Subsonic Airfoils. W.H. Mason Configuration Aerodynamics Class

Transcription

1 Subsonic Airfoils W.H. Mason Configuration Aerodynamics Class Most people don t realize that mankind can be divided into two great classes: those who take airfoil selection seriously, and those who don t. Peter Garrison, Flying, Sept. 2002

2 Typical Subsonic Methods: Panel Methods For subsonic inviscid flow, the flowfield can be found by solving an integral equation for the potential on the surface This is done assuming a distribution of singularities along the surface, and finding the strengths of the singularities The airfoil is represented by a series of (typically) straight line segments between nodes, and the nonpenetration boundary condition is typically satisfied at control points Some version of a Kutta condition is required to close the system of equations. node N - 1 N N + 1 panel See my Applied Computation Aero page for the derivation

3 Comparison of Panel Method Pressure Distribution with Exact Conformal Transformation Results PANEL Exact Conformal Mapping C p x/c XFOIL s inviscid calculations use a panel method The conformal mapping solution is from Antony Jameson

4 Convergence with increasing numbers of panels C L NACA 0012 Airfoil, α = No. of Panels

5 How to examine convergence: Lift C L NACA 0012 Airfoil, α = /n

6 Convergence with Panels: Moment NACA 0012 Airfoil, α = 8 C m /n

7 Convergence with Panels: Drag C D NACA 0012 Airfoil, α = /n

8 Pressures: 20 and 60 panels NACA 0012 airfoil, α = panels 60 panels C P x/c

9 Pressures: 60 and 100 panels NACA 0012 airfoil, α = 8 60 panels 100 panels C P x/c

10 Comparison with WT Data: Lift - recall: panel methods are inviscid! NACA 4412 C L 1.00 NACA C L, NACA PANEL C L, NACA exp. data C L, NACA PANEL C L, NACA exp. data α

11 Comparison with Data: Pitching Moment - about the quarter chord NACA C m c/ NACA 4412 C m, NACA PANEL C m, NACA PANEL C m, NACA exp. data C m, NACA exp. data α

12 For Completeness: Drag Data Effect of Camber 2.00 Re = 6 million C L 0.50 NACA 4412 NACA 0012 data from Abbott and von Doehhoff C D

13 1.00 A Sidebar: Can you use thin airfoil theory? Camber Effects: compared to WT Data Camber effect on Alpha Zero Lift Camber effect on Cm Alpha zero lift WT Data C m WT Data Thin Airfoil Theory Thin Airfoil Theory NACA 4 digit series airfoils percent camber NACA 4 digit series airfoils percent camber WT Data From Hemke, Elementary Applied Aerodynamics Thin airfoil theory from Houghton and Carpenter, pg 252

14 WT Data used in Comparison From Hemke, Elementary Applied Aerodynamics

15 Redo our previous comparisons How Well Does Linear Theory Work? Pretty Well! C L, NACA PANEL C L, NACA PANEL C L, NACA exp. data C L, NACA exp. data CL 4412 LT CL 0012 LT C L α

16 And the Pitching Moment C m, NACA PANEL C m, NACA PANEL Cm (NACA 0012) Cm (NACA 4412) Cm 4412 LT ICm 0012 LT C m α

17 Comparison of inviscid prediction with WT Pressure Distribution data from NACA R-646 C p Predictions from PANEL α = M =.191 Re = 720,000 transition free NACA 4412 airfoil x/c Note viscous relief (loss) of full pressure recovery at the trailing edge

18 XFOIL: the code for subsonic airfoils Panel Methods: Inviscid! Couple with a BL analysis to include viscous effects The single element viscous subsonic airfoil analysis method of choice: XFOIL by Prof. Mark Drela at MIT XFOIL also has a inverse option Link available from my software site

19 Airfoil pressures: What to look for Expansion/recovery around leading edge (minimum pressure or max velocity, first appearance of sonic flow) C P lower surface Rapidly accelerating flow, favorable pressure gradient upper surface pressure recovery (adverse pressure gradient) 0.50 Trailing edge pressure recovery Leading edge stagnation point x/c NACA 0012 airfoil, α = 4

20 Effect of Angle of Attack NACA 0012 airfoil Inviscid calculation from PANEL C P α = 0 α = 4 α = x/c

21 Thickness Effects Comparison of NACA 4-Digit Airfoils 0006, 0012, NACA 0006 (max t/c = 6%) NACA 0012 (max t/c = 12%) NACA 0018 (max t/c = 18%) y/c x/c 4-digit series fixes LE radius in relation to t/c max, Modified 4-Digit allow you to control separately

22 Thickness Effects on Airfoil Pressures Zero Lift Case Inviscid calculation from PANEL C P 0.50 NACA 0006, α = 0 NACA 0012, α = 0 NACA 0018, α = x/c

23 Thickness Effects on Airfoil Pressures, C L = Inviscid calculation from PANEL NACA 0006, α = 4 NACA 0012, α = 4 NACA 0018, α = 4 C P Small LE Radius leads to high acceleration around the LE x/c

24 Camber Effects Comparison of NACA 4-Digit Airfoils the 0012 and y/c NACA 0012 (max t/c = 12%) NACA 4412 foil (max t/c = 12%) x/c

25 Highly Cambered Airfoil Pressure Distribution - NACA Inviscid calculation from PANEL NACA 4412, α = 0 NACA 4412, α = 4 C P Note: For a comparison of cambered and uncambered presuure distributions at the same lift, see Fig x/c

26 Camber Effects on Airfoil Pressures, C L = Inviscid calculation from PANEL NACA 0012, α = 4 NACA 4412, α = C P x/c

27 Camber Effects on Airfoil Pressures, C L = Inviscid calculations from PANEL NACA 0012, α = 8 NACA 4412, α = C P x/c

28 Camber Effects on Airfoil Pressures, C L = Inviscid calculations from PANEL NACA 0012, α = 12 NACA 4412, α = 8 C P x/c

29 For Completeness: Drag Data Effect of Camber Re = 6 million 1.00 C L 0.50 NACA 4412 NACA 0012 data from Abbott and von Doehhoff C D

30 NACA 6712 Airfoil - Heavy Aft Camber Geometry y/c x/c

31 NACA 6712 Airfoil - Heavy Aft Camber, Pressure Distribution Inviscid calculations from PANEL α = -.6 (C L = 1.0) C P 0.50 NACA x/c

32 y/c Whitcomb GA(W)-1 Airfoil x/c Inviscid calculations from PANEL C p GA(W)-1 Note nearly parallel upper and α = 0 lower surfaces at the trailing edge x/c

33 Another Goal for Aerodynamics: Laminar Flow For many years aerodynamicists have looked for ways to reduce skin friction drag by achieving laminar flow. One good survey, Overview of Laminar Flow Control, by Ron Joslin, NASA/ TP Oct From Astronautics and Aeronautics. July, 1966

34 Werner Pfenninger: Active laminar flow X-plane Northrop X-21: April Active Laminar Flow Control via wing slots Major re-work of Douglas WB-66D AR = 7, LE Sweep = 30 t/c = 0.10 Ultimately successful. M = 0.745, Flights 120 and 121 Courtesy Tony Landis, personal collection

35 For Airfoils: NLF (Natural Laminar Flow) Maintain a favorable pressure gradient for as long as possible, and then provide a pressure recovery as illustrated below.

36 Liebeck s Hi-Lift Airfoil: Geometry and Lift - note shape of pressure recovery - From R.T. Jones, Wing Theory

37 Liebeck s Hi-Lift Airfoil: Drag From Bertin, Aerodynamics for Engineers

38 Camberline Design: DesCam Z/C (Z-Z0)/C - DesCam Z/C - from Abbott & vondoenhoff Design Chord Loading ΔC P X/C

39 Current Trend: Morphing Also called adaptive or intelligent Airfoil changes shape with flight condition Fighters have had scheduled LE and TE device deflections - since the 1970s (F-16 and F-18) Today transports are looking to tweak surfaces Example: the X-29 Discrete Variable Camber AIAA , Mike Moore and Doug Frei

40 Effect on Lift and Drag Note: Variable camber changes the lift curve slope Results in an optimum envelope polar AIAA , Mike Moore and Doug Frei

41 Airfoil Selection Issues: Cruise C L, and C Lmax, don t forget C m0 - large LE radius? - Near parallel trailing edge closure Profile Drag: Laminar flow? Tailor pressure distribution Thickness for low weight and internal volume Tails: often symmetric, 6 series foils picked Study Abbott and von Doenhoff (both) as a start

42 To Conclude You have the tools to do single element airfoil design