1、NASA Technical Paper 3637Guide to AERO2S and WINGDES ComputerCodes for Prediction and Minimization of DragDue to LiftHarry W. CarlsonLockheed Martin Engineering normal-force integration factor for flat wing contribution to basic camberedwing loading at a = 0 acting on camber surface; axial-force int
2、egration factor for basicpressure loading of flat wing at a = 1 acting on camber surfacerate of growth of lifting force per unit distance along equivalent body axislocation correction factor for code perturbation velocityaltitudeindex of wing element longitudinal position within code grid system and
3、 index used inidentification of candidate surfacesindex of wing element lateral position within code grid system and index used in identifica-tion of candidate surfacesconstant used in curve-fit equation(CL,des) opt,expdesign lift-coefficient factor,( C L,des ) opt,thsuction parameter factor, (Ssmax
4、)exp(Ss,max)thC tattainable thrust factor, fraction of theoretical thrust actually attainable, -c tarbitrary constant used in definition of pressure distributionoooviiiProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-kQk o kfkh,1, kh,2knk,kvorkb k2LEI
5、lele, vMMemlemtePPlqRrriSSSSSTsTEtUU, I;, WAu(A.d2)o(Au )o,cconstant used in attainable thrust curve-fit equationconstants used in curve fitting of code perturbation velocities and pressure coefficients forintegration purposesconstants used in hinge-line singularity correctionarrow wing notch ratio,
6、 see figure 40constant used in candidate design surface definitionconstant used in definition of vortex force distributionconstants used in definition of camber surface slopeleading edgeoverall wing lengtheffective length of body of revolution representing distribution of equivalent area due to lift
7、as defined by area rule cutting planeseffective length of body of revolution representing distribution of volume as defined byarea rule cutting planesMach numberequivalent Mach number used in place of M n to account for values of Cp.li m differing fromCp,vacnormal Mach number, see figure 12multiplyi
8、ng factor for tangent of leading-edge flap deflection anglemultiplying factor for tangent of trailing-edge flap deflection anglefree-stream static pressurelocal static pressurefree-stream dynamic pressureReynolds number based on mean aerodynamic chordlinearized theory perturbation velocity influence
9、 functionleading-edge radiusleading-edge radius index, (r/c)rl(xlc) 2wing reference areaC L tan (CL/CL)- AC osuction parameter,C L tan (CL/CL_) -C2/(rcAR)supersonic transportdistance along section camber linetrailing edgetheoretical section leading-edge thrustfree-stream velocityperturbation velocit
10、y in x, y, and z direction, respectivelylongitudinal perturbation velocity difference across wing lifting surface as fraction of free-stream velocitylimiting value of leading-edge thrust parameter Au,_ -_ at wing leading edgelimiting value of leading-edge thrust parameter Au4r_ at wing leading edge
11、for camberedwing at x = 0 ixProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-( Au,41-XP)o,fAu cAufVx, y, zAxAx o Ax R, Ax LXcgx hXmcxvx eX , ,YcggoZ0, Zl, Z2O_O_desa_tc_ta07_c_C,H_e,n_te,seonlimiting value of leading-edge thrust parameter Au 4t_ at wi
12、ng leading edge for flat wing ato_=1 value of Au for cambered wing at _ = 0 value of Au for fiat wing at c_ = 1configuration total volumeCartesian coordinates, positive aft, right, and up, respectivelylongitudinal spacing of grid lines used in establishment of code wing grid systemlongitudinal dista
13、nces employed in influence functionlongitudinal center of gravitydistance from wing leading edge to flap hinge linelongitudinal moment centerdistance in x direction measured from wing leading edgedistance in x direction measured from wing element leading edgevalues of x at which camber surface z ord
14、inates are specifiedlateral center of gravitylimiting value of singularity parameter ACp,/_ at x = 0camber surface ordinate at x0, Xl, and x 2, respectivelyangle of attack, degangle of attack corresponding to design lift coefficient, degrange of angle of attack for full leading-edge thrust, degangle
15、 of attack for zero thrust, degangle of attack corresponding to zero lift, degratio of specific heats, 1.4incidence of canard reference plane with respect to wing reference plane, positive withleading edge up, degincidence of horizontal-tail reference plane with respect to wing reference plane, posi
16、tivewith leading edge up, degleading-edge flap deflection angle measured normal to hinge line, positive with leadingedge down (segmented flap deflection specified as inboard/outboard), degleading-edge flap streamwise deflection angle, positive with leading edge down (segmentedflap deflection specifi
17、ed as inboard/outboard), degtrailing-edge flap deflection angle measured normal to hinge line, positive with leadingedge down (segmented flap deflection specified as inboard/outboard), degtrailing-edge flap streamwise deflection angle, positive with leading edge down (segmentedflap deflection specif
18、ied as inboard/outboard), degangle between line tangent to wing section camber surface and camber surface referenceplane, degvalue of e at wing leading edgelocation of section maximum thickness, fraction of chordProvided by IHSNot for ResaleNo reproduction or networking permitted without license fro
19、m IHS-,-,-AAh,leAh,teAlekZN, _M, _R_tSubscripts:adjavbccotempevalexpflemaxminoptprereptethtotvisvor14,sweep angle of wing constant percent chord line, degleading-edge flap hinge-line sweep angle, degtrailing-edge flap hinge-line sweep angle, degwing leading-edge sweep angle, degangle between interse
20、ction of distant fore Mach cone with wing plane and wing longitudi-nal axis, deg (see fig. 39)Lagrange multipliersMach angle, sin -1 (I/M), degsection maximum thicknessazimuth angle in frontal projection between line connecting field point with wing longitudi-nal axis and wing plane, deg (see fig. 3
21、9)adjustedaverageaerodynamic characteristics due to basic pressure distributions alone (no thrust or vortexforces)cambered wingcorrectedempiricalevaluatedexperimentflat wingleading edgemaximumminimumwing section normal to leading edgeoptimumpreviousreplacementtrailing edgetheoreticaltotalviscousvort
22、exwavexiProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-AbstractThe computer codes, AER02S and WINGDES, are now widely used for the anal-ysis and design
23、 of airplane lifting surfaces under conditions that tend to induce flowseparation. These codes have undergone continued development to provide additionalcapabilities since the introduction of the original versions over a decade ago. Thiscode development has been reported in a variety of publications
24、 (NASA technicalpapers, NASA contractor reports, and society journals). Some modifications have notbeen publicized at all. Users of these codes have suggested the desirability of combin-ing in a single document the descriptions of the code development, an outline of thefeatures of each code, and sug
25、gestions for effective code usage. This report isintended to supply that need.1. IntroductionThe computer codes, AERO2S and WlNGDES, arenow widely used for the analysis and design of airplanelifting surfaces under conditions that tend to induce flowseparation and degrade performance. These codes hav
26、eundergone continued development to provide additionalcapabilities since the introduction of the original versionsover a decade ago. This code development has beenreported in a variety of publications (NASA technicalpapers, NASA contractor reports, and society journals).Some modifications have not b
27、een publicized at all.Users of these codes have suggested the desirability ofcombining in a single document the descriptions of thecode development, an outline of the features of eachcode, and suggestions for effective code usage. Thisreport is intended to supply that need.A method for estimation of
28、 attainable leading-edgethrust introduced in reference 1 provides the fundamentalbasis of a system applicable to partially attached-partially separated flow. The original computing codeemploying the attainable thrust numerical method whichwas applicable to analysis of a single lifting surface withtw
29、ist and camber at subsonic speeds is described inreference 2. A modification of the analysis method toprovide for the handling of simple hinged leading- andtrailing-edge flaps is described in reference 3. A furthermodification to permit the analysis of a wing surface incombination with a second lift
30、ing surface such as acanard or a horizontal tail is described in reference 4. Thepresent version of this code is designated “AERO2S.“The wing-design computer code described in refer-ence 5 provides for the design of a wing mean cambersurface (twist and camber in combination) to minimizedrag for give
31、n design lift and moment conditions. Thedesign method defines an optimum combination of can-didate surfaces rather than the more usual optimum com-bination of loadings. In the design process, attainableleading-edge thrust is taken into account to provide themildest possible camber surface which meet
32、s the designrequirements. The use of candidate surfaces provides anadditional capability to design mission adaptive cambersurfaces which restrict changes to designated areas of theplanform. The design code was later modified to providefor the design of leading- and trailing-edge flap deflec-tion sch
33、edules as described in appendix A of reference 3.The present code also has provision for the design ofreflexed wing surfaces in the vicinity of engine nacellesand for the handling of asymmetrical planforms. Thesetwo modifications, as well as several others, were notpreviously documented. The design
34、code is applicable toboth subsonic and supersonic speeds and provides analy-sis as well as design capabilities. The present version ofthis code is designated “WINGDES.“A survey of research on wing design for reduction ofdrag due to lift at supersonic speeds reported in refer-ence 6 led to the develo
35、pment of an empirical correctionto account for real flow effects not covered by linearizedtheory methods. This correction provides an adjustmentto the design process so that the wing design may beoptimized with nonlinear penalties associated withexcessive camber surface severity taken into account.T
36、he empirical correction, now incorporated into theWINGDES code, results in a milder camber surface thanwould otherwise be found. A second empirical correctionprovides a more realistic estimate of the achievable per-formance of the design. A further modification to theapplication of the correction, i
37、ntroduced in the presentpaper in section 7.10, now permits the additional benefitof reduced camber surface severity associated with anattainable thrust design to be included in the performanceestimate.Reference 7 describes a recent revision of the attain-able thrust prediction method used in both co
38、des. Thenewer method that provides for a greater range of airfoilshapes from very sharp to very blunt leading edges isbased on experimental data for a wider range ofReynolds numbers than the previous method. Refer-ences 8 and 9, in addition to references 2 to 7, give exam-ples of correlation of code
39、 results (both AERO2S andWlNGDES) with experimental measurements and offerProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-adviceon applicationof the codesto problemsofinterest.Thisreportis intendedto provideanunderstandingofcodecapabilitiesandguidanc
40、eineffectiveapplicationtoproblemsof practicalinterestbutnotademonstrationof codevalidity.Themanypreviouslyreportedcorrela-tionsof codedatawith experimentalresultsusedtovalidatethemethodsarereexaminedonlyif theyprovideinformationpertinentto futurecodeusage.Readersinterestedprimarilyin applicationof t
41、hecodeswill findinformationdescribingcodeinputandoutputdatainappendixA for AERO2Sand in appendixB forWINGDES.Examplesofcodeusegiveninsections11and12offerguidanceinuseof thecodesforproblemsofinterest.Data used in these examples are given in table Ifor AERO2S and in table II for WINGDES and serve asmo
42、dels for the preparation of code input.The use of area rule concepts to provide a furtherunderstanding of design for drag minimization at super-sonic speeds is the final topic of this report. Mathemati-cal relationships presented in appendix C describe thedependence of vortex drag, wave drag due to
43、lift, andwave drag due to volume on configuration geometriccharacteristics and establish minimum values for each ofthese drag components. The strategies for the estimationof drag minima outlined in appendix C have been incor-porated into a computer code, CDMIN.2. Basic Lifting Surface SolutionThe pr
44、imary component of both the WINGDES andthe AERO2S codes is a modified linearized solution forthe forces and moments acting on twisted and camberedlifting surfaces of arbitrary planform. Forces obtained byintegration of pressure distributions on the zero thicknesslifting surfaces used in these codes
45、do not include aleading-edge thrust contribution arising from the highvelocities and low pressures generated by a flow aroundthe leading edge from a stagnation point on the winglower surface, l However, methods are available that pro-vide estimates of not only the theoretical leading-edgethrust but
46、also the amount of this force that can actuallybe realized. A means of estimating attainable leading-edge thrust and also the vortex force generated as a resultof leading-edge flow separation is included in the modi-fied linearized theory solution used in these codes.Among the unique features of the
47、 linearized theorymethods used herein are (1) solutions obtained by pureiteration and (2) the use of leading-edge singularitytUnder some circumstances (wings with symmetrical sections atnegative angles of attack, for example), the stagnation point mayoccur on the upper surface. In either case, leadi
48、ng-edge thrust maybe developed.parameters to identify and separate velocity distributioncomponents with and without singularities. The first fea-ture permits an easy code expansion to accommodatemore wing elements for greater accuracy as computercapabilities improve. The second feature permits morea
49、ccurate determination of leading-edge thrust distribu-tion for wings with twist and camber and providesimproved pressure distribution integration techniques.2.1. Grid System and Lifting Surface DefinitionThe linearized theory solutions are obtained by aniterative solution of influence equations for an array ofwing elements representing the wing planform asdepicted in figure 1. Only a right-hand wing pane
