Compressible Aerodynamics
Prof. Dr. Aydın Mısırlıoğlu
1
Description
• high speed air flow in/around bodies
• faster than local speed of sound or slower
• external flows around aerodynamic bodies
• internal flows in channels of specific purposes
• very high-speed flow
• not all compressible flows are part of aerodynamics, gas dynamics
2
Sources
• Fundamentals of Aerodynamics, J.D. Anderson
• Aerodynamics for Engineering Students, E.L. Houghton and P.W.
Carpenter
• Aerodynamics for Engineers, J.J. Bertin and M.L. Smith
• Modern Compressible Flow: With Historical Perspective, J.D.
Anderson
3
Contents
• Fundamentals (9)
• Introduction
• Temperature, pressure, entropy, system,
• First law, enthalpy, energy, second law
• Perfect gas, equation of state, specific heats,
• Entropy change, isentropic process
• Conservation equations
• RTT, cons of mass, momentum, energy
• Speed of sound, Mach cone,
• Energy equation in steady state
• Isentropic processes
• Compressibility
• Wave motion in compressible medium (9)
• Normal shock relations, entropy change
• Oblique shocks relations
• Expansion waves
• Unsteady wave motion
• Simple 1-D flow (9)
• Isentropic area change (Adiabatic flow)
• General equations, CD nozzles, wind tunnels, diffuser
• Supersonic inlets
• Simple frictional (Fanno) flow
• Simple heat addition or rejection (Rayleigh) flow
• Simple mass addition or removal
• Isothermal flow
• Multidimensional flows (6)
• Equations, alternative forms,
• Potential equation
• Small disturbances
• Wavy walls
• Subsonic airfoil
• Supersonic airfoil
• Supersonic flow over a cone
• Method of characteristics (MoC)
• MoC for planar flows
• MoC for supersonic nozzles
• Generalisation of MoC
• High temperature gas dynamics
• Hypersonic flows (3)
• Lab and/or problem sessions (6)
Outline
Topic
Introduction
Fundamentals
Waves
Hour
3
6
9
Midterm exam
Internal flows
Linear theory
Hypersonic flows
Lab/Practice sessions
9
4
3
8
4
must calculate
• the gas properties in different thermodynamic states/processes,
• supersonic flow field properties around bodies,
• the properties of supersonic wind tunnels and nozzles
• compressible flow properties around airfoils
• basic hypersonic flow properties
5
Evaluation
• Midterm exam
• Homework
• Project
• Final exam
35%
10% (8)
15%
40%
• To take final exam Midterm must be min 20/100
• To pass the course Final exam grade must be at least 20/100, no
matter what the total score is.
6
sketch by Gary S. Settles
7
8
9
10
Get used to
• discontinuities and choking
11
1st Law (conservation of energy)
12
13
SPEED OF SOUND
V=0
T
p
a
dV
T+dT
p+dp
dV
14
SPEED OF SOUND
a
T
p
⇒
T+dT
p+dp
dV
V=0
1
2
T
T+dT
p
p+dp
0+a
-dV+a
1
2
15
Shocks
(1)
T
dV
p
T+dT
dV
p+dp
a1
(1)
(1)
(2)
T
T+dT1
T+dT1+dT2
p
p+dp1
p+dp1+dp2
(2)
(3)
2dV
a2
3dV
a3
16
(1) (2)
(3)
(4)
4dV
a4
(1)(2) (3) (4)
(5)
5dV
a5
17
Normal Shocks
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
PRANDTL-MEYER EXPANSION WAVES
49
50
51
52
53
54
55
56
QUASI-ONE-DIMENSIONAL FLOW
57
58
59
60
61
62
63
“
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
M = 0.72
M = 0.80.
" cos " Λ)
(1 − 𝑀!
𝐶# =
+ 𝜕"∅
+
𝜕"∅
+
=0
𝜕𝑥 " 𝜕𝑦 "
𝐶#$
"
1 − 𝑀!
cos " Λ
91
93
94
95
96
97
Hypersonic flow
98
99
100
101
102
103
104
105
106
107
HYPERSONIC SHOCK-WAVE RELATIONS AND
ANOTHER LOOK AT NEWTONIAN THEORY
Characteristics Method