Fundamentals of Gas Dynamics

Fundamentals of Gas Dynamics
اسم المؤلف
V. Babu
التاريخ
22 يناير 2022
المشاهدات
31
التقييم
(لا توجد تقييمات)
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Fundamentals of Gas Dynamics
(2nd Edition)
V. Babu
Professor
Department of Mechanical Engineering
Indian Institute of Technology
Contents
Preface iii

  1. Introduction 1
    1.1 Compressibility of Fluids . 1
    1.2 Compressible and Incompressible Flows . 2
    1.3 Perfect Gas Equation of State . 4
    1.3.1 Continuum Hypothesis . 5
    1.4 Calorically Perfect Gas 7
  2. One Dimensional Flows – Basics 11
    2.1 Governing Equations . 11
    2.2 Acoustic Wave Propagation Speed 13
    2.2.1 Mach Number 16
    2.3 Reference States . 16
    2.3.1 Sonic State 17
    2.3.2 Stagnation State . 17
    2.4 T-s and P-v Diagrams in Compressible Flows 23
    Exercises . 28
  3. Normal Shock Waves 31
    3.1 Governing Equations . 31
    3.2 Mathematical Derivation of the Normal Shock Solution . 33
    3.3 Illustration of the Normal Shock Solution on T-s and P-v
    diagrams . 36
    vvi Fundamentals of Gas Dynamics
    3.4 Further Insights into the Normal Shock Wave Solution . 41
    Exercises . 45
  4. Flow with Heat Addition- Rayleigh Flow 49
    4.1 Governing Equations . 49
    4.2 Illustration on T-s and P-v diagrams . 50
    4.3 Thermal Choking and Its Consequences . 60
    4.4 Calculation Procedure 64
    Exercises . 67
  5. Flow with Friction – Fanno Flow 69
    5.1 Governing Equations . 69
    5.2 Illustration on T-s diagram 70
    5.3 Friction Choking and Its Consequences . 75
    5.4 Calculation Procedure 75
    Exercises . 81
  6. Quasi One Dimensional Flows 83
    6.1 Governing Equations . 84
    6.1.1 Impulse Function and Thrust 84
    6.2 Area Velocity Relation 86
    6.3 Geometric Choking 88
    6.4 Area Mach number Relation for Choked Flow 90
    6.5 Mass Flow Rate for Choked Flow 92
    6.6 Flow Through A Convergent Nozzle . 93
    6.7 Flow Through A Convergent Divergent Nozzle . 97
    6.8 Interaction between Nozzle Flow and Fanno, Rayleigh
    Flows . 111
    Exercises . 122
  7. Oblique Shock Waves 127
    7.1 Governing Equations . 129
    7.2 θ-β-M curve . 131
    7.3 Illustration of the Weak Oblique Shock Solution on a T-s
    diagram 134
    7.4 Detached Shocks . 141Contents vii
    7.5 Reflected Shocks . 143
    7.5.1 Reflection from a Wall 143
    Exercises . 146
  8. Prandtl Meyer Flow 149
    8.1 Propagation of Sound Waves and the Mach Wave 149
    8.2 Prandtl Meyer Flow Around Concave and Convex Corners 153
    8.3 Prandtl Meyer Solution 155
    8.4 Reflection of Oblique Shock From a Constant Pressure
    Boundary . 160
    Exercises . 163
  9. Flow of Steam through Nozzles 165
    9.1 T-s diagram of liquid water-water vapor mixture . 165
    9.2 Isentropic expansion of steam 168
    9.3 Flow of steam through nozzles 171
    9.3.1 Choking in steam nozzles 173
    9.4 Supersaturation and the condensation shock . 179
    Exercises . 188
    Suggested Reading 191
    Table A. Isentropic table for γ = 1.4 193
    Table B. Normal shock properties for γ = 1.4 203
    Table C. Rayleigh flow properties for γ = 1.4 211
    Table D. Fanno flow properties for γ = 1.4 221
    Table E. Oblique shock wave angle β in degrees for γ = 1.4 231
    Table F. Mach angle and Prandtl Meyer angle for γ = 1.4 237
    Table G. Thermodynamic properties of steam, temperature table 243
    Table H. Thermodynamic properties of steam, pressure table 247
    Table I. Thermodynamic properties of superheated steam 251viii Fundamentals of Gas Dynamics
    Index 259
    About the author 263
    About the book 26
    Index
    Acoustic wave, 13, 149
    special case of normal shock
    wave, 36
    Afterburner, 117
    Area Mach number relation, 91
    Area velocity relation, 87
    Bow shock, 142
    Choking
    friction, 75
    geometric, 90
    thermal, 60
    Combustion wave, 61
    Combustor
    design issues, 57
    pressure oscillations, 62
    Compressibility, 1
    isentropic, 3
    isothermal, 2
    limit, 4
    Conservative form, 12
    Continuum limit, 6
    Convergent divergent nozzle, 97
    establishment of flow in
    illustration in T-s diagram,
    98
    Convergent nozzle
    establishment of flow in, 93
    illustration in T-s and P-v
    diagram, 94
    Corner
    concave, 129, 153
    convex, 155
    Critical pressure
    nozzle
    steam, 174
    Critical state, 166
    Detached shock, 141
    Dryness fraction
    definition, 167
    Enthalpy, 9
    Equilibrium
    metastable, 180
    Expansion fan, 155
    nozzle exit, 96
    reflection from constant pressure
    boundary, 161
    260 Fundamentals of Gas Dynamics
    Fanno curve, 74
    Fanno flow, 69
    changes in properties, 74
    illustration in T-s diagram, 74
    interaction with nozzle flow, 111
    sonic state, 76
    Friction
    effect of, 69
    factor, 70
    H-curve
    Normal shock wave, 44
    Rayleigh flow, 57
    sonic state, 59
    Heat addition, 49
    Impulse function, 84
    Intake
    capture area, 137
    critical mode, 137
    supersonic, 107, 136
    Internal energy
    distribution, 8
    modes, 7
    Isentropic process, 13
    illustraion in T-s and P-v
    diagram, 27
    relation, 20
    steam, 170
    Knudsen number, 6
    Mach
    angle, 133, 153
    cone, 152
    number, 3
    reflection, 145
    wave, 133, 152
    flow across, 155
    Mass flow rate
    choked, 92
    Normal shock, 31
    entropy change, 35
    illustration in P-v diagram, 44
    illustration in T-s and P-v
    diagram, 37
    loss of stagnation pressure, 35
    moving, 39
    special case of oblique shock,
    133
    strength, 35
    Oblique shock, 127
    θ − β − M relation, 131
    flow deflection angle, 129
    from nozzle exit, 139
    reflection
    from constant pressure
    boundary, 160
    from wall, 143
    Over expanded flow, 103
    Perfect gas
    calorically perfect, 7
    Equation of state, 4
    alternative forms, 5
    Specific heats, 9
    Prandtl Meyer
    angle, 159
    flow, 153Index 261
    Quasi one-dimensional, 83
    Ramjet engine
    inlet interaction, 63
    intake, 136
    schematic, 29
    Rankine-Hugoniot equation, 44
    Rayleigh curve, 54
    Rayleigh flow, 49
    changes in properties, 53
    illustration in P-v diagram, 57
    ilustration in T-s diagram, 54
    interaction with nozzle flow, 114
    sonic state, 64
    Rayleigh line
    normal shock, 42
    sonic state, 59
    Reference states, 17
    sonic state, 17
    stagnation state, 18
    Saturation
    pressure, 166
    temperature, 166
    Scramjet engine
    inlet interaction, 63
    intake, 136
    Second law
    differential form, 12
    Entropy change for a process, 13
    TdS relation, 12
    Shock
    condensation, 183
    Shock angle, 129
    Shock diamond, 141
    Slip line, 145, 154
    Sonic state, 17, 54
    Fanno flow, 76
    illustration in T-s, P-v diagram,
    27
    nozzle
    steam, 174
    nozzle flow, 90
    Rayleigh flow, 64
    Rayleigh line, 59
    Speed of sound, 15
    mixture of gases, 16
    Perfect gas, 16
    reacting flow, 16
    steam, 170
    Stagnation density, 20
    Stagnation pressure
    changes in, 22
    definition, 19
    loss, 35, 57, 74, 127, 133
    Stagnation state
    definition, 18
    illustration in T-s, P-v diagram,
    27
    Stagnation temperature
    changes in, 21
    definition, 19
    Strong oblique shock, 132
    Supersaturated flow
    degree of supercooling, 182
    degree of supersaturation, 182
    Wilson line, 183
    Thrust
    loss of, 96
    momentum, 85
    pressure, 85262 Fundamentals of Gas Dynamics
    Under expanded flow, 62, 75, 96,
    103
    Velocity triangle, 129, 156
    Wave angle, 129
    Weak oblique shock, 132
    Wilson line, 183
    Wind tunnel
    supersonic, 105

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