Jet Propulsion. Lecture-17. Ujjwal K Saha, Ph. D. Department of Mechanical Engineering Indian Institute of Technology Guwahati

Transcription

1 Lecture-17 Prepared under QIP-CD Cell Project Jet Propulsion Ujjwal K Saha, Ph. D. Department of Mechanical Engineering Indian Institute of Technology Guwahati 1

2 Lift: is used to support the weight of the aircraft Lift and Drag Drag: that directly opposes the motion of the aircraft 2

3 In straight and Level Flight, Lift = Weight and Thrust = Drag 3

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6 Airfoil Geometry α = Angle of Attack c = chord length t/c = thickness ratio =max. thickness/c camber ratio = max. camber/c 6

7 Evolution of Airfoils Airfoils Types Early Designs - Designers mistakenly believed that these airfoils with sharp leading edges will have low drag. In practice, they stalled quickly, and generated considerable drag. 7

8 Lift Equation L = C L V 2 ρ/2 S If the angle of attack and other factors remain constant and airspeed is doubled, lift will be four times greater. 8

9 Ways of Controlling Lift Increase airspeed Change the angle of attack Change the shape of the airfoil Change the total area of the wings 9

10 Drag Parasite Drag (Profile Drag) Induced Drag Form Drag (Pressure Drag) Skin Friction Drag Wave Drag Interference Drag Form Drag - Drag due to the shape of the body Skin Friction Drag - Drag due to the friction between the surface and the flow. Interference Drag - created when the airflow around one part of the airplane interacts with the airflow around another. 10

11 Parasite Drag Reduction By proper design and streamlining the shape. Avoiding Protrusions on the surface. Retracting landing gears. 11

12 Parasite Drag is simply Skin Friction Drag+ Form Drag + Interference Drag + Wave Drag 12

13 Supersonic Wave Drag For a given airfoil or wing or aircraft, as the Mach Number is increased, the drag begins to increase above a free-stream Mach number of 0.8 or so due to shock waves that form around the configuration. 13

14 Shock waves 14

15 How can shock waves be minimized? Use wing sweep. Use supercritical airfoils, which keep the flow velocity over the airfoil and the local Mach number from exceeding Mach 1.1 or so. 15

16 How can shock waves be minimized? Use sweep. 0.8cos30 30 sweep M=

17 Lift and Drag 17

18 Induced Drag For a lifting wing, the air pressure on the top of the wing is lower than the pressure below the wing. The lines marking the center of the vortices are shown as blue vortex lines leading from the wing tips. 18

19 Boeing 727 test airplane (NASA) 19

20 The wing tip vortices produce a downwash of air behind the wing which is very strong near the wing tips and decreases toward the wing root. Downwash TOP SURFACE (relative low pressure) (relative high pressure) BOTTOM SURFACE 20

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22 Induced Drag 22

23 Component of R 1 (parallel to V ) = Drag D 1 (due to skin friction and pressure drag due to separation). R = actual aerodynamic force including the effect of tip vortices. Component R (parallel to V ) is the actual Drag force D. D = D D i 1 23

24 Origin of Induced Drag Geometric angle of attack = angle between the chord line and flow direction However, local flow gets deflected downward by α i due to downwash. This angle is known as induced angle of attack (difference between local flow direction and freestream direction). α = α α eff i 24

25 D = Lsinα i Values of α I are generally small, and hence sinα i = α i Threfore D = Lα i, i i 25

26 Lift & downwash distributions The lift per unit span may vary as a function of distance along the wing because Chord varies along the length of the wing Each airfoil section is at a different geometric angle of attack (Twisted) From incompressible flow theory CL αi = π AR 26

27 For all wings, C D L i = Lαi = L AR π 1 2 C D L i = Lαi = CL ρv S 2 π AR 2 Di C = L 1 2 ρv S π AR 2 2 C C L Di = π AR 2 C C L Di = π ear where, e= span efficiency factor 27

28 For elliptical planform e=1 Lift Per Unit Span -b/2 +b/2 For other planforms e < 1 Therefore, CD i is minimum for elliptical planform 28

29 Total Drag Total Drag = Parasite Drag + Induced Drag D = D + D P C D 2 ρ 2 V S = CD ρ P 2 V S + CD ρ i 2 V S C = C + C D DP Di i 29

30 At High Values of α Wings Stall 30

31 Increasing the Angle of Attack to the Stall Point The above picture shows a normal airfoil during a typical cruise profile. The angle of attack is small and the airflow over the wing is smooth, producing lift. No stall condition exists. In the left picture, the angle of attack has been increased and is now closer to/approaching the critical angle of attack. Airflow above the wing is becoming uneven. However, the angle is still less than the critical angle, so lift is still being produced by the wing. No stall condition exists. 31

32 Stalled Wing In the picture above, the wing has now exceeded its critical angle of attack. The uneven airflow over the top of the wing has broken into a swirling air mass that can not produce lift. The wing (airfoil) is "stalled". 32

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34 Leading Edge Slats Help avoid stall near the leading edge 34

35 Lift Augmentation Devices Slat - It is placed in front of the airfoil to help increase the momentum of the boundary layer fluid. High energy air from the bottom side of the airfoil flows through the gap to the upper side, energizes slow speed molecules, and keeps the flow from stalling Thus it delays the separation and enhance the lift. Flap- It is placed at the rear of the wing it allows higher momentum fluid to replace the weaker fluid in the tail of the wing. Thus it avoid separation. It also increases the drag. 35

36 Achieving High Lift 36

37 Effect of High-Lift Devices Effect of leading edge devices on lift curve (Jenkinson). 37

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40 One form of flaps, called Fowler flaps increase the chord length as the flap is deployed. 40

41 Summary Lift and Drag, Airfoil Terminology, Types of Drag, Downwash, Induced Drag, Flaps and Slats, Types of Flaps 41

42 References & Web Resources 1. Anderson, J. D. Jr., (2000), Introduction to Flight, 4 th Edition, McGraw Hill. 2. Anderson, J. D. Jr., (1999), Aircraft Performance and Design, McGraw Hill. 3. Shevell, R. S., (1989), Fundamentals of Flight, Pearson Education. 4. Clancy, L. J., (1996), Aerodynamics, Himalayan Books