1、Provided 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-,-,-_86LqoueJ8 UOl|etuJo|u IleoluqoeL pus OllllUelOSUop,eJ_s!U!LUPVcoeds pueso!_neuoJeV leuo!),eNVSVN0009I-I
2、SVNI _aea_uoD aopunaa:mo D qaaeoso_i AOlflUw- Iaoj paa_daattv!u!_a._ A uo_cImv Hpocmao4aoou I lvuoHouaasUl uoasua)IAPII_.,Xk “_I q_ouuo3I pu_ UOSla_ D “.OAAaa_Hsuo!avaop!suo D asnaqff, olqeu!eaa Vqa!Ak s_u!Ak jo s!sXieu V pu_u_!so(I _!ua_uApoao V _!uosaodn S pu_!uosqn S aoj ua_a_Oaci aomduao Dpu_ sp
3、oq_oiA I l_!aouanN808_ *aodo_I ao*a_a*uoD VSVN: iii. r. , .,. 7i i ,i. i_i “:Provided 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-,-,-r i i_BSTRACTThis paper des
4、cribes methodology and an associated computer program forthe design of wing lifting surfaces with attainable thrust taken intoconsideration. The approach is based on the determination of an optimumcombination of a series of candidate surfaces rather than the more commonlyused candidate loadings. Spe
5、cial leading-edge surfaces are selected toprovide distributed leading-edge thrust forces which compensate for anyfailure to achieve the full theoretical leading-edge thrust, and a secondseries of general candidate surfaces is selected to minimize drag subject toconstraints on the lift coefficient an
6、d, if desired, on the pitching momentcoefficient. A primary purpose of this design approach is the introduction ofattainable leading-edge thrust considerations so that relatively mild cambersurfaces may be employed in the achievement of aerodynamic efficienciescomparable to those attainable if full
7、theoretical leading-edge thrust couldbe achieved. The program provides an analysis as well as a design capabilityand is applicable to both subsonic and supersonic flow.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-SUmmARYThis paper describes method
8、ology and an associated computer program forthe design of wing lifting surfaces with attainable thrust taken intoconsideration. The approach is based on the determination of an optimumcombination of a series of candidate surfaces rather than the more commonlyused candidate loadings. Special leading-
9、edge surfaces are selected toprovide distributed leading-edge thrust forces which compensate for anyfailure to achieve the full theoretical leading-edge thrust, and a secondseries of general candidate surfaces is selected to minimize drag subject toconstraints on the lift coefficient and, if desired
10、, on the pitching momentcoefficient. A primary purpose of this design approach is the introduction ofattainable leading-edge thrust considerations so that relatively mild cambersurfaces may be employed in the achievement of aerodynamic efficienciescomparable to those attainable if full theoretical l
11、eading-edge thrust couldbe achieved. The program provides an analysis as well as a design capabilityand is applicable to both subsonic and supersonic flow.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-IRTRODL_TIONThe aerodynamic performance of wing
12、s at subsonic speeds is criticallydependent on the amount of leading-edge thrust that can actually berealized. At supersonic speeds, leading-edge thrust plays a reduced role butis not generally negligible. In reference I, a study of the factors whichplace limits on the theoretical leading-edge thrus
13、t was made, and an empiricalmethod for estimation of attainable thrust was developed. A discussion of theway that attainable thrust considerations affect the selection of low-speedflap systems was given in reference 2. Those design notes have now served asthe basis of a system for the design of wing
14、 camber surfaces with attainablethrust taken into account.Consideration of attainable thrust necessitated a design process whichoperates on the principle of defining an optimum combination of candidatesurfaces rather than that of the more generally available design methods whichselect an optimum com
15、bination of candidate loadings or which assign chordwiseand spanwise loading distributions. Techniques for the design of supersonicwings using a set of candidate surfaces were introduced in reference 3.However, because that study did not consider leading-edge thrust, only thegeneral approach of that
16、 report-the use of surfaces rather than loadings-wasapplicable to the problem at hand.In addition to the opportunity to introduce attainable thrustconsiderations, there are several other advantages associated with the optimumcombination of surfaces approach. Because the candidate surfaces may berest
17、ricted to individually smooth surfaces, the resultant optimized surfacecan be free of irregularities due to numerical instabilities. The candidatesurfaces may also be chosen to place realistic and practical restraints oncamber surface severity, and thus the singularities in surface slope thatoften a
18、rise in optimum loading methods may be eliminated. For specialpurposes, the optimization may be carried out only on designated portions ofthe wing such as leading- and trailing-edge areas; a capability particularlyuseful in design of mission-adaptive wing surfaces.The methodology and the associated
19、computer program described in thisreport provide both a design and analysis capability for supersonic as well assubsonicspeeds. The subsonic analysis method employed in this program isfundamentally the same as that described in reference 4 and elaborated upon inProvided by IHSNot for ResaleNo reprod
20、uction or networking permitted without license from IHS-,-,-reference 2. The basic features of the supersonic analysis are as describedin reference 5. A method similar to that of reference 6 has been added toprovide for estimation of theoretical leading-edge thrust at supersonicspeeds. Methods of es
21、timating attainable thrust for both speed regimes arebased on the analysis given in reference 1. The design method, which isapplicable to both subsonic and supersonic speeds, is based on the use ofLagranges method of undetermined multipliers in selecting a combination ofcandidate surface shapes (and
22、 their corresponding loadings) to yield a minimumdrag subject to restraints on lift and moment.Because the analysis methods differ only in minor detail from methods forwhich extensive correlations of program data and experimental data have beengiven (see references I and 4 for some examples) further
23、 demonstrations ofapplicability will not be given here. However, the design features of thepresent program, which are new, will be illustrated by means of several sampleproblems. In some cases, results given by this program will be compared withresults of other theoretical design methods. “ i./“_, ,
24、“ -_i i_ ,_iil4Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-AARbc5ceClec rCteCA%AC DCLCL,desCL,optCL,e%CM,des%cpCp,oCte xeySYMBOLScandidate surface weighting factorwing aspect ratio, b2/Swing spanlocal wing chordmean aerodynamic chordelement chord
25、 at element midspanlocal chord of leading-edge surfacewing root chordlocal chord of trailing-edge surfacewing axial or chord force coefficientwing drag coefficientdrag due to lift coefficient, CD- CD,e= 0 for the samewing with no camber or twistwing lift coefficientwing design lift coefficientoptimu
26、m lift coefficient, lift coefficient correspondingto the maximum value of the suction parameterwing lift coefficient slope at _=0, per degreewing pitching moment coefficientwing design pitching moment coefficientwing normal force coefficientpressure coefficientpressure coefficient at specified initi
27、alpointsection theoretical leading-edge thrustcoefficientexponent of x used in definition of candidate cambersurfacesexponent of y used in definition of candidate cambersurfacesindex of wing element longitudinal position within theprogram grid system and index used in identification ofcandidate surf
28、acesProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-kMrRSSsindex of wing element lateral position within theprogram grid system and index used in identification ofcandidate surfacesconstant of proportionalityMach numberwing section leading-edge radiu
29、sReynolds numberwing reference areasuction parameter,CL tan (CL/CL, _) - AC DC L tan (CL/CL, _) - CL2/(_AR) r _txty,zX l! !X 1, x 2X s0_de sztAuft86L6T6 factorL6 factorTnwing section maximum thicknessCartesian coordinatesdistance in the x direction measured from the wingleading edgex values at front
30、 and rear of wing elementsx value of specified initial pointwing angle of attackdesign angle of attack, corresponding to the design liftcoefficientwing angle of attack giving a local theoretical leading-edge thrust of zero for a specified wing spanwisestationrange of angle of attack for full theoret
31、ical thrust/M2-, for M 1, _I - M2 for M (Uzt+A_ft)vor cotA, y Vtan(Szt-A_ft-e) _ (_zt-A_ft)x =vor cotAin which A is the local leading-edge sweep angle, Uzt is the wing angle ofattack for local leading-edge thrust of zero, and A_ft is the range of angleof attack for full thrust. This formulation loca
32、tes the vortex center aft ofthe leading edge only when full thrust is not realized. However, it does notaccount for the initiation of leading-edge separation at points along theleading edge other than the apex of the superimposed delta wing.Option 2. An alternate and very simple means of locating th
33、e vortexforce center is given by Lan in reference 7. When applied to the presentnumerical method the l_cation of the vortex force center is:X = CtCvor ave /tanA2+l.14Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-For options I and 2, the distributio
34、n ofthe vortex force is assumed to take theform shown in sketch (f). Since thesurface may be cambered, there will becontributions to axial force as well asnormal force. If the vortex center liesaft of the local chord midpoint, part ofthe vortex force will not affect the wingand will be lost.Only lim
35、ited information regardingthe selection of the vortex options isORiGiNAL PAGE _OF POOR QUALITY_C p,vo rXvor _ ,- , -,X8ketch (t)available at this time. The default option, with the vortex force actingperpendicular to the wing reference plane at the wing leading edge, was usedin the correlations with
36、 experimental data given in reference 4. At largeangles of attack, that approach seemed to overestimate the vortex effect-probably because much of the vortex field was actually aft of the wing surfacerather than at the leading edge. The correlations with experimental datagiven in reference 2 were ma
37、de using the vortex location option (I)oGenerally this produced better results for the examples treated there,however, as pointed out previously, this option is appropriate only for highlyswept wings with delta or modified delta planforms. Option 2, from reference7, is applicable only to wings with
38、sharp leading edges but applies to wingsof any planform.As will be discussed in a later section of this report, it may bedesirable for design purposes to know how much a local leading-edge deflectionangle may be changed from the local flow alignment condition (presumed to bedefined by Szt ) and stil
39、l retain attached flow and full theoreticalthrust. This angle of .attack range, Auft, may be found by the methoddescribed in reference 2.Force and Moment CoefficientsAerodynamic coefficients are found by use of integration techniquesdiscussed in reference 4. As discussed in that reference, the wing
40、angle ofattack for zero thrust is used to separate the perturbation velocitydistribution into two parts, one with a leading edge singularity and one15Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Lwithout. The section normal force is found by a sum
41、mation of thecontributions of individual wing elements for a given spanwise station.Within an individual element, the pressure distribution is assumed to becomposed of flat wing and pure camber contributions that depend on the localangle of attack for zero thrust and, for supersonic speeds, also on
42、therelationship between the Mach line and the leading-edge sweep. Within thelimits of the element, the pressure distribution will have a segment of one ofthe forms depicted in figure 4, with the constant k defined so as to pass thecurve through the Cp value at the element quarter chord (or the corre
43、ctedlocation). A sample curve for the flat wing component at subsonic speeds isshown in sketch (g).The individual element contributionsto the section normal force coefficientare found by use of analytic integrationtechniques which for subsonic speeds areidentical to those given in reference 4and for
44、 supersonic speeds are derived in asimilar fashion. Section axial forcecoefficients are found by summation of theproduct of the normal force and surfaceslope dz/dx within individual elements.Cp “Ix, x_Sketch (g) ,DESIGN METHODThe design method employed in the computer program is directly dependenton
45、 the previously discussed analysis methods which are applied to a series ofcandidate wing surfaces. Leading-edge flow condition considerations incombination with drag minimization techniques are used to find an optimumcombination of those surfaces. Inclusion of the influence of attainablethrust on t
46、he design dictates that the solution be found by an iterativeprocess.The process is begun with the evaluation of the aerodynamiccharacteristics of a program input surface. Except for special designpurposes to be discussed later, that surface will be flat. The importantdesign information supplied by
47、this evaluation includes the angle of attack atwhich the design lift is achieved and spanwise distributions of the angle of16Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-ii attack for zero thrust and the range of angle of attack for full thrust. T
48、hisinformation is used to tailor the wing surface in the leading-edge region toprovide distributed leading-edge thrust forces which compensate for anyfailure to achieve the full theoretical leading-edge thrust. Because thischange in the wing surface will change the overall wing lift coefficient atthe design condition, it is then necessary to introduce additional incrementalwing surfaces to restore the design lift coefficient. The Lagrange method ofundetermined multipliers is used to find a combination
