Introduction

As discussed in Chapter 6, the basic operating principle of a compressor is to impart kinetic energy to the working fluid by the means of some rotating blades and then to convert the increase in energy to an increase in total pressure. Axial flow compressors are covered in Chapter 6. These compressors are used on large engines and gas turbines. However, for small engines – particularly turboshafts and turboprops – centrifugal (or radial) compressors are used.

These compressors have higher single-stage pressure ratios than axial compressors (typically 2 to 4 compared with ~1.25). As a result, centrifugal compressors have lower cross-sectional flow areas per mass flow rate than do axial compressors. They also have larger diameters but shorter lengths per unit mass flow rate than do axial compressors. However, the rotating element (impeller) of the compressor is an integral unit of blades and a disk, and thus if one blade is damaged the entire unit is replaced. The weights of centrifugal units are approximately the same as for axial compressors used for the same application. They, however, demonstrate the characteristic of lower flow rates. As a result, they are physically small units with low flow rates, which makes them ideal for helicopter and small aircraft applications.

Introduction

Two remaining components that affect the overall performance of a turbofan engine are the bypass duct and mixer, as shown in Figure 10.1. These are relatively simple compared with the other components but should be included because they both generate losses in total pressure. Because the length-to-flow-width ratio of the bypass duct is moderate, the duct can incur significant losses. Also, it is desirable to have a uniform temperature gas entering the afterburner or nozzle so that these components operate near peak efficiency. Mixing of two fluid streams at different temperatures is a highly irreversible process, and a mixer consists of three-dimensional vanes in both the radial and circumferential (annular) directions. Thus, with good mixing of the low-temperature bypassed air and high-temperature primary air, further significant losses can occur. Owing to the temperatures exiting from the turbine, mixers are generally fabricated from a nickel-based alloy. This chapter covers total pressure losses in these two components.

Total Pressure Losses

Three irreversible mechanisms exist for pressure drops and total pressure losses to occur in ducts and mixers. The first is frictional flow in the duct primarily due to the viscous effects in the boundary layer. The second is the irreversible mixing process of two gas streams with different properties in the mixer.

History of Propulsion Devices and Turbomachines

Manmade propulsion devices have existed for many centuries, and natural devices have developed through evolution. Most modern engines and gas turbines have one common denominator: compressors and turbines or “turbomachines.” Several of the early turbomachines and propulsive devices will be described in this brief introduction before modern engines are considered. Included are some familiar names not usually associated with turbomachines or propulsion. Many of the manmade devices were developed by trial and error and represent early attempts at design engineering, and yet some were quite sophisticated for their time. Wilson (1982), Billington (1996), ASME (1997), Engeda (1998), St. Peter (1999), and others all present very interesting introductions to some of this history supplemented by photographs.

One of the earliest manmade turbomachines was the aeolipile of Heron (often called “Hero” of Alexandria), as shown in Figure 1.1. This device was conceived around 100 B.C. It operated with a plenum chamber filled with water, which was heated to a boiling condition. The steam was fed through tubes to a sphere mounted on a hollow shaft. Two exhaust nozzles located on opposite sides of the sphere and pointing in opposite directions were used to direct the steam with high velocity and rotate the sphere with torque (from the moment of momentum) around an axis – a reaction machine. By attaching ropes to the axial shaft, Heron used the developed power to perform tasks such as opening temple doors.

Introduction

As discussed in Chapters 1 to 3, the purpose of the turbine is to extract energy from the fluid to drive the compressive devices. The actual operation of the turbine is in some respects similar to, but opposite that, of the compressor. That is, energy is extracted from the fluid and the pressure and temperature drop through the turbine. Typically, 70 to 80 percent of the enthalpy increase from the burner is used by the turbine to drive the compressor. The remainder is used to generate thrust in the nozzle.

Two major differences are apparent between compressors and turbines, however. First, the pressure decreases through a turbine. In compressors, an adverse pressure gradient is present, which has the potential to cause blade stall. Such problems do not occur in a turbine, and turbine efficiency is typically higher than compressor efficiency. Also, because of this favorable pressure gradient, fewer stages are required for a turbine than for a compressor. As a result, the aerodynamic loading per stage is higher for a turbine than for a compressor. However, the inlet temperature is very high and limits the operation of the turbine. Thus, aerodynamically, the turbine is somewhat easier to design but is structurally more difficult.

Introduction

Chapter 1 identified the basic engine types and defined the important operating performance parameters of gas turbines. That chapter also reviewed the fundamental thermodynamics of cycles and established that gas turbines consist of several important components. Although the operation and design of each component are essential for the efficient operation of the entire jet engine, such details will not be covered yet. Instead, the overall engine will be analyzed for given components with given characteristics. Later chapters address component operation and design. This chapter considers the ideal components. Its objective is to review the fundamental ideal thermodynamic processes (e.g., from Keenan 1970 or Wark and Richards 1999) and the gas dynamic processes (e.g., from Anderson 1982, Zucrow and Hoffman 1976, or Shapiro 1953) and to explain the physical processes for each of the components. Components are assembled in a “cycle analysis” to make it possible to predict the overall engine performance. This chapter presents quantitative examples to demonstrate the analysis and to give the reader a physical understanding of characteristics. Trend studies are also discussed to show the dependence of the overall characteristics on individual parameters. In Chapter 3, nonideal components in which losses occur are used to evaluate the overall performance of an engine. Chapters 2 and 3 each cover all basic engine configurations. As will be seen, the ideal cycle analysis results in relatively short closed-form equations for the engine characteristics. Developing these equations serves three purposes.

Introduction

This book discusses six basic types of turbomachines directly: axial flow compressors, axial flow pumps, radial flow compressors, centrifugal pumps, axial flow gas turbines, and axial flow hydraulic turbines. Two other basic types are used in practice that are not covered in this text because of their limited application in propulsion: radial inflow gas turbines and radial inflow hydraulic turbines. The basic derivations of the equations for each machine type are covered in this appendix rather than in the chapters in which the machines are discussed. As will be shown, the resulting fundamental equations apply to all types of turbomachines, regardless of categorization. Application of the equations with complementing velocity polygons is, however, different for the different turbomachines. Advanced details can be found in texts, including Balje (1981), Cohen et al. (1996), Dixon (1998, 1975), Hah (1997), Hill and Peterson (1992), Howell (1945a, 1945b), Japikse and Baines (1994), Logan (1993), Osborn (1977), Shepherd (1956), Stodola (1927), Turton (1984), Vavra (1974), Wallis (1983), Whittle (1981), and Wilson (1984). Furthermore, Rhie et al. (1998), LeJambre et al. (1998), Adamczyk (2000), and Elmendorf et al. (1998) show how modern computational fluid dynamic (CFD) tools can effectively be used for the complex three-dimensional analysis and design of turbomachines.

Single-Stage Energy Analysis

In this section, the equations are derived so that the internal fluid velocities can be related to the pressure change, power, and other important turbomachine characteristics.

Introduction

The basic concepts of compressible flow are applied in all of the chapters in this book. Specifically, in Chapters 4 (diffusers), 5 (nozzles), 9 (combustors), and 10 (mixers), analyses of fundamental, compressible, steady-state, one-dimensional flow are used to predict total pressure losses and other characteristics in the different components. Thus, to avoid repetition of material, this appendix is presented to summarize different fundamental processes. Included in the processes are the stagnation process, ideal gas properties, isentropic flow with area changes, frictional adiabatic with constant area (Fanno) flow, flow with heat addition and constant area (Rayleigh), normal and oblique shocks, flow with drag objects, mixing flows, and generalized one-dimensional flow, which allows the combination of two or more different fundamental phenomena. In all of the preceding analyses a control volume approach is used and the flow is assumed to be steady and uniform at the different cross-sectional flow surfaces. Such processes are covered in detail in fundamental gas dynamics texts such as Anderson (1982), Liepmann and Roshko (1957), Shapiro (1953), and Zucrow and Hoffman (1976). The flow is assumed to be one-dimensional. Although flow can be two- or three-dimensional in components, a one-dimensional analysis can lead to reasonable results for many cases. For all cases the gas is assumed to be ideal.

The subject of multiphase flows encompasses a vast field, a host of different technological contexts, a wide spectrum of different scales, a broad range of engineering disciplines, and a multitude of different analytical approaches. Not surprisingly, the number of books dealing with the subject is voluminous. For the student or researcher in the field of multiphase flow this broad spectrum presents a problem for the experimental or analytical methodologies that might be appropriate for his/her interests can be widely scattered and difficult to find. The aim of the present text is to try to bring much of this fundamental understanding together into one book and to present a unifying approach to the fundamental ideas of multiphase flows. Consequently the book summarizes those fundamental concepts with relevance to a broad spectrum of multiphase flows. It does not pretend to present a comprehensive review of the details of any one multiphase flow or technological context, although reference to books providing such reviews is included where appropriate. This book is targeted at graduate students and researchers at the cutting edge of investigations into the fundamental nature of multiphase flows; it is intended as a reference book for the basic methods used in the treatment of multiphase flows.

I am deeply grateful to all my many friends and fellow researchers in the field of multiphase flows whose ideas fill these pages. I am particularly indebted to my close colleagues Allan Acosta, Ted Wu, Rolf Sabersky, Melany Hunt, Tim Colonius, and the late Milton Plesset, all of whom made my professional life a real pleasure.

Introduction

From a practical engineering point of view one of the major design difficulties in dealing with multiphase flow is that the mass, momentum, and energy transfer rates and processes can be quite sensitive to the geometric distribution or topology of the components within the flow. For example, the geometry may strongly effect the interfacial area available for mass, momentum, or energy exchange between the phases. Moreover, the flow within each phase or component will clearly depend on that geometric distribution. Thus we recognize that there is a complicated two-way coupling between the flow in each of the phases or components and the geometry of the flow (as well as the rates of change of that geometry). The complexity of this two-way coupling presents a major challenge in the study of multiphase flows and there is much that remains to be done before even a superficial understanding is achieved.

An appropriate starting point is a phenomenological description of the geometric distributions or flow patterns that are observed in common multiphase flows. This chapter describes the flow patterns observed in horizontal and vertical pipes and identifies a number of the instabilities that lead to transition from one flow pattern to another.

Topologies of Multiphase Flow

Multiphase Flow Patterns

A particular type of geometric distribution of the components is called a flow pattern or flow regime and many of the names given to these flow patterns (such as annular flow or bubbly flow) are now quite standard.