Taler Numerical Modelling and Experimental Testing of Heat Exchangers

1. Auflage 2018
ISBN: 978-3-319-91128-1
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 161, 598 Seiten

Reihe: Studies in Systems, Decision and Control

This book presents new methods of numerical modelling of tube heat exchangers, which can be used to perform design and operation calculations of exchangers characterized by a complex flow system. It also proposes new heat transfer correlations for laminar, transition and turbulent flows. A large part of the book is devoted to experimental testing of heat exchangers, and methods for assessing the indirect measurement uncertainty are presented. Further, it describes a new method for parallel determination of the Nusselt number correlations on both sides of the tube walls based on the nonlinear least squares method and presents the application of computational fluid dynamic (CFD) modeling to determine the air-side Nusselt number correlations. Lastly, it develops a control system based on the mathematical model of the car radiator and compares this with the digital proportional-integral-derivative (PID) controller. The book is intended for students, academics and researchers, as well as for designers and manufacturers of heat exchangers.


Professor Dawid Taler, D.Sc., Ph.D. received his doctoral degree in 2002, and postdoctoral degree in 2009 from the Faculty of Mechanical Engineering and Robotics of the University of Science and Technology (AGH) in Cracow. Since 2011 he has been working as a professor at the Faculty of Environmental Engineering at the Cracow University of Technology. Currently, he manages the Department of Thermal Processes, Air Protection and Waste Utilization at the Cracow University of Technology. In 2016 he received the title of professor. He specializes in heat transfer and heating systems, including experimental methods in heat and fluid science. A particular research and development interest is the mathematical modelling and experimental investigation of heat exchangers and energy machines and devices. He is an author of 3 and co-author of 5 monographs and scientific books, 3 of which have been published in English. He has also published 30 chapters in international and national books. He is the author or co-author of over 290 articles in the field of heat transfer, numerical modelling of heat and flow processes, and energy and power technologies. Professor Taler also specializes in thermal and flow measurements, including heat flux measurements, determination of heat transfer coefficient and inverse heat transfer problems, especially the dynamics of heat exchangers and steam generators.

Autoren/Hrsg.

Taler, Dawid

Inhaltsverzeichnis

1;Contents;6
2;Symbols;12
3;1 Introduction;20
4;Heat Transfer Theory;26
5;2 Mass, Momentum and Energy Conservation Equations;27
5.1;2.1 Mass Conservation Equation;28
5.2;2.2 Momentum Conservation Equation;29
5.3;2.3 Angular Momentum Conservation Equation;31
5.4;2.4 Energy Conservation Equation;33
5.5;2.5 Averaging of Velocity and Temperature;35
5.6;2.6 Basic Equations of Fluid Mechanics and Heat Transfer in the Integral Form;36
5.7;2.7 Basic Equations of Fluid Mechanics and Heat Transfer in the Differential Form;39
5.7.1;2.7.1 Continuity Equation;41
5.7.2;2.7.2 Momentum Balance Equation;41
5.7.3;2.7.3 Energy Conservation Equation;47
5.7.3.1;2.7.3.1 Mechanical Energy Balance Equation;47
5.7.3.2;2.7.3.2 Energy Conservation Equation;51
5.8;2.8 Mass, Momentum, and Energy Conservation Equations for One-Dimensional Flows;56
5.8.1;2.8.1 Mass Conservation Equation (Continuity Equation);57
5.8.2;2.8.2 Momentum Conservation Equation;58
5.8.3;2.8.3 Energy Conservation Equation;60
6;3 Laminar Flow of Fluids in Ducts;65
6.1;3.1 Developed Laminar Flow;65
6.1.1;3.1.1 Velocity Distribution and the Pressure Drop;67
6.1.2;3.1.2 Temperature Distribution;69
6.1.2.1;3.1.2.1 Temperature Distribution and the Nusselt Number at a Constant Heat Flux on the Tube Surface;72
6.1.2.2;3.1.2.2 Temperature Distribution and the Nusselt Number at the Tube Wall Constant Temperature;76
6.2;3.2 Laminar Heat Transfer in the Inlet Section;80
6.2.1;3.2.1 Laminar Plug Flow at a Constant Heat Flux on the Tube Surface;81
6.2.2;3.2.2 Laminar Plug Flow at Constant Temperature on the Tube Surface;85
6.3;3.3 Hydraulically Developed Laminar Flow and the Thermally Developing Flow;90
6.3.1;3.3.1 Hydraulically Developed Laminar Flow and the Thermally Developing Flow at Constant Heat Flux at the Tube Inner Surface;93
6.3.2;3.3.2 Hydraulically Developed Laminar Flow and the Thermally Developing Flow at Constant Temperature on the Tube Inner Surface;100
6.3.3;3.3.3 Hydraulically Developed Laminar Flow and the Thermally Developing Flow at Constant Heat Flux on the Flat Slot Inner Surface;107
6.3.4;3.3.4 Hydraulically Developed Laminar Flow and the Thermally Developing Flow at Constant Temperature at the Flat Slot Inner Surface;114
6.4;3.4 Asymptotic Solutions for Small Values of Coordinate x;118
6.4.1;3.4.1 Constant Fluid Flow Velocity Over a Flat Surface;118
6.4.1.1;3.4.1.1 Constant Temperature of the Channel Surface;118
6.4.1.2;3.4.1.2 Constant Heat Flux at the Channel Surface;119
6.4.2;3.4.2 Linear Change in the Fluid Flow Velocity Over a Flat Surface;121
6.4.2.1;3.4.2.1 Constant Temperature of the Channel Surface;121
6.4.2.2;3.4.2.2 Constant Heat Flux at the Channel Surface;127
6.4.3;3.4.3 Formulae for Determination of the Nusselt Number in Tubes and Flat Slots Valid in the Initial Part of the Inlet Section;131
6.5;3.5 Laminar Fluid Flow and Heat Transfer in the Inlet Section—Formulae Used in Engineering Practice;136
6.6;3.6 Hydrodynamically and Thermally Developing Flow in the Inlet Section;142
6.6.1;3.6.1 Flow in a Tube with a Constant Temperature of the Inner Surface;142
6.6.2;3.6.2 Flow in a Tube with a Constant Heat Flux at the Inner Surface;144
7;4 Turbulent Fluid Flow;147
7.1;4.1 Averaged Reynolds Equations;148
7.2;4.2 Turbulent Viscosity and Diffusivity;151
7.3;4.3 Mixing Path Model;154
7.4;4.4 Universal Velocity Profiles;157
7.4.1;4.4.1 Prandtl Velocity Profile;158
7.4.1.1;4.4.1.1 Velocity Profile in the Viscous Sublayer;158
7.4.1.2;4.4.1.2 Velocity Profile in the Turbulent Sublayer;159
7.4.2;4.4.2 von Kármán Velocity Profile;160
7.4.3;4.4.3 Deissler Velocity Profile;161
7.4.4;4.4.4 Reichardt Velocity Profile;164
7.4.5;4.4.5 van Driest Velocity Profile;167
8;5 Analogies Between the Heat and the Momentum Transfer;175
8.1;5.1 Reynolds and Chilton-Colburn Analogy;176
8.2;5.2 Prandtl Analogy;180
8.3;5.3 Von Kármán Analogy;185
9;6 Developed Turbulent Fluid Flow in Ducts with a Circular Cross-Section;190
9.1;6.1 Hydromechanics of the Fluid Flow in Channels;191
9.1.1;6.1.1 Determination of Fluid Velocity and Friction Factor—Integral Formulation;195
9.1.2;6.1.2 Determination of Fluid Velocity and Friction Factor—Differential Formulation;198
9.2;6.2 Friction Factor for Smooth and Rough Tubes;199
9.2.1;6.2.1 Empirical Formulae for Friction Factor in Smooth and Rough Tubes;199
9.2.2;6.2.2 Empirical Formulae for Friction Factor in Smooth and Rough Tubes;201
9.2.2.1;6.2.2.1 Friction Factor for Turbulent Flows Through Channels with a Smooth Surface;201
9.2.2.2;6.2.2.2 Friction Factor for Turbulent Flows Through Channels with a Rough Surface;202
9.2.3;6.2.3 Comparison of Friction Factors for the Fluid Turbulent Flows Through Channels with a Smooth Surface;206
9.3;6.3 Heat Transfer;211
9.3.1;6.3.1 Determination of Temperature, the Heat Flux and the Nusselt Number—Integral Formulation;216
9.3.2;6.3.2 Determination of Temperature, the Heat Flux, and the Nusselt Number—Differential Formulation;221
9.3.3;6.3.3 Distributions of the Fluid Flow Velocity, Heat Flux and Temperature;224
9.3.4;6.3.4 Correlations for the Nusselt Number;227
9.3.4.1;6.3.4.1 Correlations for the Nusselt Number for the Turbulent Flow;229
9.3.4.2;6.3.4.2 Correlations for the Nusselt Number for the Transitional Turbulent Flow;247
9.3.4.3;6.3.4.3 Tubes with a Rough Surface;263
9.3.4.4;6.3.4.4 Correlations for the Nusselt Number for Flows of Liquid Metals;265
10;Methods of the Heat Exchanger Modelling;274
11;7 Basics of the Heat Exchanger Modelling;275
11.1;7.1 Simplified Equations of Mass, Momentum and Energy Conservation;275
11.2;7.2 Determination of the Tube Wall Temperature Distribution;276
11.2.1;7.2.1 Cylindrical Wall;276
11.2.2;7.2.2 Wall with a Complex Cross-Section Shape;278
11.2.2.1;7.2.2.1 Finite Volume Method—Finite Element Method (FVM-FEM);279
11.2.2.2;7.2.2.2 Example Application of the FVM-FEM for Determination of the Temperature Distribution in a Tube with a Complex Cross-Section Shape;295
11.3;7.3 Overall Heat Transfer Coefficient;297
11.3.1;7.3.1 Bare (Non-finned) Tubes with Circular, Oval and Elliptical Cross-Sections;297
11.3.2;7.3.2 Finned Tubes;299
11.4;7.4 Fin Efficiency;302
11.4.1;7.4.1 Fins with Simple Shapes;302
11.4.2;7.4.2 Fins with Complex Shapes;309
12;8 Engineering Methods for Thermal Calculations of Heat Exchangers;319
12.1;8.1 Method Based on the Logarithmic Mean Temperature Difference;320
12.2;8.2 ?-NTU Method;325
12.2.1;8.2.1 Cocurrent Heat Exchanger;328
12.2.2;8.2.2 Countercurrent Heat Exchanger;330
12.2.3;8.2.3 Single-Row Cross-Flow Tube Heat Exchanger;331
12.2.4;8.2.4 Cross-Flow Heat Exchanger;334
13;9 Mathematical Models of Heat Exchangers;337
13.1;9.1 Tube-in-Tube Cocurrent Heat Exchanger;338
13.2;9.2 Tube-in-Tube Countercurrent Heat Exchanger;340
13.3;9.3 Single-Row Cross-Flow Tube Heat Exchanger;341
13.4;9.4 Plate-Fin Cross-Flow Heat Exchanger;348
14;10 Mathematical Modelling of Tube Cross-Flow Heat Exchangers Operating in Steady-State Conditions;354
14.1;10.1 Energy Balance Equations Describing the Heat Transfer in Tube Heat Exchangers with the Perpendicular Direction of the Flow of Mediums;354
14.2;10.2 Numerical Modelling of the Heat Transfer in Tube Cross-Flow Heat Exchangers;364
14.2.1;10.2.1 Arithmetic Averaging of the Gas Temperature on the Thickness of a Single Tube Row;366
14.2.1.1;10.2.1.1 Liquid Energy Conservation Equation;366
14.2.1.2;10.2.1.2 Gas Energy Conservation Equation;368
14.2.2;10.2.2 Integral Averaging of the Gas Temperature on the Thickness of a Single Tube Row;369
14.2.2.1;10.2.2.1 Gas Energy Conservation Equation;370
14.2.2.2;10.2.2.2 Liquid Energy Conservation Equation;374
14.2.3;10.2.3 Tube Wall Temperature;375
14.3;10.3 Mathematical Modelling of Multi-pass Heat Exchangers with Multiple Tube Rows;376
15;Experimental Testing of Heat Exchangers;385
16;11 Assessment of the Indirect Measurement Uncertainty;386
16.1;11.1 Characteristics of Basic Terms;386
16.2;11.2 Measurements of Physical Quantities;389
16.2.1;11.2.1 Calculation of the Direct Measurement Uncertainty;390
16.2.2;11.2.2 Calculation of the Indirect Measurement Uncertainty;393
16.2.2.1;11.2.2.1 Calculation of the Maximum Uncertainty;396
16.2.2.2;11.2.2.2 Indirect Measurement Uncertainty Assessment Based on System Simulations with Input Data Burdened by Pseudorandom Errors;400
16.2.2.3;11.2.2.3 Example Measurement Uncertainty Calculations;401
16.3;11.3 Least Squares Method;404
16.4;11.4 Linear Problem of the Least Squares Method;409
16.5;11.5 Indirect Measurements;421
16.5.1;11.5.1 Indirect Measurements. Linear Problem of the Least Squares Method—Multiple Regression;421
16.5.2;11.5.2 Indirect Measurements. Nonlinear Problem of the Least Squares Method;436
16.5.3;11.5.3 Dependent Measurements. Least Squares Method with Equality Constraints;446
16.5.4;11.5.4 Dependent Measurements. Nonlinear Problem;452
16.6;11.6 Final Comments;459
17;12 Measurements of Basic Parameters in Experimental Testing of Heat Exchangers;462
17.1;12.1 Determination of the Heat Flow Rate Exchanged Between Fluids and the Overall Heat Transfer Coefficient;462
17.2;12.2 Measurement of the Fluid Mean Velocity in the Channel;464
17.2.1;12.2.1 Measurement of the Fluid Volume Flow Rate Using the Velocity Distribution Integration;464
17.2.2;12.2.2 Averaging Probes;475
17.3;12.3 Measurement of the Mass-Averaged Temperature of a Fluid Flowing Through a Channel;479
18;13 Determination of the Local and the Mean Heat Transfer Coefficient on the Inner Surface of a Single Tube and Finding Experimental Correlations for the Nusselt Number Calculation;482
18.1;13.1 Determination of Dimensionless Numbers from Boundary Conditions and Differential Equations;486
18.2;13.2 Dimensional Analysis;489
18.2.1;13.2.1 Matrix of Dimensions;489
18.2.2;13.2.2 Buckingham Theorem;490
18.3;13.3 Examples of the Dimensional Analysis Application;491
18.3.1;13.3.1 Pressure Drop in the Fluid Flow Through a Rough Tube;491
18.3.2;13.3.2 Convective Heat Transfer in the Fluid Flow Through a Tube;493
19;14 Determination of Mean Heat Transfer Coefficients Using the Wilson Method;498
20;15 Determination of Correlations for the Heat Transfer Coefficient on the Air Side Assuming a Known Heat Transfer Coefficient on the Tube Inner Surface;510
20.1;15.1 Determination of the Heat Transfer Coefficient on the Water Side;515
20.2;15.2 Determination of Experimental Correlations on the Air Side for a Car Radiator;519
21;16 Parallel Determination of Correlations for Heat Transfer Coefficients on the Air and Water Sides;522
21.1;16.1 Three Unknown Parameters;525
21.2;16.2 Four Unknown Parameters;530
21.3;16.3 Five Unknown Parameters;532
22;17 Determination of Correlations for the Heat Transfer Coefficient on the Air Side Using CFD Simulations;537
22.1;17.1 Mass, Momentum and Energy Conservation Equations and the Turbulence Model;538
22.2;17.2 Heat Transfer on the Tube Inner Surface;540
22.3;17.3 Determination of Correlations for the Air-Side Nusselt Number Using CFD Modelling;542
22.3.1;17.3.1 Fin Efficiency;546
22.3.2;17.3.2 Correlation for the Air-Side Nusselt Number;548
23;18 Automatic Control of the Liquid Temperature at the Car Radiator Outlet;555
23.1;18.1 System Based on the Heat Exchanger Mathematical Model;556
23.2;18.2 Digital PID Controller;558
24;19 Concluding Remarks;564
25;Appendix A: Selected Elements of the Vector and Tensor Calculus;566
26;A.1ƒBasic Vector Operations in a Cartesian System of Coordinates;566
27;A.2ƒBasic Tensor Operations in a Cartesian System of Coordinates;567
28;Appendix B: The Navier-Stokes Equation in a Cylindrical and a Spherical System of Coordinates;571
29;Appendix C: The Energy Conservation Equation in a Cartesian, a Cylindrical and a Spherical System of Coordinates;573
30;Appendix D: Principles of Determination of the Uncertainty of Experimental Measurements and Calculation Results According to the ASME [232];575
31;Appendix E: Prediction Interval Determination;579
32;Bibliography;581