# Compact Heat Exchangers: Analysis, Design and Optimization using FEM and CFD Approach

ISBN: 978-1-119-42436-9

Feb 2018

544 pages

Select type: O-Book

## Description

A comprehensive source of generalized design data for most widely used fin surfaces in CHEs

Compact Heat Exchanger Analysis, Design and Optimization: FEM and CFD Approach brings new concepts of design data generation numerically (which is more cost effective than generic design data) and can be used by design and practicing engineers more effectively. The numerical methods/techniques are introduced for estimation of performance deteriorations like flow non-uniformity, temperature non-uniformity, and longitudinal heat conduction effects using FEM in CHE unit level and Colburn j factors and Fanning friction f factors data generation method for various types of CHE fins using CFD. In addition, worked examples for single and two-phase flow CHEs are provided and the complete qualification tests are given for CHEs use in aerospace applications.

Chapters cover: Basic Heat Transfer; Compact Heat Exchangers; Fundamentals of Finite Element and Finite Volume Methods; Finite Element Analysis of Compact Heat Exchangers; Generation of Design Data by CFD Analysis; Thermal and Mechanical Design of Compact Heat Exchanger; and Manufacturing and Qualification Testing of Compact Heat Exchanger.

• Provides complete information about basic design of Compact Heat Exchangers
• Design and data generation is based on numerical techniques such as FEM and CFD methods rather than experimental or analytical ones
• Intricate design aspects included, covering complete cycle of design, manufacturing, and qualification of a Compact Heat Exchanger
• Appendices on basic essential fluid properties, metal characteristics, and derivation of Fourier series mathematical equation

Compact Heat Exchanger Analysis, Design and Optimization: FEM and CFD Approach is ideal for senior undergraduate and graduate students studying equipment design and heat exchanger design.

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Preface xiii

Series Preface xv

1 Basic Heat Transfer 1

1.1 Importance of Heat Transfer 1

1.2 Heat Transfer Modes 2

1.3 Laws of Heat Transfer 3

1.4.1 One-Dimensional Heat Conduction 5

1.4.2 Three-Dimensional Heat Conduction Equation 7

1.4.3 Boundary and Initial Conditions 10

1.5 Transient Heat Conduction Analysis 11

1.5.1 Lumped Heat Capacity System 11

1.6 Heat Convection 13

1.6.1 Flat Plate in Parallel Flow 14

1.6.1.1 Laminar Flow Over an Isothermal Plate 14

1.6.1.2 Turbulent Flow over an Isothermal Plate 16

1.6.1.3 Boundary Layer Development Over Heated Plate 17

1.6.2 Internal Flow 18

1.6.2.1 Hydrodynamic Considerations 19

1.6.2.2 Flow Conditions 19

1.6.2.3 Mean Velocity 20

1.6.2.4 Velocity Profile in the Fully Developed Region 21

1.6.3 Forced Convection Relationships 23

1.7.1 Radiation – Fundamental Concepts 30

1.8 Boiling Heat Transfer 35

1.8.1 Flow Boiling 36

1.9 Condensation 38

1.9.1 Film Condensation 39

1.9.2 Drop-wise Condensation 39

Nomenclature 40

Greek Symbols 42

Subscripts 42

References 43

2 Compact Heat Exchangers 45

2.1 Introduction 45

2.2 Motivation for Heat Transfer Enhancement 46

2.3 Comparison of Shell and Tube Heat Exchanger 48

2.4 Classification of Heat Exchangers 49

2.5 Heat Transfer Surfaces 51

2.5.1 Rectangular Plain Fin 52

2.5.2 Louvred-Fin 52

2.5.3 Strip-Fin or Lance and Offset Fin 53

2.5.4 Wavy-Fin 53

2.5.5 Pin-Fin 53

2.5.6 Rectangular Perforated Fin 54

2.5.7 Triangular Plain Fin 54

2.5.8 Triangular Perforated Fin 54

2.5.9 Vortex Generator 55

2.6 Heat Exchanger Analysis 56

2.6.1 Use of the Log Mean Temperature Difference 58

2.6.1.1 Parallel-Flow Heat Exchanger 59

2.6.1.2 Counter-Flow Heat Exchanger 62

2.6.2 Effectiveness-NTU Method 65

2.6.3 Effectiveness-NTU Relations 69

2.6.4 Evaluation of Heat Transfer and Pressure Drop Data 73

2.6.4.1 Flow Properties and Dimensionless Numbers 73

2.6.4.2 Data Curves for j andf 75

2.7 Plate-Fin Heat Exchanger 77

2.7.1 Description 77

2.7.2 Geometric Characteristics 78

2.7.3 Correlations for Offset Strip Fin (OSF) Geometry 81

2.8 Finned-Tube Heat Exchanger 81

2.8.1 Geometrical Characteristics 82

2.8.2 Correlations for Circular-Finned-Tube Geometry 84

2.8.3 Pressure Drop 85

2.8.4 Correlations for Louvred Plate-Fin Flat-Tube Geometry 86

2.8.5 Louvre-Fin-Type Flat-Tube Plate-Fin Heat Exchangers 90

2.8.5.1 Geometric Characteristics 91

2.8.5.2 Correlations for Louvre Fin Geometry 93

2.9 Plate-Fin Exchangers Operating Limits 93

2.10 Plate-Fin Exchangers – Monitoring and Maintenance 94

Nomenclature 95

Greek Symbols 97

Subscripts 98

References 98

3 Fundamentals of Finite Element and Finite Volume Methods 101

3.1 Introduction 101

3.2 Finite Element Method 101

3.2.1 Finite Element Form of the Conduction Equation 103

3.2.2 Elements and Shape Functions 104

3.2.3 Two-Dimensional Linear Triangular Elements 109

3.2.3.1 Area Coordinates 112

3.2.4 Formulation for the Heat Conduction Equation 114

3.2.4.1 Variational Approach 115

3.2.4.2 Galerkin Method 118

3.2.5 Requirements for Interpolation Functions 119

3.2.6 Plane Wall with a Heat Source – Solution by Quadratic Element 128

3.2.7 Two-Dimensional Plane Problems 130

3.2.7.1 Triangular Elements 131

3.2.8 Finite Element Method-Transient Heat Conduction 141

3.2.8.1 Galerkin Method for Transient Heat Conduction 142

3.2.9 Time Discretization using the Finite Element Method 145

3.2.10 Finite Element Method for Heat Exchangers 146

3.2.10.1 Governing Equations 146

3.2.10.2 Finite Element Formulation 148

3.3 Finite Volume Method 164

3.3.1 Navier–Stokes Equations 165

3.3.1.1 Conservation of Momentum 168

3.3.1.2 Energy Equation 171

3.3.1.3 Non-Dimensional Form of the Governing Equations 173

3.3.1.4 Forced Convection 174

3.3.1.5 Natural Convection (Buoyancy-Driven Convection) 175

3.3.1.6 Mixed Convection 177

3.3.1.7 Transient Convection – Diffusion Problem 177

3.3.2 Boundary Conditions 178

Nomenclature 178

Greek Symbols 179

Subscripts 179

References 179

4 Finite Element Analysis of Compact Heat Exchangers 183

4.1 Introduction 183

4.2 Finite Element Discretization 184

4.3 Governing Equations 184

4.4 Finite Element Formulation 189

4.4.1 Cross Flow Plate-Fin Heat Exchanger 189

4.4.2 Counter Flow/Parallel Flow Plate-Fin Heat Exchangers 193

4.4.3 Cross Flow Tube-Fin Heat Exchanger 194

4.5 Longitudinal Wall Heat Conduction Effects 195

4.5.1 General 195

4.5.2 Validation 198

4.5.3 Cross Flow Plate-Fin Heat Exchanger 199

4.5.4 Cross Flow Tube-Fin Heat Exchanger 200

4.5.5 Parallel Flow Heat Exchanger 206

4.5.6 Counter Flow Heat Exchanger 206

4.5.7 Relative Comparison of Results 207

4.6 Inlet Flow Non-Uniformity Effects 207

4.6.1 General 207

4.6.2 Validation 214

4.6.3 Cross Flow Plate-Fin Heat Exchanger 215

4.6.4 Cross Flow Tube-Fin Heat Exchanger 221

4.6.5 Pressure Drop Variations – Flow Non-Uniformity 224

4.7 Inlet Temperature Non-Uniformity Effects 228

4.7.1 General 228

4.7.2 Validation 229

4.7.3 Cross Flow Plate-Fin Heat Exchanger 229

4.7.4 Cross Flow Tube-Fin Heat Exchanger 233

4.8 Combined Effects of Longitudinal Heat Conduction, Inlet Flow Non-Uniformity and Temperature Non-Uniformity 235

4.8.1 General 235

4.8.2 Validation 237

4.8.3 Combined Effects of Longitudinal Wall Heat Conduction and Inlet Flow Non-Uniformity 238

4.8.3.1 Cross Flow Plate-Fin Heat Exchanger – Combined Effects (LHC, FN) 238

4.8.3.2 Cross Flow Tube-Fin Heat Exchanger – Combined Effects (LHC, FN) 243

4.8.4 Combined Effects of Longitudinal Wall Heat Conduction, Inlet Flow Non-Uniformity and Temperature Non-Uniformity 247

4.8.4.1 Cross Flow Plate-Fin Heat Exchanger – Combined Effects (LHC, FN, TN) 251

4.8.4.2 Cross Flow Tube-Fin Heat Exchanger – Combined Effects (LHC, FN, TN) 257

4.8.5 Combined Effects of Inlet Flow Non-Uniformity and Temperature Non-Uniformity 260

4.8.5.1 Cross Flow Plate-Fin Heat Exchanger 263

4.8.5.2 Cross Flow Tube-Fin Heat Exchanger 267

4.9 FEM Analysis of Micro Compact Heat Exchangers 273

4.9.1 Governing Equations and Finite Element Formulation 277

4.10 Influence of Heat Conduction from Horizontal Tube in Pool Boiling 282

4.10.1 General 282

4.10.2 Governing Equations 284

4.10.3 Finite Element Analysis 285

4.10.3.1 One-Dimensional Case 286

4.10.3.2 Two-Dimensional Case (Axial and Radial) 286

4.10.3.3 Two-Dimensional Case (Azimuthal and Radial) 287

4.10.3.4 Three-Dimensional Case 287

4.10.4 Results 288

4.10.4.1 One-Dimensional Heat Conduction Case 290

4.10.4.2 Two-Dimensional Heat Conduction Case 292

4.10.4.3 Three-Dimensional Heat Conduction Case 293

4.11 Closure 298

Nomenclature 299

Greek Symbols 301

Subscripts 302

References 303

5 Generation of Design Data – Finite Volume Analysis 307

5.1 Introduction 307

5.2 Plate Fin Heat Exchanger 307

5.3 Heat Transfer Surfaces 308

5.3.1 Lance and Offset Fins 308

5.3.2 Wavy Fins 308

5.3.3 Rectangular Plain Fins 309

5.3.4 Rectangular Perforated Fins 310

5.3.5 Triangular Plain Fins 311

5.3.6 Triangular Perforated Fins 311

5.4 Performance Characteristic Curves 311

5.4.1 Working Fluids 312

5.5 CFD Analysis 312

5.5.1 Pre-Processor 313

5.5.2 Main Solver 313

5.5.3 Post-Processor 313

5.5.4 Errors and Uncertainty in CFD Modelling 313

5.6 CFD Approach 314

5.6.1 Mathematical Model 315

5.6.2 Governing Equations 315

5.6.3 Assumptions 316

5.6.4 Boundary Conditions 316

5.6.4.1 Inlet Boundary Conditions 317

5.6.4.2 Outlet Boundary Conditions 317

5.6.4.3 Wall Boundary Conditions 318

5.6.4.4 Constant Pressure Boundary Condition 318

5.6.4.5 Symmetric Boundary Condition 318

5.6.4.6 Periodic Boundary Condition 318

5.6.5 Turbulence Models 318

5.7 Numerical Simulation 319

5.7.1 Transient Analysis 320

5.7.1.1 Data Reduction and Validation 321

5.7.2.1 Wavy Fin 328

5.7.2.2 Offset Fins 334

5.7.2.3 Rectangular Plain Fin 337

5.7.2.4 Rectangular Perforated Fin 344

5.7.2.5 Triangular Plain Fin Surface 350

5.7.2.6 Triangular Perforated Fin Surface 356

5.7.3 Flow Non-Uniformity Analysis 362

5.7.4 Characterization of CHE Fins for Two-Phase Flow 366

5.7.4.1 Experimental Set-Up 367

5.7.4.2 Brazed Test Core 368

5.7.4.3 Boiling Heat Transfer Coefficient 370

5.7.4.4 Two-Phase Condensation 374

5.7.5 Estimation of Endurance Life of Compact Heat Exchanger 377

5.7.5.1 Computational Analysis 378

5.7.5.2 CFD Analysis of CHE 378

5.7.5.3 Endurance Life Estimation 382

5.7.5.4 Fatigue Life Estimation 382

5.7.5.5 Effect of Creep 383

5.7.5.6 Results of Endurance Life 384

5.8 Closure 385

Nomenclature 388

Greek Symbols 391

Subscripts 391

References 392

6 Thermal and Mechanical Design of Compact Heat Exchanger 399

6.1 Introduction 399

6.2 Basic Concepts and Initial Size Assessment 400

6.2.1 Effectiveness Method 400

6.2.2 Inverse Relationships 403

6.2.3 LMTD Method 403

6.3 Overall Conductance 407

6.3.1 Fin Efficiency and Surface Effectiveness 409

6.4 Pressure Drop Analysis 410

6.4.1 Single Phase Pressure Drop 410

6.4.2 Two-Phase Pressure Loss 413

6.4.2.1 Two-Phase Frictional Losses 414

6.4.2.2 Two-Phase Momentum Losses – Change of Quality 416

6.4.2.3 Two-Phase Gravitational Losses – Upward Flow (Boiling) 416

6.4.2.4 Downward Flow (Condensation) 417

6.5 Two-Phase Heat Transfer 417

6.5.1 Condensation 418

6.5.1.1 All Liquid Heat Transfer Coefficient 418

6.5.1.2 Correction for the Vapour Volume 418

6.5.1.3 Correction for the Multicomponent Streams 419

6.5.2 Evaporation 419

6.5.2.1 Reynolds Number Calculation 420

6.5.2.2 Determine j and f Factors 420

6.5.2.3 Heat Transfer Coefficient Calculation for Quality between 0 and 0.95 420

6.5.2.4 Heat Transfer Coefficient for High and Low Values of Quality 421

6.6 Useful Relations for Surface and Core Geometry 421

6.7 Core Design (Mechanical Design) 424

6.7.1 Fins 424

6.7.2 Separating/Parting Sheets 424

6.7.3 Cap Sheets 424

6.7.5 Supports 425

6.7.6 Fin Minimum Thickness 425

6.7.7 Parting/Separating and Cap Sheets Minimum Thickness 426

6.7.8 Side-Bar Minimum Thickness 426

6.8 Procedure for Sizing a Heat Exchanger 427

6.9 Design Procedure of a Typical Compact Heat Exchanger 430

6.10 Worked Examples 434

6.10.1 Example 1: Direct Transfer Heat Exchanger 434

6.10.2 Example 2: Two-Pass Cross Flow Heat Exchanger 442

6.10.3 Example 3: Compact Evaporator Design 450

6.10.4 Example 4: Compact Condenser Design 451

Nomenclature 454

Greek Symbols 456

Subscripts 457

References 457

7 Manufacturing and Qualification Testing of Compact Heat Exchangers 461

7.1 Construction of Brazed Plate-Fin Heat Exchanger 461

7.2 Construction of Diffusion-Bonded Plate-Fin Heat Exchanger 461

7.3 Brazing 464

7.3.1 Operations in Brazing 465

7.3.2 Brazing Filler Metals 469

7.3.3 Brazing Processes 469

7.3.4 Vacuum Brazing 470

7.3.4.1 Brazing of Aluminium and its Alloys 470

7.3.4.2 Brazing of Stainless Steels 474

7.3.4.3 Brazing of Super Alloys 475

7.3.5 Vacuum Furnace Brazing Cycles 476

7.3.5.1 Vacuum Level during Brazing 477

7.3.5.2 Cooling Gases 477

7.3.5.3 Post Brazing Inspection 478

7.4 Influence of Brazing on Heat Transfer and Pressure Drop 478

7.5 Testing and Qualification of Compact Heat Exchangers 479

7.5.1 Acceptance Tests 480

7.5.1.1 Thermal Performance and Pressure Drop Test 480

7.5.1.2 Pressure Drop Test 484

7.5.1.3 Leakage Test 484

7.5.1.4 Proof Pressure Test 484

7.5.2 Qualification Tests 485

7.5.2.1 Vibration Test 485

7.5.2.2 Combined Pressure, Temperature and Flow Cycling 487

7.5.2.3 Experimental Evaluation of Endurance Life of Compact Heat Exchanger 488

7.5.2.4 Pressure Cycling Test 490

7.5.2.5 Thermal Shock Test 491

7.5.2.6 Acceleration Test 491

7.5.2.7 Shock Test 491

7.5.2.8 Humidity Test 492

7.5.2.9 Fungus Test 493

7.5.2.10 Salt Fog Test 493

7.5.2.11 Freeze and Thaw 493

7.5.2.12 Rain Resistance 493

7.5.2.13 Sand and Dust 494

7.5.2.14 Shock Test (Arrestor Landing) 494

7.5.2.15 Gunfire Vibration Test 494

7.5.2.16 Burst Pressure Test 495

References 496

Appendices 497

A.1 Derivation of Fourier Series Mathematical Equation 497

A.2 Molar, Gas and Critical Properties 501

A.3 Thermo-Physical Properties of Gases at Atmospheric Pressure 502

A.4 Properties of Solid Materials 509

A.5 Thermo-Physical Properties of Saturated Fluids 515

A.6 Thermo-Physical Properties of Saturated Water 518

A.7 Solar Radiative Properties of Selected Materials 521

A.8 Thermo-Physical Properties of Fluids 522

References 524

Index 525