Turbomachinery - University of Connecticut School of …barbertj/Compressi… · PPT file · Web...
Transcript of Turbomachinery - University of Connecticut School of …barbertj/Compressi… · PPT file · Web...
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Units and Key Constants
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• Conventional Units
ParameterEnglish Units SI Units
– Distance Feet, Inches Meters, M– Time Seconds Seconds, s– Force Pounds (force), lbf 4.448 Newton, N– Pressure psf, psi Pascal, Pa (1N/1m2)
bar (105Pa)1 ft H2O2.989 kPa
– Mass Pounds (mass), lbm 0.4536 kilogram– Energy Btu Joule, J– Power 1 Hp 0.7457 kWatt
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Equivalent Systems of Units
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Important Constants for Air
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Useful Equivalents
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• For Liquid Water :
• U.S. Standard Atmosphere - 1976
3/4.62 ftlbm
214.696 101,325lbfpressure Pain
518.67 273otemperature R K
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Standard Atmosphere
Stratosphere >65,000 ft
59 FTemperature
Altitude
3.202 psia
14.696 psiaPressure
36,089 ft
Altitude
36,089 ft
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Thermodynamics Review
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Thermodynamics Review• Thermodynamic views
– microscopic: collection of particles in random motion. Equilibrium refers to maximum state of disorder
– macroscopic: gas as a continuum. Equilibrium is evidenced by no gradients
• 0th Law of Thermo [thermodynamic definition of temperature]: – When any two bodies are in thermal equilibrium with a third,
they are also in thermal equilibrium with each other. – Correspondingly, when two bodies are in thermal
equilibrium with one another they are said to be at the same temperature.
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Thermodynamics Review• 1st Law of Thermo [Conservation of energy]: Total work
is same in all adiabatic processes between any two equilibrium states having same kinetic and potential energy.– Introduces idea of stored or internal energy E– dE = dQ - dW
• dW = Work done by system [+]=dWout= - pdV• Some books have dE=dQ+dW [where dW is work done
ON system]• dQ = Heat added to system [+]=dQin
– Heat and work are mutually convertible. Ratio of conversion is called mechanical equivalent of heat J = joule
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Review of Thermodynamics• Stored energy E components
– Internal energy (U), kinetic energy (mV2/2), potential energy, chemical energy
• Energy definitions– Introduces e = internal energy = e(T, p)– e = e(T) de = Cv(T) dT thermally perfect – e = Cv T calorically perfect
• 2nd law of Thermo – Introduces idea of entropy S– Production of s must be positive– Every natural system, if left undisturbed, will change spontaneously
and approach a state of equilibrium or rest. The property associated with the capability of systems for change is called entropy.
revQdS TdS dE dWT
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Review of Thermodynamics• Extensive variables – depend on total mass of the system, e.g. M, E, S, V
• Intensive variables – do not depend on total mass of the system, e.g. p, T, s, (1/v)
• Equilibrium (state of maximum disorder) – bodies that are at the same temperature are called in thermal equilibrium.
• Reversible – process from one state to another state during which the whole process is in equilibrium
• Irreversible – all natural or spontaneous processes are irreversible, e.g. effects of viscosity, conduction, etc.
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Thermodynamic PropertiesPrimitive Derived
2
0 0
0
2k p
T
VE E E E or e e gz
Total or stagnation state
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1st Law of Thermodynamics• For steady flow, defining:
• We can write:
• and
2
2
0
/ 2 specific kinetic energy specific potential energy
specific internal energy
= + + specific enthalpy
e total spec2
Vgze u
ph e pv e
Ve gz
ific energy
2
0e2Vpv e gz pv
0 0h e pv and h e pv
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1st Law of Thermodynamics
• Substituting back into 1st law:
– Height term often negligible (not for hydraulic machines)
• Defining total or stagnation enthalpy:
• The first law for open systems is:
2 20 / 2 / 2
out in
E Q W m h V gz m h V gz
20 / 2h h V
0 oout in
Q W m h m h
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Equation of State• The relation between the thermodynamic properties of a pure substance is
referred to as the equation of state for that substance, i.e. F(p, v, T) = 0
• Ideal (Perfect) Gas– Intermolecular forces are neglected– The ratio pV/T in limit as p 0 is known as the universal gas constant (R).
p /T R = 8.3143e3
– At sufficiently low pressures, for all gases
p/T = R
or
• Real gas: intermolecular forces are important p RT
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Real Gas
1150 R
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Real Gas
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1st & 2nd Law of Thermodynamics
• Gibbs Eqn. relates 2nd law properties to 1st law properties:
Tds pdv deh e pvdh de pdv vdp
dpTds dh
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Gibbs Equation
• Isentropic form of Gibbs equation:
• and using specific heat at constant pressure:
dpdh
p
p
RTc dT dPP
dT R dPT c P
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Thermally & Calorically Perfect Gas
• Also, for a thermally perfect gas Cp[T]:
• Calorically perfect gas - Constant Cp
-1 =k= = pTP v
s v p
ck Rc c Rk c c
PdP
TdT
1
2
1
2
1
1PdP
TdT
1.4 3.51 0.4pR Rc R for air
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Isentropic Flow• For Isentropic Flow [if dQ=0, Adiabatic Gas Law]:
• Precise gas tables available for design work• Thermally Perfect Gas good flows at moderate
temperature.
1 /1 /2 2
1 1
1 /0 0
T P or T CPT P
also
T PT P
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Common Gases
Gas
Argon 1.67
Helium 1.67
Air 1.40
Hydrogen 1.40
Nitrogen 1.40
Oxygen 1.39
Water vapor 1.33
Carbon dioxide 1.29
Sulfur dioxide 1.29
Butane 1.10
monatomic
diatomic
polyatomic
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Important Constants for Air
2 2/ 8314.3 / 28.97 287 /
53.35 / 0.24 /1
1716 / 7.73 /1
287 / 1004.5 /1
air
p air
p air
p air
R M m s K
RR ft lb lbm R c Btu lbm R
RR ft lbf slug R c Btu lbf R
RR J kg K c J kg K
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Gibbs Equation• Rewriting Gibbs Equation:
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Gibbs Equation• Rewriting Gibbs Equation:
02 022 1
01 01
0
022 1
01
02 2 1
01
1ln ln
,
1 ln
exp 1
p
p
Apply at stagnation state
T Ps sc T P
For adiabatic processes T constant
Ps sc P
P s sP R
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Mollier Chart for Air
500
1,000
1,500
2,000
2,500
3,000
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16
Entropy - BTU/Lbm/deg R
Tem
pera
ture
Deg
R
P=50Atm
20
10
5
2
1
Isobars are not parallel
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Mollier for Static / Total States
450
650
850
1,050
1,250
1,450
1,650
-0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06
S
T
IdealReal
P in
P out
s
Poin
Poout
V2/2
h02i
h02
h01
2
0 2Vh h
We will soon see