A gas turbine engine is a device that is designed to convert the thermal energy of a fuel into some form of useful power, such as mechanical (or shaft) power or a high-speed thrust of a jet. The engine consists, basically, of a gas generator and a power conversion section, as shown in Figures 1.1 and 1.2.

In this chapter, we will get familiar with a unique performance gauge, which is not process dependent, but is rather state dependent, by definition. In other words, the newly defined, so-called “polytropic” efficiency is independent of the size of a turbomachine (in terms of the total-to-total pressure ratio). In addition, we will have a means of computing the overall efficiency of several stages, sharing the same total-to-total magnitudes of pressure ratio and efficiency, without having to resort to the thermodynamics of each individual stage. The point is made that adding more stages to a multistage turbomachine will have drastic, but totally opposite, effects on turbines as contrasted to compressors. We will prove through this exercise that adding more turbine stages enhances the performance of the final turbine configuration. The effect in compressors, on the other hand, is that of performance deterioration.

Consider the simplest nonafterburning, single-spool turbojet engine, which is schematically shown in Figure 12.1. Assuming a viable (i.e., stable compressor) operation mode, there are obvious constrains relating the gas-generator components to one another. These generally enforce the uniformity of shaft speed, as well as ensure the mass and energy conservation principles (Figure 12.2).

Utilization of axial-flow compressor stages (Figure 9.1) in gas turbine engines is a relatively recent development. The history of this compressor type began after an era when centrifugal compressors were dominant (Figure 9.2). It was later confirmed, on an experimental basis, that axial-flow compressors can run much more efficiently. Earlier attempts to build multistage axial-flow compressors entailed running multistage axial-flow turbines in the reverse direction. As presented in Chapter 4, a compressor-stage reaction, in this case, will be negative, a situation that has its own performance degradation effect. Today, carefully designed axial-flow compressor stages can very well have efficiencies in excess of 80%. A good part of this advancement is owing to the standardization of thoughtfully devised compressor-cascade blading rules.

In this chapter, a turbomachinery-related nondimensional groupings of geometric dimensions and thermodynamic properties will be derived.

In this chapter, the flow-governing equations (conservation laws) are reviewed, with applications that are purposely turbomachinery related. Particular emphasis is placed on the total (or stagnation) flow properties. A turbomachinery-adapted Mach number definition is also introduced as a compressibility measure of the flow field. A considerable part of the chapter is devoted to the total-relative properties, which, together with the relative velocity, define a legitimate thermophysical state. Different means of gauging the performance of a turbomachine, and the wisdom behind each of them, are discussed. Also explored is the entropy-production principle, as a way of assessing the performance of turbomachinery components. The point is stressed that the calculation of entropy production may indeed be desirable, for it is the only meaningful performance measure that is accumulative (or addable) by its mere definition.

From a historical viewpoint, the centrifugal compressor configuration was developed and used, even in the propulsion field, well before axial-flow compressors were. Due to their large envelope and weight (Figure 11.1), the common belief that such a “bulky” compressor type has no place except in aerospace applications is not exactly accurate. For example, with a typical total-to-total pressure ratio of, for example, 5:1, it would take up to three axial-compressor stages to absorb similar amounts of shaft work that a single centrifugal compressor stage would. In fact, the added engine length, with so many axial stages, would increase the skin friction drag on the engine exterior, almost as much as the profile drag, which is a function of the frontal area.

A brief introduction to gas turbine engines was presented in Chapter 1. Review of the different engines included in this chapter reveals that most of these engine components are composed of “lifting” bodies, termed airfoil “cascades,” some of which are rotating, while others are stationary. These are all, by necessity, bound by the hub surface and the engine casing (or housing), as shown in Figures 2.1–2.5. As a result, the problem becomes one of the internal-aerodynamics type, as opposed to such traditional external-aerodynamics topics as “wing theory” and others. Referring, in particular, to the turbofan engines in Chapter 1 (e.g., Figure 1.3), these components may come in the form of ducted fans. These, as well as compressors and turbines, can be categorically summed up under the term “turbomachines.” Being unbound, however, the propeller of a turboprop engine (Figure 1.2) does not belong to the turbomachinery category.

Historically, the first axial turbine utilizing a compressible fluid was a steam turbine. Gas turbines were later developed for engineering applications where compactness is as important as performance. However, the successful use of this turbine type had to wait for advances in the area of compressor performance. The viability of gas turbines was demonstrated upon developing special alloys that possess high strength capabilities at exceedingly high turbine inlet temperatures.

Figure 4.1 shows a general-type mixed-flow compressor rotor. The thermophysical states 1 and 2 represent average conditions over the entire inlet and exit stations, respectively. The rotor-blade-to-blade hub-to-casing passage is the control volume, and other than the continuity and energy equations (Chapter 3), we are now left with the momentum-conservation principle to implement.

Over more than three decades now, radial-inflow turbines have been established as a viable alternative to its axial-flow counterpart, specifically in power-system applications. Despite its relatively primitive means of fabrication, radial turbines are capable of extracting a large per-stage shaft work in small mass-flow rate situations. This turbine category also offers little sensitivity to tip clearances, in contrast to axial-flow turbines. Nevertheless, the turbine large envelope, bulkiness, and heavy weight (Figure 10.1) virtually prohibits its use in propulsion devices.