An introduction to granular flow:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge, Mass.
Cambridge University Press
2008
|
| Edition: | 1. publ. |
| Series: | Cambridge series in chemical engineering
|
| Subjects: | |
| Online Access: | Publisher description Table of contents only Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XXI, 490 S. Ill., graph. Darst. |
| ISBN: | 9780521571661 |
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| 100 | 1 | |a Rao, K. Kesava |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to granular flow |c K. Kesava Rao and Prabhu R. Nott |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge, Mass. |b Cambridge University Press |c 2008 | |
| 300 | |a XXI, 490 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Cambridge series in chemical engineering | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Granular materials |x Fluid dynamics | |
| 650 | 0 | 7 | |a Granulärer Stoff |0 (DE-588)4256351-3 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Nott, Prabhu R. |e Verfasser |4 aut | |
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| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0806/2007050026-t.html |3 Table of contents only | |
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| _version_ | 1804137684927512576 |
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| adam_text | AN INTRODUCTION TO GRANULAR FLOW K. KESAVA RAO PRABHU R. NOTT INDIAN
INSTITUTE OF SCIENCE INDIAN INSTITUTE OF SCIENCE CAMBRIDGE UNIVERSITY
PRESS CONTENTS PREFACE PAGE XIII NOTATION XV 1 INTRODUCTION I I. I
EXAMPLES OF GRANULAR STATICS AND FLOW 2 1.2 INTERPARTICLE FORCES I I
1.2.1 ELECTROSTATIC AND VAN DER WAALS FORCES I I 1.2.2 LIQUID BRIDGE OR
CAPILLARY FORCES 14 1.2.3 CONTACT FORCES 16 1.2.4 INTERPARTICLE FORCES
IN SATURATED GRANULAR MATERIALS 19 1.3 PACKING CHARACTERISTICS 19 )
1.3.1 REGULAR PACKINGS 21 1.3.2 RANDOM PACKINGS 22 1.4 MODELS 22 1.4.1
DISCRETE MODELS 23 1.4.2 CONTINUUM MODELS 28 1.5 BALANCE LAWS FOR
CONTINUUM MODELS 29 1.5.1 THE VELOCITY 30 1.5.2 INTEGRAL AND
DIFFERENTIAL BALANCES 31 1.5.3 THE MASS BALANCE 32 1.5.4 THE STRESS
VECTOR AND THE STRESS TENSOR , 32 1.5.5 THE LINEAR MOMENTUM BALANCE 33
1.5.6 THE ANGULAR MOMENTUM BALANCE . 34 1.5.7 THE ENERGY BALANCE 34 1.6
STATICS 36 1.7 FLUID-PARTICLE INTERACTION .. 36 1.8 SUMMARY F ~ 40 2
THEORY FOR SLOW PLANE FLOW 54 2.1 QUALITATIVE OBSERVATIONS 55 2.2 THE
WALL YIELD CONDITION 58 2.3 THE JANSSEN SOLUTION FOR THE STATIC STRESS
FIELD IN A BIN 60 2.4 THE COULOMB YIELD CONDITION 61 2.5 GENERALIZATION
OF THE COULOMB YIELD CONDITION 62 2.5.1 INVARIANTS AND PRINCIPAL
STRESSES 63 2.6 THE MOHR-COULOMB YIELD CONDITION 65 VII CONTENTS 2.7 THE
MOHR S CIRCLE FOR THE TWO-DIMENSIONAL STRESS TENSOR 65 2.8 THE RELATION
BETWEEN THE COULOMB AND MOHR-COULOMB YIELD CONDITIONS 68 2.9 ACTIVE AND
PASSIVE STATES OF STRESS AND THE VALUE OF THE JANSSEN K-FACTOR 69 2.10
SHEAR TESTS 70 2.10.1 THE CRITICAL STATE 73 2.10.2 THE HVORSLEV SURFACE
75 2.10.3 THE ROSCOE SURFACE 77 2.10.4 THE YIELD SURFACE 77 2.11 YIELD
SURFACES IN 7|- 2.12 YIELD LOCI IN THE A -AI AND A-X PLANES 81 2.13
FLOW RULES 82 2.13.1 THE LEVY-MISES AND THE PRANDTL-REUSS EQUATIONS 84
2.13.2 THE COAXIALITY CONDITION 87 2.13.3 THE PLASTIC POTENTIAL 91
2.13.4 POSITIVE DISSIPATION 91 2.13.5 ASSOCIATED AND NONASSOCIATED FLOW
RULES 92 2.14 EQUATIONS FOR PLANE FLOW 93 2.14.1 THE MOHR S CIRCLE FOR
THE RATE OF DEFORMATION TENSOR 93 2.14.2 THE COAXIALITY CONDITION 94
2.14.3 THE FLOW RULE 95 2.14.4 IMPLICATIONS OF THE ASSOCIATED FLOW RULE
96 2.14.5 ROWE S STRESS-DILATANCY RELATION 96 2.14.6 SUMMARY OF THE
GOVERNING EQUATIONS FOR PLANE FLOW 100 2.15 THE RELATION BETWEEN YIELD
LOCI IN THE N-T AND A-X PLANES 1 00 2.16 THE DOUBLE-SHEARING MODEL 101
2.17 SUMMARY 105 FLOW THROUGH HOPPERS I 16 3.1 EXPERIMENTAL OBSERVATIONS
I 16 3.1.1 FLOW RATE 116 3.1.2 KINEMATICS 121 3.1.3 SOLIDS FRACTION
PROFILES 122 3.2 THEORY FOR STEADY, PLANE FLOW 1 23 3.2.1 THE CRITICAL
STATE APPROXIMATION I 1 23 3.3 THE SMOOTH WALL, RADIAL GRAVITY (SWRQ
PROBLEM 1 25 3.4 THE EFFECT OF WALL ROUGHNESS . : 131 3.5 SOLUTIONS WITH
ALLOWANCE FOR ROUGH WALLS AND VERTICAL GRAVITY 1 34 3.5.1 THE
BRENNEN-PEARCE SOLUTION 1 34 3.5.2 THE RADIAL STRESS AND VELOCITY FIELDS
/ 138 3.5.3 LINEARIZED STABILITY ANALYSIS / 141 3.5.4 DOWNWARD
INTEGRATION FROM THE RADIAL FIELDS 143 3.5.5 THE SUCCESSIVE
APPROXIMATION PROCEDURE 1 45 3.6 A RE-EXAMINATION OF THE EXIT CONDITION
149 3.7 AN ALTERNATIVE EXIT CONDITION 1 52 3.8 THE SMOOTH WALL, RADIAL
GRAVITY PROBLEM FOR COMPRESSIBLE FLOW 1 54 3.9 SUMMARY 160 FLOW THROUGH
WEDGE-SHAPED BUNKERS 166 4. 1 EXPERIMENTAL OBSERVATIONS 1 66 VIII
CONTENTS 4.1.1 FLOW REGIMES 1 66 4.1.2 KINEMATICS 166 4.1.3 WALL
STRESSES - 175 4.1.4 BINS 1 78 4.2 MODELS FOR BUNKER FLOW 182 4.2.1 THE
BIN SECTION 1 83 4.2.2 THE TRANSITION REGION 190 4.2.3 THE HOPPER
SECTION 203 4.3 SUMMARY 208 THEORY FOR SLOW THREE-DIMENSIONAL FLOW 213
5.1 CONSTITUTIVE EQUATIONS INVOLVING A YIELD CONDITION 213 . I THE YIELD
CONDITION 213 .2 SYMMETRY CONSIDERATIONS 220 .3 CONVENTIONAL TRIAXIAL
TESTS 220 .4 ISOTROPIC COMPRESSION TESTS 222 .5 COMPRESSION TESTS 223 .6
CUBICAL TRIAXIAL TESTS 225 .7 COMPARISON OF YIELD CONDITIONS WITH DATA
226 .8 FLOW RULES 226 .9 DATA RELATED TO FLOW RULES 228 . 10 STEADY,
FULLY DEVELOPED FLOW OF A RIGID-PLASTIC MATERIAL 22 9 . 11
ONE-DIMENSIONAL DEFORMATION OF A RIGID-PLASTIC MATERIAL 230 5.2
CONSTITUTIVE EQUATIONS THAT DO NOT INVOLVE A YIELD CONDITION 233 5.2.1
HYPOELASTIC AND HYPOPLASTIC MODELS 233 5.2.2 SOME FEATURES OF (5.66) 235
5.2.3 STEADY, FULLY DEVELOPED FLOW OF A HYPOELASTIC MATERIAL 236 5.2.4
ONE-DIMENSIONAL DEFORMATION OF A HYPOELASTIC MATERIAL 236 5.3 SUMMARY
239 6 FLOW THROUGH AXISYMMETRIC HOPPERS AND BUNKERS 249 6.1 EXPERIMENTAL
OBSERVATIONS 249 6.1.1 FLOW RATE 249 6.1.2 VELOCITY PROFILES 249 6.1.3
DENSITY PROFILES 25 1 6.1.4 FLOW PATTERNS , 253 6.1.5 STRESS PROFILES
256 6.2 THEORY FOR STEADY, AXISYMMETRIC FLOW THROUGH A. HOPPER 259 6.2.1
THE HAAR-VON KARMAN HYPOTHESIS * 26 1 6.2.2 THE RADIAL STRESS AND
VELOCITY FIELDS FOR THE MOHR-COULOMB YIELD CONDITION AND THE,HAAR-VON
KARMAN HYPOTHESIS / 264 6.2.3 THE DRUCKER-PRAGER YIELD CONDITION ARID
LEVY S FLOW RULE 266 6.2.4 COMPARISON OF PREDICTED AND MEASURED VELOCITY
PROFILES 26 9 6.2.5 CRITERIA FOR MASS FLOW 269 6.3 A HYBRID
HYPOPLASTIC-VISCOUS MODEL 273 6.4 THE KINEMATIC MODEL FOR BATCH
DISCHARGE FROM A BIN 276 6.5 SUMMARY 280 7 THEORY FOR RAPID FLOW OF
SMOOTH, INELASTIC PARTICLES 285 7. 1 PRELIMINARIES AND SCALING 285
CONTENTS 7.1. 1 MODEL FOR INELASTIC COLLISIONS 288 7.1.2 HYDRODYNAMIC
DESCRIPTION OF RAPID GRANULAR FLOWS 289 7.2 HEURISTIC HYDRODYNAMIC
THEORY FOR HIGH-DENSITY FLOWS 290 7.2.1 APPLICATION TO UNIFORM PLANE
SHEAR 292 7.3 KINETIC THEORY FOR A GRANULAR GAS OF SMOOTH INELASTIC
PARTICLES 295 7.3.1 STATISTICAL PRELIMINARIES 295 7.3.2 THE EVOLUTION OF
F ! 297 7.3.3 THE EQUILIBRIUM DISTRIBUTION FUNCTION 300 7.3.4 THE
DEPARTURE FROM EQUILIBRIUM 301 7.3.5 MAXWELL TRANSPORT EQUATION 302
7.3.6 THE EQUATIONS OF MOTION 305 7.3.7 THE CHAPMAN-ENSKOG EXPANSION 30
7 7.3.8 CONSTITUTIVE RELATIONS AT LEADING ORDER 310 7.3.9 DISTRIBUTION
FUNCTION AT O(K) 311 7.3.10 SOLUTION FOR O K 316 7.3.11 CONSTITUTIVE
RELATIONS AT O(K)- 319 7.3.12 DISTRIBUTION FUNCTION AND CONSTITUTIVE
RELATIONS AT O(E) 321 7.3.13 CONSTITUTIVE RELATIONS TO FIRST ORDER IN K
AND E 323 7.4 ANISOTROPY OF THE MICROSTRUCTURE 325 7.5 EXTENSION TO
GRANULAR MIXTURES 326 7.6 SUMMARY AND DISCUSSION 328 ANALYSIS OF RAPID
FLOW IN SIMPLE GEOMETRIES 331 8.1 BOUNDARY CONDITIONS AT SOLID WALLS 33
I 8.1.1 HEURISTIC THEORY 332 8.1.2 KINETIC THEORY 334 8.2 PLANE COUETTE
FLOW 339 8.2.1 PREDICTIONS OF THE HIGH-DENSITY THEORY 340 8.2.2 SOME
FEATURES OF THE HIGH-DENSITY SOLUTIONS 345 8.2.3 PREDICTIONS OF THE
KINETIC THEORY 346 8.3 FLOW IN INCLINED CHUTES 349 8.3.1 SOME
EXPERIMENTAL OBSERVATIONS OF CHUTE FLOW 35 1 8.3.2 ANALYSIS OF STEADY,
FULLY DEVELOPED FLOW 355 8.3.3 HIGH-DENSITY THEORY 35 6 8.3.4 SOME
FEATURES OF THE HIGH-DENSITY SOLUTIONS 358 8.3.5 PREDICTIONS OF THE
KINETIC THEORY 359 8.4 STABILITY OF RAPID SHEAR FLOWS * 366 8.4.1
STABILITY OF UNBOUNDED PLANE SHEAR FLOW 366 8.4.2 STABILITY OF PLANE
COUETTE FLOW 369 8.5 SUMMARY ,* 371 THEORY FOR RAPID FLOW OF ROUGH,
INELASTIC PARTICLES 374 9.1 COLLISION MODELS FOR ROUGH PARTICLES 375 9.2
EQUATIONS OF MOTION FOR A GRANULAR GAS OF ROUGH, INELASTIC SPHERES 378
9.3 THE VELOCITY DISTRIBUTION FUNCTION 382 9.3.1 NEARLY ELASTIC, NEARLY
PERFECTLY ROUGH PARTICLES 382 9.3.2 NEARLY ELASTIC, NEARLY SMOOTH
PARTICLES 386 9.4 CONSTITUTIVE RELATIONS UP TO FIRST ORDER IN K, E, AND
E 389 9.4.1 NEARLY ELASTIC, NEARLY PERFECTLY ROUGH PARTICLES 389
CONTENTS 9.4.2 NEARLY ELASTIC, NEARLY SMOOTH PARTICLES 390 9.5 SUMMARY
392 10 HYBRID THEORIES 394 10.1 THE FRICTIONAL-KINETIC MODEL 395 10.2
APPLICATION TO FLOW IN CHUTES 39 6 10.3 OTHER HYBRID MODELS 400 10.4
SUMMARY 401 APPENDIX A: OPERATIONS WITH VECTORS AND TENSORS 403 A. I
VECTORS 403 A.2 THE SUMMATION CONVENTION 404 A.3 THE SCALAR PRODUCT OF
TWO VECTORS 404 A.4 SECOND-ORDER TENSORS 405 A.4.1 THE UNIT TENSOR 406
A.4.2 THE TRACE OF A SECOND-ORDER TENSOR 406 A.5 CARTESIAN TENSOR
NOTATION 407 A.6 THIRD AND HIGHER ORDER TENSORS 407 A.6.1 THE
ALTERNATING TENSOR 407 A.7 OPERATIONS WITH VECTORS AND TENSORS 407 A.7.1
THE VECTOR PRODUCT OF TWO VECTORS 407 A.7.2 THE PRODUCT OF TWO
SECOND-ORDER TENSORS 408 A.7.3 THE SCALAR PRODUCT OF TWO SECOND-ORDER
TENSORS 408 A.7.4 THE TRANSPOSE OF A TENSOR 409 A.7.5 THE INVERSE OF A
SECOND-ORDER TENSOR 409 A.7.6 THE DETERMINANT OF A SECOND-ORDER TENSOR
409 A.7.7 ORTHOGONAL SECOND-ORDER TENSORS 410 A.7.8 THE GRADIENT
OPERATOR 41 I A.7.9 THE GRADIENT OF SCALARS AND VECTORS 41 I A.7.10 THE
DIVERGENCE OF A SECOND-ORDER TENSOR 412 A.7.11 THE CURL OF A VECTOR 412
A.8 EQUATIONS IN ORTHOGONAL CURVILINEAR COORDINATE SYSTEMS 412 A.8.1
CYLINDRICAL COORDINATES 412 A.8.2 SPHERICAL COORDINATES 414 APPENDIX B:
THE STRESS TENSOR 418 APPENDIX C: HYPERBOLIC PARTIAL DIFFERENTIAL
EQUATIONS OF FIRST ORDER . 420 C. I SOLUTION BY THE METHOD OF
CHARACTERISTICS 424 APPENDIX D: JUMP BALANCES .- 428 D.I THE JUMP MASS
BALANCE / 428 APPENDIX E: DISCONTINUOUS SOLUTIONS OF HYPERBOLIC
EQUATIONS 430 E. I WEAK SOLUTION 430 E.2 JUMP CONDITIONS 431 E.3 JUMP
CONDITIONS FOR LINEAR EQUATIONS 432 APPENDIX F: PROOF OF THE COAXIALITY
CONDITION 434 APPENDIX G: MATERIAL FRAME INDIFFERENCE 439 G. I CHANGE OF
FRAME 439 XI CONTENTS G.2 FRAME INDIFFERENT SCALARS, VECTORS, AND
TENSORS 441 G.2.1 SCALARS 441 G.2.2 VECTORS 441 G.2.3 SECOND-ORDER
TENSORS 442 G.3 THE PRINCIPLE OF MATERIAL FRAME INDIFFERENCE 443 G.4 AN
ALTERNATIVE INTERPRETATION OF A CHANGE OF FRAME 44 3 APPENDIX H: THE
EVALUATION OF SOME INTEGRALS 449 H. I INTEGRATION OVER K 449 H.2
INTEGRATION OVER K FOR BOUNDARY CONDITIONS 450 H.3 CHANGE OF VARIABLES
451 H.4 VOLUME INTEGRALS 452 H.5 GAUSSIAN INTEGRALS 453 APPENDIX I: A
BRIEF INTRODUCTION TO LINEAR STABILITY THEORY 454 APPENDIX J: PSEUDO
SCALARS, VECTORS, AND TENSORS 456 APPENDIX K: ANSWERS TO SELECTED
PROBLEMS 459 REFERENCES 463 INDEX 483 XII
|
| adam_txt |
AN INTRODUCTION TO GRANULAR FLOW K. KESAVA RAO PRABHU R. NOTT INDIAN
INSTITUTE OF SCIENCE INDIAN INSTITUTE OF SCIENCE CAMBRIDGE UNIVERSITY
PRESS CONTENTS PREFACE PAGE XIII NOTATION XV 1 INTRODUCTION I I. I
EXAMPLES OF GRANULAR STATICS AND FLOW 2 1.2 INTERPARTICLE FORCES I I
1.2.1 ELECTROSTATIC AND VAN DER WAALS FORCES I I 1.2.2 LIQUID BRIDGE OR
CAPILLARY FORCES 14 1.2.3 CONTACT FORCES 16 1.2.4 INTERPARTICLE FORCES
IN SATURATED GRANULAR MATERIALS 19 1.3 PACKING CHARACTERISTICS 19 )
1.3.1 REGULAR PACKINGS 21 1.3.2 RANDOM PACKINGS 22 1.4 MODELS 22 1.4.1
DISCRETE MODELS 23 1.4.2 CONTINUUM MODELS 28 1.5 BALANCE LAWS FOR
CONTINUUM MODELS 29 1.5.1 THE VELOCITY 30 1.5.2 INTEGRAL AND
DIFFERENTIAL BALANCES 31 1.5.3 THE MASS BALANCE 32 1.5.4 THE STRESS
VECTOR AND THE STRESS TENSOR , 32 1.5.5 THE LINEAR MOMENTUM BALANCE 33
1.5.6 THE ANGULAR MOMENTUM BALANCE . 34 1.5.7 THE ENERGY BALANCE 34 1.6
STATICS 36 1.7 FLUID-PARTICLE INTERACTION . 36 1.8 SUMMARY F ~ 40 2
THEORY FOR SLOW PLANE FLOW 54 2.1 QUALITATIVE OBSERVATIONS 55 2.2 THE
WALL YIELD CONDITION 58 2.3 THE JANSSEN SOLUTION FOR THE STATIC STRESS
FIELD IN A BIN 60 2.4 THE COULOMB YIELD CONDITION 61 2.5 GENERALIZATION
OF THE COULOMB YIELD CONDITION 62 2.5.1 INVARIANTS AND PRINCIPAL
STRESSES 63 2.6 THE MOHR-COULOMB YIELD CONDITION 65 VII CONTENTS 2.7 THE
MOHR'S CIRCLE FOR THE TWO-DIMENSIONAL STRESS TENSOR 65 2.8 THE RELATION
BETWEEN THE COULOMB AND MOHR-COULOMB YIELD CONDITIONS 68 2.9 ACTIVE AND
PASSIVE STATES OF STRESS AND THE VALUE OF THE JANSSEN K-FACTOR 69 2.10
SHEAR TESTS 70 2.10.1 THE CRITICAL STATE 73 2.10.2 THE HVORSLEV SURFACE
75 2.10.3 THE ROSCOE SURFACE 77 2.10.4 THE YIELD SURFACE 77 2.11 YIELD
SURFACES IN 7|- 2.12 YIELD LOCI IN THE A\-AI AND A-X PLANES 81 2.13
FLOW RULES 82 2.13.1 THE LEVY-MISES AND THE PRANDTL-REUSS EQUATIONS 84
2.13.2 THE COAXIALITY CONDITION 87 2.13.3 THE PLASTIC POTENTIAL 91
2.13.4 POSITIVE DISSIPATION 91 2.13.5 ASSOCIATED AND NONASSOCIATED FLOW
RULES 92 2.14 EQUATIONS FOR PLANE FLOW 93 2.14.1 THE MOHR'S CIRCLE FOR
THE RATE OF DEFORMATION TENSOR 93 2.14.2 THE COAXIALITY CONDITION 94
2.14.3 THE FLOW RULE 95 2.14.4 IMPLICATIONS OF THE ASSOCIATED FLOW RULE
96 2.14.5 ROWE'S STRESS-DILATANCY RELATION 96 2.14.6 SUMMARY OF THE
GOVERNING EQUATIONS FOR PLANE FLOW 100 2.15 THE RELATION BETWEEN YIELD
LOCI IN THE N-T AND A-X PLANES 1 00 2.16 THE DOUBLE-SHEARING MODEL 101
2.17 SUMMARY 105 FLOW THROUGH HOPPERS I 16 3.1 EXPERIMENTAL OBSERVATIONS
I 16 3.1.1 FLOW RATE 116 3.1.2 KINEMATICS 121 3.1.3 SOLIDS FRACTION
PROFILES 122 3.2 THEORY FOR STEADY, PLANE FLOW 1 23 3.2.1 THE CRITICAL
STATE APPROXIMATION I 1 23 3.3 THE SMOOTH WALL, RADIAL GRAVITY (SWRQ
PROBLEM 1 25 3.4 THE EFFECT OF WALL ROUGHNESS . : 131 3.5 SOLUTIONS WITH
ALLOWANCE FOR ROUGH WALLS AND VERTICAL GRAVITY 1 34 3.5.1 THE
BRENNEN-PEARCE SOLUTION 1 34 3.5.2 THE RADIAL STRESS AND VELOCITY FIELDS
/ 138 3.5.3 LINEARIZED STABILITY ANALYSIS / 141 3.5.4 DOWNWARD
INTEGRATION FROM THE RADIAL FIELDS 143 3.5.5 THE SUCCESSIVE
APPROXIMATION PROCEDURE 1 45 3.6 A RE-EXAMINATION OF THE EXIT CONDITION
149 3.7 AN ALTERNATIVE EXIT CONDITION 1 52 3.8 THE SMOOTH WALL, RADIAL
GRAVITY PROBLEM FOR COMPRESSIBLE FLOW 1 54 3.9 SUMMARY 160 FLOW THROUGH
WEDGE-SHAPED BUNKERS 166 4. 1 EXPERIMENTAL OBSERVATIONS 1 66 VIII
CONTENTS 4.1.1 FLOW REGIMES 1 66 4.1.2 KINEMATICS 166 4.1.3 WALL
STRESSES - 175 4.1.4 BINS 1 78 4.2 MODELS FOR BUNKER FLOW 182 4.2.1 THE
BIN SECTION 1 83 4.2.2 THE TRANSITION REGION 190 4.2.3 THE HOPPER
SECTION 203 4.3 SUMMARY 208 THEORY FOR SLOW THREE-DIMENSIONAL FLOW 213
5.1 CONSTITUTIVE EQUATIONS INVOLVING A YIELD CONDITION 213 . I THE YIELD
CONDITION 213 .2 SYMMETRY CONSIDERATIONS 220 .3 CONVENTIONAL TRIAXIAL
TESTS 220 .4 ISOTROPIC COMPRESSION TESTS 222 .5 COMPRESSION TESTS 223 .6
CUBICAL TRIAXIAL TESTS 225 .7 COMPARISON OF YIELD CONDITIONS WITH DATA
226 .8 FLOW RULES 226 .9 DATA RELATED TO FLOW RULES 228 . 10 STEADY,
FULLY DEVELOPED FLOW OF A RIGID-PLASTIC MATERIAL 22 9 . 11
ONE-DIMENSIONAL DEFORMATION OF A RIGID-PLASTIC MATERIAL 230 5.2
CONSTITUTIVE EQUATIONS THAT DO NOT INVOLVE A YIELD CONDITION 233 5.2.1
HYPOELASTIC AND HYPOPLASTIC MODELS 233 5.2.2 SOME FEATURES OF (5.66) 235
5.2.3 STEADY, FULLY DEVELOPED FLOW OF A HYPOELASTIC MATERIAL 236 5.2.4
ONE-DIMENSIONAL DEFORMATION OF A HYPOELASTIC MATERIAL 236 5.3 SUMMARY
239 6 FLOW THROUGH AXISYMMETRIC HOPPERS AND BUNKERS 249 6.1 EXPERIMENTAL
OBSERVATIONS 249 6.1.1 FLOW RATE 249 6.1.2 VELOCITY PROFILES 249 6.1.3
DENSITY PROFILES 25 1 6.1.4 FLOW PATTERNS , 253 6.1.5 STRESS PROFILES '
256 6.2 THEORY FOR STEADY, AXISYMMETRIC FLOW THROUGH A. HOPPER 259 6.2.1
THE HAAR-VON KARMAN HYPOTHESIS * 26 1 6.2.2 THE RADIAL STRESS AND
VELOCITY FIELDS FOR THE MOHR-COULOMB YIELD CONDITION AND THE,HAAR-VON
KARMAN HYPOTHESIS / 264 6.2.3 THE DRUCKER-PRAGER YIELD CONDITION ARID
LEVY'S FLOW RULE 266 6.2.4 COMPARISON OF PREDICTED AND MEASURED VELOCITY
PROFILES 26 9 6.2.5 CRITERIA FOR MASS FLOW 269 6.3 A HYBRID
HYPOPLASTIC-VISCOUS MODEL 273 6.4 THE KINEMATIC MODEL FOR BATCH
DISCHARGE FROM A BIN 276 6.5 SUMMARY 280 7 THEORY FOR RAPID FLOW OF
SMOOTH, INELASTIC PARTICLES 285 7. 1 PRELIMINARIES AND SCALING 285
CONTENTS 7.1. 1 MODEL FOR INELASTIC COLLISIONS 288 7.1.2 HYDRODYNAMIC
DESCRIPTION OF RAPID GRANULAR FLOWS 289 7.2 HEURISTIC HYDRODYNAMIC
THEORY FOR HIGH-DENSITY FLOWS 290 7.2.1 APPLICATION TO UNIFORM PLANE
SHEAR 292 7.3 KINETIC THEORY FOR A GRANULAR GAS OF SMOOTH INELASTIC
PARTICLES 295 7.3.1 STATISTICAL PRELIMINARIES 295 7.3.2 THE EVOLUTION OF
F ! 297 7.3.3 THE EQUILIBRIUM DISTRIBUTION FUNCTION 300 7.3.4 THE
DEPARTURE FROM EQUILIBRIUM 301 7.3.5 MAXWELL TRANSPORT EQUATION 302
7.3.6 THE EQUATIONS OF MOTION 305 7.3.7 THE CHAPMAN-ENSKOG EXPANSION 30
7 7.3.8 CONSTITUTIVE RELATIONS AT LEADING ORDER 310 7.3.9 DISTRIBUTION
FUNCTION AT O(K) 311 7.3.10 SOLUTION FOR O K 316 7.3.11 CONSTITUTIVE
RELATIONS AT O(K)- 319 7.3.12 DISTRIBUTION FUNCTION AND CONSTITUTIVE
RELATIONS AT O(E) 321 7.3.13 CONSTITUTIVE RELATIONS TO FIRST ORDER IN K
AND E 323 7.4 ANISOTROPY OF THE MICROSTRUCTURE 325 7.5 EXTENSION TO
GRANULAR MIXTURES 326 7.6 SUMMARY AND DISCUSSION 328 ANALYSIS OF RAPID
FLOW IN SIMPLE GEOMETRIES 331 8.1 BOUNDARY CONDITIONS AT SOLID WALLS 33
I 8.1.1 HEURISTIC THEORY 332 8.1.2 KINETIC THEORY 334 8.2 PLANE COUETTE
FLOW 339 8.2.1 PREDICTIONS OF THE HIGH-DENSITY THEORY 340 8.2.2 SOME
FEATURES OF THE HIGH-DENSITY SOLUTIONS 345 8.2.3 PREDICTIONS OF THE
KINETIC THEORY 346 8.3 FLOW IN INCLINED CHUTES 349 8.3.1 SOME
EXPERIMENTAL OBSERVATIONS OF CHUTE FLOW 35 1 8.3.2 ANALYSIS OF STEADY,
FULLY DEVELOPED FLOW 355 8.3.3 HIGH-DENSITY THEORY 35 6 8.3.4 SOME
FEATURES OF THE HIGH-DENSITY SOLUTIONS 358 8.3.5 PREDICTIONS OF THE
KINETIC THEORY 359 8.4 STABILITY OF RAPID SHEAR FLOWS * 366 8.4.1
STABILITY OF UNBOUNDED PLANE SHEAR FLOW 366 8.4.2 STABILITY OF PLANE
COUETTE FLOW 369 8.5 SUMMARY ,* 371 THEORY FOR RAPID FLOW OF ROUGH,
INELASTIC PARTICLES 374 9.1 COLLISION MODELS FOR ROUGH PARTICLES 375 9.2
EQUATIONS OF MOTION FOR A GRANULAR GAS OF ROUGH, INELASTIC SPHERES 378
9.3 THE VELOCITY DISTRIBUTION FUNCTION 382 9.3.1 NEARLY ELASTIC, NEARLY
PERFECTLY ROUGH PARTICLES 382 9.3.2 NEARLY ELASTIC, NEARLY SMOOTH
PARTICLES 386 9.4 CONSTITUTIVE RELATIONS UP TO FIRST ORDER IN K, E, AND
E 389 9.4.1 NEARLY ELASTIC, NEARLY PERFECTLY ROUGH PARTICLES 389
CONTENTS 9.4.2 NEARLY ELASTIC, NEARLY SMOOTH PARTICLES 390 9.5 SUMMARY '
392 10 HYBRID THEORIES 394 10.1 THE FRICTIONAL-KINETIC MODEL 395 10.2
APPLICATION TO FLOW IN CHUTES 39 6 10.3 OTHER HYBRID MODELS 400 10.4
SUMMARY 401 APPENDIX A: OPERATIONS WITH VECTORS AND TENSORS 403 A. I
VECTORS 403 A.2 THE SUMMATION CONVENTION 404 A.3 THE SCALAR PRODUCT OF
TWO VECTORS 404 A.4 SECOND-ORDER TENSORS 405 A.4.1 THE UNIT TENSOR 406
A.4.2 THE TRACE OF A SECOND-ORDER TENSOR 406 A.5 CARTESIAN TENSOR
NOTATION 407 A.6 THIRD AND HIGHER ORDER TENSORS 407 A.6.1 THE
ALTERNATING TENSOR 407 A.7 OPERATIONS WITH VECTORS AND TENSORS 407 A.7.1
THE VECTOR PRODUCT OF TWO VECTORS 407 A.7.2 THE PRODUCT OF TWO
SECOND-ORDER TENSORS 408 A.7.3 THE SCALAR PRODUCT OF TWO SECOND-ORDER
TENSORS 408 A.7.4 THE TRANSPOSE OF A TENSOR 409 A.7.5 THE INVERSE OF A
SECOND-ORDER TENSOR 409 A.7.6 THE DETERMINANT OF A SECOND-ORDER TENSOR
409 A.7.7 ORTHOGONAL SECOND-ORDER TENSORS 410 A.7.8 THE GRADIENT
OPERATOR 41 I A.7.9 THE GRADIENT OF SCALARS AND VECTORS 41 I A.7.10 THE
DIVERGENCE OF A SECOND-ORDER TENSOR 412 A.7.11 THE CURL OF A VECTOR 412
A.8 EQUATIONS IN ORTHOGONAL CURVILINEAR COORDINATE SYSTEMS 412 A.8.1
CYLINDRICAL COORDINATES 412 A.8.2 SPHERICAL COORDINATES 414 APPENDIX B:
THE STRESS TENSOR 418 APPENDIX C: HYPERBOLIC PARTIAL DIFFERENTIAL
EQUATIONS OF FIRST ORDER . 420 C. I SOLUTION BY THE METHOD OF
CHARACTERISTICS 424 APPENDIX D: JUMP BALANCES .- 428 D.I THE JUMP MASS
BALANCE / 428 APPENDIX E: DISCONTINUOUS SOLUTIONS OF HYPERBOLIC
EQUATIONS 430 E. I WEAK SOLUTION 430 E.2 JUMP CONDITIONS 431 E.3 JUMP
CONDITIONS FOR LINEAR EQUATIONS 432 APPENDIX F: PROOF OF THE COAXIALITY
CONDITION 434 APPENDIX G: MATERIAL FRAME INDIFFERENCE 439 G. I CHANGE OF
FRAME 439 XI CONTENTS G.2 FRAME INDIFFERENT SCALARS, VECTORS, AND
TENSORS 441 G.2.1 SCALARS 441 G.2.2 VECTORS 441 G.2.3 SECOND-ORDER
TENSORS 442 G.3 THE PRINCIPLE OF MATERIAL FRAME INDIFFERENCE 443 G.4 AN
ALTERNATIVE INTERPRETATION OF A CHANGE OF FRAME 44 3 APPENDIX H: THE
EVALUATION OF SOME INTEGRALS 449 H. I INTEGRATION OVER K 449 H.2
INTEGRATION OVER K FOR BOUNDARY CONDITIONS 450 H.3 CHANGE OF VARIABLES
451 H.4 VOLUME INTEGRALS 452 H.5 GAUSSIAN INTEGRALS 453 APPENDIX I: A
BRIEF INTRODUCTION TO LINEAR STABILITY THEORY 454 APPENDIX J: PSEUDO
SCALARS, VECTORS, AND TENSORS 456 APPENDIX K: ANSWERS TO SELECTED
PROBLEMS 459 REFERENCES 463 INDEX 483 XII |
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| id | DE-604.BV023334978 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:59:13Z |
| indexdate | 2024-07-09T21:16:13Z |
| institution | BVB |
| isbn | 9780521571661 |
| language | English |
| lccn | 2007050026 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016518859 |
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| physical | XXI, 490 S. Ill., graph. Darst. |
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| publisher | Cambridge University Press |
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| series2 | Cambridge series in chemical engineering |
| spelling | Rao, K. Kesava Verfasser aut An introduction to granular flow K. Kesava Rao and Prabhu R. Nott 1. publ. Cambridge, Mass. Cambridge University Press 2008 XXI, 490 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge series in chemical engineering Includes bibliographical references and index Granular materials Fluid dynamics Granulärer Stoff (DE-588)4256351-3 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Granulärer Stoff (DE-588)4256351-3 s Strömungsmechanik (DE-588)4077970-1 s DE-604 Nott, Prabhu R. Verfasser aut http://www.loc.gov/catdir/enhancements/fy0806/2007050026-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0806/2007050026-t.html Table of contents only HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016518859&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rao, K. Kesava Nott, Prabhu R. An introduction to granular flow Granular materials Fluid dynamics Granulärer Stoff (DE-588)4256351-3 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4256351-3 (DE-588)4077970-1 |
| title | An introduction to granular flow |
| title_auth | An introduction to granular flow |
| title_exact_search | An introduction to granular flow |
| title_exact_search_txtP | An introduction to granular flow |
| title_full | An introduction to granular flow K. Kesava Rao and Prabhu R. Nott |
| title_fullStr | An introduction to granular flow K. Kesava Rao and Prabhu R. Nott |
| title_full_unstemmed | An introduction to granular flow K. Kesava Rao and Prabhu R. Nott |
| title_short | An introduction to granular flow |
| title_sort | an introduction to granular flow |
| topic | Granular materials Fluid dynamics Granulärer Stoff (DE-588)4256351-3 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Granular materials Fluid dynamics Granulärer Stoff Strömungsmechanik |
| url | http://www.loc.gov/catdir/enhancements/fy0806/2007050026-d.html http://www.loc.gov/catdir/enhancements/fy0806/2007050026-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016518859&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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