Introduction

A separate chapter is devoted to polymers because of their engineering importance and because their mechanical behavior is so different from that of metals and ceramics. The mechanical response of polymers is far more time-dependent than that of crystalline materials. Viscoelastic effects (Chapter 15) are much more important in polymers than in metals or ceramics. The properties of polymers are also much more sensitive to temperature than those of other materials. Changes of molecular orientation with deformation cause large changes in properties and a much greater degree of anisotropy than is observed in metals or ceramics. The phenomena of crazing and rubber elasticity have no analogs in crystalline materials. Some polymers exhibit very large tensile elongations. Although a few alloys exhibit shape-memory behavior, the effect is much greater in polymers, more common, and of greater technological importance.

Elastic behavior

Elastic strains in metals and ceramics occur by stretching of primary metallic, covalent, or ionic bonds. The elastic modulus of most crystals varies with direction by less than a factor of 3. The effects of alloying, and of thermal and mechanical treatments on the elastic moduli of crystals are relatively small. As the temperature is increased from absolute zero to the melting point, Young's modulus usually decreases by a factor of no more than 5. For polymers, however, a temperature change of 30°C may change the elastic modulus by a factor of 1000.

Introduction

In classic elasticity there is no time delay between the application of a force and the deformation that it causes. For many materials, however, there is additional time-dependent deformation that is recoverable. This is called viscoelastic or anelastic deformation. When a load is applied to a material, there is an instantaneous elastic response, but the deformation also increases with time. This viscoelasticity should not be confused with creep (Chapter 16), which is time-dependent plastic deformation. Anelastic strains in metals and ceramics are usually so small that they are ignored. In many polymers, however, viscoelastic strains can be very significant.

Anelasticity is responsible for the damping of vibrations. A high damping capacity is desirable where vibrations might interfere with the precision of instruments or machinery and for controlling unwanted noise. A low damping capacity is desirable in materials used for frequency standards, in bells, and in many musical instruments. Viscoelastic strains are often undesirable. They cause sagging of wooden beams, denting of vinyl flooring by heavy furniture, and loss of dimensional stability in gauging equipment. The energy associated with damping is released as heat, which often causes an unwanted temperature increase. Study of damping peaks and how they are affected by processing has been useful in identifying mechanisms. The mathematical descriptions of viscoelasticity and damping will be developed in the first part of this chapter. Then several damping mechanisms will be described.

Introduction

This book is concerned with the mechanical behavior of materials. The term mechanical behavior refers to the response of materials to forces. Under load, a material may either deform or break. The factors that govern a material's resistance to deformation are very different from those governing its resistance to fracture. The word strength may refer either to the stress required to deform a material or to the stress required to cause fracture; therefore, care must be used with the term strength.

When a material deforms under small stresses, the deformation may be elastic. In this case, when the stress is removed, the material will revert to its original shape. Most of the elastic deformation will recover immediately. There may be, however, some time-dependent shape recovery. This time-dependent elastic behavior is called anelastic or viscoelastic.

Larger stresses may cause plastic deformation. After a material undergoes plastic deformation, it will not revert to its original shape when the stress is removed. Usually, high resistance to deformation is desirable, so that a part will maintain its shape in service when stressed. On the other hand, it is desirable to have materials deform easily when they are being formed by rolling, extrusion, or other methods. Plastic deformation usually occurs as soon as the stress is applied. At high temperatures, however, time-dependent plastic deformation called creep may occur.

Fracture is the breaking of a material into two or more pieces. If fracture occurs before much plastic deformation occurs, we say that the material is brittle.

Introduction

Once the concept of dislocations was accepted, there were three important questions to be answered.

1. When a single crystal is deformed, slip occurs with shear offsets of thousands of atom distances on relatively widely spaced planes, rather than uniformly throughout the crystal. See Figure 10.1. Why doesn't slip occur uniformly at an atomic scale?

2. Cold working increases the dislocation content of crystals even though dislocations must run out of the crystals. See Figures 10.2 and 10.3. Where do the additional dislocations come from?

3. The yield stress increases as the number of dislocations increases even though without any dislocations, the strength would be even higher. See Figure 10.4. Why does the yield stress increase with dislocation density?

Frank–Read sources

The first two of these questions can be answered in terms of the Frank–Read source, which generates dislocations. Suppose that there is a dislocation of finite length, AB, in a slip plane (Figure 10.5). The dislocation leaves the plane at A and B, but the end points are pinned at A and B. A shear stress, τ, acting on the plane will create a force that causes the dislocation to bow. This bowing is resisted by the line tension of the dislocation. As the shear stress is increased the dislocation will bow out until it spirals back on itself. The sections that touch annihilate each other, leaving a dislocation loop that can expand under the stress and a restored dislocation segment between the pinning points.

The stereographic projection is often used to represent the angular relations between directions and planes in a crystal. This projection system can be visualized by imagining a tiny (infinitesimal) crystal at the center of a sphere. All of the planes and directions of interest are extended until they intersect the surface of the sphere. Directions intersect the sphere as points and planes intersect it as great circles, as shown in Figure B.1 These points and great circles are then projected onto a flat surface. See Figure B.2 The problem of plotting these on a flat surface is exactly the same as the mapmaker's problem of plotting the spherical surface of the earth. For crystals, it is necessary to plot only half of the spherical surface, because the opposite hemisphere is identical. Barrett and Cullity describe the details of stereographic projection.

The book entitled Fundamentals of Jet Propulsion with Applications, by Ronald D. Flack, will satisfy the strong need for a comprehensive, modern book on the principles of propulsion – both as a textbook for propulsion courses and as a reference for the practicing engineer.

Professor Flack has written an exciting book for students of aerospace engineering and design. His book offers a combination of theory, practical examples, and analysis utilizing information from actual aerospace databases to motivate students; illustrate, and demonstrate physical phenomena such as the principles behind propulsion cycles, the fundamental thermofluids governing the performance of – and flow mechanisms in – propulsion components, and insight into propulsion-system matching.

The text is directed at upper-level undergraduate students in mechanical and aerospace engineering, although some topics could be taught at the graduate level. A basic understanding of fluid mechanics, gas dynamics, and thermodynamics is presumed, although most principles are thoroughly reviewed early in the book and in the appendixes. Propulsion is the primary thrust, but the material can also be used for the fundamentals of ground- and marine-based gas turbines. Turbomachinery is a secondary target, and the fundamentals and some advanced topics in compressors and turbines are covered. The specific and unique contributions of this book and its strengths are that fundamental mathematics and modern hardware are both covered; moreover, subjects are treated with equal emphasis.

Introduction

The purposes of the diffuser or inlet are first to bring air smoothly into the engine, second to slow the fluid and to increase the pressure, and third to deliver a uniform flow to the compressor. As indicated by studies for cycle analyses in Chapters 2 and 3, engine performance improves with increasing pressure to the burner. The first component the air encounters is the diffuser, and the second component is the compressor. Thus, if the diffuser incurs a large total pressure loss, the total pressure into the burner will be reduced by the compressor total pressure ratio times this loss. For example, if 2 psia are lost in the diffuser, for a large engine this can result in 50 psia less in the burner.

The losses result from several processes and affect engine performance in several ways. First, losses in total pressure occur outside of the diffuser primarily as the result of shock interactions. The flow outside the diffuser can also actually affect the flow around the entire engine and add a drag to the aircraft. Second, ideally the flow inside the diffuser is uniform and the streamlines are smooth. However, because of the unfavorable pressure gradient, the boundary layer on the walls tends to grow and separate. This has three subeffects.

Introduction

As discussed in previous chapters, a fan or compressor is the first rotating component that the fluid encounters. A cross-sectional view of a compressor for a simple, single-shaft turbojet is shown in Figure 6.1. The basic function of a compressor is to impart kinetic energy to the working fluid (air) by means of some rotating blades and then to convert the increase in energy to an increase in total pressure, which is needed by the combustor. The limits of operation of an engine are often dictated by a compressor, as is discussed in this chapter. Furthermore, the design of an efficient axial flow fan or compressor remains such a complex process that the success or failure of an engine often revolves around the design of a compressor. Many fundamental and advanced design details are available in Cumpsty (1988), Hawthorne (1964), Horlock (1958), Howell (1945a, 1945b) and Johnsen and Bullock (1965). Rhie et al. (1998), LeJambre et al. (1998), Adamczyk (2000), and Elmendorf et al. (1998) demonstrate how modern computational fluid dynamic (CFD) tools can effectively be used for the complex three-dimensional analysis and design of compressors.

Compressors were the main stumbling block of the early engines and the primary cause of the delays in the development of jet engines for World War II. Dunham (2000) and Meher-Homji (1996, 1997a, 1999) present interesting historical perspectives and technical information on early compressor development.

Introduction

In the previous seven chapters, much emphasis has been placed on the analysis and design of individual components of gas turbines. On the other hand, in Chapters 2 and 3 cycle analyses are presented for ideal and nonideal engines as a whole in which the different components are integrated into a system. However, in Chapter 3, component efficiencies and some characteristics are assumed or assigned a priori for the overall cycle analyses. In general, however, the previous seven chapters demonstrate, through the use of either theoretical analyses or empirical characteristic curves (or “maps”), that component efficiencies and other operating characteristics change significantly at different conditions–for example, at different flow rates and rotational speeds.

To understand the overall effects of changing operating conditions, one can consider an engine initially at some steady-state operating condition. However, as the fuel injection rate in the burner is changed, the turbine inlet temperature and pressure are changed. Thus, the turbine will change rotational speeds. Because the turbine and compressor are on the same shaft, however, this change in rotational speed in turn changes the ingested mass flow rate and pressure ratio developed by the compressor, which influences the burner inlet pressure and the turbine inlet pressure, and so on. Eventually, the engine will again reach a different steady-state operating condition.

My goal with this project is to repay the gas turbine industry for the rewarding profession it has provided for me over the course of more than three decades. At this point in my career, student education is a real passion for me and this book is one way I can archive and share experiences with students. I have written this text thinking back to what I would have liked as an undergraduate student nearly 40 years ago. Thus, this work has been tailored to be a very student friendly text.

This book is intended to serve primarily as an introductory text in air-breathing jet propulsion. It is directed at upper-level undergraduate students in mechanical and aerospace engineering. A basic understanding of fluid mechanics, gas dynamics, and thermodynamics is presumed; however, thermodynamics is reviewed, and an appendix on gas dynamics is included for reference. Although the work is entitled Jet Propulsion, it can well be used to understand the fundamentals of “aeroderivative” ground- or marine-based gas turbines such as those used for marine propulsion, ground transportation, or power generation. Although turbomachinery is not the primary target of the text, it is the book's secondary focus, and thus the fundamentals of, and some advanced topics in, compressors and turbines are also covered.

This text covers the basic operating principles of jet engines and gas turbines. Both the fundamental mathematics and hardware are addressed.

Introduction

Chapter 2 has included a review of the ideal thermodynamic processes of different components, ideal cycle analyses for various types of engines, and a discussion of performance trends. All of the components were assumed to operate without any losses, and the gas was assumed to be perfect and to have constant specific heats throughout the entire engine. The objectives of this chapter are to relax these assumptions, to explain the physical conditions that lead to losses, and to review the nonideal thermodynamic processes from, for example, Keenan (1970) or Wark and Richards (1999) and the gas dynamic processes from, for example, Anderson (1982), Zucrow and Hoffman (1976), or Shapiro (1953). Efficiency levels and losses are included for the different components so that more realistic predictions can be made for overall engine performance. Even though most components operate with individually with relatively high efficiencies (upwards from 90%), when all the components are coupled the overall engine performance can be reduced drastically. However, in general, the performance trends do not change. Also, note that simple single- or two-term expressions are used to model the losses in each component in this chapter for simplicity. Each component is covered separately and in detail. At this stage these loss terms are specified a priori even though, in a real engine, the different component losses are dependent on the engine operating point and are thus dependent on each other.

Introduction

The burner and afterburner are the only components through which energy is added to the engine. That is, in these two components the total temperature of the gas increases. For the primary burner, a part of this energy is used by the turbine to drive the compressor, and the other part is left to generate a high-velocity gas from the nozzle, generating thrust. For the afterburner, all of this energy increase is used to generate an increase of the fluid enthalpy and consequently a higher velocity gas from the nozzle, generating more thrust. As a result of these direct impacts, efficient operation of these components is necessary for the overall efficiency of the engine. However, several complex considerations must be realized in the design of either of these components, and some of the more advanced topics are summarized by Lefebvre (1983) and Peters (1988). Furthermore, Malecki et al. (2001) demonstrate the application of CFD predictions to modern combustor design.

The following are essential considerations in the design of a burner:

1. A major objective is complete combustion or fuel will be wasted.

2. Minimal total pressure loss is another important design goal. As discussed in Section 9.2, these first two objectives are in direct conflict.

3. All of the combustion must take place in the combustor and not the turbine, or the turbine life will be reduced.

4. […]