486 Aerodynamics for Engineering Students devices. Accordingly, in what follows the maximization of lift for single-element aerofoils is considered in Section 8.2, followed by Section 8.3 on multi-element aerofoils and various types of flap, and Section 8.4 on other methods of boundary- layer control. Finally, the various methods used for drag reduction are described in Sections 8.5 to 8.8. 8.2 Maximizing lift for single-element aerofoils This section addresses the question of how to choose the pressure distribution, particularly that on the upper wing surface, to maximize the lift. Even when a completely satisfactory answer is found to this rather difficult question, it still remains to determine the appropriate shape the aerofoil should assume in order to produce the specified pressure distribution. This second step in the process is the so called inverse problem of aerofoil design. It is very much more demanding than the direct problem, discussed in Chapter 4, of determining the pressure distribution for a given shape of aerofoil. Nevertheless, satisfactory inverse design methods are available. They will not, however, be discussed any further here. Only the more fundamental question of choosing the pressure distribution will be considered. In broad terms the maximum lift achievable is limited by two factors, namely: (i) Boundary-layer separation; and (ii) The onset of supersonic flow. In both cases it is usually the upper wing surface that is the more critical. Boundary- layer separation is the more fundamental of the two factors, since supercritical wings are routinely used even for subsonic aircraft, despite the substantial drag penalty in the form of wave drag that will result if there are regions of supersonic flow over the wing. However, no conventional wing can operate at peak efficiency with significant boundary-layer separation. (a) The severity and quality of the adverse pressure gradient; and (b) The kinetic-energy defect in the boundary layer at the start of the adverse This latter quantity can be measured by the kinetic-energy thickness, S**, introduced in Section 7.3.2. Factor (a) is more vague. Precisely how is the severity of an adverse pressure gradient assessed? What is the optimum variation of adverse pressure distribution along the wing? Plainly when seeking an answer to the first of these questions a suitable non-dimensional local pressure must be used in order to remove, as far as possible, the effects of scale. What soon becomes clear is that the conven- tional definition of coefficient of pressure, namely In two-dimensional flow boundary-layer separation is governed by: pressure gradient. is not at all satisfactory. Use of this non-dimensional quantity invariably makes pressure distributions with high negative values of C, appear to be the most severe. It is difficult to tell from the variation of C,, along an aerofoil whether or not the boundary layer has a satisfactory margin of safety against separation. Yet it is known from elementary dimensional analysis that if the Reynolds number is the same for two aerofoils of the same shape, but different size and freestream speed, the boundary Flow control and wing design 487 layers will behave in an identical manner. Furthermore, Reynolds-number effects, although very important, are relatively weak. There is a more satisfactory definition of pressure coefficient for characterizing the adverse pressure gradient. This is the canonicaI pressure coefficient, Cp, introduced by A.M.O. Smith.* The definition of cp is illustrated in Fig. 8.1. Note that local pressure is measured as a departure from the value of pressure, prn, (the correspond- ing local velocity at the edge of the boundary layer is Urn) at the start of the pressure rise. Also note that the local dynamic pressure at the start of the pressure rise is now used to make the pressure difference non-dimensional. When the canonical repre- sentation is used, cp = 0 at the start of the adverse pressure gradient and Cp = 1, corresponding to the stagnation point where U = 0, is the maximum possible value. Furthermore, if two pressure distributions have the same shape a boundary layer experiencing a deceleration of (U/U,)2 from 20 to 10 is no more or less likely to separate than one experiencing a deceleration of (U/U,)2 from 0.2 to 0.1. With the pressure-magnitude effects scaled out it is much easier to assess the effect of the adverse pressure gradient by simple inspection than when a conventional C, distribution is used. How are the two forms of pressure coefficient related? From the Bernoulli equation it follows that u2 and Cp = l-(%) Therefore it follows that = 1-(l-Cp)(-) urn u, The factor (Urn/Um)2 is just a constant for a given pressure distribution or aerofoil shape. x /c Fig. 8.1 Smith’s canonical pressure distribution jA.M.0. Smith (1975) ‘High-Lift Aerodynamics’, J. Aircraft, 12, 501-530. Many of the topics discussed in Sections 8.1 and 8.2 are covered in greater depth by Smith. 488 Aerodynamics for Engineering Students 1 Thick boundary layer at x = 0 2 Thin boundary layer at x =O X Fig. 8.2 Effects of different types of adverse pressure variation on separation Figure 8.2 gives some idea of how the quality of the adverse pressure distribution affects boundary-layer separation. For this figure it is assumed that a length of constant pressure is followed by various types of adverse pressure gradient. Suppose that from the point x = 0 onwards C, o( 9. For the curve labelled convex, m II 4, say; for that labelled linear, m = 1; and for that labelled concave, m N 1/4. One would not normally design a wing for which the flow separates before the trailing edge is reached, so ideally the separation loci should coincide with the trailing edge. The separation loci in Fig. 8.2 depend on two additional factors, namely the thickness of the boundary layer at the start of the adverse pressure gradient, as shown in Fig. 8.2; and also the Reynolds number per unit length in the form of U,,,/v. This latter effect is not illustrated, but as a general rule the higher the value of Um/v the higher the value of Cp that the boundary layer can sustain before separating. It is mentioned above that the separation point is affected by the energy defect in the boundary layer at the start of the adverse pressure gradient, x = 0. Other things being equal this implies that the thinner the boundary layer is at x = 0, the farther the boundary layer can develop in the adverse pressure gradient before separating. This point is illustrated in Fig. 8.3. This figure is based on calculations (using Head's method) of a turbulent boundary layer in an adverse pressure gradient with a preliminary constant-pressure region of variable length, xg. It is shown very clearly that the shorter xo is, the longer the distance Axs from x = 0 to the separation point. It may be deduced from this result that it is best to keep the boundary layer laminar, and therefore thin, up to the start of the adverse pressure gradient. Ideally, transition should occur at or shortly after x = 0, since turbulent boundary layers can withstand adverse pressure gradients much better than laminar ones. Fortunately the physics of transition, see Section 7.9, ensures that this desirable state of affairs can easily be achieved. The canonical plot in Fig. 8.2 contains much information of practical value. For example, suppose that at typical cruise conditions the value of ( U/U,)2 at the trailing edge is 0.8 corresponding to C, = 0.2, and typically C, = 0.4 (say) there. In this case any of the c, curves in Fig. 8.2 would be able to sustain the pressure rise without leading to separation. Therefore, suitable aerofoils with a wide variety of pressure distributions could be designed to meet the specification. If, on the other hand, the goal is to achieve the maximum possible lift, then a highly concave pressure-rise curve with m N 1/4 would be the best choice. This is because, assuming that separation Flow control and wing design 489 G 0p-K Separation 0 Axs x 1.0 xO Fig. 8.3 Variation of location of separation with length of initial flat plate for a turbulent boundary layer in a specified adverse pressure variation occurs at the trailing edge, the highly concave distribution not only gives the largest possible value of (CP)TE and therefore the largest possible value of U,/UTE; but also because the pressure rises to its value at the trailing edge the most rapidly. This latter attribute is of great advantage because it allows the region of constant pressure to be maintained over as much of the aerofoil surface as possible, leading to the greatest possible average value of I C, I on the upper surface and, therefore, the greatest possible lift. For many people this conclusion is counter-intuitive, since it seems to violate the classic rules of streamlining that seek to make the adverse pressure gradient as gentle as possible. Nevertheless, the conclusions based on Fig. 8.2 are practically sound. The results depicted in Fig. 8.2 naturally suggest an important practical question. Is there, for a given situation, a best choice of adverse pressure distribution? The desired goals would be as above, namely to maximize U,/UTE and to maximize the rate of pressure rise. This question, or others very similar, have been considered by many researchers and designers. A widely quoted method of determining the optimum adverse pressure distribution is due to Stratford.* His theoretically derived pressure distributions lead to a turbulent boundary layer that is on the verge of separation, but remains under control, for much of the adverse pressure gradient. It is quite similar qualitatively to the concave distribution in Fig. 8.2. Two prominent features of Stratford’s pressure distribution are: (a) The initial pressure gradient dC,/dx is infinite, so that small pressure rises can be accomplished in very short distances. (b) It can be shown that in the early stages C, 0: x1/3. If compressible effects are taken into account and it is considered desirable to avoid supersonic flow on the upper wing surface, the minimum pressure must correspond to sonic conditions. The consequences of this requirement are illustrated in Fig. 8.4. Here it can be seen that at comparatively low speeds very high values of suction pressure can be sustained before sonic conditions are reached, resulting in a pronounced peaky pressure distribution. For high subsonic Mach numbers, on the * B.S. Stratford (1959) The prediction of separation of the turbulent boundary layer. J. Fhid Mech., 5, 1-16. 490 Aerodynamics for Engineering Students X L F 1 Fig. 8.4 Upper-wing-surface pressure distributions with laminar rooftop other hand, only modest maximum suction pressures are permissible before sonic conditions are reached. In this case, therefore, the pressure distribution is very flat. An example of the practical application of these ideas for low flight speeds is illustrated schematically in Fig. 8.5. This shows a Liebeck* aerofoil. This sort of aerofoil was used as a basis for the aerofoil designed by Lissamant specially for the successful man-powered aircraft Gossamer Albatross and Condor. In this application high lift and low drag were paramount. Note that there is a substantial fore-portion of the aerofoil with a favourable pressure gradient, rather than a very rapid initial acceleration up to a constant-pressure region. The favourable pressure gradient ensures that the boundary layer remains laminar until the onset of the adverse pressure gradient, thereby minimizing the boundary-layer thickness at the start of the pressure rise. Incidentally, note that the maximum suction pressure in Fig. 8.5 is considerably less than that in Fig. 8.4 for the low-speed case. But, it is not, of course, suggested here that at the speeds encountered in man-powered flight the flow over the upper wing surface is close to sonic conditions. There is some practical disadvantage with aerofoils designed for concave pressure- recovery distributions. This is illustrated in Fig. 8.6 which compares the variations of lift coefficient with angle of incidence for typical aerofoils with convex and concave pressure distributions. It is immediately plain that the concave distribution leads to much higher values of (CL)~~. But the trailing-edge stall is much more gentle, initially at least, for the aerofoil with the convex distribution. This is a desirable * R.H. Liebeck (1973) A class of aerofoils designed for high lift in incompressible flow. J. ofdircraft, 10, 61M17. P.B.S. Lissaman (1983) ‘Low-Reynolds-number airfoils’, Annual Review of Fluid Mechanics, 15: 223-239. Flow control and wing design 491 G 2 1 -3r - Fig. 8.5 Typical low-speed high-lift aerofoil - schematic representation of a Liebeck aerofoil ox ox X X X 0 8 0 1x0 I I I I -1 0 0 10 20 30 a (ded Fig. 8.6 Comparison of the variations of lift coefficient versus angle of incidence for aerofoils with concave and convex pressure-recovery distributions. Re = 2 x 1 05. x, Wortmann FX-137 aerofoil (convex); 0, Selig-Guglielmo SI 223 aerofoil (concave) Source: Based on Figs 7 and 14 of M.S. Selig and J.J. Guglielmo (1997) 'High-lift low Reynolds number airfoil design', AlAA Journal of Aircraft, 34(1), 72-79 492 Aerodynamics for Engineering Students Sonic line I 1 Fig. 8.7 Schematic figure illustrating a modern supercritical aerofoil feature from the viewpoint of safety. The much sharper fall in CL seen in the case of the aerofoil with the concave pressure distribution is explained by the fact that the boundary layer is close to separation for most of the aerofoil aft of the point of minimum pressure. (Recall that the ideal Stratford distribution aims for the boundary layer to be on the verge of separation throughout the pressure recovery.) Conse- quently, when the angle of incidence that provokes separation is reached, any further rise in incidence sees the separation point move rapidly forward. As indicated above, it is not really feasible to design efficient wings for aircraft cruising at high subsonic speeds without permitting a substantial region of supersonic flow to form over the upper surface. However, it is still important to minimize the wave drag as much as possible. This is achieved by tailoring the pressure distribution so as to minimize the strength of the shock-wave system that forms at the end of the supersonic-flow region. A schematic figure illustrating the main principles of modern supercritical aerofoils is shown in Fig. 8.7. This sort of aerofoil would be designed for M, in the range of 0.75-0.80. The principles behind this design are not very dissimilar from those exemplified by the high-speed case in Fig. 8.4, in the sense that a constant pressure is maintained over as much of the upper surface as possible. 8.3 Multi-element aerofoils At the low speeds encountered during landing and take-off, lift needs to be greatly augmented and stall avoided. Lift augmentation is usually achieved by means of flaps* of various kinds - see Fig. 8.8. The plain flap shown in Fig. 8.8a increases the camber and angle of incidence; the Fowler flap (Fig. 8.8b) increases camber, angle of *The most complete account is given by A.D. Young (1953) ‘The aerodynamic characteristics of flaps’, Aero. Res. Council, Rep. & Mem. No. 2622. Flow control and wing design 493 ( T a The plain flap I ( b) The split flap ( c The Zap flap Shroud Shroud lip Air flow through slot ( d The single slotted flap Shroud ( e) The Fowler flap Shroud Aerafoil chord line ._ Main fIapqF’ Position of ( f )The double slotted flap aerofoil chord line on flap when The angle Sf is the \ flap is flap deflection (9 )The nose flap Fig. 8.8 Some types of flaps incidence and wing area; and the nose flap (Fig. 8.8g) increases camber. The flaps shown in Fig. 8.8 are relatively crude devices and are likely to lead to boundary-layer separation when deployed. Modern aircraft use combinations of these devices in the form of multi-element wings - Fig. 8.9. The slots between the elements of these wings effectively suppress the adverse effects of boundary-layer separation, providing that they are appropriately designed. Multi-element aerofoils are not a new idea. The basic concept dates back to the early days of aviation with the work of Handley Page in Britain and Lachmann in Germany. Nature also exploits the concept in the wings of birds. In many species a group of small feathers, attached to the thumb-bone and known as the alula, acts as a slat. Main aerofoil Fig. 8.9 Schematic sketch of a four-element aerofoil 494 Aerodynamics for Engineering Students How do multi-element aerofoils greatly augment lift without suffering the adverse effects of boundary-layer separation? The conventional explanation is that, since a slot connects the high-pressure region on the lower surface of a wing to the relatively low-pressure region on the top surface, it therefore acts as a blowing type of boundary-layer control (see Section 8.4.2). This explanation is to be found in a large number of technical reports and textbooks, and as such is one of the most widespread misconceptions in aerodynamics. It can be traced back to no less an authority than Prandtl* who wrote: The air coming out of a slot blows into the boundaiy layer on the top of the wing and imparts fresh momentum to the particles in it, which have been slowed down by the action of viscosity. Owing to this help the particles are able to reach the sharp rear edge without breaking away. This conventional view of how slots work is mistaken for two reasons. Firstly, since the stagnation pressure in the air flowing over the lower surface of a wing is exactly the same as for that over the upper surface, the air passing through a slot cannot really be said to be high-energy air, nor can the slot act like a kind of nozzle. Secondly, the slat does not give the air in the slot a high velocity compared to that over the upper surface of the unmodified single-element wing. This is readily apparent from the accurate and comprehensive measurements of the flow field around a realistic multi-element aerofoil reported by Nakayama etaZ.+ In fact, as will be explained below, the slat and slot usually act to reduce the flow speed over the main aerofoil. The flow field associated with a typical multi-element aerofoil is highly complex. Its boundary-layer system is illustrated schematically in Fig. 8.10 based on the measure- ments of Nakayama et al. It is noteworthy that the wake from the slot does not interact strongly with the boundary layer on the main aerofoil before reaching the trailing edge of the latter. The wake from the main aerofoil and boundary layer from the flap also remain separate entities. As might well be expected, given the complexity of the flow field, the true explanation of how multi-element aerofoils augment lift, while avoiding the detrimental effects of boundary-layer separation, is multifaceted. And, the bene- ficial aerodynamic action of a well-designed multi-element aerofoil is due to a number of different primary effects, that will be described in turn.t Fig. 8.10 Typical boundary-layer behaviour for a three-element aerofoil * L. Prandtl and O.G. Tietjens Applied Hydro- and Aeromechanics, Dover, New York, p. 227. multielement airfoil’, AfAA J., 26, 14-21. A. Nakayama, H P. Kreplin and H.L. Morgan (1990) ‘Experimental investigation of flowfield about a Many of the ideas described in the following passages are due to A.M.O. Smith (1975) ibid. Flow control and wing design 495 8.3.1 The slat effect To appreciate qualitatively the effect of the upstream element (e.g. the slat) on the immediate downstream element (e.g. the main aerofoil) the former can be modelled by a vortex. The effect is illustrated in Fig. 8.1 1. When one considers the component of the velocity induced by the vortex in the direction of the local tangent to the aerofoil contour in the vicinity of the leading edge (see inset in Fig. 8.1 l), it can be seen that the slat (vortex) acts to reduce the velocity along the edge of the boundary iayer on the upper surface and has the opposite effect on the lower surface. Thus the effect of the slat is to reduce the severity of the adverse pressure gradient on the main aerofoil. In the case illustrated schematically in Fig. 8.11 it can be seen that the consequent reduction in pressure over the upper surface is counter-balanced by the rise in pressure on the lower surface. For a well-designed slat/main-wing combination it can be arranged that the latter effect predominates resulting in a slight rise in lift coefficient. Fig. 8.1 X i -Vortex alone 1 Effect of a slat (modelled by a vortex) on the velocity distribution over the main aerofoil [...]... 5 10 15 a, degrees (a) 2.0 - ,,." / / ," - _ I 1.5 - 4 - - - - - - - I_C .-. - .-. -. _._ G 1.0 - 0.5 I Fig 8.16 The effects of Gurney flaps placed at the trailing edge of a NACA 4412 wing on the variation of lift and drag with angle of incidence The flap height varies from 0.005 to 0.02 times the chord, c , baseline without flap; - -, 0.005~ ;- - -, 0.01 c; , 0.015~; -, 0 0 2 ~ Source: Based on... reduce 1 o P-PP0-P- 0 Main section -1 o Distance along sutface Fig 8.15 Effects of ground proximity and a Gurney flap on the pressure distribution over a two-element , wing in free flow; - - - -, wing in close proximin/ to the ground; - - -, front wing - schematic only Key: wing fitted with a Gurney flap and in close proximity to the ground Source: Based on Figs 5 and 6 of R.G Dominy ( 199 2) 'Aerodynamics. .. the *The information for this section comes from two main sources, namely, R.G Dominy ( 199 2) Aerodynamics of Grand Prix Cars’, Proc I Mech E., Parr D: J of Automobile Engineering, 206, 26 7-2 74; and P.G Wright ( 198 2) ‘The influence of aerodynamics on the design of Formula One racing cars’, J of Vehicle Design, 3 4 ,38 3-3 97 Int () Flow control and wing design 499 Gurney flap \ skirt Semi-tubular guides... D.W Hurst (2001) 'Some aspects of the aerodynamics of Gurney flaps on a double-element wing', Trans of ASME, J of Fluids Engineering, 123 ,9 9- 1 04 502 Aerodynamics for Engineering Students Fig 8.17 Flow pattern downstream of a Gurney flap Source: Based on figures in D Jeffrey, X Zhang and D.W Hurst (2000) 'Aerodynamics of Gurney flaps on 29 5-3 01 a single-element high-lift wing', AlAA J of Aircraft, 37(2),... amplification of Tollmien-Schlichting waves is the main route to Electron-beam perforated De-icer insert 600 pm skiithickness Fig 8.33 Leading-edge arrangement for 198 3-1 98 7 flight tests conducted on a JetStar aircraft at NASA Dryden Flight Research Center Important features were: (1) Suction on upper surface only; (2) Suction through electron-beam-perforated skin; (3) Leading-edge shield extended for insect protection;... vortex; as is the leading-edge strake (Fig 8.32d) In this last case the vortex reenergizes the complex, three-dimensional, boundary-layer flow that develops along the wing-body junction ‘8.5 Reduction of skin-friction drag Four main types of drag are found in aerodynamics - see Section 1.5.5 - namely: skin-friction drag, form drag, induced drag, and wave drag The methods in use for * For example, see J.P... J.P Johnston and M Nishi ( 199 0) ‘Vortex generator jets - means for flow separation control’, AIAA J., 2 ( ) 98 9- 9 94 ; see also the recent reviews by Greenblatt and Wygnanski (2000) refer86, enced in Section 8.4.2 and Gad-el-Hak (2000) referenced at the beginning of Section 8.4., and J.C Magill and K.R McManus (2001) ‘Exploring the feasibility of pulsed jet separation control for aircraft configurations’,... generators -5 Y ( b ) Wing fence Fig 832 * R.A Wallis ( 195 2) ‘The use of air jets for boundary layer control’, Aerodynamic Research Laboratories, Australia, Aero Note 110 (N-34736);H.H Pearcey ( 196 1) ‘Shock-induced separation and its prevention’, in Boundary Layer & Flow Control, Vol 2 (edited by G.V.Lwhmann), Pergamon, pp 117 0-1 344 514 Aerodynamics for Engineering Students Streamwise vortex ( c 1 Saw-tooth... 60" (Fig 8.25) In this way the circulation around the wing can be greatly enhanced *For a recent review on the aerodynamicsof the Coanda effect, see P.W Carpenter and P.N Green ( 199 7) 'The aeroacousticsand aerodynamics of high-speed Coanda devices', J Sound & Vibration, 208(5), 77 7-8 01 510 Aerodynamics for Engineering Students Jet sheet Fig 8.27 A jet flap with a vestigial control flap A more extreme... D.C ( 199 0) H Holstein ( 194 0) ‘Messungen zur Laminarhaltung der Grenzschicht an einem Fliigel’, Lilienthal Bericht, S10, 1 7-2 7; 3 Ackeret, M Ras, and W Pfenninger ( 194 1) ‘Verhinderung des Turbulentwerdens einer Grenzschicht durch Absaugung’, Naturwissenschaften, 29, 62 2-6 23; and M Ras and J Ackeret ( 194 1) ‘Uber Verhinderung der Grenzschicht-Turbulenz durch Absaugung’, Helv Phys Acta, 14, 323 516 Aerodynamics . Lissaman ( 198 3) ‘Low-Reynolds-number airfoils’, Annual Review of Fluid Mechanics, 15: 22 3-2 39. Flow control and wing design 491 G 2 1 -3 r - Fig. 8.5 Typical low-speed high-lift. and J.J. Guglielmo ( 199 7) 'High-lift low Reynolds number airfoil design', AlAA Journal of Aircraft, 34(1), 7 2-7 9 492 Aerodynamics for Engineering Students Sonic line I. R.G. Dominy ( 199 2) &apos ;Aerodynamics of Grand Prix Cars', Proc. 1. Mech. E., Part D: J. of Automobile Engineering, 206, 26 7-2 74 500 Aerodynamics for Engineering Students the