Category Aerodynamics for Engineering Students

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

the reduction of each type of drag are discussed in turn in the sections that follow. A more detailed recent account of drag reduction is given by Gad-el-Hak.[69]

In broad terms skin-friction drag* can be reduced in one of two ways. Either laminar flow can be maintained by postponing laminar-turbulent transition, this is the so-called laminar-flow technology, or ways are found to reduce the surface shear stress generated by the turbulent boundary layer. The maintenance of laminar-flow by prolonging a favourable or constant-pressure region over the wing surface is discussed briefly in Section 7.9. Active laminar-flow control requires the use of boundary-layer suction and this is described in Section 8.5.1. Another laminar-flow technique based on the use of compliant walls (artificial dolphin skin) is described in Section 8.5.2. Riblets are the main technique available for reducing turbulent skin-friction and their use is described in Section 8.5.3.

Passive flow control through the generation of streamwise vortices is frequently used on aircraft and other applications. Some of the devices commonly in use are depicted
in Fig. 8.32. Figure 8.32a shows a row of vortex generators on the upper surface of a wing. These take a variety of forms and often two rows at two different chordwise locations are used. The basic principle is to generate an array of small streamwise vortices. These act to promote increased mixing between the high-speed air in the main stream and outer boundary layer with the relatively low-speed air nearer the surface. In this way the boundary layer is re-energized. Vortex generators promote the reattachment of separated boundary layers within separation bubbles, thereby postponing fully developed stall.

Fixed vortex generators are simple, cheap, and rugged. Their disadvantages are that they cannot be used for active stall control, a technology now being used for highly manoeuvrable fighter aircraft; also they generate parasitic drag at cruise conditions where stall suppression is not required. These disadvantages have led to the development of vortex-generator jets (VGJ) whereby angled small jets are blown, either steadily or in a pulsatory mode, through orifices in the wing surface. The concept was first proposed by Wallis in Australia and Pearcey in the U. K.* primarily

Fig. 8.32

* R. A. Wallis (1952) ‘The use of air jets for boundary layer control’, Aerodynamic Research Laboratories, Australia, Aero. Note 110 {N-34736)’, H. H. Pearcey (1961) ‘Shock-induced separation and its prevention’, in Boundary Layer & Flow Control, Vol. 2 (edited by G. V. Lachmann), Pergamon, pp. 1170-1344.

for the control of shock-induced separation. More recently the concept has been reexamined as an alternative to conventional vortex generators[68].

Wing fences (Fig. 8.32b) and ‘vortilons’ act as a barrier to Upward flow on swept – back wings. They also generate powerful streamwise vortices. The saw-tooth leading edge (Fig. 8.32c) is another common device for generating a powerful streamwise 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.

Since flow separation is due to the complete loss of kinetic energy in the boundary layer immediately adjacent to the wall, another method of preventing it is to re-energize the ‘tired’ air by blowing a thin, high-speed jet into it. This method is often used with trailing-edge flaps (Fig. 8.25). To obtain reasonable results with this

Coanda effect over this curved surface

method, great care must be taken with the design of the blowing duct. It is essential that good mixing takes place between the blown air and the boundary layer.

Most applications of tangential blowing for flow control exploit the so-called Coanda effect. This name is used for the tendency of a fluid jet issuing tangentially on to a curved or angled solid surface to adhere to it, as illustrated in Fig. 8.26. The name derives from the Franco-Romanian engineer, Henri Coanda, who filed a French patent in 1932 for a propulsive device exploiting the phenomenon. The explanation for the phenomenon can be understood by considering the radial equilibrium of the fluid element depicted in Fig. 8.26a. This can be expressed in simple terms as follows: where p is the pressure within the jet boundary layer (strictly, the wall jet) issuing from the nozzle exit slot, r is the radial distance from the centre of curvature of the surface, p is the fluid density, and V is the local flow speed. It is easy to see that the pressure field thereby created forces the flow issuing from the nozzle to adhere to the surface. But this does not explain why the equally valid flow solution shown in Fig. 8.26b is only found in practice when the Coanda effect breaks down. Presumably the slightly enhanced viscous drag, experienced by the jet on its surface side as it emerges from the nozzle, tends to deflect it towards the surface. Thereafter, the pressure field set up by the requirements of radial equilibrium will tend to force the jet towards the surface. Another viscous effect, namely entrainment of the fluid between the jet and the surface, may also help pull the jet towards the surface.

The practical limits on the use of the Coanda effect can also be understood to a certain extent by considering the radial equilibrium of the fluid element depicted in Fig. 8.26a. Initially we will assume that the flow around the curved surface is inviscid so that it obeys Bernoulli’s equation

(8.2)

where po is the stagnation pressure of the flow issuing from the nozzle. Equation (8.2) may be substituted into Eqn (8.1) which is then rearranged to give

(8.3)

(a) Normal coanda flow (b) Jet break-away

Fig. 8.26 The Coanda effect – the flow of a jet around a circular cylinder Source: Based on Fig. 1 of P. W. Carpenter and P. N. Green (1997) The aeroacoustics and aerodynamics of high-speed Coanda devices’, J. Sound & Vibration, 208(5), 777-801

where Vw is the (inviscid) flow speed along the wall and Rc is the radius of curvature of the surface. When the ratio of the exit-slot width, b, to the radius of curvature is small, r ~ Rc and V ~ Vw. It then follows from Eqn (8.1) that near the exit slot the pressure at the wall is given by

where Рос is the ambient pressure outside the Coanda flow.

It can be seen from Eqn (8.4) that the larger pV2b/Rc is, the more the wall pressure falls below poo. In the actual viscous flow the average flow speed tends to fall with distance around the surface. As a consequence, the wall pressure rises with distance around the surface, thereby creating an adverse pressure gradient and eventual separation. This effect is intensified for large values of pV2b/Rc, so the nozzle exit – slot height, b, must be kept as small as possible. For small values of b/Rc the Coanda effect may still break down if the exit flow speed is high enough. But the simple analysis leading to Eqn (8.4) ignores compressible-flow effects. In fact, the blown air normally reaches supersonic speeds before the Coanda effect breaks down. At sufficiently high supersonic exit speeds shock-wave/boundary-layer interaction will provoke flow separation and cause the breakdown of the Coanda effect.* This places practical limits on the strength of blowing that can be employed.

The Coanda principle may be used to delay separation over the upper surface of a trailing-edge flap. The blowing is usually powered by air ducted from the engines. By careful positioning of the flap surface relative to the blown air jet and the main wing surface, advantage can be taken of the Coanda effect to make the blown jet adhere to the upper surface of the flap even when it is deflected downwards by as much as 60° (Fig. 8.25). In this way the circulation around the wing can be greatly enhanced.

A more extreme version of the principle is depicted in Fig. 8.27 where only a vestigial flap is used. This arrangement is occasionally found at the trailing edge of a conven­tional blown flap. The term jet flap has sometimes been applied to this device, but the term is used rather imprecisely; it has even been applied to blown-flap systems in general. Here we will reserve the term for the case where the air is blown so strongly as to be supersonic. Such an arrangement is found on fighter aircraft with small wings, such as the Lockheed F-104 Starfighter, the Mig-21 PFM, and the McDonnell Douglas F-4 Phantom. This was done in order to increase lift at low speeds, thereby reducing the landing speed. The air is bled from the engine compressor and blown over the trailing-edge flaps. According to McCormick,* prior to 1951 it was thought that, if supersonic blown air were to be used, it would not only fail to adhere to the flap surface, but also lead to unacceptable losses due to the formation of shock waves. This view was dispelled by an undergraduate student, John Attinello, in his honours thesis at Lafayette College in the United States. Subsequently, his concept was subjected to more rigorous and sophisticated experimental studies before being flight tested and ultimately used on many aircraft, including the examples mentioned above.

B. W. McCormick (1979) Aerodynamics, Aeronautics and Flight Mechanics, Wiley.

Internally blown flaps give the best performance of any high-lift system, see Table 8.1, but upper surface blowing (Fig. 8.28) is also very effective. This arrangement is used on various versions of the Antonov An 72/74 transport aircraft. A slightly less efficient system is the externally blown flap (Fig. 8.29). A version of this is used on the Boeing C-17 Globemaster heavy transport aircraft. The engine exhaust flow is directed below and through slotted flaps to produce an additional lifting force. This allows the aircraft to make a steep, low-speed, final approach with a low landing speed for routine short-field landings. Many STOL (Short Take-Off and Landing) aircraft and fighter aircraft make use of thrust vectoring that also exploits the Coanda effect. One possible arrangement is depicted in Fig. 8.30.

Blown flaps and some other high-lift systems actually generate substantial additional circulation and do not just generate the required high lift owing to an increased angle of attack. For this reason in some applications the term circulation-control wings is often used. It is not necessary to install a flap on a circulation-control wing. For example, see the system depicted in Fig. 8.31. Rotors have been fitted with both suction-type circulation control (see Fig. 8.23) and the more common blown and jet flaps, and have been tested on a variety of helicopter prototypes.[66] But, as yet, circulation-control rotors

have not been used on any production aircraft. A recent research development, mainly in the last 10 years, is the use of periodic blowing for separation control.[67] Significant lift enhancement can be achieved efficiently with the use of very low flow rates. Almost all the experimental studies are at fairly low Reynolds number, but Seifert and Pack* have carried out wind-tunnel tests at Reynolds numbers typical of flight conditions.

Tangential blowing can only be applied to the prevention of separation, unlike suction that can be employed for this purpose or for laminar-flow control. The flow created by blowing tends to be very vulnerable to laminar-turbulent transition, so tangential blowing almost inevitably triggers transition.

Many of the widely used techniques have already been described in Section 8.3. But there are various other methods of flow-separation control that are used on aircraft and in other engineering applications. These are described here.[64] Some of the devices used are active, i. e. they require the expenditure of additional power from the propulsion units; others are passive and require no additional power. As a general rule, however, the passive devices usually lead to increased drag at cruise when they are not required. The active techniques are discussed first.

8.4.1 Boundary-layer suction

The basic principle was demonstrated experimentally in Prandtl’s paper that intro­duced the boundary-layer concept to the world.* He showed that the suction through a slot could be used to prevent flow separation from the surface of a cylinder. The basic principle is illustrated in Fig. 8.22. The layer of low-energy (‘tired’) air near the surface approaching the separation point is removed through a suction slot.

The result is a much thinner, more vigorous, boundary layer that is able to progress further along the surface against the adverse pressure gradient without separating.

Suction can be used to suppress separation at high angles of incidence, thereby obtaining very high lift coefficients. In such applications the trailing edge may be permitted to have an appreciable radius instead of being sharp. The circulation is then adjusted by means of a small spanwise flap, as depicted in Fig. 8.23. If sufficient boundary layer is removed by suction, then a flow regime, that is virtually a potential flow, may be set up and, on the basis of the Kutta-Zhukovsky hypothesis, the sharp – edged flap will locate the rear stagnation point. In this way aerofoils with elliptic, or even circular, cross-sections can generate very high-lift coefficients.

Fig. 8.23

There are great practical disadvantages for this type of high-lift device. First of all it is very vulnerable to dust blocking the suction slots. Secondly, it is entirely reliant on the necessary engine power being available for suction. Either blockage or engine failure would lead to catastrophic failure. For these reasons suction has not been used in this way for separation control in production aircraft. But it has been tested on rotors in prototype helicopters.

Many supersonic aircraft feature forms of suction in the intakes to their engines in order to counter the effects of shock-wave/boundary-layer interaction. Without such measures the boundary layers in the inlets would certainly thicken and be likely to separate. And some form of shock-wave system is indispensible because the air needs to be slowed down from the supersonic flight speed to about a Mach number of 0.4 at entry to the compressor. Two commonly used methods of implementing boundary- layer suction (or bleed) are porous surfaces and a throat slot by-pass. Both were used for the first time in a production aircraft on the McDonnell Douglas F-4 Phantom. Another example is the wide slot at the throat that acts as an effective and sophis­ticated form of boundary-layer bleed on the Concorde, thereby making the intake tolerant of changes in engine demand or the amount of bleed. The McDonnell Douglas F-15 Eagle also incorporates a variety of such boundary-layer control methods, as illustrated in Fig. 8.24. This aircraft has porous areas on the second and third engine-inlet ramps, plus a throat by-pass in the form of a slot and a porous region on the sideplates in the vicinity of the terminal shock wave. All the porous areas together account for about 30% of the boundary-layer removal with the throat by-pass accounting for the remainder.

This concept is illustrated in Fig. 8.20. Superficially it appears similar to the Gurney flap. However, the mode of operation is quite different. And, in any case, for positive high lift the Gurney flap would be attached to the trailing edge pointing downwards. The basic idea here is that at high angles of attack when flow separation starts to occur near the trailing edge, the associated reversed flow causes the movable flap to be raised. This then acts as a barrier to the further migration of reversed flow towards the leading edge, thereby controlling flow separation.

The movable flap concept originated with Liebe* who was the inventor of the boundary-layer fence (see Section 8.4.3). He observed that during the landing approach or in gusty winds, the feathers on the upper surface of many bird wings tend to be raised near the trailing edge. (Photographs of the phenomenon on a skua wing are to be found in Bechert etal. 1997.) Liebe interpreted this behaviour as a form of biological high-lift device and his ideas led to some flight tests on a Messerchmitt Me 109 in 1938. The device led to the development of asymmetric lift distributions that made the aircraft difficult to control and the project was abandoned. Many years later a few preliminary flight tests were carried out in Aachen on a glider.* In this case small movable plastic sheets were installed on the upper surface of the wing. Apparently it improved the glider’s handling qualities at high angles of attack.

There are problems with movable flaps. Firstly, they have a tendency to flip over at high angles of attack when the reversed flow becomes too strong. Secondly, they tend not to lie flat at low angles of attack, leading to a deterioration in aerodynamic performance. This is because when the boundary layer is attached the pressure rises towards the trailing edge, so the space under the flap connects with a region of slightly higher pressure that tends to lift it from the surface. These problems were largely overcome owing to three features of the design depicted in Fig. 8.21 which was fitted to a laminar glider aerofoil (see Bechert etal. 1997). Ties limited the maximum deflection of the flaps. And making the flap porous and the trailing edge jagged both helped to equalize the static pressure on either side of the flap during attached-flow conditions. These last two features are also seen in birds’ feathers. The improvement in the aerodynamic characteristics can also be seen in Fig. 8.21.

Movable flap

Successful flight tests on similar movable flaps were carried out later on a motor glider.

As well as being a great racing-car driver, Dan Gurney is also well-known for his technical innovations. His most widely emulated innovation is probably the now – obligatory practice of winning drivers spraying their supporters with champagne from vigorously shaken bottles. But it is for the Gurney flap that he is known in aerodynamics. This is a deceptively simple device consisting merely of a small plate fixed to and perpendicular to the trailing edge of a wing. It can be seen attached to the trailing edge of the multi-element rear wing in Figs 8.14 and 8.15.

Gurney first started fitting these ‘spoilers’ pointing upwards at the end of the rear deck of his Indy 500 cars in the late 1960s in order to enhance the generation of the downforce. The idea was completely contrary to the classic concepts of aerodynamics. Consequently, he was able to disguise his true motives very effectively by telling his competitors that the devices were intended to prevent cut hands when the cars were pushed out. So successful was this deception that some of his competitors attached the tabs projecting downwards in order to better protect the hands. Although this ‘improved’ arrangement undoubtedly impaired, rather than enhanced, the generation of a downforce, it was several years before they eventually realized the truth.

Gurney flaps became known in aerodynamics after Dan Gurney discussed his ideas with the aerodynamicist and wing designer, Bob Liebeck of Douglas Aircraft. They reasoned that if the tabs worked at the rear end of a car, they should be capable of enhancing the lift generated by conventional wings. This was confirmed experi­mentally by Liebeck.[60] The beneficial effects of a Gurney flap in generating an enhanced downforce is illustrated by the pressure distribution over the flap of the two-element aerofoil shown in Fig. 8.15. The direct effects of Gurney flaps of various heights on the lift and drag of wings were demonstrated by other experimental studies, see Fig. 8.16. It can be seen that the maximum lift rises as the height of the flap is increased from 0.005 to 0.02 chord. It is plain, though, that further improve­ment to aerodynamic performance diminishes rapidly with increased flap height. The drag polars plotted in Fig. 8.16b show that for a lift coefficient less than unity the drag is generally greater with a Gurney flap attached. They are really only an advantage for generating high lift.

Why do Gurney flaps generate extra lift? The answer is to be found in the twin-vortex flow field depicted in Fig. 8.17. Something like this was hypothesized by Liebeck (1978).[61] However, it has only been confirmed comparatively recently by the detailed laser-Doppler measurements carried out at Southampton University (England)* of the flow fields created by Gurney flaps. As can be seen in Fig. 8.17, two contra-rotating vortices are created behind the flap. A trapped vortex is also included immediately ahead of the flap even though this is not shown clearly in the

measurements. This must be present, as was originally suggested by Liebeck. In an important respect, however, Fig. 8.17 is misleading. This is because it cannot depict the unsteady nature of the flow field. The vortices are, in fact, shed alternately in a similar fashion to the von Karman vortex street behind a circular cylinder (see Section 7.5). It can be also seen in Fig. 8.17 (showing the configuration for enhancing downforce) that the vortices behind the Gurney flap deflect the flow downstream upwards. In some respects the vortices have a similar circulation-enhancing effect as the downstream flap in a multi-element aerofoil (see Section 8.3.2).

The principle of the Gurney flap was probably exploited in aeronautics almost by accident many years before its invention. Similar strips had been in use for many years, but were intended to reduce control-surface oscillations caused by patterns of flow separation changing unpredictably. It is also likely that the split and Zap flaps, shown in Fig. 8.8b and c, that date back to the early 1930s, produced similar flow fields to the Gurney flap. Nevertheless, it is certainly fair to claim that the Gurney flap is unique as the only aerodynamic innovation made in automobile engineering that has been transferred to aeronautical engineering. Today Gurney flaps are widely used to increase the effectiveness of the helicopter stabilizers.[62] They were first used in helicopters on the trailing edge of the tail on the Sikorsky S-76B because the first flight tests had revealed insufficient maximum (upwards) lift. This problem was overcome by fitting a Gurney flap to the inverted NACA 2412 aerofoil used for the horizontal tail. Similar circumstances led to the use of a Gurney flap on the horizontal stabilizer of the Bell JetRanger (Fig. 8.18.). Apparently, in this case the design engineers had difficulty estimating the required incidence of the stabilizer. Flight tests indicated that they had not guessed it quite correctly. This was remedied by adding a Gurney flap.

Another example is the double-sided Gurney flap installed on the trailing edge of the vertical stabilizer of the Eurocopter AS-355 TwinStar. This is used to cure a problem on thick surfaces with large trailing-edge angles. In such a case lift reversal

can occur for small angles of attack, as shown in Fig. 8.19, thereby making the stabilizer a ‘destabilizer’! The explanation for this behaviour is that at small positive angle of attack, the boundary layer separates near to the trailing edge on the upper (suction) side of the aerofoil. On the lower side the boundary layer remains attached. Consequently the pressure is lower there than over the top surface. The addition of a double Gurney flap stabilizes the boundary-layer separation and eliminates the lift reversal.

In the 1960s and early 1970s several catastrophic accidents occurred in which racing cars became airborne. In some cases aerodynamic interference from nearby competing vehicles was undoubtedly a factor. Nevertheless, these accidents are a grim reminder of what can happen to a racing car if insufficient aerodynamic downforce is generated. Modern Grand Prix cars generate their prodigious aerodynamic downforces from two main sources, namely ‘ground effect’ and inverted wings. Under current Formula-One rules the undertray of the car must be completely flat between the front and rear wheels. This severely limits the ability of the racing-car designer to exploit ground effect for generating downforce.[59]

Inverted wings, mounted in general above the front and rear axles (Fig. 8.14), first began to appear on Formula-One cars in 1968. The resultant increase in the down­ward force between the tyre and road immediately brought big improvements in cornering, braking and traction performance. The front wing is the most efficient aerodynamic device on the car. Except when closely following another car, this wing operates in undisturbed airflow, so there is nothing preventing the use of conven­tional aerofoils to generate high downforce (negative lift) with a relatively small drag. If the wing is located close to the ground the negative lift is further enhanced owing to increased acceleration of the air between the bottom of the wing and the ground, leading to lower suction pressure. (Fig. 8.15.) However, if the ground clearance is too small, the adverse pressure gradient over the rear of the wing becomes more severe, resulting in stall. Even if stall is avoided, too close a proximity to the ground may result in large and uncontrollable variations in downforce when there are unavoid­able small changes in ride height due to track undulations or to roll and pitch of the vehicle. Sudden large changes in downward force that are inevitably accompanied by sudden changes to the vehicle’s centre of pressure could make the car extremely difficult to drive. Racing-car designers must therefore compromise between optimum aerodynamic efficiency and controllability.

Under Formula-One rules the span of each wing is limited, so that the adverse three-dimensional effects found with wings of low aspect ratio are relatively severe. One of these adverse effects is the strong reduction in the spanwise lift distribution from root to tip. A common solution to this problem is to use plane end-plates, as illustrated in Fig. 8.14; these help keep the flow quasi-two-dimensional over the

entire span. End-plates do not eliminate the generation of strong wing-tip vortices which have other undesirable effects. Consequently, semi-tubular guides along the lower edges of the end-plates are often used in an attempt to control these vortices (see Fig. 8.14). It can also be seen in Fig. 8.14 that the front wing comprises a main wing and a flap. The chord and camber of the flap are very much greater over its outer section compared with inboard. This arrangement is adopted in order to reduce

the adverse effects of the front wing’s wake on the cooling air entering the radiator intakes.

The rear wing has to operate in the vehicle’s wake. So the generation of high downforce by the rear wing is inevitably much less efficient than for the front wing. The car’s wake is a highly unsteady, turbulent flow containing complex vortical flow structures. As a consequence, the effective angle of incidence along the leading edge of the rear wing may vary by up to 20°. Also the effective onset speeds may be much reduced compared with the front wings, further impairing aerodynamic efficiency. Despite all these problems, in order to maintain the required position for the centre of pressure, the design engineers have to ensure that the rear wing generates more than twice the downforce of the front wings. This is achieved by resorting to the sort of highly cambered, multi-element, aerofoils deployed by aircraft wings for landing. The high drag associated with the rear wing places severe limits on the top speed of the cars. But the drag penalty is more than offset by the much higher cornering speeds enabled by the increased downforce.

It is evident from Fig. 8.10 that the boundary layer on each element develops largely independently from those on the others. This has the advantage of ensuring a fresh thin boundary layer, and therefore small kinetic-energy defect, at the start of the adverse pressure gradient on each element. The length of pressure rise that the boundary layer on each element can withstand before separating is thereby maximized – c. f. Fig. 8.3.

What happens with a typical multi-element aerofoil, as shown in Figs 8.9 and 8.13, is that the boundary layer develops in the adverse pressure gradient of the slat,

reaches the trailing edge in an unseparated state, and then leaves the trailing edge forming a wake. The slat wake continues to develop in the adverse pressure gradient over the main aerofoil; but for well-designed multi-element aerofoils the slot is sufficiently wide for the slat wake and main-aerofoil boundary layer to remain separate, likewise the wake of the main aerofoil and flap boundary layer. It is perfectly possible for the flow within the wakes to decelerate to such an extent in the downstream adverse pressure gradient that reversed flow occurs in the wake. This would give rise to stall, immediately destroying any beneficial effect. For well – designed cases it appears that the wake flows can withstand adverse pressure gradients to a far greater degree than attached boundary layers. Accordingly, flow reversal and wake breakdown are usually avoided. Consequently, for a multi-element aerofoil the total deceleration (or recovery, as it is often called) of the velocity along the edge of the boundary layer can take place in stages, as illustrated schematically in Fig. 8.13. In terms of the canonical pressure coefficient, UIUm takes approximately the same value at the trailing edge of each element and, moreover, the boundary layer is on the verge of separation at the trailing edge of each element. (In fact, owing to the vane effect, described above, the value of (U/Um^ for the flap will be lower than that for the main aerofoil.) It is then evident that the overall reduction in (UjU^) from (f7m/I/0C)s]ilt to ( Ute/I7oo)fiap will be very much greater than the overall reduction for a single-element aerofoil. In this way the multi-element aerofoil can withstand a

very much greater overall velocity ratio or pressure difference than a comparable single-element aerofoil.

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. 8.11. 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. 8.11), it can be seen that the slat (vortex) acts to reduce the velocity along the edge of the boundary layer 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.

8.3.2 The vane effect

In a similar way the effect of the downstream element (e. g. the vane) on the immediate upstream element (e. g. the main aerofoil) can also be modelled approxi­mately by placing a vortex near the trailing edge of the latter. This effect is illustrated in Fig. 8.12. This time the vane (vortex) near the trailing edge induces a velocity over the main aerofoil surface that leads to a rise in velocity on both upper and lower surfaces. In the case of the upper surface this is beneficial because it raises the velocity at the trailing edge, thereby reducing the severity of the adverse pressure gradient. In addition to this, the vane has a second beneficial effect. This can be understood from the inset in Fig. 8.12. Note that owing to the velocity induced by the vane at the trailing edge, the effective angle of attack has been increased. If matters were left unchanged the streamline would not now leave smoothly from the trailing edge of the main aerofoil. This would violate the Kutta condition – see Section 4.1.1. What must happen is that viscous effects generate additional circulation in order that the Kutta condition be satisfied once again. Thus the presence of the vane leads to enhanced circulation and, therefore, higher lift.