1、I f EXPERIMENTAL AND ANALYTICAL INVESTIGATION OF SUBSONIC LONGITUDINAL AND LATERAL AERODYNAMIC CHARACTERISTICS OF SLENDER SHARP-EDGE 740 SWEPT WINGS by Edwin E. Davenport and Jarrett K. Hfiffman Langley Research Center Hdmpton, vu. 23365 NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C
2、. JULY 1971 iII1 t Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECH LIBRARY KAFB, NM Illllll11111llllllllllllllllllllHlllllll1111 1. Report No. 2. Government Accession No. NASA TN D-6344 4. Title and Subtitle EXPERIMENTAL AND ANALYTICAL INVESTIGA
3、TION OF SUB SONIC LONGITUDINAL AND LATERAL AERODYNAMIC CHAR. ACTERISTICS OF SLENDER SHARP-EDGE 74 SWEPT WINGS 7. Author(s) Edwin E. Davenport and Jarrett K. Huffman 9. Performing Organization Name and Address NASA Langley Research Center Hampton, Va. 23365 2. Sponsoring Agency Name and Address Natio
4、nal Aeronautics and Space Administration Washington, D.C. 20546 5. Supplementary Notes 6. Abstract 3. Recipients Catalog No. 5. Report Date July 1971 6. Performing Organization Code 8. Performing Organization Report No. L-7599 10. Work Unit No. 126-13-10-01 11. Contract or Grant No. 13. Type of Repo
5、rt and Period Covered Technical Note 14. Sponsoring Agency Code Slender sharp-edge wings having leading-edge sweep angies of 74 have been studied at Mach numbers from 0.2 to 0.8. The wings had arrow, delta, and diamond planforms and were tested at angles of attack from -4 to 30 and angles of sidesli
6、p from -8O to 8. The study consisted of wind-tunnel tests in the Langley high-speed 7- by 10-foot tunnel and pre dictions of the characteristics by the theories of NASA TN D-3767 and TN D-6243. 17. Key-Words (Suggested by Author(s) Separated flow Thin airfoils Arrow wings Vortex lift _ 19. Security
7、Classif. (of this report) Unclassified -. 18. Distribution Statement Unclassified - Unlimited 20. Security Classif. (of this page) Unclassified $3.00 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-EXPERIMENTAL AND ANALYTICAL INVESTIGATION OF SUBSONI
8、C LONGITUDINAL AND LATERAL AERODYNAMIC CHARACTERISTICS OF SLENDER SHARP-EDGE 74 SWEPT WINGS By Edwin E. Davenport and Jarrett K. Huffman Langley, Research Center SUMMARY Slender sharp-edge wings having leading-edge sweep angles of 74 have been studied at Mach numbers from 0.2 to 0.8, angles of attac
9、k from about -4O to 30, and angles of sideslip from -8 to 8. The wings had arrow, delta, and diamond planforms. The study consisted of wind-tunnel tests in the Langley high-speed 7- by 10-foot tunnel and predic tions of the longitudinal and lateral aerodynamic characteristics by the theories of NASA
10、 TN D-3767 and TN D-6243. The results of the study indicated that the longitudinal characteristics as affected by planform and Mach number could be reasonably well predicted by the leading-edge suction analogy theories with the exception of the pitching-moment characteristics. With regard to the lat
11、eral characteristics, the present analytical method, although an improve ment over potential-flow theory, still underpredicted the effective-dihedral parameter for all three planforms. INTRODUCTION The advent of supersonic aircraft in recent years has focused attention on thin sharp-edge delta wings
12、 and has prompted many theoretical and experimental studies of the vortex-lift characteristics associated with these wings. A promising concept for the calculation of the vortex lift of sharp-edge highly swept wings has been developed at the Langley Research Center of the National Aeronautics and Sp
13、ace Administration. This concept, which is based on a leading-edge-suction analogy, has been applied to wings of various planforms in both incompressible flow and supersonic flow. (See refs. 1 to 3.) From comparisons which have been made between theoretical and experimental data, it has been found t
14、hat the lift and drag due to lift can be predicted accurately up to the point of vortex breakdown for incompressible flow and supersonic flow. Extension of the leading-edge-suction analogy to include the effects of subsonic compressibility has recently been made in reference 4 for arrow, delta, and
15、diamond wings. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-The purpose of the present investigation was to provide a correlation between experimental and theoretical data for slender sharp-edge wings of arrow, delta, and dia mond planforms and to
16、 study the effects of sideslip angle. The experimental data were obtained in the Langley high-speed 7- by 10-foot tunnel over a Mach number range from 0.2 to 0.8. SYMBOLS The results are presented with the longitudinal aerodynamic parameters referred to the stability axes and the lateral aerodynamic
17、 parameters referred to the body axes. The origin for these axes is the moment reference center which was at the 50-percent root chord of the 90 trailing-edge wing. (See fig. 1.) This origin was held with respect to the wing apex for the 37O recessed trailing-edge and 37O extended trailing-edge wing
18、s. Values are given in both SI Units and U.S. Customary Units. The measurements and cal culations were made in the U.S. Customary Units. Conversion factors between SI Units and U.S. Customary Units are presented in reference 5. f0llows: aspect ratio wing span mean aerodynamic chord of wing root chor
19、d drag coefficient drag coefficient due to lift Liftlift coefficient, qs lift-curve slope The symbols are defined as pitching-moment coefficient, Pitching moment qSF pitching-moment-curve slope 2 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-C2 CN
20、Cn CS CY 2P M q R S a P AYb/2 rolling-moment coefficient, Rolling moment qSb normal-f orce coefficient, Normal force qs yawing-moment coefficient, Yawing moment qSb suction coefficient, Suction force (2s side-force coefficient, Side force qs effective-dihedral parameter, ACl-AP directional-stability
21、 parameter, ACn-AB side-force parameter, ACY-AP constant in potential-flow-lift term constant in vortex-lift term lift-drag ratio free-stream Mach number free-stream dynamic pressure Reynolds number per meter reference wing area angle of attack, deg angle of sideslip, deg center-of-pressure location
22、 C Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Subscripts: P potential-f low- lift contribution V vortex-lift contribution t total contribution MODEL DESCRIPTION Photographs of one model (diamond planform) mounted in the tunnel and the trailing-e
23、dge components of the other two models (arrow and delta planforms) are shown as fig ure 2. The physical characteristics and dimensions of the models are presented in fig ure 1. Pertinent geometric characteristics are given in table I. The model forward portion comprising the main forward wing and ba
24、lance housing was machined from solid aluminum. The three interchangeable wing-balance-housing portions were also machined from solid aluminum and were bolted to the forward portion for a complete model. The wings were thin flat-plate airfoils with sharp tapered edges. TESTS, APPARATUS, AND CORRECTI
25、ONS The investigation was made in the Langley high-speed 7- by 10-foot tunnel which is a rectangular, atmospheric, single-rehrn wind tunnel. Tests were conducted over a Mach number range from 0.2 to 0.8, a nominal angle-of-attack range from about -4 to 30, and an angle-of-sideslip range from -8 to 8
26、O at a = 4 and cr = 12O. The approx imate variation of the test Reynolds number per meter with Mach number is shown in figure 3. Force and moment measurements were made with a six-component internally mounted strain-gage balance. Angles of attack and sideslip were corrected for sting deflection. Axi
27、al force was corrected to a condition of free-stream static pressure acting on the base of the model and the balance cavity. Jet-boundary corrections and blockage corrections, which were applied to the data, were obtained by the methods of references 6 and 7, respectively. No artificial transition w
28、as used on the models. RESULTS AND DISCUSSION In the discussion of the results of the investigation, the 90 trailing-edge configura tion, the 37O recessed trailing-edge configuration, and the 37O extended trailing-edge configuration are referred to as the delta wing, the arrow wing, and the diamond
29、wing, respectively. 4 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Longitudinal Aerodynamic Characteristics The basic longitudinal aerodynamic characteristics for the three wings at zero side slip are shown in figure 4. These data show no signific
30、ant differences in the lift and drag characteristics of the three wings although the aspect ratios are not the same. The lift curves show an increase in CLCY for all models f.or all Mach numbers above an angle of attack of about 5O. This nonlinearity is due to the lift contributed by the leading-edg
31、e vortex. The pitching-moment curves show that Cm, becomes less negative as wing area at the trailing edge is removed and more negative as wing area is added. Also, CmCY was seen to become more negative as Mach number increased. All three models exhibited about the same values of L/D for all Mach nu
32、mbers as can be seen in figure 5. The longitudinal aerodynamic characteristics obtained at a sideslip angle of 4 show the same general trends observed at zero sideslip. (See figs. 4 and 6.) Lateral Aerodynamic Characteristics The variation of the lateral stability derivatives CIP CnP, and Cyp with a
33、ngle of attack is shown in figure 7 for a sideslip angle increment of 4. The effective-dihedral parameter was positive (-Clp) for all models at all Mach numbers and was essentially linear with increase in a. This parameter was relatively unaffected by Mach number. The effects of trailing-edge modifi
34、cation on the side-force derivative CyB were minor except at the lowest test Mach number (M = 0.2). Values of CyP generally remained within *0.002 over most of the angle-of-attack range for all Mach numbers. The lateral aerodynamic coefficients Cz, Cn, and Cy as a function of sideslip angle were det
35、er mined for a Mach number of 0.4 and are shown in figure 8 to be essentially linear with sideslip angle for both a! = 4O and 12. Comparison of Theoretical and Experimental Data The method used to obtain theoretical lift and drag-due-to-lift coefficients was developed in references 1 to 4. The expre
36、ssion used to obtain total theoretical lift coef ficient (CL)t is (cL)= K sin a cos2cr + K, cos CY sinan Values of Kp and Kv were obtained by the method of reference 4. Comparison of the experimental data with data obtained by using this theory is made in figures 9(a), (b), (c), and (d) for M = 0.2,
37、 0.4, 0.6, and 0.8, respectively. Both the potential-flow-theory lift coefficient (CL)P and the total lift coefficient (CL)t which includes the theoretical vortex-lift effect, are shown. The theoretical results are in excellent agreement with the experimental results for the delta wing and in reason
38、ably good agreement for the diamond 5 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,- and arrow wings. Although the effects of Mach number are rather small for these slender wings, the experimental results indicate that the large vortex-lift effect
39、predicted by the theory are maintained up to the highest Mach number of the tests. The reduction of lift for the arrow wing and the increase in lift for the diamond wing at the higher angles of attack relative to the theory is discussed in reference 3. Comparison of theoretically and experimentally
40、obtained values of drag due to lift -as a function of CL is made in figure 10. For zero leading-edge suction, it can CL2 tan O.be shown (ref. 3) that - The short-dash curves represent -which CL2 PL)t (CL); corresponds to the condition of potential lift only (that is, (CL)P = Kp sin Q! COSQ!,)whereas
41、 the solid curves represent -(vortex plus potential). Some of the dis (CLf crepancy between theoretical and experimental values of lift are reflected in the drag due-to-lift curves at M = 0.2 and 0.4 where theory underpredicts drag for the arrow wing and overpredicts drag for the diamond wing. At M
42、= 0.6 and 0.8 the agreement has become better and there is less effect of planform. This same trend was noted for the lift curves (fig. 9). The long-dash lines of constant value represent drag for poten tial flow with full leading-edge suction (a. The increment between the -TA curves and the curves
43、for drag with total lift (CL)p + (CL),) gives some indication of the drag pen alty associated with leading-edge separation. It should be noted, however, that the pen alty is substantially less than that indicated by zero suction theory with vortex lift ignored. A similar comparison of these paramete
44、rs is made in reference 3. An attempt was made to predict the variation of Cm with . The results are presented in figure 11. The expression used to obtain the total theoretical pitching-moment coefficient is where (CN)= Kp sin ct cos Q! (CN), = Kv sin the method of reference 8 was used. Fairly good
45、agreement between theoretical and experimental values of Cm was obtained at M = 0.6 and M = 0.8 for the delta wing over the complete angle-of-attack range (figs. ll(c) and ll(d). A possible explanation for the poor agreement for the arrow wing is that there is insufficient area in the tip region on
46、which the suction near the tip can be converted to vortex lift. (See ref. 3 .) It is likewise possible that additional vor tex lift is produced on the aft extension of the diamond wing. Corresponding agreement for the arrow and diamond wings appears to show about the same trends shown for the variat
47、ion of CL with a! (fig. 9). Comparison of predicted and experimental values of effective-dihedral parameter IP is made in figure 12. The predicted CzP was obtained by calculating the rolling-moment coefficient at p = 5 for both the potential flow and the vortex flow and then combining the results; t
48、hat is, and Cs is suction coefficient. Values of CL) C, Kp, and Ay were obtained from a Wagner program (ref. 8).b/2 Although the theory consistently underpredicted the experimental results, the inclusion of the vortex-flow term does provide an improvement over the potential-flow theory. Whether this
49、 underprediction of the effective-dihedral parameter is associated primarily with inadequacies in the method of predicting the leading-edge-suction distribution or with the fact that such effects as redistribution of the potential-flow lift or vortex breakdown are not accounted for is not known, and further study is needed. 7 C Provided by IHSNot for ResaleN
