Category Aircraft Flight

High speed flow

Differences between high and low speed flows

Sound waves consist of a succession of weak pressure disturbances which pro­pagate through the air. The speed at which these disturbances advance through the air is called the speed of sound, and we find that this speed is of great significance in aerodynamics. The speed of sound is not constant but depends upon the square root of the absolute air temperature. Thus, at low altitudes, where the temperature is relatively high, the speed of sound is higher than it is at high altitudes where the temperature is less (see Chapter 7).

Подпись: Fig. 5.1 Flow over aerofoil at low and high speeds At high speed, flow is undisturbed until it crosses the shock wave where speed is suddenly reduced, and air pressure, temperature and density, suddenly increase (a) Low speed (b) High speed

Figure 5.1 shows the difference between the flows over a simple aerofoil on an aircraft flying at (a) a speed below the speed of sound (subsonic) and

(b) a speed greater than the speed of sound (supersonic). A number of signi­ficant differences are apparent. Firstly in the low speed flow the air is disturbed a long way in front of the aerofoil, while, for the supersonic flow, the area of disturbance is strictly limited and ahead of this region the air is totally un­affected by the presence of the aerofoil. Secondly, the local direction of the flow varies relatively smoothly at the low speed, while at high speed there is a very abrupt change where the air is first disturbed.

More detailed examination of the flow also shows that there are cor­respondingly abrupt changes in speed, temperature and pressure along a streamline. The line along which these abrupt changes take place is known as a shock wave. As can be seen in Fig. 5.1, shock waves form both at the leading and trailing edges of our aerofoil. The formation of shock waves is of great importance in high speed flow and we shall be looking at them in greater detail shortly.

Supercharging and turbocharging

The power output of a piston engine can be considerably increased by using a supercharger to pressurise the air being fed into the cylinders, so that a larger mass of air is used in each working stroke. The use of a supercharger can, there­fore, improve the engine’s power-to-weight ratio.

An important advantage of a supercharger is that it enables an engine to operate at higher altitude than it could in normally aspirated (un-supercharged) form. As the altitude increases, the air density falls, and without supercharg­ing the mass of air taken in per working stroke would fall. Since there is less oxygen, less fuel can be burned, and there is a consequent loss of power.

The supercharger enables an aircraft to take off heavily laden from high altitude airfields on hot days. By cruising at high altitude, the aircraft may also sometimes be able to take advantage of strong tail winds.

A supercharger usually consists of a centrifugal compressor driven from the crankshaft. A turbocharger is similar to a supercharger, except that the com­pressor is driven by a turbine, which is powered by the residual energy in the exhaust gases. Unlike the supercharger, the speed of the turbocharger is, there­fore, not directly related to the engine speed. Because it makes use of otherwise wasted heat, the turbocharger is inherently more efficient than a plain super­charger, and has become the type normally used. Both devices can roughly double the power output for a given size and weight of engine.

For small aircraft, the disadvantage of turbocharging is that it adds to the cost and complication of the engine, and the boost pressure is yet another vari­able that the pilot has to monitor or control. There is little advantage in using a turbocharger, unless the pilot is able to take advantage of the benefits of high altitude operation. This in turn means that either the aircraft must be pres­surised, or an oxygen mask and supply system must be provided. Civil aviation regulations require that for high altitude operation, additional instruments, navigation and communication equipment must be installed, and the pilot must be suitably qualified to use them. In recent years, a number of pressurised turbocharged light aircraft have appeared, such as the Cessna Centurion. Garrison (1981) gives a good description of the pros and cons of turbocharged light aircraft.

Design for endurance

The purpose of an aircraft is not always to transport people or cargoes between two locations, sometimes the aircraft is used as a radar or visual observation platform, and in this case the main design consideration will be the length of time it can remain airborne, or its endurance.

In this case we require, not the minimum fuel flow over a given distance, but the minimum fuel flow in unit time. Here we will adopt the same approach as before and look at the airframe from an idealised point of view to get an initial idea of the way things behave. Following this we will look at the real engine behaviour to get a more accurate picture of the operational requirements of the complete aircraft.

If we take an initial guess, we would suppose that the best way to operate the airframe for maximum endurance would be to fly at the condition at which the smallest amount of work needs to be expended in unit time in order to overcome the drag force. The rate at which work is done is equal to power, so this operating point is equivalent to the flying speed and cor­responding aircraft attitude which results in minimum power, rather than minimum drag.

Because we are now concerned with power, rather than drag, we will con­sider the power required by the airframe and powerplant and plot them in a similar manner to the drag curves of Fig. 7.4. The power required curve is very easily derived from the drag curve. All we have to do is multiply each value of the drag by the speed at which it occurs and replot as in Fig. 7.10. Then we superimpose the power, rather than the thrust, curve for the particular power – plant we are using.

We find that the power reaches a minimum value at a speed slightly lower than the minimum drag speed. In constructing the power curves we must again remember that we are talking about an aircraft flying straight and level at a constant weight.

Now we have decided what the airframe is doing, we will take a simpli­fied look at the compromise which must be reached for the different power plant types, as we did when considering how to operate for best economy and range.

Fig. 7.10 Aircraft and engine power curves

Power curve is obtained by multiplying drag values (Fig. 7.5) by aircraft speed. Minimum power speed is about – minimum drag speed

Adding a fuselage

If a fuselage is now added to the wing we have basically the same problems which occurred on the isolated wing from the point of view of correcting the local load distribution, but we now also have to superimpose the flow pro­duced by the fuselage.

In isolation the fuselage will speed up the local air stream as it flows past, and that is precisely what happens to the local air stream at the wing centre section when the fuselage is added. This means that the local Mach number on the wing will be increased, thus adding to the possibility of locally strong shock waves being formed. The detailed flow in the junction between the wing and fuselage can be very complicated, and in general acute angles are best avoided. This leads to the conclusion that a centre-mounted wing is likely to be the best bet. However this solution is not desirable in such designs as transport aircraft, where a clear fuselage is essential. Indeed whether the wing is mounted low or high may be decided by such factors as ground engine clearance or under­carriage length rather than by pure aerodynamic considerations.

If, however, we are faced with a situation in which there is some choice over the fuselage geometry and we are not simply restricted to using a straight tube, we find that we have another design parameter at our disposal. As well as modifying the local flow at the wing centre section by changes in the shape of the wing itself, we can also change the flow by modifying the local cross­sectional shape of the fuselage in order to make the local streamlines follow the shape they would adopt on the infinite wing. Alternatively, if the basic form of the fuselage must remain unaltered, a suitable fillet can be used at the wing/fuselage junction.

Longitudinal and lateral stability

In the previous chapter, in Fig. 10.1, we defined the three turning motions; pitch, yaw and roll. Pitching stability (nose-up/nose-down motion) is known as longitudinal stability.

Lateral stability is a term used rather loosely to refer to both rolling and yawing. These two motions are very closely interconnected, as we noted when describing control surfaces.

Fortunately, the coupling between longitudinal and lateral static stability is normally weak, and for the purposes of our simple introduction, it is conveni­ent to treat them separately. This again, was part of the traditional approach. It should be noted, however, that in highly manoeuvrable aircraft, the cross­coupling can be significant.

Longitudinal static stability

Aerofoil centre of pressure and aerodynamic centre

For an aerofoil, the point along the chordline through which the resultant lift force is acting, is known as the centre of lift, or centre of pressure. On a cam­bered aerofoil, the centre of pressure moves forward with increasing angle of attack, as shown in Fig. 11.2(a).

When a cambered aerofoil is set at an angle of attack where it produces no lift, we find that it still gives a nose-down pitching moment. Since there is no force, this moment must be a pure couple. Figure 11.3 shows how this arises physically. The downforce on the front of the aerofoil is balanced by an upward force at the rear, so there is no net force, but a couple is produced.

It is a surprising feature of aerofoils that there is one position on the chord line where the magnitude of this pitching moment does not change significantly with varying angle of attack. Therefore, as illustrated in Fig. 11.2(b), we can represent the forces on an aerofoil as being a combination of a couple and a lift force (L) acting through that position. The position is known as the aero­dynamic centre. It is useful to have such a fixed reference point, because, as the angle of attack reduces towards zero, the centre of pressure moves further and further aft, eventually disappearing off towards infinity.

Flying down the glide path

The above description perhaps gives a deceptively simple view of the landing procedure. Flying an accurate approach is a very demanding exercise and there is more than one way of going about it, the choice being determined by the aircraft type and pilot preference. The term ‘glide path’ for this part of the landing is somewhat misleading. It is perfectly possible to fly this part of the approach with the engine idling and this was a popular method some years ago.

With a gas-turbine engine in particular, the safer method is to fly down the glide path using a significant amount of power with the aircraft flaps being

used to provide a high drag setting. This procedure gives better control. The throttle setting can be decreased as well as increased, the latter being the only option available in the true gliding approach. Even more important is the fact that a gas turbine engine is very slow to pick up from idling speed when the throttle is suddenly opened. It is therefore a safer procedure to fly the approach under power to facilitate recovery from an aborted landing. The improved control afforded by this procedure has, however, led to its wide adoption even for light piston-engined aircraft.

Assuming that the pilot has broadly got the aircraft set up at the correct angle of attack and throttle setting to follow the required glide path, there will inevitably be small corrections needed from time to time. Here again the pilot has some choice in the matter. Provided the aircraft is not dangerously near the stall, such corrections can be made by controlling the aircraft angle of attack by elevator movement. This will result in some change in speed as well as glide angle. The alternative is to change the throttle setting and for piston-engined aircraft this method is frequently preferred because of the smaller change in speed. For jet aircraft and especially large ones, the former method is frequently used. This is because of the slow response of the engine, which makes accurate correction difficult. Further, if the aircraft is heavy, it will take a long time for the speed to change, which minimises the main dis­advantage of the method.

When flying down the glide path the pilot must have some means of check­ing that he is flying to the correct glide slope. Nowadays a variety of aids are available, and some of these are discussed below. In the absence of more complex aids he will need some reference markers, which may be simple radio beacons, at known distances from the runway threshold. He can check the height on the altimeter on passing these markers and estimate the required descent rate appropriate to the speed of the aircraft. In order to help to the correct descent rate the aircraft is fitted with a Vertical Speed Indicator (VSI) which works by sensing the rate of change of atmospheric pressure as the aircraft descends.

Wing planform

The lift and drag produced by a wing of a given cross-sectional profile are dependent on the dynamic pressure, the angle of attack and the wing plan area. In this chapter, we shall describe how the the wing planform shape also has an important influence.

Aspect ratio

The ratio of the overall wing span (length) to the average chord (width) is known as its aspect ratio. The terms span and chord are defined in Fig. 2.1. A wing such as that shown in Fig. 2.2, has a high aspect ratio, while Concorde, shown in plan view in Fig. 2.24, is a rare example of an aircraft with a wing aspect ratio of less than 1.

The early pioneers noted that the wings of birds always have a much greater span than chord. Simple experiments confirmed that high aspect ratio wings produced a better ratio of lift to drag than short stubby ones for flight at subsonic speeds. The reasons are given later in this chapter.

Active high lift devices

In addition to the passive devices described above, the engines can be used to help maintain flow attachment. The upper surface boundary layer can be

Active high lift devices

Fig. 3.17 Active boundary layer control devices

(a) Upper surface suction removes the boundary layer and can thus maintain attached flow downstream of the slot. The aerofoil can therefore be shaped so as to provide a favourable pressure gradient over most of the chord, encouraging a low drag laminar boundary layer (b) Upper surface blowing also encourages attached flow by forming a fresh boundary layer with sufficient energy to overcome the adverse pressure gradient (c) Trailing edge blowing to produce a ‘jet flap’ can produce extremely large lift coefficients

sucked away by placing a suction slot on the upper surface as illustrated in Fig. 3.17(a), or near the trailing edge. This method has the added benefit that it helps to maintain a favourable pressure gradient, and hence, a thin laminar boundary layer, over a large proportion of the wing surface, thus reducing drag. A major problem with suction, however, is the tendency to ingest foreign objects, and to clog the intake slots or holes.

Surprisingly, a similar effect to that of suction can be achieved by blowing air into the boundary layer, as shown in Fig. 3.17(b). The high energy of the surface flow over the flap helps to prevent separation, and also, in effect, draws the air from upstream. The favourable pressure gradient that this produces induces a smoother thinner boundary layer over the forward portion. The high energy air may be bled from the compressor of a gas turbine engine.

Using the engine to blow gives far fewer problems than using suction. Blown flaps were used on the carrier-based Buccaneer shown in Fig. 3.7, in order to achieve the low landing speeds required for deck landing. They were also used on the F-104 (Fig. 8.8), which had extremely small wings, and required a high landing speed even with the blown flaps. In the event of an engine flame-out, and failure to relight (a fairly common occurrence), pilots were advised to abandon the aircraft rather than attempt to land.

Really dramatically high lift coefficients can be produced by means of an air jet at the trailing edge, as illustrated in Fig. 3.17(c). This jet flap works by entraining the upstream air. The flow is induced around in a strongly curved path. A small amount of downward thrust may also be produced by the jet directly, but this is a secondary effect. The Hunting H-126 experimental aircraft was flown successfully using the jet flap principle, and CL values as high as 7.5 were obtained (see Harris 1971). One problem with the jet flap, as with other really effective devices, is that strong pitching moments are produced.

These, and many other active high lift coefficient production methods have been demonstrated on experimental aircraft, but despite the investment of vast sums of money in their development over a period of more than fifty years they have so far found little favour in the mainstream of production aircraft. This is principally because of the weight, cost and complexity involved, but also because there are problems of control and stability associated with very low speed flight. The tail surfaces need to be large to provide sufficient force to keep the aircraft under control. These large surfaces produce a drag penalty at high speed, and can cause problems of stability, as discussed later. Notice the very large fin on the short take-off and landing (STOL) C-17 in Fig. 10.20. An excel­lent account of early research in boundary layer control is given by Lachmann (1961).

The simplest practical method of using engines to help the lift generation process is to place the wing in the wake of propellers or fans. Alternatively, the propellers or jet engine can be placed so as to either blow, or suck air over the wing. The problem with the latter method is that the propeller or fan is then placed in a highly non-uniform flow, and thus tends to run inefficiently, with an undesirable alternating load.

Using propeller wash is the preferred method for commercial STOL (Short Take-Off and Landing) aircraft at the time of writing. The DH Canada Dash-8 (Fig. 13.4) takes some advantage from propeller wash, and uses slotted extending rear flaps with leading-edge slats. This relatively conservative approach to high lift coefficient generation nevertheless gives the aircraft a remarkably short landing and take-off, while maintaining a simple design.

The boundary layer and high speed flow

In the above section we saw that, in supersonic flow as well as subsonic, boundary layers exist and can separate. There is a great deal of similarity in the behaviour of the boundary layer at both high and low speeds. Chapter 3 is applicable above as well as below the speed of sound. The requirement that the flow is at rest relative to the surface (the no-slip condition) is still applic­able and so somewhere in the boundary layer the flow goes from subsonic to supersonic speed (Fig. 5.20).

A Local velocity is zero В Local velocity = speed of sound C Local velocity = 99% external velocity

The boundary layer and high speed flow

Fig. 5.20 Sonic line in supersonic boundary layer

Even at supersonic speeds the velocity still falls to zero at the surface at the bottom of the boundary layer

The boundary layer and high speed flow

Fig. 5.21 Shock wave reflection at surface

Shock wave does not reach surface because flow at the bottom of the boundary layer is subsonic

One way in which the boundary layer in supersonic flow can be subjected to a severe pressure gradient is when a shock wave, which may be generated by another part of an aircraft, strikes the surface. In this case the shock wave reflects as is shown in Fig. 5.21. It will be observed that the shock wave cannot penetrate right to the surface but only as far as the sonic line (see Fig. 5.21), but the pressure rise is transmitted through the boundary layer and may well cause separation to occur.

Figure 5.21 shows that the reflection process is quite complex. As the flow speed falls within the boundary layer so the shock wave angle becomes steeper to give the same pressure rise, as the local Mach number is reduced. The increase in pressure in the boundary layer will cause it to thicken and may well cause separation. The picture shown in Fig. 5.21 is therefore just one of a number of possibilities.

It should be noted that we have been guilty of some simplification in some of the previous figures. For example the shock wave in Fig. 5.12 has been drawn right down to the surface as if there were no boundary layer present. This may be an acceptable approximation in many cases, but if the boundary layer should separate then the picture may be changed considerably.

Shock wave reflections of this sort are important in determining how the flow behaves, and reflections are by no means always as simple as that shown in Fig. 5.21. The boundary layer at the point of reflection as well as the strength of the shock wave may be complicated by such factors as local separation bubbles or complete boundary layer separation. Three­dimensional effects will also have an important bearing on the nature of the reflection process. A detailed discussion of the various types of reflection which may be encountered is outside the scope of this book, and the interested reader will find a great deal on the subject in the literature, e. g. Cox and Crabtree (1965).

Kinetic heating

In Chapter 2 we saw how the pressure and velocity for a low speed flow could be related by Bernoulli’s equation. This equation is only approximately true, however, and, for a compressible fluid, becomes less accurate as the speed of flow increases. This is because significant changes start to occur not only in the kinetic energy of the fluid but also in the internally stored energy within the gas. This means that, as the speed increases, not only does the pressure fall but so does the temperature. Conversely, when a high speed air stream is slowed down there is an accompanying rise in the temperature.

Again it makes no difference if we consider the aircraft moving through the air rather than the air streaming past the stationary aircraft. The rise in tem­perature is most severe when the air is brought to rest, relative to the aircraft, at a stagnation point. Figure 5.22 shows the air temperatures encountered, at different flight Mach numbers, in such a stagnation region at a cruising height roughly equivalent to that of Concorde. Such temperature rises can have important implications in terms of structural strength and distortion.

We have seen that another way in which the air can be suddenly slowed in supersonic flow is by the presence of a shock wave. Frequently very severe heating problems can be encountered where the flow passes through a local shock wave near the surface. One example of this is provided by the high local heating rates which can occur at a junction between a fin and a fuselage.

The boundary layer provides another mechanism which can raise the air temperature with important structural consequences for high speed aircraft. The boundary layer slows the flow near the surface with a consequential

The boundary layer and high speed flow

Fig. 5.22 Variation of stagnation temperature with flight Mach number at high altitude above 11 km

temperature rise. This temperature increase is only of any significance at high flight speeds.

The state of the boundary layer is also important in determining the rate of heat transfer to the surface. In general a turbulent boundary layer will transmit heat into the structure more readily than a laminar layer because in the turbu­lent layer the regions of the boundary layer close to the surface are continually replenished with high temperature air.

This heat transfer process can also affect the way in which the boundary layer behaves. The extreme temperatures which may be encountered at very high (hypersonic) speed may cause significant changes in the properties of the air itself, as we shall discuss briefly in the next section.

Reheat or afterburning

In gas-turbine-propelled aircraft, there is frequently a requirement for short bursts of increased thrust, particularly for high performance military aircraft, which need to accelerate rapidly. Unlike the reciprocating engine, the gas tur­bine only uses, for combustion, a small proportion of the available oxygen in the air that passes through it. It is, therefore, possible to obtain a significant boost in thrust by burning more fuel in an extended tailpipe section known as an afterburner or reheat chamber, as illustrated in Fig. 6.30.

The thrust can be approximately doubled in this way with only a relatively small increase in weight. At low flight speeds, reheat is extremely inefficient, and is normally only used for take-off, and to produce short bursts of rapid acceleration. In supersonic flight, it becomes more efficient. Most modern supersonic aircraft use reheated low by-pass turbo-fans.

Reheat necessitates the use of a variable-area exhaust nozzle, and the extra tailpipe length and burner produce additional friction losses when not in use.