Aircraft Propulsion and Gas Turbine Engines

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Features

  • Provides performance analysis of ramjet, turbojet and turbofan engines
  • Examines turboprop and propfan engines
  • Presents a comprehensive step-by-step design of multi-stage axial compressors and turbines
  • Delineates the analysis of radial compressors and turbines
  • Details Vertical Take Off and Landing aircraft
  • Addresses industrial problems such as erosion and engine fouling
  • Includes a glossary and end-of-chapter problems
  • The inclusion of a comprehensive analysis of hypersonic engines makes this one-of-a-kind volume an invaluable reference for both civil and military engineers and researchers, as well as mechanical and aeronautical students.

    Summary

    The escalating use of aircraft in the 21st century demands a thorough understanding of engine propulsion concepts, including the performance of aero engines. Among other critical activities,gas turbines play an extensive role in electric power generation, and marine propulsion for naval vessels and cargo ships.

    In the most exhaustive volume to date, this text examines the foundation of aircraft propulsion: aerodynamics interwoven with thermodynamics, heat transfer, and mechanical design. With a finely focused approach, the author devotes each chapter to a particular engine type, such as ramjet and pulsejet, turbojet, and turbofan. Supported by actual case studies, he illustrates engine performance under various operating conditions.

    Part I discusses the history, classifications, and performance of air breathing engines. Beginning with Leonardo and continuing on to the emergence of the jet age and beyond, this section chronicles inventions up through the 20th century. It then moves into a detailed discussion of different engine types, including pulsejet, ramjet, single- and multi-spool turbojet, and turbofan in both subsonic and supersonic applications.

    The author discusses Vertical Take Off and Landing aircraft, and provides a comprehensive examination of hypersonic scramjet and turbo ramjet engines. He also analyzes the different types of industrial gas turbines having single-and multi-spool with intercoolers, regenerators, and reheaters.

    Part II investigates the design of rotating compressors and turbines, and non-rotating components, intakes, combustion chambers, and nozzles for all modern jet propulsion and gas turbine engine systems, along with their performance. Every chapter concludes with illustrative examples followed by a problems section; for greater clarity, some provide a listing of important mathematical relations.

    Table of Contents

    Part I Aero Engines and Gas Turbines
    Chapter 1 History and Classifications of Aero Engines  . .  . 3
    1.1 Prejet Engines—History 4
    1.1.1 Early Activities in Egypt and China 4
    1.1.2 Leonardo da Vinci .  ..  ...  .5
    1.1.3 Branca’s Stamping Mill .  . . 5
    1.1.4 Newton’s SteamWagon .  . . 6
    1.1.5 Barber’s Gas Turbine .  .. 6
    1.1.6 Miscellaneous Aero-Vehicles’Activities in the Eighteenth and Nineteenth
    Centuries .  ..  . 7
    1.1.7 TheWright Brothers .  ..  . 8
    1.1.8 Significant Events up to 1940s .  .. 10
    1.1.8.1 Aero-Vehicle Activities .  . 10
    1.1.8.2 Reciprocating Engines .  . . 12
    1.2 Jet Engines .  . .  . 13
    1.2.1 Jet Engine Inventors: Dr. Hans von Ohain and Sir FrankWhittle .  . 13
    1.2.1.1 Sir Frank Whittle (1907–1996) .  .. 13
    1.2.1.2 Dr. Hans von Ohain (1911–1998) .  . . 14
    1.2.2 Turbojet Engines.  ..  .. 15
    1.2.3 Turboprop and Turboshaft Engines . 18
    1.2.4 Turbofan Engines .  ..  .21
    1.2.5 Propfan Engine 23
    1.2.6 Pulsejet, Ramjet, and Scramjet Engines .  ..  . . 24
    1.2.6.1 Pulsejet Engine .  ..  .. 24
    1.2.6.2 Ramjet and Scramjet Engines .  ..  . 25
    1.2.7 Industrial Gas Turbine Engines .  .27
    1.3 Classifications of Aerospace Engines .  ..  . . 28
    1.4 Classification of Jet Engines.  ..  . . 29
    1.4.1 Ramjet.  ..  .29
    1.4.2 Pulsejet .  ..  . .  . 30
    1.4.3 Scramjet .  ..  . . 31
    1.4.4 Turboramjet .  . .  . 31
    1.4.5 Turborocket .  . .  . 32
    1.5 Classification of Gas Turbine Engines .  ..  . 32
    1.5.1 Turbojet Engines.  ..  .. 33
    1.5.2 Turboprop .  .. 34
    1.5.3 Turboshaft.  .. 35
    1.5.4 Turbofan Engines .  ..  .37
    1.5.5 Propfan Engines .  ..  .. 41
    1.5.6 Advanced Ducted Fan .  .42
    1.6 Industrial Gas Turbines . 43
    1.7 Non–Air-Breathing Engines .  ..  . . 44
    1.8 Future of Aircraft and Power Plant Industries .  ..  .. 44
    Closure .  . .  . 52
    Problems .  . 52
    References 54
    Chapter 2 Performance Parameters of Jet Engines .  ..  . .  . 57
    2.1 Introduction .  . . 57
    2.2 Thrust Force .  . . 57
    2.3 Factors Affecting Thrust 67
    2.3.1 Jet Nozzle .  .. 67
    2.3.2 Air Speed .  ..  . 68
    2.3.3 Mass Air Flow . 68
    2.3.4 Altitude .  ..  . .  . 68
    2.3.5 Ram Effect .  .69
    2.4 Engine Performance Parameters .  . . 70
    2.4.1 Propulsive Efficiency .  .. 70
    2.4.2 Thermal Efficiency .  ..  . . 75
    2.4.3 Propeller Efficiency.  ..  . . 76
    2.4.4 Overall Efficiency .  ..  . .  . 77
    2.4.5 Takeoff Thrust . 80
    2.4.6 Specific Fuel Consumption .  ..  . .  . 81
    2.4.7 Aircraft Range . 82
    2.4.8 Range Factor .  . . 85
    2.4.9 Endurance Factor .  ..  .85
    2.4.10 Specific Impulse .  ..  .. 87
    Problems .  . 91
    References 94
    Chapter 3 Pulsejet and Ramjet Engines .  ..  . .  . 97
    3.1 Introduction .  . . 97
    3.2 Pulsejet Engines.  ..  . .  . 97
    3.2.1 Introduction .  . .  . 97
    3.2.2 Valved Pulsejet 98
    3.2.3 Valveless Pulsejet.  ..  .102
    3.2.4 Pulse Detonation Engine .  . 103
    3.3 Ramjet Engines .  ..  . .  . 106
    3.3.1 Ideal Ramjet .  . . 107
    3.3.2 Real Cycle .  .110
    3.4 Case Study.  .129
    3.5 Summary and Governing Equations for ShockWaves and Isentropic Flow .  ..  .. 141
    3.5.1 Summary .  ..  . 141
    3.5.2 Normal ShockWave Relations .  .141
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    3.5.3 Oblique ShockWave Relations .  .142
    3.5.4 Rayleigh-Flow Equations .  ..  .. 142
    3.5.5 Isentropic Relation .  ..  . . 142
    Problems .  . 143
    References 145
    Chapter 4 Turbojet Engine . 147
    4.1 Introduction .  . . 147
    4.2 Single Spool .  . . 149
    4.2.1 Examples of Engines .  .. 149
    4.2.2 Thermodynamic Analysis .  ..  .. 150
    4.2.3 Ideal Case .  .. 150
    4.2.4 Actual Case .  . .  . 165
    4.2.5 Comparison Between Operative and Inoperative Afterburner .  ..  . 175
    4.3 Two-Spool Engine .  .. 178
    4.3.1 Nonafterburning Engine.  . . 179
    4.3.1.1 Example of Engines .  .. 179
    4.3.2.2 Thermodynamic Analysis 180
    4.3.3 Afterburning Engine .  ..  . 183
    4.3.3.1 Examples for Two-Spool Afterburning Turbojet Engines .  ..  .183
    4.3.2.2 Thermodynamic Analysis 184
    4.4 Statistical Analysis .  .. 188
    4.5 Thrust Augmentation .  . . 189
    4.5.1 Water Injection 189
    4.5.2 Afterburning .  . . 190
    4.5.3 Pressure Loss in Afterburning Engine .  ..  .191
    4.6 Supersonic Turbojet .  .195
    4.7 Optimization of the Turbojet Cycle .  ..  .198
    Problems .  . 209
    References 213
    Chapter 5 Turbofan Engines .  ..  .. 215
    5.1 Introduction .  . . 215
    5.2 Forward Fan Unmixed Single-Spool Configuration.  .216
    5.3 Forward Fan Unmixed Two-Spool Engines . 221
    5.3.1 The Fan and Low-Pressure Compressor on One Shaft.  . . 221
    5.3.2 Fan Driven by the LPT and the Compressor Driven by the HPT .  . . 232
    5.3.3 A Geared Fan Driven by the LPT and the Compressor Driven
    by the HPT.  .233
    5.4 Forward Fan Unmixed Three-Spool Engine . 235
    5.5 Forward Fan Mixed-Flow Engine .  . 242
    5.5.1 Mixed-Flow Two-Spool Engine .  . .  . 242
    5.6 Mixed Turbofan with Afterburner .  . 255
    5.6.1 Introduction .  . .  . 255
    5.6.2 Ideal Cycle .  .256
    5.6.3 Real Cycle .  .258
    5.7 AFT Fan .  ..  . 258
    5.8 V/STOL.  ..  . . 261
    5.8.1 Swiveling Nozzles .  ..  . .  . 261
    5.8.2 Switch-In Deflector System .  ..  . .  . 266
    5.9 Performance Analysis.  . . 273
    Summary.  . 294
    Problems .  . 297
    References 305
    Chapter 6 Turboprop, Turboshaft, and Propfan Engines .  . . 307
    6.1 Introduction to Turboprop Engines .  ..  .307
    6.2 Classification of Turboprop Engines .  ..  . .  . 310
    6.3 Thermodynamic Analysis of Turboprop Engines.  ..  . . 312
    6.3.1 Single-Spool Turboprop .  . . 312
    6.3.2 Two-Spool Turboprop .  .316
    6.4 Analogy with Turbofan Engines.  . .  . 319
    6.5 Equivalent Engine Power .  ..  .. 320
    6.5.1 Static Condition320
    6.5.2 Flight Operation .  ..  .. 320
    6.6 Fuel Consumption .  .. 320
    6.7 Turboprop Installation .  . 321
    6.8 Performance Analysis.  . . 329
    6.9 Comparison Between Turbojet, Turbofan, and Turboprop Engines .  ..  .330
    6.10 Turboshaft Engines .  .333
    6.11 Power Generated by Turboshaft Engines .  . .  . 334
    6.11.1 Single-Spool Turboshaft .  . 334
    6.11.2 Double-Spool Turboshaft .  ..  .. 335
    6.12 Examples for Turboshaft Engines .  . 336
    6.13 Propfan Engines.  ..  . .  . 337
    Summary of Turboprop Relations .  ..  . .  . 340
    Problems .  . 340
    References 344
    Chapter 7 High-Speed Supersonic and Hypersonic Engines .  ..  . .  . 345
    7.1 Introduction .  . . 345
    7.2 Supersonic Aircraft and Programs .  ..  .. 345
    7.2.1 Anglo-French Activities .  . . 346
    7.2.2 Russian Activities .  ..  .347
    7.2.3 The U.S. Activities .  ..  . .  . 347
    7.3 Future of Commercial Supersonic Technology .  ..  .349
    7.4 Technology Challenges of the Future Flight . 350
    7.5 High-Speed Supersonic and Hypersonic Propulsion .  . .  . 350
    7.5.1 Introduction .  . .  . 350
    7.5.2 Hybrid Cycle Engine .  .. 351
    7.6 Turboramjet Engine .  .352
    7.7 Wraparound Turboramjet .  ..  .. 352
    7.7.1 Operation as a Turbojet Engine .  .352
    7.7.2 Operation as a Ramjet Engine .  .. 355
    7.8 Over/Under Turboramjet .  ..  .. 356
    7.8.1 Turbojet Mode . 358
    7.8.2 Dual Mode .  .358
    7.8.3 Ramjet Mode .  . 358
    7.9 Turboramjet Performance .  ..  .358
    7.9.1 Turbojet Mode . 358
    7.9.2 Ramjet Mode .  . 359
    7.9.3 Dual Mode .  .359
    7.10 Case Study.  .360
    7.11 Examples for Turboramjet Engines .  ..  .365
    7.12 Hypersonic Flight .  ..  . 367
    7.12.1 History of Hypersonic Vehicles.  .367
    7.12.2 Hypersonic Commercial Transport . 369
    7.12.3 Military Applications .  .. 370
    7.13 Scramjet Engines.  ..  . . 370
    7.13.1 Introduction .  . .  . 370
    7.13.2 Thermodynamics .  ..  .372
    7.14 Intake of a Scramjet Engine .  ..  . . 372
    7.15 Combustion Chamber.  . . 373
    7.16 Nozzle .  ..  . .  . 376
    7.17 Performance Parameters 376
    Problems .  . 380
    References 383
    Chapter 8 Industrial Gas Turbines .  .385
    8.1 Introduction .  . . 385
    8.2 Categories of Gas Turbines .  ..  . .  . 386
    8.3 Types of Industrial Gas Turbines .  . . 387
    8.4 Single-Shaft Engine.  .388
    8.4.1 Single Compressor and Turbine .  . .  . 389
    8.4.1.1 Ideal Cycle.  .. 389
    8.4.1.2 Real Cycle .  .. 392
    8.4.2 Regeneration .  . . 395
    8.4.3 Reheat .  ..  .398
    8.4.4 Intercooling .  . .  . 399
    8.4.5 Combined Intercooling, Regeneration, and Reheat .  .. 401
    8.5 Double-Shaft Engine.  . .  . 406
    8.5.1 Free Power Turbine .  ..  . . 406
    8.5.2 Two Discrete Shafts (Spools) .  ..  . 408
    8.6 Three Spool .  . . 415
    8.7 Combined Gas Turbine . 422
    8.8 Marine Applications .  . .  . 423
    8.8.1 Additional Components for Marine Applications .  ..  . . 424
    8.8.2 Examples for Marine Gas Turbines . 426
    8.9 Offshore Gas Turbines .  . 427
    8.10 Micro Gas Turbines (μ-Gas Turbines) .  ..  . 428
    8.10.1 Microturbines versus Typical Gas Turbines .  . .  . 429
    8.10.2 Design Challenges .  ..  . .  . 429
    8.10.3 Applications .  . .  . 430
    Problems .  . 431
    References 433
    Part II Component Design .  ..  .435
    Chapter 9 Power Plant Installation and Intakes . 437
    9.1 Introduction .  . . 437
    9.2 Power Plant Installation 437
    9.3 Subsonic Aircraft.  ..  . . 437
    9.3.1 Turbojet and Turbofan Engines .  .438
    9.3.1.1 Wing Installation .  ..  . .  . 438
    9.3.1.2 Fuselage Installation .  .442
    9.3.1.3 CombinedWing and Tail Installation (Three Engines) .  . . 443
    9.3.1.4 Combined Fuselage and Tail Installation .  .444
    9.3.2 Turboprop Installation .  .444
    9.4 Supersonic Aircraft .  .446
    9.4.1 Civil Transports 446
    9.4.2 Military Aircrafts .  ..  .447
    9.5 Air Intakes or Inlets .  .448
    9.6 Subsonic Intakes .  ..  . . 449
    9.6.1 Inlet Performance .  ..  .451
    9.6.2 Performance Parameters .  . . 453
    9.6.3 Turboprop Inlets .  ..  .. 457
    9.7 Supersonic Intakes .  .. 457
    9.7.1 Review of Gas Dynamic Relations for Normal and Oblique Shocks .  ..  . .  . 460
    9.7.1.1 Normal ShockWaves .  . .  . 460
    9.7.1.2 Oblique ShockWaves .  . .  . 461
    9.7.2 External Compression Intake (Inlet) 462
    9.7.3 Internal Compression Inlet (Intake) 467
    9.7.4 Mixed Compression Intakes .  ..  . . 468
    9.8 Matching Between Intake and Engine .  ..  . 470
    9.9 Case Study.  .472
    Problems .  . 475
    References 479
    Chapter 10 Combustion Systems.  ..  . . 481
    10.1 Introduction .  . . 481
    10.2 Subsonic Combustion Chambers .  . . 482
    10.2.1 Tubular (or Multiple) Combustion Chambers .  . 482
    10.2.2 Tubo-Annular Combustion Chambers .  ..  .483
    10.2.3 Annular Combustion Chambers.  .484
    10.3 Supersonic Combustion Chamber.  . 485
    10.4 Combustion Process .  . .  . 485
    10.5 The Chemistry of Combustion .  .487
    10.6 Combustion Chamber Performance .  ..  .490
    10.6.1 Pressure Losses 490
    10.6.2 Combustion Efficiency .  . .  . 491
    10.6.3 Combustion Stability .  .. 491
    10.6.4 Combustion Intensity .  .. 492
    10.7 Cooling .  ..  . . 493
    10.8 Material .  ..  . . 495
    10.9 Aircraft Fuels .  . 496
    10.10 Emissions and Pollutants .  ..  .. 497
    10.10.1 Pollutant Formation .  ..  . 497
    10.11 The Afterburner .  ..  . .  . 498
    10.12 Supersonic Combustion System.  . .  . 499
    Problems .  . 501
    References 503
    Chapter 11 Exhaust System . 505
    11.1 Introduction .  . . 505
    11.2 Nozzle .  ..  . .  . 507
    11.2.1 Governing Equations .  .. 508
    11.2.1.1 Convergent–Divergent Nozzle .  .. 508
    11.2.1.2 Convergent Nozzle .  ..  . 511
    11.2.2 Variable Geometry Nozzles .  ..  . .  . 512
    11.2.3 Afterburning Nozzles .  .. 514
    11.3 Calculation of the Two-Dimensional Supersonic Nozzle .  ..  . .  . 517
    11.3.1 Convergent Nozzle .  ..  . . 518
    11.3.2 Divergent Nozzle .  ..  .522
    11.3.2.1 Analytical Determination of the Contour of a Nozzle .  . .  . 525
    11.3.2.2 Design Procedure for a Minimum Length Divergent Nozzle .  .. 527
    11.3.2.3 Procedure of Drawing the ExpansionWaves Inside the Nozzle .  . . 528
    11.4 Thrust Reversal .  ..  . .  . 529
    11.4.1 Classification of Thrust Reverser Systems .  .531
    11.4.2 Calculation of Ground Roll Distance .  ..  .. 536
    11.5 Thrust Vectoring .  ..  . . 537
    11.5.1 Governing Equations .  .. 540
    11.6 Noise.  ..  .. 541
    11.6.1 Introduction .  . .  . 541
    11.6.2 Acoustics Model Theory .  . 543
    11.6.3 Methods Used to Decrease the Jet Noise .  ..  . 544
    Problems .  . 547
    References 548
    Chapter 12 Centrifugal Compressors .  . . 551
    12.1 Introduction .  . . 551
    12.2 Layout of Compressor .  . 553
    12.2.1 Impeller .  ..  . . 553
    12.2.2 Diffuser .  ..  . . 554
    12.2.3 Scroll or Manifold .  ..  . .  . 556
    12.3 Classification of Centrifugal Compressors .  . 556
    12.4 Governing Equations .  . . 559
    12.4.1 The Continuity Equation .  . 562
    12.4.2 The Momentum Equation or Euler’s Equation for Turbomachinery .  ..  .562
    12.4.3 The Energy Equation or the First Law of Thermodynamics .  ..  . .  . 563
    12.4.4 Slip Factor σ .  . . 567
    12.4.5 Prewhirl .  ..  . . 570
    12.4.6 Types of Impeller .  ..  .581
    12.5 Diffuser .  ..  . . 589
    12.5.1 Vaneless Diffuser .  ..  .590
    12.5.2 Vaned Diffuser. 592
    12.6 Discharge Systems .  .. 598
    12.7 Characteristic Performance of a Centrifugal Compressor .  ..  . . 598
    12.8 Erosion .  ..  . . 602
    12.8.1 Introduction .  . .  . 602
    12.8.2 Theoretical Estimation of Erosion .  . 605
    Problems .  . 609
    References 616
    Chapter 13 Axial-Flow Compressors and Fans.  . . 619
    13.1 Introduction .  . . 619
    13.2 Comparison Between Axial and Centrifugal Compressors .  ..  . 621
    13.2.1 Advantages of the Axial-Flow Compressor Over
    the Centrifugal Compressor .  ..  . .  . 621
    13.2.2 Advantages of Centrifugal-Flow Compressor Over the Axial-Flow
    Compressor .  . .  . 622
    13.2.3 Main Points for Comparison Between Centrifugal and Axial Compressors .  . 623
    13.3 Mean Flow (Two-Dimensional Approach) .  . 623
    13.3.1 Types of Velocity Triangles .  ..  . .  . 625
    13.3.2 Variation of Enthalpy Velocity and Pressure of an
    Axial Compressor .  ..  .627
    13.4 Basic Design Parameters .  ..  .. 635
    13.4.1 Centrifugal Stress .  ..  .635
    13.4.2 Tip Mach Number .  ..  . .  . 637
    13.4.3 Fluid Deflection638
    13.5 Design Parameters .  .. 639
    13.5.1 Degree of Reaction .  ..  . . 640
    13.6 Three-Dimensional Flow .  ..  .. 642
    13.6.1 Axisymmetric Flow.  ..  . . 643
    13.6.2 Simplified Radial Equilibrium Equation .  ..  . 644
    13.6.3 Free Vortex Method .  ..  . 646
    13.6.4 General Design Procedure .  ..  .651
    13.7 Complete Design Process for Compressor.  . . 659
    13.8 Rotational Speed (RPM) and Annulus Dimensions .  .659
    13.9 Determine Number of Stages (Assuming Stage Efficiency) .  .. 662
    13.10 Calculation of Air Angles for Each Stage at the Mean Section .  . . 663
    13.10.1 First Stage .  .. 663
    13.10.2 Stages from (2) to (n1) .  ..  .. 664
    13.10.3 Last Stage .  .. 665
    13.11 Variation of Air Angles from Root to Tip Based on the Type of Blading (Free
    Vortex-Exponential-First Power) .  . . 666
    13.12 Blade Design .  . 667
    13.12.1 Cascade Measurements.  . .  . 667
    13.12.2 Choosing the Type of Airfoil .  ..  . . 672
    13.12.3 Stage Performance .  ..  . .  . 672
    13.12.3.1 Blade Efficiency and Stage Efficiency .  ..  . . 677
    13.13 Compressibility Effects . 679
    13.14 Performance .  . . 687
    13.14.1 Single Stage .  . .  . 687
    13.14.2 Multistage Compressor .  . .  . 689
    13.14.3 Compressor Map .  ..  .690
    13.14.4 Stall and Surge . 691
    13.14.5 Surge Control Methods.  . .  . 694
    13.14.5.1 Multispool Compressor .  . 694
    13.14.5.2 Variable Vanes .  . 694
    13.14.5.3 Air Bleed.  ..  . . 695
    13.15 Case Study.  .701
    13.15.1 Mean Section Data .  ..  . . 701
    13.15.2 Variations from Hub to Tip .  ..  . .  . 701
    13.15.3 Details of Flow in Stage Number 2 . 703
    13.15.4 Number of Blades and Stresses of the Seven Stages.  .704
    13.15.5 Compressor Layout .  ..  . . 705
    13.16 Erosion .  ..  . . 708
    13.17 Fouling .  ..  . . 712
    Problems .  . 714
    References 725
    Chapter 14 Axial Turbines.  . . 727
    14.1 Introduction .  . . 727
    14.2 Comparison Between Axial Flow Compressors and Turbines .  . .  . 729
    14.3 Aerodynamics and Thermodynamics for a Two-Dimensional Flow .  ..  . .  . 730
    14.3.1 Velocity Triangles .  ..  . .  . 730
    14.3.2 Euler’s Equation .  ..  .. 732
    14.3.3 Efficiency, Losses, and Pressure Ratio .  ..  . .  . 734
    14.3.4 Nondimensional Quantities .  ..  . .  . 738
    14.3.5 Several Remarks .  ..  .. 746
    14.4 Three Dimensional .  .. 752
    14.4.1 Free Vortex Design .  ..  . . 753
    14.4.2 Constant Nozzle Angle Design 2) 753
    14.4.3 General Case .  . . 756
    14.4.4 Constant Specific Mass Flow Stage 757
    14.5 Preliminary Design .  .772
    14.5.1 Main Design Steps.  ..  . .  . 772
    14.5.2 Aerodynamic Design .  .. 772
    14.5.3 Blade Profile Selection .  . .  . 774
    14.5.4 Mechanical and Structural Designs . 775
    14.5.4.1 Centrifugal Stresses .  .. 775
    14.5.4.2 Centrifugal Stresses on Blades .  .. 776
    14.5.4.3 Centrifugal Stresses on Discs .  ..  . . 777
    14.5.4.4 Gas Bending Stress .  ..  . 779
    14.5.4.5 Centrifugal Bending Stress .  ..  .781
    14.5.4.6 Thermal Stress .  . 781
    14.5.5 Turbine Cooling .  ..  .. 782
    14.5.5.1 Turbine Cooling Techniques .  ..  . .  . 782
    14.5.5.2 Mathematical Modeling.  . 784
    14.5.6 Losses and Efficiency .  .790
    14.5.6.1 Profile Loss (Yp) .  ..  . .  . 790
    14.5.6.2 Annulus Loss .  . . 791
    14.5.6.3 Secondary Flow Loss .  . .  . 791
    14.5.6.4 Tip Clearance Loss (Yk) . 792
    14.6 Turbine Map.  . . 793
    14.7 Case Study.  .797
    14.7.1 Design Point .  . . 797
    Summary.  . 804
    Problems .  . 805
    References 811
    Chapter 15 Radial Inflow Turbines .  .813
    15.1 Introduction .  . . 813
    15.2 Thermodynamics.  ..  . . 814
    15.3 Dimensionless Parameters .  ..  .818
    15.4 Preliminary Design .  .819
    15.5 Breakdown of Losses .  . . 822
    15.6 Design for Optimum Efficiency .  . .  . 825
    15.7 Cooling .  ..  . . 829
    Problems .  . 830
    References 832
    Chapter 16 Module Matching .  ..  .. 833
    16.1 Introduction .  . . 833
    16.2 Off-Design Operation of a Single-Shaft Gas Turbine Driving a Load .  ..  . 833
    16.2.1 Matching Procedure .  ..  . 834
    16.2.2 Different Loads 839
    16.3 Off Design of Free Turbine Engine .  ..  .839
    16.3.1 Gas Generator.  . 840
    16.3.2 Free Power Turbine .  ..  . . 841
    16.4 Off Design of Turbojet Engine .  .846
    Problems .  . 851
    References 853
    Appendix A Glossary
    Appendix B Data base for turbofan engines
    Appendix C Gas Turbines

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