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Theme 78

  1. 1. SECTION 1. AERODYNAMICS OF LIFTING SURFACES THEME 7. AERODYNAMICS OF THE WING HIGH-LIFT DEVICES Swept wings of rather small area with an airfoil of rather small camber andrelative thickness are applied in modern aircraft with the purpose of flight speedincreasing. Such wings can not provide large lift on landing modes because of earlyflow stall. The problem of increasing lifting properties for modern wings at high anglesof attack for shortening of take-off and landing distance is very actual now. For thispurpose wings are equipped with special design elements which allow to increase thevalue of C ya max in the area of critical angles of attack α st . These elements working onmodes of takeoff, landing and maneuver are called wing high-lift devices. The set of effective high-lift devices applied in aircraft is wide enough (table 7.1).There distinguish rigid, jet, combination high-lift devices and high-lift devices based onthe boundary layer control (BLC). The high-lift devices are installed on the leading and trailing wing edges. Thehigh-lift devices of the wing trailing edge are realized by flaps of various types (Fig.7.1): simple flap, one-slotted flap, Fowler extension flap, double-slotted flap, plane flapetc. Flaps are applied to increase the lift of an airplane at keeping of its position(keeping the angle of attack). They are extended while taking off and landing. The liftgrows due to increase of wing camber. Extension flaps consisting of several sections are used on modern airplanes.Multi-section configuration allows bending the wing smoothly, and air jets streaming onthe upper surfaces of sections through slots, providing smooth continuous flow at highangles of sections deflection. The theoretical substantiation of multi-slotted flaps wasgiven byS. A. Chaplygin. Such flaps additionally increase lift due to the growth of wing area. 81
  2. 2. Fig. 7.1. High-lift devices of the wing trailing edge: a) - flap ΔC yа h − l .dev . = 0 .7 δ flap = 30 o ; b) - one-slotted flap; c) - one-slotted extended flap ΔC yа h− l .dev . = 1.1 ; d) - double-slotted flap ΔC yа h − l .dev . = 1.4 ; e) - Fowler flap; f) - plane flap ΔC yа h− l .dev . = 0 .8 ÷ 0 .9 δ flap = 60 o . An angle between chords of main flap section in deflected and non-deflectedpositions is called flap setting δ flap . It is measured in a plane, perpendicular to axis ofrotation; δ flap > 0 if flap is deflected downwards. The flap are used not only for improvement of take-off and landingcharacteristics, but also for direct control of lift, rational redistribution of loading whicheffects a wing, and also for drag reduction. The high-lift devices of the wing leading edge are usually made as the deflectedslats (Fig. 7.2): movable slat, Krueger slat, deflecting nose etc. The slats are intended for prevention of premature flow stalling from wing. It isreached due to wing camber at the leading edge and jet blowing onto the upper wingsurface through a slot. An angle characterizing turn of coordinate system related with the slat at itsdeflection is called slat setting δ slat . The slat is the wing-shaped and locates along the wing leading edge. Atincreasing of angle α under the influence of sucking force the slat is put forward intooperative location. 82
  3. 3. Fig. 7.2. High-lift devices of the wing leading edge: a) - sliding slat; b) - extended slat ΔC yа h − l .dev . = 0 .6 ÷ 0 .9 ; c) - deflected nose ΔC yа h− l .dev . = 0 .55 ÷ 0 .75 δ з = 60 o . Choice of high-lift devices in each particular case is determined by such criteria,as increment of the lift coefficient ΔC yа h− l .dev . provided with it (Fig. 7.3, 7.4) andinevitable drag increment. The high-lift devices type allowing to receive the requiredtake-off and landing characteristics of the airplane should be got out right at thebeginning of the designing process.Fig. 7.3. Influence of deflection of split flap, Fig. 7.4. Influence of slat deflection flap and slotted wing onto C ya = f ( α ) onto C ya = f ( α ) The major factor causing an increasing of a wing C ya factor at deflection of high-lift devices is the growing of its cross-sections concavity. The growth of C ya is alsopromoted by increase of the wing area at using movable flaps. 83
  4. 4. Lets consider the influence of high-lift devices deflection of the trailing edge onto structure of flow about the wing. Comparison of pressure factor C p distributions chordwise at non-deflected and extended flaps (fig. 7.5) shows, that the flap deflection causes an essential growth of rarefaction along total upper wing surface, and not just on its deflected part. The appreciable increase of overpressure is observed along the total lower surface. As a result the lift coefficient Fig. 7.5. Pressure factor distribution increases. along airfoil outline with flap and For effective realization of factor C ya without it increasing it is necessary to provide attachedflow about wing with the extended high-lift devices. As its known, this is promoted byboundary layer control (BLC) by increasing of kinetic energy of decelerated air layer(blown off) or its removal from the flow (suction) (Fig. 7.6). The change of dependenceof lift coefficient is similar to slat application (Fig. 7.4). The control system ofcirculation ΔC yа h − l .dev . = 0 .6 ÷ 0 .8 at C μ = 0 .3 , systems with flow blowing-off fromslot on a wing tail part (Fig. 7.7) and system of blower of wing surface by jets from theengine (Fig. 7.8) are also examples of jet high-lift devices. The intensity of blower(blowing-off) is characterized by a factor of momentum: kg ⋅ m msV j s s , Cμ = (7.1) q∞ S j N 2 2 ⋅m mwhere m s is the air consumption per second, V j is the jet speed, S j is the wing areamaintained by high-lift devices, q∞ is the dynamic pressure. 84
  5. 5. Fig. 7.6. Systems for boundary layer control ΔC yа h − l .dev . = 0 .6 ÷ 0 .8 : a) - suction through a slot, b) - distributed suction through the porous or punched surface, c) - blow-off from a slot. Fig. 7.7. Systems with flow blow-off from a slot on wing tail part: a) - flap with blowing of the upper surface ΔC yа h− l .dev . = 7 ÷ 8 , C μ ≈ 2 ; b) - jet flap ΔC yа h− l .dev . = 4 ÷ 5 ; c) - ejector flap ΔC yа h− l .dev . = 6 ÷ 7 , C μ ≈ 2 . Fig. 7.8. A system of wing surface blowing by engine jets: à) - blowing of the flap upper surface δ flap = π 3 , C μ ≈ 2 , ΔC yа h− l .dev . ≈ 8 ; b) flap lower surface δ flap = 40 o 60 o , ΔC yа h− l .dev . = 6 ...7 . The spoilers are panels installed on the wing which can be deflected outside tospoil the flow over the wing. They are made as rotary or extended (fig. 7.9) andinstalled both on the upper and on the lower wing surfaces. Spoiler either turbulizes orstalls the flow depending on altitude of its moving out. The pressure redistributes bothon the upper and on the lower surfaces. 85
  6. 6. Fig. 7.9. Spoilers: a) - rotary; b) - extended. Spoilers are used for roll control (instead of ailerons). Spoilers are also applied for shortening of run at landing and aborted takeoff. Insuch case they are mounted on the wing upper surface directly ahead of flaps anddeflected simultaneously on both wings. It causes flow stalling from the wing uppersurface and high-lift devices. As a result, the lift coefficient C yа abruptly decreases andthe drag coefficient C xа grows, loading onto wheels also grows, that allows to increasebraking force considerably. Such spoilers are called ground spoilers. For landing anglesof attack ΔC yа h− l .dev . = −0 .7 ...0 .75 . Generally, a type and span of high-lift devices, wing plan form, panel flap chordb flap , flap chord b flap , type of wing airfoil and its relative thickness с , etc. influenceΔC yа h− l .dev . value. For swept wings the effectiveness of high-lift devices is abruptly reduced atangles close to α st . Similar effect is caused by aspect ratio decreasing. 86
  7. 7. The table 7.1. High-lift devices. Increase of Angle of High-lift devices maximum lift basic airfoil at Remarks max. lilt Effects of all high-lift devices depend on shape of basic airfoil. - 15 °Basic airfoil Increase camber. Much drag when fully lowered. Nose-down pitching 50 % 12 °Plain or camber moment.flap Increase camber. Even more drag than plain flap. Nose-down pitching 60 % 14 ° moment.Split flap Increase camber and wing area. Much drag. Nose-down pitching 90 % 13 ° moment.Zap flap Control of boundary layer. Increase camber. Stalling delayed. Not so 65 % 16 ° much drag.Slotted flap Same as single-slotted flap only more so. Treble slots sometimes 70 % 18 ° used.Double-slotted flap Increase camber and wing area. Best flaps for lift. Complicated 90 % 15 ° mechanism. Nose-down pitchingFowler flap moment. Same as Fowler flap only more so. Treble slots sometimes used. 100 % 20 °Double-slottedFowler flap Nose-flap hinging about leading edge. Reduces lift at small 50 % 25 ° deflections. Nose-up pitchingKrueger slat moment. 87
  8. 8. Table 7.1. High-lift devices. Increase of Angle of High-lift devices maximum lift basic airfoil at Remarks max. lilt Controls boundary layer. Slight extra drag at high speeds. 40 % 20 °Slotted wing Controls boundary layer. Extra drag at high speeds. Nose-up pitching 50 % 20 ° moment.Fixed slat Controls boundary layer. Increases camber and area. Greater angles of 60 % 22 ° attack. Nose-up pitching moment.Movable slat More control of boundary layer. Increased camber and area. Pitching 75 % 25 ° moment can be neutralized.Slat and slottedfl Complicated mechanisms. The best combination for lift; treble slots may 120 % 28 °Slat and double- be used. Pitching moment can beslotted Fowler flap neutralized. Effect depends very much on details of arrangement. 80 % 16 °Blown flap Depends even more on angle and velocity of jet. 60 % ?Jet flap Note. Since the effects of these devices depend upon the shape of the basicairfoil, and the exact design of the devices themselves, the values given can only beconsidered as approximations. To simplify the diagram the airfoils and the flaps havebeen set at small angles, and not at the angles giving maximum lift. 88
  9. 9. THEME 8. WING PROFILE DRAG The profile drag is the sum of surface- friction drag and drag of pressure causedby pressure redistribution along the streamlined surface due to viscosity influence(sometimes latter item is called form drag). It is necessary to mean that surface-friction drag is the main part of profile drag ofstreamlined bodies (therefore it is often considered that C xp ≈ C x fr ). This circumstanceis taken into account in approximate methods of C xp calculation. It is possible to adopt,that C xp does not depend on angles of attack in modes of attached flow and thencalculation of C xp is performed at α = 0 (small change of C xp on angles of attack istaken into account at definition of induced drag, having put an effective aspect ratioλ eff , or separate items at polar calculating). In range of Mach numbers less than 4 ...5all drag components (wave, induced, profile) can be determined separately from eachother. At that the wave and induced drag are well calculated without the account ofviscosity. However at M∞ ≥ 4 ...5 (zone of hypersonic speeds) there are effects ofviscous interaction, which cause the necessity of the account of viscosity and pressuremutual influence, that makes wave and profile drag inter-related. Below we shall consider the method of calculation for streamlined bodies atM∞ ≤ 4 ...5 (without the account of viscous interaction). The most widespread engineering method of C xp calculation is method CAGI.According to this method the profile drag is determined as surface-friction drag of a flatplate with introduction of correction multipliers which are taking into account anadditional part of drag from pressure forces. According to CAGI method the wingprofile drag is determined by the formula C xp = 2С f η c η м (8.1)where С f is the drag coefficient of friction of one side of a flat plate in a flow ofincompressible fluid at identical to wing: Reynolds number Re and position of a pointof laminar boundary layer transition into turbulent x t ; the factor double value takes into 89
  10. 10. account flow about the upper and lower surfaces; η м is the multiplier which is takinginto account a compressibility (Mach number M ∞ ); η c is the factor taking intoaccount contribution of pressure forces into profile drag. Generally С f , η c and η м are also the function of x t , Re , с , M i.e. V∞ lС f = f ( Re, x t ) ; ηc = f (c , x t ) ; η м = f ( M , x t ) . At that Re = , where length ν∞of a mean aerodynamic chord bA is used as characteristic length l . It is convenient towrite Reynolds number as a function dependent on Mach number and flight altitude Re = Vb A ν = M b A f ( H ) , (8.2)where f ( H ) = a∞ ν∞ , a∞ is the speed of a sound and ν∞ is the kinematic factor ofviscosity are determined under the tables of standard atmosphere depending on flightaltitude. Or f ( H ) = 2 .33⎛ 1 − H + H ⎜ ⎝ 12 2 ⎞ ⋅ 107 , m − 1 ⎟ 535⎠ [ ] (8.3) The most complex and insufficiently investigated is the definition of position oftransition point x T . From the standpoint of drag decreasing it is desirable to have thebody (wing) streamlined completely by laminar flow (i.e. x t = 1 ). Only profile C xp andinduced C xi drags exist in subsonic flow. Polar formula is written as 2C xa = C x 0 + AC ya , where C x0 = C xp . The parameter K max is determined as 1K max = and at this mode C xa = 2C x 0 = 2C xp , i.e. the profile drag is a half of 2 AC x 0full drag). However it practically can not be achieved. Any irregularities, rivets, weldedseams etc. are a source of turbulence. As a rule, at a preliminary designing stage theprecise value of x t is not known. Usually one assumes that the body (wing) isstreamlined completely by turbulent flow ( x t = 0 ), that overestimates full drag andrequired thrust of the power plant. At actual value ( x t > 0 ) the excess of a thrust(power) is received which can go onto increasing of maneuverable properties of the 90
  11. 11. airplane. Nevertheless, it is necessary to note deep researches, which are beingperformed on decreasing of C xp . In case of x т = 0 it is possible to assume thefollowing computational formulae for C xp definition: 0 ,087 2 1 + 5c 2 M Cf = ; ηc = 1 + 2c + 9 c ; η м = . (8.4) ( lg Re − 1,6 ) 2 1 + 0 .2 M 2 If the value x t ≠ 0 is known, then it is necessary to address to the diagrams. It isalso possible to use approximate formulae (at x t ≤ 0 .5 ): 0 ,087 Cf = (1 − x t ) + 1,Re 33 xt ; ( lg Re − 1,6 ) 2 ηc = 1 + 2ce − 2 ,4 x t + 9 c 2 e − 4 x t ; (8.5) ⎛ ⎞ ⎜ ηм = ⎜ 1 ⎜ 1 + 0 ,2 M 2 2 ⎟ ( + 0 ,055 x t M ⎟ 1 + 5 c 2 M . ⎟ ) ⎝ ⎠ If there are various sources of turbulence on a streamlined surface (designsuperstructures, joints of skin sheets, riveted and welded seams, slot of high-lift devicesof the wing leading edge etc.), then it is necessary to locate the point of transition in aplace of source presence. 91