INTRODUCTION

The engine for a high-speed aircraft is required to operate over a wide range of conditions and some of these have been discussed in Chapters 13, 14 and 15. Of particular importance is the variation in inlet stagnation temperature, which can vary from around 216 K up to nearly 400 K for a Mach-2 aircraft. As a result the ratio of turbine inlet temperature to engine inlet temperature T04/T02 alters substantially, even when the engine is producing the maximum thrust it is capable of. In contrast, for the subsonic civil aircraft the value of T04/T02 changes comparatively little between take off, climb and cruise, the conditions critical in terms of thrust and fuel consumption, and it is normally only when a civil aircraft is descending to land or is forced to circle an airport that T04/T02 is reduced radically.

In Chapter 8 the dynamic scaling and dimensional analysis of engines was considered. There the engine non-dimensional operating point was held constant, for example T04/T02 is not constant, so the engine remained ‘on-design’. To designate the engine operating condition the value of N/√(c pT0) or any of the pressure ratios or non-dimensional mass flows could also be used, but T04/T02 has the intuitive advantage since engine thrust is altered by varying fuel flow rate to change T04. In Chapter 12 the more challenging issue of a civil engine operating away from its design condition was addressed, i.e. the case when T04/T02 ≠ constant, and the subject of this chapter is the similar case for military engines.

INTRODUCTION

This chapter returns to some general issues related to both civil and military engines. These are topics which can more satisfactorily be addressed with the background of earlier chapters.

CHOICE OF NUMBER OF ENGINES FOR CIVIL AIRCRAFT

The design for the New Large Aircraft assumed that there would be four engines and indeed the Airbus A380 does have four engines. When the first jet aircraft were beginning to fly across the Atlantic ocean four engines were necessary to cope with the possibility of loss in thrust in one engine at take off; to have had to accommodate loss of one engine with fewer than four engines would have involved carrying a lot of unnecessary engine weight (and available thrust) during cruise. Even when the Boeing 747 entered service around 1970, four engines were considered optimum for a transatlantic flight; the large twin-engine aircraft introduced by Airbus, the A300, seemed suited only to shorter routes. By the 1990s the most widely used aircraft on the transatlantic route were twin-engine aircraft, such as the Boeing 767 or Airbus 300, providing non-stop flights from, for example, London to Los Angeles (4700 nautical miles). The more recent twin, the Boeing 777, is used mainly for flights under 5000 nautical miles but the newer long-range version will have a range of 8810 nautical miles. It is reasonable to ask what has changed to make it possible and second what has made it attractive to use twin-engine aircraft on such long routes?

INTRODUCTION

In Chapter 11 the performance of the main aerodynamic and thermodynamic components of the engine were considered. In earlier chapters the design point of a high bypass ratio engine had been specified and a design arrived at for this condition. At the design point all the component performances would ideally fit together and only the specification of their performance at this design condition would be required. Unfortunately engine components never exactly meet their aerodynamic design specification and we need to be able to assess what effect these discrepancies have. Furthermore engines do not only operate at one non-dimensional condition, but over a range of power settings and there is great concern that the performance of the engine should be satisfactory and safe at all off-design conditions. For the engines intended for subsonic civil transport the range of critical operating conditions is relatively small, but for engines intended for high-speed propulsion, performance may be critical at several widely separated operating points.

The treatment in this chapter is deliberately approximate and lends itself to very simple estimates of performance without the need for large computers or even for much detail about the component performance. The ideas which underpin the approach adopted are physically sound and the approximations are sufficiently good that the correct trends can be predicted; if greater precision is required the method for obtaining this, and the information needed about component performance, should be clear.

INTRODUCTION

Up to this point consideration has been given only to the design point of the engine. This is clearly not adequate for a variety of reasons. Engines sometimes have to give less than their maximum thrust to make the aircraft controllable and to maintain an adequate life for the components. Furthermore all engines have to be started, and this requires the engine to accelerate from very low speeds achieved by the starter motor. The inlet temperature and pressure vary with altitude, climate, weather and forward speed and this needs to be allowed for.

To be able to predict the off-design performance it is necessary to have some understanding of the way the various components behave and this forms the topic of the present chapter. It is fortunate that to understand off-design operation and to make reasonably accurate predictions of trends it is possible to approximate some aspects of component performance. The most useful of these approximations is that the turbines and the final propelling nozzle are perceived by the flow upstream of them as choked. Another useful approximation is that turbine blades operate well over a wide range of incidence so that it is possible to assume a constant value of turbine efficiency independent of operating point. These approximations make it possible to consider the matching of a gas turbine jet engine – how the various components operate together at the conditions for which they are designed (the design point) and at off-design conditions – and this will form the topic of Chapter 12.

INTRODUCTION

The creation of thrust is the obvious reason for having engines and this chapter looks at how it occurs. This is a simple consequence of Newton's laws of motion applied to a steady flow. It requires the momentum to be higher for the jet leaving the engine than the flow entering it, and this inevitably results in higher kinetic energy for the jet. The higher energy of the jet requires an energy input, which comes from burning the fuel. This gives rise to the definition of propulsive efficiency (considering only the mechanical aspects) and overall efficiency (considering the energy available from the combustion process).

MOMENTUM CHANGE

The creation of thrust is considered briefly here, but a more detailed treatment can be found in other texts, for example Hill and Peterson (1992). Figure 3.1 shows an engine on a pylon under a wing. Surrounding the engine a control surface has been drawn, across which passes the pylon. The only force applied to the engine is applied through the pylon. We assume that the static pressure is uniform around the control surface, which really requires that the pylon is long enough that the surface is only weakly affected by the wing. In fact we assume that the wing lift and drag are unaffected by the engine and the engine unaffected by the wing; this is not strictly true, but near enough for our purposes.

The emphasis of Part 1 of the book has been overwhelmingly towards the aerodynamic and thermodynamic aspects of a jet engine. These are important, but must not be allowed to obscure the obvious importance of a wide range of mechanical and materials related issues. In terms of time, cost and number of people mechanical aspects of design consume more than those which are aerodynamic or thermodynamic. Nevertheless this book is concerned with the aerodynamic and thermodynamic aspects and it is these which play a large part in determining what are the desired features and layout of the engine. Nevertheless an aerodynamic specification which called for rotational speed beyond what was possible, or temperatures beyond those that materials could cope with, would be of no practical use.

An aircraft engine simultaneously calls for high speeds and temperatures, light weight and phenomenal reliability; each of these factors is pulling in a different direction and compromises have to be made. Ultimately an operator of jet engines, or a passenger, cares less about the efficiency of an engine than that it should not fall apart. Engines are now operating for times in excess of 20000 hours between major overhauls (at which point they must be removed from the wing), and this may entail upward of 10000 take-off and landing cycles. In flight shut-downs are now rare and many pilots will not experience a compulsory shut-down during their whole careers.

INTRODUCTION

The compressor, which raises the pressure of the air before combustion, and the turbine, which extracts work from the hot pressurised combustion products, are at the very heart of the engine. Up to now we have assumed that it is possible to construct a suitable compressor and turbine without giving any attention to how this might be done. In this chapter an elementary treatment is given with the emphasis being to find the overall diameter of various components and the flow-path this entails, the number of stages of compressor and turbine, and suitable rotational speeds. The details of blade shape will not be addressed. Further information is obtainable at an elementary level in Dixon (1995) and at a more advanced level in Cumpsty (1989).

For the large engine that we are considering the most suitable compressor and turbine will be of the axial type. These are machines for which the flow is predominantly in the axial and tangential directions, and stand in contrast to radial machines for which the flow is radial at inlet or outlet.

Because the pressure rises in the direction of flow for the compressor there is always a great risk of the boundary layers separating, and when this happens the performance of the compressor drops precipitously and is said to stall. To obtain a large pressure rise (or, as it is more commonly expressed, pressure ratio) the compression is spread over a large number of stages.

INTRODUCTION

It would be possible to calculate the performance of an engine in the manner of Exercise 7.1 and 7.2 for every conceivable operating condition, e.g. for each altitude, forward speed, rotational speed of the components. This is not an attractive way of considering variations and it does not bring out the trends as clearly as it might. An alternative is to predict the variations by using the appropriate dynamic scaling – apart from its usefulness in the context of engine prediction, the application of dimensional analysis is illuminating. The creation of groups which are actually non-dimensional is less important than obtaining groups with the correct quantities in them. The reasoning behind these ideas is discussed in Chapter 1 of Cumpsty (1989). For compatibility with the usual terminology the phrase ‘dimensional analysis’ will be retained here.

Using the ideas developed on the basis of dynamic scaling it is possible to estimate the engine performance at different altitudes and flight Mach numbers when the engine is operating at the same non-dimensional condition. From this it is possible to assess the consequences of losing thrust from an engine and the provision that needs to be made to cope with this at either take off or cruise.

ENGINE VARIABLES AND DEPENDENCE

Figure 8.1 shows a schematic engine installed under a wing. The only effects of the pylon are assumed here to be the transmission of a force between the engine and the wing and the passage of fuel to the engine.

In practice we frequently encounter “thin” plates whose thickness is small compared with all other dimensions. Such a plate, undergoing small displacements, may be analyzed with the approximations that the strains vary linearly across the plate, (out-of-plane) shear deformations are negligible, and the out-of-plane normal stress σz and shear stresses τxz, τyz are small compared with the in-plane normal σx, σy, and shear τxy stresses.

Under certain conditions, solutions may be obtained for thin plates either by the solution of the differential equations representing equilibrium or by energy methods. Here we demonstrate the use of the first method via the example of long plates and the second method via examples of rectangular plates either with symmetrical layup or with orthotropic and symmetrical layup. (For orthotropic plates the directions of orthotropy are parallel to the edges of the plate.) We chose these three types of problems because (i) they illustrate the analytical approaches and the use of the relevant equations, (ii) solutions can be obtained without extensive numerical algorithms, and last, but not least, (iii) they are of practical interest. Additionally, and importantly, these problems provide insights that are useful when analyzing plates by numerical methods.

Although the specification of orthotropy may seem to be overly restrictive, in fact it does not unduly limit the applicability of the analyses. The reason for this is that plates are often made according to the 10-percent rule, and such plates behave similarly to orthotropic plates.

In this chapter we consider thin composite shells, which we analyze on the basis of the main assumptions employed in the theory of thin plates. However, there is a major difference in the behavior of plates and shells subjected to external loads. Plates resist transverse loads by bending and by transverse shear forces. On the other hand, thin shells resist the transverse loads mostly by membrane forces, which, at any given point, are in the plane tangential to the reference surface (Fig. 8.1). These membrane forces are determined by the “membrane theory of shells,” which neglects bending moments. The resulting stresses, strains, and deformations are reasonable except near supports and in the vicinities of abrupt changes in loads. For thick shells (whose thickness is comparable to the radii of curvature) or when regions near supports or concentrated loads are of interest, more complex analytical solutions or finite element methods must be employed. The decision as to which method to use rests with the individual and depends on his or her experience with analytical solutions and finite element calculations.

Herein we treat thin shells whose thickness h is small compared with all other dimensions and with the radii of curvatures (Fig. 8.2).