1. Aero Engineering 315 Lesson 20 Supersonic Flow Part II

2. Supersonic Flow Objectives  Define speed of sound Calculate speed of sound in air  Calculate Mach Number  Describe the different “Mach” regimes  Describe how lift and drag curves vary with Mach number  Define critical Mach number and drag divergence Mach number  Describe how A.C. moves with increasing Mach  Describe ways to increase critical Mach  Describe ways to minimize wave drag

3. As an aircraft approaches Mach 1, the flow at some point on the aircraft will reach Mach 1 before the freestream velocity (V ∞ ) does, since the flow accelerates over the aircraft’s surface. The freestream Mach number (M ∞ ) where this occurs is called the critical Mach number. M crit is always less than 1. Critical Mach number = M crit

4. M  M < 1 Terminating Shock Separated Wake As Mach number increases beyond M crit, shock waves form on the wings, fuselage and other surfaces. The shock moves aft as Mach continues to increase. Normal Shock M > 1 Shock-induced separation - Huge increase in drag - Significant loss of lift

5. Transonic Region

6. Normal Shock Parameters P o1 > P o2 V 1 > V 2 P 1 < P 2 T 1 < T 2  1 <  2

7. Bow Shock When the freestream Mach number > 1, bow shocks form on bodies with blunt leading edges M > 1  M> 1 Bow Shock M < 1 Oblique Shock

8. M > 1  Oblique Shock When the freestream Mach number > 1, oblique shocks form on bodies with sharp leading edges. M > 1 everywhere in the flowfield. M> 1 M M Oblique Shocks

9. Mach Sweep Video

10. Effect of Mach on Lift Prandtl-Glauert ( 0.3 < M < 0.7 )

11. Mach Effects NACA 0012 – 3 degrees AOA Mach M = 0.6 = M CR ClCl Local Mach = 1.0 Mach Shock moves to TE Prandtl-Glauert Shock Stall

12. M C Do Profile Drag Wave Drag M CRIT Effect of Mach on Drag M=1 M Drag Divergence

13. Mach Effects NACA 0012 – 3 degrees AOA Mach M=0.8 Shock Separated Flow Shock Wave CdCd M CR M DD

14. Effect of Mach on A.C. When the Mach number > 1, the aerodynamic center of all aerodynamic surfaces moves from approximately the quarter chord point (c/4) to the half chord (c/2) point. c/4 Subsonic c/2 Supersonic

15. Mach Effects NACA 0012 – 3 degrees AOA X ac Trailing Edge Shock Detached Bow Shock M=1.6 Mach

16. Ways to Increase M CRIT In order to fly faster before shock waves form, we need to increase M CRIT. This requires that the flow accelerate less over the aircraft. The drawback of these methods is that less lift is generated, so high Mach aircraft must have effective high lift devices.  Thin wings (F-16)  Less camber (T-38)  Swept wings (F-15)  Sharp, slender leading edges and fuselage (F-104)  Supercritical airfoil (C-17)

17. Wing Sweep Anderson, J. D., Introduction to Flight, 4 th Edition, page 300 Wing sweep increases the critical Mach number by decreasing the velocity component the airfoil “sees” 

18. Supercritical Wings Anderson, J. D., Introduction to Flight, 4 th Edition, page 274

19. Stretching M CRIT  Boeing 707 – Mach.80 727 – Mach.82 767 – Mach.80 747 – Mach.85 777 – Mach.84 Sonic Cruiser – Mach.95-.98  Airbus A320 – Mach.82 A380 – Mach.89 Boeing Sonic Cruiser

20. Minimizing Wave Drag  Blended wing-body Eliminates sharp corners which cause shock waves to form  Area-ruled (coke bottle) fuselage Smooth transition of aircraft cross-sectional area (T-38)  Tailplane offset above or below wing Gets tailplane out of separated, turbulent wake from shock and reduces vibration (F-104)  Sharp, slender wing leading edges and fuselage Causes oblique shocks to form, which produce less wave drag than bow shocks (F-106, F-104 etc)  Variable geometry wings (F-111, B-1) Wings swept increases M CRIT and allows aircraft to fly faster Wings unswept increases Aspect Ratio and improves lift characteristics for slower flight conditions such as takeoff and landing Penalties in weight, cost, and reliability

21. Blended wing-body

22. Area Rule

23. Tailplane Offset & Sharp, Slender Shapes

24. Variable Geometry Wings

25. Next Lesson (21)…  Prior to class Review 3.5.1 – 3.5.8, 3.5.10, and 4.1- 4.6 Review/rework problems 16 - 25  In Class Review for GR#2