Category Aircraft Flight

Controlling the type of boundary layer

Since the type of boundary layer influences both surface friction drag and flow separation, it is important to know what factors control the transition from laminar to turbulent boundary layer flow.

We have already mentioned that if the pressure is decreasing in the direction of flow (a favourable pressure gradient) transition is delayed. Transition is also delayed if the surface is smooth and without undulations.

The position of transition to turbulent flow on an aerofoil moves forwards with increasing speed V and also if the air density p is increased. It moves rear­wards if the coefficient of viscosity R (a measure of the stickiness) increases. The distance of the transition from the leading edge also depends on the aero­foil chord length c for a given section shape, since increasing the chord, and hence the overall size, will increase the length of the region of favourable pres­sure gradient.

The dependence of the transition position on the speed, density viscosity and chord, as described above, can be expressed in terms of a single quantity known as the wing Reynolds number, where

density x speed x wing chord

Wing Reynolds number is

viscosity coefficient

or in mathematical symbols

Re = (PVC)

R

The transition position moves forward as the Reynolds number increases.

Reynolds number is just a number with no dimensions, like a ratio. It is a term that frequently crops up in aerodynamic literature, and always has the form (pVl)/R where l is a length.

Flow in a supersonic wind-tunnel

The fact that radically different flows occur at sub – and supersonic speeds with objects having identical geometric features is also graphically illustrated by the flow in a duct of the type which is used in supersonic wind-tunnels (Fig. 5.4).

If the tunnel is run subsonically then, as would be expected from Chapter 1 the speed of flow increases until the narrowest portion (the throat) is reached and decreases again as the duct area increases. If, however, the tunnel is running supersonically, the speed continues to increase downstream of the throat, even though the cross-sectional area is getting larger.

At first sight it may seem that this is impossible because the same mass flow must pass each section in unit time. Thus it would appear that a lower speed of flow will be needed at a point in the duct where the cross-sectional area is high, and vice versa.

The solution to this dilemma lies in the fact that the density of the air reduces as the speed is increased. At low speed this effect is not very significant, but as the speed increases the effect becomes so pronounced that an increase in duct area is required to pass the mass flow in spite of the fact that the speed is also increasing (Fig. 5.4).

This change of density starts to become noticeable some time before the flow actually becomes supersonic in that pressures predicted by the Bernoulli equation (Chapter 1) become progressively less accurate. Thus one way of distinguishing between high and low speed flows is to ask the question whether the density changes within the flow are significant or not. For this reason flow at high speed is sometimes referred to as compressible flow. This distinction is valid for ‘external’ flows, such as the flow round the aerofoil discussed above, as well as ‘internal’ flows such as the supersonic wind-tunnel duct.

The gas turbine

The gas turbine was originally developed primarily as a practical device for providing jet propulsion, since it was realised that this would overcome the speed limitations imposed by propeller propulsion. The other factor that prompted its original development, was the realisation that it would operate satisfactorily at high altitudes. As with the high speed ducted fan described earlier, the air slows down as it enters a gas turbine in high speed flight, which means that the air pressure and density increase at inlet. This increase can com­pensate for the low atmospheric air density at high altitude. Both high speed and high altitude flight have obvious advantages for military aircraft.

A major feature of the gas turbine is the considerable amount of power that it can produce at high forward speeds. The effective power produced is the product of the thrust and the forward speed. For example, a large turbo-jet engine giving 250 kN (approx. 50,000 lb) of thrust would be producing around 60 megawatts (approx 80,000 bhp) at 240 m/s (approx 500 mph). The most powerful piston engines produced no more than about 2.5 megawatts (approx 3400 bhp). On the first experimental turbo-jet flight by the Heinkel He-178 (Fig. 6.17) in 1939, the engine was producing about as much equiva­lent power at maximum speed as the most powerful production piston engines of that time.

Other advantages of the gas-turbine engine compared to reciprocating engines are the high power-to-weight ratio, the virtual absence of reciprocating parts, and simpler less frequent maintenance.

The gas turbine

Fig. 6.17 The first turbo-jet aircraft

The Heinkel He-178 made its maiden flight in August 1939 (Photo courtesy of the Royal Aeronautical Society)

Endurance with turbo-jet propulsion

For a turbo-jet, the fuel flow rate is approximately proportional to the thrust produced by the engine, regardless of speed or altitude. The best endurance will thus occur at the minimum thrust setting because this will give the lowest fuel flow. The lowest possible thrust, and hence best endurance, will be obtained when the aircraft is flying at its minimum drag speed rather than the minimum power condition.

The maximum time for which the aircraft can be kept airborne will be approximately independent of both wing loading and altitude, because the magnitude of the minimum drag is not influenced by these parameters. How­ever the speed at which minimum drag is obtained, and hence the speed for best endurance, increases with both wing loading and altitude.

Some further non-aerodynamic considerations in wing design

We have mentioned structural problems and how they influence the final design of a wing. There are also a number of other considerations which we will discuss briefly here in order to remind ourselves that the aerodynamicist cannot have things all his own way in the design process.

As well as providing lift the wing usually has other important functions. One of these functions in most aircraft is to act as the main fuel tank. Using the wings for this has a number of advantages. Firstly it uses up an otherwise

Fig. 9.18 Area rule

The Rockwell B1 bomber has a narrow fuselage ‘waist’ at the junction with the wing in order to preserve the correct lengthwise distribution of overall cross­sectional area

unattractively shaped storage volume for a useful purpose. Secondly the fuel weight can be spread over the span of the wing, rather than concentrating it all in the fuselage. Thus we can get away with a lighter wing structure because of the reduced bending moments along the wing.

In many aircraft, particularly transport aircraft, it is very convenient to store all the fuel in the wings and this immediately leads to the requirement that the wing must have a certain minimum volume quite apart from the structural problems we have already mentioned. This may well mean that some comprom­ise had to be made in the aerodynamic performance of the wing. This sort of problem gives some idea of the complexity of the design process. Because the aerodynamic performance is reduced, more fuel will be required, and so the designer must go round the loop of choosing wing capacity and performance until a satisfactory solution is obtained.

Before we leave the subject let us look at a couple of less obvious design choices which must be made. The first of these concerns the question of where we put the main undercarriage legs. With a nose wheel undercarriage these must clearly be behind the aircraft centre of gravity, or the aircraft will topple onto its tail while at rest on the ground. To get a reasonable wheel separation and to keep the fuselage clear it is generally preferable to mount the undercarriage in the wings. However, with a swept wing, the centre of gravity may lie near the trailing edge where the wing is too thin to house the retracted gear, and too weak locally to support the weight of the aircraft. One solution which is commonly employed is to use a cranked trailing edge (Fig. 9.19). This, fortunately, fits in quite well with some of the other requirements which have

Fig. 9.19 Cranked trailing edge

This may be necessary to get the undercarriage in the right place. It also provides a convenient place for engine pylons

already been seen to apply at the centre section. Furthermore, extending the wing chord in this region enables a thick physical section to be used, which is needed for the structure and to house the undercarriage; alternatively the thickness-to-chord ratio can be reduced to give an aerodynamically thinner wing. This again can be helpful in keeping the local Mach number down at the centre section where the local flow speed has been raised by the presence of the fuselage. Another important advantage is that the use of a straight trailing edge close to the fuselage makes it much easier to fit trailing-edge flaps close to the wing fuselage junction.

Another unexpected factor may enter into the design of the cranked inboard portion of the wing. There will clearly have to be a break in the trailing-edge flap to accommodate an underwing pylon-mounted engine. It is therefore con­venient to mount the engine at the junction between the swept and unswept trailing-edge regions (Fig. 9.19). The distance of the engines from the centreline has important implications from the point of view of aircraft controllability in the event of engine failure, particularly at take-off when full thrust is being employed. The further outboard the engine is mounted the larger the fin and rudder assembly needed to provide adequate control in these circumstances. This is one more factor which must be carefully considered, and so we see that we cannot just consider the wing itself in trying to achieve our optimum design for changes in the wing design can have important repercussions elsewhere on the aircraft.

Another factor which may limit the way in which we can achieve our desired wing geometry is the manufacturing process itself. If a conventional wing con­struction of light alloy is to be used, the complexity of the three-dimensional surface which can be achieved is limited, and it may not be possible to build in economically all the variations of twist and camber that we would like if given an entirely free hand. This is another potential advantage presented by more modern composite materials – they offer the possibility, not only of building in tailored stiffness characteristics, but the facility to make more complicated shapes than is possible with more conventional constructional materials (see Fig. 14.6).

Conditions for longitudinal static stability

It will be seen that the centre of gravity is further forward in the stable case of Fig. 11.5 than in the unstable one of Fig. 11.6. Also, in the stable case, the wing is set at a higher incidence than the tail. The difference between the incidence angles at which the wing and tail are set is called the longitudinal dihedral. By comparing Figs 11.5 and 11.6 it can be seen that the longitudinal dihedral influences the production of a favourable restoring moment. In the stable case of Fig. 11.5 the longitudinal dihedral angle is positive. In the unstable case of Fig. 11.6 the angle is negative. The A-10 Thunderbolt shown in Fig. 11.7 shows a noticeable degree of positive longitudinal dihedral.

In fact, it is not actually the longitudinal dihedral (the difference between wing and tail incidences) that matters, but the difference between wing and tail lift coefficients in the initial trimmed condition. From mathematical analysis we find that for stability, the tail lift coefficient in the trimmed condition should be less than that of the wing by a sufficient margin to overcome the destabilising effects of the camber etc. The longitudinal dihedral effect, though important, is only one of the many influences on stability that appear in a full analysis.

If the centre of gravity of the aircraft is moved forward, the tail down – force has to be increased, to keep the aircraft trimmed. This requires that the

Fig. 11.7 The Fairchild-Republic A-10 Thunderbolt, showing high thrust line and a noticeable longitudinal dihedral

tail incidence should be made more negative, or that the elevator should be raised. Either of these effects will increase the effective longitudinal dihedral, and increase the static stability. Thus, the further forward the centre of gravity position is moved, the greater will be the longitudinal static stability.

It should be noted that the centre of gravity does not have to be in front of the aerodynamic centre of the wing for stability, although this is a common condition for conventional aircraft.

The rearward CG position at which the aircraft is just on the verge of being unstable or is neutrally stable is called the neutral point.

For a conventional aircraft trimmed for steady level flight, the tailplane normally has to produce very little lift, or even a downforce. For this reason, a symmetrical aerofoil is often used for the tailplane.

In situations where the tailplane has to produce a downforce, the wing and tail are effectively fighting each other, so the overall lift is less than that produced by the wing. The tailplane, however, still produces positive drag, and thus serves no useful purpose other than as a means of controlling and stabil­ising the aircraft. The extra drag produced in this way is called trim drag.

Some Aerofoil Characteristics

The NACA series of aerofoils was introduced in Chapter 4. In this appendix, we examine three of these aerofoils in more detail and look at the ways in which changes in cross-sectional shape, particularly camber and thickness distribution, influence their performance. In each case, the aerofoil section is shown, together with a typical distribution of pressure around the lifting sec­tion, the variation of lift with angle of attack and the variation of section drag with lift. The lift and drag are plotted in coefficient form (Chapters 1 and 3). For the pressure distribution, a coefficient form is also used. The pressure coefficient is defined as the local pressure on the aerofoil surface minus the ambient pressure divided by the dynamic pressure (p. 12). Negative pressure coefficients are plotted upwards, so that the upper surface of the aerofoil appears as the upper line on the graph.

The first aerofoil, the NACA 0012 (Fig. A.1), is a 12 per cent thick symmet­rical ‘4 digit’ series aerofoil. It is commonly used for tail surfaces and for wind – tunnel test models. It is also used as the wing section on a number of aircraft including the Cessna 152. This is a popular light general aviation aircraft and the NACA 0012 is used for the outboard wing section. From the graph of lift coefficient against angle of attack for this aerofoil, it can be seen that there is a sharp stall at about 15° angle of attack. The pressure distribution also shows quite a sharp suction peak on the upper surface.

The second aerofoil, the NACA 2214 (Fig. A.2), is used on the centre wing section of the Cessna 152. With a 14 per cent thickness/chord ratio, it is slightly thicker than the NACA 0012 and has some camber. The effect of the camber is evident in the positive lift coefficient that is seen at zero angle of attack. Minimum drag is obtained at a lift coefficient of approximately 0.2, rather than 0.0 for the NACA 0012. The drag is, however, higher for this thicker cambered section and the stall is somewhat more gentle.

The final aerofoil, the NACA 6618 (Fig. A.3), is one of the ‘low drag’ 6 series and is used on the Phantom supersonic fighter. Only the low speed char­acteristics are given here. This aerofoil was designed using a so-called ‘inverse method’. The pressure distribution on the upper surface was chosen to be as flat as possible at a particular ‘design’ lift coefficient and the resulting cross­section was then determined. The flat top surface pressure distribution allows a laminar boundary layer to be maintained over much of the surface, leading to a reduced drag. The laminar layer can be maintained over a small range of angle of attack, either side of the angle of attack at the design lift coefficient, resulting in the typical ‘laminar bucket’ drag variation which is seen in the graph of drag coefficient plotted against lift coefficient. The position of max­imum thickness on this aerofoil is further aft than on either the NACA 0012 or the NACA 2214. This leads to a much gentler acceleration of the air near the front of the aerofoil and the absence of the associated suction peak that pro­motes the transition to a turbulent boundary layer. The data are for a Reynolds Number of 6 x 106.

Angle of attack (degrees)

c) Variation of lift with angle of d) Variation of drag with lift attack

Fig. A.1 NACA 0012

c) Variation of lift with angle of attack

Fig. A.2 NACA 2214

a) Aerofoil section

Angle of attack (degrees)

c) Variation of lift with angle of attack

Fig. A.3 NACA 6618

Trailing vortex formation

The physical mechanism by which the trailing vortices are formed may be understood by reference to Fig. 2.6. On the underside of a wing, the pressure

Trailing vortex formation

Fig. 2.5 Trailing vortex formation

Flow visualisation using helium-filled microscopic soap bubbles. The flow spirals around a stable core originating from just inboard of the wing tip (Photo courtesy of ENSAM, Paris)

Trailing vortex formation

Fig. 2.6 Spanwise flow on a wing

(a) The air flows inwards on the upper surface and outwards on the lower. This is the source of the trailing vortices

(b) View from just downstream of the trailing edge

is higher than the surrounding atmosphere, so the air flows outwards towards the tips. On the upper surface, the pressure is low, and the air flows inwards. This results in a twisting motion in the air as it leaves the trailing edge. Thus, if we look at the air flow leaving the trailing edge from a viewpoint just downstream, as in Fig. 2.6(b), it will appear to rotate. Near each wing tip, the air forms into a well defined concentrated vortex, but a rotational tendency or vorticity occurs all along the trailing edge. Further downstream, all of the vorticity collects into the pair of concentrated trailing vortices (as shown in Fig. 2.10).

If the wing is completely constrained between the walls of a wind-tunnel, the outflow will not occur, and trailing vortices will not form. This ties up with the theory of vortex behaviour mentioned above: the vortices must either form a closed loop, or terminate in a wall. It also points to one of the problems of wind-tunnel testing; the fact that the presence of the tunnel walls influences the flow behaviour.

Effect on wind-tunnel testing

A major problem in wind-tunnel model testing arises if we rely solely on increasing the speed to correct the Reynolds number. Since the chord c of the model is smaller, we must make (pV )/u larger. This in turn means that, unless we do something about the density and viscosity, a 1/10 scale model would need to be run at 10 times the full-scale speed.

Unfortunately aircraft are large objects, and we often wish to make models of 1/10 scale or less. To simulate 100 m/s at 1/10 scale, we would need to

run the tunnel at 1000 m/s which is nearly three times the speed of sound at sea level! Clearly, the resulting supersonic conditions would ensure that the flow around the model was nothing like that for the full-size aircraft.

One way to avoid this difficulty, is to use a pressurised wind-tunnel. By increasing the pressure in the tunnel, the density and hence the Reynolds num­ber may be increased at any given air speed. A similar effect can be obtained by using a so-called cryogenic tunnel where the air is cooled (usually with liquid nitrogen) to decrease the viscosity coefficient p. Gases, unlike liquids, become less viscous as they are cooled. The density is also increased.

In order to obtain similar flow characteristics between model and full scale (a condition known as dynamic similarity), it turns out that there are other quantities that need to be matched in addition to the Reynolds number. For aeronautical work, the other really important one is the Mach number, the ratio of the relative flow speed (or aircraft speed) to the speed of sound. As we shall see, the speed of sound depends on the temperature, and thus quite a bit of juggling with speed, pressure and temperature is required, in order to get both the Reynolds and the Mach numbers in a test simultaneously matched to the full-scale values.

Although less important, we should really try to match the levels of tur­bulence in the oncoming air stream, which can be difficult, because in full scale, the aircraft can sometimes be flying through still, and hence non-turbulent air.

For fundamental investigations, and exploratory test programmes, it is still customary to use simple unpressurised tunnels. When the low speed character­istics of the aircraft are being investigated, the Mach number mismatch is un­important. The Reynolds number error can sometimes be reduced by sticking strips of sandpaper on the surface to provoke transition at the correct position, which can either be estimated, or determined from flight tests.

For tests at supersonic speeds the Mach number must be matched, which is quite easy, and the Reynolds number effect is often less important. Unfortunately, most airliners, and quite a few military aircraft spend most of their time flying faster than 70 per cent of the speed of sound, where both the Mach and Reynolds numbers are important. Wind-tunnels in which the pressure, temperature and Mach number can be controlled accurately to suit the size of model are expensive to build and run, especially for speeds close to the speed of sound, but they are essential for accurate development work.

Thrust and propulsion

Propulsion systems

It is tempting to try to divide the conventional aircraft propulsion systems into two neat categories; propeller and jet. Real propulsion devices, however, do not always fall into such simple compartments. In particular, gas-turbine propulsion covers a wide range from turbo-props to turbo-jets. To simplify matters, we shall look first at the two ends of this spectrum; by considering propeller propulsion at one end, and simple turbo-jet propulsion at the other. Later on, we shall look at the intermediate types such as turbo-fans and prop – fans, and also some unconventional systems.

Propeller propulsion

At one time, it looked as though the propeller was in danger of becoming obso­lete. Since the early 1960s, however, the trend has been reversed, and nowa­days nearly all subsonic aircraft use either a propeller or a ducted fan. Even the fan has lost some ground to advanced propellers, and we shall therefore pay more attention to propeller design than might have seemed appropriate a few years ago. It is worth noting, that in 1986, half a century after the first successful running of a jet engine, 70 per cent of the aircraft types on display at the Farnborough Air Display were propeller driven.

The blades of a propeller like those of the helicopter rotor can be thought of as being rotating wings. Since the axis of rotation of the propeller is hori­zontal, the aerodynamic force produced is directed forwards to provide thrust rather than upwards to generate lift. The thrust force is therefore related to the differences in pressure between the forward – and the rearward-facing surfaces of the blades.

Thrust and propulsionRelative flow

Surrounding

Подпись: stream-tube Thrust and propulsion Подпись: Surrounding

Fig. 6.1 The flow past a propeller in flight

In the process of producing this pressure difference, the propeller creates a slipstream of faster-moving air. In Fig. 6.1, the dashed lines represent the streamlines that pass through the tips of the propeller. In three dimensions we have to imagine a stream-tube that encloses or surrounds the propeller disc. Downstream of the propeller, this surrounding stream-tube roughly defines the boundary of the slipstream. The rate of change of momentum of the air within this stream-tube gives a good indication of the overall thrust.