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.
Zhigang Suo, Harvard University
Thermodynamics = heat + motion
Too many devices to classify neatly
• Application: mobile power plant (transpiration in air, land, sea),
stationary power plant (electricity generation), refrigerator, heat
pump.
• Fuel. biomass, fossil, solar thermal, geothermal, nuclear, electricity.
• Site of burning: external combustion, internal combustion.
• Working fluid: gas (air), vapor (steam).
• Fluid-solid coupling: piston (reciprocating, crankshaft), turbine (jet,
compressor).
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Plan
•
•
•
•
•
Internal combustion engines
Gas turbines
Stirling and Ericsson engines
Vapor power cycle
Refrigeration cycle
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Combustion engine
burns to move
BOILER
STEAM
WATER
Fayette Internal
Combustion Engiine I
COMBUSTION CHAMBER
PISTON
PISTON
External combustion engine
•
•
•
Steam engine
Stirling engine
Ericsson engine
Internal combustion engine (ICE)
•
•
•
•
Otto (gasoline) engine
Diesel engine
Gas turbine
Jet propulsion
US Navy Training Manual, Basic Machines
4
Reciprocating engine
also known as piston engine, converts linear motion to rotation
CYLINDER
PISTON
CONNECTING ROD
CRANKSHAFT
US Navy Training Manual, Basic Machines
5
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
COPRESSION STROKE
both valves
closed
exhaust valve
open
intake valve
closed
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
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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Ideal cycle for analysis
•
•
•
•
•
No friction
No pressure drop when unintended
No heat transfer when unintended
Internally reversible. Quasi-equilibrium cycle.
Externally irreversible. Heat transfer between the engine and
surroundings of finite difference in temperature.
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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
Quick review: air as an ideal gas of variable specific heat
Pv = RT, R = 0.2870kJ/kg×K
( )
u=u T
ds =
du P
+ dv
T T
P
s2 - s1 = s0 T2 - s0 T1 - R log 2
P1
( )
isentropic process
( )
P1 Pr (T1 )
=
,
P2 Pr (T2 )
( )
( )
v T
= r 1
v2 vr T2
v1
See section 7.9 for the use of this table
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Cold air-standard assumption
Model air as an ideal gas of constant specific heat at room temperature
(25°C).
Quick review: Ideal gas of constant specific heat
2 independent variables to name all states of thermodynamic equilibrium
6 functions of state: PTvush
2 constants: R = 0.2870 kJ/kg K, cv = 0.718 kJ/kg K
4 equations of state
Pv = RT
u = cvT
(
)
h = cv + R T
æT ö
v
s2 - s1 = cv log çç 2 ÷÷ + R log 2
v1
è T1 ø
isentropic process
Pvk = constant, Tvk-1 = constant, k = 1 +
R
= 1.4
cv
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Spark-ignition engine (gasoline engine, Otto engine)
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Cold air-standard Otto cycle
s
3
4
qin
2
qout
1
v
Ideal gas of constant specific heat
2 independent variables to name all states of thermodynamic equilibrium
5 functions of state: PTvus
2 constants: R, cv
3 equations of state
Pv = RT
u = cvT
æT ö
v
s2 - s1 = cv log çç 2 ÷÷ + R log 2
v1
è T1 ø
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Thermal efficiency of Otto cycle
Definition of compression ratio:
Conservation of energy:
V
r = BDC
VTDC
(
)
qin = u3 - u2 = cv T3 -T2 ,
(
qout = u4 - u1 = cv T4 -T1
)
wnet,out = qin - qout
Isentropic processes:
Definition of thermal efficiency:
Algebra:
æ v ök-1
= çç 1 ÷÷ = r k-1 ,
T1 è v2 ø
T2
hth, Otto =
wnet,out
æ v ök-1
= ç 4 ÷ = r k-1
T4 çè v3 ÷ø
T3
qin
hth, Otto = 1 -
T -T
1
=1- 4 1 =1qin
T3 -T2
r k-1
qout
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Compression-ignition engine (Diesel engine)
compression ratio:
cut-off ratio:
v
r= 1
v2
rc =
v3
v2
é k
1 ê rc -1
hth, Diesel = 1 r k-1 êë k rc -1
(
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)
ù
ú
ú
û
Plan
•
•
•
•
•
Internal combustion engines
Gas turbines
Stirling and Ericsson engines
Vapor power cycle
Refrigeration
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Gas turbine (Brayton cycle)
4 steady-flow components
Pressure ratio
P
qin
3
2
1
4
qout
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s
Gas turbine for jet propulsion
two thousand plus 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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Plan
•
•
•
•
•
Internal combustion engines
Gas turbines
Stirling and Ericsson engines
Vapor power cycle
Refrigeration cycle
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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 -
v2
ò
v1
æv ö
dv = R TH -TL log çç 2 ÷÷
v
è v1 ø
RTL
Specific gas constant
Gas
(
R=
Formula
Air
)
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
•
•
•
•
•
Internal combustion engines
Gas turbines
Stirling and Ericsson engines
Vapor power cycle
Refrigeration cycle
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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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Rankine cycle
4 steady-flow components
wpump,in = h2 - h1
qboiler,in = h3 - h2
wturbine,out = h3 – h4
qcondenser,out = h4 – h1
hthermal =
wturbine,out - wpump,in
qboiler,in
P
qboiler,in
2
3
wturbine,out
wpumo,in
1
qcondenser, out
4
s
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Plan
•
•
•
•
•
Internal combustion engines
Gas turbines
Stirling and Ericsson engines
Vapor power cycle
Refrigeration cycle
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Refrigerator and heat pump
4 steady-flow components
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.
•
•
•
Large enthalpy of vaporization
Sufficiently low freezing temperature
Sufficiently high critical temperature
Low condensing pressure
Do no harm: non-toxic, non-corrosive, non-flammable, environmentallyfriendly
Low cost
R-717 (Ammonia, NH3) used in industrial and heavy-commercial 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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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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