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• Heat engines / heat cycles
Review of ideal‐gas efficiency equations
Efficiency upper limit – Carnot Cycle
• Water as working fluid in Rankine Cycle
Role of rotating equipment inefficiency
• Advanced heat cycles
Reheat & heat recycle
• Organic Rankine Cycle
• Real devices
Gas & steam turbines
2
Heat Engines / Heat Cycles• Carnot cycle
Most efficient heat cycle possible
• Rankine cycle
Usually uses water (steam) as working fluid
Creates the majority of electric power used throughout the world
Can use any heat source, including solar thermal, coal, biomass, & nuclear
• Otto cycle
Approximates the pressure & volume of the combustion chamber of a spark‐ignited engine
• Diesel cycle
Approximates the pressure & volume of the combustion chamber of the Diesel engine
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Hot Reservoir @ TH
Cold Sink @ TC
QH
QC
Wnet
net H Cth
H H
W Q QQ Q
Carnot Cycle
• Most efficient heat cycle possible
• Steps
Reversible isothermal expansion of gas at TH. Combination of heat absorbed from hot reservoir & work done on the surroundings.
Reversible isentropic & adiabatic expansion of the gas to TC. No heat transferred & work done on the surroundings.
Reversible isothermal compression of gas at TC. Combination of heat released to cold sink & work done on the gas by the surroundings.
Reversible isentropic & adiabatic compression of the gas to TH. No heat transferred & work done on the gas by the surroundings.
• Thermal efficiency
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1H C H C Cth th
H H H
Q Q T T TQ T T
Rankine/Brayton Cycle
• Different application depending on working fluid
Rankine cycle to describe closed steam cycle.
Brayton cycle approximates gas turbine operation.
• Steps
Heat at constant PH. Heat absorbed from hot reservoir & no work done.
Isentropic & adiabatic expansion to PL. Work done on surroundings.
Cool at constant PL. Heat released to cold sink & no work done.
Isentropic & adiabatic compression to PH. Work done on fluid by surroundings.
• Ideal gas thermal efficiency – not appropriate for condensing water
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1 /
1 1L Lth
H H
T PT P
Thermal Efficiency Ideal‐Gas Brayton Cycle
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0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 5 10 15 20 25 30 35
Compression Ratio (P2/P1)
Thermal Efficiency ( )
Air, =1.4
Argon, =1.7
Propane, =1.1
Otto Cycle
• Steps
Reversible isentropic compression from V1 to V2. No heat transferred & work done on the fluid. Initial conditions are TL & PL.
Heat at constant volume. Heat absorbed from hot reservoir & no work done.
Reversible isentropic & adiabatic expansion from V2 to V1. No heat transferred & work done by the fluid on the surroundings.
Cool at constant volume to TL with resulting pressure PL. Heat released to cold sink & no work done.
• Thermal efficiency – ideal gas
• This cycle ignores input of new air/fuel mixture, change in composition with combustion, & exhaust of combustion products
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1 21
11 where /V is the volumetric compression ratioth R V
R
Thermal Efficiency Ideal‐Gas Otto Cycle
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0%
10%
20%
30%
40%
50%
60%
0 5 10 15 20 25
Volumetric Compression Ratio
Ther
mal
Eff
icie
ncy
0
100
200
300
400
500
600
Tem
per
atu
re [
°C]
Inlet Conditions: 25°C & 1.0 bar=1.3 (typical air+fuel)
Diesel Cycle
• Steps
Reversible isentropic compression from V1 to V2. No heat transferred & work done on the fluid. Initial conditions are TL & PL.
Heat at constant pressure. Heat absorbed from hot reservoir & no work done. Volume increases from V2 to V3.
Reversible isentropic & adiabatic expansion from V3 to V1. No heat transferred & work done by the fluid on the surroundings.
Cool at constant volume to TL with resulting pressure PL. Heat released to cold sink & no work done.
• Thermal efficiency – ideal gas
where R=V1/V2 (the compression ratio) & =V3/V2 (the cut‐off ratio).
• This cycle ignores input of new air, injection of fuel, change in composition with combustion, & exhaust of combustion products
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1
1 11
1th R
Thermal Efficiency Ideal‐Gas Diesel Cycle
10
0%
10%
20%
30%
40%
50%
60%
70%
80%
0 5 10 15 20 25
Volumetric Compression Ratio
Ther
mal
Eff
icie
ncy
0
100
200
300
400
500
600
700
800
Tem
per
atu
re [
°C]
Inlet Conditions: 25°C & 1.0 bar=1.4 (air)
=3.0
Example: Actual Gasoline Engine Thermal Efficiency
• BMW M54B30 (2,979 cc) engine stated to produce 228 hp @ 5900 rpm (with 10.2:1 compression ratio)
• Calculation steps to determine thermal efficiency
Unit conversion: 228 hp = 10,200 kJ/min 1.729 kJ/rev
2 revolutions needed for full volume displacement: 1.161 kJ/L
Air+fuel mix has LHV of 3.511 kJ/L (ideal gas)
• Assumptions
o Characterize air as 21 mol% O2 / 79 mol% N2 & gasoline as isooctane (iC8, C8H18, LHV of 5065 kJ/mol)
o Air+fuel mix an ideal‐gas stoichiometric mixture of @ 1.0 bar & 25°C
o Air+fuel mix molar density is 0.0403 mol/L (i.g.) with 1.72 mol% iC8
• Thermal efficiency is 33% at these stated conditions
Ideal‐gas Otto Cycle shows upper limit of 50.2% (=1.3)
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Gasoline Thermal Efficiency Using Aspen Plus
• 44.7% thermal efficiency assuming isentropic compression & expansion
Care must be taken to calculate heats & works from internal energy values, not enthalpy values
iC8 as model gasoline component
10:1 volumetric compression ratio
33% thermal efficiency & 33% lost heat to exhaust using 89% isentropic efficiency & 5% mechanical losses during compression & expansion
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HIERARCHY
FLAMEVAL
HIERARCHY
HEATVAL
3842460521.00
MIX-HP 2A
2511000.00
FUEL
Q-RESID
Q
267411664871.00
CMBSTGAS
251
59521.00
AIR
71
60521.00FUELMIX
W-12W
15447
64871.00
EXHAUST
W-34W
BURN-1
B1
B2
B4
Temperature (C)
Pressure (bar)
Molar Flow Rate (kmol/hr)
Vapor Fraction
Duty (kJ/sec)
Power(kW) LOSTHEAT
251
64870.89
AMBIENT
Water as Working Fluid in Rankine Cycle
• Aspen Plus flowsheet
Flow system
• Energy considerations from enthalpy, not internal energy
Cycle represented by once‐through flow system
• LP‐WATER must match conditions of LP‐WATR2
• “Out” direction of Energy & Work streams represent calculated values
• Can use arbitrary flow rate for thermal efficiency calculation
Thermal efficiency from heat & work values
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W‐TURBIN W‐PUMP Q‐BOILER
netth
in
WQ
Typical operating parameters• TURBINE exhaust fully condensed in CONDSR
Outlet saturated liquid (i.e., vapor fraction is zero) or subcooled
• No vapor to PUMP to prevent cavitation
Temperature controlled by available cooling media
• 15 – 35oC (60 – 95oF) typical for cooling water
• 45 – 50oC (110 – 125oF) typical for air cooling
Pressure will “float” to match this saturation temperature
• PUMP increases pressure of water to high‐pressure conditions
Pressure chosen to match common TURBINE inlet pressures – 1500, 1800, & 2400 psig for large power applications
Real isentropic efficiencies 75 – 90% at optimal flowrates
• Inefficiency causes temperature rise in water
Mechanical efficiency represents energy loss in drive train
• BOILER increases temperature & changes phase (liquid vapor)
At minimum, exit at saturated vapor conditions (i.e., vapor fraction is one).
May be superheated to much higher temperature.
Exit temperature controlled by heat source available & materials of construction – maximum about 420 –580oC (790 – 1075oF)
• Highest temperatures require expensive nickel & cobalt alloys
• Shaft work produced in TURBINE when pressure of steam let down to CONDSR inlet conditions
Very complicated rotating machinery that can have multiple number of stages, multiple entry & extraction points, …
Real isentropic efficiencies 70 – 90% at optimal flowrates
May be designed to exhaust gas phase or water/steam phase (condensing turbine)
Mechanical efficiency represents energy loss in drive train
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Example #1 Steam Turbine Operation• Operating conditions
Condenser outlet saturated liquid @ 35oC
• No pressure loss through exchanger
Pump outlet 1500 psig
• Ideal compression
Boiler outlet saturated vapor
• No pressure loss through exchanger
Turbine
• Ideal expansion
No pressure losses through piping
No mechanical losses in rotating equipment
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W‐TURBIN W‐PUMP 2789 29 0.388 Q‐BOILER 7111th
Example #2 Steam Turbine Operation• Operating conditions
Condenser outlet saturated liquid @ 35oC
• No pressure loss through exchanger
Pump outlet 1500 psig
• 80% isentropic efficiency
Boiler outlet saturated vapor
• No pressure loss through exchanger
Turbine
• 75% isentropic efficiency
No pressure losses through piping
No mechanical losses in rotating equipment
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W‐TURBIN W‐PUMP 2092 36 0.289 Q‐BOILER 7104th
Advanced Heat Cycles
• Reheat
Multiple step expansion, turbine exhaust reheated before next step
Keep the steam gas‐phase for as much of the process as possible
Increased thermal efficiency with increased capital cost
• Heat recycle
Multiple step expansion, turbine exhaust split before next step
• Majority sent to low‐pressure turbine
• Remainder condensed against the high‐pressure boiler feed water
Trades off the heat of vaporization relative to power from expansion process
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Example Steam Turbine With Reheat• Operating conditions
Condenser outlet saturated liquid @ 45oC
• No pressure loss through exchanger
Pump outlet 120 bar‐a
• Ideal compression
Boiler outlet 150oC superheat
• No pressure loss through exchanger
Turbine intermediate 24 bar
• 80% isentropic efficiency
Reheat to 475oC
• No pressure loss through exchanger
No pressure losses through piping
No mechanical losses in rotating equipment
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921 2465 34
0.3418555 1277th
Example Steam Turbine With Reheat
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Example Steam Turbine With Heat Recycle• Operating conditions
Condenser outlet saturated liquid @ 45oC
• No pressure loss through exchanger
Pump outlet 120 bar‐a
• Ideal compression
Boiler outlet 150oC superheat
• No pressure loss through exchanger
Turbine intermediate 10 bar
• 80% isentropic efficiency
10% split to recycle
No pressure losses through piping
No mechanical losses in rotating equipment
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1306 1414 340.336
7986th
Example Steam Turbine With Heat Recycle
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