ENGINES, REFRIGERATORS,
AND HEAT PUMPS
This lecture highlights aspects in Chapters 9,10,11 of Cengel and Boles.
Every thermodynamic device has moving parts. To understand these
movements, it is important that you watch some videos on the Internet. I will
go through these slides in two 90-minutes lectures.
Zhigang Suo, Harvard University
How humans tell each other something?
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The thing itself
Pictures
Words
Equations
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Language
Books
Movies
The Internet
2
Thermodynamics = heat + motion
Too many devices to classify neatly
• Fuel (input): biomass, fossil, solar thermal, geothermal, nuclear,
electricity.
• Application (output): mobile power plant (transpiration in air, land,
sea), stationary power plant (electricity generation), refrigerator,
heat pump. Power cycle, refrigeration cycle.
• Working fluid: Gas cycle (air), vapor cycle (steam, phase change).
• Fluid-solid coupling: piston engine (reciprocating, crankshaft),
turbine engine (jet, compressor).
• Site of burning: external combustion, internal combustion.
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Plan
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Internal combustion engines
Gas turbines
Stirling and Ericsson engines
Vapor power cycle
Refrigeration cycle
Thermodynamics in a nutshell
4
Combustion engine
burns to move
BOILER
STEAM
WATER
Fayette Internal
Combustion Engiine I
COMBUSTION CHAMBER
PISTON
PISTON
External combustion engine
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Steam engine
Stirling engine
Ericsson engine
Internal combustion engine (ICE)
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Otto (gasoline) engine
Diesel engine
Gas turbine
Jet propulsion
US Navy Training Manual, Basic Machines
5
Reciprocating engine
also known as piston engine, converts linear motion to rotation
CYLINDER
PISTON
CONNECTING ROD
CRANKSHAFT
US Navy Training Manual, Basic Machines
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fuel-air mixture
entering cylinder
air entering
exhaust valve
closed
fuel-air mixture
being compressed
both valves
closed
Fuel discharging
intake from nozzle
valve open
piston
moving down
piston
moving up
valve tappet
lifting valve
cam lobe lifting
valve tappet
1 cycle
4 strokes
2 revolutions
INTAKE STROKE
spark igniting
mixture
COMPRESSION STROKE
both valves
closed
exhaust valve
open
intake valve
closed
Animated engines
http://www.animatedengines.com/
piston
moving up
piston
moving down
valve tappet
lifting valve
cam lobe lifting
valve tappet
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US Navy Training Manual, Basic Machines
POWER STROKE
EXHAUST STROKE
Spark-ignition engine (gasoline engine, petrol engine, Otto
engine)
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Air-standard assumptions
1.
2.
3.
4.
Model the engine as a closed system, and the working fluid as air (an ideal gas).
The cycle is internally reversible.
Model combustion by adding heat from an external source
Model exhaust by rejecting heat to an external sink
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Cold air-standard assumption
Model air as an ideal gas of constant specific heat at room temperature (25°C).
2 independent variables to name all states of thermodynamic equilibrium
6 functions of state: PTvush
4 equations of state
Pv = RT
(
)
h2 - h1 = cP (T2 - T1 )
u2 - u1 = cv T2 - T1
æT ö
v2
2
ç
÷
s2 - s1 = cv log ç ÷ + R log
v1
è T1 ø
Gibbs equation
ds =
1
P
du + dv
T
T
cP / cv = k, cP - cv = R, R = 0.2870kJ/kg ×K, k = 1.4
isentropic process
Pvk = constant, Tvk-1 = constant, TP
-
k-1
k
= constant
10
Thermal efficiency of Otto cycle
Compression ratio:
Conservation of energy:
Isentropic processes:
Thermal efficiency:
V
r = BDC
VTDC
(
)
qin = u3 - u2 = cv T3 -T2 ,
(
)
win = u2 - u1 = cv T2 -T1 ,
æ v ök-1
= çç 1 ÷÷ = r k-1 ,
T1 è v2 ø
T2
hth, Otto =
wout - win
qin
(
qout = u4 - u1 = cv T4 -T1
(
)
wout = u3 - u4 = cv T3 -T4
)
æ v ök-1
= ç 4 ÷ = r k-1
T4 çè v3 ÷ø
T3
=1-
T4 -T1
T3 -T2
=1-
1
r k-1
wout
win
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Otto cycle represented
in planes of different variables
s
3
qin
2
Pv = RT
4
qout
(
u2 - u1 = cv T2 - T1
)
æT ö
v2
2
ç
÷
s2 - s1 = cv log ç ÷ + R log
v1
è T1 ø
1
v
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Reciprocating engines of two types
Spark-ignition engine (Otto, 1876)
Compression-ignition engine (Diesel, 1892)
https://ccrc.kaust.edu.sa/pages/HCCI.aspx
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Compression-ignition engine (Diesel engine)
compression ratio:
cut-off ratio:
Conservation of energy:
Isentropic processes
Thermal efficiency:
r = v1 / v2
rc = v3 / v2
(
)
qin = h3 - h2 = cP T3 -T2 ,
(
qout = u4 - u1 = cv T4 -T1
)
wnet,out = qin - qout
æ v ök-1
= çç 1 ÷÷ = r k-1 ,
T1 è v2 ø
T2
æ v ök-1 æ ök-1
r
= ç 4 ÷ = çç ÷÷
T4 çè v3 ÷ø
è rc ø
T3
é k
1 ê rc -1
hth, Diesel = 1 =1=1qin
k T3 -T2
r k-1 êë k rc -1
qout
T4 -T1
(
)
(
)
ù
ú
ú
û
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Plan
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Internal combustion engines
Gas turbines
Stirling and Ericsson engines
Vapor power cycle
Refrigeration
Thermodynamics in a nutshell
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Gas turbine (Brayton cycle)
4 steady-flow components: isobaric and isentropic
P
qin
3
2
1
4
qout
16
s
Thermal efficiency of Brayton cycle
Definition of pressure ratio:
Conservation of energy:
rp = P2 / P1
)
(
qin = h3 - h2 = cP T3 -T2 ,
(
)
win = h2 - h1 = cP T2 -T1 ,
k-1
Isentropic processes:
Thermal efficiency:
T2
T1
k-1
æP ö k
2
= çç ÷÷
= rP k ,
P
è 1ø
hth, Brayton =
(
)
wout = h3 - h4 = cP T3 -T4
)
k-1
T3
T4
wout - win
qin
(
qout = h4 - h1 = cP T4 -T1
k-1
æP ö k
3
=ç ÷
= rP k
çP ÷
è 4ø
T -T
1
=1- 4 1 =1T3 -T2
(k-1)/k
rP
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Brayton cycle has large back work ratio
win
wout
=
T2 -T1
T3 -T4
=
T1
T4
wout
win
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Intercooling, reheating, regeneration
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Gas turbine for jet propulsion
Thousands of years of history
Who invented this?
Hero of Alexandria
(first century AD)
Frank Whittle (UK), Hans von Ohain (Germany)
(during World War II)
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http://www.techknow.org.uk/wiki/index.php?title=File:Hero_4.jpg
Gas turbine for jet propulsion
6 steady-flow components
Propulsive force:
Propulsive power:
Propulsive efficiency:
(
F = m Vexit -Vinlet
)
WP = FV
h=
WP
Qin
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http://www.ae.utexas.edu/~plv955/class/propulsion/Cp_air.GIF
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Air as an ideal gas of variable specific heat
Pv = RT, R = 0.2870kJ/kg×K
( )
h = h (T )
u=u T
ds =
1
P
du + dv
T
T
P
s2 - s1 = s0 T2 - s0 T1 - R log 2
P1
( )
isentropic process
( )
( ),
=
P2 Pr (T2 )
P1
Pr T1
v1
v2
=
( )
vr (T2 )
vr T1
See section 7.9 for the use of this table
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Plan
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Internal combustion engines
Gas turbines
Stirling and Ericsson engines
Vapor power cycle
Refrigeration cycle
Thermodynamics in a nutshell
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Displacer-type Stirling engine
https://www.stirlingengine.com/faq/
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Stirling engine and regenerator (1816)
reversible cycle between two fixed temperatures, having the Carnot efficiency
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https://people.ok.ubc.ca/jbobowsk/Stirling/how.html
Stirling vs. Carnot
for given limits of volume, pressure, and temperature
• On PV plane, the black area represents the Carnot cycle, and shaded areas
represent addition work done by the Stirling cycle.
• On TS plane, the black area represents the Carnot cycle, and the shaded areas
represent additional heat taken in by the Stirling cycle.
• The Stirling cycle and the Carnot cycle have the same thermal efficiency.
• The Stirling cycle take in more heat and give more work than the Carnot cycle.
Walker, Stirling Engine, 1980.
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Work out by Stirling cycle
Specific work
wout =
v2
ò P dv = ò
v1
RTH
v
dv -
Specific gas constant
Gas
v2
v1
R=
Formula
Air
ò
æv ö
dv = R TH -TL log çç 2 ÷÷
v
è v1 ø
RTL
(
)
kB
mmolecule
R (kJ/kgK)
0.2870
Steam
H2O
0.4615
Ammonia
NH3
0.4882
Hydrogen
H2
4.124
Helium
He
2.077
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Ericsson engine with regenerator (1853)
reversible cycle between two fixed temperatures, having the Carnot efficiency
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Plan
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Internal combustion engines
Gas turbines
Stirling and Ericsson engines
Vapor power cycle
Refrigeration cycle
Thermodynamics in a nutshell
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Coal power station
coverts coal to electricity
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Brayton Point Power Station
Sommerset, Massachusetts
Mount Hope Bay
http://www.clf.org/blog/clean-energy-climate-change/brayton-point-retirement-means-game-coal-new-england/
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Nuclear power station
converts uranium to electricity
Animation
https://www.awesomestories.com/images/user/be4285df4b.gif
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http://www.nuclear-power.net/nuclear-power-plant/
Nine Mile Point Nuclear Power Plant, New York
Lake Ontario
Cooling
tower
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Why water? Why steam?
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Water is cheap.
Water flows!
Water is a liquid at the temperature of heat sink (rivers, lakes,...).
Vaporization changes specific volume greatly: a lot of work at relatively low pressure.
https://www.ohio.edu/mechanical/thermo
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Rankine cycle
4 steady-flow components: isobaric and isentropic
wpump,in = h2 - h1
qboiler,in = h3 - h2
hthermal =
wturbine,out - wpump,in
qboiler,in
wturbine,out = h3 – h4
back-work ratio =
qcondenser,out = h4 – h1
wpump,in
wturbine,out
P
qboiler,in
2
3
wturbine,out
wpumo,in
1
qcondenser, out
4
s
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Rankin cycle has small back work ratio
back-work ratio =
wpump,in
wturbine,out
dh = Tds + vdP
wpump,in = h2 - h1 =
P2
ò vdP
P1
wturbine,out = h3 - h4 =
P3
ò vdP
P4
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Rankin cycle
Vapor cycle
Steam turbine
Small back-work ratio
Brayton cycle
Gas cycle
Gas turbine
Large back-work ratio
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Carnot cycle is unsuitable as vapor power cycle
Issues with the in-dome Carnot cycle
Process 1-2 limits the maximum temperature below the
critical point (374°C for water)
Process 2-3. The turbine cannot handle steam with a high
moisture content because of the impingement of liquid
droplets on the turbine blades causing erosion and wear.
Process 4-1. It is not practical to design a compressor
that handles two phases.
Issues with supercritical Carnot cycle
Process 1-2 requires isothermal heat transfer at variable
pressures.
Process 4-1 requires isentropic compression to extremely
high pressures.
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Cogeneration
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Plan
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Internal combustion engines
Gas turbines
Stirling and Ericsson engines
Vapor power cycle
Refrigeration cycle
Thermodynamics in a nutshell
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Refrigerator and heat pump
4 steady-flow components
animation
COPR =
h -h
= 1 4
Wnet,in h2 - h1
COPHP =
QL
h -h
= 2 3
Wnet,in h2 - h1
QH
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Selecting Refrigerant
1.
2.
3.
4.
5.
6.
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Large enthalpy of vaporization
Sufficiently low freezing temperature
Sufficiently high critical temperature
Low condensing pressure
Do no harm: non-toxic, non-corrosive, non-flammable,
environmentally-friendly
Low cost
R-717 (Ammonia, NH3) used in industrial and heavycommercial sectors. Toxic.
R-12 (Freon 12, CCl2F2). Damage ozone layer. Banned.
R-134a (HFC 134a, CH2FCF3) used in domestic refrigerators,
as well as automotive air conditioners.
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Plan
•
•
•
•
•
•
Internal combustion engines
Gas turbines
Stirling and Ericsson engines
Vapor power cycle
Refrigeration cycle
Thermodynamics in a nutshell
46
Brayton cycle
Rankin cycle
Refrigeration cycle
Jet propulsion, power station
Internal combustion
Gas cycle
Gas turbine
Compressor
Large back-work ratio
Power station
External Combustion
Vapor cycle
Steam turbine
Pump
Small back-work ratio
Refrigerator, heat pump
Electricity
Vapor cycle
No turbine
Vapor compressor
No back work
wout
win
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https://flowcharts.llnl.gov/
48
Pure substance
T
liquid
weights
vapor
gas
P = 0.1 MPa
liquid
s
fire
2 independent variables to name all states of thermodynamic equilibrium
6 functions of state: PTvush
4 equations of state
Incompressible liquid
v = constant
(
u2 - u1 = cv T2 - T1
)
æT ö
s2 - s1 = cv log çç 2 ÷÷
è T1 ø
h = u + Pv
liquid-gas mixture
( )
v = (1 - x ) v f (T ) + xvg (T )
u = (1 - x ) u f (T ) + xug (T )
s = (1 - x ) s f (T ) + xsg (T )
h = (1 - x ) h f (T ) + xhg (T )
P = Psat T
ideal gas
Pv = RT
(
u2 - u1 = cv T2 - T1
)
æT ö
v
s2 - s1 = cv log çç 2 ÷÷ + R log 2
v1
è T1 ø
h = u + Pv
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Concepts and definitions
Isolated system
Quantum states of an isolated system
Fundamental postulate
States of thermodynamic equilibrium
Functions of state
Phases
Number of quantum states of an isolated system: W
Entropy of an isolated system: S = kB logW
Isolated system generates entropy. Irreversibility
Isolated system conserves energy and volume: U,V
Model a closed system as a family of isolated systems: S (U ,V )
Definition of temperature (Gibbs equation 1):
Definition of pressure (Gibbs equation 2):
Definition of enthalpy:
Definition of Helmholtz function (free energy):
Definition of Gibbs function:
Definition of heat capacities:
(
1 ¶S U ,V
=
T
¶U
)
(
P ¶S U ,V
=
T
¶V
)
H =U + PV
F =U -TS
G =U -TS + PV
CV =
(
¶U T ,V
¶T
),
CP =
(
¶H T ,P
¶T
)
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Theory of everything
the world according to entropy
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Entropy
Equilibrium
Irreversibility
Temperature, energy
Pressure, volume
Phases
Ideal gas
Osmosis
Turbines, compressors, throttling valves, heat exchangers, diffusers, nozzles
Engines, refrigerators, heat pumps
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Summary
• Engine converts fuel to motion.
• Refrigerator and heat pump use work to pump heat from a place of low
temperature to a place of high temperature.
• Many ideal cycles are internally reversible, but externally irreversible.
• Stirling and Ericsson cycles are internally and externally reversible, so they
have the same thermal efficiency as the Carnot cycle.
• Use ideal-gas model to analyze gas as working fluid.
• Use property table to analyze vapor as working fluid.
• Model piston engine as a closed system (Otto, Diesel, Stirling, Ericsson).
• Model turbine (or compressor) device as steady-flow components in
series (Brayton cycle, Rankine cycle, refrigeration cycle).
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