Computational fluid dynamics and energy modelling in buildings : fundamentals and applications / Parham A. Mirzaei.

Includes index.

Includes bibliographical references and index.

Contents
Preface xiii
1 An Overview of Heat and Mass Transport in Buildings 1
1.1 Introduction 1
1.2 Heat and Mass Transport in Traditional Buildings 2
1.3 Heat and Mass Transports in Modern Buildings 8
1.4 Modelling of Heat and Mass Transport in Buildings 15
1.4.1 Modelling Objectives 16
1.5 Modelling Approaches 17
1.5.1 Observational Methods 17
1.5.2 Mathematical Methods 18
1.5.2.1 Spatial Scale of Modelling 19
1.5.2.2 Temporal Scale of Modelling 22
References 22
2 An Overview on Fundamentals of Fluid Mechanics in Buildings 25
2 An Overview of Fluid 25
2.1 Definition of Fluid 25
2.1.1 System of Units 25
2.2 Properties of Fluid 26
2.2.1 Density 26
2.2.2 Specific Weight 26
2.2.3 Viscosity 27
2.3 Pressure and State of Fluid 29
2.3.1 Definition 29
2.3.2 Static Pressure 29
2.3.3 Hydrostatic Pressure 31
2.3.4 Buoyancy 35
2.3.5 Vapour Pressure and Boiling 37
2.3.6 Pressure Measurement Devices 38
2.3.7 Gas Law 40
2.3.8 Bernoulli Equation 41
2.3.9 Dynamic Pressure 46
2.4 Fluid in Motion 50
2.4.1 Steady and Unsteady Flows 50
2.4.2 Laminar and Turbulent Flows 51
2.4.3 Multiple-Dimensional Flow 52
2.5 Governing Equation of Fluids 52
2.5.1 Reynolds Transport Theorem 52
2.5.2 Continuity Equation 57
2.5.3 Momentum Equation 59
2.5.4 Energy Equation 60
2.6 Differential Form of Fluid Flow 62
2.6.1 Fluid Element Kinematic 62
2.6.2 Differential Form of Continuity Equation 65
2.6.3 Differential Form of Linear Momentum Equation 66
2.6.4 Euler’s Equation of Motion 69
2.6.5 Navier–Stokes Equations 69
2.7 Dimensionless Analysis 75
2.7.1 Flow Similarities 75
2.7.2 Buckingham π-Theorem 76
2.8 Internal Flow 79
2.8.1 Laminar Internal Flow 80
2.8.2 Turbulent Internal Flow 82
2.8.3 Pressure Drop in Conduit 83
2.9 External Flow 86
2.9.1 Drag and Lift 86
2.9.2 Uniform Flow on a Flat Plate 90
2.9.3 Boundary Layer Structure 90
References 92
3 Applications of Fluid Mechanics in Buildings 93
3 Applications of Fluid Mechanics in Buildings 93
3.1 Atmospheric Boundary Layer 93
3.2 Wind Profile and Directions 93
3.3 Building Aerodynamics 97
3.3.1 Cp and Similarity in Buildings 98
3.3.2 Building Openings 105
3.3.3 Wind-Driven Ventilation 107
3.3.4 Buoyancy-Driven Ventilation 111
3.4 Turbulent Jet and Plume 115
3.4.1 Jet Structure 117
3.4.2 Jet and Plume in Ventilation 118
3.5 Wall Effect 121
3.5.1 Inner Layer 121
3.5.2 Viscous Sublayer 122
3.5.3 Log-Law Layer 122
3.5.4 Buffer Layer 123
3.5.5 Outer Layer 123
3.6 Piping and Ducting in Buildings 125
vi Contents
3.6.1 Major Losses 125
3.6.2 Minor Losses 125
3.6.3 Piping System 128
3.6.4 Parallel and Series Piping Systems 132
3.7 Fan and Pump in Buildings 140
3.7.1 Dimensionless Analysis 142
3.7.2 System Characteristics and Pumps 145
3.7.3 Parallel and Series Pumps 149
References 155
4 An Overview on Fundamentals of Thermodynamics in Buildings 157
4 An Overview of Thermodynamics 157
4.1 Saturation Temperature 157
4.2 First Law of Thermodynamics 162
4.2.1 Enthalpy 166
4.2.2 Specific Heats 167
4.2.3 First Law of Thermodynamics for a Control Volume (Open System) 169
4.2.4 Steady-State Steady-Flow (SSSF) Process 173
4.2.5 Uniform-State Uniform-Flow (USUF) Process 175
4.3 Second Law of Thermodynamics and Entropy 177
4.4 Mixture of Ideal Gases 178
4.4.1 Mixture of Air and Vapour 180
4.4.2 Saturated Air, Relative Humidity, and Humidity Ratio 180
4.4.3 Dew Point, Dry-Bulb, and Wet-Bulb 182
4.4.4 Psychrometric Chart 182
4.5 Moisture Transport 184
4.5.1 Mixing 185
4.5.2 Mass Diffusion Mechanism 185
4.5.3 Mass Convection 186
4.5.4 Conservation of Mass 188
References 189
5 Applications of Thermodynamics in Buildings 191
5 Introduction 191
5.1 Human Thermal Comfort 191
5.2 Thermal Comfort Measures in Building 193
5.3 Thermodynamic Processes in Air-Conditioning Systems 193
5.3.1 Adiabatic Saturation 195
5.3.2 Cooling and Heating 198
5.3.3 Heating and Humidification 200
5.3.4 Cooling and Dehumidification 201
5.3.5 Adiabatic Humidification 203
5.3.6 Adiabatic Mixing 204
5.4 Moist Air Transport in Buildings 205
5.4.1 Mass Transport of Moist Air 205
Contents vii
5.4.3 Pores 209
5.4.4 Air Transport Through Pores 210
5.4.5 Vapour Transport Through Pores 211
5.4.6 Mass Transport Through Openings 214
References 215
6 An Overview on Fundamentals of Heat Transfer in Buildings 217
6 An Overview of Heat Transfer 217
6.1 Conduction 217
6.1.1 Heat Diffusion Equation 220
6.2 Convection 223
6.2.1 Thermal Boundary Layer 223
6.2.2 Local and Average Convection Coefficients 224
6.2.3 Convection in External Flows 226
6.2.4 Convection in Internal Flow 231
6.2.4.1 Thermally Fully Developed Condition 233
6.2.4.2 Mean Temperature at Internal Flows 235
6.2.4.3 Nusselt Number of Internal Flows 238
6.2.5 Free Convection 241
6.2.5.1 Empirical Correlations for Vertical Surfaces 244
6.2.5.2 Empirical Correlations for Horizontal and Inclined Surfaces 245
6.2.5.3 Empirical Correlations for Channel Flows and Cavities 248
6.3 Radiation 248
6.3.1 Total Emission, Irradiation, and Radiosity 251
6.3.2 Black and Grey Bodies 253
6.3.3 View Factor 254
6.3.4 Radiation Exchange at Surfaces 260
6.3.5 Radiation Network 261
References 265
7 Applications of Heat Transfer in Buildings 267
7 Introduction 267
7.1 Conduction in Walls 267
7.2 Thermal Resistance Analogy 270
7.3 Walls with Heat Generation 277
7.4 Convective Heat Transfer Coefficient of Exterior Walls 278
7.4.1 Wind on Buildings’ Exterior Surfaces 278
7.4.2 Simple-Combined Correlation 279
7.4.3 TARP Correlation 280
7.4.4 MoWiTT Correlation 281
7.4.5 DOE-2 Correlation 282
7.4.6 Adaptive Correlations 282
7.5 Convection on Interior Walls 287
viii Contents
7.5.5 Fisher–Pedersen Correlation 289
7.5.6 Goldstein–Novoselac Correlation 289
7.5.7 Fohanno–Polidori Correlation 290
7.6 Radiations 295
7.6.1 Solar Radiation on Building Surfaces 296
7.6.2 ASHRAE Clear Sky Model 297
7.6.3 ASHRAE Revised Clear Sky Model 297
7.6.4 Zhang–Huang Model 300
7.6.5 Diffuse Solar Radiation Model 300
7.7 Long-wave Radiation on Building Surfaces 306
7.7.1 View Factors of Surrounding Environment 307
7.7.2 Emissivity of Surrounding Environment 308
7.7.3 Bulk Temperature of Surrounding Environment 308
References 311
8 Fundamental of Energy Modelling in Buildings 313
8 Introduction 313
8.1 Definition of a Zone 313
8.2 Conservation Law in Buildings 315
8.3 Governing Equations at Zones 316
8.4 Energy Balance Equation 316
8.5 Nodal Analogy of the Governing Equation 318
8.5.1 Convective Heat Fluxes 320
8.5.2 Advective Heat Fluxes 320
8.5.3 Heat Generation Fluxes 321
8.5.4 Short-wave Radiative Fluxes in Zone 321
8.5.5 Long-wave Radiative Fluxes in Zone 323
8.5.6 Conduction Heat Fluxes Through Solid Surfaces 330
8.5.7 Short-wave Radiative Fluxes on Exterior Surfaces 331
8.5.8 Long-wave Radiative Fluxes on Exterior Surfaces 331
8.5.8.1 Surface to Surface Long-wave Radiative Fluxes 331
8.5.8.2 Surface to Environment Long-wave Radiative Fluxes 333
8.5.8.3 Linearization of Long-wave Radiative fluxes 335
8.5.9 Thermal Mass 336
8.5.9.1 Thermal Mass in Solid Surfaces 336
8.5.9.2 Multi-layer Walls 339
8.5.9.3 Thermal Mass in Furniture 341
8.6 Walls, Windows, and Thermal Bridges 343
8.7 Mass Balance Equation 348
8.7.1 Airflow Network Model 350
8.7.2 Mass Flow Resistance 352
Contents ix
8.7.3 Infiltration Mass Flow 356
8.7.4 Design Flow Rate Model 356
8.7.5 Effective Leakage Area Model 357
8.7.6 Flow Coefficient Model 357
8.7.7 Moist Air 360
References 361
9 Dynamic Energy Modelling in Buildings 363
9 Physics of an Energy Balance Problem in Buildings 363
9.1 Mathematical Representation of Buildings with Integrated Nodal System 366
9.2 Numerical Solution Method for Nodal System 370
9.2.1 Zone Equations 370
9.2.2 Solid Material Equations 371
9.3 Inputs 381
9.3.1 User-inputs 381
9.3.2 Non-time Variant Inputs 382
9.3.3 Time-Variant Inputs 382
9.3.3.1 HVAC System 383
9.3.3.2 Internal Load Model 383
9.3.3.3 Climatic Input 388
9.4 Solution Strategies 392
9.4.1 Integrated Solution 393
9.4.2 Coupled Solution 399
9.4.3 Nodes Connectivity 406
9.5 Temporal Variation of Parameters 406
9.6 Linearization of the Radiation 409
9.7 Mass Imbalance 410
References 412
10 Fundamental of Computational Fluid Dynamics – A Finite
Volume Approach 413
10 What Is CFD 413
10.1 Steps in CFD 413
10.1.1 Preprocessing 414
Understanding the Physics of a Problem 414
Geometry and Domain Creation 414
Mesh Generation 414
Assigning Boundary and Initial Conditions 414
Definition of Solid and Fluid Materials’ Properties 415
10.1.2 Solution 415
10.1.3 Post-processing 415
10.2 Classification of Conservation Equations 415
10.3 Difference of Finite Difference and Finite Volume 418
10.4 Integral Form of the Conservation Equations 418
10.5 Grid (Mesh) 419
x Contents
10.5.1.1 Skewness 423
10.5.1.2 Smoothness 425
10.5.1.3 Aspect Ratio 425
10.6 Diffusion Equation 429
10.7 Boundary Treatment 431
10.7.1 Neumann Boundary Type I 435
10.7.2 Neumann Boundary Type II 436
10.8 Expansion to Higher Dimensions 439
10.9 Discretization Methods 446
10.10 Steady-State Diffusion–Convection Equation 449
10.11 Other Approximation Methods 456
10.12 Scheme Evaluation 458
10.12.1 Conservativeness 458
10.12.2 Boundedness 459
10.12.3 Transportiveness 460
10.13 Common Schemes 460
10.13.1 Central Difference 461
10.13.2 First-Order Upwind 461
10.13.3 Second-Order Upwind 465
10.13.4 Power Law 469
10.13.5 Hybrid 469
10.13.6 QUICK 470
10.14 Unsteady Diffusion Equation 475
10.14.1 Explicit Scheme 476
10.14.2 Implicit Scheme 480
10.15 Unsteady Diffusion–Convection Equation 484
10.16 Pressure–Velocity Coupling 484
References 488
11 Solvers and Solution Analysis 489
11 Introduction 489
11.1 Solvers of Algebraic Equation Systems 489
11.2 Direct Method 489
11.2.1 Cramer’s Rule 490
11.2.2 Gaussian Elimination 491
11.2.3 1D TDMA 493
11.3 Iterative Method 496
11.3.1 Jacobi 497
11.3.2 Gauss–Seidel 499
11.3.3 Higher-order TDMA 500
11.4 Solution Analysis 502
11.4.1 Consistency 503
11.4.2 Stability 504
11.4.3 Grid Convergence 504
Contents xi
11.4.5 Initial Guess 507
11.4.6 Under-Relaxation 508
11.5 Physical Uncertainty 509
11.6 Numerical Errors 510
11.6.1 Roundoff Error 511
11.6.2 Truncation Error 512
11.6.3 Iterative Convergence Error 513
11.7 Verification and Validation 513
11.8 Measures to Minimize Errors 517
11.8.1 Simulation Resource Assessment 518
11.8.2 Geometry Simplification 519
11.8.3 Grid Sensitivity Analysis 520
11.8.4 Iterative Convergence Control 523
11.8.5 Comparison with Experimental Benchmarks 525
11.8.6 Best Practice 531
References 532
12 Application of CFD in Buildings and Built Environment 533
12.1 CFD Models in Built Environment 533
12.1.1 Spatial Scale 533
12.1.2 Temporal Variation 533
12.2 Inputs to CFD Models 535
12.2.1 Boundary Conditions 536
12.2.1.1 Enclosed Spaces 536
12.2.1.2 Microclimates 537
12.3 Practical Examples 539
12.3.1 Conduction in Solid Materials 539
12.3.2 Wall Treatment of Boundary Layer 547
12.3.3 Airflow in Microclimate 556
12.3.4 Convective Heat Transfer Coefficient 576
References 588
Index 589

"This book will explain how heat and mass transport in buildings can be modelled using commercial and educational tools, with a focus on helping those who want to use those tools to understand and predict the performance of buildings, but who may not be experts in CFD. The fundamentals of modelling will be fully covered and then extended to show how those models can be used to simulate the behaviour of buildings. The aim is to ensure the reader understands the essentials of modelling and can use the existing tools effectively and knowledgably. Modelling and simulation involve many assumptions and simplifications, so the book covers these topics fully, ensuring the reader understands and can justify those assumptions and simplifications. In addition, it addresses uncertainties in the selection of possible options to ensure the reader can get the most from existing heat and mass transport modelling tools."-- Provided by publisher.