Multiphase flow dynamics: 1 Fundamentals
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| Format: | Book |
| Language: | English |
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Berlin [u.a.]
Springer
2007
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| Edition: | 3. ed. |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XL, 758 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 9783540221067 9783540698326 3540430172 |
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| 245 | 1 | 0 | |a Multiphase flow dynamics |n 1 |p Fundamentals |c Nikolay I. Kolev |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2007 | |
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| adam_text | NIKOLAY I. KOLEV MULTIPHASE FLOW DYNAMICS 1 FUNDAMENTALS 3RD EDITION
WITH 149 FIGURES AND CD-ROM &J SPRINGER TABLE OF CONTENTS CHAPTER 14 OF
VOLUME 1 AND CHAPTER 26 OF VOLUME 2 ARE AVAILABLE IN PDF FORMAT ON THE
CD-ROM ATTACHED TO VOLUME 1. THE SYSTEM REQUIREMENTS ARE WINDOWS 98 AND
HIGHER. BOTH PDF FILES CONTAIN LINKS TO COMPUTER ANIMATIONS. TO SEE THE
ANIMA- TIONS, ONE DOUBLE CLICKS ON THE ACTIVE LINKS CONTAINED INSIDE THE
PDF DOCUMENTS. THE ANIMATIONS ARE THEN DISPLAYED IN AN INTERNET BROWSER,
SUCH MICROSOFT INTERNET EXPLORER OR NETSCAPE. ALTERNATIVELY, GIF-FILE
ANIMATIONS ARE ALSO PROVIDED. NOMENCLATURE XXV INTRODUCTION XXXV 1 MASS
CONSERVATION 1 1.1 INTRODUCTION ;...L 1.2 BASIC DEFINITIONS 2 1.3
NON-STRUCTURED AND STRUCTURED FIELDS 9 1.4 SLATTERY AND WHITAKER S
LOCAL SPATIAL AVERAGING THEOREM 10 1.5 GENERAL TRANSPORT EQUATION
(LEIBNITZ RULE) 12 1.6 LOCAL VOLUME-AVERAGED MASS CONSERVATION EQUATION
13 1.7 TIME AVERAGE .* 16 1.8 LOCAL VOLUME-AVERAGED COMPONENT
CONSERVATION EQUATIONS 18 1.9 LOCAL VOLUME- AND TIME-AVERAGED
CONSERVATION EQUATIONS 20 1.10 CONSERVATION EQUATIONS FOR THE NUMBER
DENSITY OF PARTICLES 24 1.11 IMPLICATION OF THE ASSUMPTION OF
MONO-DISPERSITY IN A CELL 30 1.11.1 PARTICLE SIZE SPECTRUM AND AVERAGING
30 1.11.2 CUTTING OF THE LOWER PART OF THE SPECTRUM DUE TO MASS TRANSFER
31 1.11.3 THE EFFECT OF THE AVERAGING ON THE EFFGPTIVE VELOCITY
DIFFERENCE 33 1.12 STRATIFIED STRUCTURE 35 1.13 FINAL REMARKS AND
CONCLUSIONS 35 REFERENCES 37 2 MOMENTUMS CONSERVATION 41 2.1
INTRODUCTION 41 2.2 LOCAL VOLUME-AVERAGED MOMENTUM EQUATIONS 42 2.2.1
SINGLE-PHASE MOMENTUM EQUATIONS 42 2.2.2 INTERFACE FORCE BALANCE
(MOMENTUM JUMP CONDITION) 42 XVI TABLE OF CONTENTS 2.2.3 LOCAL VOLUME
AVERAGING OF THE SINGLE-PHASE MOMENTUM EQUATION 49 2.3 REARRANGEMENT OF
THE SURFACE INTEGRALS 51 2.4 LOCAL VOLUME AVERAGE AND TIME AVERAGE 55
2.5 DISPERSED PHASE IN LAMINAR CONTINUUM - PSEUDO TURBULENCE 57 2.6
VISCOUS AND REYNOLDS STRESSES 57 2.7 NON-EQUAL BULK AND BOUNDARY LAYER
PRESSURES 62 2.7.1 CONTINUOUS INTERFACE 62 2.7.2 DISPERSED INTERFACE 77
2.8 WORKING FORM FOR DISPERSED AND CONTINUOUS PHASE 93 2.9 GENERAL
WORKING FORM FOR DISPERSED AND CONTINUOUS PHASES 98 2.10 SOME PRACTICAL
SIMPLIFICATIONS 100 2.11 CONCLUSION 104 APPENDIX 2.1 104 APPENDIX 2.2
105 APPENDIX 2.3 106 REFERENCES 109 3 DERIVATIVES FOR THE EQUATIONS OF
STATE 115 3.1 INTRODUCTION 115 3.2 MULTI-COMPONENT MIXTURES OF MISCIBLE
AND NON-MISCIBLE COMPONENTS 117 3.2.1 COMPUTATION OF PARTIAL PRESSURES
FOR KNOWN MASS CONCENTRATIONS, SYSTEM PRESSURE AND TEMPERATURE 118 3.2.2
PARTIAL DERIVATIVES OF THE EQUATION OF STATE 125 3.2.3 PARTIAL
DERIVATIVES IN THE EQUATION OF STATE T = T( 2 ,..., T J), WHERE
130 3.2.4 CHEMICAL POTENTIAL 139 3.2.5 PARTIAL DERIVATIVES IN THE
EQUATION OF STATE P = P(P, 2 , I, WHERE Q = S,H,E 150 3.3 MIXTURE OF
LIQUID AND MICROSCOPIC SOLID PARTICLES OF DIFFERENT CHEMICAL SUBSTANCES
153 3.3.1 PARTIAL DERIVATIVES IN THE EQUATION OF STATE 3.3.2 PARTIAL
DERIVATIVES IN THE EQUATION OF STATE T = T{P,(P,C 2 ,. ) WHERE (P-H,E,S
154 3.4 SINGLE-COMPONENT EQUILIBRIUM FLUID 155 3.4.1 SUPERHEATED VAPOR
155 3.4.2 RECONSTRUCTION OF EQUATION OF STATE BY USING A LIMITED AMOUNT
OF DATA AVAILABLE 156 3.4.3 VAPOR-LIQUID MIXTURE IN THERMODYNAMIC
EQUILIBRIUM 163 TABLE OF CONTENTS XVII 3.4.4 LIQUID-SOLID MIXTURE IN
THERMODYNAMIC EQUILIBRIUM 164 3.4.5 SOLID PHASE 164 3.5 EXTENSION STATE
OF LIQUIDS 165 APPENDIX 3.1 APPLICATION OF THE THEORY TO STEAM-AIR
MIXTURES 165 APPENDIX 3.2 USEFUL REFERENCES FOR COMPUTING PROPERTIES OF
SINGLE CONSTITUENTS 167 APPENDIX 3.3 USEFUL DEFINITIONS AND RELATIONS
BETWEEN THERMODYNAMIC QUANTITIES . 169 REFERENCES 170 4 ON THE VARIETY
OF NOTATIONS OF THE ENERGY CONSERVATION FOR SINGLE-PHASE FLOW 173 4.1
INTRODUCTION 173 4.2 MASS AND MOMENTUM CONSERVATION, ENERGY CONSERVATION
174 4.3 SIMPLE NOTATION OF THE ENERGY CONSERVATION EQUATION 175 4.4 THE
ENTROPY 176 4.5 EQUATION OF STATE 177 4.6 VARIETY OF NOTATION OF THE
ENERGY CONSERVATION PRINCIPLE 177 4.6.1 TEMPERATURE 177 4.6.2 SPECIFIC
ENTHALPY 178 4.7 SUMMARY OF DIFFERENT NOTATIONS 179 4.8 THE EQUIVALENCE
OF THE CANONICAL FORMS 179 4.9 EQUIVALENCE OF THE ANALYTICAL SOLUTIONS
182 4.10 EQUIVALENCE OF THE NUMERICAL SOLUTIONS? 183 4.10.1 EXPLICIT
FIRST ORDER METHOD OF CHARACTERISTICS 183 4.10.2 THE PERFECT GAS SHOCK
TUBE: BENCHMARK FOR NUMERICAL METHODS 187 4.11 INTERPENETRATING FLUIDS
196 4.12 SUMMARY OF DIFFERENT NOTATIONS FOR INTERPENETRATING FLUIDS 201
APPENDIX 4.1 ANALYTICAL SOLUTION OF THE SHOCK TUBE PROBLEM 203 APPENDIX
4.2 ACHIEVABLE ACCURACY OF THE DONOR-CELL METHOD FOR SINGLE-PHASE FLOWS
-. 207 REFERENCES 210 5 FIRST AND SECOND LAWS OF THE THERMODYNAMICS 213
5.1 INTRODUCTION 213 5.2 INSTANTANEOUS LOCAL VOLUME AVERAGE ENERGY
EQUATIONS 216 5.3 DALTON AND FICWS LAWS , CENTER OF MASS MFXTURE
VELOCITY, CALORIC MIXTURE PROPERTIES 223 5.4 ENTHALPY EQUATION 225 5.5
INTERNAL ENERGY EQUATION 229 5.6 ENTROPY EQUATION 230 5.7 LOCAL VOLUME-
AND TIME-AVERAGED ENTROPY EQUATION 234 5.8 LOCAL VOLUME- AND
TIME-AVERAGED INTERNAL ENERGY EQUATION 239 XVIII TABLE OF CONTENTS 5.9
LOCAL VOLUME- AND TIME-AVERAGED SPECIFIC ENTHALPY EQUATION 241 5.10
NON-CONSERVATIVE AND SEMI-CONSERVATIVE FORMS OF THE ENTROPY EQUATION 243
5.11 COMMENTS ON THE SOURCE TERMS IN THE MIXTURE ENTROPY EQUATION 245
5.12 VISCOUS DISSIPATION 250 5.13 TEMPERATURE EQUATION 255 5.14 SECOND
LAW OF THE THERMODYNAMICS . . 259 5.15 MIXTURE VOLUME CONSERVATION
EQUATION 260 5.16 LINEARIZED FORM OF THE SOURCE TERM FOR THE TEMPERATURE
EQUATION 265 5.17 INTERFACE CONDITIONS 272 5.18 LUMPED PARAMETER VOLUMES
273 5.19 STEADY STATE 274 5.20 FINAL REMARKS 278 REFERENCES 279 SOME
SIMPLE APPLICATIONS OF THE MASS AND ENERGY CONSERVATION 283 6.1 INFINITE
HEAT EXCHANGE WITHOUT INTERFACIAL MASS TRANSFER 283 6.2 DISCHARGE OF GAS
FROM A VOLUME 285 6.3 INJECTION OF INERT GAS IN A CLOSED VOLUME
INITIALLY FILLED WITH INERT GAS 287 6.4 HEAT INPUT IN A GAS IN A CLOSED
VOLUME 288 6.5 STEAM INJECTION IN A STEAM-AIR MIXTURE 289 6.6 CHEMICAL
REACTION IN A GAS MIXTURE IN A CLOSED VOLUME 292 6.7 HYDROGEN COMBUSTION
IN AN INERT ATMOSPHERE 294 6.7.1 SIMPLE INTRODUCTION TO COMBUSTION
KINETICS 294 6.7.2 IGNITION TEMPERATURE AND IGNITION CONCENTRATION
LIMITS 296 6.7.3 DETONABILITY CONCENTRATION LIMITS 297 6.7.4 THE HEAT
RELEASE DUE TO COMBUSTION 297 6.7.5 EQUILIBRIUM DISSOCIATION 298 6.7.6
SOURCE TERMS^OF THE ENERGY CONSERVATION OF THE GAS PHASE 303 6.7.7
TEMPERATURE AND PRESSURE CHANGES IN A CLOSED CONTROL VOLUME; ADIABATIC
TEMPERATURE OF THE BURNED GASES 305 REFERENCES 309 EXERGY OF MULTI-PHASE
MULTI-COMPONENT SYSTEMS 311 7.1 INTRODUCTION 311 7.2 THE PSEUDO-EXERGY
EQUATION FOR SINGLE-FLUID SYSTEMS 311 7.3 THE FUNDAMENTAL EXERGY
EQUATION .?. 313 7.3.1 THE EXERGY DEFINITION IN ACCORDANCE WITH REYNOLDS
AND PERKINS 313 7.3.2 THE EXERGY DEFINITION IN ACCORDANCE WITH GOUY
(PENERGIE UTILISABLE, 1889) 314 7.3.3 THE EXERGY DEFINITION APPROPRIATE
FOR ESTIMATION OF THE VOLUME CHANGE WORK 315 7.3.4 THE.EXERGY DEFINITION
APPROPRIATE FOR ESTIMATION OF THE TECHNICAL WORK 316 7.4 SOME
INTERESTING CONSEQUENCES OF THE FUNDAMENTAL EXERGY EQUATION.... 316
TABLE OF CONTENTS XIX 7.5 JUDGING THE EFFICIENCY OF A HEAT PUMP AS AN
EXAMPLE OF APPLICATION OF THE EXERGY 318 7.6 THREE-FLUID MULTI-COMPONENT
SYSTEMS 320 7.7 PRACTICAL RELEVANCE 323 REFERENCES 323 8 ONE-DIMENSIONAL
THREE-FLUID FLOWS 325 8.1 SUMMARY OF THE LOCAL VOLUME- AND TIME-AVERAGED
CONSERVATION EQUATIONS 325 8.2 TREATMENT OF THE FIELD PRESSURE GRADIENT
FORCES 328 8.2.1 DISPERSED FLOWS 328 8.2.2 STRATIFIED FLOW 329 8.3 PIPE
DEFORMATION DUE TO TEMPORAL PRESSURE CHANGE IN THE FLOW 329 8.4 SOME
SIMPLE CASES 331 8.5 SLIP MODEL - TRANSIENT FLOW 338 8.6 SLIP MODEL -
STEADY STATE. CRITICAL MASS FLOW RATE 342 8.7 FORCES ACTING ON THE PIPES
DUE TO THE FLOW - THEORETICAL BASICS 350 8.8 RELIEF VALVES 356 8.8.1
INTRODUCTION 356 8.8.2 VALVE CHARACTERISTICS, MODEL FORMULATION 357
8.8.3 ANALYTICAL SOLUTION 361 8.8.4 FITTING THE PIECEWISE SOLUTION ON
TWO KNOWN POSITION - TIME POINTS 363 8.8.5 FITTING THE PIECEWISE
SOLUTION ON KNOWN VELOCITY AND POSITION FOR A GIVEN TIME 365 8.8.6
IDEALIZED VALVE CHARACTERISTICS 366 8.8.7 RECOMMENDATIONS FOR THE
APPLICATION OF THE MODEL IN SYSTEM COMPUTER CODES 368 8.8.8 SOME
ILLUSTRATIONS OF THE VALVE PERFORMANCE MODEL 370 8.8.9 NOMENCLATURE FOR
SECTION 8.8 376 8.9 PUMP MODEL 378 8.9.1 VARIABLES DEFINING THE PUMP
BEHAVIOR 378 8.9.2 THEORETICAL BASICS 381 8.9.3 SUTER DIAGRAM 388 8.9.4
COMPUTATIONAL PROCEDURE 394 8.9.5 CENTRIFUGAL PUMP DRIVE MODEL 395 8.9.6
EXTENSION OF THE THEORY TO MULTI-PHASE FLOW 396 APPENDIX 1:
CHRONOLOGICAL REFERENCES TO THE SUBJECT CRITICAL TWO-PHASE FLOW 399
REFERENCES 405 9 DETONATION WAVES CAUSED BY CHEMICAL REACTIONS OR BY
MELT-COOLANT INTERACTIONS 407 9.1 INTRODUCTION 1 407 9.2 SINGLE-PHASE
THEORY 409 9.2.1 CONTINUUM SOUNDWAVES (LAPLACE) 409 9.2.2 DISCONTINUUM
SHOCKWAVES (RANKINE-HUGONIOT) 410 XX TABLE OF CONTENTS 9.2.3 THE LANDAU
AND LIFTSHITZ ANALYTICAL SOLUTION FOR DETONATION IN PERFECT GASES 414
9.2.4 NUMERICAL SOLUTION FOR DETONATION IN CLOSED PIPES 418 9.3
MULTI-PHASE FLOW 421 9.3.1 CONTINUUM SOUND WAVES 421 9.3.2 DISCONTINUUM
SHOCKWAVES 423 9.3.3 MELT-COOLANT INTERACTION DETONATIONS 424 9.3.4
SIMILARITY TO AND DIFFERENCES FROM THE YUEN AND THEOFANOUS FORMALISM 429
9.3.5 NUMERICAL SOLUTION METHOD 430 9.4 DETONATION WAVES IN WATER MIXED
WITH DIFFERENT MOLTEN MATERIALS 431 9.4.1 UO 2 WATER SYSTEM 431 9.4.2
EFFICIENCIES 435 9.4.3 THE MAXIMUM COOLANT ENTRAINMENT RATIO 438 9.5
CONCLUSIONS 439 9.6 PRACTICAL SIGNIFICANCE 441 APPENDIX 9.1 SPECIFIC
HEAT CAPACITY AT CONSTANT PRESSURE FOR URANIA AND ALUMINA 442 REFERENCES
443 10 CONSERVATION EQUATIONS IN GENERAL CURVILINEAR COORDINATE SYSTEMS
445 10.1 INTRODUCTION 445 10.2 FIELD MASS CONSERVATION EQUATIONS 446
10.3 MASS CONSERVATION EQUATIONS FOR COMPONENTS INSIDE THE FIELD -
^CONSERVATIVE FORM 449 10.4 FIELD MASS CONSERVATION EQUATIONS FOR
COMPONENTS INSIDE THE FIELD - NON-CONSERVATIVE FORM 451 10.5 PARTICLES
NUMBER CONSERVATION EQUATIONS FOR EACH VELOCITY FIELD 451 10.6 FIELD
ENTROPY CONSERVATION EQUATIONS - CONSERVATIVE FORM 452 10.7 FIELD
ENTROPY CONSERVATION EQUATIONS - NON-CONSERVATIVE FORM 453 10.8
IRREVERSIBLE POWER DISSIPATION CAUSED BY THE VISCOUS FORCES 454 10.9 THE
NON-CONSERVATIVE ENTROPY EQUATION IN TERMS OF TEMPERATURE AND PRESSURE
456 10.10 THE VOLUME CONSERVATION EQUATION 458 10.11 THE MOMENTUM
EQUATIONS 459 10.12 THE FLUX CONCEPT, CONSERVATIVE AND SEMI-CONSERVATIVE
FORMS 466 10.12.1 MASS CONSERVATION EQUATION .: 466 10.12.2 ENTROPY
EQUATION 468 10.12.3 TEMPERATURE EQUATION 468 10.12.4 MOMENTUM
CONSERVATION IN THE JC-DIRECTION 469 10.12.5 MOMENTUM CONSERVATION IN
THE ^-DIRECTION 470 10.12.6 MOMENTUM CONSERVATION IN THE Z-DIRECTION 472
10.13 CONCLUDING REMARKS 473 REFERENCES ,.- 473 TABLE OF CONTENTS XXI 11
TYPE OF THE SYSTEM OF PDES 475 11.1 EIGENVALUES, EIGENVECTORS, CANONICAL
FORM 475 11.2 PHYSICAL INTERPRETATION 478 11.2.1 EIGENVALUES AND
PROPAGATION VELOCITY OF PERTURBATIONS 478 11.2.2 EIGENVALUES AND
PROPAGATION VELOCITY OF HARMONIC OSCILLATIONS 478 11.2.3 EIGENVALUES AND
CRITICAL FLOW 479 REFERENCES R 480 12 NUMERICAL SOLUTION METHODS FOR
MULTI-PHASE FLOW PROBLEMS 481 12.1 INTRODUCTION 481 12.2 FORMULATION OF
THE MATHEMATICAL PROBLEM 481 12.3 SPACE DISCRETIZATION AND LOCATION OF
THE DISCRETE VARIABLES 483 12.4 DISCRETIZATION OF THE MASS CONSERVATION
EQUATIONS 488 12.5 FIRST ORDER DONOR-CELL FINITE DIFFERENCE
APPROXIMATIONS 490 12.6 DISCRETIZATION OF THE CONCENTRATION EQUATIONS
492 12.7 DISCRETIZATION OF THE ENTROPY EQUATION 493 12.8 DISCRETIZATION
OF THE TEMPERATURE EQUATION 494 12.9 PHYSICAL SIGNIFICANCE OF THE
NECESSARY CONVERGENCE CONDITION 497 12.10 IMPLICIT DISCRETIZATION OF
MOMENTUM EQUATIONS 499 12.11 PRESSURE EQUATIONS FOR IVA2 AND IVA3
COMPUTER CODES 505 12.12 A NEWTON-TYPE ITERATION METHOD FOR MULTI-PHASE
FLOWS 508 12.13 INTEGRATION PROCEDURE: IMPLICIT METHOD 517 12.14 TIME
STEP AND ACCURACY CONTROL 519 12.15 HIGH ORDER DISCRETIZATION SCHEMES
FOR CONVECTION-DIFFUSION TERMS 520 12.15.1 SPACE EXPONENTIAL SCHEME 520
12.15.2 HIGH ORDER UPWINDING 523 12.15.3 CONSTRAINED INTERPOLATION
PROFILE (CIP) METHOD 525 12.16 PROBLEM SOLUTION EXAMPLES TO THE BASICS
OF THE CIP METHOD 530 12.16.1 DISCRETIZATION CONCEPT 530 12.16.2 SECOND
ORDER CONSTRAINED INTERPOLATION PROFILES 531 12.16.3 THIRD ORDER
CONSTRAINED INTERPOLATION PROFILES 533 12.16.4 FOURTH ORDER CONSTRAINED
INTERPOLATION PROFILES 534 12.17 PIPE NETWORKS: SOME BASIC DEFINITIONS
554 12.17.1 PIPES .554 12.17.2 AXIS IN THE SPACE 556 12.17.3 DIAMETERS
OF PIPE SECTIONS 557 12.17.4 REDUCTIONS FF 557 12.17.5 ELBOWS 558
12.17.6 CREATING A LIBRARY OF PIPES 559 12.17.7 SUB SYSTEM NETWORK 559
12.17.8 DISCRETIZATION OF PIPES 560 12.17.9 KNOTS * 560 APPENDIX 12.1
DEFINITIONS APPLICABLE TO DISCRETIZATION OF THE MASS CONSERVATION
EQUATIONS 562 APPENDIX 12.2 DISCRETIZATION OF THE CONCENTRATION
EQUATIONS 565 XXII TABLE OF CONTENTS APPENDIX 12.3 HARMONIC AVERAGED
DIFFUSION COEFFICIENTS 567 APPENDIX 12.4. DISCRETIZED RADIAL MOMENTUM
EQUATION 568 APPENDIX 12.5 THE A COEFFICIENTS FOR EQ. (12.46) 573
APPENDIX 12.6 DISCRETIZATION OF THE ANGULAR MOMENTUM EQUATION 573
APPENDIX 12.7 DISCRETIZATION OF THE AXIAL MOMENTUM EQUATION 575 APPENDIX
12.8 ANALYTICAL DERIVATIVES FOR THE RESIDUAL ERROR OF EACH EQUATION WITH
RESPECT TO THE DEPENDENT VARIABLES 577 APPENDIX 12.9 SIMPLE INTRODUCTION
TO ITERATIVE METHODS FOR SOLUTION OF ALGEBRAIC SYSTEMS 580 REFERENCES
581 13 NUMERICAL METHODS FOR MULTI-PHASE FLOW IN CURVILINEAR COORDINATE
SYSTEMS 587 13.1 INTRODUCTION 587 13.2 NODES, GRIDS, MESHES, TOPOLOGY -
SOME BASIC DEFINITIONS 589 13.3 FORMULATION OF THE MATHEMATICAL PROBLEM
590 13.4 DISCRETIZATION OF THE MASS CONSERVATION EQUATIONS 592 13.4.1
INTEGRATION OVER A FINITE TIME STEP AND FINITE CONTROL VOLUME 592 13.4.2
THE DONOR-CELL CONCEPT 594 13.4.3 TWO METHODS FOR COMPUTING THE FINITE
DIFFERENCE APPROXIMATIONS OF THE CONTRAVARIANT VECTORS AT THE CELL
CENTER 597 13.4.4 DISCRETIZATION OF THE DIFFUSION TERMS 599 13.5
DISCRETIZATION OF THE ENTROPY EQUATION 603 13.6 DISCRETIZATION OF THE
TEMPERATURE EQUATION 604 13.7 DISCRETIZATION OF THE PARTICLE NUMBER
DENSITY EQUATION 605 13.8 DISCRETIZATION OF THE X MOMENTUM EQUATION 605
13.9 DISCRETIZATION OF THE Y MOMENTUM EQUATION 607 13.10 DISCRETIZATION
OF THE Z MOMENTUM EQUATION 608 13.11 PRESSURE-VELOCITY COUPLING 608
13.12 STAGGERED X MOMENTUM EQUATION 613 APPENDIX 13.1 HARMONIC AVERAGED
DIFFUSION COEFFICIENTS 623 APPENDIX 13.2 OFF-DIAGONAL VISCOUS DIFFUSION
TERMS OF THE X MOMENTUM EQUATION 625 APPENDIX 13.3 OFF-DIAGONAL VISCOUS
DIFFUSION TERMS OF THE Y MOMENTUM EQUATION R.. 628 APPENDIX 13.4
OFF-DIAGONAL VISCOUS DIFFUSION TERMS OF THE Z MOMENTUM EQUATION 630
REFERENCES 633 APPENDIX 1 BRIEF INTRODUCTION TO VECTOR ANALYSIS 637
APPENDIX 2 BASICS OF THE COORDINATE TRANSFORMATION THEORY 663 TABLE OF
CONTENTS XXIII 14 VISUAL DEMONSTRATION OF THE METHOD 715 14.1 MELT-WATER
INTERACTIONS 715 14.1.1 CASES 1 TO 4 715 14.1.2 CASES 5, 6 AND 7 721
14.1.3 CASES 8 TO 10 725 14.1.4 CASES 11 AND 12 736 14.1.5 CASE 13 739
14.1.6 CASE 14 740 14.2 PIPE NETWORKS 743 14.2.1 CASE 15 743 14.3 3D
STEAM-WATER INTERACTION 745 14.3.1 CASE 16 745 14.4 THREE DIMENSIONAL
STEAM-WATER INTERACTION IN PRESENCE OF NON-CONDENSABLE GASES 746 14.4.1
CASE 17 746 14.5 THREE DIMENSIONAL STEAM PRODUCTION IN BOILING WATER
REACTOR 748 14.5.1 CASE 18 748 REFERENCES 749 INDEX 751
|
| adam_txt |
NIKOLAY I. KOLEV MULTIPHASE FLOW DYNAMICS 1 FUNDAMENTALS 3RD EDITION
WITH 149 FIGURES AND CD-ROM &J SPRINGER TABLE OF CONTENTS CHAPTER 14 OF
VOLUME 1 AND CHAPTER 26 OF VOLUME 2 ARE AVAILABLE IN PDF FORMAT ON THE
CD-ROM ATTACHED TO VOLUME 1. THE SYSTEM REQUIREMENTS ARE WINDOWS 98 AND
HIGHER. BOTH PDF FILES CONTAIN LINKS TO COMPUTER ANIMATIONS. TO SEE THE
ANIMA- TIONS, ONE DOUBLE CLICKS ON THE ACTIVE LINKS CONTAINED INSIDE THE
PDF DOCUMENTS. THE ANIMATIONS ARE THEN DISPLAYED IN AN INTERNET BROWSER,
SUCH MICROSOFT INTERNET EXPLORER OR NETSCAPE. ALTERNATIVELY, GIF-FILE
ANIMATIONS ARE ALSO PROVIDED. NOMENCLATURE XXV INTRODUCTION XXXV 1 MASS
CONSERVATION 1 1.1 INTRODUCTION ;.L 1.2 BASIC DEFINITIONS 2 1.3
NON-STRUCTURED AND STRUCTURED FIELDS 9 1.4 SLATTERY AND WHITAKER 'S
LOCAL SPATIAL AVERAGING THEOREM 10 1.5 GENERAL TRANSPORT EQUATION
(LEIBNITZ RULE) 12 1.6 LOCAL VOLUME-AVERAGED MASS CONSERVATION EQUATION
13 1.7 TIME AVERAGE .* 16 1.8 LOCAL VOLUME-AVERAGED COMPONENT
CONSERVATION EQUATIONS 18 1.9 LOCAL VOLUME- AND TIME-AVERAGED
CONSERVATION EQUATIONS 20 1.10 CONSERVATION EQUATIONS FOR THE NUMBER
DENSITY OF PARTICLES 24 1.11 IMPLICATION OF THE ASSUMPTION OF
MONO-DISPERSITY IN A CELL 30 1.11.1 PARTICLE SIZE SPECTRUM AND AVERAGING
30 1.11.2 CUTTING OF THE LOWER PART OF THE SPECTRUM DUE TO MASS TRANSFER
31 1.11.3 THE EFFECT OF THE AVERAGING ON THE EFFGPTIVE VELOCITY
DIFFERENCE 33 1.12 STRATIFIED STRUCTURE 35 1.13 FINAL REMARKS AND
CONCLUSIONS 35 REFERENCES 37 2 MOMENTUMS CONSERVATION 41 2.1
INTRODUCTION 41 2.2 LOCAL VOLUME-AVERAGED MOMENTUM EQUATIONS 42 2.2.1
SINGLE-PHASE MOMENTUM EQUATIONS 42 2.2.2 INTERFACE FORCE BALANCE
(MOMENTUM JUMP CONDITION) 42 XVI TABLE OF CONTENTS 2.2.3 LOCAL VOLUME
AVERAGING OF THE SINGLE-PHASE MOMENTUM EQUATION 49 2.3 REARRANGEMENT OF
THE SURFACE INTEGRALS 51 2.4 LOCAL VOLUME AVERAGE AND TIME AVERAGE 55
2.5 DISPERSED PHASE IN LAMINAR CONTINUUM - PSEUDO TURBULENCE 57 2.6
VISCOUS AND REYNOLDS STRESSES 57 2.7 NON-EQUAL BULK AND BOUNDARY LAYER
PRESSURES 62 2.7.1 CONTINUOUS INTERFACE 62 2.7.2 DISPERSED INTERFACE 77
2.8 WORKING FORM FOR DISPERSED AND CONTINUOUS PHASE 93 2.9 GENERAL
WORKING FORM FOR DISPERSED AND CONTINUOUS PHASES 98 2.10 SOME PRACTICAL
SIMPLIFICATIONS 100 2.11 CONCLUSION 104 APPENDIX 2.1 104 APPENDIX 2.2
105 APPENDIX 2.3 106 REFERENCES 109 3 DERIVATIVES FOR THE EQUATIONS OF
STATE 115 3.1 INTRODUCTION 115 3.2 MULTI-COMPONENT MIXTURES OF MISCIBLE
AND NON-MISCIBLE COMPONENTS 117 3.2.1 COMPUTATION OF PARTIAL PRESSURES
FOR KNOWN MASS CONCENTRATIONS, SYSTEM PRESSURE AND TEMPERATURE 118 3.2.2
PARTIAL DERIVATIVES OF THE EQUATION OF STATE 125 3.2.3 PARTIAL
DERIVATIVES IN THE EQUATION OF STATE T = T( 2 ,., T J), WHERE '
130 3.2.4 CHEMICAL POTENTIAL 139 3.2.5 PARTIAL DERIVATIVES IN THE
EQUATION OF STATE P = P(P, 2 , I, WHERE Q = S,H,E 150 3.3 MIXTURE OF
LIQUID AND MICROSCOPIC SOLID PARTICLES OF DIFFERENT CHEMICAL SUBSTANCES
153 3.3.1 PARTIAL DERIVATIVES IN THE EQUATION OF STATE 3.3.2 PARTIAL
DERIVATIVES IN THE EQUATION OF STATE T = T{P,(P,C 2 ,. ) WHERE (P-H,E,S
154 3.4 SINGLE-COMPONENT EQUILIBRIUM FLUID 155 3.4.1 SUPERHEATED VAPOR
155 3.4.2 RECONSTRUCTION OF EQUATION OF STATE BY USING A LIMITED AMOUNT
OF DATA AVAILABLE 156 3.4.3 VAPOR-LIQUID MIXTURE IN THERMODYNAMIC
EQUILIBRIUM 163 TABLE OF CONTENTS XVII 3.4.4 LIQUID-SOLID MIXTURE IN
THERMODYNAMIC EQUILIBRIUM 164 3.4.5 SOLID PHASE 164 3.5 EXTENSION STATE
OF LIQUIDS 165 APPENDIX 3.1 APPLICATION OF THE THEORY TO STEAM-AIR
MIXTURES 165 APPENDIX 3.2 USEFUL REFERENCES FOR COMPUTING PROPERTIES OF
SINGLE CONSTITUENTS 167 APPENDIX 3.3 USEFUL DEFINITIONS AND RELATIONS
BETWEEN THERMODYNAMIC QUANTITIES .' 169 REFERENCES 170 4 ON THE VARIETY
OF NOTATIONS OF THE ENERGY CONSERVATION FOR SINGLE-PHASE FLOW 173 4.1
INTRODUCTION 173 4.2 MASS AND MOMENTUM CONSERVATION, ENERGY CONSERVATION
174 4.3 SIMPLE NOTATION OF THE ENERGY CONSERVATION EQUATION 175 4.4 THE
ENTROPY 176 4.5 EQUATION OF STATE 177 4.6 VARIETY OF NOTATION OF THE
ENERGY CONSERVATION PRINCIPLE 177 4.6.1 TEMPERATURE 177 4.6.2 SPECIFIC
ENTHALPY 178 4.7 SUMMARY OF DIFFERENT NOTATIONS 179 4.8 THE EQUIVALENCE
OF THE CANONICAL FORMS 179 4.9 EQUIVALENCE OF THE ANALYTICAL SOLUTIONS
182 4.10 EQUIVALENCE OF THE NUMERICAL SOLUTIONS? 183 4.10.1 EXPLICIT
FIRST ORDER METHOD OF CHARACTERISTICS 183 4.10.2 THE PERFECT GAS SHOCK
TUBE: BENCHMARK FOR NUMERICAL METHODS 187 4.11 INTERPENETRATING FLUIDS
196 4.12 SUMMARY OF DIFFERENT NOTATIONS FOR INTERPENETRATING FLUIDS 201
APPENDIX 4.1 ANALYTICAL SOLUTION OF THE SHOCK TUBE PROBLEM 203 APPENDIX
4.2 ACHIEVABLE ACCURACY OF THE DONOR-CELL METHOD FOR SINGLE-PHASE FLOWS
-. 207 REFERENCES 210 5 FIRST AND SECOND LAWS OF THE THERMODYNAMICS 213
5.1 INTRODUCTION 213 5.2 INSTANTANEOUS LOCAL VOLUME AVERAGE ENERGY
EQUATIONS 216 5.3 DALTON AND FICWS LAWS , CENTER OF MASS MFXTURE
VELOCITY, CALORIC MIXTURE PROPERTIES 223 5.4 ENTHALPY EQUATION 225 5.5
INTERNAL ENERGY EQUATION 229 5.6 ENTROPY EQUATION 230 5.7 LOCAL VOLUME-
AND TIME-AVERAGED ENTROPY EQUATION 234 5.8 LOCAL VOLUME- AND
TIME-AVERAGED INTERNAL ENERGY EQUATION 239 XVIII TABLE OF CONTENTS 5.9
LOCAL VOLUME- AND TIME-AVERAGED SPECIFIC ENTHALPY EQUATION 241 5.10
NON-CONSERVATIVE AND SEMI-CONSERVATIVE FORMS OF THE ENTROPY EQUATION 243
5.11 COMMENTS ON THE SOURCE TERMS IN THE MIXTURE ENTROPY EQUATION 245
5.12 VISCOUS DISSIPATION 250 5.13 TEMPERATURE EQUATION 255 5.14 SECOND
LAW OF THE THERMODYNAMICS .'. 259 5.15 MIXTURE VOLUME CONSERVATION
EQUATION 260 5.16 LINEARIZED FORM OF THE SOURCE TERM FOR THE TEMPERATURE
EQUATION 265 5.17 INTERFACE CONDITIONS 272 5.18 LUMPED PARAMETER VOLUMES
273 5.19 STEADY STATE 274 5.20 FINAL REMARKS 278 REFERENCES 279 SOME
SIMPLE APPLICATIONS OF THE MASS AND ENERGY CONSERVATION 283 6.1 INFINITE
HEAT EXCHANGE WITHOUT INTERFACIAL MASS TRANSFER 283 6.2 DISCHARGE OF GAS
FROM A VOLUME 285 6.3 INJECTION OF INERT GAS IN A CLOSED VOLUME
INITIALLY FILLED WITH INERT GAS 287 6.4 HEAT INPUT IN A GAS IN A CLOSED
VOLUME 288 6.5 STEAM INJECTION IN A STEAM-AIR MIXTURE 289 6.6 CHEMICAL
REACTION IN A GAS MIXTURE IN A CLOSED VOLUME 292 6.7 HYDROGEN COMBUSTION
IN AN INERT ATMOSPHERE 294 6.7.1 SIMPLE INTRODUCTION TO COMBUSTION
KINETICS 294 6.7.2 IGNITION TEMPERATURE AND IGNITION CONCENTRATION
LIMITS 296 6.7.3 DETONABILITY CONCENTRATION LIMITS 297 6.7.4 THE HEAT
RELEASE DUE TO COMBUSTION 297 6.7.5 EQUILIBRIUM DISSOCIATION 298 6.7.6
SOURCE TERMS^OF THE ENERGY CONSERVATION OF THE GAS PHASE 303 6.7.7
TEMPERATURE AND PRESSURE CHANGES IN A CLOSED CONTROL VOLUME; ADIABATIC
TEMPERATURE OF THE BURNED GASES 305 REFERENCES 309 EXERGY OF MULTI-PHASE
MULTI-COMPONENT SYSTEMS 311 7.1 INTRODUCTION 311 7.2 THE PSEUDO-EXERGY
EQUATION FOR SINGLE-FLUID SYSTEMS 311 7.3 THE FUNDAMENTAL EXERGY
EQUATION .?. 313 7.3.1 THE EXERGY DEFINITION IN ACCORDANCE WITH REYNOLDS
AND PERKINS 313 7.3.2 THE EXERGY DEFINITION IN ACCORDANCE WITH GOUY
(PENERGIE UTILISABLE, 1889) 314 7.3.3 THE EXERGY DEFINITION APPROPRIATE
FOR ESTIMATION OF THE VOLUME CHANGE WORK 315 7.3.4 THE.EXERGY DEFINITION
APPROPRIATE FOR ESTIMATION OF THE TECHNICAL WORK 316 7.4 SOME
INTERESTING CONSEQUENCES OF THE FUNDAMENTAL EXERGY EQUATION. 316
TABLE OF CONTENTS XIX 7.5 JUDGING THE EFFICIENCY OF A HEAT PUMP AS AN
EXAMPLE OF APPLICATION OF THE EXERGY 318 7.6 THREE-FLUID MULTI-COMPONENT
SYSTEMS 320 7.7 PRACTICAL RELEVANCE 323 REFERENCES 323 8 ONE-DIMENSIONAL
THREE-FLUID FLOWS 325 8.1 SUMMARY OF THE LOCAL VOLUME- AND TIME-AVERAGED
CONSERVATION EQUATIONS 325 8.2 TREATMENT OF THE FIELD PRESSURE GRADIENT
FORCES 328 8.2.1 DISPERSED FLOWS 328 8.2.2 STRATIFIED FLOW 329 8.3 PIPE
DEFORMATION DUE TO TEMPORAL PRESSURE CHANGE IN THE FLOW 329 8.4 SOME
SIMPLE CASES 331 8.5 SLIP MODEL - TRANSIENT FLOW 338 8.6 SLIP MODEL -
STEADY STATE. CRITICAL MASS FLOW RATE 342 8.7 FORCES ACTING ON THE PIPES
DUE TO THE FLOW - THEORETICAL BASICS 350 8.8 RELIEF VALVES 356 8.8.1
INTRODUCTION 356 8.8.2 VALVE CHARACTERISTICS, MODEL FORMULATION 357
8.8.3 ANALYTICAL SOLUTION 361 8.8.4 FITTING THE PIECEWISE SOLUTION ON
TWO KNOWN POSITION - TIME POINTS 363 8.8.5 FITTING THE PIECEWISE
SOLUTION ON KNOWN VELOCITY AND POSITION FOR A GIVEN TIME 365 8.8.6
IDEALIZED VALVE CHARACTERISTICS 366 8.8.7 RECOMMENDATIONS FOR THE
APPLICATION OF THE MODEL IN SYSTEM COMPUTER CODES 368 8.8.8 SOME
ILLUSTRATIONS OF THE VALVE PERFORMANCE MODEL 370 8.8.9 NOMENCLATURE FOR
SECTION 8.8 376 8.9 PUMP MODEL 378 8.9.1 VARIABLES DEFINING THE PUMP
BEHAVIOR 378 8.9.2 THEORETICAL BASICS 381 8.9.3 SUTER DIAGRAM 388 8.9.4
COMPUTATIONAL PROCEDURE 394 8.9.5 CENTRIFUGAL PUMP DRIVE MODEL 395 8.9.6
EXTENSION OF THE THEORY TO MULTI-PHASE FLOW 396 APPENDIX 1:
CHRONOLOGICAL REFERENCES TO THE SUBJECT CRITICAL TWO-PHASE FLOW 399
REFERENCES 405 9 DETONATION WAVES CAUSED BY CHEMICAL REACTIONS OR BY
MELT-COOLANT INTERACTIONS 407 9.1 INTRODUCTION 1 407 9.2 SINGLE-PHASE
THEORY 409 9.2.1 CONTINUUM SOUNDWAVES (LAPLACE) 409 9.2.2 DISCONTINUUM
SHOCKWAVES (RANKINE-HUGONIOT) 410 XX TABLE OF CONTENTS 9.2.3 THE LANDAU
AND LIFTSHITZ ANALYTICAL SOLUTION FOR DETONATION IN PERFECT GASES 414
9.2.4 NUMERICAL SOLUTION FOR DETONATION IN CLOSED PIPES 418 9.3
MULTI-PHASE FLOW 421 9.3.1 CONTINUUM SOUND WAVES 421 9.3.2 DISCONTINUUM
SHOCKWAVES 423 9.3.3 MELT-COOLANT INTERACTION DETONATIONS 424 9.3.4
SIMILARITY TO AND DIFFERENCES FROM THE YUEN AND THEOFANOUS FORMALISM 429
9.3.5 NUMERICAL SOLUTION METHOD 430 9.4 DETONATION WAVES IN WATER MIXED
WITH DIFFERENT MOLTEN MATERIALS 431 9.4.1 UO 2 WATER SYSTEM 431 9.4.2
EFFICIENCIES 435 9.4.3 THE MAXIMUM COOLANT ENTRAINMENT RATIO 438 9.5
CONCLUSIONS 439 9.6 PRACTICAL SIGNIFICANCE 441 APPENDIX 9.1 SPECIFIC
HEAT CAPACITY AT CONSTANT PRESSURE FOR URANIA AND ALUMINA 442 REFERENCES
443 10 CONSERVATION EQUATIONS IN GENERAL CURVILINEAR COORDINATE SYSTEMS
445 10.1 INTRODUCTION 445 10.2 FIELD MASS CONSERVATION EQUATIONS 446
10.3 MASS CONSERVATION EQUATIONS FOR COMPONENTS INSIDE THE FIELD -
^CONSERVATIVE FORM 449 10.4 FIELD MASS CONSERVATION EQUATIONS FOR
COMPONENTS INSIDE THE FIELD - NON-CONSERVATIVE FORM 451 10.5 PARTICLES
NUMBER CONSERVATION EQUATIONS FOR EACH VELOCITY FIELD 451 10.6 FIELD
ENTROPY CONSERVATION'EQUATIONS - CONSERVATIVE FORM 452 10.7 FIELD
ENTROPY CONSERVATION EQUATIONS - NON-CONSERVATIVE FORM 453 10.8
IRREVERSIBLE POWER DISSIPATION CAUSED BY THE VISCOUS FORCES 454 10.9 THE
NON-CONSERVATIVE ENTROPY EQUATION IN TERMS OF TEMPERATURE AND PRESSURE
456 10.10 THE VOLUME CONSERVATION EQUATION 458 10.11 THE MOMENTUM
EQUATIONS 459 10.12 THE FLUX CONCEPT, CONSERVATIVE AND SEMI-CONSERVATIVE
FORMS 466 10.12.1 MASS CONSERVATION EQUATION .: 466 10.12.2 ENTROPY
EQUATION 468 10.12.3 TEMPERATURE EQUATION 468 10.12.4 MOMENTUM
CONSERVATION IN THE JC-DIRECTION 469 10.12.5 MOMENTUM CONSERVATION IN
THE ^-DIRECTION 470 10.12.6 MOMENTUM CONSERVATION IN THE Z-DIRECTION 472
10.13 CONCLUDING REMARKS 473 REFERENCES ,.- 473 TABLE OF CONTENTS XXI 11
TYPE OF THE SYSTEM OF PDES 475 11.1 EIGENVALUES, EIGENVECTORS, CANONICAL
FORM 475 11.2 PHYSICAL INTERPRETATION 478 11.2.1 EIGENVALUES AND
PROPAGATION VELOCITY OF PERTURBATIONS 478 11.2.2 EIGENVALUES AND
PROPAGATION VELOCITY OF HARMONIC OSCILLATIONS 478 11.2.3 EIGENVALUES AND
CRITICAL FLOW ' 479 REFERENCES R 480 12 NUMERICAL SOLUTION METHODS FOR
MULTI-PHASE FLOW PROBLEMS 481 12.1 INTRODUCTION 481 12.2 FORMULATION OF
THE MATHEMATICAL PROBLEM 481 12.3 SPACE DISCRETIZATION AND LOCATION OF
THE DISCRETE VARIABLES 483 12.4 DISCRETIZATION OF THE MASS CONSERVATION
EQUATIONS 488 12.5 FIRST ORDER DONOR-CELL FINITE DIFFERENCE
APPROXIMATIONS 490 12.6 DISCRETIZATION OF THE CONCENTRATION EQUATIONS
492 12.7 DISCRETIZATION OF THE ENTROPY EQUATION 493 12.8 DISCRETIZATION
OF THE TEMPERATURE EQUATION 494 12.9 PHYSICAL SIGNIFICANCE OF THE
NECESSARY CONVERGENCE CONDITION 497 12.10 IMPLICIT DISCRETIZATION OF
MOMENTUM EQUATIONS 499 12.11 PRESSURE EQUATIONS FOR IVA2 AND IVA3
COMPUTER CODES 505 12.12 A NEWTON-TYPE ITERATION METHOD FOR MULTI-PHASE
FLOWS 508 12.13 INTEGRATION PROCEDURE: IMPLICIT METHOD 517 12.14 TIME
STEP AND ACCURACY CONTROL 519 12.15 HIGH ORDER DISCRETIZATION SCHEMES
FOR CONVECTION-DIFFUSION TERMS 520 12.15.1 SPACE EXPONENTIAL SCHEME 520
12.15.2 HIGH ORDER UPWINDING 523 12.15.3 CONSTRAINED INTERPOLATION
PROFILE (CIP) METHOD 525 12.16 PROBLEM SOLUTION EXAMPLES TO THE BASICS
OF THE CIP METHOD 530 12.16.1 DISCRETIZATION CONCEPT 530 12.16.2 SECOND
ORDER CONSTRAINED INTERPOLATION PROFILES 531 12.16.3 THIRD ORDER
CONSTRAINED INTERPOLATION PROFILES 533 12.16.4 FOURTH ORDER CONSTRAINED
INTERPOLATION PROFILES 534 12.17 PIPE NETWORKS: SOME BASIC DEFINITIONS
554 12.17.1 PIPES .554 12.17.2 AXIS IN THE SPACE 556 12.17.3 DIAMETERS
OF PIPE SECTIONS 557 12.17.4 REDUCTIONS FF 557 12.17.5 ELBOWS 558
12.17.6 CREATING A LIBRARY OF PIPES 559 12.17.7 SUB SYSTEM NETWORK 559
12.17.8 DISCRETIZATION OF PIPES 560 12.17.9 KNOTS * 560 APPENDIX 12.1
DEFINITIONS APPLICABLE TO DISCRETIZATION OF THE MASS CONSERVATION
EQUATIONS 562 APPENDIX 12.2 DISCRETIZATION OF THE CONCENTRATION
EQUATIONS 565 XXII TABLE OF CONTENTS APPENDIX 12.3 HARMONIC AVERAGED
DIFFUSION COEFFICIENTS 567 APPENDIX 12.4. DISCRETIZED RADIAL MOMENTUM
EQUATION 568 APPENDIX 12.5 THE A COEFFICIENTS FOR EQ. (12.46) 573
APPENDIX 12.6 DISCRETIZATION OF THE ANGULAR MOMENTUM EQUATION 573
APPENDIX 12.7 DISCRETIZATION OF THE AXIAL MOMENTUM EQUATION 575 APPENDIX
12.8 ANALYTICAL DERIVATIVES FOR THE RESIDUAL ERROR OF EACH EQUATION WITH
RESPECT TO THE DEPENDENT VARIABLES 577 APPENDIX 12.9 SIMPLE INTRODUCTION
TO ITERATIVE METHODS FOR SOLUTION OF ALGEBRAIC SYSTEMS 580 REFERENCES
581 13 NUMERICAL METHODS FOR MULTI-PHASE FLOW IN CURVILINEAR COORDINATE
SYSTEMS 587 13.1 INTRODUCTION 587 13.2 NODES, GRIDS, MESHES, TOPOLOGY -
SOME BASIC DEFINITIONS 589 13.3 FORMULATION OF THE MATHEMATICAL PROBLEM
590 13.4 DISCRETIZATION OF THE MASS CONSERVATION EQUATIONS 592 13.4.1
INTEGRATION OVER A FINITE TIME STEP AND FINITE CONTROL VOLUME 592 13.4.2
THE DONOR-CELL CONCEPT 594 13.4.3 TWO METHODS FOR COMPUTING THE FINITE
DIFFERENCE APPROXIMATIONS OF THE CONTRAVARIANT VECTORS AT THE CELL
CENTER 597 13.4.4 DISCRETIZATION OF THE DIFFUSION TERMS 599 13.5
DISCRETIZATION OF THE ENTROPY EQUATION 603 13.6 DISCRETIZATION OF THE
TEMPERATURE EQUATION 604 13.7 DISCRETIZATION OF THE PARTICLE NUMBER
DENSITY EQUATION 605 13.8 DISCRETIZATION OF THE X MOMENTUM EQUATION 605
13.9 DISCRETIZATION OF THE Y MOMENTUM EQUATION 607 13.10 DISCRETIZATION
OF THE Z MOMENTUM EQUATION 608 13.11 PRESSURE-VELOCITY COUPLING 608
13.12 STAGGERED X MOMENTUM EQUATION 613 APPENDIX 13.1 HARMONIC AVERAGED
DIFFUSION COEFFICIENTS 623 APPENDIX 13.2 OFF-DIAGONAL VISCOUS DIFFUSION
TERMS OF THE X MOMENTUM EQUATION 625 APPENDIX 13.3 OFF-DIAGONAL VISCOUS
DIFFUSION TERMS OF THE Y MOMENTUM EQUATION R. 628 APPENDIX 13.4
OFF-DIAGONAL VISCOUS DIFFUSION TERMS OF THE Z MOMENTUM EQUATION 630
REFERENCES 633 APPENDIX 1 BRIEF INTRODUCTION TO VECTOR ANALYSIS 637
APPENDIX 2 BASICS OF THE COORDINATE TRANSFORMATION THEORY 663 TABLE OF
CONTENTS XXIII 14 VISUAL DEMONSTRATION OF THE METHOD 715 14.1 MELT-WATER
INTERACTIONS 715 14.1.1 CASES 1 TO 4 715 14.1.2 CASES 5, 6 AND 7 721
14.1.3 CASES 8 TO 10 725 14.1.4 CASES 11 AND 12 736 14.1.5 CASE 13 739
14.1.6 CASE 14 740 14.2 PIPE NETWORKS 743 14.2.1 CASE 15 743 14.3 3D
STEAM-WATER INTERACTION 745 14.3.1 CASE 16 745 14.4 THREE DIMENSIONAL
STEAM-WATER INTERACTION IN PRESENCE OF NON-CONDENSABLE GASES 746 14.4.1
CASE 17 746 14.5 THREE DIMENSIONAL STEAM PRODUCTION IN BOILING WATER
REACTOR 748 14.5.1 CASE 18 748 REFERENCES 749 INDEX 751 |
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| author | Kolev, Nikolay Ivanov 1951- |
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| index_date | 2024-07-02T18:40:29Z |
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| spelling | Kolev, Nikolay Ivanov 1951- Verfasser (DE-588)110653262 aut Multiphase flow dynamics 1 Fundamentals Nikolay I. Kolev 3. ed. Berlin [u.a.] Springer 2007 XL, 758 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier (DE-604)BV014569143 1 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016027428&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kolev, Nikolay Ivanov 1951- Multiphase flow dynamics |
| title | Multiphase flow dynamics |
| title_auth | Multiphase flow dynamics |
| title_exact_search | Multiphase flow dynamics |
| title_exact_search_txtP | Multiphase flow dynamics |
| title_full | Multiphase flow dynamics 1 Fundamentals Nikolay I. Kolev |
| title_fullStr | Multiphase flow dynamics 1 Fundamentals Nikolay I. Kolev |
| title_full_unstemmed | Multiphase flow dynamics 1 Fundamentals Nikolay I. Kolev |
| title_short | Multiphase flow dynamics |
| title_sort | multiphase flow dynamics fundamentals |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016027428&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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