Badescu Optimal Control in Thermal Engineering

1. Auflage 2017
ISBN: 978-3-319-52968-4
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 93, 584 Seiten

Reihe: Studies in Systems, Decision and Control

This book is the first major work covering applications in thermal engineering and offering a comprehensive introduction to optimal control theory, which has applications in mechanical engineering, particularly aircraft and missile trajectory optimization. The book is organized in three parts: The first part includes a brief presentation of function optimization and variational calculus, while the second part presents a summary of the optimal control theory. Lastly, the third part describes several applications of optimal control theory in solving various thermal engineering problems. These applications are grouped in four sections: heat transfer and thermal energy storage, solar thermal engineering, heat engines and lubrication.Clearly presented and easy-to-use, it is a valuable resource for thermal engineers and thermal-system designers as well as postgraduate students.

Autoren/Hrsg.

Badescu, Viorel

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;1 Introduction;17
3.1;1.1 Control of Systems;17
3.2;1.2 Optimization Classes;19
3.3;References;23
4;Introductory Elements;24
5;2 Functions Optimization;25
5.1;2.1 Weierstrass Theorem;25
5.2;2.2 Conditions of Extreme;26
5.2.1;2.2.1 Real Functions of One Variable;26
5.2.2;2.2.2 Functions of Several Variables;27
5.2.2.1;2.2.2.1 Functions of Two Variables;27
5.2.2.2;2.2.2.2 Functions with Arbitrary Finite Number of Variables;28
5.2.2.3;2.2.2.3 Examples;30
5.3;2.3 Constrained Optimization;32
5.3.1;2.3.1 Functions of Two Variables;32
5.3.2;2.3.2 Functions with Arbitrary Finite Number of Variables;34
5.4;Reference;36
6;3 Elements of Variational Calculus;37
6.1;3.1 Short History;37
6.2;3.2 Preliminary Issues;38
6.2.1;3.2.1 Necessary Conditions for Extremization of Functionals;38
6.2.2;3.2.2 Dual Methods in Variational Calculus;40
6.3;3.3 Euler Extremization Procedure;43
6.4;3.4 The Basic Lemma;45
6.4.1;3.4.1 The Statement and Proof of the Fundamental Lemma;48
6.5;3.5 The Euler-Lagrange Equation for Other Cases of Practical Interest;49
6.5.1;3.5.1 Integrands Depending on Several Functions;49
6.5.2;3.5.2 Integrands Containing Higher Order Derivatives;52
6.5.3;3.5.3 Integrands Depending on Several Independent Variables;54
6.6;3.6 Analytical Solutions of Euler-Lagrange Equations;55
6.6.1;3.6.1 The Case When F = F\left( {x,u^{{\prime }} } \right);55
6.6.2;3.6.2 The Case When F = F\left( {u,u^{{\prime }} } \right);57
6.6.3;3.6.3 The Case When F\left( {x,y,y^{{\prime }} } \right) Is Total Derivative;59
6.7;3.7 Boundary Conditions;60
6.7.1;3.7.1 Natural Boundary Conditions;60
6.7.2;3.7.2 Transversality Conditions;61
6.8;3.8 Extremals and Isoextreme Curves;63
6.8.1;3.8.1 Another Interpretation of the Transversality Condition;63
6.8.2;3.8.2 The Regularity Assumption;65
6.8.3;3.8.3 Obtaining Extremals from Isoextreme and Vice Versa;66
6.8.4;3.8.4 Example;66
6.8.4.1;3.8.4.1 Euler-Lagrange Approach;67
6.8.4.2;3.8.4.2 Hamilton-Jacobi Approach;69
6.8.5;3.8.5 Corner Conditions (Erdmann-Weierstrass);70
6.9;3.9 Variational Notation;71
6.10;3.10 Constrained Extremization;74
6.11;3.11 Isoperimetric Problems;78
6.11.1;3.11.1 Extreme with More Constraints;85
6.11.2;3.11.2 The Case of Multiple Dependent Variables;86
6.12;References;87
7;Theory;88
8;4 Generalities Concerning the Optimal Control Problems;89
8.1;4.1 Variational Problems with Differential Equations as Constraints;89
8.1.1;4.1.1 Generalization of Some Notions of Variational Calculus;89
8.1.2;4.1.2 Differential Equations Acting as Constraints. Consequences;91
8.1.3;4.1.3 Problems of Type Lagrange, Mayer and Bolza;94
8.2;4.2 Solving Optimal Control Problems;95
8.2.1;4.2.1 Constraints on the Solutions;96
8.2.2;4.2.2 The Principle of Optimality for Parts of the Optimal Trajectory;97
8.2.3;4.2.3 Direct and Indirect Methods;98
8.3;References;100
9;5 The Maximum Principle (Pontryagin);101
9.1;5.1 Preliminaries;101
9.2;5.2 The Fundamental Theorem;103
9.3;5.3 Comments on the Fundamental Theorem;107
9.3.1;5.3.1 Strategies of Using the Necessary Conditions;107
9.3.2;5.3.2 The Case of Non-autonomous Systems;108
9.3.3;5.3.3 Functionals Depending on Parameters;109
9.4;5.4 Other Useful Theorems;110
9.4.1;5.4.1 Non-autonomous Systems: Processes with Unspecified Duration;110
9.4.2;5.4.2 Non-autonomous Systems: Optimal Rapid Reaction;112
9.4.3;5.4.3 Processes with Specified Duration;113
9.5;5.5 Linear Rapid Reaction Systems;114
9.6;5.6 The Synthesis Problem;117
9.7;5.7 Example;118
9.8;References;121
10;6 The Gradient Method;122
10.1;6.1 Common Extreme Problems;122
10.1.1;6.1.1 Unconstrained Optimization;122
10.1.2;6.1.2 Constrained Optimization;127
10.2;6.2 Simple Variational Problems;128
10.3;6.3 Optimal Control Problems;130
10.3.1;6.3.1 The Fundamental Equation;131
10.3.2;6.3.2 Process with Specified Duration but Without Final Conditions;135
10.3.3;6.3.3 Process with Specified Duration and One Final Condition;137
10.3.4;6.3.4 Process with Unspecified Duration and Without Final Conditions;138
10.4;6.4 Constraints for the Control Functions and State Variables;139
10.4.1;6.4.1 Constraints for the Control Functions;139
10.4.2;6.4.2 Constraints for the State Variables;141
10.5;6.5 General Approach;142
10.6;References;147
11;7 Dynamic Programming (Bellman Method);148
11.1;7.1 Common Optimization Problems;148
11.1.1;7.1.1 The Grid Method;148
11.1.2;7.1.2 The Bellman Method;148
11.1.3;7.1.3 Example;151
11.2;7.2 Problems of Variational Calculus;154
11.3;7.3 Optimal Control Problems;157
11.3.1;7.3.1 Extension of the Variational Calculus Method;157
11.3.2;7.3.2 Bellman Equation;159
11.3.3;7.3.3 Example;163
11.4;7.4 Linear Processes and Quadratic Objective Functions;164
11.5;7.5 Comments;168
11.6;References;168
12;Applications: Heat Transfer and Storage;169
13;8 Heat Transfer Processes;170
13.1;8.1 Optimal Strategies for Common Heat Transfer Processes;170
13.1.1;8.1.1 Determination of Optimal Strategies;170
13.1.2;8.1.2 The Case When the Value of n Is Arbitrary;172
13.1.3;8.1.3 The Case When n = 1;173
13.1.3.1;8.1.3.1 Source Temperature Constant in Time;173
13.1.3.2;8.1.3.2 Thermal Flux Constant in Time;174
13.1.3.3;8.1.3.3 Comparison;174
13.1.4;8.1.4 The Case When n = ?1;175
13.1.5;8.1.5 The Case When n = 4;176
13.1.6;8.1.6 The Case of Entropy Generation at Constant Speed;177
13.2;8.2 Optimal Paths for Minimizing Lost Available Work;177
13.2.1;8.2.1 Introduction;177
13.2.2;8.2.2 Theory;178
13.2.2.1;8.2.2.1 Model;178
13.2.2.2;8.2.2.2 Measures of Dissipation;179
13.2.2.3;8.2.2.3 Optimization Problem;181
13.2.2.4;8.2.2.4 Dimensionless Formulation;182
13.2.3;8.2.3 Results;184
13.2.3.1;8.2.3.1 Newtonian Heat Convection ( n = 1 );187
13.2.3.2;8.2.3.2 Special Conduction Case ( n = - 1 );189
13.2.3.3;8.2.3.3 Radiative Heat Transfer ( n = 4 );190
13.2.4;8.2.4 Conclusions;192
13.3;Appendix 8A;193
13.4;Appendix 8B;195
13.5;References;196
14;9 Heat Exchangers;197
14.1;9.1 Simple Approach;197
14.1.1;9.1.1 Usual and Optimized Operation Strategies;198
14.2;9.2 Optimal Strategies for Steady State Heat Exchanger Operation;200
14.2.1;9.2.1 Introduction;200
14.2.2;9.2.2 Optimal Heating/Cooling Strategies;201
14.2.3;9.2.3 Optimization of Heat Exchanger Operation Based on Minimum Entropy Generation;203
14.2.4;9.2.4 Optimization of Steady-State Heat Exchanger Operation for Arbitrary Criteria;206
14.3;9.3 Conclusions;210
14.4;References;211
15;10 Storage of Thermal Energy and Exergy;212
15.1;10.1 Unsteady Operation of Storage Elements;212
15.2;10.2 The Exergy Loss During the Storage Process;214
15.3;10.3 Thermal Energy Storage in Stratified and Fully Mixed Water Tanks;216
15.3.1;10.3.1 Introduction;216
15.3.2;10.3.2 Stratified Liquid Storage Tanks;217
15.3.2.1;10.3.2.1 Model;217
15.3.2.2;10.3.2.2 Performance Indicator;222
15.3.2.3;10.3.2.3 Results and Discussion;225
15.3.3;10.3.3 Fully Mixed Liquid Storage Tanks;228
15.3.3.1;10.3.3.1 Model;228
15.3.3.2;10.3.3.2 Indicator of Performance;229
15.3.3.3;10.3.3.3 Results;229
15.3.4;10.3.4 Conclusions;231
15.4;Appendix 10A;233
15.5;Appendix 10B;234
15.6;References;235
16;11 Heating and Cooling Processes;237
16.1;11.1 Optimization of Heating and Cooling Processes by Variational Calculus;237
16.1.1;11.1.1 Cooling Process Without Time Limitation;237
16.1.2;11.1.2 Cooling Process in Limited Time;239
16.2;11.2 Optimal Control of Forced Cool-Down Processes;241
16.2.1;11.2.1 Introduction;241
16.2.2;11.2.2 Forced Cooling Processes with Minimization of Cooling Fluid Mass;241
16.2.3;11.2.3 Forced Cooling Processes with Minimization of Dissipation Measures;245
16.2.3.1;11.2.3.1 Dissipation Measures;245
16.2.3.2;11.2.3.2 Minimization of Dissipation Measures;246
16.3;11.3 Conclusion;251
16.4;References;251
17;12 Optimization of Thermal Insulation of Seasonal Water Storage Tanks;253
17.1;12.1 Optimization of the Distribution of Thermal Insulation;253
17.2;12.2 Optimization of the Total Volume of Thermal Insulation;259
17.3;Reference;261
18;13 Optimization of Pin Fin Profiles;262
18.1;13.1 Optimal Control Methods;263
18.1.1;13.1.1 Methodology;263
18.1.1.1;13.1.1.1 Geometry;263
18.1.1.2;13.1.1.2 Heat Transfer Model;265
18.1.1.3;13.1.1.3 Optimal Control Problem;267
18.1.1.4;13.1.1.4 Optimal Control Method;269
18.1.1.5;13.1.1.5 Implementation;270
18.1.1.5.1;Geometry;270
18.1.1.5.2;Reference Parameters;270
18.1.1.5.3;Technological Constraints;270
18.1.1.6;13.1.1.6 Particular Cases;271
18.1.1.6.1;Temperature Imposed at z = 0 (or \xi = 0 );271
18.1.1.6.2;Temperature Imposed at z = L (or \xi = 1 );271
18.1.2;13.1.2 Results;272
18.1.2.1;13.1.2.1 Expected Accuracy;272
18.1.2.2;13.1.2.2 Particular Cases;272
18.1.2.2.1;Temperature Imposed at z = 0 (or \xi = 0 );272
18.1.2.2.2;Temperature Imposed at z = L (or \xi = 1 ).;278
18.1.3;13.1.3 Conclusions;283
18.2;Appendix 13A;283
18.3;References;285
19;Applications: Solar Energy Conversion into Thermal Energy Part;287
20;14 Optimization of Solar Energy Collection Systems;288
20.1;14.1 General Approach;288
20.1.1;14.1.1 Determination of the Optimal Solution;289
20.1.2;14.1.2 Collectors with Uniform Properties;293
20.1.3;14.1.3 Collectors with Non-uniform Properties;295
20.1.4;14.1.4 Example and Discussion;296
20.2;14.2 More Involved Treatment;299
20.2.1;14.2.1 Introduction;299
20.2.2;14.2.2 Theory;300
20.2.2.1;14.2.2.1 The Optimization Problem;300
20.2.2.2;14.2.2.2 Time Averaged Energy Balance Equation;300
20.2.3;14.2.3 Solar Energy Applications;302
20.2.4;14.2.4 Economical Indices;303
20.2.5;14.2.5 Meteorological and Actinometric Data;306
20.2.6;14.2.6 Model Implementation;306
20.2.6.1;14.2.6.1 Computing Procedure;306
20.2.6.2;14.2.6.2 Model Validation;307
20.2.6.3;14.2.6.3 Input Values;308
20.2.7;14.2.7 Solar Collectors with Optimal Uniformly Distributed Parameters;309
20.2.8;14.2.8 Solar Collectors with Optimal Non-uniformly Distributed Parameters;314
20.2.9;14.2.9 Conclusions;318
20.3;References;318
21;15 Flat-Plate Solar Collectors. Optimization of Absorber Geometry;320
21.1;15.1 Optimization of Absorber Geometry by Using Economic Considerations;320
21.1.1;15.1.1 Absorber Plate of Uniform Thickness;321
21.1.1.1;15.1.1.1 Example;324
21.1.2;15.1.2 Absorber Plate of Variable Thickness;324
21.1.3;15.1.3 The Optimal Fin Width;327
21.1.3.1;15.1.3.1 Example;328
21.1.4;15.1.4 Discussion and Conclusions;329
21.2;15.2 More Realistic Approach;329
21.2.1;15.2.1 Introduction;329
21.2.2;15.2.2 Meteorological Data;330
21.2.3;15.2.3 Model Implementation;331
21.2.4;15.2.4 Uniform Fin Thickness;331
21.2.5;15.2.5 Variable Fin Thickness;337
21.2.6;15.2.6 Conclusions;345
21.3;Appendix 15A;345
21.3.1;15.A.1 Optical Efficiency;345
21.3.2;15.A.2 Overall Heat Loss Coefficient;347
21.3.3;15.A.3 Collector Heat Removal Factor;348
21.3.4;15.A.4 Iterative Procedure;349
21.3.5;15.A.5 Shape of Collection Area;350
21.4;Appendix 15B;350
21.5;References;351
22;16 Optimal Time-Dependent Operation of Open Loop Solar Collector Systems;352
22.1;16.1 Simple Variational Approach for Maximum Exergy Extraction;353
22.1.1;16.1.1 Model of Flat Plate Solar Collector Operation;353
22.1.2;16.1.2 Optimal Strategy for Maximizing the Collected Exergy;354
22.2;16.2 Optimal Control of Flow for Maximum Exergy Extraction;357
22.2.1;16.2.1 Introduction;357
22.2.2;16.2.2 Meteorological Database;358
22.2.3;16.2.3 Transient Solar Energy Collection Model;358
22.2.4;16.2.4 Optimum Operation;360
22.2.4.1;16.2.4.1 Variational Approach for a Simple Case;362
22.2.4.2;16.2.4.2 Variational Approaches for the General Case;363
22.2.4.3;16.2.4.3 Direct Optimal Control Approach;365
22.2.5;16.2.5 Optimum Operation;366
22.2.6;16.2.6 Aspects of Controller Design;370
22.2.7;16.2.7 Conclusions;372
22.3;References;373
23;17 Optimal Time-Dependent Operation of Closed Loop Solar Collector Systems;375
23.1;17.1 Classification and Simple Approach;375
23.1.1;17.1.1 Performance Criteria;376
23.1.2;17.1.2 Systems with Storage at Uniform Temperature;377
23.1.3;17.1.3 Systems with Stratified Storage Tanks;380
23.1.4;17.1.4 Comparison and Discussions;384
23.2;17.2 More Realistic Approach for Systems with Fully Mixed Water Storage Tanks;385
23.2.1;17.2.1 Introduction;385
23.2.2;17.2.2 Closed Loop System;385
23.2.3;17.2.3 Flow Controllers;386
23.2.4;17.2.4 Operation Model;387
23.2.4.1;17.2.4.1 Configuration of Fig. 17.2a;388
23.2.4.2;17.2.4.2 Configuration of Fig. 17.2b;389
23.2.4.3;17.2.4.3 Model Validation;390
23.2.5;17.2.5 Optimal Control;390
23.2.5.1;17.2.5.1 Configuration of Fig. 17.2a;391
23.2.5.2;17.2.5.2 Configuration of Fig. 17.2b;392
23.2.6;17.2.6 Model Implementation;392
23.2.6.1;17.2.6.1 Primary Circuit;392
23.2.6.2;17.2.6.2 Water Storage Tank;393
23.2.6.3;17.2.6.3 Secondary Circuit;394
23.2.6.4;17.2.6.4 Meteorological and Actinometric Data;394
23.2.6.5;17.2.6.5 Computational Procedures;395
23.2.7;17.2.7 Results and Discussions;396
23.2.8;17.2.8 Conclusions;405
23.3;Appendix 17A;406
23.4;Appendix 17B;406
23.5;Appendix 17C;408
23.5.1;17C.1 Computation of Pump Power;408
23.5.2;17C.2 Computation of Pressure Loss Coefficients;410
23.6;References;411
24;18 Optimal Flow Controllers;413
24.1;18.1 Optimal Control;413
24.2;18.2 Implementation;418
24.3;18.3 Comparison and Discussions;419
24.4;References;421
25;Applications: Heat Engines;422
26;19 Endoreversible Heat Engines;423
26.1;19.1 Endoreversible Heat Engine Model;423
26.2;19.2 Implementation of the Optimal Control Theory;425
26.2.1;19.2.1 Definitions;425
26.2.2;19.2.2 Formulation of the Optimal Control Problem;426
26.2.3;19.2.3 Application of the Maximum Pontryagin Principle;427
26.2.4;19.2.4 Properties of the Solutions of Optimal Control Problems;428
26.3;19.3 Optimal Performances;428
26.3.1;19.3.1 Maximum Power;429
26.3.1.1;19.3.1.1 Application of the Maximum Principle;429
26.3.1.2;19.3.1.2 Optimal Solutions;431
26.3.1.3;19.3.1.3 Switchings;432
26.3.1.4;19.3.1.4 Optimal Controls and Trajectories;433
26.3.2;19.3.2 Maximum Efficiency;438
26.3.2.1;19.3.2.1 Application of the Maximum Principle;438
26.3.2.2;19.3.2.2 Optimal Solutions;439
26.3.2.3;19.3.2.3 Switchings;441
26.3.2.4;19.3.2.4 Optimal Controls and Trajectories;441
26.3.3;19.3.3 Conclusion;444
26.4;References;444
27;20 Diesel Engines;445
27.1;20.1 Engine Model;445
27.1.1;20.1.1 Fuel Combustion at Finite Speed;445
27.1.2;20.1.2 Modeling of Losses;446
27.1.2.1;20.1.2.1 Friction Losses;447
27.1.2.2;20.1.2.2 Pressure Drops;447
27.1.2.3;20.1.2.3 Thermal Losses;447
27.1.2.4;20.1.2.4 Losses at Fuel Injection;448
27.1.2.5;20.1.2.5 Incomplete Combustion;448
27.1.2.6;20.1.2.6 Exhaust Pressure Losses;448
27.1.3;20.1.3 Conventional Piston Path;448
27.2;20.2 Optimization Procedure;449
27.2.1;20.2.1 Steps (1)–(3). Processes When Power Is not Generated;450
27.2.1.1;20.2.1.1 Unbounded Acceleration;450
27.2.1.2;20.2.1.2 Bounded Acceleration;451
27.2.2;20.2.2 Stage (4). Allocation of Time Durations for Processes When Power Is not Generated;452
27.2.3;20.2.3 (5) Expansion;453
27.2.3.1;20.2.3.1 Unbound Acceleration;454
27.2.3.2;20.2.3.2 Bounded Acceleration;456
27.2.4;20.2.4 (6) Maximizing the Net Mechanical Work;457
27.3;20.3 Optimal Trajectories and Controls;457
27.3.1;20.3.1 Heat Engine Configuration;457
27.3.2;20.3.2 Optimized Engine Operation;459
27.4;References;465
28;21 Optimization of Daniel Cam Engines;466
28.1;21.1 Introduction;466
28.2;21.2 Model;467
28.2.1;21.2.1 Daniel Cam Engine Representation;467
28.2.2;21.2.2 Mechanical and Thermal Model;468
28.2.2.1;21.2.2.1 Movement and Energy Laws. Work Production;468
28.2.2.2;21.2.2.2 Heat Loss Model;469
28.2.3;21.2.3 Dimensionless Formulation;472
28.2.4;21.2.4 Optimization;473
28.2.5;21.2.5 Numerical Procedure;474
28.2.6;21.2.6 Model Implementation;475
28.3;21.3 Results and Discussions;477
28.3.1;21.3.1 Present Model Versus Simpler Approaches;477
28.3.1.1;21.3.1.1 Comparison with Classical Rod-Crank System;477
28.3.1.2;21.3.1.2 Comparison with Simplified Treatment of Convection Heat Loss Process;480
28.3.1.3;21.3.1.3 Comparison with Simplified Treatment of the Overall Heat Loss Process;484
28.3.1.4;21.3.1.4 Comparison with Unconstrained Piston Acceleration;484
28.3.2;21.3.2 Optimal Solution. Dependence on Design and Operation Parameters;486
28.3.2.1;21.3.2.1 Cylinder Wall and Thermal Insulation. Materials and Thickness;486
28.3.2.2;21.3.2.2 Auto-ignition Moment;491
28.3.2.3;21.3.2.3 Cooling Convection Coefficient;495
28.4;21.4 Conclusions;498
28.5;Appendix 21A;499
28.5.1;21.A.1 Combustion;499
28.5.2;21.A.2 Heat Losses;500
28.5.3;21.A.3 Frictional Losses;502
28.6;Appendix 21B;502
28.6.1;21.B.1 Classical Rod-Crank System;502
28.7;Appendix 21C;504
28.8;References;509
29;22 Photochemical Engines;512
29.1;22.1 Engine Model;512
29.2;22.2 Engine Operation Mode;518
29.3;22.3 Optimal Trajectories of the System;519
29.3.1;22.3.1 Maximizing the Work Produced;521
29.3.2;22.3.2 Minimizing the Entropy Production;521
29.4;22.4 Results and Discussions;522
29.5;References;524
30;Applications: Lubrication;525
31;23 Optimization of One Dimensional Slider Bearings;526
31.1;23.1 Introduction;526
31.2;23.2 Model;527
31.3;23.3 Optimal Control;530
31.4;23.4 Optimum Design and Operation;534
31.4.1;23.4.1 Direct Optimal Control Method;536
31.4.1.1;23.4.1.1 Numerical Procedures and Implementation;536
31.4.1.2;23.4.1.2 Testing the Direct Optimal Control Method;537
31.4.1.3;23.4.1.3 Analytic Approach;537
31.4.1.4;23.4.1.4 Optimal Control Approach;539
31.4.1.5;23.4.1.5 Sensibility Analysis;540
31.4.2;23.4.2 Constraints and Approximations;541
31.4.2.1;23.4.2.1 Maximum Pressure;541
31.4.2.2;23.4.2.2 Maximum Temperature;543
31.4.2.3;23.4.2.3 Maximum Bearing Load;544
31.4.2.4;23.4.2.4 Minimum Bearing Height;545
31.4.2.5;23.4.2.5 Levels of Approximation;547
31.4.3;23.4.3 Design Parameters;548
31.4.3.1;23.4.3.1 Lubricant Type;548
31.4.3.2;23.4.3.2 Bearing Length;550
31.4.3.3;23.4.3.3 Bearing Inlet Height;551
31.4.3.4;23.4.3.4 Sliding Velocity;552
31.4.3.5;23.4.3.5 Inlet Lubricant Pressure;553
31.4.3.6;23.4.3.6 Inlet Lubricant Temperature2;555
31.5;23.5 Conclusions;556
31.6;Appendix 23A;556
31.6.1;23.A1 Sensibility Analysis;556
31.6.2;23.A2 Constraints and Approximation;561
31.6.2.1;23.A2.1 Maximum Temperature Constraint;561
31.6.2.2;23.A2.2 Maximum Bearing Load;564
31.6.2.3;23.A2.3 Levels of Approximation;567
31.6.3;23.A3 Design Parameters;567
31.6.3.1;23.A3.1 Lubricant Type;567
31.6.3.2;23.A3.2 Bearing Length;570
31.6.3.3;23.A3.3 Bearing Inlet Height;572
31.6.3.4;23.A3.4 Sliding Velocity;573
31.6.3.5;23.A3.5 Inlet Lubricant Pressure;575
31.7;References;576
32;Index;579