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Loading...Fundamentals of Gas Dynamics
Second Edition
V. Babu
Contents
1 Introduction . 1
1.1 Compressibility of Fluids 1
1.2 Compressible and Incompressible Flows . 2
1.3 Perfect Gas Equation of State . 3
1.3.1 Continuum Hypothesis . 4
1.4 Calorically Perfect Gas 5
2 One-Dimensional Flows—Basics 9
2.1 Governing Equations . 9
2.2 Acoustic Wave Propagation Speed . 11
2.2.1 Mach Number . 13
2.3 Reference States . 13
2.3.1 Sonic State . 14
2.3.2 Stagnation State 14
2.4 T-s and P-v Diagrams in Compressible Flows . 18
Problems 22
3 Normal Shock Waves 25
3.1 Governing Equations . 25
3.2 Mathematical Derivation of the Normal Shock Solution 27
3.3 Illustration of the Normal Shock Solution on T-s and P-v
Diagrams 30
3.4 Further Insights into the Normal Shock Wave Solution . 33
3.4.1 Normal Shock Compression and Isentropic
Compression 35
Problems 37
4 Flow with Heat Addition—Rayleigh Flow . 41
4.1 Governing Equations . 41
4.2 Illustration on T-s and P-v Diagrams 42
ix4.3 Thermal Choking and Its Consequences 49
4.4 Calculation Procedure . 52
Problems 54
5 Flow with Friction—Fanno Flow . 57
5.1 Governing Equations . 57
5.2 Illustration on T-s Diagram . 58
5.3 Friction Choking and Its Consequences 62
5.4 Calculation Procedure . 63
Problems 66
6 Quasi One Dimensional Flows . 69
6.1 Governing Equations . 69
6.1.1 Impulse Function and Thrust 70
6.2 Area Velocity Relation 71
6.3 Geometric Choking . 73
6.4 Area Mach Number Relation for Choked Flow 75
6.5 Mass Flow Rate for Choked Flow 76
6.6 Flow Through a Convergent Nozzle 77
6.7 Flow Through a Convergent Divergent Nozzle . 81
6.8 Interaction Between Nozzle Flow and Fanno, Rayleigh Flows 91
Problems 99
7 Oblique Shock Waves 103
7.1 Governing Equations . 105
7.2 h-b-M Curve . 106
7.3 Illustration of the Weak Oblique Shock Solution on a T-s
Diagram . 109
7.4 Detached Shocks 114
7.5 Reflected Shocks 116
7.5.1 Reflection from a Wall . 116
Problems 117
8 Prandtl-Meyer Flow . 121
8.1 Propagation of Sound Waves and the Mach Wave 121
8.2 Prandtl Meyer Flow Around Concave and Convex Corners 124
8.3 Prandtl Meyer Solution 125
8.4 Reflection of Oblique Shock from a Constant Pressure
Boundary 131
Problems 133
9 Flow of Steam Through Nozzles 135
9.1 T-s Diagram of Liquid Water-Water Vapor Mixture . 135
9.2 Isentropic Expansion of Steam 137
x Contents9.3 Flow of Steam Through Nozzles . 139
9.3.1 Choking in Steam Nozzles 141
9.4 Supersaturation and the Condensation Shock 146
Problems 151
Suggested Readings . 153
Index .
Index
A
Acoustic wave, 11, 121
special case of normal shock wave, 29
Afterburner, 96
Area Mach number relation, 76
Area velocity relation, 72
B
Bow shock, 114
C
Choking
friction, 62
geometric, 75
thermal, 49
Combustion wave, 50
Combustor
design issues, 47
pressure oscillations, 52
Compressibility, 1
isentropic, 3
isothermal, 2
limit, 3
Conservative form, 10
Continuum limit, 5
Convergent divergent nozzle, 81
establishment of flow in
illustration in T-s diagram, 81
Convergent nozzle
establishment of flow in, 77
illustration in T-s and P-v diagram, 77
Corner
concave, 104, 124
convex, 125
Critical pressure
nozzle
steam, 141
Critical state, 136
D
Detached shock, 114
Dryness fraction
definition, 136
E
Enthalpy, 7
Equilibrium
metastable, 146
Expansion fan, 125
nozzle exit, 79
reflection from constant pressure boundary, 131
F
Fanno curve, 60
Fanno flow, 57
changes in properties, 60
illustration in T-s diagram, 60
interaction with nozzle flow, 91
sonic state, 64
Friction
effect of, 57
factor, 58
H
H-curve
normal shock wave, 35
Rayleigh flow, 47
sonic state, 49
Heat addition, 41
I
Impulse function, 70
Intake
capture area, 111
critical mode, 111
supersonic, 88, 110
Internal energy
distribution, 6
modes, 6
Isentropic process, 10
illustration in T-s and P-v diagram, 22
relation, 16
steam, 139
K
Knudsen number, 5
M
Mach
angle, 107, 124
cone, 124
number, 2
reflection, 116
wave, 107, 124
flow across, 125
Mass flow rate
choked, 76
N
Normal shock, 25
entropy change, 28
illustration in P-v diagram, 35
illustration in T-s and P-v diagram, 31
loss of stagnation pressure, 29
moving, 32
special case of oblique shock, 107
strength, 29
O
Oblique shock, 103
θ − β − M relation, 106
flow deflection angle, 103
from nozzle exit, 112
reflection
from constant pressure boundary, 131
from wall, 116
Over expanded flow, 83
P
Perfect gas
calorically perfect, 6
equation of state, 3
alternative forms, 4
specific heats, 7
Prandtl Meyer
angle, 129
flow, 124
Q
Quasi one-dimensional, 69
R
Ramjet engine
inlet interaction, 52
intake, 110
schematic, 23
Rankine-Hugoniot equation, 35
Rayleigh curve, 45
Rayleigh flow, 41
changes in properties, 44
illustration in P-v diagram, 47
illustration in T-s diagram, 45
interaction with nozzle flow, 95
sonic state, 52
Rayleigh line
normal shock, 34
sonic state, 49
Reference states, 14
sonic state, 14
stagnation state, 14
S
Saturation
pressure, 135
temperature, 136
Scramjet engine
inlet interaction, 52
intake, 110
Second law
differential form, 9
entropy change for a process, 10
TdS relation, 10Index 195
Shock
condensation, 148
Shock angle, 104
Shock diamond, 114
Slip line, 116, 124
Sonic state, 14, 45
Fanno flow, 64
illustration in T-s, P-v diagram, 22
nozzle
steam, 141
nozzle flow, 75
Rayleigh flow, 52
Rayleigh line, 49
Speed of sound, 12
mixture of gases, 13
perfect gas, 13
reacting flow, 13
steam, 139
Stagnation density, 16
Stagnation pressure
changes in, 18
definition, 15
loss, 29, 47, 61, 103, 108
Stagnation state
definition, 14
illustration in T-s, P-v diagram, 22
Stagnation temperature
changes in, 17
definition, 15
Strong oblique shock, 107
Supersaturated flow
degree of supercooling, 147
degree of supersaturation, 147
Wilson line, 148
T
Thrust
loss of, 80
momentum, 71
pressure, 71
U
Under expanded flow, 52, 62, 79, 83
V
Velocity triangle, 103, 126
W
Wave angle, 104
Weak oblique shock, 107
Wilson line, 148
Wind tunnel
supersonic, 87
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