INTRODUCTION TO COMPRESSIBLE FLOW
INTRODUCTION TO COMPRESSIBLE FLOW
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MOTIVATION TO LEARN COMPRESSIBLE FLOW
Applications of compressible flow in Aeronautics and Non Aeronautics 1. Jet engines 2. Intake Supersonic Fighter aircraft 3. Blended Wing Body 4. Engine Four strokes
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MOTIVATION TO LEARN COMPRESSIBLE FLOW
Applications in Jet Engines
T-s Diagram T
s T0
0
2 Tt0 =Tt2
Tt4
4
9β
3 Tt3
Tt9
Tt5
t5
t9
9
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MOTIVATION TO LEARN COMPRESSIBLE FLOW
Applications in Engine Four Strokes
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MOTIVATION TO LEARN COMPRESSIBLE FLOW
Applications in Engine Four Strokes
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MOTIVATION TO LEARN COMPRESSIBLE FLOW
Applications in Intake Supersonic
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MOTIVATION TO LEARN COMPRESSIBLE FLOW
Applications in Blended Wing Body
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What is Compressible Flow?
πΎ = β ππ
ππ/π= βπ
ππ
ππ
βπ±
π±
π + βπ π
Compressible flow deals with fluids in which the fluid density varies significantly in response to a change in pressure
Modulus Bulk
πΎ = π ππ
ππ
waterK
At sea level (1 atm)
airK
5 x 10-10 m2/N
1 x 10-5 m2/N
Is it possible to change Ξp with dynamic pressure?
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What is Compressible Flow?
Molecular Approach
ππ = πΏπ + πΏπ
Change in Internal Energy : 1. Heat added to the system 2. Work done on the system
Molecule activities (e) increase or decrease by two things: Heat, πΉπ Work, πΉπ
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State Condition
Perfect gas :
Intermolecular forces are neglected
10 x molecule diameter
Repulsive
force (+)
Attractive
force (-)
Distance from molecule
π = ππ π
π = pressure [π/π2]
π = ππππ ππ‘π¦[kg/π3]
π = π‘πππππππ‘π’ππ [ππΎ]
π = π΅πππ‘π§ππππ constant = 287 [π2/π 2ππΎ]
ππ£ = π π
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What is Compressible Flow?
ππ = πΏπ + πΏπ
Molecule activities (e) increase or decrease by two things: Heat, πΉπ Work, πΉπ
β’ 1st Law: dU = dQ + dW o Find more useful expression for dw, in
terms of p and r (or v = 1/r)
β’ When volume varies β work is
done β’ Work done on balloon, volume β β’ Work done by balloon, volume β
Change in
Volume (-) πΏπ = β ππ ππ΄ = β π ππ
ππ = πΏπ β πππ ππ’ = πΏπ β πππ£ Per unit mass
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What is Compressible Flow?
β = π’ + ππ£ = π’ + π π
Enthalpy : Useful Quantity, h
Differentiate
πβ = ππ’ + πππ£ + π£ππ
ππ’ = πΏπ β πππ£
πβ = πΏπ β πππ£ + πππ£ + π£ππ
πβ = πΏπ β πππ£ + πππ£ + π£ππ
πΏπ = πβ β π£ππ πΏπ = ππ’ + πππ£
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What is Compressible Flow?
Heat Addition and Specific Heat
β’ Addition of dq will cause a small change in temperature dT of system
dq
dT
Kkg
J
dT
qc
d
β’ Specific heat is heat added per unit change in temperature of system
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What is Compressible Flow?
β’ Different materials have different specific heats
β Balloon filled with He, N2, Ar, water, lead, uranium, etcβ¦
β’ For a fixed dq, resulting dT depends on type of processβ¦
Kkg
J
dT
qc
d
Heat Addition and Specific Heat
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What is Compressible Flow?
Process type I : constant volume
Kkg
J
dT
qc
d
dq
dT
dTcdu
dTcq
dT
qc
v
v
v
d
d
olumeconstant v
Tcu v
Heat Addition and Specific Heat
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What is Compressible Flow?
Process type I I : constant pressure
Tch p
dq
dT
Kkg
J
dT
qc
d
dTcdh
dTcq
dT
qc
p
p
p
d
d
pressureconstant
Heat Addition and Specific Heat
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No Intermolecular
forces Real Gas
Intermolecular forces
P = 1000 atm
T = 30K
Thermally PG 800-2500 OK
Chemically reacting 2500-9000 OK
Calorically PG 0-800 Ok
For air
What is Compressible Flow?
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β = π’ + ππ£ For real gas and chemically reacting mixture of PG
π’ = π’(π, π£) β = β(π, π)
For thermally PG
ππ’ = ππ£ππ πβ = ππππ
For calorically PG
π’ = ππ£π β = πππ
What is Compressible Flow?
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For calorically PG
ππ= ππ£ + π
Ratio of specific heat
ππ
ππ£= Ξ³
ππ£ =π
πΎ β 1 ππ£ =
πΎπ
πΎ β 1
What is Compressible Flow?
Relation of Spesific heats and Ratio of specific heat
Specific heat ratio
For air, g = 1.4
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Entropy
πΏπ + πΏπ€ = ππ’ ππ β₯ ππ/π πππ β₯ ππ
πΏπ€ = ππ’ β πππ
πππ + π£ππ = πβ
Helmholtz function : maximum work that can be obtained from a system
πππ β πππ£ = ππ’
Gibbs function : maximum useful work that can be obtained from a system
πΏπ€ = πβ β πππ
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