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7862 results in Fluid dynamics and solid mechanics

Page 288 of 394

  • 11 - Centrifugal Compressors

  • Erian A. Baskharone, Texas A & M University
  • Book:
    Principles of Turbomachinery in Air-Breathing Engines
    Published online:
    05 September 2012
    Print publication:
    31 July 2006, pp 471-528

  • Summary

    From a historical viewpoint, the centrifugal compressor configuration was developed and used well before axial-flow compressors, even in the propulsion field. The common belief that such a “bulky” compressor type, because of its large envelope and weight (Fig. 11.1), has no place except in ground applications is not exactly accurate. For example, with a typical total-to-total pressure ratio of, say, 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.

    Despite the preceding argument, the tradition remains that the centrifugalcompressor propulsion applications are unpopular. Exceptions to this rule include turboprop engines and short-mission turbofan engines, as shown in Figure 11.2.

    An attractive feature of centrifugal compressors has to do with their off-design performance. Carefully designed, a centrifugal compressor will operate efficiently over a comparatively wider shaft speed range. This exclusive advantage helps alleviate some of the problems associated with the turbine-compressor matching within the gas generator.

    One of the inherent drawbacks of centrifugal compressors has to do with multiple staging. As illustrated in Figure 2.12, the excessive 180 flow-turning angle of the annular return duct, in this case, will increase the flow rotationality (in terms of vorticity) and encourage the cross-stream secondary flow migration. This simply sets the stage for high magnitudes of total pressure loss and boundary-layer separation.

  • 8 - Axial-Flow Turbines

  • Erian A. Baskharone, Texas A & M University
  • Book:
    Principles of Turbomachinery in Air-Breathing Engines
    Published online:
    05 September 2012
    Print publication:
    31 July 2006, pp 250-346

  • Summary

    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.

    In the history of axial turbines, most of the experience relating to the behavior of steam-turbine blading was put to use in gas-turbine blading and vice versa. This holds true as long as the steam remains in the superheated phase and not in the wet-mixture zone, for the latter constitutes a two-phase flow with its own problems (e.g., liquid impingement forces and corrosion).

    Stage Definition

    Figure 8.1 shows an axial-flow turbine stage consisting of a stator that is followed by a rotor. Figure 8.2 shows a hypothetical cylinder that cuts through the rotor blades at a radius that is midway between the hub and tip radii. The unwrapped version of the cylindrical surface in this figure is that where the stage inlet and exit velocity triangles will be required. As has been the terminology in preceding chapters, a stator airfoil will be termed a vane, and the rotor cascade consists of blades. An axial-flow turbine operating under a high (inlet-over-exit) pressure ratio would normally consist of several stages, each of the type shown in Figure 8.1, in an arrangement where the annulus height is rising in the through-flow direction (Fig. 8.3).

  • 6 - Radial-Equilibrium Theory

  • Erian A. Baskharone, Texas A & M University
  • Book:
    Principles of Turbomachinery in Air-Breathing Engines
    Published online:
    05 September 2012
    Print publication:
    31 July 2006, pp 208-233

  • Summary

    In Chapters 3 and 4, we studied major changes in the thermophysical properties of a flow as it traverses a turbine or compressor stage. The analysis then was onedimensional, with the underlying assumption that average flow properties will prevail midway between the endwalls. Categorized as a pitch-line flow model, this “bulk-flow” analysis proceeds along the “master” streamline (or pitch line), with no attention given to any lateral flow-property gradients.

    However, we know of, at least, one radius-dependent variable, namely the tangential “solid-body” velocity vector (U). The question addressed in this chapter is how the other thermophysical properties vary along the local annulus height at any streamwise location. The stator and rotor inlet and exit stations, being important “control” locations, are particularly important in this context. In the following, the so-called radial equilibrium equation is derived and specific simple solutions offered. Despite the flow-model simplicity, the radial-equilibrium equation enables the designer early on to take a look at preliminary magnitudes of such important variables as the hub and tip reactions prior to the detailed design phase.

    Assumptions

    For any axial stator-to-rotor or interstage gap in Figure 6.1, the following assumptions are made:

  • 1) The flow is under a steady-state condition.

  • 2) The flow is inviscid as well as adiabatic.

  • 3) The flow is axisymmetric (i.e., θ-independent).

  • 4) There are no radial shifts of the meridional streamlines (Fig. 6.2).

  • Preface

  • Erian A. Baskharone, Texas A & M University
  • Book:
    Principles of Turbomachinery in Air-Breathing Engines
    Published online:
    05 September 2012
    Print publication:
    31 July 2006, pp xv-xviii

  • Summary

    Beginning with the class-notes version, this book is the outcome of teaching the courses of Principles of Turbomachinery and Aerospace Propulsion in the mechanical and aerospace engineering departments of Texas A&M University. Over a period of fourteen years, the contents were continually altered and upgraded in light of the students' feedback. This has always been insightful, enlightening, and highly constructive.

    The book is intended for junior- and senior-level students in the mechanical and aerospace engineering disciplines, who are taking gas-turbine or propulsion courses. In its details, the text serves the students in two basic ways. First, it refamiliarizes them with specific fundamentals in the fluid mechanics and thermodynamics areas, which are directly relevant to the turbomachinery design and analysis aspects. In doing so, it purposely deviates from such inapplicable subtopics as external (unbound) flows around geometrically standard objects and airframe-wing analogies. Instead, turbomachinery subcomponents are utilized in such a way to impart the element of practicality and highlight the internal-flow nature of the subject at hand. The second book task is to prepare the student for practical design topics by placing him or her in appropriate real-life design settings. In proceeding from the first to the second task, I have made every effort to simplify the essential turbomachinery concepts, without compromising their analytical or design-related values.

    Judging by my experience, two additional groups are served by the book. First, practicing engineers including, but not necessarily limited to, those at the entry level. As an example, the reader in this category will benefit from the practical means of estimating the stage aerodynamic losses.

  • 9 - Axial-Flow Compressors

  • Erian A. Baskharone, Texas A & M University
  • Book:
    Principles of Turbomachinery in Air-Breathing Engines
    Published online:
    05 September 2012
    Print publication:
    31 July 2006, pp 347-397

  • Summary

    Introduction

    The utilization of axial-flow compressors (Fig. 9.1) in gas-turbine engines has been relatively recent. The history of this compressor type began following an era when centrifugal compressors (Fig. 9.2) were dominant. 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 because of the standardization of thoughtfully devised compressor-cascade blading rules.

    Comparison with Axial-Flow Turbines

    In passing through a reaction-turbine blade row, the flow stream will continually lose static pressure and enthalpy. The result is a corresponding rise in kinetic energy, making the process one of the flow-acceleration type. In axial compressors, by contrast, an unfavorable static pressure gradient prevails under which large-scale losses become more than likely. It is therefore sensible to take greater care in the compressor-blading phase. Another major difference, by reference to Figure 9.3, is that the compressor meridional flow path is geometrically converging as opposed to the typically diverging flow path of a turbine. This is a direct result of the streamwise density rise in this case, as will be discussed later. Referring to Figure 9.4, another difference in this context is a substantially greater blade count compared wth axial-turbine rotors, where the number of blades is typically in the low twenties.

  • 3 - Aerothermodynamics of Turbomachines and Design-Related Topics

  • Erian A. Baskharone, Texas A & M University
  • Book:
    Principles of Turbomachinery in Air-Breathing Engines
    Published online:
    05 September 2012
    Print publication:
    31 July 2006, pp 26-111

  • Summary

    In this chapter, the flow-governing equations (so-called 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 so-called 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 entropy production may indeed be desirable, for it is the only meaningful performance measure that is accumulative (or addable) by its mere definition.

    The flow behavior and loss mechanisms in two unbladed components of gas turbines are also presented. The first is the stator/rotor and interstage gaps in multistage axial-flow turbomachines. The second component is necessarily part of a turboshaft engine. This is the exhaust diffuser downstream from the turbine section. The objective of this component is to convert some of the turbine-exit kinetic energy into a static pressure rise. Note that it is by no means unusual for the turbine-exit static pressure to be less than the ambient magnitude, which is where the exhaust-diffuser role presents itself.

    In terms of the flow-governing equations, two nonvectorial equations will be covered in this chapter. These are the energy- and mass-conservation equations (better known as the First Law of Thermodynamics and the continuity equation, respectively).

  • 5 - Dimensional Analysis, Maps, and Specific Speed

  • Erian A. Baskharone, Texas A & M University
  • Book:
    Principles of Turbomachinery in Air-Breathing Engines
    Published online:
    05 September 2012
    Print publication:
    31 July 2006, pp 172-207

  • Summary

    Introduction

    In this chapter, a turbomachinery-related nondimensional groupings of geometrical dimensions and thermodynamic properties will be derived. These will aid us in many tasks, such as:

  • Investigating the full-size version of a turbomachine by testing (instead) a much smaller version of it (in terms of the total-to-total pressure ratio), an alternative that would require a much smaller torque and shaft speed, particularly in compressors;

  • Alleviating the need for blade cooling in the component test rig of a high-pressure turbine section by reducing (in light of specific rules) the inlet total temperature;

  • Predicting the consequences of the off-design operation by a turbomachine using the so-called turbine and compressor maps;

  • Making a decision, at an early design phase, in regard to the flow path type (axial or radial) of a turbomachine for optimum performance.

    • A good starting point is to outline the so-called similitude principle, beginning with the definition of geometric and dynamic similarities as they pertain to turbomachines.

    Geometrical Similarity

    Two turbomachines are said to be geometrically similar if the corresponding dimensions are proportional to one another. In this case, one turbomachine is referred to as a scaled-up (or scaled-down) version of the other. An obvious (but not silly) case here is the turbomachine and itself.

    Dynamic Similarity

    Two geometrically similar turbomachines are said to be dynamically similar if the velocity vectors at all pairs of corresponding locations are parallel to one another and with proportional magnitudes. In this case, the fluid-exerted forces, at corresponding locations, will be proportional to each other.

  • 2 - Overview of Turbomachinery Nomenclature

  • Erian A. Baskharone, Texas A & M University
  • Book:
    Principles of Turbomachinery in Air-Breathing Engines
    Published online:
    05 September 2012
    Print publication:
    31 July 2006, pp 9-25

  • Summary

    A brief introduction to gas-turbine engines was presented in Chapter 1. A 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 and others stationary. These are all, by necessity, bound by the hub surface and the engine casing (or housing), as shown in Figures. 2.1 through 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., Fig. 1.3), these components may come in the form of ducted fans. These, as well as compressors and turbines, can be categorically lumped under the term “turbomachines.” Being unbound, however, the propeller of a turboprop engine (Fig. 1.2) does not belong to the turbomachinery category.

    The turbomachines just mentioned, however, are no more than a subfamily of a more inclusive category. These only constitute the turbomachines that commonly utilize a compressible working medium, which is totally, or predominantly, air. In fact, a complete list of this compressible-flow subfamily should also include such devices as steam turbines, which may utilize either a dry (superheated) or wet (liquid/vapor) steam mixture with high quality (or dryness factor). However, there exists a separate incompressible-flow turbomachinery classification, where the working medium may be water or, for instance, liquid forms of oxygen or hydrogen, as is the case in the Space Shuttle Main Engine turbopumps. This subcategory also includes powerproducing turbomachines, such as water turbines.

Principles of Turbomachinery in Air-Breathing Engines
  • Erian A. Baskharone
  • Published online:
    05 September 2012
    Print publication:
    31 July 2006
  • This book is intended for advanced undergraduate and graduate students in mechanical and aerospace engineering taking a course commonly called Principles of Turbomachinery or Aerospace Propulsion. It begins with a review of basic thermodynamics and fluid mechanics principles to motivate their application to aerothermodynamics and real-life design issues. This approach is ideal for the reader who will face practical situations and design decisions in the gas turbine industry. Among the features of the book are:An emphasis on the role of entropy in assessing machine performanceA timely review of flow structuresRevisiting the subsonic and supersonic De Laval nozzle as it applies to bladed turbomachinery componentsAn applied review of boundary layer principlesAnd highlighting the importance of invariant properties across a turbomachinery component in carrying out real computational tasks.The text is fully supported by over two hundred figures, numerous examples and homework problems.

  • 1 - Introduction to Gas-Turbine Engines

  • Erian A. Baskharone, Texas A & M University
  • Book:
    Principles of Turbomachinery in Air-Breathing Engines
    Published online:
    05 September 2012
    Print publication:
    31 July 2006, pp 1-8

  • Summary

    Definition

    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 highspeed 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.

    As is clear in these figures, the gas generator consists of the compressor, combustor, and turbine sections. In this assembly, the turbine extracts shaft power to at least drive the compressor, which is the case of a turbojet. Typically, in most other applications, the turbine will extract more shaft work by comparison. The excess amount in this case will be transmitted to a ducted fan (turbofan engine) or a propeller (turboprop engine), as seen in Figure 1.2. However, the shaft work may also be utilized in supplying direct shaft work, or producing electricity in the case of a power plant or an auxiliary power unit (Fig. 1.1). The fact, in light of Figures 1.1 through 1.5, is that different types of gas-turbine engines clearly result from adding various inlet and exit components, to the gas generator. An always interesting component in this context is the thrust-augmentation devices known as afterburners in a special class of advanced propulsion systems (Fig. 1.4).

    Gas-turbine engines are exclusively used to power airplanes because of their high power-to-weight ratio. They have also been used for electric-power generation in pipeline-compressor drives, as well as to propel trucks and tanks. In fact, it would be unwise to say that all possible turbomachinery applications have already been explored.

Page 288 of 394