MAE 3241: AERODYNAMICS AND FLIGHT MECHANICS

1. MAE 3241: AERODYNAMICS AND FLIGHT MECHANICS Review of Basic Aerodynamics February 28, 2011 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk

2. MAE 3241: AERODYNAMICS AND FLIGHT MECHANICSAIRFOIL DATAFROM: INTRODUCTION TO FLIGHT, APPENDIX DJOHN D. ANDERSON, JR. Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk

3. LECTURE OUTLINE • Review of Euler’s Equation • Euler’s equation for incompressible flow → Bernoulli’s Equation • Basic Definitions • Airfoils, Wings and Other Objects • Airfoil Nomenclature • Lift, Drag, Moments • Aerodynamics • How does an airfoil or wing generate lift? • What are effects of viscosity? • Why does an airfoil stall? • Summary

4. WHAT DOES EULER’S EQUATION TELL US? • Euler’s Equation (Differential Equation) • Relates changes in momentum to changes in force (momentum equation) • Relates a change in pressure (dp) to a chance in velocity (dV) • Assumptions we made: • Steady flow • Neglected friction (inviscid flow), body forces, and external forces • dp and dV are of opposite sign • IF dp increases dV goes down → flow slows down • IF dp decreases dV goes up → flow speeds up • Valid for Incompressible and Compressible flows • Valid for Irrotational and Rotational flows

5. INVISCID FLOW ALONG STREAMLINES Relate p1 and V1 at point 1 to p2 and V2 at point 2 Integrate Euler’s equation from point 1 to point 2 taking r=constant

6. BERNOULLI’S EQUATION Constant along a streamline • If flow is irrotational p+1/2rV2 = constant everywhere • Remember: • Bernoulli’s equation holds only for inviscid (frictionless) and incompressible (r=constant) flows • Relates properties between different points along a streamline or entire flow field if irrotational • For a compressible flow Euler’s equation must be used (r is a variable) • Both Euler’s and Bernoulli’s equations are expressions of F=ma expressed in a useful form for fluid flows and aerodynamics

7. AIRFOILS VERSUS WINGS

8. AIRFOILS VERSUS FINITE WINGS High AR Aspect Ratio Low AR

9. AIRFOIL NOMENCLATURE • Mean Chamber Line:Set of points halfway between upper and lower surfaces • Measured perpendicular to mean chamber line itself • Leading Edge:Most forward point of mean chamber line • Trailing Edge:Most reward point of mean chamber line • Chord Line:Straight line connecting the leading and trailing edges • Chord, c:Distance along the chord line from leading to trailing edge • Chamber:Maximum distance between mean chamber line and chord line • Measured perpendicular to chord line

10. NACA FOUR-DIGIT SERIES • First set of airfoils designed using this approach was NACA Four-Digit Series • First digit specifies maximum camber in percentage of chord • Second digit indicates position of maximum camber in tenths of chord • Last two digits provide maximum thickness of airfoil in percentage of chord Example: NACA 2415 • Airfoil has maximum thickness of 15% of chord (0.15c) • Camber of 2% (0.02c) located 40% back from airfoil leading edge (0.4c) NACA 2415

11. AIRFOIL THICKNESS: WWI AIRPLANES English Sopwith Camel Thin wing, lower maximum CL Bracing wires required – high drag German Fokker Dr-1 Higher maximum CL Internal wing structure Higher rates of climb Improved maneuverability

12. “HOW IS THIS USEFUL TO ME?”

13. STREAMLINE FLOW PATTERNS • Uniform flow + source produces a shape that looks something like the leading edge of an airfoil • Concept of vortex sheet • Uniform flow + vortex sheet can create an airfoil shape of interest • Mathematical model mimics that shape of airfoil in flow field

14. STREAMLINES OVER AN AIRFOIL

15. WHAT CREATES AERODYNAMIC FORCES? • Aerodynamic forces exerted by airflow comes from only two sources • Pressure, p, distribution on surface • Acts normal to surface • Shear stress, tw, (friction) on surface • Acts tangentially to surface • Pressure and shear are in units of force per unit area (N/m2) • Net unbalance creates an aerodynamic force “No matter how complex the flow field, and no matter how complex the shape of the body, the only way nature has of communicating an aerodynamic force to a solid object or surface is through the pressure and shear stress distributions that exist on the surface.” “The pressure and shear stress distributions are the two hands of nature that reach out and grab the body, exerting a force on the body – the aerodynamic force”

16. RESOLVING THE AERODYNAMIC FORCE • Relative Wind: Direction of V∞ • We used subscript ∞ to indicate far upstream conditions • Angle of Attack, a:Angle between relative wind (V∞) and chord line • Total aerodynamic force, R, can be resolved into two force components • Lift, L: Component of aerodynamic force perpendicular to relative wind • Drag, D: Component of aerodynamic force parallel to relative wind

17. RESOLVING THE AERODYNAMIC FORCE • Aerodynamic force, R, may also be resolved into components perpendicular and parallel to chord line • Normal Force, N: Perpendicular to chord line • Axial Force, A: Parallel to chord line • L and D are easily related to N and A • For airfoils and wings, L and D most common • For rockets, missiles, bullets, etc. N and A more useful

18. AERODYNAMIC MOMENT • Total aerodynamic force on airfoil is summation of F1 and F2 • Lift is obtained when F2 > F1 • Misalignment of F1 and F2 creates Moments, M, which tend to rotate airfoil/wing • Value of induced moment depends on point about which moments are taken • Moments about leading edge, MLE or quarter-chord point, c/4, Mc/4 • In general MLE≠ Mc/4 F1 F2

19. VARIATION OF L, D, AND M WITH a • Lift, Drag and M on a airfoil or wing will change as a changes • Variations of these quantities are some of most important information that an airplane designer needs to know • Aerodynamic Center • Point about which moments essentially do not vary with a • Mac=constant (independent of a) • For low speed airfoils aerodynamic center is near quarter-chord point

20. HOW DOES AN AIRFOIL GENERATE LIFT? • Lift due to imbalance of pressure distribution over top and bottom surfaces of airfoil (or wing) • If pressure on top is lower than pressure on bottom surface, lift is generated • Why is pressure lower on top surface? • We can understand answer from basic physics: • Continuity (Mass Conservation) • Newton’s 2nd law (Euler or Bernoulli Equation) Lift = PA

21. HOW DOES AN AIRFOIL GENERATE LIFT? • Flow velocity over top of airfoil is faster than over bottom surface • Streamtube A senses upper portion of airfoil as an obstruction • Streamtube A is squashed to smaller cross-sectional area • Mass continuity rAV=constant: IF A↓ THEN V↑ Streamtube A is squashed most in nose region (ahead of maximum thickness) A B

22. HOW DOES AN AIRFOIL GENERATE LIFT? • As V ↑ p↓ • Incompressible: Bernoulli’s Equation • Compressible: Euler’s Equation • Called Bernoulli Effect • With lower pressure over upper surface and higher pressure over bottom surface, airfoil feels a net force in upward direction → Lift Most of lift is produced in first 20-30% of wing (just downstream of leading edge) Can you express these ideas in your own words?

23. EVEN A FLAT PLATE WILL GENERATE LIFT • Curved surface of an airfoil is not necessary to produce lift A B

24. LIFT, DRAG, AND MOMENT COEFFICIENTS Behavior of L, D, and M depend on a, but also on velocity and altitude V∞, r∞, Wing Area (S), Wing Shape, m∞, compressibility Characterize behavior of L, D, M with coefficients (cl, cd, cm) Matching Mach and Reynolds (called similarity parameters) M∞, Re M∞, Re cl, cd, cm identical

25. LIFT, DRAG, AND MOMENT COEFFICIENTS Behavior of L, D, and M depend on a, but also on velocity and altitude V∞, r∞, Wing Area (S), Wing Shape, m∞, compressibility Characterize behavior of L, D, M with coefficients (cl, cd, cm) Note on Notation: We use lower case, cl, cd, and cm for infinite wings (airfoils) We use upper case, CL, CD, and CM for finite wings

26. SAMPLE DATA: NACA 23012 AIRFOIL Flow separation Stall Lift Coefficient cl Moment Coefficient cm, c/4 a

27. AIRFOIL DATA (5.4 AND APPENDIX D)NACA 23012 WING SECTION Re dependence at high a Separation and Stall cd vs. a Dependent on Re cl cl vs. a Independent of Re cd R=Re cm,a.c. vs. cl very flat cm,a.c. cm,c/4 a cl

28. EXAMPLE: SLATS AND FLAPS

29. AIRFOIL DATA (5.4 AND APPENDIX D)NACA 1408 WING SECTION Flap extended Flap retracted

30. SAMPLE DATA TRENDS • Lift coefficient (or lift) linear variation with angle of attack, a • Cambered airfoils have positive lift when a=0 • Symmetric airfoils have zero lift when a=0 • At high enough angle of attack, the performance of the airfoil rapidly degrades → stall Lift (for now) Cambered airfoil has lift at a=0 At negative a airfoil will have zero lift

31. SAMPLE DATA: STALL BEHAVIOR Lift (for now) What is really going on here What is stall? Can we predict it? Can we design for it?

32. AIRFOIL DATA (APPENDIX D)NACA 23012 WING SECTION Re dependence at high a cd vs. cl Dependent on Re cl cl vs. a Independent of Re cd cm,a.c. vs. cl very flat cm,a.c. cm,c/4 a cl

33. REAL EFFECTS: VISCOSITY (m) • To understand drag and actual airfoil/wing behavior we need an understanding of viscous flows (all real flows have friction) • Inviscid (frictionless) flow around a body will result in zero drag! • Called d’Alembert’s paradox (Must include friction in theory)

34. REAL EFFECTS: VISCOSITY (m) • Flow adheres to surface because of friction between gas and solid boundary • At surface flow velocity is zero, called ‘No-Slip Condition’ • Thin region of retarded flow in vicinity of surface, called a ‘Boundary Layer’ • At outer edge of B.L., V∞ • At solid boundary, V=0 “The presence of friction in the flow causes a shear stress at the surface of a body, which, in turn contributes to the aerodynamic drag of the body: skin friction drag”

35. THE REYNOLDS NUMBER • One of most important dimensionless numbers in fluid mechanics/ aerodynamics • Reynolds number is ratio of two forces • Inertial Forces • Viscous Forces • c is length scale (chord) • Reynolds number tells you when viscous forces are important and when viscosity can be neglected Outside B.L. flow Inviscid (high Re) Within B.L. flow highly viscous (low Re)

36. WHY DOES AN AIRFOIL STALL? • Key to understanding: Friction causes flow separation within boundary layer • Separation then creates another form of drag called pressure drag due to separation

37. WHY DOES AN AIRFOIL STALL? • Key to understanding • Friction causes flow separation within boundary layer • Separation then creates another form of drag called pressure drag due to separation

38. WHY DOES BOUNDARY LAYER SEPARATE? • Adverse pressure gradient interacting with velocity profile through B.L. • High speed flow near upper edge of B.L. has enough speed to keep moving through adverse pressure gradient • Lower speed fluid (which has been retarded by friction) is exposed to same adverse pressure gradient is stopped and direction of flow can be reversed • This reversal of flow direction causes flow to separate • Turbulent B.L. more resistance to flow separation than laminar B.L. because of fuller velocity profile • To help prevent flow separation we desire a turbulent B.L.

39. WHY DOES AN AIRFOIL STALL? • Two major consequences of separated flow over airfoil • Dramatic loss of lift (stalling) • Separated flow causes higher pressure on upper surface of airfoil • Major increase in drag • Separation causes lower pressure on trailing edge • Unbalance of pressure force causes pressure drag due to separation

40. AOA = 2°

41. AOA = 3°

42. AOA = 6°

43. AOA = 9°

44. AOA = 12°

45. AOA = 20°

46. AOA = 60°

47. AOA = 90°

48. SUMMARY OF VISCOUS EFFECTS ON DRAG • Friction has two effects: • Skin friction due to shear stress at wall • Pressure drag due to flow separation Total drag due to viscous effects Called Profile Drag Drag due to skin friction Drag due to separation + = Less for laminar More for turbulent More for laminar Less for turbulent So how do you design? Depends on case by case basis, no definitive answer!

49. COMPARISON OF DRAG FORCES

50. GOLF BALL AERODYNAMICS Drag dominated by pressure drag behind sphere