ROAD MAP... D-1: Aerodynamics of 3-D Wings D-2: Boundary Layer and Viscous Effects D-3: XFLR (Aerodynamics Analysis Tool)

Transcription

1 Unit D-1: Aerodynamics of 3-D Wings Page 1 of 5 AE301 Aerodynamics I UNIT D: Applied Aerodynamics ROAD MAP... D-1: Aerodynamics of 3-D Wings D-: Boundary Layer and Viscous Effects D-3: XFLR (Aerodynamics Analysis Tool) AE301 Aerodynamics I Unit D-1: List of Subjects Infinite v.s. Finite Wings Wing Tip Vortices Downwash and Induced Drag Lift and Downwash The Total Drag 3-D Drag Polar Change in the Lift Curve Swept Wings Flaps

2 Unit D-1: Aerodynamics of 3-D Wings Page of 5 Infinite v.s. Finite Wings INFINITE V.S. FINITE WINGS Infinite wing: the span stretched from to +. An airfoil represents a unit span (width of 1) of an infinite wing. Finite wing: 3-D effects (wing tip vortices and spanwise flows) are all included. For a finite wing, we need to consider a parameter, called aspect ratio of the wing: b AR = S

3 Unit D-1: Aerodynamics of 3-D Wings Page 3 of 5 Wing Tip Vortices FINITE WINGS The pressure difference between top and bottom surfaces of wing causes a pair of trailing circular motion flows, called the wing-tip vortices. The wing-tip vortices tend to drag the surrounding air around with them, and this secondary movement induces a small velocity component in the downward direction at the wing, called the downwash. The existence of downwash creates an additional drag on wings that cannot be expected on -D airfoil (called, induced drag). If a careful and detailed design/selection of -D airfoil is completed, one can still do a poor job designing a 3-D wing... resulting in very high induced drag. The quality of wing performance depends on how to minimize the induced drag by carefully choosing 3-D shape of the wing. Induced drag depends on: Aspect Ratio (AR) of the wing How efficient is your wing (called, the span efficiency factor), in which depends on your wing taper, wing sweep, wingtip design, twist, dihedral, etc. etc. Lift coefficient (CL) of the wing: IRONICALLY... if your wing produces large amount of lift, it increases the induced drag... hence, the induced drag is often called, drag due to lift.

4 Unit D-1: Aerodynamics of 3-D Wings Page 4 of 5 Downwash and Induced Drag INDUCED DRAG The downwash (w) will have several consequences: Angle of attack of the airfoil sections of the wing ( eff) is referenced from the local flow direction, which is reduced (by the amount of i) in comparison to the angle of attack of the wing ( ) referenced to V. There is an increase in the drag, called the induced drag. Because of the local relative wind is canted downward, the lift vector itself is tilted back, hence it contributes a certain component of force parallel to V (drag force) Induced drag can be obtained from the figure as: D = Lsin i i Usually the induced angle of attack ( i) is small, hence for small angles: sin i i, so Di = L i

5 Unit D-1: Aerodynamics of 3-D Wings Page 5 of 5 Lift and Downwash LIFT DISTRIBUTION ALONG THE SPAN OF THE WING If we observe a 3-D wing, the lift is distributed along the span. This is called, the lift distribution. The lift distribution depends on: (1) Varying the chord length along the span (tapered wing) () Varying the angle of attack along the span (geometric twist) (3) Varying the airfoil along the span of the wing (aerodynamic twist) Let us first look at an ideal case. An elliptical lift distribution produces a uniform downwash distribution along a span of the wing. In such a case: CL i = where, AR C L : lift coefficient of the finite wing AR: aspect ratio = b /S Let us substitute this into the equation of induced drag: CL Di = L i = L Note that: L = q SCL, so: AR D i CL = q S or AR Di qs CL = AR Therefore, the induced drag coefficient: C Di, CL = AR Note: this is the ideal case (elliptical lift distribution across the wing span)

6 The Total Drag Unit D-1: Aerodynamics of 3-D Wings Page 6 of 5 Airfoil (-D) 3-D Effect SPAN EFFICIENCY FACTOR An elliptical lift distribution produces a uniform downwash distribution along a span of the wing (ideal case). An elliptical lift distribution can usually be achieved by having an elliptical wing planform. However, not all airplanes have elliptic planform. In general, a span efficiency factor (e) is defined, such that: C Di, CL = ear For elliptical planform wings (or elliptical lift distribution ): e = 1 For all other wing planforms: e < 1 In conclusion, the total drag on a finite wing is: C D CL = cd + ear Total drag of a finite wing = Profile drag (drag of -D airfoil) + Induced drag (3-D effect) The induced drag is often called the drag due to lift.

7 3-D Drag Polar Unit D-1: Aerodynamics of 3-D Wings Page 7 of 5 THE DRAG POLAR The induced drag ( C Di. ) is the drag due to lift (3-D effect) The profile drag (cd) is a drag on a -D airfoil, from which includes: (i) drag due to skin friction ( or parasite) drag and (ii) drag due to pressure (or separation) drag: c = c + c d d, f d, p The total drag on an airplane is: C D CL = "Profile" Drag + "Induced" Drag = cd + e AR The plot of C L v.s. C D is called the drag polar. The drag polar provides important information of how much drag is associated with a given increase of lift. In aircraft design, usually several varieties of drag polar is presented (clean, flap up or down, gear up or down for TO or L).

8 Unit D-1: Aerodynamics of 3-D Wings Page 8 of 5 Class Example Problem D-1-1 Related Subjects... The Total Drag Consider a flying wing (such as Northrop B-) with a wing area of 00 m, aspect ratio of 10, span efficiency factor of 0.95, and NACA 441 airfoil. The weight of the airplane is N. For the level-flight condition (assume L = W and minimum profile drag) with 0.5 Mach at 10 km altitude, estimate the total drag on the aircraft.

9 Unit D-1: Aerodynamics of 3-D Wings Page 9 of 5 Class Example Problem D-1-1 (cont.) Related Subjects... The Total Drag

10 Name: Student ID: Homework D-1-1 R4-10 Unit D-1: Aerodynamics of 3-D Wings Page 10 of 5 Consider a NACA 4415 airfoil. Repeat the same class example problem D-1-1 as we discussed. Estimate the total drag coefficient and total drag (in N ) on the aircraft (S = 00 m and L = W = N) for 0.5 Mach cruising at 10 km altitude (equipped with NACA 4415 airfoil with span efficiency factor of 0.95). Compare the results against the class example problem D-1-1: what is the difference? Assume that the Reynolds number is and clean (no split flap deflection) for minimum profile drag estimation. Hints... Repeat the same process for level-flight condition: L = W Does your result make sense?

11 Unit D-1: Aerodynamics of 3-D Wings Page 11 of 5 Change in the Lift Curve (1) a = 1+ a0 a0 / ear a0 a = (for high aspect ratio wing: AR > 4) + ( a / ear) + a / ear a0 cos a = (for swept wing) 1+ [( a cos ) /( ear)] + [( a cos ) /( ear)] CHANGE IN THE LIFT CURVE (1) 0 0

12 Unit D-1: Aerodynamics of 3-D Wings Page 1 of 5 Change in the Lift Curve () CHANGE IN THE LIFT CURVE () CORRECTIONS FOR HIGH ASPECT RATIO AND WING SWEEP For high aspect ratio wing (AR > 4): a = a 1+ ( a0 / ear) + a0 0 / ear For swept wing (with half chord line sweep angle ): a0 cos a = 1+ [( a cos ) /( ear)] + [( a cos ) /( ear)] 0 0

13 Unit D-1: Aerodynamics of 3-D Wings Page 13 of 5 Class Example Problem D-1- Related Subjects... Change in the Lift Curve Consider a wing with an aspect ratio of 10 with NACA 301 airfoil. Assume that the Reynolds number is approximately and span efficiency factor is If the wing is at 4 degrees angle of attack, calculate the lift and drag coefficients.

14 Unit D-1: Aerodynamics of 3-D Wings Page 14 of 5 Class Example Problem D-1- (cont.) Related Subjects... Change in the Lift Curve

15 Name: Student ID: Homework D-1-a R4-9 Unit D-1: Aerodynamics of 3-D Wings Page 15 of 5 As we learned in class, the effective angle of attack of an airfoil ( eff ) is less than the geometric angle of attack ( ), such that:, where: = eff i CL i = ear (induced angle of attack) dc Starting from the definition of lift curve slope of -D airfoils: a l 0 =, d derive the equation of lift curve slope of 3-D finite wings (in terms of a 0): dc L a0 a = = d 1 + a / ear 0

16 Name: Student ID: Homework D-1-b R4-11 Unit D-1: Aerodynamics of 3-D Wings Page 16 of 5 Consider a NACA 301 airfoil. Repeat the same class example problem D-1- as we discussed, but this time, angle of attack 8 degrees. Calculate the lift and drag coefficients (assume the same aspect ratio and span efficiency factor: 10 and 0.95, respectively). Compare the results against the class example problem D-1-: what is the difference? Assume that the Reynolds number is and clean (no split flap deflection) for profile drag estimation. Hints... Repeat the same process with 8 degrees angle of attack Does your result make sense?

17 Name: Student ID: Homework D-1-c 4-4 Unit D-1: Aerodynamics of 3-D Wings Page 17 of 5 Consider NACA 301 airfoil. A finite wing is designed, using this airfoil, with aspect ratio of 1 and span efficiency factor is 0.9. Calculate the lift and induced drag coefficients for this wing at an angle of attack of 4. Assume that the Reynolds number is approximately Hints... Determine lift curve slope ( a 0 ) from NACA 301 airfoil data.

18 Name: Student ID: Homework D-1-d R4-8 Unit D-1: Aerodynamics of 3-D Wings Page 18 of 5 Answer the followings (explain in your own words). (a) What is the difference between airfoil and finite wing? (b) What is downwash? (c) Explain the mechanism of induced drag. (d) What is drag polar plot? (e) What is the difference between -D (airfoil) lift curve slope (a 0) and 3-D (finite wing lift curve slope (a)?

19 Swept Wings (1) Unit D-1: Aerodynamics of 3-D Wings Page 19 of 5 SWEPT WINGS By sweeping the wings of subsonic aircraft, drag divergence is delayed to higher Mach numbers. cos (1) By sweeping the wing, each airfoil section of the wing sees unparallel freestream velocity. As a result, each airfoil section needs to deal only with a velocity component normal to its direction (which is less than freestream itself). () By sweeping the wing, the freestream sees an increased geometric chord length. Hence, the effective thickness ratio is reduced. (3) By sweeping the wing, the lift curve slope is effectively reduced.

20 Swept Wings () Unit D-1: Aerodynamics of 3-D Wings Page 0 of 5 DRAG COUNT A drag count is a single unit of drag as defined by aerospace engineers. A drag count is 1/10,000 of a CD. For example, if a drag is increased by 0.01, it is called, 100 count of drag increase. Drag count is used as a crude measure for the change in drag coefficient (it is not a direct measure of drag as it is not associated with any reference area). EFFECTS OF WING SWEEP AND THICKNESS RATIO By decreasing the thickness ratio from 9% => 6% => 4%: t/c 9% => 6%: approximately 100 drag count decrease t/c 6% => 4%: approximately 70 drag count decrease By increasing wing sweep from 11 => 35 => 47 : 11 => 35 : approximately 30 drag count decrease 35 => 47 : approximately 50 drag count decrease

21 Flaps (1) Unit D-1: Aerodynamics of 3-D Wings Page 1 of 5 AIRCRAFT STALL SPEED The minimum sustainable airspeed for an aircraft without stall is called the stall speed. This is an important parameter, as this is a driving factor of TO-L performance (also a flight safety). 1 From the definition of lift: L = q SCL = V SC => L V = L SC L In steady, level flight, the lift is just sufficient to support the weight (W) of the aircraft. That is, L = W. Therefore: V = W SC L In order to minimize this flight airspeed (minimum flight speed is usually equal to the stall speed), one needs to maximize the lift coefficient. V Thus, stall = W SC L, max

22 Flaps () Unit D-1: Aerodynamics of 3-D Wings Page of 5 HIGH LIFT DEVICES Maximum lift coefficient of an airfoil ( c l, max ) is in the range of However, this is -D airfoil. 3-D finite wing s maximum lift coefficient is slightly less than that. Usually, airplanes need C L, max in the range of for TO-L operations. It is required to deploy high lift devices to achieve this high C L, max Trailing edge devices are called flaps Leading edge devices are called slats By deploying the flaps/slats, one can increase C L, max. However, the stall angle of attack is also decreased (airplane stalls in much lower angle of attack).

23 Flaps (3) Unit D-1: Aerodynamics of 3-D Wings Page 3 of 5 VARIATION OF HIGH LIFT DEVICES Airfoil only Plain Flap Split Flap Leading Edge Slat Single-Slotted Flap Double-Slotted Flap Double-Slotted Flap + Leading Edge Slat Double-Slotted Flap + Leading Edge Slat + Top Surface Boundary layer Suction

24 Unit D-1: Aerodynamics of 3-D Wings Page 4 of 5 Class Example Problem D-1-3 Related Subjects... Swept Wings and Flaps For swept wings and flaps, what are positive (favorable) and negative (adverse) aerodynamic effects of each device. Pros for swept wings: Delay critical Mach number to a much higher Mach number. Decrease drag at transonic/supersonic flights. Cons for swept wings: Lift curve slope is decreased for maintaining the same stall speed, the wing area needs to be increased. For integrated wing-tank configuration, the shift of CG is an issue. Pros for flaps: Increase maximum lift coefficient (thus, decrease stall speed). Cons for flaps: Decrease stall angle of attack. Safe TO-L operation entirely depends upon flaps. The malfunction of flaps usually links directly to the cause of serious problems.

25 Name: Student ID: Homework D-1-3 R4-1 Unit D-1: Aerodynamics of 3-D Wings Page 5 of 5 Answer the followings (explain in your own words). (a) Discuss: (i) advantages and (ii) disadvantages of wing sweep of a 3-D finite wing of an aircraft. (b) What is drag count? (c) What is stall speed of aircraft? Starting from the definition of lift ( L = q SCL = 0.5 V SCL), derive the equation of stall speed for straight level flight (L = W). (d) By carefully considering the stall speed equation, what are possible engineering solutions to minimize the stall speed? (e) Discuss: (i) advantages and (ii) disadvantages of high-lift devices of a 3-D finite wing of an aircraft.