Airbreathing Propulsion

The earliest efficient reversible thermodynamic cycle was proposed by Nicolas Léonard Sadi Carnot (1796–1832) with two isotherms and two isentropes in a cycle, but it remained mostly a curiosity until today. One of the earliest engine types used for aircraft applications was piston engines running on Otto and diesel cycles. The inventor of the Otto engine, Nicholas A. Otto (1832–1891), built a successful engine in 1876. These engines helped drive the Industrial Revolution in Europe. However, the workshops had low roofs, and some early engines built vertically required holes in the roof. In the absence of spark-plugs, ignition was done by positioning a flame near the top of the cylinder and a sliding valve would open to ignite the air–fuel mixture. There was no crank shaft, and the force of the cylinder was transferred through an arrangement of linear gear and some “catcher” pins to transfer the linear motion to a rotary motion. Sometimes the “catcher” would fail and the linear rod would go through the hole in the roof. Later these engines were built with a horizontal axis. Such early engines are on display at the German Museum in Munich, Germany. The inventor of the diesel cycle, Rudolf Diesel (1853–1913), was born in Paris to German parents who later moved to London because of Franco-Prussian War in 1870. He built the first engine in 1893 in MAN’s German factory in Augsburg. Diesel planned initially to build an engine based on an earlier proposal of the reversible Carnot cycle, which was to have the best thermodynamic efficiency within a given temperature ratio. He realized very quickly, however, that to realize a Carnot cycle, one would have to run the thermodynamic process of two isotherms as slowly as possible, but in an actual engine the two adiabatic processes must be run as fast as possible, with the result that the two opposite requirements cannot be satisfied. Further, he realized that the Carnot cycle, in spite of the best thermodynamic efficiency, has a very small specific work output. On the other hand, an Otto cycle, because the air and fuel are premixed, could have a very low compression ratio with the resultant low thermodynamic efficiency. Diesel therefore proposed a cycle consisting of two adiabatic processes: one constant-pressure and one constant-volume. Diesel disappeared in 1913 while crossing the English Channel during a storm.

In studying an ideal cycle relevant to aircraft propulsion, one can have a good insight into the relevant important parameters that give the performance parameters of a given system. For such a study, the following assumptions are usually taken:

and no losses. In this chapter, we will discuss the various components of the losses in a one-dimensional channel and their application in various components of a gas-turbine engine.

A turbomachine consists of rows of blades, some of which rotate (rotor) while others remain stationary (stator). As explained earlier, work can be extracted or added in a rotating row of blades only, where the stagnation pressure and stagnation temperature change, while in the stationary row of blades, the stagnation temperature and stagnation pressure do not change (except for the small effect of friction on the stagnation pressure). Hence, in a compressor, the air is accelerated in the rotor (the stagnation pressure is increased) and is decelerated in the stator, where the kinetic energy of air is converted into the pressure (same total pressure; the static pressure is increased). On the other hand, air is accelerated in a nozzle or stator blades’ row at constant stagnation temperature and static pressure with increasing air (gas) speed, and subsequently the kinetic energy is converted into mechanical energy in a rotating row of blades, where the stagnation pressure and temperature decrease. For a single stage of turbomachinery blades, we thus have a row of rotating blades and a row of stationary blades; for compressors, the rotating blades come first, but for turbines, the stationary blades come first. We therefore have two rows of blades, and depending on the direction of motion of air (gas), they act as a compressor or turbine stage, as shown in Fig. 4.1. They are numbered 1–3 from the rotor side. If it is a compressor, air is scooped at blade edge 1 in the rotor and is pushed toward edge 2 of the rotor after accelerating it; it is subsequently decelerated in the stator row from 2 to 3. On the other hand, as turbine air (or gas) enters the stator at 3, it is accelerated up to 2 while the static pressure is lowered, but the stagnation temperature and stagnation pressure remain the same (except for a small loss in stagnation pressure due to friction), and then while passing through the rotor and exhausting at 1, it converts the kinetic energy into mechanical energy.

Earlier we defined the blade efficiency in terms of both the static enthalpy change and the kinetic energy. For axial turbomachinery with or without friction losses, the total enthalpy should remain constant, and thus the energy equation is written as

For the design of turbomachines as a whole, as well as for individual stages, and to understand the performance of stages, certain similarity rules are used. For this purpose, the following notations are used:

With the definition of the work coefficient in (6.4a) and (6.4b), we can now write from (4.22a) to (4.22d) the nondimensional azimuthal velocity component expressions as follows:

While single- and multiple-stage centrifugal compressors are used exclusively for terrestrial applications, since per stage, a centrifugal compressor gives a much higher compression ratio, they have not been used for aircraft applications, except in small engines, such as the old Goblin or the Rolls-Royce DART turboprop engine for the Avro-748 aircraft; in the latter, a two-stage centrifugal compressor is used. There are several reasons for the infrequent use of centrifugal compressors over axial compressors: (a) Centrifugal compressors have a slightly lower efficiency than axial compressors; (b) centrifugal compressors have a much smaller air throughput over axial compressors, and they also have a very large frontal area, giving a large drag. However, the centrifugal compressor rotors are structurally much more robust and can be built, especially for terrestrial applications, by simple welding of the blades and by using materials like plastics for applications with hazardous gases.

While the aircraft gas turbines are designed to run efficiently in a given environment and at given operating conditions, it is evident that, except under cruise conditions, the engine is off the design conditions. In this chapter, we therefore consider operation of the gas turbine with respect to operation of the design conditions.

Before the jet-propelled, engine-driven aircrafts came into existence, propellers were used in aircrafts with piston and turboprop engines. In addition, they have been used for multiple applications, such as in cooling towers, cooling of car radiators, windmill generators, etc. As an example of the last application, Fig. 10.1 is a photograph of a series of windmills set up on a hill in a California desert.