Fluid dynamics: theoretical and computational approaches
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| Format: | Buch |
| Sprache: | English |
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Boca Raton [u.a.]
Taylor & Francis
2006
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| Ausgabe: | 3. ed. |
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| Beschreibung: | 845 S. graph. Darst. |
| ISBN: | 0849333970 |
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| 100 | 1 | |a Warsi, Zahir U. A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fluid dynamics |b theoretical and computational approaches |c Z. U. A. Warsi |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Boca Raton [u.a.] |b Taylor & Francis |c 2006 | |
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| 650 | 7 | |a Dynamica |2 gtt | |
| 650 | 4 | |a Fluides, Dynamique des | |
| 650 | 7 | |a Idealen (wiskunde) |2 gtt | |
| 650 | 7 | |a Navier-Stokes-vergelijkingen |2 gtt | |
| 650 | 7 | |a Reologie |2 gtt | |
| 650 | 7 | |a Turbulentie |2 gtt | |
| 650 | 7 | |a Viscositeit |2 gtt | |
| 650 | 4 | |a Fluid dynamics | |
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Datensatz im Suchindex
| _version_ | 1804135019148476416 |
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| adam_text | THIRD EDITION FLUID DYNAMICS THEORETICAL AND COMPUTATIONAL APPROACHES
Z.U.A. WARSI TAYLOR & FRANCIS TAYLOR & FRANCIS CROUP BOCA RATON LONDON
NEW YORK SINGAPORE A CRC TITLE, PART OF THE TAYLOR & FRANCIS IMPRINT, A
MEMBER OF THE TAYLOR & FRANCIS GROUP, THE ACADEMIC DIVISION OF T&F
INFORMA PIC. TABLE OF CONTENTS CHAPTER 1 KINEMATICS OF FLUID MOTION 1
1.1 INTRODUCTION TO CONTINUUM MOTION 1 1.2 FLUID PARTICLES 1 1.3
INERTIAL COORDINATE FRAMES 2 1.4 MOTION OF A CONTINUUM 2 1.5 THE TIME
DERIVATIVES 6 1.6 VELOCITY AND ACCELERATION 6 1.7 STEADY AND NONSTEADY
FLOW 10 1.8 TRAJECTORIES OF FLUID PARTICLES AND STREAMLINES 11 1.9
MATERIAL VOLUME AND SURFACE 12 1.10 RELATION BETWEEN ELEMENTAL VOLUMES
13 1.11 KINEMATIC FORMULAS OF EULER AND REYNOLDS 13 1.12 CONTROL VOLUME
AND SURFACE 16 1.13 KINEMATICS OF DEFORMATION 17 1.14 KINEMATICS OF
VORTICITY AND CIRCULATION 22 VORTEX LINE 22 VORTEX TUBE 22 CIRCULATION
OF VELOCITY 24 RATE OF CHANGE OF CIRCULATION 24 REFERENCES 25 PROBLEMS
26 CHAPTER 2 THE CONSERVATION LAWS AND THE KINETICS OF FLOW 33 2.1 FLUID
DENSITY AND THE CONSERVATION OF MASS 33 2.2 PRINCIPLE OF MASS
CONSERVATION 33 TIME VARIATION OF PP 34 PARTICULAR FORMS OF THE
CONTINUITY EQUATION 35 2.3 MASS CONSERVATION USING A CONTROL VOLUME 35
2.4 KINETICS OF FLUID FLOW 36 STRESS PRINCIPLE OF CAUCHY 36 2.5
CONSERVATION OF LINEAR AND ANGULAR MOMENTUM 37 CONSERVATION OF LINEAR
MOMENTUM 37 CONSERVATION OF ANGULAR MOMENTUM 38 NATURE OF STRESS VECTOR
, 38 SYMMETRY OF T 41 2.6 EQUATIONS OF LINEAR AND ANGULAR MOMENTUM 42
2.7 MOMENTUM CONSERVATION USING A CONTROL VOLUME 44 2.8 CONSERVATION OF
ENERGY 44 2.9 ENERGY CONSERVATION USING A CONTROL VOLUME 47 2.10 GENERAL
CONSERVATION PRINCIPLE 47 2.11 THE CLOSURE PROBLEM 48 2.12 STOKES LAW
OF FRICTION 51 THE POSTULATES OF STOKES 52 STOKESIAN STRESS TENSOR 52
2.13 INTERPRETATION OF PRESSURE 57 .14 THE DISSIPATION FUNCTION 58 2.15
CONSTITUTIVE EQUATION FOR NON-NEWTONIAN FLUIDS 59 2.16 THERMODYNAMIC
ASPECTS OF PRESSURE AND VISCOSITY 61 IDEAL GASES 62 CONCEPT OF VISCOSITY
IN FLUIDS 64 SUTHERLAND FORMULA FOR VISCOSITY 66 2.17 EQUATIONS OF
MOTION IN LAGRANGIAN COORDINATES 67 REFERENCES 71 PROBLEMS 71 CHAPTER 3
THE NAVIER-STOKES EQUATIONS 75 3.1 FORMULATION OF THE PROBLEM 75 3.2
VISCOUS COMPRESSIBLE FLOW EQUATIONS 78 CONSERVATION OF MASS 78
CONSERVATION OF MOMENTUM 78 EQUATIONS OF MECHANICAL ENERGY 78 EQUATIONS
OF INTERNAL ENERGY 78 EQUATIONS OF ENTROPY AND ENTHALPY 79 CONSERVATION
OF TOTAL KINETIC ENERGY 80 3.3 VISCOUS INCOMPRESSIBLE FLOW EQUATIONS 80
CONSERVATION OF MASS 80 CONSERVATION OF MOMENTUM 80 EQUATION OF
VORTICITY 81 EQUATION OF INTERNAL ENERGY 82 EQUATION FOR PRESSURE 82 3.4
EQUATIONS OF INVISCID FLOW (EULER S EQUATIONS) 83 CONSERVATION OF MASS
83 CONSERVATION OF MOMENTUM 84 EQUATIONS OF ENTROPY AND ENTHALPY 84
CONSERVATION OF ENERGY 84 CONSERVATION OF TOTAL KINETIC ENERGY 84
INVISCID BAROTROPIC FLOW 84 3.5 INITIAL AND BOUNDARY CONDITIONS 85 3.6
MATHEMATICAL NATURE OF THE EQUATIONS 86 3.7 VORTICITY AND CIRCULATION 86
VORTICITY AND CIRCULATION FOR INVISCID FLUIDS , 87 THE BERNOULLI
EQUATION 89 3.8 SOME RESULTS BASED ON THE EQUATIONS OF MOTION 90 FORCE
ACTING ON A SOLID BODY 90 STRESS VECTOR AND TENSOR AT A SURFACE , 91
VORTICITY VECTOR AT A SURFACE 92 RATE-OF-STRAIN TENSOR AT A SURFACE 93
3.9 NONDIMENSIONAL PARAMETERS IN FLUID MOTION 94 PRINCIPLE OF SIMILARITY
97 DYNAMIC SIMILARITY 97 VARIABLE NONDIMENSIONAL PARAMETERS 97 PRINCIPLE
OF REYNOLDS NUMBER SIMILARITY 98 3.10 COORDINATE TRANSFORMATION 99
ORTHOGONAL COORDINATES 100 NAVIER-STOKES EQUATIONS IN ORTHOGONAL
COORDINATES 105 NONORTHOGONAL CURVILINEAR COORDINATES 107 STEADY
EULERIAN COORDINATES 107 NONSTEADY EULERIAN COORDINATES *-. 110
EQUATIONS IN GENERAL COORDINATES 115 EQUATIONS IN GENERAL COORDINATES
USING CONTRAVARIANT COMPONENTS 117 EQUATIONS IN GENERAL COORDINATES
USING COVARIANT COMPONENTS 117 EQUATIONS IN GENERAL COORDINATES WITH
VECTORS AND TENSOR DENSITIES 118 EQUATIONS IN NONSTEADY EULERIAN
COORDINATES 120 EQUATIONS IN CURVILINEAR COORDINATES WITH CARTESIAN
VELOCITY COMPONENTS 124 3.11 STREAMLINES AND STREAM SURFACES 125
TWO-DIMENSIONAL STREAM FUNCTION 125 STREAM FUNCTIONS IN THREE DIMENSIONS
127 3.12 NAVIER-STOKES EQUATIONS IN STREAM FUNCTION FORM 129
TWO-DIMENSIONAL AND AXIALLY SYMMETRIC FLOWS 129 FLOWS IN THREE
DIMENSIONS 130 PROFILE DRAG 131 FREE SURFACE PROBLEM FORMULATION 139
KINEMATIC CONDITIONS 139 DYNAMIC CONDITIONS 144 REFERENCES 146 PROBLEMS
146 *I CHAPTER 4 FLOW OF INVISCID FLUIDS 161 4.1 INTRODUCTION 161 PART
I: INVISCID INCOMPRESSIBLE FLOW 162 4.2 THE BERNOULLI CONSTANT 162 4.3
IRROTATIONAL FLOWS 163 BOUNDARY CONDITIONS 164 IRROTATIONAL FLOWS IN TWO
DIMENSIONS 165 EXAMPLES OF ANALYTIC FUNCTIONS FOR INVISCID FLOWS 167
BLASIUS FORMULAS FOR FORCE AND MOMENT 173 4.4 METHOD OF CONFORMAL
MAPPING IN INVISCID FLOWS 176 KUTTA-JOUKOWSKII TRANSFORMATION 178 PURE
CIRCULATORY MOTION AROUND A PLATE 180 FLOW PAST A WING PROFILE 181 AN
ITERATIVE METHOD FOR THE NUMERICAL GENERATION OF Z =/() 184 4.5
SOURCES, SINKS, AND DOUBLETS IN THREE DIMENSIONS 185 SOURCES AND SINKS
IN THREE DIMENSIONS 187 DOUBLETS IN THREE DIMENSIONS * 188 INDUCED
VELOCITIES DUE TO LINE AND SHEET VORTICES 189 * PART II: INVISCID
COMPRESSIBLE FLOW 191 4.6 BASIC THERMODYNAMICS 191 I FIRST LAW OF
THERMODYNAMICS 192 T SECOND LAW OF THERMODYNAMICS 194 DEDUCTIONS FROM
THE TWO THERMODYNAMIC LAWS 196 SPECIFIC HEATS 198 ENTHALPY 199
MAXWELL EQUATIONS 200 ISENTROPIC STATE 202 I SPEED OF SOUND 202
THERMODYNAMIC RELATIONS FOR AN IDEAL GAS 203 F PERFECT GASES 204 4.7
SUBSONIC AND SUPERSONIC FLOW 205 4.8 CRITICAL AND STAGNATION QUANTITIES
207 4.9 ISENTROPIC IDEAL GAS RELATIONS 208 4.10 UNSTEADY INVISCID
COMPRESSIBLE FLOW IN ONE-DIMENSION 210 4.11 STEADY PLANE FLOW OF
INVISCID GASES 219 STREAM FUNCTION FORMULATION 219 IRROTATIONAL FLOW OF
AN INVISCID GAS 221 CASE OF SMALL PERTURBATIONS 222 SUBSONIC FLOW 223
SUPERSONIC FLOW 224 4.12 THEORY OF SHOCK WAVES 228 SHOCK RELATIONS FOR
AN ARBITRARILY MOVING SHOCK 229 FIRST SHOCK CONDITION 230 SECOND SHOCK
CONDITION 230 THIRD SHOCK CONDFFION 231 FOURTH SHOCK CONDITION 231 SHOCK
SURFACE, SLIP SURFACE, AND CONTACT DISCONTINUITY 233 ENERGY EQUATION FOR
A SHOCK SURFACE 233 HUGONOIT EQUATION 233 SUMMARY OF ALL SHOCK RELATIONS
234 CASE I: SHOCK RELATIONS WITHOUT USING AN EQUATION OF STATE 234 CASE
II: SHOCK RELATIONS WHILE USING AN EQUATION OF STATE 235 THE ROLE OF
ENTROPY 236 STATIONARY SHOCKS 238 STATIONARY NORMAL SHOCK 238 STATIONARY
OBLIQUE SHOCKS 238 PRANDTL S RELATION 240 SHOCK POLAR FOR STATIONARY
OBLIQUE SHOCKS 242 REFERENCES 243 PROBLEMS 243 CHAPTER 5 LAMINAR VISCOUS
FLOW 263 PARTI: EXACT SOLUTIONS 263 5.1 INTRODUCTION 263 5.2 EXACT
SOLUTIONS 264 FLOW ON AN INFINITE PLATE 264 HOW BETWEEN TWO INFINITE
PARALLEL PLATES 264 FLOW BETWEEN ROTATING COAXIAL CYLINDERS (CIRCULAR
COUETTE FLOW) 266 STEADY FLOW THROUGH A CYLINDRICAL PIPE
(HAGEN-POISEUILLE FLOW) 267 ROW IN THE ENTRANCE REGION OF A CIRCULAR
PIPE 270 NONSTEADY UNIDIRECTIONAL FLOW 271 STOKES PROBLEMS 272 EKMAN
LAYER PROBLEM 274 MOTION PRODUCED DUE TO A VORTEX FILAMENT 276
TWO-DIMENSIONAL STAGNATION POINT FLOW (HIEMENZ FLOW) 278 AXIALLY
SYMMETRIC STAGNATION POINT FLOW (HOMANN FLOW) 279 MOTION BETWEEN TWO
INCLINED PLATES 280 5.3 EXACT SOLUTIONS FOR SLOW MOTION 284 FLOW PAST A
RIGID SPHERE 285 FLOW PAST A RIGID CIRCULAR CYLINDER 289 PART II:
BOUNDARY LAYERS 294 |I ! 5.4 INTRODUCTION 294 FORMULATION OF THE
BOUNDARY LAYER PROBLEM 296 METHOD OF INNER AND OUTER LIMITS 301 BOUNDARY
LAYER ON 2-D CURVED SURFACES 302 BOUNDARY LAYER PARAMETERS 305
SEPARATION OF THE 2-D STEADY BOUNDARY LAYERS 307 TRANSFORMED BOUNDARY
LAYER EQUATIONS 312 SIMILAR BOUNDARY LAYERS 314 BOUNDARY LAYER ON A
SEMI-INFINITE PLATE 316 SOLUTION OF THE BLASIUS EQUATION 316 BOUNDARY
LAYER ON A WEDGE 320 NUMERICAL SOLUTION OF THE FALKNER-SKAN EQUATION 322
NONSIMILAR BOUNDARY LAYERS 324 GORTLER S SERIES SOLUTION 325 MOMENTUM
INTEGRAL EQUATION 330 SOLUTION OF THE MOMENTUM INTEGRAL EQUATION 332
CHOICE OF THE VELOCITY PROFILE 335 FREE BOUNDARY LAYERS 336 FLOW IN THE
WAKE OF A FLAT PLATE 337 TWO-DIMENSIONAL JET 338 AXIALLY SYMMETRIC JET
340 NUMERICAL SOLUTION OF THE BOUNDARY LAYER EQUATION 342 NUMERICAL
SOLUTION OF THE DIFFUSION EQUATION 342 ERRORS: TRUNCATION AND ROUND OFF
343 CRANK AND NICOLSON 345 DUFORT AND FRANKEL 345 THREE-POINT SCHEME 345
SOLUTION OF THE BOUNDARY LAYER EQUATION 345 THE BOX METHOD 349
THREE-DIMENSIONAL BOUNDARY LAYERS 352 THE METRIC COEFFICIENTS 352 THE
MATCHING CONDITIONS 353 EQUATIONS IN ROTATING COORDINATES 357 CHOICE
OF SURFACE COORDINATES 358 INTERNAL CARTESIAN COORDINATES R 361 *
NONDEVELOPABLE SURFACES 362 PHYSICAL CONSEQUENCE S OF THREE
PIMENSIONALITY 363 INTRINSIC COORDINATES 363 DOMAINS OF DEPENDENCE AND
INFLUENCE 365 MOMENTUM INTEGRAL EQUATIONS IN THREE DIMENSIONS 365
SEPARATION AND ATTACHMENT IN THREE DIMENSIONS 366 LIMITING STREAMLINES
AND VORTEX LINES 368 BOUNDARY LAYERS ON BODIES OF REVOLUTION AND YAWED
CYLINDERS 370 MANGLER S TRANFORMATION 371 BOUNDARY LAYER ON YAWED
CYLINDERS 373 P-OSSFLOW 374 *TRANSFORMED EQUATIONS FOR YAWED CYLINDERS
376 THREE-DIMENSIONAL STAGNATION POINT FLOW 376 BOUNDARY LAYER ON
ROTATING BLADES 377 5.18 NUMERICAL SOLUTION OF 3-D BOUNDARY LAYER
EQUATIONS 378 5.19 UNSTEADY BOUNDARY LAYERS 380 PURELY UNSTEADY BOUNDARY
LAYERS 380 PERIODIC BOUNDARY LAYERS 383 SEPARATION OF UNSTEADY BOUNDARY
LAYERS 386 MATHEMATICAL FORMULATION OF THE M-R-S PRINCIPLE 387 NUMERICAL
METHOD OF SOLUTION OF UNSTEADY EQUATIONS 388 5.20 SECOND-ORDER BOUNDARY
LAYER THEORY 389 METHOD OF MATCHED ASYMPTOTIC EXPANSION 391 OUTER
EXPANSION 392 SOME IMPORTANT DERIVATIVES AT THE WALL 395 INNER EXPANSION
/T. 396 THE FIRST- AND SECOND-ORDER BOUNDARY LAYER PROBLEMS 397 MATCHING
OF INNER AND OUTER SOLUTIONS 398 A UNIFIED SECOND-ORDER-CORRECT VISCOUS
MODEL 401 MATCHING 402 5.21 INVERSE PROBLEMS IN BOUNDARY LAYERS 404
INVERSE FORMULATION WITH ASSIGNED DISPLACEMENT THICKNESS 405 5.22
FORMULATION OF THE COMPRESSIBLE BOUNDARY LAYER PROBLEM 407 ESTIMATION OF
THE VISCOUS TERMS 409 EXTERNAL-ROW EQUATIONS AND THE BOUNDARY CONDITIONS
413 PARTICULAR CASES 413 NUMERICAL SOLUTION OF COMPRESSIBLE BOUNDARY
LAYER EQUATIONS 414 PART III: NAVIER-STOKES FORMULATION 418 5.23
INCOMPRESSIBLE FLOW 418 FORMULATION OF THE PROBLEM IN PRIMITIVE
VARIABLES 419 AD HOC MODIFICATIONS 420 FORMULATION OF THE PROBLEM IN
VORTICITY/POTENTIAL FORM 421 VORTICITY-STREAM FUNCTION FORMULATION 421
VORTICITY-POTENTIAL FUNCTION FORMULATION 422 INTEGRO-DIFFERENTIAL
FORMULATION 424 APPLICATION OF THE BOUNDARY CONDITIONS 426 BASIC
COMPUTATIONAL ASPECTS 427 5.24 COMPRESSIBLE FLOW 427 DETERMINATION OF
TEMPERATURE 429 CASEOFM R - 0 . . 430 NUMERICAL FORMULATION 431 5.25
HYPERBOLIC EQUATIONS AND CONSERVATION LAWS 434 SYSTEM OF QUASI-LINEAR
EQUATIONS FROM THE CONSERVATION EQUATIONS 442 HYPERBOLIC EQUATIONS IN
HIGHER DIMENSIONS 447 5.26 NUMERICAL TRANSFORMATION AND GRID GENERATION
448 EQUATIONS FOR GRID GENERATION 449 GAUSSIAN EQUATIONS FOR GRID
GENERATION 450 5.27 NUMERICAL ALGORITHMS FOR VISCOUS COMPRESSIBLE FLOWS
451 NATURE OF THE DIFFERENCE SCHEMES 456 FORMULATION FOR COMPRESSIBLE
NAVIER-STOKES EQUATIONS 461 5.28 THIN-LAYER NAVIER-STOKES EQUATIONS
(TLNS) 466 PARABOLIZED NAVIEP-STOKES EQUATIONS (PNS) 466 REFERENCES 467
PROBLEMS 470 IPTER6 TURBULENT FLOW 489 PART I: STABILITY THEORY AND THE
STATISTICAL DESCRIPTION OF TURBULENCE 489 »1 INTRODUCTION 489 STABILITY
OF LAMINAR FLOWS 489 FORMULATION OF THE PROBLEM 490 FORMULATION FOR
PLANE-PARALLEL LAMINAR FLOWS 492 SQUIRE S THEOREM 495 TEMPORAL AND
SPATIAL INSTABILITIES 496 BOUNDARY CONDITIONS FOR THE ORR-SOMMERFELD
EQUATION 496 TEMPORAL STABILITY 500 1.4 TEMPORAL STABILITY AT INFINITE
REYNOLDS NUMBER 500 RAYLEIGH S FIRST THEOREM 501 RAYLEIGH S SECOND
THEOREM 501 1.5 NUMERICAL ALGORITHM FOR THE ORR-SOMMERFELD EQUATION 505
1*6 TRANSITION TO TURBULENCE 507 17 STATISTICAL METHODS IN TURBULENT
CONTINUUM MECHANICS 509 AVERAGE OR MEAN OF TURBULENT QUANTITIES 510 TIME
AND SPACE AVERAGING 510 TIME AVERAGE 511 ENSEMBLE AVERAGE 511 SPACE
AVERAGE 513 BASIC AXIOMS OF AVERAGING 515 STATISTICAL CONCEPTS 515
PROBABILITY DISTRIBUTION FUNCTIONS 516 PROBABILITY DENSITY 517
MATHEMATICAL EXPECTATION 518 CORRELATION FUNCTIONS 519 STATIONARY
PROCESSES 519 CHARACTERISTIC FUNCTIONS 519 GAUSSIAN DISTRIBUTION 521 |.9
INTERNAL STRUCTURE IN PHYSICAL SPACE 522 SECOND- AND THIRD-ORDER
CORRELATIONS 522 DYNAMIC EQUATION OF CORRELATIONS 524 HOMOGENEOUS
TURBULENCE 527 HOMOGENEOUS SHEAR TURBULENCE 528 ISOTROPIC TURBULENCE 528
ANALYSIS OF ISOTROPIC TURBULENCE 530 LONGITUDINAL AND LATERAL
CORRELATIONS 532 APPROXIMATE ANALYSIS 535 DYNAMIC EQUATION FOR ISOTROPIC
TURBULENCE 537 L0 INTERNAL STRUCTURE IN THE WAVE-NUMBER SPACE 538 SOME
GENERAL DEFINITIONS 538 DYNAMIC EQUATION OF HOMOGENEOUS TURBULENCE IN
K-SPACE 540 ANALYSIS OF ISOTROPIC TURBULENCE IN K-SPACE 542 CONNECTION
BETWEEN U 2 F(R, T) AND E(K, T) 545 FORMULATION OF 1-D SPECTRUM 547
TAYLOR S FORMULAS 549 TIL THEORY OF UNIVERSAL EQUILIBRIUM 550
DETERMINATION OF E IK, T) BASED ON KOLMOGOROV S HYPOTHESIS 551 TRANSFER
THEORIES 552 HEISENBERG S TRANSFER THEORY 553 PAO S TRANSFER THEORY 555
COMPARISON OF TAYLOR S AND KOLMOGOROV S DISSIPATION LENGTHS 556 INTEGRAL
LENGTH AND TIMESCALES 558 PART II: DEVELOPMENT OF AVERAGED EQUATIONS 559
6.12 INTRODUCTION 559 6.13 AVERAGED EQUATIONS FOR INCOMPRESSIBLE FLOW
559 EQUATION OF TURBULENCE KINETIC ENERGY 562 EQUATION OF MEAN-SQUARE
VORTICITY FLUCTUATIONS 565 RATE EQUATION FOR REYNOLDS STRESSES 567 RATE
EQUATION FOR THE DISSIPATION 569 PHYSICAL INTERPRETATION OF THE TERMS
569 ANALYSIS OF THE PRESSURE-STRAIN CORRELATION 571 6.14 AVERAGED
EQUATIONS FOR COMPRESSIBLE FLOW 573 EQUATION OF TURBULENCE ENERGY AND
THE REYNOLDS STRESSES 577 DISSIPATION FUNCTION 578 6.15 TURBULENT
BOUNDARY LAYER EQUATIONS 580 EQUATIONS IN RECTANGULAR CARTESIAN
COORDINATES 580 TWO-DIMENSIONAL EQUATIONS 583 THREE-DIMENSIONAL
EQUATIONS 583 EQUATIONS IN ORTHOGONAL CURVILINEAR COORDINATES 585 PART
III: BASIC EMPIRICAL AND BOUNDARY LAYER RESULTS IN TURBULENCE 586 6.16
THE CLOSURE PROBLEM 586 6.17 PRANDTL S MIXING-LENGTH HYPOTHESIS 587
TURBULENT FLOW NEAR A WALL 588 EXPERIMENTAL DETERMINATION OF U X 592
APPLICATION OF THE LOGARITHMIC FORMULA IN PIPE FLOW 592 POWER LAWS FOR
THE VELOCITY DISTRIBUTION 594 ROUGH PIPES 595 6.18 WALL-BOUND TURBULENT
FLOWS 596 6.19 ANALYSIS OF TURBULENT BOUNDARY LAYER VELOCITY PROFILES
605 LAW OF THE WALL FOR COMPRESSIBLE FLOW 612 6.20 MOMENTUM INTEGRAL
METHODS IN BOUNDARY LAYERS 613 METHOD OF TRUCKENBRODT 617 METHOD OF HEAD
V 622 6.21 DIFFERENTIAL EQUATION METHODS IN 2-D BOUNDARY LAYERS 624
ZERO-EQUATION MODELING IN BOUNDARY LAYERS 626 ONE-EQUATION MODEL OF
GLUSHKO 628 PART IV: TURBULENCE MODELING 630 6.22 GENERALIZATION OF
BOUSSINESQ S HYPOTHESIS 630 SPECIFICATION OF THE LENGTH SCALE 632 6.23
ZERO-EQUATION MODELING IN SHEAR LAYERS 633 THIN SHEAR LAYERS 634 6.24
ONE-EQUATION MODELING 635 CHOICE OF THE CONSTANTS B X , B 3 , AND B 5
636 MODIFICATIONS DUE TO THE EXPLICIT EFFECTS OF VISCOSITY 638 6.25
TWO-EQUATION (K-^.) MODELING . 641 MODELING OF THE DISSIPATION RATE
EQUATION 641 MODELING FOR SEPARATED FLOWS * 643 REYNOLDS STRESS
EQUATION MODELING 643 DETERMINATION OF THE CONSTANTS C X AND C 2 646
ANOTHER MODELING OF THE ENERGY EQUATION 648 THE WALL BOUNDARY CONDITIONS
649 APPLICATION TO 2-D THIN SHEAR LAYERS 650 ALGEBRAIC REYNOLDS STRESS
CLOSURE 652 DEVELOPMENT OF A NONLINEAR CONSTITUTIVE EQUATION 655 .
EXTENSION TO COMPRESSIBLE FLOW 657 TURBULENCE ENERGY EQUATION 659
ASSUMPTIONS TO BE JUSTIFIED 661 IMPLICIT ALGEBRAIC STRESS MODEL 661 .
EXPLICIT ALGEBRAIC STRESS MODEL 662 .. THE DISSIPATION EQUATION 663 THE
TOTAL ENERGY EQUATION 664 MODELING OF THE CORRELATIONS IN THE TOTAL
ENERGY EQUATION 664 , CURRENT APPROACHES TO NONLINEAR MODELING 665
.HEURISTIC MODELING 669 MODELING FOR COMPRESSIBLE FLOW 671 STOKES LAW
OF FRICTION 671 COMPLETE STRESS TENSOR 672 HEAT FLUX 672 PRODUCTION OF
TURBULENCE ENERGY 673 , MODEL EQUATIONS 674 JUSTIFICATION OF THE
MODELING CONSTANTS FOR COMPRESSIBLE FLOW 675 THREE-DIMENSIONAL BOUNDARY
LAYERS 676 . EDDY VISCOSITY APPROACH TO 3-D BOUNDARY LAYERS 680
.ILLUSTRATIVE ANALYSIS OF INSTABILITY 682 REYNOLDS-ORR EQUATION 682 .
CHOAS AND LORENZ MODEL 684 BASIC FORMULATION OF LARGE EDDY SIMULATION
689 FILTERS 689 FILTERED NAVIER-STOKES EQUATIONS 693 LINEAR MODEL 697
.SCALE-SIMILARITY MODEL 698 .^DYNAMIC MODELING 699 .ALGEBRAIC MODEL 701
IJNONLINEAR CONSTITUTIVE EQUATION . 702 ;ES 703 706 ICAL EXPOSITION 1
BASE VECTORS AND VARIOUS REPRESENTATIONS 721 INTRODUCTION 721
.REPRESENTATIONS IN RECTANGULAR CARTESIAN SYSTEMS 723 .SCALARS, VECTORS,
AND TENSORS 723 .DIFFERENTIAL OPERATION S ON TENSORS 725 ^GRADIENT 725
^DIVERGENCE 726 XURL 727 ^MULTIPLICATION OF A TENSOR AND A VECTOR 727
SCALAR MULTIPLICATION OF TWO TENSORS 728 1.7 A COLLECTION OF USABLE
FORMULAS 729 1.8 TAYLOR EXPANSION IN VECTOR FORM 731 1.9 PRINCIPAL AXES
OF A TENSOR 732 1.10 TRANSFORMATION OF T TO THE PRINCIPAL AXES 734 1.11
QUADRATIC FORM AND THE EIGENVALUE PROBLEM 735 1.12 REPRESENTATION IN
CURVILINEAR COORDINATES 736 FUNDAMENTAL METRIC COMPONENTS 739 ELEMENTAL
DISPLACEMENT VECTOR 741 DIFFERENTIATION OF BASE VECTORS 742 GRADIENT OF
A VECTOR 744 DIVERGENCE AND CURL OF A VECTOR 745 DIVERGENCE OF
SECOND-ORDER TENSORS 747 1.13 CHRISTOFFEL SYMBOLS IN THREE DIMENSIONS
748 CHRISTOFFEL SYMBOLS OF THE FIRST KIND 748 CHRISTOFFEL SYMBOLS OF THE
SECOND KIND 749 1.14 SOME DERIVATIVE RELATIONS 754 NORMAL DERIVATIVE OF
FUNCTIONS 755 PHYSICAL COMPONENTS IN CURVILINEAR COORDINATES 756 1.15
SCALAR AND DOUBLE DOT PRODUCTS OF TWO TENSORS 756 MATHEMATICAL
EXPOSITION 2 THEOREMS OF GAUSS, GREEN, AND STOKES 759 2.1 GAUSS THEOREM
759 2.2 GREEN S THEOREM 760 2.3 STOKES THEOREM 760 MATHEMATICAL
EXPOSITION 3 GEOMETRY OF SPACE AND PLANE CURVES 763 3.1 BASIC THEORY OF
CURVES 763 TANGENT VECTOR 763 PRINCIPAL NORMAL 764 BINORMAL VECTOR 765
SERRET-FRENET EQUATIONS 765 PLANE CURVES 766 MATHEMATICAL EXPOSITION 4
FORMULAS FOR COORDINATE TRANSFORMATION 769 4.1 INTRODUCTION 769 4.2
TRANSFORMATION LAW FOR SCALARS 769 4.3 TRANSFORMATION LAWS FOR VECTORS
770 4.4 TRANSFORMATION LAWS FOR TENSORS 772 4.5 TRANSFORMATION LAWS FOR
THE. CHRISTOFFEL SYMBOLS 775 4.6 SOME FORMULAS IN CARTESIAN AND
CURVILINEAR COORDINATES 775 LAPLACIAN OF AN ABSOLUTE SCALAR 776
MATHEMATICAL EXPOSITION 5 POTENTIAL THEORY 779 5.1 INTRODUCTION 779 5.2
FORMULAS OF GREEN 779 GREEN S FORMULAS FOR LAPLACE OPERATOR 780 5.3
POTENTIAL THEORY 781 INTEGRAL REPRESENTATION , 781 THE DELTA FUNCTIOA
782 INTEGRAL REPRESENTATION OF THE DELTA FUNCTION 784 THE DELTA FUNCTION
IN HIGHER DIMENSIONS 785 DELTA FUNCTION AND THE FUNDAMENTAL SOLUTION OF
THE LAPLACE EQUATION 785 THE DIRICHLET PROBLEM FOR THE POISSON EQUATION
786 PARTICULAR SOLUTION OF POISSON S EQUATION 787 4 GENERAL
REPRESENTATION OF A VECTOR 787 P.5 AN APPLICATION OF GREEN S FIRST
FORMULA 788 EMATICAL EXPOSITION 6 SINGULARITIES OF THE FIRST-ORDER ODES
791 1 INTRODUCTION 791 2 SINGULARITIES AND THEIR CLASSIFICATION 791
THEMATICAL EXPOSITION 7 GEOMETRY OF SURFACES 795 BASIC DEFINITIONS 795 2
FORMULAS OF GAUSS 795 CHRISTOFFEL SYMBOLS BASED ON SURFACE COEFFICIENTS
796 3 FORMULAS OF WEINGARTEN 798 A EQUATIONS OF GAUSS 799 NORMAL AND
GEODESIC CURVATURES 799 LONGITUDINAL AND TRANSVERSE CURVATURES 802 GRID
GENERATION IN SURFACES 803 EMATICAL EXPOSITION 8 FINITE DIFFERENCE
APPROXIMATION APPLIED TO PDES 805 INTRODUCTION 805 CALCULUS OF FINITE
DIFFERENCES 805 METHODS OF INTERPOLATION 808 CUBIC SPLINE FUNCTIONS 809
ITERATIVE ROOT FINDING 810 NUMERICAL INTEGRATION 812 FINITE DIFFERENCE
APPROXIMATIONS OF PARTIAL DERIVATIVES 813 FIRST DERIVATIVES 813 SECOND
DERIVATIVES 814 FINITE DIFFERENCE APPROXIMATION OF PARABOLIC PDES 814
STABLE SCHEMES FOR PARABOLIC EQUATIONS 818 F FINITE DIFFERENCE
APPROXIMATION OF ELLIPTIC EQUATIONS 819 TICAL EXPOSITION 9 FRAME
INVARIANCY 825 INTRODUCTION ., 825 ORTHOGONAL TENSOR 825 TIME
DIFFERENTIATION 826 CHANGE OF BASIS 827 ARBITRARY RECTANGULAR FRAMES OF
REFERENCE 828 CHECK FOR FRAME INVARIANCY 829 USE OF Q 830 ES FOR THE
MATHEMATICAL EXPOSITIONS 831 833
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THIRD EDITION FLUID DYNAMICS THEORETICAL AND COMPUTATIONAL APPROACHES
Z.U.A. WARSI TAYLOR & FRANCIS TAYLOR & FRANCIS CROUP BOCA RATON LONDON
NEW YORK SINGAPORE A CRC TITLE, PART OF THE TAYLOR & FRANCIS IMPRINT, A
MEMBER OF THE TAYLOR & FRANCIS GROUP, THE ACADEMIC DIVISION OF T&F
INFORMA PIC. TABLE OF CONTENTS CHAPTER 1 KINEMATICS OF FLUID MOTION 1
1.1 INTRODUCTION TO CONTINUUM MOTION 1 1.2 FLUID PARTICLES 1 1.3
INERTIAL COORDINATE FRAMES 2 1.4 MOTION OF A CONTINUUM 2 1.5 THE TIME
DERIVATIVES 6 1.6 VELOCITY AND ACCELERATION 6 1.7 STEADY AND NONSTEADY
FLOW 10 1.8 TRAJECTORIES OF FLUID PARTICLES AND STREAMLINES 11 1.9
MATERIAL VOLUME AND SURFACE 12 1.10 RELATION BETWEEN ELEMENTAL VOLUMES
13 1.11 KINEMATIC FORMULAS OF EULER AND REYNOLDS 13 1.12 CONTROL VOLUME
AND SURFACE 16 1.13 KINEMATICS OF DEFORMATION 17 1.14 KINEMATICS OF
VORTICITY AND CIRCULATION 22 VORTEX LINE 22 VORTEX TUBE 22 CIRCULATION
OF VELOCITY 24 RATE OF CHANGE OF CIRCULATION 24 REFERENCES 25 PROBLEMS
26 CHAPTER 2 THE CONSERVATION LAWS AND THE KINETICS OF FLOW 33 2.1 FLUID
DENSITY AND THE CONSERVATION OF MASS 33 2.2 PRINCIPLE OF MASS
CONSERVATION 33 TIME VARIATION OF PP 34 PARTICULAR FORMS OF THE
CONTINUITY EQUATION 35 2.3 MASS CONSERVATION USING A CONTROL VOLUME 35
2.4 KINETICS OF FLUID FLOW 36 STRESS PRINCIPLE OF CAUCHY 36 2.5
CONSERVATION OF LINEAR AND ANGULAR MOMENTUM 37 CONSERVATION OF LINEAR
MOMENTUM 37 CONSERVATION OF ANGULAR MOMENTUM 38 NATURE OF STRESS VECTOR
, 38 SYMMETRY OF T 41 2.6 EQUATIONS OF LINEAR AND ANGULAR MOMENTUM 42
2.7 MOMENTUM CONSERVATION USING A CONTROL VOLUME 44 2.8 CONSERVATION OF
ENERGY 44 2.9 ENERGY CONSERVATION USING A CONTROL VOLUME 47 2.10 GENERAL
CONSERVATION PRINCIPLE 47 2.11 THE CLOSURE PROBLEM 48 2.12 STOKES' LAW
OF FRICTION 51 THE POSTULATES OF STOKES 52 STOKESIAN STRESS TENSOR 52
2.13 INTERPRETATION OF PRESSURE 57 .14 THE DISSIPATION FUNCTION 58 2.15
CONSTITUTIVE EQUATION FOR NON-NEWTONIAN FLUIDS 59 2.16 THERMODYNAMIC
ASPECTS OF PRESSURE AND VISCOSITY 61 IDEAL GASES 62 CONCEPT OF VISCOSITY
IN FLUIDS 64 SUTHERLAND FORMULA FOR VISCOSITY 66 2.17 EQUATIONS OF
MOTION IN LAGRANGIAN COORDINATES 67 REFERENCES 71 PROBLEMS 71 CHAPTER 3
THE NAVIER-STOKES EQUATIONS 75 3.1 FORMULATION OF THE PROBLEM 75 3.2
VISCOUS COMPRESSIBLE FLOW EQUATIONS 78 CONSERVATION OF MASS 78
CONSERVATION OF MOMENTUM 78 EQUATIONS OF MECHANICAL ENERGY 78 EQUATIONS
OF INTERNAL ENERGY 78 EQUATIONS OF ENTROPY AND ENTHALPY 79 CONSERVATION
OF TOTAL KINETIC ENERGY 80 3.3 VISCOUS INCOMPRESSIBLE FLOW EQUATIONS 80
CONSERVATION OF MASS 80 CONSERVATION OF MOMENTUM 80 EQUATION OF
VORTICITY 81 EQUATION OF INTERNAL ENERGY 82 EQUATION FOR PRESSURE 82 3.4
EQUATIONS OF INVISCID FLOW (EULER'S EQUATIONS) 83 CONSERVATION OF MASS
83 CONSERVATION OF MOMENTUM 84 EQUATIONS OF ENTROPY AND ENTHALPY 84
CONSERVATION OF ENERGY 84 CONSERVATION OF TOTAL KINETIC ENERGY 84
INVISCID BAROTROPIC FLOW 84 3.5 INITIAL AND BOUNDARY CONDITIONS 85 3.6
MATHEMATICAL NATURE OF THE EQUATIONS 86 3.7 VORTICITY AND CIRCULATION 86
VORTICITY AND CIRCULATION FOR INVISCID FLUIDS , 87 THE BERNOULLI
EQUATION 89 3.8 SOME RESULTS BASED ON THE EQUATIONS OF MOTION 90 FORCE
ACTING ON A SOLID BODY 90 STRESS VECTOR AND TENSOR AT A SURFACE , 91
VORTICITY VECTOR AT A SURFACE 92 RATE-OF-STRAIN TENSOR AT A SURFACE 93
3.9 NONDIMENSIONAL PARAMETERS IN FLUID MOTION 94 PRINCIPLE OF SIMILARITY
97 DYNAMIC SIMILARITY 97 VARIABLE NONDIMENSIONAL PARAMETERS 97 PRINCIPLE
OF REYNOLDS NUMBER SIMILARITY 98 3.10 COORDINATE TRANSFORMATION 99
ORTHOGONAL COORDINATES 100 NAVIER-STOKES EQUATIONS IN ORTHOGONAL
COORDINATES 105 NONORTHOGONAL CURVILINEAR COORDINATES 107 STEADY
EULERIAN COORDINATES 107 NONSTEADY EULERIAN COORDINATES *-. 110
EQUATIONS IN GENERAL COORDINATES 115 EQUATIONS IN GENERAL COORDINATES
USING CONTRAVARIANT COMPONENTS 117 EQUATIONS IN GENERAL COORDINATES
USING COVARIANT COMPONENTS 117 EQUATIONS IN GENERAL COORDINATES WITH
VECTORS AND TENSOR DENSITIES 118 EQUATIONS IN NONSTEADY EULERIAN
COORDINATES 120 EQUATIONS IN CURVILINEAR COORDINATES WITH CARTESIAN
VELOCITY COMPONENTS 124 3.11 STREAMLINES AND STREAM SURFACES 125
TWO-DIMENSIONAL STREAM FUNCTION 125 STREAM FUNCTIONS IN THREE DIMENSIONS
127 3.12 NAVIER-STOKES EQUATIONS IN STREAM FUNCTION FORM 129
TWO-DIMENSIONAL AND AXIALLY SYMMETRIC FLOWS 129 FLOWS IN THREE
DIMENSIONS 130 PROFILE DRAG 131 FREE SURFACE PROBLEM FORMULATION 139
KINEMATIC CONDITIONS 139 DYNAMIC CONDITIONS 144 REFERENCES 146 PROBLEMS
146 *I CHAPTER 4 FLOW OF INVISCID FLUIDS 161 4.1 INTRODUCTION 161 PART
I: INVISCID INCOMPRESSIBLE FLOW 162 4.2 THE BERNOULLI CONSTANT 162 4.3
IRROTATIONAL FLOWS 163 BOUNDARY CONDITIONS 164 IRROTATIONAL FLOWS IN TWO
DIMENSIONS 165 EXAMPLES OF ANALYTIC FUNCTIONS FOR INVISCID FLOWS 167
BLASIUS FORMULAS FOR FORCE AND MOMENT 173 4.4 METHOD OF CONFORMAL
MAPPING IN INVISCID FLOWS 176 KUTTA-JOUKOWSKII TRANSFORMATION 178 PURE
CIRCULATORY MOTION AROUND A PLATE 180 FLOW PAST A WING PROFILE 181 AN
ITERATIVE METHOD FOR THE NUMERICAL GENERATION OF Z =/() 184 4.5
SOURCES, SINKS, AND DOUBLETS IN THREE DIMENSIONS 185 SOURCES AND SINKS
IN THREE DIMENSIONS 187 DOUBLETS IN THREE DIMENSIONS * 188 INDUCED
VELOCITIES DUE TO LINE AND SHEET VORTICES 189 * PART II: INVISCID
COMPRESSIBLE FLOW 191 4.6 BASIC THERMODYNAMICS 191 I FIRST LAW OF
THERMODYNAMICS 192 T SECOND LAW OF THERMODYNAMICS 194 ' DEDUCTIONS FROM
THE TWO THERMODYNAMIC LAWS 196 \ SPECIFIC HEATS 198 ENTHALPY 199
MAXWELL EQUATIONS 200 ISENTROPIC STATE 202 I SPEED OF SOUND 202
THERMODYNAMIC RELATIONS FOR AN IDEAL GAS 203 F PERFECT GASES 204 4.7
SUBSONIC AND SUPERSONIC FLOW 205 4.8 CRITICAL AND STAGNATION QUANTITIES
207 4.9 ISENTROPIC IDEAL GAS RELATIONS 208 4.10 UNSTEADY INVISCID
COMPRESSIBLE FLOW IN ONE-DIMENSION 210 4.11 STEADY PLANE FLOW OF
INVISCID GASES 219 STREAM FUNCTION FORMULATION 219 IRROTATIONAL FLOW OF
AN INVISCID GAS 221 CASE OF SMALL PERTURBATIONS 222 SUBSONIC FLOW 223
SUPERSONIC FLOW 224 4.12 THEORY OF SHOCK WAVES 228 SHOCK RELATIONS FOR
AN ARBITRARILY MOVING SHOCK 229 FIRST SHOCK CONDITION 230 SECOND SHOCK
CONDITION 230 THIRD SHOCK CONDFFION 231 FOURTH SHOCK CONDITION 231 SHOCK
SURFACE, SLIP SURFACE, AND CONTACT DISCONTINUITY 233 ENERGY EQUATION FOR
A SHOCK SURFACE 233 HUGONOIT EQUATION 233 SUMMARY OF ALL SHOCK RELATIONS
234 CASE I: SHOCK RELATIONS WITHOUT USING AN EQUATION OF STATE 234 CASE
II: SHOCK RELATIONS WHILE USING AN EQUATION OF STATE 235 THE ROLE OF
ENTROPY 236 STATIONARY SHOCKS 238 STATIONARY NORMAL SHOCK 238 STATIONARY
OBLIQUE SHOCKS 238 PRANDTL'S RELATION 240 SHOCK POLAR FOR STATIONARY
OBLIQUE SHOCKS 242 REFERENCES 243 PROBLEMS 243 CHAPTER 5 LAMINAR VISCOUS
FLOW 263 PARTI: EXACT SOLUTIONS 263 5.1 INTRODUCTION 263 5.2 EXACT
SOLUTIONS 264 FLOW ON AN INFINITE PLATE 264 HOW BETWEEN TWO INFINITE
PARALLEL PLATES 264 FLOW BETWEEN ROTATING COAXIAL CYLINDERS (CIRCULAR
COUETTE FLOW) 266 STEADY FLOW THROUGH A CYLINDRICAL PIPE
(HAGEN-POISEUILLE FLOW) 267 ROW IN THE ENTRANCE REGION OF A CIRCULAR
PIPE 270 NONSTEADY UNIDIRECTIONAL FLOW 271 STOKES PROBLEMS 272 EKMAN
LAYER PROBLEM 274 MOTION PRODUCED DUE TO A VORTEX FILAMENT 276
TWO-DIMENSIONAL STAGNATION POINT FLOW (HIEMENZ FLOW) 278 AXIALLY
SYMMETRIC STAGNATION POINT FLOW (HOMANN FLOW) 279 MOTION BETWEEN TWO
INCLINED PLATES 280 5.3 EXACT SOLUTIONS FOR SLOW MOTION 284 FLOW PAST A
RIGID SPHERE 285 FLOW PAST A RIGID CIRCULAR CYLINDER 289 PART II:
BOUNDARY LAYERS 294 |I ! 5.4 INTRODUCTION 294 FORMULATION OF THE
BOUNDARY LAYER PROBLEM 296 METHOD OF INNER AND OUTER LIMITS 301 BOUNDARY
LAYER ON 2-D CURVED SURFACES 302 BOUNDARY LAYER PARAMETERS 305
SEPARATION OF THE 2-D STEADY BOUNDARY LAYERS 307 TRANSFORMED BOUNDARY
LAYER EQUATIONS 312 SIMILAR BOUNDARY LAYERS 314 BOUNDARY LAYER ON A
SEMI-INFINITE PLATE 316 SOLUTION OF THE BLASIUS EQUATION 316 BOUNDARY
LAYER ON A WEDGE 320 NUMERICAL SOLUTION OF THE FALKNER-SKAN EQUATION 322
NONSIMILAR BOUNDARY LAYERS 324 GORTLER'S SERIES SOLUTION 325 MOMENTUM
INTEGRAL EQUATION 330 SOLUTION OF THE MOMENTUM INTEGRAL EQUATION 332
CHOICE OF THE VELOCITY PROFILE 335 FREE BOUNDARY LAYERS 336 FLOW IN THE
WAKE OF A FLAT PLATE 337 TWO-DIMENSIONAL JET 338 AXIALLY SYMMETRIC JET
340 NUMERICAL SOLUTION OF THE BOUNDARY LAYER EQUATION 342 NUMERICAL
SOLUTION OF THE DIFFUSION EQUATION 342 ERRORS: TRUNCATION AND ROUND OFF
343 CRANK AND NICOLSON 345 DUFORT AND FRANKEL 345 THREE-POINT SCHEME 345
SOLUTION OF THE BOUNDARY LAYER EQUATION 345 THE BOX METHOD 349
THREE-DIMENSIONAL BOUNDARY LAYERS 352 THE METRIC COEFFICIENTS 352 THE
MATCHING CONDITIONS 353 EQUATIONS IN ROTATING COORDINATES 357 " CHOICE
OF SURFACE COORDINATES 358 ' INTERNAL CARTESIAN COORDINATES R 361 *
NONDEVELOPABLE SURFACES 362 PHYSICAL CONSEQUENCE S OF THREE
PIMENSIONALITY 363 "INTRINSIC COORDINATES 363 "DOMAINS OF DEPENDENCE AND
INFLUENCE 365 "MOMENTUM INTEGRAL EQUATIONS IN THREE DIMENSIONS 365
SEPARATION AND ATTACHMENT IN THREE DIMENSIONS 366 LIMITING STREAMLINES
AND VORTEX LINES 368 "BOUNDARY LAYERS ON BODIES OF REVOLUTION AND YAWED
CYLINDERS 370 "MANGLER'S TRANFORMATION 371 'BOUNDARY LAYER ON YAWED
CYLINDERS 373 P-OSSFLOW 374 "*TRANSFORMED EQUATIONS FOR YAWED CYLINDERS
376 THREE-DIMENSIONAL STAGNATION POINT FLOW 376 "BOUNDARY LAYER ON
ROTATING BLADES 377 5.18 NUMERICAL SOLUTION OF 3-D BOUNDARY LAYER
EQUATIONS 378 5.19 UNSTEADY BOUNDARY LAYERS 380 PURELY UNSTEADY BOUNDARY
LAYERS 380 PERIODIC BOUNDARY LAYERS 383 SEPARATION OF UNSTEADY BOUNDARY
LAYERS 386 MATHEMATICAL FORMULATION OF THE M-R-S PRINCIPLE 387 NUMERICAL
METHOD OF SOLUTION OF UNSTEADY EQUATIONS 388 5.20 SECOND-ORDER BOUNDARY
LAYER THEORY 389 METHOD OF MATCHED ASYMPTOTIC EXPANSION 391 OUTER
EXPANSION 392 SOME IMPORTANT DERIVATIVES AT THE WALL 395 INNER EXPANSION
/T. 396 THE FIRST- AND SECOND-ORDER BOUNDARY LAYER PROBLEMS 397 MATCHING
OF INNER AND OUTER SOLUTIONS 398 A UNIFIED SECOND-ORDER-CORRECT VISCOUS
MODEL 401 MATCHING 402 5.21 INVERSE PROBLEMS IN BOUNDARY LAYERS 404
INVERSE FORMULATION WITH ASSIGNED DISPLACEMENT THICKNESS 405 5.22
FORMULATION OF THE COMPRESSIBLE BOUNDARY LAYER PROBLEM 407 ESTIMATION OF
THE VISCOUS TERMS 409 EXTERNAL-ROW EQUATIONS AND THE BOUNDARY CONDITIONS
413 PARTICULAR CASES 413 NUMERICAL SOLUTION OF COMPRESSIBLE BOUNDARY
LAYER EQUATIONS 414 PART III: NAVIER-STOKES FORMULATION 418 5.23
INCOMPRESSIBLE FLOW 418 FORMULATION OF THE PROBLEM IN PRIMITIVE
VARIABLES 419 AD HOC MODIFICATIONS 420 FORMULATION OF THE PROBLEM IN
VORTICITY/POTENTIAL FORM 421 VORTICITY-STREAM FUNCTION FORMULATION 421
VORTICITY-POTENTIAL FUNCTION FORMULATION 422 INTEGRO-DIFFERENTIAL
FORMULATION 424 APPLICATION OF THE BOUNDARY CONDITIONS 426 BASIC
COMPUTATIONAL ASPECTS 427 5.24 COMPRESSIBLE FLOW 427 DETERMINATION OF
TEMPERATURE 429 CASEOFM R - 0 .'. 430 NUMERICAL FORMULATION 431 5.25
HYPERBOLIC EQUATIONS AND CONSERVATION LAWS 434 SYSTEM OF QUASI-LINEAR
EQUATIONS FROM THE CONSERVATION EQUATIONS 442 HYPERBOLIC EQUATIONS IN
HIGHER DIMENSIONS 447 5.26 NUMERICAL TRANSFORMATION AND GRID GENERATION
448 EQUATIONS FOR GRID GENERATION 449 GAUSSIAN EQUATIONS FOR GRID
GENERATION 450 5.27 NUMERICAL ALGORITHMS FOR VISCOUS COMPRESSIBLE FLOWS
451 NATURE OF THE DIFFERENCE SCHEMES 456 FORMULATION FOR COMPRESSIBLE
NAVIER-STOKES EQUATIONS 461 5.28 THIN-LAYER NAVIER-STOKES EQUATIONS
(TLNS) 466 PARABOLIZED NAVIEP-STOKES EQUATIONS (PNS) 466 REFERENCES 467
PROBLEMS 470 IPTER6 TURBULENT FLOW 489 PART I: STABILITY THEORY AND THE
STATISTICAL DESCRIPTION OF TURBULENCE 489 »1 INTRODUCTION 489 STABILITY
OF LAMINAR FLOWS 489 FORMULATION OF THE PROBLEM 490 FORMULATION FOR
PLANE-PARALLEL LAMINAR FLOWS 492 SQUIRE'S THEOREM 495 TEMPORAL AND
SPATIAL INSTABILITIES 496 BOUNDARY CONDITIONS FOR THE ORR-SOMMERFELD
EQUATION 496 TEMPORAL STABILITY 500 1.4 TEMPORAL STABILITY AT INFINITE
REYNOLDS NUMBER 500 RAYLEIGH'S FIRST THEOREM 501 RAYLEIGH'S SECOND
THEOREM 501 1.5 NUMERICAL ALGORITHM FOR THE ORR-SOMMERFELD EQUATION 505
1*6 TRANSITION TO TURBULENCE 507 17 STATISTICAL METHODS IN TURBULENT
CONTINUUM MECHANICS 509 AVERAGE OR MEAN OF TURBULENT QUANTITIES 510 TIME
AND SPACE AVERAGING 510 TIME AVERAGE 511 ENSEMBLE AVERAGE 511 SPACE
AVERAGE 513 BASIC AXIOMS OF AVERAGING 515 STATISTICAL CONCEPTS 515
PROBABILITY DISTRIBUTION FUNCTIONS 516 PROBABILITY DENSITY 517
MATHEMATICAL EXPECTATION 518 CORRELATION FUNCTIONS 519 STATIONARY
PROCESSES 519 CHARACTERISTIC FUNCTIONS 519 GAUSSIAN DISTRIBUTION 521 |.9
INTERNAL STRUCTURE IN PHYSICAL SPACE 522 SECOND- AND THIRD-ORDER
CORRELATIONS 522 DYNAMIC EQUATION OF CORRELATIONS 524 HOMOGENEOUS
TURBULENCE 527 HOMOGENEOUS SHEAR TURBULENCE 528 ISOTROPIC TURBULENCE 528
ANALYSIS OF ISOTROPIC TURBULENCE 530 LONGITUDINAL AND LATERAL
CORRELATIONS 532 APPROXIMATE ANALYSIS 535 DYNAMIC EQUATION FOR ISOTROPIC
TURBULENCE 537 L0 INTERNAL STRUCTURE IN THE WAVE-NUMBER SPACE 538 SOME
GENERAL DEFINITIONS 538 DYNAMIC EQUATION OF HOMOGENEOUS TURBULENCE IN
K-SPACE 540 ANALYSIS OF ISOTROPIC TURBULENCE IN K-SPACE 542 CONNECTION
BETWEEN U 2 F(R, T) AND E(K, T) 545 FORMULATION OF 1-D SPECTRUM 547
TAYLOR'S FORMULAS 549 TIL THEORY OF UNIVERSAL EQUILIBRIUM 550
DETERMINATION OF E IK, T) BASED ON KOLMOGOROV'S HYPOTHESIS 551 TRANSFER
THEORIES 552 HEISENBERG'S TRANSFER THEORY 553 PAO'S TRANSFER THEORY 555
COMPARISON OF TAYLOR'S AND KOLMOGOROV'S DISSIPATION LENGTHS 556 INTEGRAL
LENGTH AND TIMESCALES 558 PART II: DEVELOPMENT OF AVERAGED EQUATIONS 559
6.12 INTRODUCTION 559 6.13 AVERAGED EQUATIONS FOR INCOMPRESSIBLE FLOW
559 EQUATION OF TURBULENCE KINETIC ENERGY 562 EQUATION OF MEAN-SQUARE
VORTICITY FLUCTUATIONS 565 RATE EQUATION FOR REYNOLDS STRESSES 567 RATE
EQUATION FOR THE DISSIPATION 569 PHYSICAL INTERPRETATION OF THE TERMS
569 ANALYSIS OF THE PRESSURE-STRAIN CORRELATION 571 6.14 AVERAGED
EQUATIONS FOR COMPRESSIBLE FLOW 573 EQUATION OF TURBULENCE ENERGY AND
THE REYNOLDS STRESSES 577 DISSIPATION FUNCTION 578 6.15 TURBULENT
BOUNDARY LAYER EQUATIONS 580 EQUATIONS IN RECTANGULAR CARTESIAN
COORDINATES 580 TWO-DIMENSIONAL EQUATIONS 583 THREE-DIMENSIONAL
EQUATIONS 583 EQUATIONS IN ORTHOGONAL CURVILINEAR COORDINATES 585 PART
III: BASIC EMPIRICAL AND BOUNDARY LAYER RESULTS IN TURBULENCE 586 6.16
THE CLOSURE PROBLEM 586 6.17 PRANDTL'S MIXING-LENGTH HYPOTHESIS 587
TURBULENT FLOW NEAR A WALL 588 EXPERIMENTAL DETERMINATION OF U X 592
APPLICATION OF THE LOGARITHMIC FORMULA IN PIPE FLOW 592 POWER LAWS FOR
THE VELOCITY DISTRIBUTION 594 ROUGH PIPES 595 6.18 WALL-BOUND TURBULENT
FLOWS 596 6.19 ANALYSIS OF TURBULENT BOUNDARY LAYER VELOCITY PROFILES
605 LAW OF THE WALL FOR COMPRESSIBLE FLOW 612 6.20 MOMENTUM INTEGRAL
METHODS IN BOUNDARY LAYERS 613 METHOD OF TRUCKENBRODT 617 METHOD OF HEAD
V 622 6.21 DIFFERENTIAL EQUATION METHODS IN 2-D BOUNDARY LAYERS 624
ZERO-EQUATION MODELING IN BOUNDARY LAYERS 626 ONE-EQUATION MODEL OF
GLUSHKO 628 PART IV: TURBULENCE MODELING 630 6.22 GENERALIZATION OF
BOUSSINESQ'S HYPOTHESIS 630 SPECIFICATION OF THE LENGTH SCALE 632 6.23
ZERO-EQUATION MODELING IN SHEAR LAYERS 633 THIN SHEAR LAYERS 634 6.24
ONE-EQUATION MODELING 635 CHOICE OF THE CONSTANTS B X , B 3 , AND B 5
636 MODIFICATIONS DUE TO THE EXPLICIT EFFECTS OF VISCOSITY 638 6.25
TWO-EQUATION (K-^.) MODELING '. 641 MODELING OF THE DISSIPATION RATE
EQUATION 641 MODELING FOR SEPARATED FLOWS * 643 REYNOLDS' STRESS
EQUATION MODELING 643 DETERMINATION OF THE CONSTANTS C X AND C 2 646
ANOTHER MODELING OF THE ENERGY EQUATION 648 THE WALL BOUNDARY CONDITIONS
649 APPLICATION TO 2-D THIN SHEAR LAYERS 650 ALGEBRAIC REYNOLDS' STRESS
CLOSURE 652 DEVELOPMENT OF A NONLINEAR CONSTITUTIVE EQUATION 655 .
EXTENSION TO COMPRESSIBLE FLOW 657 TURBULENCE ENERGY EQUATION 659
ASSUMPTIONS TO BE JUSTIFIED 661 IMPLICIT ALGEBRAIC STRESS MODEL 661 .
EXPLICIT ALGEBRAIC STRESS MODEL 662 . THE DISSIPATION EQUATION 663 THE
TOTAL ENERGY EQUATION 664 MODELING OF THE CORRELATIONS IN THE TOTAL
ENERGY EQUATION 664 , CURRENT APPROACHES TO NONLINEAR MODELING 665
.HEURISTIC MODELING 669 MODELING FOR COMPRESSIBLE FLOW 671 STOKES' LAW
OF FRICTION 671 COMPLETE STRESS TENSOR 672 HEAT FLUX 672 PRODUCTION OF
TURBULENCE ENERGY 673 , MODEL EQUATIONS 674 JUSTIFICATION OF THE
MODELING CONSTANTS FOR COMPRESSIBLE FLOW 675 THREE-DIMENSIONAL BOUNDARY
LAYERS 676 . EDDY VISCOSITY APPROACH TO 3-D BOUNDARY LAYERS 680
.ILLUSTRATIVE ANALYSIS OF INSTABILITY 682 REYNOLDS-ORR EQUATION 682 .
CHOAS AND LORENZ MODEL 684 BASIC FORMULATION OF LARGE EDDY SIMULATION
689 FILTERS 689 FILTERED NAVIER-STOKES EQUATIONS 693 LINEAR MODEL 697
.SCALE-SIMILARITY MODEL 698 .^DYNAMIC MODELING 699 .ALGEBRAIC MODEL 701
IJNONLINEAR CONSTITUTIVE EQUATION '. 702 ;ES 703 706 ICAL EXPOSITION 1
BASE VECTORS AND VARIOUS REPRESENTATIONS 721 INTRODUCTION 721
.REPRESENTATIONS IN RECTANGULAR CARTESIAN SYSTEMS 723 .SCALARS, VECTORS,
AND TENSORS 723 .DIFFERENTIAL OPERATION S ON TENSORS 725 ^GRADIENT 725
^DIVERGENCE 726 XURL 727 ^MULTIPLICATION OF A TENSOR AND A VECTOR 727
SCALAR MULTIPLICATION OF TWO TENSORS 728 1.7 A COLLECTION OF USABLE
FORMULAS 729 1.8 TAYLOR EXPANSION IN VECTOR FORM 731 1.9 PRINCIPAL AXES
OF A TENSOR 732 1.10 TRANSFORMATION OF T TO THE PRINCIPAL AXES 734 1.11
QUADRATIC FORM AND THE EIGENVALUE PROBLEM 735 1.12 REPRESENTATION IN
CURVILINEAR COORDINATES 736 FUNDAMENTAL METRIC COMPONENTS 739 ELEMENTAL
DISPLACEMENT VECTOR 741 DIFFERENTIATION OF BASE VECTORS 742 GRADIENT OF
A VECTOR 744 DIVERGENCE AND CURL OF A VECTOR 745 DIVERGENCE OF
SECOND-ORDER TENSORS 747 1.13 CHRISTOFFEL SYMBOLS IN THREE DIMENSIONS
748 CHRISTOFFEL SYMBOLS OF THE FIRST KIND 748 CHRISTOFFEL SYMBOLS OF THE
SECOND KIND 749 1.14 SOME DERIVATIVE RELATIONS 754 NORMAL DERIVATIVE OF
FUNCTIONS 755 PHYSICAL COMPONENTS IN CURVILINEAR COORDINATES 756 1.15
SCALAR AND DOUBLE DOT PRODUCTS OF TWO TENSORS 756 MATHEMATICAL
EXPOSITION 2 THEOREMS OF GAUSS, GREEN, AND STOKES 759 2.1 GAUSS'THEOREM
759 2.2 GREEN'S THEOREM 760 2.3 STOKES'THEOREM 760 MATHEMATICAL
EXPOSITION 3 GEOMETRY OF SPACE AND PLANE CURVES 763 3.1 BASIC THEORY OF
CURVES 763 TANGENT VECTOR 763 PRINCIPAL NORMAL 764 BINORMAL VECTOR 765
SERRET-FRENET EQUATIONS 765 PLANE CURVES 766 MATHEMATICAL EXPOSITION 4
FORMULAS FOR COORDINATE TRANSFORMATION 769 4.1 INTRODUCTION 769 4.2
TRANSFORMATION LAW FOR SCALARS 769 4.3 TRANSFORMATION LAWS FOR VECTORS
770 4.4 TRANSFORMATION LAWS FOR TENSORS 772 4.5 TRANSFORMATION LAWS FOR
THE. CHRISTOFFEL SYMBOLS 775 4.6 SOME FORMULAS IN CARTESIAN AND
CURVILINEAR COORDINATES 775 LAPLACIAN OF AN ABSOLUTE SCALAR 776
MATHEMATICAL EXPOSITION 5 POTENTIAL THEORY 779 5.1 INTRODUCTION 779 5.2
FORMULAS OF GREEN 779 GREEN'S FORMULAS FOR LAPLACE OPERATOR 780 5.3
POTENTIAL THEORY 781 INTEGRAL REPRESENTATION , 781 THE DELTA FUNCTIOA
782 INTEGRAL REPRESENTATION OF THE DELTA FUNCTION 784 THE DELTA FUNCTION
IN HIGHER DIMENSIONS 785 DELTA FUNCTION AND THE FUNDAMENTAL SOLUTION OF
THE LAPLACE EQUATION 785 THE DIRICHLET PROBLEM FOR THE POISSON EQUATION
786 PARTICULAR SOLUTION OF POISSON'S EQUATION 787 4 GENERAL
REPRESENTATION OF A VECTOR 787 P.5 AN APPLICATION OF GREEN'S FIRST
FORMULA 788 EMATICAL EXPOSITION 6 SINGULARITIES OF THE FIRST-ORDER ODES
791 1 INTRODUCTION 791 2 SINGULARITIES AND THEIR CLASSIFICATION 791
THEMATICAL EXPOSITION 7 GEOMETRY OF SURFACES 795 BASIC DEFINITIONS 795 2
FORMULAS OF GAUSS 795 CHRISTOFFEL SYMBOLS BASED ON SURFACE COEFFICIENTS
796 3 FORMULAS OF WEINGARTEN 798 A EQUATIONS OF GAUSS 799 NORMAL AND
GEODESIC CURVATURES 799 LONGITUDINAL AND TRANSVERSE CURVATURES 802 GRID
GENERATION IN SURFACES 803 EMATICAL EXPOSITION 8 FINITE DIFFERENCE
APPROXIMATION APPLIED TO PDES 805 INTRODUCTION 805 CALCULUS OF FINITE
DIFFERENCES 805 METHODS OF INTERPOLATION 808 CUBIC SPLINE FUNCTIONS 809
ITERATIVE ROOT FINDING 810 NUMERICAL INTEGRATION 812 FINITE DIFFERENCE
APPROXIMATIONS OF PARTIAL DERIVATIVES 813 FIRST DERIVATIVES 813 SECOND
DERIVATIVES 814 FINITE DIFFERENCE APPROXIMATION OF PARABOLIC PDES 814
STABLE SCHEMES FOR PARABOLIC EQUATIONS 818 F FINITE DIFFERENCE
APPROXIMATION OF ELLIPTIC EQUATIONS 819 TICAL EXPOSITION 9 FRAME
INVARIANCY 825 INTRODUCTION ., 825 ORTHOGONAL TENSOR 825 TIME
DIFFERENTIATION 826 CHANGE OF BASIS 827 ARBITRARY RECTANGULAR FRAMES OF
REFERENCE 828 CHECK FOR FRAME INVARIANCY 829 USE OF Q 830 ES FOR THE
MATHEMATICAL EXPOSITIONS 831 833 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Warsi, Zahir U. A. |
| author_facet | Warsi, Zahir U. A. |
| author_role | aut |
| author_sort | Warsi, Zahir U. A. |
| author_variant | z u a w zua zuaw |
| building | Verbundindex |
| bvnumber | BV021250296 |
| callnumber-first | Q - Science |
| callnumber-label | QC151 |
| callnumber-raw | QC151 |
| callnumber-search | QC151 |
| callnumber-sort | QC 3151 |
| callnumber-subject | QC - Physics |
| classification_rvk | UF 4000 |
| classification_tum | MTA 300f |
| ctrlnum | (OCoLC)58051428 (DE-599)BVBBV021250296 |
| dewey-full | 532/.05 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.05 |
| dewey-search | 532/.05 |
| dewey-sort | 3532 15 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV021250296 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:39:15Z |
| indexdate | 2024-07-09T20:33:51Z |
| institution | BVB |
| isbn | 0849333970 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014571709 |
| oclc_num | 58051428 |
| open_access_boolean | |
| owner | DE-20 DE-91G DE-BY-TUM DE-634 |
| owner_facet | DE-20 DE-91G DE-BY-TUM DE-634 |
| physical | 845 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Taylor & Francis |
| record_format | marc |
| spelling | Warsi, Zahir U. A. Verfasser aut Fluid dynamics theoretical and computational approaches Z. U. A. Warsi 3. ed. Boca Raton [u.a.] Taylor & Francis 2006 845 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dynamica gtt Fluides, Dynamique des Idealen (wiskunde) gtt Navier-Stokes-vergelijkingen gtt Reologie gtt Turbulentie gtt Viscositeit gtt Fluid dynamics Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014571709&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Warsi, Zahir U. A. Fluid dynamics theoretical and computational approaches Dynamica gtt Fluides, Dynamique des Idealen (wiskunde) gtt Navier-Stokes-vergelijkingen gtt Reologie gtt Turbulentie gtt Viscositeit gtt Fluid dynamics Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4077970-1 |
| title | Fluid dynamics theoretical and computational approaches |
| title_auth | Fluid dynamics theoretical and computational approaches |
| title_exact_search | Fluid dynamics theoretical and computational approaches |
| title_exact_search_txtP | Fluid dynamics theoretical and computational approaches |
| title_full | Fluid dynamics theoretical and computational approaches Z. U. A. Warsi |
| title_fullStr | Fluid dynamics theoretical and computational approaches Z. U. A. Warsi |
| title_full_unstemmed | Fluid dynamics theoretical and computational approaches Z. U. A. Warsi |
| title_short | Fluid dynamics |
| title_sort | fluid dynamics theoretical and computational approaches |
| title_sub | theoretical and computational approaches |
| topic | Dynamica gtt Fluides, Dynamique des Idealen (wiskunde) gtt Navier-Stokes-vergelijkingen gtt Reologie gtt Turbulentie gtt Viscositeit gtt Fluid dynamics Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Dynamica Fluides, Dynamique des Idealen (wiskunde) Navier-Stokes-vergelijkingen Reologie Turbulentie Viscositeit Fluid dynamics Strömungsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014571709&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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