Series Preface .............................................. XI
Preface of Volume 1 ......................................... XV
List of Contributors ....................................... XXI
Recommended Notation ....................................... XXV
EFCE Working Party on Drying: Address List ................ XXXI
1 Comprehensive Drying Models based on Volume Averaging:
Background, Application and Perspective ...................... 1
P. Perré, R. Rémond, I.W. Turner
1.1 Microscopic Foundations of the Macroscopic Formulation .. 1
1.2 The Macroscopic Set of Equations ........................ 6
1.3 Physical Phenomena Embedded in the Equations ............ 7
1.3.1 Low-temperature Convective Drying ................ 7
1.3.1.1 The Constant Drying Rate Period ......... 8
1.3.1.2 The Decreasing Drying Rate Period ....... 9
1.3.2 Drying at High Temperature: The Effect of
Internal Pressure on Mass Transfer .............. 10
1.4 Computational Strategy to Solve the Comprehensive Set
of Macroscopic Equations ............................... 11
1.4.1 The Control-volume Finite-element (CV-FE)
Discretization Procedure ........................ 13
1.4.2 Evaluation of the Tensor Terms at the С V Face .. 14
1.4.3 Solution of the Nonlinear System ................ 15
1.4.3.1 Outer (Nonlinear) Iterations ........... 16
1.4.3.2 Construction of the Jacobian ........... 17
1.4.3.3 Inner (Linearized System) Iterations ... 17
1.5 Possibilities Offered by this Modeling Approach:
Convective Drying ...................................... 19
1.5.1 High-temperature Convective Drying of Light
Concrete ........................................ 19
1.5.1.1 Test 1: Superheated Steam .............. 20
1.5.1.2 Tests 2 and 3: Moist Air, Soft and
Severe Conditions ...................... 22
1.5.2 Typical Drying Behavior of Softwood:
Difference Between Sapwood and Heartwood ........ 25
1.6 Possibilities Offered by this Modeling Approach:
Less-common Drying Configurations ...................... 29
1.6.1 Drying with Volumetric Heating .................. 29
1.6.2 The Concept of Identity Drying Card (IDC) ....... 32
1.6.3 Drying of Highly Deformable Materials ........... 34
1.7 Homogenization as a Way to Supply the Code with
Physical Parameters .................................... 37
1.8 The Multiscale Approach ................................ 42
1.8.1 Limitations of the Macroscopic Formulation ...... 42
1.8.2 The Stack Model: An Example of Multiscale
Model ........................................... 43
1.8.2.1 Global Scale ........................... 46
1.8.2.2 Local Scale ............................ 46
1.8.2.3 Coupling Approach ...................... 46
1.8.2.4 Samples Simulations .................... 47
1.8.2.5 Accounting for Wood Variability ........ 49
1.8.2.6 Accounting for Drying Quality .......... 50
Conclusion .................................................. 52
2 Pore-network Models: A Powerful Tool to Study Drying
at the Pore Level and Understand the Influence of
Structure on Drying Kinetics ................................ 57
T. Metzger, E. Tsotsas, M. Prat
2.1 Introduction ........................................... 57
2.2 Isothermal Drying Model ................................ 58
2.2.1 Model Description ............................... 58
2.2.1.1 Network Geometry and Corresponding
Data Structures ........................ 59
2.2.1.2 Boundary-layer Modeling ................ 60
2.2.1.3 Saturation of Pores and Throats ........ 62
2.2.1.4 Vapor Transfer ......................... 63
2.2.1.5 Capillary Pumping of Liquid ............ 64
2.2.1.6 Cluster Labeling ....................... 65
2.2.1.7 Drying Algorithm ....................... 66
2.2.2 Simulation Results and Experimental Validation .. 68
2.2.3 Gravity and Liquid Viscosity - Stabilized
Drying Front .................................... 73
2.2.3.1 Modeling Gravity ....................... 71
2.2.3.2 Modeling Liquid Viscosity .............. 72
2.2.3.3 Dimensionless Numbers and Length
Scales ................................. 75
2.2.3.4 Phase Distributions and Drying Curves .. 77
2.2.4 Film Flow ....................................... 79
2.2.5 Wettability Effects ............................. 83
2.2.6 First Drying Period ............................. 85
2.3 Model Extensions ....................................... 87
2.3.1 Heat Transfer ................................... 87
2.3.2 Multicomponent Liquid ........................... 92
2.4 Influence of Pore Structure ............................ 92
2.4.1 Pore Shapes ..................................... 92
2.4.2 Coordination Number ............................. 94
2.4.3 Bimodal Pore-size Distributions ................. 95
2.4.4 Outlook ........................................ 100
2.5 Towards an Assessment of Continuous Models ............ 100
3 Continuous Thermomechanical Models using Volume-averaging
Theory ..................................................... 103
F. Couture, P. Bernada, M.A. Roques
3.1 Introduction .......................................... 103
3.2 Modeling .............................................. 105
3.2.1 Nature of Product Class ........................ 106
3.2.2 Averaged Internal Equations .................... 107
3.2.2.1 State Equations and Volume
Conservation .......................... 108
3.2.2.2 Mass-conservation Equations ........... 109
3.2.2.3 Momentum-conservation Equations ....... 109
3.2.2.4 Energy-conservation Equations ......... 112
3.2.3 Boundary Conditions for Convective Drying ...... 113
3.3 Simulation ............................................ 114
3.3.1 Numerical Resolution Technique ................. 114
3.3.2 Comparison between Real Viscoelatic and
Assumed Elastic Behavior ....................... 115
3.4 Liquid Pressure as Driving Force ...................... 120
3.5 Conclusions ........................................... 122
4 Continuous Thermohydromechanical Model using the Theory
of Mixtures ................................................ 125
S.J. Kowalski
4.1 Preliminaries ......................................... 125
4.2 Global Balance Equations .............................. 326
4.3 Constitutive Equations in the Skeletal Frame of
Reference ............................................. 130
4.4 Rate Equations for Heat and Mass Transfer ............. 132
4.5 Differential Equations for Heat and Mass Transfer ..... 134
4.5.1 Differential Equation for Heat Transfer ........ 134
4.5.2 Determination of the Microwave Heat Source 9t .. 135
4.5.3 Differential Equation for Mass Transfer ........ 139
4.6 Thermomechanical Equations for a Drying Body .......... 141
4.6.1 Physical Relations ............................. 141
4.6.2 Differential Equations for Body Deformation .... 143
4.7 Drying of a Cylindrical Sample made of Kaolin ......... 144
4.7.1 Convective Drying of a Kaolin Cylinder ......... 144
4.7.2 Microwave Drying of a Kaolin Cylinder .......... 150
4.8 Final Remarks ......................................... 152
Acknowledgments ............................................ 152
Additional Notation used in Chapter 4 ...................... 153
5 CFD in Drying Technology - Spray-Dryer Simulation .......... 155
S. Blei, M. Sommerfeld
5.1 Introduction .......................................... 155
5.1.1 Introduction to CFD ............................ 155
5.1.2 Introduction to Multiphase Flow Modeling ....... 258
5.1.3 State-of-the-art in Spray-dryer Computations ... 160
5.2 The Euler-Lagrange Approach: an Extended Model for
Spray-dryer Calculations .............................. 162
5.2.1 Fluid-phase Modeling ........................... 163
5.2.2 Fundamentals of Lagrangian Particle Tracking ... 166
5.2.2.1 Drag Force ............................ 167
5.2.2.2 Virtual Mass Force .................... 168
5.2.2.3 Basset History Force .................. 168
5.2.2.4 Forces Caused by Pressure Gradients
in the Fluid .......................... 168
5.2.2.5 Magnus Force .......................... 168
5.2.2.6 Saffman Force ......................... 169
5.2.2.7 Gravitational Force ................... 169
5.2.3 Particle Tracking .............................. 169
5.2.4 Particle Turbulent Dispersion Modeling ......... 171
5.2.5 Two-way Coupling Procedure ..................... 173
5.3 Droplet-drying Models ................................. 173
5.3.1 Introduction ................................... 173
5.3.2 Review of Droplet-drying Models ................ 175
5.3.3 Exemplary Drying Model for Whey-based Milk
Products ....................................... 176
5.3.4 Numerical Implementation ....................... 178
5.4 Collisions of Particles ............................... 181
5.4.1 Introduction ................................... 181
5.4.2 Extended Stochastic Collision Model ............ 182
5.4.3 Modeling of Particle Collisions: Coalescence
and Agglomeration .............................. 187
5.4.3.1 Surface-tension Dominated Droplets
(STD Droplets) ........................ 187
5.4.3.2 Droplets Dominated by Viscous Forces
(VD Droplets) ......................... 188
5.4.3.3 Dry Particles ......................... 189
5.4.4 Collisions of Surface-tension Dominated
Droplets (STD-STD) ............................. 190
5.4.5 Collisions of Viscous Droplets ................. 290
5.4.6 Collisions of Dry Particles .................... 292
5.5 Example of a Spray-dryer Calculation .................. 192
5.5.1 Geometry and Spatial Discretization of the
Spray Dryer .................................... 192
5.5.2 Results for the Fluid Phase .................... 193
5.5.3 Results of the Dispersed Phase ................. 195
5.6 Prediction of Product Properties ...................... 200
5.6.1 Particle-size Distribution ..................... 200
5.6.2 Heat Damage .................................... 201
5.6.3 Particle Morphology ............................ 201
5.7 Summary ............................................... 203
Additional Notation used in Chapter 5 ...................... 204
6 Numerical Methods on Population Balances ................... 209
J. Kumar, M. Peglow, C. Warnecke, S. Heinrich,
E. Tsotsas, L. Mörl, M. Hounslow, C. Reynolds
6.1 Introduction .......................................... 209
6.2 Pure Breakage ......................................... 214
6.2.1 Population-balance Equation .................... 214
6.2.2 Numerical Methods .............................. 214
6.2.2.1 The Cell-average Technique ............ 216
6.2.2.2 The Finite-volume Scheme .............. 222
6.3 Pure Aggregation ...................................... 225
6.3.1 Population-balance Equation .................... 225
6.3.2 Numerical Methods .............................. 226
6.3.2.1 The Fixed-pivot Technique ............. 226
6.3.2.2 The Cell-average Technique ............ 227
6.3.2.3 The Finite-volume Scheme .............. 231
6.4 Pure Growth ........................................... 233
6.4.1 Population balance Equation .................... 233
6.4.2 Numerical Methods .............................. 233
6.5 Combined Aggregation and Breakage ..................... 239
6.6 Combined Aggregation and Nucleation ................... 242
6.7 Combined Growth and Aggregation ....................... 244
6.8 Combined Growth and Nucleation ........................ 245
6.9 Multidimensional Population Balances .................. 247
6.9.1 Reduced Model .................................. 247
6.9.2 Complete Model ................................. 250
Additional Notation used in Chapter 6 ...................... 256
7 Process-systems Simulation Tools ........................... 261
I.C. Kemp
7.1 Introduction .......................................... 261
7.1.1 Summary of Contents ............................ 261
7.1.2 The Solids Processing Challenge ................ 262
7.1.3 Types of Software for Dryers ................... 263
7.2 Numerical Calculation Procedures ...................... 263
7.2.1 Categorization of Dryer Models ................. 264
7.2.2 Equipment and Material Model ................... 265
7.2.3 Parametric Models .............................. 266
7.3 Heat and Mass Balances ................................ 268
7.4 Scoping Design Methods ................................ 269
7.4.1 Continuous Convective Dryers ................... 269
7.4.2 Continuous-contact Dryers ...................... 270
7.4.3 Batch Dryers ................................... 270
7.4.4 Simple Allowance for Falling-rate Drying ....... 271
7.5 Scaling Methods ....................................... 272
7.5.1 Basic Scale-up Principles ...................... 273
7.5.2 Integral Model ................................. 274
7.5.3 Application to Fluidized-bed Dryers ............ 274
7.6 Detailed Design Models ................................ 276
7.6.1 Incremental Model .............................. 277
7.6.2 Application to Pneumatic Conveying, Rotary
and Band Dryers ................................ 278
7.6.2.1 Pneumatic Conveying Dryers ............ 278
7.6.2.2 Cascading Rotary Dryers ............... 281
7.6.3 Advanced Methods - Computational Fluid
Dynamics (CFD) ................................. 281
7.7 Ancillary Calculations ................................ 283
7.7.1 Processing Experimental Data ................... 283
7.7.2 Humidity and Psychrometry ...................... 284
7.7.2.1 British Standard BS1339 for Humidity
Calculations .......................... 284
7.7.2.2 Plotting Psychrometric Charts ......... 286
7.7.3 Physical-properties Databanks .................. 286
7.8 Process Simulators .................................... 287
7.8.1 Current Simulators and their Limitations ....... 287
7.8.2 Potential Developments ......................... 288
7.9 Expert Systems and Decision-making Tools .............. 289
7.9.1 Dryer Selection ................................ 289
7.9.1.1 Tree-search Algorithms ................ 289
7.9.1.2 Matrix-type Rule-based Algorithms ..... 289
7.9.1.3 Qualitative Information ............... 292
7.9.1.4 Alternative Tree-search Approach ...... 292
7.9.2 Troubleshooting and Problem Solving in Dryers .. 294
7.10 Knowledge Bases and Qualitative Information ........... 295
7.10.1 Internet Websites .............................. 295
7.10.2 The Process Manual Knowledge Base .............. 295
7.11 Commercialization of Drying Software .................. 296
7.11.1 Barriers to Drying-software Development ........ 297
7.11.1.1 Complexity of the Calculations ........ 297
7.11.1.2 Difficulties in Modeling Solids ....... 297
7.11.1.3 Limited Market and Lack of
Replicability ......................... 298
7.11.1.4 Changes in Operating-system Software .. 298
7.11.2 The Future: Possible Ways Forward .............. 300
7.12 Conclusions ........................................... 301
7.12.1 Range of Application of Software in Drying ..... 301
7.12.2 Overall Conclusion ............................. 302
Additional Notation used in Chapter 7 ...................... 303
Index ...................................................... 307
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