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Pharos University ME 253 Fluid Mechanics II

Pharos University ME 253 Fluid Mechanics II. Flow over bodies; Lift and Drag. External External Flows. Bodies in motion, experience fluid forces and moments. Examples include: aircraft, automobiles, buildings, ships, submarines, turbo machines.

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Pharos University ME 253 Fluid Mechanics II

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  1. Pharos UniversityME 253 Fluid Mechanics II Flow over bodies;Lift and Drag

  2. External External Flows • Bodies in motion, experience fluid forces and moments. • Examples include: aircraft, automobiles, buildings, ships, submarines, turbo machines. • Fuel economy, speed, acceleration, stability, and control are related to the forces and moments. Airplane in level steady flight: drag = thrust & lift = weight.

  3. Flow over immersed bodies • flow classification: 2D, axisymmetric, 3D • bodies: streamlined and blunt

  4. Airplane • Upper surface (upper side of wing): low pressure • Lower surface (underside of wing): high pressure

  5. Lift and Drag • shear stress and pressure integrated over body surface • drag: force component in the direction of upstream velocity • lift: force normal to upstream velocity

  6. AIRFOIL NOMENCLATURE • Mean Chamber Line:Points halfway between upper and lower surfaces • Leading Edge: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

  7. 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

  8. Pressure Forces acting on the Airfoil Low Pressure High velocity High Pressure Low velocity Low Pressure High velocity High Pressure Low velocity Bernoulli’s equation says where pressure is high, velocity will be low and vice versa.

  9. Relationship between L´ and p V

  10. Relationship between L´ and p(Continued) Divide left and right sides by We get:

  11. Pressure Coefficient Cp From the previous slide, The left side was previously defined as the sectional lift coefficient Cl. The pressure coefficient is defined as: Thus,

  12. Fluid dynamic forces are due to pressure and viscous forces. • Drag: component parallel to flow direction. • Lift: component normal to flow direction.

  13. Drag and Lift • Lift and drag forces can be found by integrating pressure and wall-shear stress.

  14. Drag and Lift • Lift FLand drag FD forces fn (  , A,V ) • Dimensional analysis: lift and drag coefficients. • Area A can be frontal area (drag applications), plan form area (wing aerodynamics).

  15. Example: Automobile Drag bile Drag CD = 1.0, A = 2.5 m2, CDA = 2.5m2 CD = 0.28, A = 1 m2, CDA = 0.28m2 • Drag force FD=1/2V2(CDA) will be ~ 10 times larger for Scion XB • Source is large CD and large projected area • Power consumption P = FDV =1/2V3(CDA) for both scales with V3!

  16. Drag and Lift • If CLand CD fn of span location x. • A local CL,x and CD,x are introduced. • The total lift and drag is determined by integration over the span L

  17. Friction and Pressure Drag • Fluid dynamic forces: pressure and friction effects. FD = FD,friction + FD,pressure CD = CD,friction + CD,pressure Friction drag Pressure drag Friction & pressure drag

  18. Flow Around Objects

  19. Streamlining • Streamlining reduces drag by reducing FD,pressure, • Eliminate flow separation and minimize total drag FD

  20. Streamlining

  21. CD of Common Geometries • For many shapes, total drag CDis constant for Re > 104

  22. CD of Common Geometries

  23. CD of Common Geometries

  24. Flat Plate Drag Drag on flat plate is due to friction created by laminar, transitional, and turbulent boundary layers.

  25. Flat Plate Drag • Local friction coefficient • Laminar: • Turbulent: • Average friction coefficient • Laminar: • Turbulent:

  26. Cylinder and Sphere Drag

  27. Cylinder and Sphere Drag • Flow is strong function of Re. • Wake narrows for turbulent flow since turbulent boundary layer is more resistant to separation. • sep, lam ≈ 80º • sep,Tur ≈ 140º

  28. Lift • Lift is the net force (due to pressure and viscous forces) perpendicular to flow direction. • Lift coefficient • A=bc is the planform area

  29. Characteristics of Cl vs. a Stall Cl Slope= 2p if a is in radians. a = a0 Angle of zero lift Angle of Attack, a in degrees or radians

  30. EXAMPLE: AIRFOIL STALL Lift Angle of Attack, a

  31. Effect of Angle of Attack • CL≈2 for  < stall • Lift increases linearly with  • Objective:Maximum CL/CD • CL/CD increases until stall.

  32. Effect of Foil Shape Thickness and camber affects pressure distribution and location of flow separation.

  33. End Effects of Wing Tips • Tip vortex created by flow from high-pressure side to low-pressure side of wing. • Tip vortices from heavy aircraft far downstream and pose danger to light aircraft.

  34. Lift Generated by Spinning Superposition of Uniform stream + Doublet + Vortex

  35. Drag Coefficient: CD Stokes’ Flow, Re<1 Supercritical flow turbulent B.L. Relatively constant CD

  36. Drag • Drag Coefficient with or

  37. DRAG FORCE • 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

  38. COMPARISON OF DRAG FORCES d d Same total drag as airfoil

  39. AOA = 2°

  40. AOA = 3°

  41. AOA = 6°

  42. AOA = 9°

  43. AOA = 12°

  44. AOA = 20°

  45. AOA = 60°

  46. AOA = 90°

  47. Drag Coefficient of Blunt and Streamlined Bodies • Drag dominated by viscous drag, the body is __________. • Drag dominated by pressure drag, the body is _______. streamlined Flat plate bluff

  48. Drag • Pure Friction Drag: Flat Plate Parallel to the Flow • Pure Pressure Drag: Flat Plate Perpendicular to the Flow • Friction and Pressure Drag: Flow over a Sphere and Cylinder • Streamlining

  49. Drag • Flow over a Flat Plate Parallel to the Flow: Friction Drag Boundary Layer can be 100% laminar, partly laminar and partly turbulent, or essentially 100% turbulent; hence several different drag coefficients are available

  50. Drag • Flow over a Flat Plate Perpendicular to the Flow: Pressure Drag Drag coefficients are usually obtained empirically

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