Subsonic Airfoils. W.H. Mason Configuration Aerodynamics Class

Transcription

1 Subsonic Airfoils W.H. Mason Configuration Aerodynamics Class

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

3 Comparison of Panel Method Pressure Distribution with Exact Conformal Transformation Results PANEL Exact Conformal Mapping C p

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

5 A better way 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

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

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 Re = 6 million 1.00 C L 0.50 NACA 4412 NACA 0012 data from Abbott and von Doehhoff C D

13 Comparison 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

14 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 Link available from my software site

15 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 NACA 0012 airfoil, α = 4

16 Effect of Angle of Attack NACA 0012 airfoil Inviscid calculation from PANEL C P α = 0 α = 4 α =

17 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

18 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 =

19 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

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

21 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

22 Camber Effects on Airfoil Pressures, C L = Inviscid calculation from PANEL NACA 0012, α = 4 NACA 4412, α = C P

23 Camber Effects on Airfoil Pressures, C L = Inviscid calculations from PANEL NACA 0012, α = 8 NACA 4412, α = C P

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

25 NACA 6712 Airfoil - Heavy Aft Camber Geometry y/c

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

27 y/c Whitcomb GA(W)-1 Airfoil Inviscid calculations from PANEL C p 0.50 GA(W)-1 α =

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

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

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

31 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? Thickness for low weight and internal volume Tails: often symmetric, 6 series foils picked

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