1、NASA TECHNICAL NOTE!ZZNASA TN D-7921SUBSONIC AERODYNAMIC CHARACTERISTICSOF INTERACTING LIFTING SURFACES WITHSEPARATED FLOW AROUND SHARP EDGESPREDICTED BY A VORTEX-LATTICE METHODJohn E. Lamar and Blair B. GlossLangley Research CenterHampton, Va. 23665I,76 _192 _NATIONAL AERONAUTICSAND SPACE ADMINISTR
2、ATION WASHINGTON, D. C. , SEPTEMBER1975Provided 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-,-,-1. Report No, 2, Government Accession No.NASA TN D-79214. Title a
3、nd SubtitleSUBSONIC AERODYNAMIC CHARACTERISTICS OF INTERACT-ING LIFTING SURFACES WITH SEPARATED FLOW AROUNDSHARP EDGES PREDICTED BY A VORTEX-LATTICE METHOD7. Author(s) 8.3. Recipients Catalog No.5, Report DateSeptember 19756. Performing Organization CodePerforming Orgamzation Report No.John E. Lamar
4、 and Blair B. Gloss9. Performing Organization Name and AddressNASA Langley Research CenterHampton, Va. 2366512. Sponsoring Agency Name and AddressNational Aeronautics and Space AdministrationWashington, D.C. 20546L- 1000110. Work Unit No.505-06 -14-0111. Contract or Grant No,13. Type of Report and P
5、eriod CoveredTechnical Note14. Sponsoring Agency Code-15, Supplementary Notes16. AbstractBecause the potential flow suction along the leading and side edges of a planform can beused to determine both leading- and side-edge vortex lift, the present investigation was under-taken to apply the vortex-la
6、ttice method to computing side-edge suction force for isolated orinteracting planforms. Although there is a small effect of bound vortex sweep on the compu-tation of the side-edge suction force, the results obtained for a number of different isolatedplanforms produced acceptable agreement with resul
7、ts obtained from a method employingcontinuous induced-velocity distributions. By using the method outlined in this report, betteragreement between theory and experiment was noted for a wing in the presence of a canardthan had previously been obtained.17. Key Words (Suggested by Author(s)Subsonic flo
8、wGeneralized suction analogyVortex latticeInteracting lifting surfaces19. Security Classif, (of this reportUnclassified18. Distribution StatementUnclassified - UnlimitedSubject Category 0220. Security Ctassif. (of this page) 21. No. of Pages 22. Price“Unclassified 90 $ 4.75 For sale by the National
9、Technical Information Service, Springfield, Virginia 22161Provided 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-,-,-SUBSONIC AERODYNAMIC CHARACTERISTICS OF INTERA
10、CTING LIFTINGSURFACES WITH SEPARATED FLOW AROUND SHARP EDGESPREDICTED BY A VORTEX-LATTICE METHODJohn E. Lamar and Blair B. GlossLangley Research CenterSUMMARYBecause the potential flow suction along the leading and side edges of a planformcan be used to determine both leading- and side-edge vortex l
11、ift, the present investiga-tion was undertaken to apply the vortex-lattice method to computing side-edge suctionforce for both isolated and interacting planforms. Although there is a small effect ofbound vortex sweep on the computation of the side-edge suction force, the resultsobtained for a number
12、 of different isolated planforms produced acceptable agreementwith results obtained from an application of the suction analogy to a method employingcontinuous induced-velocity distributions. The computed side-edge suction results gen-erally remained within 1 percent of the converged ones for 6 singu
13、larities chordwise ateach of 20 spanwise locations.The lift characteristics obtained from the present method for several isolatedwings agreed as closely with experimental data as did those obtained from the methodemploying continuous induced-velocity distributions. In addition, by using the methodou
14、tlined in this report, better agreement between theory and experiment was noted for awing in the presence of a canard than had previously been obtained.INTRODUCTIONThe development of methods for predicting the aerodynamic characteristics of air-craft, which during portions of their flight envelopes,
15、 develop separated flow with reat-tachment around the leading and side edges of the wing, has been the subject of studiesfor many years and has had varying degrees of success. Polhamus in references 1, 2,and 3 provided a method by which the effects of separated flow around a sharp leadingedge on lif
16、t and drag could be estimated by an analogy that relates these forces to theattached flow leading-edge suction force. Hence, current lifting-surface computer pro-grams which estimate leading-edge suction are useful in predicting the leading-edge sep-aration effects on the forces.Provided by IHSNot f
17、or ResaleNo reproduction or networking permitted without license from IHS-,-,-The effects of side-edge separation on the aerodynamic characteristics have beenestimated by determining the attached flow side force and then employing a “suctionanalogy“ similar to that used at the leading edge. This con
18、cept was developed and cor-related with experiment and other methods in reference 4. The procedure employed inreference 4 is based on a modified Multhopp method which is outlined in reference 5.The technique of reference 4 is well suited to single, isolated planforms. However,for lifting planforms i
19、n combinations or for flat body-wing configurations, the vortex-lattice method (i.e., ref. 6) is better suited because its elemental panel representationprovides a straightforward extension to the more complex configurations.This paper is concerned with the extension of the vortex-lattice method of
20、refer-ence 6 to the computation of the attached flow side force. Others have published similarwork recently (refs. 7, 8, and 9, for example) but they do not provide comparisons ofalternate paneling arrangements or convergence studies with their analyses. Thus, thepurposes of this paper are (1) to pr
21、ovide comparisons of alternate paneling arrangements,(2) to provide convergence studies, (3) to provide the details of side-force and pitching-moment computation, and (4) to present comparisons between experimental and theoreti-cal results for single planform configurations and interacting planform
22、configurations.The program changes made in Langley computer program A2794 since the publica-tion of reference 6 are discussed in appendix A. These changes include corrections,improvements, and the additions relating the the side-edge-suction computations. Inaddition, input and output data for a samp
23、le case are presented in appendix B, and a list-ing of the program is provided in appendix C.SYMBOLSA aspect ratiob wing spanC D drag coefficient, DragqooSrefC D,o experimental value of drag coefficient at C L = 0C L lift coefficient, LiftqooSrefC m2pitching-moment coefficient about Y axis, Pitching
24、 momentqooSrefCrefProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-hCm,i contribution to pitching-moment coefficient from vortex system operating onan elemental panelCN normal-force coefficient, qooSrefCS total leading-edge suction-force coefficient,2
25、(Leading-edge suction force on one panel)qooSrefCy, se twice total side-edge-suction-force coefficient of one wing panel,N/22(Side force along side edge on one wing panel) = 2 _ (aCy, se)iq_oSref i= 1(ACY, se) i contribution to side-edge-force coefficient from ith elemental panelCref reference chord
26、ctAFy, itip chordcontribution to side force from ith elemental panelaCNnp = 0(sin ot cos _)acSKv,/e 8 sin 2Kv,se8Cy, seo sin 2length of trailing filament between adjacent chordwise horseshoe vorticesbound vortex filament length in chord directionM Mach number3Provided by IHSNot for ResaleNo reproduc
27、tion or networking permitted without license from IHS-,-,-NNc!Nsq=oSrefUWX,Y,ZX,Y,Zx,yXrefAXAXrr tA4total number of horseshoe vortices that contribute to the side-edge suctionforcenumber of elemental panels in chordwise rownumber of chordwise rows on wing semispanfree-stream dynamic pressurereferenc
28、e areafree-stream velocityinduced downwash velocityaxis system of a given horseshoe vortex (see fig. 1)body-axis system for planform input (see fig. 1)distance along X- and Y-axis, respectivelymoment reference point (taken to be zero herein)distance along tip chord to centroid of side-edge forcechor
29、dwise distance from midpoint of particular vortex filament to momentreference pointangle of attack, deg=_/-1 _M 2vortex strengthchordwise sum of vortex strengths to a particular elemental panel, _F (seefig. 1)leading-edge sweep angle, positive for sweepback, degProvided by IHSNot for ResaleNo reprod
30、uction or networking permitted without license from IHS-,-,-k taper ratiodensitysweepangleof boundvortex, degSubscripts:B boundvortexcentroidLparticular horseshoevortexparticular item of locationleftlePRleading edgepotential or attached flowrightse side edgetot totalv/e vortex effectat leading edgev
31、se vortex effect at side edgeTHEORETICAL DEVELOPMENTThe attached flow side force is developed in accordance with the Kutta-Joukowskilaw for forces generated by a vortex filament. Figure 1 shows vortex filaments whichhave a streamwise component interacting with the net downwash at the filament midpoi
32、ntto produce an elemental side force. The net side force on an elemental panel due to aswept horseshoe vortex system on the left wing panel isProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-tan iandthe contribution to the side-force coefficient is(AC
33、y,se) - 2 _-_I(-_-_)/L-(-_-_)/R ltan_ FIWB-(_)A/_i Sref + tan U-U- i(z)(2)The side force is of order ot2, which is appropriate since it is associated withedge suction. If the trigonometric terms were retained, the side force is actually afunction of sin 2 _ since the _ term is really a sin _ term an
34、d F/U, F/U, andw/U are all proportional to sin _ for the wind and body axes coincident. Hence,Kv,s e can be formulates ast2 N/2_ (ACy, se)i=lKv,se = (3)sin 2For small _ the sin _ _ _ which, for numerical purposes, is taken to be 1 radian inequations (2) and (3) and leads toN/2Kv,se = 2 _ (ACy, se) i
35、i=lThis provides an additional contribution to the total lift, as indicated in the followingequation:(4)CL,pCL,to t =% sin a cosCL,v/e CL,vsesin otI sin el cos+ Kv,/e lsin _l sin ot cos ot +rKv,seFor planforms having sharp edges, the drag coefficient can be written asCD = CD,o + CL,to t tan(5)Provid
36、ed by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-In the numerical determination of the side force, it is realized that computationaltime savings could be made with the utilization of a swept horseshoe vortex system. Thesavings are due to the vortex filament
37、 length and the net downwash associated with theright trailing filament of a swept horseshoe vortex being the same as those for the lefttrailing filament on the adjoining inboard swept horseshoe vortex. However, the sweptbound vortex may lead to local and overall errors in the side force, just as it
38、 did forleading-edge thrust 1 (ref. 10). This potential problem will be investigated although itshould be less serious than that for thrust because in the side-force computation, thebound vortex interaction with the net downwash at its midpoint will only contribute a por-tion to the total side force
39、, rather than the entire result.To assess the importance of the inclusion of the swept bound vortex, numericalstudies are presented in the next section. They are based on paneling the wing in vari-ous ways to emphasize the influence of the bound vortex differently.The pitching-moment contribution ab
40、out the Y-axis associated with the side _edge-suction force is determined from each elemental horseshoe vortex by_I _ tan _ FIW_B c_lA/ Axt31F _ _)lL Ax h Ax - -ACmi = Sref Cref iThe sign of each term is chosen with the realization that the overall rotation of thetrailing flow field on the left wing
41、 panel is clockwise as viewed from the rear. Thisrotation causes the vortex elements behind the moment reference point to contribute anoseup moment if associated with the left trailing leg or a sweptback bound vortex and anosedown moment for the vortex elements associated with the right trailing leg
42、 (fig. 1).The total pitching moment is obtained by using the following expression:Cm,p Cm,v/e Cm,vs e = ACm, Isin _I sin c_i=l_ _ _ _ r _._I_. _F- _ -z , r - _ xc)se _Cm,to t = Kp sin ce cos _ Xcp Xc/e Isin _1 sin _ -+ Kv,/e Isin _1 sin _ _ + Kv,seCref Cref Crefwhen the particular Ec-terms equal Xre
43、f - Xc,.Only those horseshoe vortices or portions thereof whichwould intersect the sideedge if they were projected laterally to the local spanwise extent of the planform (those1The leadingedge thrust problem and the program changes made to correct it aredescribed in appendix A.7Provided by IHSNot fo
44、r ResaleNo reproduction or networking permitted without license from IHS-,-,-that do so are said to directly opposethe side edge)are included in the summationforthe side force andpitching moment. This procedure is the sameas that usedfor com-puting the leading-edgethrust, where all the distributed t
45、hrust alongthe chord is pro-jected forward and assumedto act at the leading edge. Onereasonfor computingtheside-edge suction force in this manner, rather thanwith the methodpresented in refer-ence 8, is that, in the application of the methodof reference 8 to a croppeddiamondwing,the entire side-edge
46、suction force wouldbe calculated over a wing panelwith the onlyreduction coming from the removal of the contribution from the leading-edgesuction.This retains the contribution to the side force from the aft part of the croppeddelta wingfrom which no edgeforce is expected.NUMERICAL STUDIESPanel Arran
47、gementsTable I presents a comparison of Kv,se and the side-edgeload centroid obtainedby four different methodsfor the three wing planforms presented in figure 2. Method 1is the continuousloading methodof reference 4 andthe results of this methodare takento be the standard. Method2 is the present met
48、hod,which was described previously.Method3 is the sameas method 2 excepteachplanform is consideredas two wings (thedashedlines in fig. 2 showbreak lines) and the side-edge suction force is computedonlyonthe aft wing. Method4 is the vortex-lattice methoddescribed in reference 7 with theresults beingsupplied by R. G. Bradley of General Dynamics Corp.The layout of the boundvortices directly opposingthe side edgeof a wing tip willhave less sweepfor method3 thanfor method2 becausemethod3 panelsthe wing as twoplanforms. In fact the croppeddelta
