Axial Turbine Aerodynamics for Aero engines Flow Analysis and Aerodynamics Design

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Axial Turbine Aerodynamics for Aero engines Flow Analysis and Aerodynamics Design

Preface

With the progress of aviation technology, turbine aerodynamic, as one of the major
support subjects for the development of aero-gas turbine, has experienced a rapid
development in the recent 20 years, with new physical phenomena being discovered
and understood constantly, as well as new design methods emerging continuously.
Thanks to these achievements, aerodynamic design capability for aero-gas turbines
has increased rapidly, and the design level has reached a new stage. It is exactly the
application of the latest fine aerodynamics design technologies in aero-gas turbines
greatly improves the aerodynamic load and efficiency of turbines in modern
aero-engines. In order to timely introduce the latest achievements and provide some
reference for fundamental research on turbine aerodynamics and for the development
of engineering design methods, the authors carried out a thorough sorting of
research progresses on turbine aerodynamics in the recent 20 years, and based on
that, wrote this book. This book systematically introduces the research achievements
on mechanisms of complex flows in turbines and aerodynamic design
methods, and is expected to be able to make some contributions to the theoretical
research on aero-gas turbine aerodynamics and development of turbine aerodynamic
design technology.
This book has eight chapters. Chapter 1 introduces the basic turbine aerodynamics
concepts involved in this book, particularly highlighting some new concepts
and supplements and extensions to original concepts, which were proposed
recently, such as the Zweifel coefficient, used to represent the blade loading, and
efficiency definitions of cooled turbines. Chapter 2 expounds the mechanisms of
complex flows in high-pressure turbines, including aerodynamic and geometrical
features of high-pressure turbines, complex wave systems with its flow structures
and organizations, secondary flows and the relevant influencing factors, and mixing
between cooling flow and the main flow. Chapter 3 presents the complex flows in
inter-turbine ducts and its influencing factors, and discuss the relevant aerodynamic
design methods. Chapter 4 expounds the geometrical and aerothermodynamic
features of low-pressure turbines and the development trends, and gives a systematical
introduction to the research achievements concerning the current hot
issues, such as spatial-temporal evolution of blade boundary layer, interaction
between complex flows in shrouds and the main flow, secondary flows in the
endwall regions of high-loading low-pressure turbines, and flows in low pressure
turbines at low Reynolds number. Chapter 5 shows the complex flows in turbine
rear frame ducts with its influencing factors, and its aerodynamic design methods.
Chapter 6 presents the achievements about the aerodynamic design methods for
turbines, including loss models, turbine parameters selection in low dimensional
design numerical evaluation methods, blade profiling and 3D stacking technology,
and refined turbine design technology, which is a research hot spot in recent years.
Chapter 7 introduces the application of flow control technologies in turbines,
including control of turbine boundary layers, secondary flows and tip leakage flows,
and turbine working state adjusting technology, which is also a research hot spot in
recent years. Chapter 8 gives a brief introduction to multidisciplinary conjugate
problems involved with turbines, including conjugate heat transfer, flow–structure
interaction, aero-acoustic conjugate, and multidisciplinary design optimization,
which are still hot topics in turbine research.
The authors of this book comes from Beihang University and Harbin Institute of
Technology. Chapter 1 was written by Prof. Zhengping Zou and Dr. Weihao
Zhang; Chapter 2 was written by Prof. Songtao Wang; Chapter 3 was written by
Prof. Huoxing Liu; Chapter 4 was written by Prof. Zhengping Zou and Dr. Weihao
Zhang; Chapter 5 was written by Prof. Huoxing Liu; Sections 6.4.1 and 6.4.2 of
Chap. 6 were written by Prof. Songtao Wang, and the rest of this chapter was
written by Prof. Zhengping Zou; Chapter 7 was written by Prof. Huoxing Liu;
Chapter 8 was written by Dr. Weihao Zhang and Prof. Zhengping Zou.
This book can be used as a reference book for teachers engaged in gas turbine
teaching, researchers engaged in fundamental and applied research of aerodynamics
of aviation, ground, and ship gas turbines, technicians engaged in engineering
design of turbines, and graduate students and senior undergraduate students in
relevant majors.

Contents

1 Fundamental Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction to Gas Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Primary Geometrical Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Fundamental Equations of Turbine Aerothermodynamics . . . . . . . . 4
1.3.1 Continuity Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.2 Energy Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.3 Moment of Momentum Equation . . . . . . . . . . . . . . . . . . . 6
1.4 Velocity Triangles of Conventional Axial Turbine Stages . . . . . . . 7
1.5 Boundary Layer on Blade Surface . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5.1 Boundary Layer Thickness . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5.2 Boundary Layer Transition . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5.3 Boundary Layer Separation . . . . . . . . . . . . . . . . . . . . . . . . 13
1.6 Wakes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.7 Secondary Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.8 Tip Leakage Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.9 Potential Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.10 Shock Waves and Expansion Waves . . . . . . . . . . . . . . . . . . . . . . . 20
1.11 Flow Mixing in Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.12 Blade Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.13 Loss and Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.13.1 Loss and Efficiency of Turbine Cascades . . . . . . . . . . . . . 27
1.13.2 Efficiency of Uncooled Turbine. . . . . . . . . . . . . . . . . . . . . 29
1.13.3 Efficiency of Cooled Turbine. . . . . . . . . . . . . . . . . . . . . . . 31
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2 Flow Mechanism in High Pressure Turbines. . . . . . . . . . . . . . . . . . . . 37
2.1 Introduction to High Pressure Turbines . . . . . . . . . . . . . . . . . . . . . 37
2.1.1 Structure and Characteristics of High
Pressure Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
ix
2.1.2 Development Status and Trends of High
Pressure Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.1.3 Factors on Efficiency of High Pressure Turbines. . . . . . . . 42
2.1.4 Further Development of High Pressure Turbines
and New Features of Aerodynamic Research . . . . . . . . . . 44
2.2 Aerodynamic and Geometrical Features of High Pressure
Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.2.1 Aerodynamic Design Features of High Pressure
Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.2.2 Blade Profile Features of High Pressure Turbines . . . . . . . 45
2.3 Complex Wave System in High-Loaded High-Pressure
Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.3.1 Wave Systems in High Pressure Turbines . . . . . . . . . . . . . 46
2.3.2 Interaction Between Shock Waves
and Boundary Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.4 Secondary Flow of High Pressure Turbines and Control
Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.4.1 Secondary Flow in High Pressure Turbines. . . . . . . . . . . . 62
2.4.2 Factors of Influencing Secondary Flows in High
Pressure Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.5 Leakage Flows of High Pressure Turbines and Control
Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.5.1 Geometrical and Aerodynamic Parameters on Tip
Leakage Flows in High Pressure Turbines. . . . . . . . . . . . . 74
2.5.2 Active Clearance Controls. . . . . . . . . . . . . . . . . . . . . . . . . 91
2.6 Influence of Interaction Between Cooling Flow and the Main
Flow on Aerodynamic Performance . . . . . . . . . . . . . . . . . . . . . . . . 93
2.6.1 Influence of Film Cooling on Aerodynamic
Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
2.6.2 Influence of Endwalls and Sealing Flow on
Aerodynamic Performance. . . . . . . . . . . . . . . . . . . . . . . . . 99
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3 Flow Mechanism in Inter Turbine Ducts. . . . . . . . . . . . . . . . . . . . . . . 115
3.1 Geometrical and Aerodynamic Characteristics of Inter-turbine
Duct and Development Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.2 Influence of Geometrical Parameters on Flow Structures
and Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
3.2.1 Influence of Curvature of Meridian Passage . . . . . . . . . . . 119
3.2.2 Influence of Area Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.2.3 Influence of Struts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.3 Influence of Aerodynamic Parameters on Flow Structures
and Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3.3.1 Influence of Inlet Mach Number . . . . . . . . . . . . . . . . . . . . 125
x Contents
3.3.2 Influence of Turbulence Intensity . . . . . . . . . . . . . . . . . . . 126
3.3.3 Influence of Inlet flow Angle . . . . . . . . . . . . . . . . . . . . . . 127
3.3.4 Influence of Wakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3.3.5 Influence of Leakage Flows. . . . . . . . . . . . . . . . . . . . . . . . 130
3.4 Optimal Design of ITDs and Flow Control . . . . . . . . . . . . . . . . . . 135
3.4.1 Optimal Design of ITDs . . . . . . . . . . . . . . . . . . . . . . . . . . 135
3.4.2 Flow Control in ITDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4 Flow Mechanisms in Low-Pressure Turbines . . . . . . . . . . . . . . . . . . . 143
4.1 Geometrical and Aero-Thermal Characteristics of Low-Pressure
Turbines and their Development Trends . . . . . . . . . . . . . . . . . . . . . 143
4.1.1 The Geometrical and Aero-Thermal Characteristics
of LP Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.1.2 Flow Characteristics and Losses in LP Turbine
Passages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
4.1.3 Development Trends of LP Turbine Design . . . . . . . . . . . 147
4.2 Boundary Layer Spatial-Temporal Evolution Mechanism
in LP Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
4.2.1 Flat Plate Boundary Layer Evolution
and Flow Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
4.2.2 LP Turbine Boundary Layer Spatial-Temporal
Evolution Under Steady Uniform Inflow. . . . . . . . . . . . . . 160
4.2.3 Single Stage LP Turbine Boundary Layer
Spatial-Temporal Evolution Mechanism . . . . . . . . . . . . . . 165
4.2.4 Unsteady Flow and Boundary Layer Evolution
in Multi-stage LP Turbines . . . . . . . . . . . . . . . . . . . . . . . . 184
4.2.5 Boundary Layer Losses and Prediction Models. . . . . . . . . 190
4.3 Complex Flow in Shroud and Its Interaction
with the Main Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
4.3.1 Leakage Flow in the Shroud Cavities . . . . . . . . . . . . . . . . 196
4.3.2 Interaction Between Leakage Flow and Main Flow
and Its Effects on the Aerodynamic Performance . . . . . . . 203
4.3.3 Shroud Leakage Flow Low-Dimensional Models
and Multi-dimensional Coupling Simulation . . . . . . . . . . . 209
4.3.4 Shroud Leakage Flow Control Technology . . . . . . . . . . . . 217
4.4 Secondary Flow in High-Loaded LP Turbine Endwall Region . . . . 223
4.4.1 Secondary Flow Structure and Loss Characteristics
in LP Turbine Endwall Region . . . . . . . . . . . . . . . . . . . . . 223
4.4.2 Pressure Surface Separation and Its Impacts on Flow
in LP Turbine Endwall Region . . . . . . . . . . . . . . . . . . . . . 226
4.4.3 Endwall Boundary Layer Evolution Mechanism
and Its Impacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
4.4.4 LP Turbine Endwall Flow Under Unsteady
Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
Contents xi
4.5 Low Reynolds Number Effects in LP Turbines . . . . . . . . . . . . . . . 238
4.5.1 Effects of Reynolds Number on the LP Turbine
Aerodynamic Performance. . . . . . . . . . . . . . . . . . . . . . . . . 239
4.5.2 LP Turbine Internal Flow Under Low Reynolds
Number Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
5 Flow Mechanism in Turbine Rear Frame Ducts. . . . . . . . . . . . . . . . . 259
5.1 Geometrical and Aerodynamic Characteristics of Turbine Rear
Frame and Their Development Trends . . . . . . . . . . . . . . . . . . . . . . 259
5.2 Influence of Geometrical Parameters on Flow Structures
and Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
5.2.1 Influence of Meridian Profile of Duct . . . . . . . . . . . . . . . . 261
5.2.2 Influence of OGVs’ Profile Parameters . . . . . . . . . . . . . . . 262
5.2.3 Influence of Hanging Structure . . . . . . . . . . . . . . . . . . . . . 264
5.2.4 Influence of OGV Surface Deformations. . . . . . . . . . . . . . 266
5.3 Influence of Aerodynamic Parameters on Flow Structures
and Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
5.3.1 Influence of Inlet Flow Angle . . . . . . . . . . . . . . . . . . . . . . 268
5.3.2 Influence of Turbulence Intensity . . . . . . . . . . . . . . . . . . . 270
5.3.3 Influence of Inlet Mach Number . . . . . . . . . . . . . . . . . . . . 271
5.4 Methods for Designing TRF Ducts with Large Turning-Angle
OGVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
5.4.1 Design of Duct Profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
5.4.2 Design of OGV Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
5.4.3 Selection of Axial Length of the Duct. . . . . . . . . . . . . . . . 274
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
6 Aerodynamic Design Technologies for Turbines . . . . . . . . . . . . . . . . . 277
6.1 Introduction to Aerodynamic Design Process for Turbines. . . . . . . 277
6.2 Aerodynamic Loss Models for Turbines. . . . . . . . . . . . . . . . . . . . . 279
6.2.1 Deviation Angle Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
6.2.2 Ainley and Mathieson Loss Model . . . . . . . . . . . . . . . . . . 282
6.2.3 AMDC Loss Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
6.2.4 Kacker and Okapuu Loss Model . . . . . . . . . . . . . . . . . . . . 288
6.2.5 Traupel Loss Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
6.2.6 Craig and Cox Loss Model . . . . . . . . . . . . . . . . . . . . . . . . 297
6.2.7 Denton Loss Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
6.2.8 Coull and Hodson Profile Loss Model . . . . . . . . . . . . . . . 309
6.2.9 Cooling Flow Mixing Loss Models. . . . . . . . . . . . . . . . . . 313
6.3 Selection of Geometrical and Aerodynamic Parameters
in Low-Dimensional Design Space. . . . . . . . . . . . . . . . . . . . . . . . . 320
6.3.1 Methods for Assessing Aerodynamic Performance
of Turbines in Low-Dimensional Design Space. . . . . . . . . 320
xii Contents
6.3.2 Selection and Optimization of Aerodynamic Parameters
for Multi-stage LP Turbine in Low-Dimensional
Design Space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
6.3.3 Design of Low-Dimensional Design Parameters
for Variable-Speed Power Turbines. . . . . . . . . . . . . . . . . . 338
6.3.4 Selection of Low-Dimensional Design Parameters
for Versatile Core-Engine Turbines . . . . . . . . . . . . . . . . . . 345
6.3.5 Selection of Low-Dimensional Design Parameters
for Counter-Rotating Turbines. . . . . . . . . . . . . . . . . . . . . . 349
6.4 Multi-dimensional Numerical Evaluation System of Turbine
Aerodynamic Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
6.4.1 S2 Calculation for Air-Cooled Turbines . . . . . . . . . . . . . . 364
6.4.2 Error Analysis of Various Factors in CFD-Based
Air-Cooled Turbine Calculation. . . . . . . . . . . . . . . . . . . . . 374
6.4.3 Numerical Simulation Methods with Geometric/
Aerodynamic Uncertainty Being Considered . . . . . . . . . . . 388
6.4.4 Numerical Simulation Methods with Multi-dimensional
Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
6.5 Blade Profiling Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
6.5.1 Traditional Blade Profiling Methods . . . . . . . . . . . . . . . . . 400
6.5.2 Parametric Blade Profiling Methods and Procedures . . . . . 402
6.5.3 Blade Leading Edge Profiling/Modifying Methods
and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410
6.6 Influence of 3D Blade Stacking on Turbine Flows and
Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
6.6.1 Basic Concept of 3D Profiling. . . . . . . . . . . . . . . . . . . . . . 414
6.6.2 Influence of Blade Curving on Turbine Flows
and Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416
6.6.3 Influence of Blade Sweeping on Turbine Flows
and Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424
6.6.4 Influence of Combination Blade Profiling on Turbine
Flows and Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
6.6.5 Influence of Blade Stacking Errors . . . . . . . . . . . . . . . . . . 430
6.7 Fine Flow Organizing and Design Technologies . . . . . . . . . . . . . . 433
6.7.1 Basic Concept of Fine Flow Organizing and Design. . . . . 433
6.7.2 Applications of Fine Flow Organizing and Design . . . . . . 434
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472
7 Flow Control Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
7.1 Introduction to Flow Control Technology. . . . . . . . . . . . . . . . . . . . 485
7.2 Flow Control Technology for Boundary Layer. . . . . . . . . . . . . . . . 490
7.2.1 Transition Inducing Technology Based
on Surface Trip Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490
7.2.2 Transition Controlling Technology Based
on Rough Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492
Contents xiii
7.2.3 Vortex Generator Technology . . . . . . . . . . . . . . . . . . . . . . 493
7.2.4 Plasma Boundary Layer Exciting Technology. . . . . . . . . . 497
7.3 Flow Control Technology for Secondary Flow. . . . . . . . . . . . . . . . 499
7.3.1 Control Technology Based on End-Wall Fence. . . . . . . . . 500
7.3.2 Control Technology Based on Vortex Generator. . . . . . . . 502
7.4 Tip Leakage Flow Control Technology . . . . . . . . . . . . . . . . . . . . . 505
7.4.1 Blade Tip Jet Technology . . . . . . . . . . . . . . . . . . . . . . . . . 505
7.4.2 Casing Air Injection Control Technology . . . . . . . . . . . . . 507
7.4.3 Vortex Generator and Plasma Exciting Control
Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
7.4.4 Shroud Air Curtain Jet Technology. . . . . . . . . . . . . . . . . . 511
7.5 Turbine Working State Adjustment Technology . . . . . . . . . . . . . . . 514
7.5.1 Geometric Adjustment Technology for Turbines . . . . . . . . 515
7.5.2 Aerodynamic Adjustment Technology for Turbines . . . . . 519
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523
8 Multidisciplinary Coupling Analysis and Design. . . . . . . . . . . . . . . . . 527
8.1 Conjugate Heat Transfer Problems . . . . . . . . . . . . . . . . . . . . . . . . . 527
8.1.1 Conjugate Heat Transfer in Turbines. . . . . . . . . . . . . . . . . 527
8.1.2 Research Methods for Aerodynamic-Heat Transfer
Coupling in Turbines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529
8.1.3 Mechanism of Interaction Between Flow Field
and Temperature Field in Turbines . . . . . . . . . . . . . . . . . . 533
8.2 Flow-Structure Interaction Problems. . . . . . . . . . . . . . . . . . . . . . . . 536
8.2.1 Flow-Structure Interaction Problem in Turbines . . . . . . . . 536
8.2.2 Forced Response of Turbine Blades . . . . . . . . . . . . . . . . . 537
8.2.3 Blade Flutter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541
8.3 Aero-acoustic Conjugate Problems . . . . . . . . . . . . . . . . . . . . . . . . . 544
8.3.1 Noise and Aero-acoustic Conjugate Problems
in Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544
8.3.2 Noise Reduction in Low-Dimensional Aerodynamic
Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547
8.3.3 Aero-acoustic Integrated Design Based on Fully
3D-Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549
8.4 Multidisciplinary Design Optimization Technologies . . . . . . . . . . . 550
8.4.1 General Description of MDO Problem . . . . . . . . . . . . . . . 551
8.4.2 Application of MDO Technology in Turbines. . . . . . . . . . 553
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561