Numerical Modelling and Experimental Testing of Heat Exchangers (eBook)

Dawid Taler (Autor)

eBook Download: PDF

2018
XVIII, 588 Seiten
Springer International Publishing (Verlag)
978-3-319-91128-1 (ISBN)

Infos

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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 17.5.2018
• Reihe/Serie: Studies in Systems, Decision and Control
• Reihe/Serie: Studies in Systems, Decision and Control
• Zusatzinfo: XVIII, 588 p. 192 illus., 89 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• Schlagworte: Experimental Testing of Heat Exchangers • fluid- and aerodynamics • fluid mechanics • Heat Exchanger Modelling • Heat Exchangers • Heat Transfer Theory
• ISBN-10: 3-319-91128-7 / 3319911287
• ISBN-13: 978-3-319-91128-1 / 9783319911281