edge radius and wingcamber appear to weaken the leading-edge vortex. How-ever, note that all three configurations have equivalentvalues ofCp at the leading edge forαnom≥ 8°.
The angle of attack at which leading-edge separationbegins is also dependent upon the cross-sectional shapeof wing. The data in figures 15 and 16 show that theangle of attack at which the onset of leading-edge separa-tion is first detectedαsep is 2.22° for the elliptical wingand 3.72° for the cambered wing. The pressure coeffi-cient distribution inflection that indicates the onset ofleading-edge separation occurs at 0.9< η < 1.0. Notefrom figures 15 and 16 that the pressure coefficient dis-tribution for the sharp wing ends atη = 0.9 for the stationat x = 12 in. The pressure coefficient distribution for thesharp wing for the station atx = 6 in. ends atη = 0.82.Therefore, from the data in figures 15 and 16 and the datafor x = 6 in. (not presented here), it is difficult to deter-mine at whatα the onset of leading-edge separationoccurs for the sharp wing. However, Stanbrook andSquire (ref. 1) observed that increasing wing leading-edge radius increasesαsep. Therefore, leading-edge sepa-ration on the sharp wing would be expected to occur at alower angle of attack than the elliptical wing.
The cambered wing has a wing leading-edge geome-try that effectively lowers the incidence angle of the flowat the leading edge when compared with the uncamberedwings. The geometrical angle of the cambered wing atthe leading edge is−9.75° in the cross-flow plane. Thisangle corresponds to 3.76° in the streamwise direction.Thus the effective angle of flow approaching the leadingedge of the elliptical wing is 3.76° higher than thatobserved for the cambered wing at any given angle ofattack. The data in figure 15 show that the incidenceof αsep increased only 1.5° from the elliptical wing(αsep= 2.22°) to the cambered wing (αsep= 3.72°). Theelliptical and the cambered wing data in figure 16 showthat, at the wing centerline, camber had a much smallerimpact on the angle of flow. Thus, the geometrical cam-ber essentially lowers the incidence angle of flow overthe cambered wing with a more pronounced effect at thewing leading edge.
9
Lower surface-pressure coefficient data.Figure 17presents the effect of angle of attack on the lowersurface-pressure coefficient distribution for each wingwithout grit atx = 12 in.,M = 1.60, andR= 2 × 106 ft−1.The data show that for each wing, the flow is attached atthe wing leading edge. The surface-pressure coefficientis seen to increase with increasingη and angle of attack.
Vapor-screen data.Presented in figure 18 are vapor-screen photographs for the elliptical wing without grit atx = 12 in., M = 1.60, andR= 2 × 106 ft−1. The effect ofangle of attack on the flow structure is illustrated. Thevapor-screen data do not show any leading-edge vorticalstructure until theα = 3.7° condition (fig. 18(f)). How-ever, the surface-pressure coefficient data in figure 15(b)indicate that leading-edge separation is present atα = 2.22°. This inconsistency is related to the glare of thelaser light sheet off the surface of the wind-tunnel model.At the onset of leading-edge separation (αsep= 2.22° forthe elliptical wing), the leading-edge separation is sosmall and close to the surface of the wing that the glarecould obscure the flow structure. Atα = 3.7° (fig. 18(f)),there is an inboard region of separation that has been pre-viously observed with leading-edge vortical flows com-putationally. (See ref. 19.) This region of separation isalso evident at theα = 2.7° (fig. 18(d)) condition andcould indicate a leading-edge separation that is maskedby the glare of the laser sheet off the wind-tunnel model.
For α ≥ 3.7°, the vortical structure of the leading-edge separation is apparent. For eachα ≥ 3.7° theinboard edge of the vortex is within theη range of thesudden pressure change in the pressure distribution(fig. 15).
Painted- and injected-oil-flow data.Figure 19 pre-sents painted-oil-flow photographs for the elliptical wingwithout grit atα = 3.14°, 4.17°, 6.26°, and 8.34°, M =1.60, andR= 2 × 106 ft−1. Figure 20 presents injected-oil-flow photographs for the elliptical wing without gritat M = 1.60, R= 2 × 106 ft−1, and 0° ≤ α ≤ 9.39° atapproximately 1° increments. The data illustrate theeffect of angle of attack on vortex growth. The injected-oil-flow data in figure 20 indicate attached flow on theupper surface of the elliptical wing forα < 2.08°. Forαnom= 2° and 3° (figs. 19(a), 20(c), and20(d)), the oilaccumulated along the leading edge of the wing, whichindicates a narrow leading-edge separation bubble. Theinjected-oil-flow data (fig. 20(c)) and the surface-pres-sure coefficient data (fig. 15(b)) indicate similar valuesof αsep, 2.08° and 2.22°, respectively. In contrast, thevapor-screen data (fig. 18(f)) indicateαsep = 3.7°, agreater angle than those observed in the injected-oil-flowand surface-pressure coefficient data.
For eachαnom≥ 4°, the oil-flow patterns indicate areattachment line that separates the inboard streamwiseflow and the outboard spanwise flow induced by thepresence of the leading-edge separation. Forα = 4.17°(figs. 19(b) and 20(e)), the location of the flow reattach-ment point corresponds to the location of the inboardedge of the leading-edge separation bubble, which isshown in the vapor-screen data (fig. 18(g)). Thus, theleading-edge separation atα = 4.17° would be classifiedas a leading-edge separation bubble. For eachαnom≥ 5°,the location of the reattachment line as shown in the oil-flow data (figs. 19 and 20) falls slightly inboard of theedge of the leading-edge separation as shown in the cor-responding vapor-screen data in figure 18. Thus forαnom≥ 5°, the leading-edge separation is defined as aclassical leading-edge vortex.
For eachα ≥ 4.17°, the location of the flow reattach-ment point as shown in the oil-flow data (figs. 19 and 20)lies in theη range over which a sudden pressure changeoccurs in the corresponding pressure distribution(fig. 15(b)). Also recall that the vapor-screen data in fig-ure 18 showed that the inboard edge of the primary vor-tex lies in the sameη range.
Liquid-crystal data. Figure 21 presents liquid-crystal photographs for the elliptical wing without gritat M = 1.60 andR= 2 × 106 ft−1 for various angles ofattack. The photographs provide quantitative and qualita-tive data about the flow characteristics of the surface ofthe elliptical wing. The color of the liquid crystals isrelated to the temperature on the surface of the wind-tunnel model. Figures 21(k) and 21(l) present the colorband for the temperature range on the right and the leftside of the wing, respectively.
The data in figures 21(a) and 21(b) show that forα ≤ 1.03°, the temperature on the surface increases sud-denly along a line roughly parallel to the leading edge ofthe wing. Atα = 2.08° (fig. 21(c)) the higher temperatureextends to the leading edge of the wing. This observationcorresponds to the pressure distribution data (fig. 15(b))and the injected-oil-flow data (fig. 20(c)), which showvalues ofα of 2.22° and 2.08°, respectively. The data infigures 21(d) to 21(j) forα ≥ 3.14° also show a distinctline at which the surface temperature changes dramati-cally. However, this line is not parallel to the wing lead-ing edge, but extends from the wing apex to the wingtrailing edge. The angle between this line and the leadingedge of the wing increases with increasing angle ofattack. The location of this line corresponds to the flowreattachment line evident in the corresponding oil-flowdata in figures 19 and20. This line represents a tempera-ture change on the surface of the model due to reattach-ment of the leading edge vortical flow to the surface ofthe wing. (See figs.19(d), 20(i), and 21(i) forαnom= 8°.)
10
The temperature variation occurring over the wing atαnom= 0° and 1.03° (figs. 21(a) and 21(b)) is believed tobe an indication of boundary-layer transition. When theflow separates from the wing leading edge and reattachesinboard, the temperature of the wing surface inboard ofthe reattachment line is that of the turbulent flow atα = 0°. Thus, the flow inboard of the leading-edge sepa-ration for α ≥ 2.08° is believed to have a turbulentboundary-layer condition. The temperature of the wingsurface outboard of the flow reattachment line is that ofthe laminar flow atα = 0°. Also note from the pressuredistribution data in figure 15(b) that the flow outboard ofthe flow reattachment point is in a proverse pressure gra-dient until the pressure distribution levels to a larger neg-ative value ofCp than that at the centerline of the wing.A proverse pressure gradient is a favorable condition fora laminar boundary layer. Thus, the flow outboard ofthe reattachment point is believed to have a laminarboundary-layer condition.
Effect of Longitudinal Position
Flow conicity.A comparison of the pressure distri-butions at two longitudinal positions on the model indi-cates whether the flow over the wing grows conicallydown the length of the wing. Figure 22 shows the uppersurface-pressure distribution for each wing atx = 6 in.and x = 12in. for M = 1.60 andR= 2 × 106 ft−1. Thesharp wing data in figure 22(a) show that the pressuredistributions atx = 6 in. andx = 12 in. are very similar,thus indicating that the flow over the leeside of the sharpwing grows conically down the length of the wing.
The elliptical wing data in figure 22(b) show that thepressure distributions atx = 6 in. andx = 12in. vary sig-nificantly beginning fromα = 2.22° (the angle of attackat which leading-edge separation was first detected in thepressure data) to, but not including,α = 5.23° (the angleof attack at which a classical leading-edge vortex wasfirst detected in the injected-oil-flow data, which isshown in fig. 20(f)). For 1.23° < α < 5.23°, the inboardedge of the leading-edge separation (denoted by a suddenchange in the pressure distribution) occurs at differentη conditions for thex = 6 in. and x = 12in. stations,which indicates that the flow does not grow conicallydown the length of the elliptical wing. This observationcorresponds to the painted and the injected-oil-flow datafor 1° < αnom< 5° (figs. 19(a), 19(b), 20(c), 20(d),and 20(e)), which show a leading-edge separation bubblethat does not grow conically down the length of the wing.
For α > 5.23°, the pressure distributions at thex = 6in. andx = 12in. stations (fig. 22(b)) are similar from thecenterline to the flow reattachment point (determinedfrom the oil-flow data), which indicates that the flowgrows conically down the length of the wing. This obser-
vation corresponds to the injected-oil-flow data forαnom= 5° (fig. 20(f)), which show a conical growth ofthe leading-edge separation. Outboard of the flow reat-tachment point forα = 5.23°, the pressure distributionlevels to a surface-pressure coefficient that is lower at thex = 12 in. station than that observed at thex = 6 in. sta-tion. This observation indicates that, for angles of attackjust above theα range of nonconical growth of the flow,the leading-edge vortex grows conically, but variesslightly in strength down the length of the wing. Forα > 5.23°, the surface-pressure coefficients near the wingleading edge (fig. 22(b)) are essentially the same at thetwo x stations.
The pressure data in figure 22(c) and the flow-visualization data (not presented here) of the camberedwing show similar trends to the data for the ellipti-cal wing. The flow over the wing is nonconical at3.18° < α < 7.18°. Recall thatαsep= 3.72° for the cam-bered wing atM = 1.60 andR= 2 × 106 ft−1. The vapor-screen data and oil-flow data for the cambered wing (notpresented here) show that the leading-edge vortex is firstdetected atαnom= 7°.
Figure 23 shows the upper surface-pressure distribu-tion for each wing without grit atx = 6 in. andx = 12 in.for M = 1.60 andR= 5 × 106 ft−1. For the angle of attackrange where nonconical growth of the flow was observedat R= 2 × 106 ft−1 for the elliptical wing and the cam-bered wing, theR= 5 × 106 ft−1 data in figures 23(b)and23(c) show that the pressure distributions atx = 6and 12 in. vary in theη range from the wing leading edgeto the sudden pressure change that denotes the inboardedge of the leading-edge separation. However, the varia-tions between the pressure distributions at thex = 6 in.and x = 12in. stations are much smaller than wasobserved atR= 2 × 106 ft−1. Thus, Reynolds numberaffects the conicity of the flow over the 65° swept deltawing.
Rx held constant.The surface-pressure coefficientdata presented in figures 22 and 23 show the effect oflongitudinal position on the wing at a constantR. Thelocal Reynolds number for eachx station Rx changeswhenR is held constant. ForR= 2 × 106 ft−1 at x = 6 in.,Rx = 1 × 106, and atx = 12 in., Rx = 2 × 106. Thus, thenonconical growth of the flow could be attributed toReynolds number effects. Figure 24 shows the uppersurface-pressure distributions atx = 6 in. andx = 12 in.for several wing geometry and constantRx. The sharpwing data in figure 24(a) show that the longitudinal posi-tion on the wing does not have a profound affect on theshape of the pressure distribution whenRx is held con-stant. The data in figures 24(b) to 24(d) show that in theangle of attack range where nonconical growth of theflow was observed (1.23° < α < 5.23° for the elliptical
11
wing and3.18° < α < 7.18° for the cambered wing), thepressure distributions at the twox stations agree well.This observation indicates that the nonconical growth ofthe flow observed on the elliptical and the camberedwings is partially a function ofRx. The sharp wing andelliptical wing data in figures 24(a) to 24(c) also showslightly lower values ofCp across the whole span of thewing at higherR. This trend was not observed in thecambered wing data in figure 24(d).
Effect of Reynolds Number
Surface-pressure coefficient data.Data wereobtained over anR range of 1× 106 ft−1 to 5× 106 ft−1 todetermine the effect of Reynolds number on the onsetof leading-edge separation. Figure 25 presents uppersurface-pressure coefficient data obtained at variousRxconditions on the sharp wing model without grit atx = 12 in. The data in figure 25 were obtained atM = 1.60 over the angle of attack range of 0° to 9°. Thepressure data in figure 25 show the development of aleading-edge vortex over the leeside of the sharp wing asthe angle of attack increases. The leading-edge vortexinfluences the pressure distribution so that there is a sud-den pressure change over a range ofη. The flow reat-tachment point falls within this range ofη. The pressuredistribution outboard of thisη range levels to a constantCp near the wing leading edge. The pressure data in fig-ures 25(b) and 25(c) show that theη range over whichthe sudden pressure change occurs decreases withincreasingRx and the amount of the sudden pressurechange increases with increasingRx. These observationsindicate that the strength of the leading-edge vortexincreases with increasingRx. It should be noted thatRxappears to have little affect on theCp near the centerlineor near the leading edge of the sharp wing.
Figure 26 presents upper surface-pressure coefficientdata obtained at variousRx conditions on the ellipticalwing without grit at x = 12 in., M = 1.60, and0° ≤ α ≤ 9°. The data in figure 26 show that Reynoldsnumber has the most effect on the pressure distribution inthe range of 1° < αnom< 5° where nonconical growthof the flow over the upper surface of the ellipticalwing was observed forR= 2 × 106 ft−1 (fig. 22(b)). Atαnom= 2.0°, the pressure distribution atRx = 1 × 106 hasan inflection near the wing leading edge, which indicatesa leading-edge separation bubble. Because the locationof the inflection in the pressure distribution atαnom= 3°has moved more inboard than was observed atαnom= 2.0°, the leading-edge separation bubble growslarger with an increase in angle of attack. However, for agiven angle of attack, the location of the inflection in thepressure distribution moves outboard with increasingRx.This characteristic is seen more clearly in the surface-
pressure coefficient data in figure 27, which presents thepressure distributions at∆α = 0.25° increments for theelliptical wing. Thus, the leading-edge separation bubblefor 2° ≤ αnom< 5° on the elliptical wing becomessmaller with increasingRx.
As the leading-edge separation bubble weakens withincreasing Reynolds number, the pressure distributionmoves to a distribution more typical of an attached flowat the wing leading edge (figs. 26(a), 26(b), and 27). As aresult, the surface-pressure coefficient near the leading-edge decreases as Reynolds number increases. The datain figure 27 show that forRx = 1 × 106, the onsetof leading-edge separation was first detected atαsep= 1.97°. The data forRx = 5 × 106 in figure 27 showthatαsep increases to 2.49° where the leading-edge sepa-ration is detected by a leveling of the pressure distribu-tion at the leading edge. Thus,αsep increases withincreasingRx.
The pressure data in figures 26(b) and 26(c) indicatethat increasing theRx slightly increases the strength ofthe leading-edge vortex present over the upper surface ofthe elliptical wing at the higher angles of attack(αnom≥ 5°). However, the pressure data in figures 26(b)and 26(c) also show that the value ofCp near the wingleading edge is insensitive toRx.
Figure 28 presents upper surface-pressure coeffi-cient data obtained at variousRx conditions on the cam-bered wing model without grit atx = 12 in., M = 1.60,and 0° ≤ α ≤ 9°. The cambered wing data in figure 28show similar trends to those observed in the ellipticalwing data. The pressure data in figure 28 show thatReynolds number has the most effect on the pressure dis-tribution in the angle of attack range (3° < αnom< 7°)where nonconical growth of the flow over the uppersurface of the cambered wing was observed atR= 2 × 106 ft−1 (fig. 22(c)). As was found on the ellipti-cal wing data, the pressure data for the cambered wing at3° < αnom< 7° (fig. 28) show that asRx increases, thesize of the leading-edge separation bubble decreases andthe surface-pressure coefficient near the leading edgedecreases. Also the angle of attack at which leading-edgeseparation begins increases with increasingRx as shownin figure 29, which presents the pressure distributions forthe cambered wing at∆α = 0.5° increments. The pres-sure data in figure 29 show that the angle of attack atwhich leading-edge separation was first detected on thecambered wing increases from 3.70° for Rx = 1 × 106
to 4.20° for Rx = 5 × 106.
As seen with the elliptical wing data, the camberedwing data in figure 28 show that Reynolds number has amuch smaller influence atαnom≥ 7°, where a leading-edge vortex has formed over the cambered wing. Thepressure data in figure 28 show that as Reynolds number
12
increases from 1× 106 to 5× 106, the size of the leading-edge vortex is unaffected. However, the strength of thevortex increases slightly with increasingRx. Also theCpvalue near the wing leading edge is unaffected byRx forαnom> 7°.
The Rx affects the onset of leading-edge separationon the leeside of the elliptical and the cambered wings.One explanation for this observation is the effect ofRxon the boundary layer of the model. With an increase inRx, the boundary layer of the model would be expectedto transition from a laminar condition to a turbulentcondition closer to the wing apex and the wing leadingedge. When a boundary layer is turbulent, the flow ismore energetic than when the boundary layer is laminar.Thus, the closer the turbulent boundary layer is to thewing leading edge, the more energy the flow requires toremain attached at the wing leading edge. The onset ofleading-edge separation would occur at a higherangle ofattack.
The sharp wing data were not affected significantlyby increasingRx. The sharp wing data are available onthe CD-ROM and in appendix D. The sharp wing devel-oped a strong leading-edge separation as soon as angle ofattack was increased from zero. The state of the bound-ary layer does not appear to affect flow structures thatresult from a very strong expansion at the wing leadingedge. A strong expansion at the wing leading edge wouldoccur for a sharp-edged wing at anyangle of attack andfor any wing at high angles of attack.
Vapor-screen data.The effect of Reynolds numberon the flow structure over the cambered wing is illus-trated in figure 30, which presents vapor-screenphotographs for the cambered wing without grit atx = 12 in.,αnom= 5°, M = 1.60, and variousRx. The datain figure 30 show a leading-edge separation bubble atRx = 1 × 106. The separation bubble becomes smaller asRx increases until it finally is hidden by the glare of thelaser light sheet off the surface of the model atRx = 5 × 106. This observation is supported by the pres-sure data in figure 28(b). The pressure data show that forαnom = 5°, a leading-edge separation exists atRx = 1 × 106, as indicated by a sudden change in thepressure distribution. Theη location of this suddenchange inpressure corresponds to the inboard edge of theseparation bubble as shown in the vapor-screen data infigure30(a). As Rx increases, the separation bubblebecomes smaller, which is indicated by the outboardmovement of the location of inflection in the pressuredistribution near the leading edge (fig. 28(b)).
The effect ofRx on the flow over the cambered wingat a higher angle of attack is shown in figure 31. This fig-ure presents vapor-screen photographs for the cambered
wing without grit atM = 1.60,x = 12 in.,αnom= 8°, andvariousRx. The data in figure 31 show thatRx does notsignificantly impact the size of the leading-edge vortex atαnom= 8°. This observation is supported by the surface-pressure coefficient data in figure 28(c).
Painted- and injected-oil-flow data.The painted-and the injected-oil-flow techniques were used to exam-ine the effect of Reynolds number on the flow character-istics of the surface of the wings. Figure 32 presentspainted-oil-flow photographs for the cambered wingwithout grit atαnom= 4°, M = 1.60, and variousR. Fig-ure 33 presents the injected-oil-flow photographs for thesame conditions. The oil-flow data in figures 32 and 33show an accumulation of oil along the leading edge ofthe wing atR= 1 × 106 ft−1 for αnom= 4°. This accumu-lation is indicative of a leading-edge separation bubble,which is also evident in the surface-pressure coefficientdata in figures28 and 29. The data in figures 32 and 33show that asR increases, the accumulation of oil alongthe leading edge becomes thinner, which indicates adecrease in the size of the separation bubble. Decreasingseparation bubble size with increasing Reynolds numberis also seen in the surface-pressure coefficient data infigures 28 and 29.
The pressure distribution data for the elliptical andthe cambered wings (figs. 27 and 29) showed thatincreasing Reynolds number increased the angle ofattack at which leading-edge separation begins. Recallthat figure 20 presents the injected-oil-flow data for theelliptical wing without grit atM = 1.60,R= 2 × 106, andvarious angles of attack. Figure 34 presents injected-oil-flow photographs for the elliptical wing without gritat αnom= 2° and 3°, M = 1.60, andR= 5 × 106 ft−1. ForRx = 2 × 106, the oil-flow data in figure 20 show an accu-mulation of oil along the leading edge (indicating aleading-edge separation bubble) that first occurs atα = 2.08° (αnom= 2°, fig. 20(c)). However, theRx = 5 × 106 data infigure 34 do not show a leading-edge separation bubble occurring untilα = 3.25°(αnom= 3°). This observation corresponds to the pres-sure data in figure 27, which show thatαsep increasedfrom 2.22° (αnom= 2°) to 2.49° (αnom= 2.25°) as theRxincreased from 2× 106 to 5× 106.
The surface-pressure coefficient data in figures 26and 28 indicated little influence of Reynolds number onthe size of the leading-edge vortex at the higher angles ofattack where a leading-edge vortex was present. Fig-ure35 presents injected-oil-flow photographs for thecambered wing without grit atαnom= 8°, M = 1.60, andvariousR. The data show thatR does not significantlyaffect the position of the flow reattachment point of theleading-edge vortex. However, the secondary separation
13
occurring beneath the primary vortex appears to weakenwith increasing Reynolds number.
Liquid-crystal data. Liquid-crystal data wereobtained atR= 2 × 106 ft−1 and 5 × 106 ft−1 to examinethe effect of Reynolds number on the flow characteristicsof the leeside surface of the model. The liquid-crystaldata in figure 21 for the elliptical wing atR = 2× 106 ft−1
first detected the onset of leading-edge separation atα = 2.08° (αnom= 2°). Figure 36 presents liquid-crystalphotographs for the elliptical wing atM = 1.60 andR= 5 × 106 ft−1 for various angles of attack. The data infigure 36 also showed the onset of leading-edge separa-tion occurring atα = 2.17° (αnom= 2°). This observationdoes not correspond to those made in the surface-pressure coefficient data (fig. 27) and injected-oil-flowdata (fig. 34) as shown in table 12. Table 12 presents theangle of attack at which leading-edge separation wasdetected with the surface-pressure, the injected-oil-flow,and the liquid-crystal data. Table 12 also shows the lastangle of attack where attached flow was observedαatt ineach data set. The angle of attack where leading-edgeseparation begins falls betweenαatt andαsep. The data intable 12 show that the trend of an increase inαsep with anincrease in Reynolds number is supported by the pressureand injected-oil-flow data sets. The trend of an increasein αsep with an increase in Reynolds number is not sup-ported by the liquid-crystal data.
However, the liquid-crystal data did indicate asmaller leading-edge separation bubble at theR= 5 × 106 ft−1 condition than that observed for theR= 2 × 106 ft−1 condition (figs. 21(c) and 36(c) forαnom= 2°). This observation is supported by the surface-pressure coefficient data in figure 27, which show adecrease in the size of the leading-edge separation bubblewith an increase inRx. Because all the data sets indicatethat an increase in Reynolds number decreases the size ofthe leading-edge separation bubble for a given angle ofattack, the onset of leading-edge separation occurs at ahigher angle of attack as Reynolds number increases.This observation could be explained by noting thatincreasing the Reynolds number moves the boundary-layer transition location closer to the leading edge. Thisexplanation is supported by the liquid-crystal data for theelliptical wing at αnom= 0° and 1° (figs. 21(a), 21(b),36(a), and 36(b)). The liquid-crystal data show, inboardof the leading edge, a temperature variation that indicatesboundary-layer transition. However, the temperaturevariation for theR= 5 × 106 ft−1 condition occurs muchcloser to the leading edge than that observed for theR= 2 × 106 ft−1 condition. This observation supports theexplanation that boundary-layer condition affects theonset of leading-edge separation.
Effect of Transition Grit
Surface-pressure coefficient data.Data wereobtained on the three models with and without gritapplied to determine the effect of grit on the onset offlow separation at the wing leading edge. Figure 37 pre-sents upper surface-pressure coefficient data obtained onthe sharp wing model atx = 12in. without grit and withtransition grit. The data in figure 37 were obtained atx = 12 in., M = 1.60, andRx = 2 × 106 over the angle ofattack range of 0° to 9°. The data in figure 37 show thatthe application of transition grit appears to have no effecton the development of the vortex over the leeside of thesharp wing with increasing angle of attack. This observa-tion is not unexpected as leading-edge separation occurson the sharp wing as soon asα is increased from 0°.Thus, the spanwise flow does not encounter the transitionstrip until it has reattached inboard of the wing leadingedge and moves back to the wing leading edge as illus-trated in figure 11.
Figure 38 presents a similar set of data for the ellipti-cal wing with and without grit atx = 12 in., M = 1.60,and Rx = 2 × 106 over theαnom range of 0° to 9°. Forαnom ≥ 4°, the application of grit appears to have no sig-nificant impact on the leading-edge vortex (figs. 38(b)and 38(c)). Forαnom ≥ 4°, the flow separates at the wingleading edge, reattaches inboard of the leading edge, anddoes not encounter the transition strip. However, at theangle of attack where leading-edge separation wasfirst detected on the elliptical wing without grit(αsep= 2.22°), grit has an effect on the separation bubbleemanating from the wing leading edge. The separationbubble influences the upper surface-pressure coefficientdistribution so that an inflection appears in the pressuredistribution at the inboard edge of the separation bubble.The pressure data in figure 38(a) show that when grit isapplied to the model, the location of the inflection movesoutboard. Also, with the application of the grit to themodel, the pressure distribution moves to a distributionmore typical of an attached flow at the wing leading edge(fig. 38(a)). As a result, the surface-pressure coefficientnear the leading edge decreases with the application ofgrit to the model. These trends indicate a weaker leading-edge separation bubble for the case with grit than wasobserved for the case without grit. These features areseen more clearly in the surface-pressure coefficient datain figure 39, which presents the pressure distributions forthe elliptical wing in∆α = 0.5° increments atx = 12 in.,M = 1.60, andRx = 2 × 106.
Figure 40 presents surface-pressure coefficient datawith and without grit for the cambered wing atx = 12 in.,M = 1.60, andRx = 2 × 106 overαnom range of 0° to 9°.The effect of transition grit on the cambered wing data
14
was similar to the effect seen in the elliptical wing data(fig. 38). Forαnom≥ 6°, the application of grit appears tohave no significant effect on the leading-edge vortexover the leeside of the cambered wing (figs. 40(b)and40(c)). However, atαnom= 4° (near the angle ofattack where leading-edge separation was first detectedon the cambered wing without grit,αsep= 3.72°), thepresence of transition grit weakens the leading-edge sep-aration bubble. This observation is more clearly evidentin the surface-pressure coefficient data in figure 41,which present the pressure distributions for the camberedwing in increments of∆α = 0.5° at x = 12 in.,M = 1.60,andRx = 2 × 106.
The surface-pressure coefficient data in figures 38to 41 indicate that the application of transition grit weak-ens the leading-edge separation bubble that occurs at lowangles of attack on the elliptical and the cambered wings.An explanation for this observation is that the transitiongrit moves the boundary-layer transition location closerto the wing leading edge than when transition grit wasnot on the model. Because the flow has more energy in aturbulent boundary layer than in a laminar boundarylayer, the cases with grit remain attached at the wingleading edge to a higher angle of attack than the caseswithout grit. Thus, the cases with grit would have aweaker separation bubble than the cases without grit foran angle of attack where both grit conditions yieldleading-edge separation.
Painted- and injected-oil-flow data.The painted-and injected-oil-flow techniques were used to examinethe effect of grit on the flow characteristics of the surfaceof each model. Figure 42 presents the painted-oil-flowphotograph for the cambered wing with grit atαnom= 4°,M = 1.60, andR= 2 × 106 ft−1. Figure 43 presents theinjected-oil-flow photograph for the same condition. Aswas observed for the case without grit (figs. 32(b)and33(b)), the oil-flow data in figures 42 and 43 show anaccumulation of oil along the leading edge of the cam-bered wing atR= 2 × 106 ft−1 for αnom= 4°. However,the accumulation of oil on the leading edge is smaller forthe case with grit than that observed for the case withoutgrit. This observation indicates that the leading-edge sep-aration bubble is weaker for the condition with grit. Thistrend is also evident in the surface-pressure coefficientdata in figure 41.
Concluding Remarks
An experimental investigation of the effect ofleading-edge radius, camber, Reynolds number, and
boundary-layer state on the incipient separation of a deltawing at supersonic speeds was conducted at the LangleyUnitary Plan Wind Tunnel. The three delta wing modelsexamined had a 65° swept leading edge and varied incross-sectional shape: a sharp wedge, a 20:1 ellipse, anda 20:1 ellipse with a−9.75° circular camber imposedacross the span. The three wings were tested at aMachnumber of 1.60 over a free-stream Reynolds num-ber range of 1× 106 to 5× 106 ft−1. The wings weretested with and without transition grit applied. Surface-pressure coefficient data were obtained, as well asflow-visualization data. The flow-visualization tech-niquesemployed were the vapor-screen, the painted-oil-flow, the injected-oil-flow, and the liquid-crystaltechniques. The surface-pressure coefficient data andflow-visualization data are electronically stored on aCD-ROM that accompanies this report.
The data indicated that by rounding the wing leadingedge or cambering the wing in the spanwise direction,the onset of leading-edge separation on a delta wing atsupersonic speeds occurs at a higher angle of attack thanthat observed on a sharp-edged delta wing. Specifically,the 20:1 elliptical cross section increased the angle ofattack at which leading-edge separation begins byabout 2° over that observed on a sharp-edged delta wing.The cambered elliptical cross section, which decreasedthe local angle of attack at the wing leading edgeby 3.76°, effectively increased the angle of attack atwhich leading-edge separation begins by 1.5° over thatobserved on the uncambered elliptical cross section. Thedata showed that the wing leading-edge radius and/orcamber lowers the incidence angle of the flow over thewing with a more pronounced effect on the flow at thewing leading edge.
The application of transition grit on the wing or anincrease in free-stream Reynolds number increased theangle of attack at which leading-edge separation began.Fixing transition or increasing free-stream Reynoldsnumber causes the boundary-layer transition to occurcloser to the wing apex and leading edge of the wing. Aturbulent boundary layer has more energy than a laminarboundary layer and will therefore allow the flow toremain attached at the wing leading edge at higher anglesof attack than is possible with a laminar boundary layer.
NASA Langley Research CenterHampton, VA 23681-0001December 11, 1995
15
Table 1. Geometric Characteristics of Delta Wing Models
Figure 1. Location of 65° delta wing atM = 1.60 with respect to Stanbrook-Squire boundary at various angles of attack.
α = 8°
α = 4°
Separated flow
Attached flow
65° Delta wing at M = 1.60
Stanbrook-Squire boundary
αN, deg
20
16
12
8
4
0.2 .4 .6 .8 1.0 1.2
MN
57
(a) Sharp wing.
Figure 2. Two-view sketches of three delta wing models. All dimensions are in inches unless otherwise noted.
65°
+y+z
Screw holes for sting attachment
16.787
13.9872.600
Removable wingtip
18.000
+y+x
58
(b) Elliptical wing.
Figure 2. Continued.
65°
+y+z
Screw holes for sting attachment
16.787
13.9872.600
Removable wingtip
18.000
+y+x
59
(c) Cambered wing.
Figure 2. Concluded.
65°
+y+z
Screw holes for sting attachment
16.787
13.9872.600
Removable wingtip
18.000
+y+x
.486
60
L-90-04477(a) View of upper surface.
L-90-04479(b) View of lower surface.
Figure 3. Photographs of elliptical wing model installed in Langley UPWT.
61
Fig
ure
4. D
etai
ls o
f stin
g. A
ll di
men
sion
s ar
e in
inch
es.
18.0
00
14.9
91
9.22
6
1.50
0
1.20
6
2.60
0
4.00
0
Scr
ew h
oles
for
atta
chm
ent o
f win
g
Scr
ew h
oles
for
atta
chm
ent o
f A
OA
hou
sing
2.50
0
1.18
8.8
40.6
78
Mou
ntin
g pa
d
62
Figure 5. Details of AOA sensor housing. All linear dimensions are in inches.
30°
3.991
1.3691.613
.684
.594
Sized to fit AOA sensor
Screw holes for attachment to sting
1.375
63
(a) Upper surface atx = 6 in.
Figure 6. Effect of dew point on surface-pressure coefficient data for cambered wing without transition grit atM = 1.60andR= 5 × 106 ft−1.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
.15
.10
.05
0
-.05
-.10
-.15
-.20
-.25
-.30
-.35
Cp
α, deg
0.23 1.21 2.21 3.21 4.20 5.19 6.21 7.20 8.22 9.22
α, deg
0.20 1.19 2.18 3.22 4.15 5.25 6.19 7.24 8.17 9.25
Acceptable dew point
Unacceptable dew point
64
(b) Lower surface atx = 6 in.
Figure 6. Continued.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
.40
.35
.30
.25
.20
.15
.10
.05
0
-.05
Cp
α, deg
0.23 1.21 2.21 3.21 4.20 5.19 6.21 7.20 8.22 9.22
α, deg
0.20 1.19 2.18 3.22 4.15 5.25 6.19 7.24 8.17 9.25
Acceptable dew point
Unacceptable dew point
65
(c) Upper surface atx = 12 in.
Figure 6. Continued.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
.15
.10
.05
0
-.05
-.10
-.15
-.20
-.25
-.30
-.35
Cp
α, deg
0.23 1.21 2.21 3.21 4.20 5.19 6.21 7.20 8.22 9.22
α, deg
0.20 1.19 2.18 3.22 4.15 5.25 6.19 7.24 8.17 9.25
Acceptable dew point
Unacceptable dew point
66
(d) Lower surface atx = 12 in.
Figure 6. Concluded.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
.40
.35
.30
.25
.20
.15
.10
.05
0
-.05
Cp
α, deg
0.23 1.21 2.21 3.21 4.20 5.19 6.21 7.20 8.22 9.22
α, deg
0.20 1.19 2.18 3.22 4.15 5.25 6.19 7.24 8.17 9.25
Acceptable dew point
Unacceptable dew point
67
Figure 7. Flow angularity, angle of attack, and knuckle assembly.
Figure 8. Sting deflections forR= 1 × 106 ft−1 andM = 1.60 from data for elliptical wing without transition grit.
Knuckle
αknu
αacθf
Flow
10
9
8
7
6
5
4
3
2
1
0
αknu, deg
1 2 3 4 5 6 7 8 9 10
αac, deg
68
(a) Sharp wing.
Figure 9. Location of transition grit on model with respect to pressure orifices.
A
B
Grit transition strip
Plugged orifice
Pressure orifice
Section A upper surface at x = 6 in.
Section A lower surface at x = 6 in.
Section B upper surface at x = 12 in.
Section B lower surface at x = 12 in.
.169
Leading edge
Grit transition strip
Location of sections on model.
69
(b) Elliptical wing.
Figure 9. Continued.
A
B
Grit transition strip
Plugged orifice
Pressure orifice
Section A upper surface at x = 6 in.
Section A lower surface at x = 6 in.
Section B upper surface at x = 12 in.
Section B lower surface at x = 12 in.
.169
Leading edge
Grit transition strip
Location of sections on model.
70
(c) Cambered wing.
Figure 9. Concluded.
A
B
Grit transition strip
Plugged orifice
Pressure orifice
Section A upper surface at x = 6 in.
Section A lower surface at x = 6 in.
Section B upper surface at x = 12 in.
Section B lower surface at x = 12 in.
.169
Leading edge
Grit transition strip
Location of sections on model.
71
(a) Upper surface atx = 6 in.
Figure 10. Effect of transition grit on surface-pressure coefficient data for cambered wing atM = 1.60 andR= 5 × 106 ft−1. Shaded area is width and location of transition strip.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
.15
.10
.05
0
-.05
-.10
-.15
-.20
-.25
-.30
-.35
Cp
α, deg
0.23 1.21 2.21 3.21 4.20 5.19 6.21 7.20 8.22 9.22
α, deg
0.18 1.16 2.21 3.21 4.21 5.22 6.23 7.25 8.21 9.18
Without grit Grit
72
(b) Lower surface atx = 6 in.
Figure 10. Continued.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
.40
.35
.30
.25
.20
.15
.10
.05
0
-.05
-.10
Cp
α, deg
0.23 1.21 2.21 3.21 4.20 5.19 6.21 7.20 8.22 9.22
Without grit α, deg
0.18 1.16 2.21 3.21 4.21 5.22 6.23 7.25 8.21 9.18
Grit
73
(c) Upper surface atx = 12 in.
Figure 10. Continued.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
.15
.10
.05
0
-.05
-.10
-.15
-.20
-.25
-.30
-.35
Cp
α, deg
0.23 1.21 2.21 3.21 4.20 5.19 6.21 7.20 8.22 9.22
Without grit α, deg
0.18 1.16 2.21 3.21 4.21 5.22 6.23 7.25 8.21 9.18
Grit
74
(d) Lower surface atx = 12 in.
Figure 10. Concluded.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
.40
.35
.30
.25
.20
.15
.10
.05
0
-.05
Cp
α, deg
0.23 1.21 2.21 3.21 4.20 5.19 6.21 7.20 8.22 9.22
Without grit α, deg
0.18 1.16 2.21 3.21 4.21 5.22 6.23 7.25 8.21 9.18
Grit
75
Figure 11. Sketch of vortex emanating from wing leading edge (from ref. 5).
Figure 16. Effect of cross-sectional shape on upper surface-pressure coefficient distribution for delta wing without tran-sition grit atx = 12 in.,M = 1.60, andR = 2 × 106 ft−1.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
0 αnom = 3°
0αnom = 2°
.1
0
-.1
-.2
-.3
-.4 Cp
Configuration
Sharp Elliptical Cambered
αnom = 1°
1.28 1.23 1.19
αnom = 2°
2.25 2.22 2.18
αnom = 3°
3.28 3.24 3.18
αnom = 1°
α, deg at—
87
(b) αnom= 4°, 5°, and 6°.
Figure 16. Continued.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
0 αnom = 6°
0 αnom = 5°
.1
0
-.1
-.2
-.3
-.4 Cp
4.27 4.25 4.18
5.25 5.23 5.17
6.27 6.23 6.17
αnom = 4°
Configuration
Sharp Elliptical Cambered
αnom = 4° αnom = 5° αnom = 6°
α, deg at—
88
(c) αnom= 7°, 8°, and 9°.
Figure 16. Concluded.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
0 αnom = 9°
0 αnom = 8°
.1
0
-.1
-.2
-.3
-.4 Cp
7.26 7.177.18
8.27 8.188.17
9.28 9.229.23
αnom = 7°
Configuration
Sharp Elliptical Cambered
αnom = 7° αnom = 8° αnom = 9°
α, deg at—
89
(a) Sharp wing.
Figure 17. Effect of angle of attack on lower surface-pressure coefficient distributions for three delta wings withouttransition grit atx = 12 in., M = 1.60, andR= 2 × 106 ft−1.
Figure 32. Painted-oil-flow photographs illustrating effect of Reynolds number on flow structure on leeside of cam-bered wing without transition grit atαnom= 4° andM = 1.60.
139
(a) R= 1 × 106 ft−1 andα = 4.00°.
(b) R= 2 × 106 ft−1 andα = 4.00°.
(c) R= 5 × 106 ft−1 andα = 4.00°.
Figure 33. Injected-oil-flow photographs illustrating effect of Reynolds number on flow structure on leeside of cam-bered wing without transition grit atαnom= 4° andM = 1.60.
140
(a) α = 2.17°.
(b) α = 3.25°.
Figure 34. Injected-oil-flow photographs of leeside of elliptical wing without transition grit atαnom= 2° and 3°,M = 1.60, andR= 5 × 106 ft−1.
141
(a) R= 1 × 106 ft−1 andα = 8.00°.
(b) R= 2 × 106 ft−1 andα = 8.00°.
(c) R= 5 × 106 ft−1 andα = 8.00°.
Figure 35. Injected-oil-flow photographs illustrating effect of Reynolds number on flow structure on leeside of cam-bered wing without transition grit atαnom= 8° andM = 1.60.
142
(a) α = 0°.
(b) α = 1.10°.
Figure 36. Liquid-crystal photographs illustrating vortex growth with angle of attack on leeside of elliptical wing with-out transition grit atM = 1.60,R= 5 × 106 ft−1, andTo = 125°F.
143
(c) α = 2.17°.
(d) α = 3.25°.
Figure 36. Concluded.
144
(a) αnom= 1°, 2°, and 3°.
Figure 37. Effect of transition grit on upper surface-pressure coefficient distribution for sharp wing atx = 12 in.,M = 1.60, andR= 2 × 106 ft−1.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
0 αnom = 3°
0αnom = 2°
.1
0
-.1
-.2
-.3
-.4 Cp
Without grit Grit
1.28 1.29
2.25 2.29
3.28 3.30
αnom = 1°
αnom = 1° αnom = 2° αnom = 3°
α, deg at—
145
(b) αnom= 4°, 5°, and 6°.
Figure 37. Continued.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
0 αnom = 6°
0 αnom = 5°
.1
0
-.1
-.2
-.3
-.4 Cp
Without grit Grit
4.27 4.29
5.25 5.25
6.27 6.28
αnom = 4°
αnom = 4° αnom = 5° αnom = 6°
α, deg at—
146
(c) αnom= 7°, 8°, and 9°.
Figure 37. Concluded.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
0 αnom = 9°
0 αnom = 8°
.1
0
-.1
-.2
-.3
-.4 Cp
Grit 7.26 7.27
8.27 8.26
9.28 9.28
αnom = 7°
Without grit
αnom = 7° αnom = 8° αnom = 9°
α, deg at—
147
(a) αnom= 1°, 2°, and 3°.
Figure 38. Effect of transition grit on upper surface-pressure coefficient distribution for elliptical wing atx = 12 in.,M = 1.60, andR= 2 × 106 ft−1.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
0 αnom = 3°
0αnom = 2°
.1
0
-.1
-.2
-.3
-.4 Cp
Grit 1.23 1.22
2.22 2.22
3.24 3.20
αnom = 1°
Without grit
αnom = 1° αnom = 2° αnom = 3°
α, deg at—
148
(b) αnom= 4°, 5°, and 6°.
Figure 38. Continued.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
0 αnom = 6°
0 αnom = 5°
.1
0
-.1
-.2
-.3
-.4 Cp
Grit 4.25 4.18
5.23 5.21
6.23 6.21
αnom = 4°
Without grit
αnom = 4° αnom = 5° αnom = 6°
α, deg at—
149
(c) αnom= 7°, 8°, and 9°.
Figure 38. Concluded.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
0 αnom = 9°
0 αnom = 8°
.1
0
-.1
-.2
-.3
-.4 Cp
Grit 7.17 7.16
8.18 8.20
9.22 9.20
αnom = 7°
Without grit
αnom = 7° αnom = 8° αnom = 9°
α, deg at—
150
Figure 39. Effect of transition grit on onset of leading-edge separation for elliptical wing atx = 12 in.,M = 1.60, andR= 2 × 106 ft−1.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
0αnom = 2.5°
0αnom = 2°
.05
0
-.05
-.10
-.15
-.20
-.25
Cp
Grit 1.75 1.74
2.22 2.22
2.69 2.69
αnom = 1.5°
Without grit
αnom = 1.5° αnom = 2° αnom = 2.5°
α, deg at—
151
(a) αnom= 1°, 2°, and 3°.
Figure 40. Effect of transition grit on upper surface-pressure coefficient distribution for cambered wing atx = 12 in.,M = 1.60, andR= 2 × 106 ft−1.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
0 αnom = 3°
0αnom = 2°
.1
0
-.1
-.2
-.3
-.4 Cp
Grit 1.19 1.19
2.18 2.21
3.18 3.21
αnom = 1°
Without grit
αnom = 1° αnom = 2° αnom = 3°
α, deg at—
152
(b) αnom= 4°, 5°, and 6°.
Figure 40. Continued.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
0 αnom = 6°
0 αnom = 5°
.1
0
-.1
-.2
-.3
-.4 Cp
Grit 4.18 4.21
5.17 5.21
6.17 6.19
αnom = 4°
Without grit
αnom = 4° αnom = 5° αnom = 6°
α, deg at—
153
(c) αnom= 7°, 8°, and 9°.
Figure 40. Concluded.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
0 αnom = 9°
0 αnom = 8°
.1
0
-.1
-.2
-.3
-.4 Cp
Grit 7.18 7.22
8.17 8.25
9.23 9.23
αnom = 7°
Without grit
αnom = 7° αnom = 8° αnom = 9°
α, deg at—
154
Figure 41. Effect of transition grit on onset of leading-edge separation for cambered wing atx = 12 in.,M = 1.60, andR= 2 × 106 ft−1.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 η
0αnom = 4°
0αnom = 3.5°
.05
0
-.05
-.10
-.15
-.20
-.25
Cp
Grit 3.18 3.21
3.72 3.69
4.18 4.21
αnom = 3°
Without grit
αnom = 3° αnom = 3.5° αnom = 4°
α, deg at—
155
Figure 42. Painted-oil-flow photograph of leeside of cambered wing with transition grit atα = 4.17°, M = 1.60, andR= 2 × 106 ft−1.
Figure 43. Injected-oil-flow photograph of leeside of cambered wing with transition grit atα = 4.00°, M = 1.60, andR= 2 × 106 ft−1.
156
Appendix A
Analytical Expressions for Cross-SectionalShapes of Delta Wing Models
The three cross-sectional shapes that were tested canbe expressed analytically. The equations given in thisappendix are in terms ofy andz normalized by the localsemispan (η andζ, respectively). The equation definingthe sharp cross-sectional shape is as follows for the uppersurface:
(A1)
for the lower surface
(A2)
The equation defining a 20:1 ellipse is as follows forthe upper surface:
(A3)
for the lower surface:
(A4)
To obtain a conical cambered geometry, a spanwisecircular-arc camber was imposed on the elliptical cross-section geometry in the cross-flow plane. The equationfor a circular arc with the center aty = 0, z = z1 is asfollows:
(A5)
whererc, the radius of curvature, is
(A6)
wheres is the arc length andθc is the angle of camberin radians. A given condition is that aty = 0, z wouldequal 0. Therefore,z1 would equal rc. Thus, the equationfor the camber line is
(A7)
Instead of the arc length, the semispanb/2 was usedin generating the cambered geometry. Thus, the equationfor the camber line is as follows:
(A8)
The equation defining the camber line in terms ofη andζis as follows:
(A9)
The angle of camber selected was−10°. The cam-bered cross-section equations are derived by adding thecamber line equation (eq. (A9)) to the elliptical cross-section equations (eqs. (A3) and (A4)). The equations forthe cambered cross section in terms ofη andζ are as fol-lows for the upper surface:
(A10)
for the lower surface:
(A11)
As stated before, the arc length was set equal to thesemispan. However, the arc length of the camber linewould be greater than the semispan. The angle of camberθc can be corrected by taking the derivative of the cam-ber line equation (eq. (A5)) with respect toz. Solving for∂y/∂z yields
(A12)
The angle of camber can be determined by using theknown values ofy andz at the end of the camber line.At the trailing edge, the following conditions apply:y = 8.3935,z = −0.7381, andz1 = 48.0912. The correctangle of camber is−9.75°.
ζ 0.05 0.05η–=
ζ 0.05– 0.05η+=
ζ 0.05 1 η2–=
ζ 0.05 1 η2––=
z z1 r c( )2y
2–+=
r c s θc⁄=
zs
θc-----
sθc-----
2y
2–+=
zb 2⁄( )θc
--------------b 2⁄θc
---------- 2
y2
–+=
ζ 1θc-----
1θc-----
2η( )2
–+=
ζ 0.05 1 η2– 5.72958 32.8281 η2
–+–=
ζ 0.05–( ) 1 η2– 5.72958 32.8281 η2
–+–=
y∂z∂
-----z z1–
y------------- 1
θc( )tan------------------= =
157
Appendix B
Determination of Flow Angle
The flow angularity that exists in both test sectionsof UPWT is described in reference 9 and is illustrated infigure 7. A positive flow angularity indicates that theflow is deflected upward in the test section. The data inreference 9 were used to develop unpublished flow angu-larity charts for each test section over a range of Machnumbers and Reynolds number. However, in actual prac-tice, the flow angle is determined by obtaining force orpressure data with the model upright (φ = 0°) andinverted (φ = 180°) at several angles of attack. The datafor both upright and inverted runs are plotted with angleof attack. A straight line is faired through the data foreach run with emphasis on−2° < α < 2°. The incrementbetween the two faired lines is twice the flow angleθf.
In this study, two approaches were used to determineθf. In the first approach, individual pressure measure-ments were used to calculateθf. In the second approach,all pressure data at eachx station were integratedto determineCN. TheCN was then used to calculateθf.The pressure data in this study were obtained on theelliptical wing at M = 1.60 andR= 1 × 106, 2 × 106,3 × 106, 4 × 106, and 5× 106 ft−1. The R= 1 × 106 and5 × 106 ft−1 data were obtained without transition grit onthe elliptical wing.TheR= 2 × 106, 3 × 106, and4 × 106 ft−1 data were obtained with transition gritinboard of the leading edge of the elliptical wing.
Figure B1 gives an example of the method for deter-mining θf with individual pressure measurements. Fig-ure B1 shows the measured pressure coefficient from theorifice A on the lower surface atx = 6 in. andη = 0.20plotted with angle of attack atφ = 0° and180° forR= 1 × 106 ft−1. Also shown are the faired lines for boththe upright and the inverted runs. The increment betweenthe two faired lines is twice the flow angle,θf. Table B1showsθf determined with this approach for six individualorifices at M = 1.60 andR=1 × 106, 2 × 106, 3 × 106,4 × 106, and 5× 106 ft−1. Three pressure orifices werelocated at the forward station (x = 6 in.) and three werelocated at the aft station (x = 12in.). At each station, one
pressure orifice was located on the lower surface andtwo pressure orifices were located on the upper surface.Thedata in table B1 show that flow angle is depen-dent uponchordwise location. The flow angle decreasesabout 0.25° betweenx = 6 in. to x = 12in. at the lowerReynolds numbers. The data atx = 12in. indicate adependency on Reynolds number, which results in flowangle increases with increasing Reynolds number. Alsonote that the variation ofθf with x becomes smaller withan increase in Reynolds number.
Figure B2 shows an example of the second approachfor determiningθf. This approach usesCN, which is cal-culated by integrating all the measured pressures at agiven x station. Figure B2 shows the calculated valuesof CN plotted with angle of attack forx = 6 in. andφ = 0°and 180° at R = 1× 106 ft−1. Also shown are the fairedlines for both the upright and the inverted runs. Theincrement between the two faired lines is twice the flowangle, θf. Table B2 showsθf determined with thisapproach forx = 6 and 12 in. atM = 1.60 andR =1 × 106, 2× 106, 3× 106, 4× 106, and 5× 106 ft−1. TableB2 shows that the trends in theθf data are similar to thoseobserved in theθf data obtained from individual pressuremeasurements. However, the change inθf with a varia-tion in x or Reynolds number is approximately 0.1° orless, which is smaller than that observed in theθf dataobtained from individual pressure measurements.
The two approaches for determiningθf yielded simi-lar trends inθf with respect tox and Reynolds number.Reference 9 documents a dependency of flow angle onx location in the test section. However, the variation offlow angle withx is very slight in the region of test sec-tion where the model is located. Reference 9 does notdocument a dependency ofθf on Reynolds number. Theapproach using the calculated force data yielded smallervariations inθf with changes inx or Reynolds numberthan the approach using individual pressure measure-ments. The usual choice in determining flow angle atUPWT is force data. Because of these two observations,the calculated force data were used to determineθf. Thedata in table B2 were averaged so that the flow angle thatwas applied to all data was 0.4°.
158
Table B1. Flow Angles From Individual Pressure Measurements
Location θf, deg atR, ft−1, of—
Orifice Surface x, in. η 1 × 106 2 × 106 3 × 106 4 × 106 5 × 106
A Lower 6 0.2 0.50 0.50 0.45 0.48 0.35
B Upper 6 0.1 0.45 0.45 0.45 0.45 0.52
C Upper 6 0.2 0.50 0.45 0.46 0.46 0.58
D Lower 12 0.2 0.20 0.28 0.30 0.35 0.40
E Upper 12 0.1 0.22 0.30 0.35 0.38 0.40
F Upper 12 0.2 0.22 0.25 0.33 0.40 0.40
Table B2. Flow Angles From Integrated Force Data
x, in.
θf, deg atR, ft−1, of—
1 × 106 2 × 106 3 × 106 4 × 106 5 × 106
6 0.45 0.45 0.40 0.40 0.38
12 0.30 0.35 0.38 0.42 0.40
159
Figure B1. Example of method used to determineθf with individual pressure data from orifice A (lower surface,x = 6 in.,η = 0.2) on elliptical wing without grit atR= 1 × 106 ft−1.
-5 -4 -3 -2 -1 0 1 2 3 4 5
αac, deg
-.08
-.06
-.04
-.02
0
.02
.04
.06
.08
.10
.12
.14
Cp
φ, deg
0 (upright)
180.0 (inverted) Least square fit
160
Figure B2. Example of method to determineθf with CN obtained by integrating pressure data atx = 6 in. on ellipticalwing without grit atR= 1 × 106 ft−1.
-5 -4 -3 -2 -1 1 2 3 4 5 -.20
-.16
-.12
-.08
-.04
0
.04
.08
.12
.16
.20
CN
0
αac, deg
φ, deg
0 (upright)
180.0 (inverted) Least square fit
161
Appendix C
Description of CD-ROM
This appendix gives a description of the process usedto transfer the experimental data recorded with photog-raphy into digital form. The digital data are stored on aCD-ROM disc that conforms to the ISO 9660 standard.
Scanning
The four flow-visualization techniques used toobtain data on the three delta wing models were thevapor-screen, painted-oil-flow, injected-oil-flow, andliquid-crystal techniques. The flow-visualization datawere obtained by photography. The photographic imageswere digitized by using two standard charge coupleddevice (CCD) based scanners. Scanning resolution wasselected to balance the need to represent the detailed flowfield information and the requirement that all imageswould be distributed on one 650 MB CD-ROM disc.Table C1 summarizes the scanning process. The scannedimages were stored in the TIFF format.
The vapor-screen data were digitized by scanningthe 70-mm negatives with a flatbed scanner capable ofscanning color images. The flatbed scanner has a resolu-tion of 600 dots/in. (dpi) and uses a three-color fluores-cent lamp system and a CCD image sensor. Thisequipment generates an image that has 8 bits per channel.The image size varies, but is usually 720 columns by504rows. To scan the negatives, it was necessary tospecify their contrast level to achieve an accurate image.
The flatbed scanner is limited to three contrast set-tings. For some of the images, it was not possible toobtain optimal contrast because of the discrete nature ofthe contrast levels and the large variations in opacity ofthe negatives. When a suboptimal result was obtained,the image was automatically scaled to effectivelyincrease the contrast. To determine those scans that weresuboptimal, a region of the image that should have beengray level zero, or black, was probed. If the region wasnot reading an average gray level less than 30, the imagewas linearly scaled, with common data analysis software,between the average region value and the maximumimage brightness value of 255. The integrity of eachimage was visually verified after scaling by comparisonwith photographic prints.
In addition to adjusting the contrast, two other cor-rections for the scanned vapor-screen technique imageswere necessary. The first correction was to invert thescanned image so that the final product was similar to aphotographic print. This correction was done with com-mon data analysis software. The second correction wasto remove artifact lines—bright scan lines that propa-
gated along the vertical, or subscan, direction in thescanned images. A procedure was developed that woulddetect an artifact line and replace it with a line equal tothe average of the scan lines to the left and the right ofthe artifact line. Proper removal of these artifact lineswas verified after processing was completed.
The liquid-crystal images were digitized by scanningthe 70-mm negatives with a tabletop scanner which canscan color images. This tabletop scanner probes with atriband phosphor fluorescent lamp and measures the datawith a 6000 element linear CCD array. The scanner wasdriven from a commercial image manipulation softwarepackage on a Macintosh computer system. Twenty-four-bit (three color planes of eight bits per plane) imageswere produced and the images on the CD-ROM are24bits as well. The negatives were scanned at 350 dpiresolution, which produced images that are 637columnsby 619 rows. The scanning software was used to convertthe negative scan into a positive image by sensing andremoving the orange mask present in color negatives.
The 70-mm negatives of the injected-oil-flow tech-nique and the 4 in. by 5 in. positives of the painted-oil-flow technique were also scanned by the tabletopcolor scanner with a 6000 element linear CCD array.Both sets of images were scanned at 350 dpi resolutionwith the scanner producing 8-bit gray scale images.Again, the scanning software generated a positive fromnegatives of the injected-oil-flow technique by invertingthe image. The size of all the injected-oil-flow images is619 pixels× 637 pixels, while the painted-oil-flow imagesize is 622 pixels× 520 pixels.
Image Display
The digitized images were carefully reviewed afterscanning. The gray levels in the scanned digital imagesaccurately represent the flow-field information in the tra-ditional positive prints. However, each monitor andprinting device has a unique way of presenting the samedigital gray level information. A sample image is givenin figure C1 to illustrate this point. The image in fig-ureC1(a) is displayed on a monitor that has a displayγ = 1.0, while the image in figure C1(b) is displayed on amonitor withγ = 1.7. The parameterγ is a measure of thecontrast response of the display;γ values greater or lessthan 1.0 will expand or compress the dark or bright endof the display range. Generally,γ values are different foreach system and monitor, so image displays betweenmonitors are not consistent even though the same digitalimage file is used. References 20–22 discuss the stan-dardization of monitors so that image display is con-sistent between computer systems. It is suggested thatan image display be adjusted so the model surface isessentially all black and there is a visible transitionbetween the model and the flow field.
162
The above observations are also true with printers.Printers vary in the number of gray levels they can pro-duce and the maximum resolution that can be printed.These two factors determine the fidelity of the image andadjustments may be needed to obtain a realistic print ofthe digital images.
In addition to being aware of system, printer, andmonitor variations, there is another factor to considerwhen displaying 24-bit images on monitors that do nothave full color capability. Ideally, the liquid-crystalimages would be displayed on a monitor capable of dis-playing 24-bit images. Otherwise, the image must bequantized from 24 to 8 bits before displaying. Quantiza-tion is a procedure that will produce a pseudocoloredimage with 8 bits of data that have coloring similar to the24-bit image. There are many different quantizationschemes and some image display software packages willhave a quantization code that is used automatically. Thecolor range in the image is usually an input into a quanti-zation algorithm. Therefore, it is suggested that the cali-bration images (the images containing the temperaturescales to the colors viewed in the data images) be pastedinto a data image file before quantization. If the flow-field image and the calibration images are quantizedindependently, comparisons of colors in the quantizeddata image to colors in the quantized calibration imagesmay be invalid. References 23 to 24 contain moredetailed discussion of quantization methods.
The CD-ROM
The CD-ROM distributed with this paper conformsto the ISO 9660 standard. Included on the CD are theimages mentioned in the scanning section, a table ofpressure data, and a description of header size and imagedimensions for each TIFF image file. The remainder ofthis section will discuss the directory structure, imagefile format, image format conversion, and available soft-ware for three commonly used computer systems: UNIX,PC with DOS, and Macintosh.
The root directory of the CD-ROM contains threedirectories: PRESSDAT, IMAGES, and FILEINFO. TheREADME file in each directory provides information onthe contents of that directory. A schematic of the direc-tory hierarchy is given in figure C2 and table C2 containsa brief description of each directory.
Pressure data files and formats.The files in thePRESSDAT directory are stored as ASCII files. Fig-ureC3 shows the two formats in which the pressure dataare given. Figure C3(a) shows a table format where, for agiven condition, each pressure measurement is listedwith its location on the wing. Table C3 contains the filename convention for the tabulated pressure data files.
Appendix D gives a detailed description of the vari-ables found in each pressure file and a summary ofthe pressure data. Figure C3(b) shows a listing of allpressures and flow conditions for each data point.The pressure-listing file name on the CD-ROM isPRESS.LST. The pressure-listing data identifies eachpressure measurement by the variable name CP#(tables2 to 4). The pressure-listing file does not containthe location of each pressure. Tables 2 to 4 contain thelocation on the wing and the corresponding CP# for eachpressure measurement. Thus, for plotting purposes, thepressure-listing data must be used with a curve definitionfile that gives the location for each pressure. Figure C4shows a portion of the curve definition file, which isnamed CURDEF on the CD-ROM. The first curvedefined in figure C4 is identified as curve “ellu1a” and isthe pressure distribution on the upper surface of the ellip-tical wing atx = 6 in. for runs 4–21. Theη location foreach pressure measurement is given in the “xlist” sectionand the corresponding variable name for each pressuremeasurement from the pressure-listing file is given in the“ylist” section.
Image files and formats.The image files in theIMAGES directory are stored in a directory hierarchythat indicates the wing type, transition grit application,the flow-visualization technique,R, andTo. The direc-tory hierarchy is given in figure C2. A brief descriptionof each directory is given in table C2. The file name foreach image indicates the previously mentioned condi-tions as well as the angle of attack, while adhering to theDOS 8.3 file naming convention. Table C4 contains adescription of the file name convention that was used onthe CD-ROM.
Images are stored in the tagged image file format(TIFF). The TIFF files on this CD have some finiteamount of supplemental information stored at the begin-ning of the file (often called a header) followed by theimage information stored in sequential rows. If softwarethat reads either one of these formats is unavailable, it ispossible to read the TIFF images as raw data into mostimage display software packages. To read an image asraw data, the length of the header and the number of rowsand columns in the image must be known. For all oftheTIFF files, this information is provided in the file,FILESIZE.TXT under the FILEINFO directory.
The calibration images (the images containing thetemperature scales to the colors viewed in the dataimages) for the liquid-crystal data are contained in theroot directory. The file names are LEFTCB andRIGHTCB referring, respectively, to the left and rightside of the wing when looking upstream of the modelfrom the trailing edge.
163
UNIX workstation systems.There are many conver-sion and display routines written for UNIX workstations.Below is a listing of software that can be used to con-vert and display the TIFF images. The software is avail-able by anonymous file transfer. The FTP directorieslisted are the current locations, but they are subject tochange. Restrictions on the use and licensing for anyof the software may be obtained from the associateddocumentation.
Conversion:
Software: imtools
Developer: San Diego Supercomputing Center(SDSC)
FTP site: ftp.sdsc.edu
Directory location: pub/sdsc/graphics/imtools
Description: Software that will read and write avariety of formats. The software, at thiswriting, only runs on UNIX based machines,but will write and read some typical PC andMacintosh formats.
Software: pbmplus
Developer: Jef Poskanzer
FTP site: ftp.x.org
Directory location: R5contrib
Description: Software that will read and write avariety of formats.
Display:
Software: ImageMagick
Developer: John Cristy, E. I. du Pontde Nemours and Company, Incorporated
Developer: John Bradley, Grasp Laboratory atU. Penn.
FTP site: edhs1.gsfc.nasa.gov
Directory location: pub/freeware/unix/src/xv
Description: Software to display images on Xcompatible windowing environments. Thissoftware also has built-in quantization codeand provides some flexibility on the methodused to quantize 24-bit images.
PC with DOS systems.There are many conversionand display routines written in DOS for PC or PC-compatible systems using DOS. Listed below are a pack-age, pbmplus, that can convert images and a package,imdisp, that can be used to display images. These areavailableby anonymous file transfer (FTP) at the sitesgiven in each package description. The FTP directorieslisted are the current locations, but they are subject tochange. Restrictions on the use and licensing for any ofthe software may be obtained from the associateddocumentation.
Conversion:
Software: pbmplus
Developer: Jef Poskanzer
FTP site: wuarchive.wustl.edu
Directory location: SimTel/msdos/graphics
Description: Image format conversion tools thatread and write a large variety of imageformats.
Display:
Software: imdisp
Developer: Jet Propulsion Laboratory (JPL)
FTP site: oak.oakland.edu
Directory location: simtel/msdos/graphics
Description: Written at JPL to display planetarydata. It provides support for a very largevariety of PC graphics cards (EGA, CGA,and VGA). The software will read and writeout the special image formats used todistribute planetary data; however, the TIFFimages can be read in as raw data with theheader and size information as previouslydiscussed. The package also provides somelimited image processing and enhancementcapabilities.
Macintosh systems.There are several display pack-ages for the Macintosh systems that also have extensiveimage processing capabilities. Some of these packagesare listed below along with anonymous file transfer sitesfrom which the user can download the binaries for eachpackage. Most of the packages listed have additional out-put formats and can also serve as conversion software.The FTP directories listed are the current locations, butthey are subject to change. Restrictions on the use andlicensing of any of the software may be obtained fromthe associated documentation.
164
Software: NIH Image
Developer: NIH
FTP site: zippy.nimh.nih.gov
Directory location: pub/nih-image
Description: This is a general purpose imageprocessing package for the Macintosh. It canread 8-bit images only.
Software: JPEGView 3.3
Developer: Aaron Giles, Cornell University
FTP site: edhs1.gsfc.nasa.gov
Description: Can read and display (if hardwareis capable) 24-bit and 8-bit TIFF files
Directory location: pub/freeware/mac
Table C1. Scanning Summary
Flow-visualizationtechnique Film type
Scanning resolution,dpi
Image size (pixels)
Pixel depth, bitsColumns Rows
Vapor screen 70-mm black andwhite negatives
600 Variable Variable 8
Liquid crystal 70-mm colornegatives
350 673 619 24
Painted oil flow 4 in. by 5 in. self-developing film
350 622 520 8
Injected oil flow 70-mm black andwhite negatives
350 619 637 8
165
Table C2. Description of Directories on CD-ROM
Directory Description
IMAGES.INF Directory containing information on images.
PRESSDAT Directory containing pressure data.
IMAGES Directory containing all scanned images.
SNWING Subdirectory containing all scanned images for sharp wing without transition grit.
ENWING Subdirectory containing all scanned images for elliptical wing without transition grit.
EYWING Subdirectory containing all scanned images for elliptical wing with transition grit.
CNWING Subdirectory containing all scanned images for cambered wing without transition grit.
CYWING Subdirectory containing all scanned images for cambered wing with transition grit.
IMAGES/??WING/V_SCREEN
Subdirectory containing all vapor-screen images for configuration associated withIMAGES/??WING directory (where ??WING is SNWING, ENWING, EYWING,CNWING, or CYWING directory).
IMAGES/??WING/I_OILFLO
Subdirectory containing all injected-oil-flow images for configuration associated withIMAGES/??WING directory.
IMAGES/??WING/P_OILFLO
Subdirectory containing all painted-oil-flow images for configuration associated withIMAGES/??WING directory.
IMAGES/??WING/LIQ_CRY
Subdirectory containing all liquid-crystal images for configuration associated withIMAGES/??WING directory.
IMAGES/??WING/*_*/R1
Subdirectory containing data atR= 1 × 106 ft−1 associated with IMAGES/??WING/*_*directory (where *_* is V_SCREEN, I_OIFLO, P_OILFLO, or LIQ_CRY directory).
IMAGES/??WING/*_*/R2
Subdirectory containing data atR= 2 × 106 ft−1 associated with IMAGES/??WING/*_*directory.
IMAGES/??WING/*_*/R5
Subdirectory containing data atR= 5 × 106 ft−1 associated with IMAGES/??WING/*_*directory.
IMAGES/??WING/LIQ_CRY/R#/T120
Subdirectory containing liquid-crystal data atTo = 120°F. Configuration and free-streamReynolds number condition is that associated with IMAGES/??WING/LIQ_CRY/R#directory (where R# is R1, R2, or R5 directory).
IMAGES/??WING/LIQ_CRY/R#/T125
Subdirectory containing liquid-crystal data atTo = 125°F. Configuration and free-streamReynolds number condition is that associated with IMAGES/??WING/Liq_cry/R#directory.
IMAGES/??WING/LIQ_CRY/R#/T130
Subdirectory containing liquid-crystal data atTo = 130°F. Configuration and free-streamReynolds number condition is that associated with IMAGES/??WING/Liq_cry/R#directory.
166
Table C3. Description of Tabulated Pressure Data File Names on CD-ROM
[Tabulated Pressure File Name -1 2 PRESS . TAB]
File name characters Description
1 - Model geometry S ... Sharp wingE ... Elliptical wingC ... Cambered wing
2 - Grit N ... No transition grit appliedY ... Transition grit applied
Example: ENPRESS.TAB File for all pressures for elliptical wing with no transition grit
Table C4. Description of Image File Names on CD-ROM
[Image File Name -1 2 3 4 T 5 . A 6 ]
File name characters Description
1 - Model geometry S ... Sharp wingE ... Elliptical wingC ... Cambered wing
2 - Grit N ... No transition grit appliedY ... Transition grit applied
Example: ENV2T125.A50 Image file for vapor-screen photograph of elliptical wing with-out grit atR= 2 × 106 ft−1, To = 125°F, andαnom= 5.0°. Allimage data were obtained atx = 12 in.
167
(a) γ = 1.0.
(b) γ = 1.7.
Figure C1. Comparison of same image from different display systems.
Figure C4. Example of curve definition file for pressure data.
172
Appendix D
Surface-Pressure Coefficient Data
The surface-pressure coefficient data (referred tohereafter as pressure data) are referenced to the free-stream dynamic pressureq. The pressure data are pre-sented in figures D1 to D22. The pressure data for eachrow of orifices on the upper and the lower surface arepresented for each configuration. For example, figure D1presents the surface-pressure coefficient data for thesharp wing without grit atR= 1 × 106 ft−1 and angles ofattack from 0.25° to 9.27° in approximately 0.5° incre-ments. Table D1 presents an index to the data and thewind-tunnel conditions for each figure.
The surface-pressure coefficient data are also pre-sented on the CD-ROM in a simple pressure-listing for-
mat and a table format. The pressure-listing formatpresents a row of pressures for each data point. For plot-ting purposes, the pressure-listing file must be used witha curve definition file, which gives the location of eachpressure for a given run. The curve definition file is alsolocated on the CD-ROM. The pressure data are alsostored on the CD-ROM in table format where, for a givencondition, each pressure measurement is listed with itslocation on the wing. Appendix C contains the details onthe pressure data files and CD-ROM. Table D1 presents,for each run, the test conditions and the CD-ROM filethat contains the tabulated pressure data. Tables 6 to 11contain a point andα index to the pressure data. Allsurface-pressure coefficient data were taken atβ = 0° andTo = 125°F.
173
aData used in determiningθf.
Table D1. Index to Figures D1 to D22 and Tabulated Data atM = 1.60 andTo = 125°F on CD-ROM
FigurePressure data table
file name Configuration RunR,
million/ftθf,deg
φ,deg
D1 SNPRESS.TAB Sharp wing without grit 40 1 0.4 0
D2 SNPRESS.TAB Sharp wing without grit 41 2 0.4 0
D3 SNPRESS.TAB Sharp wing without grit 42 5 0.4 0
D4 SYPRESS.TAB Sharp wing with grit 43 1 0.4 0
D5 SYPRESS.TAB Sharp wing with grit 44 2 0.4 0
D6 SYPRESS.TAB Sharp wing with grit 45 5 0.4 0
ENPRESS.TAB Elliptical wing without grit 4a 1 0 0
ENPRESS.TAB Elliptical wing without grit 5a 1 0 180.0
D7 ENPRESS.TAB Elliptical wing without grit 6 1 0.4 0
D8 ENPRESS.TAB Elliptical wing without grit 7 2 0.4 0
D9 ENPRESS.TAB Elliptical wing without grit 8 3 0.4 0
D10 ENPRESS.TAB Elliptical wing without grit 10 4 0.4 0
ENPRESS.TAB Elliptical wing without grit 13a 5 0 0
ENPRESS.TAB Elliptical wing without grit 11a 5 0 180.0
D11 ENPRESS.TAB Elliptical wing without grit 14 5 0.4 0
D12 EYPRESS.TAB Elliptical wing with grit 22 1 0.4 0
EYPRESS.TAB Elliptical wing with grit 23a 2 0 0
EYPRESS.TAB Elliptical wing with grit 24a 2 0 180.0
D13 EYPRESS.TAB Elliptical wing with grit 25 2 0.4 0
EYPRESS.TAB Elliptical wing with grit 26a 3 0 0
EYPRESS.TAB Elliptical wing with grit 27a 3 0 180.0
D14 EYPRESS.TAB Elliptical wing with grit 28 3 0.4 0
EYPRESS.TAB Elliptical wing with grit 30a 4 0 0
EYPRESS.TAB Elliptical wing with grit 31a 4 0 180.0
D15 EYPRESS.TAB Elliptical wing with grit 32 4 0.4 0
D16 EYPRESS.TAB Elliptical wing with grit 29 5 0.4 0
D17 CNPRESS.TAB Cambered wing without grit 36 1 0.4 0
D18 CNPRESS.TAB Cambered wing without grit 34 2 0.4 0
CNPRESS.TAB Cambered wing without grit(Unacceptable dew point)
33 5 0.4 0
D19 CNPRESS.TAB Cambered wing without grit 35 5 0.4 0
D20 CYPRESS.TAB Cambered wing with grit 37 1 0.4 0
D21 CYPRESS.TAB Cambered wing with grit 38 2 0.4 0
D22 CYPRESS.TAB Cambered wing with grit 39 5 0.4 0
174
(a) Upper surface atx = 6 in.
Figure D1. Surface-pressure coefficient data for sharp wing without transition grit atM = 1.60 andR= 1 × 106 ft−1 forrun 40.
1. Stanbrook, A.; and Squire, L. C.: Possible Types of Flowat Swept Leading Edges.Aeronaut. Q., vol. XV, pt. 1,Feb. 1964, pp. 72–82.
2. Whitehead, A. H.: Lee-Surface Vortex Effects Over Configu-rations in Hypersonic Flow. AIAA-72-77, 1972.
3. Szodruch, Joachim; and Ganzer, Uwe: On the Lee-Side FlowOver Delta Wings at High Angle of Attack.High Angle ofAttack Aerodynamics,AGARD-CP-247, 1979, pp. 21-1–21-7.
4. Szodruch, Joachim:Lee Side Flow for Slender Delta Wings ofFinite Thickness.NASA TM-75753, 1980.
5. Miller, David S.; and Wood, Richard M.:Lee-Side Flow OverDelta Wings at Supersonic Speeds.NASA TP-2430, 1985.
6. Seshadri, S. N.; and Narayan, K. Y.: Lee-Surface Flow OverDelta Wings at Supersonic Speeds.TM AE 8610, NationalAeronautical Lab. (Bangalore, India), Sept. 1986.
7. Covell, Peter F.; and Wesselmann, Gary F.: Flow-Field Char-acteristics and Normal-Force Correlations for Delta WingsFrom Mach 2.4 to 4.6. AIAA-89-0026, Jan. 1989.
8. Szodruch, Joachim G.:Leeward Flow Over Delta Wings atSupersonic Speeds.NASA TM-81187, 1980.
9. Jackson, C. M., Jr.: Description and Calibration of theLangley Unitary Plan Wind Tunnel.NASA TP-1905, 1981.
10. Braslow, Albert L.; and Knox, Eugene C.:Simplified Methodfor Determination of Critical Height of Distributed RoughnessParticles for Boundary-Layer Transition at Mach NumbersFrom 0 to 5.NACA TN-4363, 1958.
11. Braslow, Albert L.; Hicks, Raymond M.; and Harris,Roy V., Jr.:Use of Grit-Type Boundary-Layer-Transition Tripson Wind-Tunnel Models.NASA TN D-3579, 1966.
12. Stallings, Robert L., Jr.; and Lamb, Milton:Effects of Rough-ness Size on the Position of Boundary-Layer Transition and onthe Aerodynamic Characteristics of a 55°° Swept Delta Wing atSupersonic Speeds.NASA TP-1027, 1977.
13. McMillin, S. N.; Pittman, James L.; and Thomas, James L.:Computational Study of Incipient Leading-Edge Separation on
a Supersonic Delta Wing. J. Aircr. vol. 29, Mar.–Apr. 1992,pp. 203–209.
14. Gray, G. W., ed.: Thermotropic Liquid Crystals. CriticalReports on Applied Chemistry, Volume 22, John Wiley &Sons, Inc., 1987.
15. Holmes, Bruce J.; Gall, Peter D., Croom, Cynthia C.; Manuel,Gregory S.; and Kelliher, Warren C.:A New Method for Lami-nar Boundary Layer Transition Visualization in Flight—ColorChanges in Liquid Crystal Coatings.NASA TM-87666, 1986.
16. Parmar, D. S.; Singh, Jag J.; and Eftekhari, Abe: A Shear Sen-sitive Monomer-Polymer Liquid Crystal System for WindTunnel Applications.Rev. Sci. Inst. vol. 63, Jan. 1992,pp. 225–229.
17. Ireland, P. T.; and Jones, T. V.: Response Time of a Sur-face Thermometer Employing Encapsulated ThermochromicLiquid Crystals.J. Phys. E: Sci. Instrum., vol. 20, no. 10,Oct. 1987, pp. 1195–1199.
18. Schlichting, Hermann (J. Kestin, transl.):Boundary-LayerTheory.Seventh ed., McGraw-Hill Book Co., 1979.
19. McMillin, S. Naomi; Thomas, James L.; and Murman,Earll M.: Navier-Stokes and Euler Solutions for Lee-SideFlows Over Supersonic Delta Wings—A Correlation WithExperiment.NASA TP-3035, 1990.
20. Cromartie, Robert C.; Johnston, R. Eugene; Pizer, Stephen M.;and Rogers, Diane:Standardization of Electronic DisplayDevices Based on Human Perception. TR88-002, Univ. ofNorth Carolina, 1988.
21. Johnston, R. E.; Zimmerman, J. B.; Rogers, D. C.; and Pizer,S. M.: Preceptual Standardization.SPIE, vol. 236, 1985,pp. 44–50.
22. Pizer, S. M.; Johnsont, R. E.; Zimmerman, J. B.; and Chan,F. H.: Contrast Perception With Video Displays.1st Interna-tional Conference and Workshop on Picture Archiving, Part 1,A. J. Duerinckx, ed., SPIE, vol. 318, Jan. 1982, pp. 223–230.
23. Dixit, Sudhir S.: Quantization of Color Images for Display/Printing on Limited Color Output Devices.Comput. & Graph.,vol. 15, no. 4, 1991, pp. 561–567,
24. Pearson, D. E.:Transmission and Display of Pictorial Infor-mation.John Wiley & Sons, Inc., 1975.
Form ApprovedOMB No. 0704-0188
Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of thiscollection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 JeffersonDavis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.
1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED
4. TITLE AND SUBTITLE 5. FUNDING NUMBERS
6. AUTHOR(S)
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
11. SUPPLEMENTARY NOTES
8. PERFORMING ORGANIZATIONREPORT NUMBER
10. SPONSORING/MONITORINGAGENCY REPORT NUMBER
12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE
13. ABSTRACT (Maximum 200 words)
14. SUBJECT TERMS
17. SECURITY CLASSIFICATIONOF REPORT
18. SECURITY CLASSIFICATIONOF THIS PAGE
19. SECURITY CLASSIFICATIONOF ABSTRACT
20. LIMITATIONOF ABSTRACT
15. NUMBER OF PAGES
16. PRICE CODE
NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)Prescribed by ANSI Std. Z39-18298-102
REPORT DOCUMENTATION PAGE
December 1996 Technical Memorandum
Surface-Pressure and Flow-Visualization Data at Mach Number of 1.60for Three 65° Delta Wings Varying in Leading-Edge Radius and Camber WU 505-59-53-05
S. Naomi McMillin, James E. Byrd, Devendra S. Parmar,Gaudy M. Bezos-O’Connor, Dana K. Forrest, and Susan Bowen
L-17443
NASA TM-4673
McMillin, Bezos-O’Connor, and Forrest: Langley Research Center, Hampton, VA; Byrd: Lockheed Engineering &Sciences Company, Hampton, VA; Parmar: Old Dominion University, Norfolk, VA; Bowen: Computer SciencesCorporation, Hampton, VA.
An experimental investigation of the effect of leading-edge radius, camber, Reynolds number, and boundary-layerstate on the incipient separation of a delta wing at supersonic speeds was conducted at the Langley Unitary PlanWind Tunnel at Mach number of 1.60 over a free-stream Reynolds number range of 1× 106 to 5× 106 ft−1. Thethree delta wing models examined had a 65° swept leading edge and varied in cross-sectional shape: a sharp wedge,a 20:1 ellipse, and a 20:1 ellipse with a−9.750 circular camber imposed across the span. The wings were testedwith and without transition grit applied. Surface-pressure coefficient data and flow-visualization data are electroni-cally stored on a CD-ROM. The data indicated that by rounding the wing leading edge or cambering the wing in thespanwise direction, the onset of leading-edge separation on a delta wing can be raised to a higher angle of attackthan that observed on a sharp-edged delta wing. The data also showed that the onset of leading-edge separation canbe raised to a higher angle of attack by forcing boundary-layer transition to occur closer to the wing leading edgeby the application of grit or the increase in free-stream Reynolds number.
