Selected Topics of Computational and Experimental Fluid Mechanics (eBook)

Preface 6
Acknowledgments 10
Contents 11
Contributors 16
Part I Invited Lectures 25
Compositional Flow in Fractured Porous Media: Mathematical Background and Basic Physics 26
1 Introduction 27
2 Multiphase Flow in Porous Media 29
2.1 Undeformable Porous Media 30
2.2 Deformable Porous Media 36
3 Multicomponent Flow in a Single Fluid Phase 40
4 Compositional Flow in a Porous Medium 43
5 Chemical Flooding Compositional Flow in Porous Media 47
6 Compositional Flow in Fractured Porous Media 50
6.1 Dual-Continuum Model 51
6.2 Triple-Continuum Model 55
References 57
Turbulent Thermal Convection 60
1 Introduction 60
2 Rayleigh-Bénard Convection 62
3 High Ra and Ultimate Regime 64
4 Large Aspect Ratio and Large Scales 65
5 Conclusions 68
References 69
Dissipative Particle Dynamics: A Method to Simulate Soft Matter Systems in Equilibrium and Under Flow 73
1 Introduction 74
2 Details of the Dissipative Particle Dynamics Method 75
2.1 Basic Molecular Dynamics Simulation 75
2.2 Simulating at Constant Temperature: The Langevin Thermostat 76
2.3 The Dissipative Particle Dynamics Thermostat 78
3 Interaction Models: Soft and Hard Potentials 79
3.1 DPD with Soft Potentials 79
3.2 Selected Examples of Soft Matter Systems in Equilibrium 81
3.3 DPD with Hard Potentials 83
4 Selected Examples of DPD in Flow Simulations 84
4.1 Polymer Brushes with Soft Potentials 84
4.2 Hard Coarse-Grained Potentials 93
5 The Conservation of Temperature in Flow Simulations 96
6 Concluding Remarks 98
References 99
Flow Coherence: Distinguishing Cause from Effect 102
1 Introduction 102
2 Mathematical Setup 103
3 Geodesic Transport Theory 105
4 Application to an Oceanic Flow Dataset 105
5 Final Remarks 108
References 109
Parametrisation in Dissipative Particle Dynamics: Applications in Complex Fluids 111
1 Introduction 111
2 Electrostatic Dissipative Particle Dynamics: A Brief Overview 114
3 Parametrisation for Realistic Systems 117
3.1 Concentration Dependence of the DPD Interaction Parameters 119
3.2 Temperature Dependence of the DPD Interaction Parameters 120
4 Applications 122
4.1 Interfacial Tension 122
4.2 Adsorption Isotherms 125
4.3 Disjoining Pressure 128
4.4 Radius of Gyration 129
5 Scaling 134
6 Conclusions 136
References 137
Smoothed Particle Hydrodynamics for Free-Surface Flows 139
1 Introduction 139
2 Theory 140
2.1 SPH Interpolant 141
2.2 The Smoothing Kernel 141
2.3 Momentum Equation 142
2.4 Continuity Equation 142
2.5 Equation of State 142
2.6 Moving the Particles 143
2.7 Time Stepping 143
2.8 Variable Time Step 145
2.9 Boundary Conditions 145
3 Validation Case 146
4 DualSPHysics Capabilities 150
4.1 Wave Propagation 151
4.2 Wave Interaction with a Fixed Complex Structure 151
4.3 Wave Interaction with a Floating Object 155
5 Conclusions 155
References 155
Numerical Modelling of the Extratropical Storm Delta Over Canary Islands: Importance of High Resolution 157
1 Introduction 158
2 Methods 159
3 Numerical Solution and Results 160
4 Conclusions 164
References 165
Four-Winged Flapping Flyer in Forward Flight 167
1 Introduction 167
2 Experimental Setup 168
3 Results 170
4 Discussion 174
5 Conclusions 176
References 177
Flows from Bins: New Results 179
1 Introduction 179
2 Dry Friction: A Historical Review 181
3 The Mass Flow Rate Problem 184
3.1 Mass Flow Rate for Large Grains Through Side Walls 186
4 Tilted Bins 188
4.1 The Problem 188
4.2 The Franklin and Johanson Formula 189
4.3 Experiments 190
4.4 The Formulation of a Correlation 191
5 Pressures in a Silo 193
5.1 Calculation of the Pressure and Traction Force in the Silo 194
6 Conclusions 196
References 196
Some Aspects of Turbulence Role in Oceanic Currents 198
1 Introduction 198
1.1 Ocean General Circulation 199
1.2 Turbulence in the Ocean 200
2 In-Situ Measurements 201
2.1 Fine-Structure Parameterization 202
2.2 Microstructure Direct Measurements 202
2.3 Tracer-Release Experiment 203
3 Observations and Results 203
4 Summary 205
References 206
Alya Red CCM: HPC-Based Cardiac Computational Modelling 207
1 Introduction 208
2 Alya, an HPC-Based Computational Mechanics Tool 209
2.1 General Description 209
3 Parallel Computational Aspects 215
3.1 Parallel Efficiency 215
4 Examples 216
4.1 Electro-Mechanical Coupling in a Bi-Ventricular Geometry 217
4.2 Electro-Mechanical-Fluid Coupling in a Simplified Ventricular Geomety 220
5 Conclusions and Future Lines 221
References 224
Singularities in Surface Waves 226
1 Introduction 226
2 Spatial Focusing, Caustics and Dislocations 229
3 Optical Methods to Study Surface Waves 232
3.1 Experimental Setup 233
4 Numerical Method 234
5 Experimental and Numerical Results 235
6 Conclusions 242
References 243
Part II Multiphase Flow and Granular Media 244
Isotherms of Natural and Forced Convection Around a Heated Horizontal Cylinder Embedded in a Porous Medium 245
1 Introduction 246
2 Theoretical Model 246
3 Experimental Setup 247
4 Isotherms Around the Source 248
5 Isotherms Under Free Convection 249
5.1 Isotherms for a Horizontal Line Source of Heat Under a Uniform Stream 251
6 Conclusions 252
References 253
Parameter Estimation in a Model for Tracer Transport in One-Dimensional Fractals 254
1 Introduction 254
2 The Model 255
2.1 The Fractal Continuum Model 255
2.2 The Tracer Advection-Dispersion Equation 256
2.3 Boundary and Initial Conditions 258
2.4 Numerical Solution of the Advection-Dispersion Equation 258
3 Parameter Estimation Procedure 259
3.1 Fitting Parameters 260
3.2 The Inverse Problem 260
3.3 Optimization Algorithm 261
4 Synthetic Data Generation 261
5 Robustness of the Method 262
5.1 Sensitivity to the Level of Data Noise 262
5.2 Sensitivity to the Amount of Data 263
5.3 Sensitivity to the Amount of Fitting Parameters 264
6 Discussion of Results 265
7 Conclusions 266
References 267
Mixed Convection in a Rectangular Enclosure with Temperature-Dependent Viscosity and Viscous Dissipation 268
1 Introduction 268
2 Problem Formulation 269
3 Numerical Results and Model Validation 271
4 Results 272
5 Conclusions 274
References 274
Characterization of a Bubble Curtain for PIV Measurements 275
1 Introduction 275
1.1 Theoretical Framework 276
2 Background 277
3 Methodology 278
4 Results and Discussion 279
4.1 Results for One Column of Bubbles 279
4.2 Results for Three Bubbles 281
4.3 Results Obtained When Waves Were Introduced 282
5 Conclusions 282
References 283
Numerical Simulation of a Gas-Stirred Ladle 284
1 Introduction 285
2 Two-Phase Fluid Flow Model 286
3 Results and Discussion 288
4 Conclusions 292
References 292
Folding of the Apolipoprotein A1 Driven by the Salt Concentration as a Possible Mechanism to Improve Cholesterol Trapping 294
1 Introduction 294
2 Model and Methodology 295
3 Results and Discussion 296
4 Conclusions 302
References 303
Graphical Analysis of Fluid Flow Through Polymeric Complex Structures Using Multi-scale Simulations 305
1 Introduction 306
2 Smoothed Particle Hydrodynamics and Dissipative Particle Dynamics 306
2.1 Smoothed Particle Hydrodynamics 306
2.2 Dissipative Particle Dynamics 308
3 Simulations and Visualization 309
4 Conclusions 314
References 314
Mass Flow Rate of Granular Material from an L-Valve Without Aeration 315
1 Introduction 315
2 Gravity Flow: A Simple Model 317
3 Experiments 318
4 Conclusions 320
References 320
Part III Convection and Diffusion 322
Heat Transfer in Biological Tissues 323
1 Introduction 323
2 Model Description 324
2.1 Dimensionless Equation 325
3 Results and Discussion 327
3.1 Steady State Temperature 327
4 Conclusions 329
References 329
Simulation of In-situ Combustion in a Matrix-Fracture System at Laboratory Scale 331
1 Introduction 331
2 Theoretical Model 332
3 The Base Case 334
4 The Matrix-Fracture Case 336
5 Concluding Remarks 337
References 338
Numerical Simulation of In-situ Combustion in a Fracture-Porous Medium System 339
1 Introduction 339
2 Governing Equations, Boundary and Initial Conditions 340
3 Homogeneous System Simulation 341
4 Fracture-Porous Medium System Simulation 343
5 Conclusions 347
References 347
Mathematical Modeling of Steam Injection in Vertical Wells 349
1 Introduction 349
2 Model Formulation 350
2.1 Physical Model 350
2.2 Mathematical Model 350
3 Numerical Implementation 353
4 Results and Discussions 354
5 Conclusions 356
References 356
Oxygen Transport Under Combustion Conditions in a Fracture-Porous Medium System 357
1 Introduction 358
2 Physical and Mathematical Models 358
2.1 Governing Equations, Initial and Boundary Conditions 360
3 Results and Discussions 362
3.1 Effect of the Fracture Peclet Number 362
3.2 Effect of the Fracture Width 363
4 Conclusions 363
References 364
Numerical Simulation of the Flow in an Open Cavity with Heat and Mass Transfer 366
1 Introduction 367
2 Problem Formulation 367
3 Numerical Solution and Validation of the Results 369
4 Results and Discussions 369
5 Conclusions 373
References 374
3D Numerical Simulation of Rayleigh-Bénard Convection in a Cylindrical Container 375
1 Introduction 375
2 Methodology 376
2.1 Fourier Series Approximation 378
2.2 Projection Method 378
2.3 Initial and Boundary Conditions 379
3 Results 379
4 Conclusions 381
References 382
Solidification in the Presence of Natural Convection in a Hele-Shaw Cell 383
1 Introduction 384
2 Experimental Device and Visualization Methods 385
3 Results 386
4 Discussion and Conclusions 391
References 392
Confinement and Interaction Effects on the Diffusion of Passive Particles 393
1 Introduction 394
2 Model 395
3 Results 397
4 Conclusions 401
References 401
Thermal Convection in a Cylindrical Enclosure with Wavy Sidewall 403
1 Introduction 403
2 Problem Statement 405
3 Mathematical Formulation 406
4 Results and Discussion 409
4.1 Enclosure Heated from Below 409
4.2 Enclosure Heated from the Top 413
5 Conclusions 416
References 418
Part IV Vortex, Oceanography and Meteorology 420
Numerical Simulation of the Flow Past a Pair of Magnetic Obstacles 421
1 Introduction 421
2 Formulation of the Problem 422
3 Numerical Results 426
4 Concluding Remarks 430
References 431
Steady and Unsteady Vortex Flow Generated by Electromagnetic Forcing 432
1 Introduction 432
2 Experimental Setup and Flow Visualization 433
3 Quasi-Two-Dimensional Numerical Model 436
4 Comparison Between Numerical and Experimental Results 437
5 Conclusions 441
References 442
Numerical Simulation of a Spanwise Vortex in a Periodic Forced Flow 443
1 Introduction 443
2 Description of the System and Numerical Simulation 444
3 Results 446
3.1 The Pulse 446
3.2 Periodic Forced Flow, S =0.02 447
4 Time Convergence 448
5 Conclusions 449
References 449
Erosion and Deposition of Particles in a Periodic Forced Flow 450
1 Introduction 450
2 Experimental Setup 451
3 Results 453
3.1 Channel Width of 2.5Centimeters 453
3.2 Channel Width of 3Centimeters 454
3.3 Channel Width of 5Centimeters 454
4 Conclusions 455
References 456
Part V General Fluid Dynamics and Applications 457
Numerical and Simplified Analytical Solutions for Typical Spillways 458
1 Introduction 459
2 Problem Formulation 459
3 Results and Discussion 461
4 Conclusions 463
References 464
Modeling and Simulation of a Biopolymer Processing in a Single Screw Extruder 465
1 Introduction 465
2 Development 466
3 Results and Discussion 468
4 Conclusions 471
References 471
An Analytical Solution for Friction Stir Welding of an AISI 1018 Steel 472
1 Introduction 472
2 Mathematical Models 473
2.1 Perzyna's Model 473
2.2 Viscosity Power Law Model 473
2.3 Heat Generation Schmidt Model 473
3 Mathematical Formulation 474
4 Conclusions 478
References 478
Numerical Simulation of Water Flow in a Venturi Tube Using the Smoothed Particle Hydrodynamics Method 480
1 Introduction 480
2 The SPH Method 481
3 Experimental Setup 483
4 Numerical Simulations 483
5 Results and Discussion 484
6 Conclusions 486
References 486
Dynamic Behavior of a Drop on a Vertically Oscillating Surface 487
1 Introduction 487
2 Background 488
3 Experimental Set-Up 488
4 Results 488
4.1 Harmonic Phase 488
4.2 Geometric Phase 489
4.3 Chaotic Phase 490
5 Conclusions and Future Work 493
References 494
Critical Phenomena of a Drop Through a Stratified Fluid 495
1 Introduction 495
2 Experimental Set-Up 496
3 Results 497
3.1 Settling 498
3.2 Chandelier 498
3.3 Core Fallout 498
3.4 Rebound 499
4 Conclusions and Future Work 501
References 501
Accretion Centers Induced in a Molecular Cloud Core After a Penetrating Collision 502
1 Introduction 502
2 The Colliding Cores 503
3 The Computational Method 505
4 Results 506
5 Conclusions 510
References 510
Numerical Simulations of Interacting Galaxies: Bar Morphology 511
1 Introduction 512
2 Initial Conditions and Geometry of the Collision 513
3 Results 517
4 Conclusions 520
References 520
A Newtonian Approach to the Cosmological Dark Fluids 522
1 Introduction 523
2 Homogeneous and Isotropic Cosmology in Newtonian Gravity 524
3 Small Perturbations in Newtonian Cosmology 527
4 The Dark Fluid 531
5 Conclusions 533
References 534
Capillary Rise in a Taylor-Hauksbee Cell with a Tilted Edge 535
1 Introduction 535
2 Capillary Rise in the Taylor-Hauksbee Cell 536
2.1 Cell with a Vertical Edge 536
2.2 Cell with Tilted Edge 537
3 Dynamical Evolution 540
4 Conclusions 541
References 542