Drag (2) Induced Drag Friction Drag Form Drag Wave Drag

Transcription

1 Drag () Induced Drag Friction Drag Form Drag Wave Drag

2 Outline Nomenclature and Concepts Farfield Drag Analysis Induced Drag Multiple Lifting Surfaces Zero Lift Drag :Friction and Form Drag Supersonic Wave Drag Trim Drag Current Issues for Drag Calculation Using CA

3 Drag = friction drag + induced drag +wave drag + form drag 1 D = ρ [( M 1) u + v + w ] dydz ρ uvrrdθdx II III Farfield Drag Analysis

4 Induced Drag The induced drag is a function of the Γ distribution (spanload) alone. D i ρ 4π b/ b/ = b/ b/ dγ( y dy 1 ) dγ( y dy ) ln y 1 y dy dy 1

5 Induced Drag The three-dimensional flowfield over a lifting surface does result in a drag force, even if the flow is inviscid. This is due to the effective change in the angle of attack along the wing induced by the trailing vortex system. It is one part of the total drag due to lift and written as. C D i CL = π AR e e in this equation is known as the span e. How to evaluate e?

6 Determination of e D i ρ 4π b/ b/ = b/ b/ dγ( y dy 1 ) dγ( y dy ) ln y 1 y dy dy 1 representing as Γ a Fourier Series Γ = U b n= 1 A n sinθ and D i πρ U b = na 8 π L = ρ U 4 b n= 1 A 1 n where CD i = C L πar e 1 [1 + A e = n( A n= n 1 ) ]

7 where CD i = C L πar e 1 [1 + A e = n( A = n n 1 ) ] Comments These expressions show that e max = 1 for a planar lifting surface. If the slit representing the trailing vortex system is not a simple flat surface, and C di is based on the projected span, a nonplanar or multiple lifting surface system can result in values of e > 1.

8 Comments Induced drag is a function of circulation distribution alone, independent of Mach number except in the manner which Mach number influences the circulation distribution (a minor effect in subsonic and transonic flow). Given Γ, e can be determined by finding the A n s of the Fourier series for the simple planar wing case.

9 Program LIDRAG A simple Fourier analysis of the spanload to determine the e using a Fast Fourier Transform for single planar surfaces. For an elliptic spanload, the e is 1.0 For a triangular spanload, the e is You can try other distributions of spanload

10 How to Make e Bigger Exploiting non-planar surface concepts such as winglets canard configurations. Using advanced wing tip shapes on nominally planar configuration.

11 Multiple Lifting Surfaces Munk's Stagger Theorem The induced drag of a multi-surface system does not change when the elements of the system are translated parallel to the direction of the flow, provided that the circulation distributions on the elements are left unchanged. The fore and aft positions of multiple lifting surfaces do not affect drag as long as the circulation distribution remains fixed.

12 Application of the theorem to aerodynamic design If the lifting elements are in the same plane, then the sum of the spanloads should be elliptic for minimum drag.

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14 Zero Lift Drag (subsonic) Friction drag Form drag The importance of streamlining A wire and airfoil with the same drag

15 Zero Lift Drag (subsonic) Approach A typical turbulent flow skin friction formula (for one side of a flat plate surface only) is used to evaluate friction drag The form factor is used to account for effects due to thickness and additional trailing edge pressure drag.

16 Formulation C D 0 C F S S wet ref FF Form factor A turbulent flow skin friction C F = [log Re] For planar surface t t FF = ( ) + 50( c c For bodies d 1.5 d FF = ( ) + 7( l l ) 4 ) 3

17 C D 0 C F S S wet ref FF Comments These simple formulas are used in conceptual design, and provide good initial estimates until more detailed calculations using the boundary layer methods. Some configurations can now take advantage of at least some laminar flow, with its significant reduction in friction drag. Advanced airfoils can have as much as 30 to 40% laminar flow.

18 Program FRICTION Computing the skin friction and form drag over each component, including laminar and turbulent flow. Including compressibility The input requires geometric information the Mach and altitude combination, or the Mach and Reynolds number Valid from subsonic to moderate supersonic speeds (about M3) Providing an estimate of laminar and turbulent skin friction suitable for use in aircraft preliminary design.

19 Wave Drag Drag = friction drag + induced drag + wave drag + form drag 1 D = ρ [( M 1) u + v + w ] dydz ρ uvrrdθdx II III Farfield Drag Analysis

20 Consider the integral over III D w = lim r ( ρ r π 0 dθ + uv r dx) If u,v r 0 as r then D w = 0 For the subsonic flow, D w = 0 For the supersonic flow _ ρ U = l l 0 0 '' D( θ ) w S ( x1) S ( x)ln x1 x dx1dx 4π '' Where S(x) the cross-sectional area distribution, and satisfies S'(0) = S'(l) = 0.

21 Consider the integral over III Comments on the wave drag integral The method is available in a program known as the Harris Wave Drag program. The Mach number doesn t appear explicitly. A refined analysis for bodies that aren t extremely slender extends this approach by taking slices, or Mach cuts, of the area through the body at the Mach angle. For non-axisymmetric bodies D w = 1 π π 0 D w _ ( θ ) dθ

22 1 0 1 '' 1 '' 0 _ )ln ( ) ( 4 ) ( dx dx x x x S x S U D l l w = π ρ θ where the S(x) values represent the area from an oblique (Mach angle) cut to find the cross section area of the aircraft at a specific theta. = π θ θ π 0 ( _ ) 1 d D D w w

23 l _ ρ U '' '' D( θ ) w = S ( x1 ) S ( x )ln x1 x dx1dx 4π 0 l 0 The importance of the distribution of the cross-sectional area To minimize the integral the area change should be very smooth. Low drag is achieved by minimizing the maximum crosssectional area. Increasing the fineness ratio decreases the wave drag.

24 Area rule Proposed by Richard Whitcomb at the NACA It states that the body should develop in a smooth fashion as the air moves around and along the body, with no sudden discontinuities. The total aircraft area distribution should form a smooth progression. For wing-body configuration, results in the distinctive area ruled, or coke bottle, fuselage shape.

25 The validity of area rule The key result obtained by Whitcomb The increase in drag for a wingbody combination

26 The famous application of the area rule YF-10, F-10, F-106 YF-10 When it first flew, the prototype is unable to break the sound barrier

27 F-10 The fuselage fineness ratio and area distribution had been increased and refined. The fuselage mid-section cross-sectional area had been reduced The cockpit canopy was reduced in cross-section with a near triangular cross-section The cockpit and the side-mounted engine inlets were moved forward to reduce their sudden area build-up, or impact on the fuselage area. The aft fuselage bustles ( 裙撑 ) were retained to avoid the rapid collapse of the cross-sectional area at the delta wing trailing edge. It was able to fly at low supersonic speeds (M = 1.).

28 Area ruling of F-10A airplane

29 Zero lift drag for the YF-10 and F-10A airplanes The resulting change in drag from the YF-10 to the F-10 was about 5 counts

30 F-106 The F-10 configuration was completely redesigned incorporating a more refined, integrated area rule. Further slimmed down by a reduced weapon bay capacity and shortened and repositioned engine air intake ducts, and powered by a fifty percent more powerful engine. It was capable of routine Mach + speeds.

31 Estimation of wave drag D w = 1 π π 0 D w _ ( θ ) dθ l _ ρ U '' '' D( θ ) w = S ( x1 ) S ( x)ln x1 x dx1dx 4 π 0 l 0 Harris wave drag program At each roll angle θ a number of x-cuts are made. Determining the cross sectional area distribution of the aircraft Evaluating the integral numerically. Typically, 50 to 100 x-cuts are made for each of from 4 to 36 θ values.

32 Estimation of wave drag Validation of the wave drag program

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34 Examples High Speed Civil Transport(HSCT)

35 Examples: high speed civil transport(hsct) distribution of the drag for each circumferential cut

36 normal area distribution (capture area removed)

37 Mach 3 area distribution, θ = 0

38 Mach 3 area distribution, θ = 90

39 Examples: F-16 The revision is to improve the contour forward and aft of the maximum cross-sectional area to fill in the shape This is the original area distribution Small aircraft are much more difficult to lay out to ensure a smooth distribution of area.

40 Trim Drag surface lift requirements for trim

41 What is trim drag? Control surface deflections change the drag from the reference undeflected value. This difference in drag could be termed a trim drag.

42 Where trim drag comes from? For a given flight conditions the total lift must be fixed. Any change in lift on the trimming surface requires a change in lift on the primary surface. The change in lift on the primary surface will result in additional drag, i.e. trim drag.

43 Cases with Big Trim Drag Trim drag is especially important for several specific classes of aircraft. Supersonic aircraft A.C. shift from subsonic to supersonic flight. To control trim drag as well as stability, fuel is transferred fore and aft between subsonic and supersonic flight. Variable sweep wing aircraft Aerodynamic center locations vary with sweep Potentially leading to high values of trim drag The maneuvering aircraft high trim drag at high lift coefficients, severely limiting sustained turn performance.

44 Minimum drag for different configurations For aft swept wings aft tail configurations the minimum trimmed drag occurs at a slightly unstable center of gravity (5-10%). For canard configurations minimum trim drag at slightly more unstable conditions (15%). Forward swept wing canard configurations even more unstable to achieve minimum trimmed drag the X-9 is about 30-35% unstable

45 How to Reduce Trim Drag New configurations Innovative configurations for small trim drag Using stability and control augmentation systems Allowing the designers much more freedom in the choice of a center gravity location Controlling C.G. placement in a configuration

46 Canard Configuration Canard concept are often considered advantageous because both the canard and wing supply positive lift to trim.

47 Current Issues for Drag Calculation Improving the accuracy of drag computation for complex configurations How to reduce drag reducing drag due to lift tip shaping use of winglets tip sails reducing skin friction drag. laminar flow through passive means (NLF) suction using riblets to reduce turbulent friction reduction