Preface	5
	Contents	7
	About the Authors	18
	Acknowledgements	20
	Introduction	21
	Simulation Tasks	23
	1 New Engine Design	24
	1.1 Nomenclature	24
	1.2 Generation of Shaft Power	26
	1.2.1 Ideal Thermodynamic Cycles	26
	1.2.1.1 Methods to Increase the Power Output	28
	1.2.1.2 Methods for Reducing Fuel Consumption	31
	1.2.2 The Efficiency of Shaft Power Generation	32
	1.2.2.1 Ideal Cycles	32
	1.2.2.2 Real Cycles	36
	1.2.2.3 Back to the Definition of Efficiency	38
	1.2.3 Combined Cycle	40
	1.2.3.1 The Heat Recovery Steam Generator (HRSG)	40
	1.2.3.2 Steam Turbine	42
	1.2.3.3 Combined Cycle Output	43
	1.3 Aircraft Propulsion	43
	1.3.1 Turbojet	43
	1.3.1.1 Ideal Turbojet Cycle	44
	1.3.1.2 A Method to Increase Turbojet Thrust	44
	1.3.1.3 Effect of Flight Velocity	46
	1.3.2 More Definitions of Efficiency	47
	1.3.2.1 Real Turbojet Cycle	49
	1.3.2.2 Efficiency of the Turbojet with Reheat (Afterburner)	51
	1.3.3 Turbofan	55
	1.4 Fundamental Design Decisions	63
	1.4.1 Turbofan: Mixed Flow or Separate Flow?	64
	1.4.1.1 Separate Flow Turbofan	64
	1.4.1.2 Mixed Flow Turbofan	65
	1.4.1.3 Comparison at Constant Propulsive Efficiency	65
	1.4.2 Dry or Reheated Turbofan?	69
	1.4.2.1 Reheated Turbofans for Supersonic Flight	70
	1.4.2.2 Dry Turbofans for Supersonic Flight	73
	1.4.3 Convergent or Convergent-Divergent Nozzle?	74
	1.4.4 Single or Two Stage High Pressure Turbine?	77
	1.4.4.1 Simple Cycle Study	79
	1.4.4.2 Realistic Optimization	80
	1.4.4.3 Engines with Single Stage Turbines	81
	1.4.4.4 Design with Prescribed Rotor Blade Metal Temperature	83
	1.4.4.5 Engines with Two-Stage Turbines	85
	1.4.4.6 Conclusion	86
	1.5 Conceptual Turbofan Design	87
	1.5.1 Flow Annulus	87
	1.5.1.1 Local Mach Numbers	87
	1.5.1.2 Hub/Tip Radius Ratio	87
	1.5.1.3 Relationships Between Components	88
	1.5.1.4 Spool Speed	89
	1.5.1.5 Core Size	89
	1.5.2 Direct Drive or with a Gearbox?	91
	1.5.3 Conventional Turbofans with Bypass Ratios Between 6 and 14	93
	1.5.3.1 Fan and Booster	94
	1.5.3.2 Bypass	95
	1.5.3.3 Low Pressure Turbine	96
	1.5.3.4 Effect of Spool Speed	99
	1.5.4 Turbofan with Gearbox	102
	1.5.5 Comparison	103
	1.5.5.1 Mechanics	105
	1.5.5.2 Aerodynamics	106
	1.5.6 The Fundamental Differences	109
	1.6 Mission Analysis	111
	1.6.1 General Requirements	111
	1.6.2 Single Point Design	112
	1.6.3 Multi-point Design	114
	1.6.3.1 Commercial Aircraft	115
	1.6.3.2 Fighter Aircraft	116
	1.6.4 High Speed Propulsion	121
	1.6.4.1 Point Performance	121
	1.6.4.2 Turbojet	121
	1.6.4.3 Turbojet with Reheat (Afterburner)	125
	1.6.4.4 Turbofan with Reheat	127
	1.6.4.5 Ramjet	128
	1.6.4.6 Acceleration to High Mach Numbers	128
	1.7 References	135
	2 Engine Families	136
	2.1 Baseline Engine	137
	2.2 Derivative Engine	139
	2.2.1 Fan and Booster	139
	2.2.2 Core Compressor	141
	2.2.3 Combustor	142
	2.2.4 High Pressure Turbine	142
	2.2.5 Low Pressure Turbine	143
	2.3 Optimizing the Growth Engine	143
	2.3.1 Design Variables	143
	2.3.2 Design Constraints	144
	2.3.3 Figure of Merit	145
	2.3.4 Ranges for the Design Variables	145
	2.3.5 Starting Point	146
	2.3.6 Graphical User Interface	146
	2.4 Exploring the Design Space	149
	2.5ƒReferences	151
	3 Modeling an Engine	152
	3.1 Sources of Data	153
	3.1.1 Magazines and Marketing Brochures	153
	3.1.2 Official Engine Data	153
	3.1.3 Calculated Engine Cycle Data	154
	3.1.4 Measurements Made by the Gas Turbine User	154
	3.1.5 Measurements in an Engine Maintenance Shop	155
	3.1.5.1 Contractual Performance	155
	3.1.5.2 Thermodynamic Performance	155
	3.2 Data Correction	156
	3.2.1 Correction to Standard Day Atmosphere	157
	3.2.1.1 Humidity Corrections	157
	3.2.1.2 Condensation Corrections	158
	3.2.2 Data Enrichment	160
	3.2.2.1 Indirect Test Data	161
	3.2.2.2 Hybrid Test Data	162
	3.3 Cycle Reference Point	162
	3.3.1 Trial and Error Method	162
	3.3.2 Multi Point Analysis	163
	3.3.3 Optimized Data Match	163
	3.3.4 Unable to Create a Reasonable Model?	164
	3.4 Off-Design	164
	3.4.1 Compressor Maps	165
	3.4.1.1 Corrected Flow—Efficiency Correlation	165
	3.4.1.2 Corrected Flow—Corrected Speed Correlation	166
	3.4.2 Turbine Maps	166
	3.4.3 More Simulation Details	167
	3.5ƒReferences	167
	4 Engine Model Examples	168
	4.1 J57-19W	168
	4.1.1 Cycle Reference Point	169
	4.1.2 Off-Design Simulation	174
	4.1.2.1 Simulation with GasTurb Standard Maps	174
	4.1.2.2 Replacing the LPC Map	178
	4.1.2.3 The High Altitude Case	179
	4.1.2.4 Spool Speed Model	180
	4.1.2.5 Final Remarks	187
	4.2 CFM56-3	187
	4.2.1 Check of the Data	188
	4.2.1.1 Humidity	191
	4.2.1.2 Mass Flow	191
	4.2.1.3 Thrust	191
	4.2.1.4 Fuel Flow	193
	4.2.1.5 Temperatures	195
	4.2.1.6 Pressures	196
	4.2.1.7 Spool Speeds	197
	4.2.2 Cycle Reference Point	200
	4.2.2.1 Some Remarks	204
	4.2.3 Off-Design	204
	4.2.3.1 Test Data Enrichment	205
	4.2.3.2 Fan Map	205
	4.2.3.3 Booster Map	206
	4.2.3.4 HPC Map	209
	4.2.3.5 HPT Map	209
	4.2.3.6 LPT Map	209
	4.2.4 Preliminary Model Calibration	210
	4.2.4.1 Booster Map	211
	4.2.4.2 Second Thoughts About the Booster Map	211
	4.2.4.3 HPC Map	213
	4.2.4.4 Bypass Ratio	213
	4.2.4.5 Fan and LPT Map	214
	4.2.4.6 Spool Speeds	215
	4.2.4.7 Model Check	216
	4.2.5 Refined Model	218
	4.2.6 Some Final Remarks	220
	4.3 F107-WR-400	222
	4.3.1 Cycle Reference Point Max Continuous ISA SLS	222
	4.3.2 Off-Design Model	228
	4.4 References	233
	5 Model-Based Performance Analysis	234
	5.1 The Analysis by Synthesis Methodology	235
	5.1.1 The Model	236
	5.1.1.1 Degree of Detail	236
	5.1.1.2 Calibration	236
	5.1.2 Data Preprocessing	236
	5.1.2.1 Data Correction to Standard Day Conditions	237
	5.1.2.2 Comparing the Measurements with the Model	237
	5.1.3 Definition of the AnSyn Factors	237
	5.1.3.1 Compressor	237
	5.1.3.2 Turbine	240
	5.1.4 A Simple Analysis Example	241
	5.1.5 How to Deal with Missing and Additional Measurements	243
	5.1.6 AnSyn and Optimization	244
	5.1.7 Application of the AnSyn Factors	245
	5.1.7.1 ISA Correction	245
	5.1.7.2 EGT Margin	246
	5.1.7.3 Rated Power	246
	5.2 AnSyn During Engine Development	247
	5.2.1 Sensor Checking	248
	5.2.2 Test Analysis	250
	5.2.3 Model Improvement Potential	250
	5.3 AnSyn in Engine Maintenance Shops	253
	5.3.1 Baseline Model for Diagnostics	254
	5.3.2 Engine Diagnostics	254
	5.4 AnSyn for Engine Performance Monitoring	256
	5.4.1 Baseline Model for Monitoring	256
	5.4.2 Trend Monitoring	257
	5.5 Interpretation of the AnSyn Factors	258
	5.5.1 Component Degradation	259
	5.5.2 Model Faults	261
	5.5.3 Sensor Faults	261
	5.5.4 Measurement Errors	264
	5.6 Concluding Remarks	267
	5.7 References	268
	6 Inlet Flow Distortion	269
	6.1 Types of Inlet Flow Distortion	270
	6.1.1 Pressure Distortion	270
	6.1.2 Temperature Distortion	273
	6.2 Parallel Compressor Theory	273
	6.2.1 Theory and Experiment	277
	6.2.2 Compressor Coupling	281
	6.3 Impact of Distortion on Thermodynamics	283
	6.4 Changes Due to Control System Actions	285
	6.4.1 Unintended Reactions	286
	6.4.2 Intended Actions	286
	6.5 Reprise	286
	6.6 References	287
	7 Transient Performance Simulation	288
	7.1 Transient Basics	289
	7.1.1 Overcoming Rotor Inertia	289
	7.1.2 Transient Control Strategies	290
	7.2 Engine Geometry	292
	7.2.1 Steady State Geometry	292
	7.2.2 A Turbofan Example	293
	7.3 An Enhanced Approach	296
	7.3.1 Tip Clearance	296
	7.3.2 Heat Transfer	297
	7.3.3 Burner	300
	7.3.4 Other Transient Phenomena	300
	7.4 Transient Behavior of a Turbofan	301
	7.4.1 Accelerating the Cold Engine	301
	7.4.2 Decelerating the Hot Engine and Re-slam	305
	7.5 Concluding Remarks	309
	7.6 References	310
	Preliminary Design	311
	1 Engines	312
	1.1 The Role of Preliminary Design in Systems Studies	312
	1.2 Approach and Implementation	316
	1.2.1 Building an Engine Model	316
	1.2.2 Component Models	316
	1.2.3 Design Constraints	318
	1.2.4 Trade Studies Revisited	319
	1.2.5 Component Hierarchy	321
	1.2.6 The Cycle Design Point	322
	1.2.7 Individual Component Design Points	323
	1.2.7.1 LP Compressor	324
	1.2.7.2 HP Compressor	324
	1.2.7.3 Combustion Chamber	325
	1.2.7.4 HP Turbine	325
	1.2.7.5 LP Turbine	325
	1.3 Engine Development—The Role of Performance	326
	2 Compressors	330
	2.1 Function, Environment, and Basic Efficiency	330
	2.1.1 Introduction	330
	2.1.2 Limitations of Isentropic Efficiency	334
	2.1.3 Polytropic Efficiency	335
	2.1.4 Additional Operational Functions	337
	2.2 Velocity Diagrams	338
	2.2.1 Introduction	338
	2.2.2 Sign Convention for Angles and Circumferential Velocities	341
	2.2.3 Construction	343
	2.2.4 Use of Velocity Diagrams	343
	2.2.5 Stage Characteristics	346
	2.3 Preliminary Compressor Design	350
	2.3.1 Flow in a Blade Passage	351
	2.3.2 Mean Line Analysis	352
	2.3.3 Three-Dimensional Flow and Radial Equilibrium	352
	2.3.4 Diffusion, Turning and Blockage	353
	2.3.5 Mean Line Loss Models	359
	2.3.6 The Structure of the Mean Line Design Code CSPAN	361
	2.3.7 Structure of the Mean Line Analysis in GasTurb	363
	2.4 Compressor Design Envelopes	364
	2.4.1 Introduction	364
	2.4.2 Specification of Design Space	365
	2.4.3 Primary Design Variables	367
	2.4.4 A Core Compressor with 11 Stages—An Example	368
	2.4.5 A Core Driven Fan—A More Complex Example	372
	2.5 References	373
	3 Turbines	374
	3.1 Function, Environment and Basic Efficiency	374
	3.1.1 Limitations of Isentropic Efficiency	379
	3.1.2 Polytropic Efficiency	381
	3.2 Velocity Diagrams	384
	3.2.1 Introduction	384
	3.2.2 Sign Convention for Angles and Circumferential Velocities	387
	3.2.3 Construction	388
	3.2.4 Use of Velocity Diagrams	388
	3.2.5 Stage Characteristics	391
	3.3 Preliminary Turbine Design	397
	3.3.1 HP Turbine	397
	3.3.2 LP Turbine	398
	3.3.3 Mean Line Analysis	399
	3.3.4 Development of a Mean Line Code	402
	3.3.5 Structure of a Mean Line Code	403
	3.3.6 Mean Line Loss Models	405
	3.3.7 Loss Components	408
	3.3.7.1 Profile Loss	408
	3.3.7.2 Secondary Loss	409
	3.3.7.3 Trailing Edge Loss	409
	3.3.7.4 Over-Tip Leakage Loss	409
	3.3.8 Effects of Cooling Air	410
	3.4 Turbine Design Envelopes	411
	3.4.1 Introduction	411
	3.4.2 Specification	412
	3.4.3 Primary Design Variables	413
	3.4.4 Solution and Interpretation	414
	3.5 Vaneless Counter-Rotation	418
	3.6ƒReferences	425
	4 Mechanical Design	427
	4.1 Introduction	427
	4.2 Flow Path	429
	4.2.1 Compressors	429
	4.2.2 Low-Bypass-Ratio Fan or LP Compressor	429
	4.2.3 High-Bypass-Ratio Fan	430
	4.2.4 Splitters	432
	4.2.5 Booster	432
	4.2.6 HP Compressor	432
	4.2.7 Combustor	434
	4.2.8 HP Turbine	434
	4.2.9 LP Turbine	436
	4.2.10 Afterburners	437
	4.2.11 Nozzles	437
	4.2.11.1 Subsonic Nozzle	438
	4.2.11.2 Supersonic Nozzle	438
	4.3 Frames and Ducts	438
	4.3.1 Front Frame	438
	4.3.2 Main Frame	439
	4.3.3 Turbine Center Frame	439
	4.3.4 Rear Frame	440
	4.4 Shafts	440
	4.5 Disks	441
	4.5.1 Disk Design Methodology	442
	4.5.2 Rim Load	443
	4.5.3 Disk Temperature	445
	4.5.4 Disk Stress	446
	4.5.5 Material Properties	447
	4.5.6 Design Margins	448
	4.5.7 Stress Distribution	449
	4.6 Engine Weight	449
	4.7 References	452
	Off-Design	453
	1 Component Performance	454
	1.1 Inlet	454
	1.1.1 Aircraft Engines	454
	1.1.1.1 Loss Description	455
	1.1.1.2 Subsonic Aircraft	456
	1.1.1.3 Supersonic Aircraft	459
	1.1.1.4 Spillage Drag	462
	1.1.2 Power Generation	463
	1.2 Off-Design Behavior of Compressors	466
	1.2.1 About Compressor Maps	467
	1.2.1.1 The Shape of Speed Lines	469
	1.2.1.2 The Zero-Speed Line	470
	1.2.1.3 “Supersonic” Speed Lines	471
	1.2.1.4 Specific Work	473
	1.2.1.5 Torque	475
	1.2.2 Compressor Map Coordinates	476
	1.2.2.1 Efficiency Correlations	479
	1.2.2.2 Work and Flow Correlations with Spool Speed	482
	1.2.3 Compressors with Variable Guide Vanes	483
	1.2.4 Fan Maps	488
	1.2.4.1 The Flow Field in a Single Stage Fan	490
	1.2.4.1.1 Core Section	490
	1.2.4.1.2 Bypass Section	493
	1.2.4.2 Extended Fan Map	494
	1.2.4.2.1 The Algorithm	494
	1.2.4.2.2 How to Get Such a Map	494
	1.2.5 Secondary Effects	498
	1.2.5.1 Bleed Air from an Intermediate Stage	498
	1.2.5.2 Tip Clearance	498
	1.2.5.3 Blade Untwist	501
	1.2.6 Scaling Compressor Maps	502
	1.2.6.1 How to Find the Mach Number Scale in a Fan Map	506
	1.2.6.2 Mach Number Scale for Other Compressor Maps	510
	1.2.7 The Map Preparation Program Smooth C	511
	1.2.8 A Simple Map Scaling Procedure	513
	1.2.9 Advanced Map Scaling	514
	1.2.10 Map Scaling During Off-Design	516
	1.3 Turbine Performance	518
	1.3.1 Operational Behavior	518
	1.3.1.1 Corrected Mass Flow	518
	1.3.1.2 Specific Work	522
	1.3.1.3 Efficiency	524
	1.3.1.4 Exit Angle	527
	1.3.2 The Map Preparation Program Smooth T	527
	1.3.3 Turbine Map Format	530
	1.3.3.1 Beta Lines	531
	1.3.3.2 Turbine Map Scaling	532
	1.3.4 Tip Clearance	533
	1.3.5 Variable Geometry Turbines	535
	1.3.6 Vaneless Counter-Rotating Turbines	535
	1.4 Combustor	537
	1.4.1 Efficiency	537
	1.4.2 Pressure Loss	540
	1.4.3 Temperature Distribution at the Combustor Exit	543
	1.5 Mixer	544
	1.5.1 How Mixing Increases Thrust	545
	1.5.2 Mixer Geometry	546
	1.5.3 Fully Mixed Thrust	547
	1.5.4 Unmixed Thrust	548
	1.5.5 Mixer Efficiency and Mixer Velocity Coefficient	548
	1.5.6 Thrust Gain Potential	549
	1.5.7 Practical Mixers	551
	1.5.8 Mixer Design Example	552
	1.5.9 Mixer Off-Design	554
	1.6 Afterburner	556
	1.6.1 The Need for a Precise Afterburner Simulation	557
	1.6.2 Geometry and Nomenclature	558
	1.6.3 Afterburner Operation	559
	1.6.3.1 Pressure Losses	560
	1.6.3.2 Flow Field	560
	1.6.4 Reheat Efficiency	561
	1.6.4.1 Definition	561
	1.6.4.2 Methods of Determining Efficiency	563
	1.6.4.3 Efficiency at Part Load	564
	1.6.5 EJ 200 Example	565
	1.6.5.1 Modeling Results from the Altitude Test Facility	566
	1.6.5.2 Conclusions	573
	1.7 Nozzles	573
	1.7.1 Convergent Nozzles	574
	1.7.1.1 Discharge Coefficient	574
	1.7.1.2 Thrust Coefficient	575
	1.7.2 Convergent-Divergent Nozzles	578
	1.7.2.1 Theory	578
	1.7.2.2 Reality	579
	1.7.2.3 Implementation	587
	1.8 References	588
	2 Understanding Off-Design Behavior	591
	2.1 Turbojet	592
	2.1.1 Off-Design Behavior of the Components	592
	2.1.1.1 Compressor	592
	2.1.1.2 Burner	594
	2.1.1.3 Turbine	595
	2.1.1.4 Exhaust Nozzle	596
	2.1.2 Component Synergy	596
	2.1.2.1 Flow Conservation Between Compressor and Turbine	598
	2.1.2.2 Flow Conservation Between Turbine and Nozzle	599
	2.1.2.3 Flow Conservation Between Compressor Exit and Turbine Inlet	600
	2.1.2.4 Energy Balance Between Compressor and Turbine	601
	2.1.2.5 Compressor and Turbine Operating Lines	602
	2.1.2.6 How Accurate Are These Equations?	602
	2.1.2.7 Variable Compressor Geometry	604
	2.1.3 Booster Operating Line	607
	2.2 Turbofan	608
	2.2.1 Fan Operating Line	609
	2.2.2 Turbofan Booster Operating Line	611
	2.2.2.1 Shape of the Operating Line	612
	2.2.2.2 Map Selection and Scaling	614
	2.2.2.3 Variable Geometry	615
	2.2.2.4 Wrap up	619
	2.2.3 Low Pressure Turbine	619
	2.3 Multi-spool Turboshaft	621
	2.4 Single Spool Turboshaft	622
	2.5 References	624
	Basics	625
	1 Gas Properties and Standard Atmosphere	626
	1.1 The Half Ideal Gas	626
	1.1.1 Enthalpy	627
	1.1.2 Entropy Function	628
	1.2 Numerical Values	628
	1.2.1 Specific Heat, Enthalpy and Entropy Function	628
	1.2.2 Temperature Rise Due to Combustion	629
	1.2.3 Fuel	629
	1.3 Standard Atmosphere	630
	1.4 Reference	631
	2 Spreadsheet Calculations	632
	2.1 Frequently Needed Equations	632
	2.1.1 Some Simple Correlations	632
	2.1.2 Compressor	633
	2.1.3 Turbine	635
	2.1.4 Isentropic and Polytropic Efficiency	638
	2.1.5 Combustor	638
	2.1.6 Nozzle	639
	2.2 Cycle Calculation for a Turbojet Engine	640
	2.2.1 Requirement	640
	2.2.2 Solution	640
	2.2.3 Summary	650
	3 Non-dimensional Performance	651
	3.1 Non-dimensional Compressor Performance	651
	3.2 Non-dimensional Engine Performance	656
	3.2.1 Practical Correction to Standard Day Conditions	659
	3.2.2 How to Determine the Exponents	660
	3.2.3 Aircraft Engines with Afterburners	661
	3.2.4 Gas Turbines with Heat Exchanger	662
	3.3 References	662
	4 Reynolds Number Corrections	663
	4.1 Reynolds Number Index	663
	4.2 Turbomachinery Loss Correlations with Reynolds Number	665
	4.2.1 Compressor	666
	4.2.2 Turbine	667
	4.2.3 Some Additional Remarks	668
	4.3 Applying the Pipe Flow Analogy in Performance Programs	669
	4.4 Variations of the Pipe Flow Analogy	670
	4.5 Mass Flow Correction	671
	4.6 References	672
	5 Efficiency of a Cooled Turbine	673
	5.1 Single Stage Turbine	675
	5.1.1 Simulation Principle	675
	5.1.2 About NGV Cooling Air	678
	5.1.3 Exchange Rates	679
	5.2 Two-Stage Turbine	680
	5.3 Equivalent Single Stage Turbine	682
	5.3.1 The Virtual RIT Method	685
	5.3.2 The Virtual T4 Method	686
	5.3.3 Sensitivity Analysis	686
	5.3.4 Application	689
	5.4 Thermodynamic Efficiency	689
	5.4.1 Comparison of Turbine Efficiency Estimates	691
	5.4.2 Efficiency Definition Affects the Results of Cycle Studies	693
	5.5 Efficiency Losses Due to Cooling	694
	5.5.1 Some Numbers	694
	5.5.2 A Real-World Example	695
	5.6 References	697
	6 Secondary Air System	698
	6.1 SAS in the Performance Model	698
	6.2 SAS Calculation	701
	6.2.1 Interstage Bleed	702
	6.3 Turbine Cooling Air	703
	6.3.1 Multi-stage Turbines	705
	6.4 References	707
	7 Mathematics	708
	7.1 The Off-Design Simulation Task	708
	7.2 Basic Algorithms	711
	7.2.1 Newton	711
	7.2.2 Regula Falsi	712
	7.2.3 Newton-Raphson	713
	7.3 Application to Performance Calculations	715
	7.4 More About the Analytical Technique	715
	7.4.1 Hierarchy of Iterations	717
	7.4.2 Steady State Performance	718
	7.4.3 Limiters	719
	7.4.4 Dynamic Engine Simulation	720
	7.5 About Convergence Problems	722
	7.5.1 A Solution Exists, but the Program Does not Find It	722
	7.5.1.1 Poor Variable Estimates	722
	7.5.1.2 Reasonable Variable Estimates	722
	7.5.1.3 Problem Formulation	723
	7.5.1.4 Problematic Component Maps	724
	7.5.2 No Solution Exists	724
	7.5.2.1 Operating Point Is Outside One or More Component Maps	724
	7.5.2.2 Cycle Is not Feasible	724
	7.5.2.3 Garbage in—Garbage Out	724
	7.6 References	725
	8 Optimization	726
	8.1 Parametric Studies	726
	8.2 Numerical Optimization	727
	8.2.1 A Gradient Strategy	728
	8.2.2 Adaptive Random Search Strategy	729
	8.2.3 Constraints	731
	8.2.4 Application	731
	8.3 References	733
	9 Monte Carlo Simulations	734
	9.1 Statistical Background	734
	9.1.1 Normal Distribution and Standard Deviation	734
	9.1.2 Probability Distribution and Confidence Level	737
	9.2 Measurement Uncertainty	738
	9.2.1 Systematic Errors	738
	9.2.2 A Conventional Test Analysis Procedure	738
	9.2.3 Core Flow Analysis	739
	9.3 Engine Design Uncertainty	741
	9.4 Engine Manufacturing Tolerance	746
	9.4.1 Random Variations	747
	9.4.2 Correlations	747
	9.4.3 Control System Tolerance	747
	9.4.4 A Turboshaft Example	748
	9.5 References	749
	Appendix	750
	Nomenclature*	750
	Index	756