Heat Cycles, Heat Engines, & Real Devices
John Jechura – jjechura@mines.edu
Updated: January 4, 2015
Topics
• 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
Hot Reservoir @ TH
• Rankine cycle
QH
 Usually uses water (steam) as working fluid
Wnet
 Creates the majority of electric power used throughout the world
 Can use any heat source, including solar thermal, coal, biomass, & nuclear
QC
Cold Sink @ TC
• 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
th 
Wnet QH  QC

QH
QH
3
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
th 
QH  QC
QH
 th 
TH  TC
T
1 C
TH
TH
4
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
 PL 
TL
th  1   1   
TH
 PH 
 1/ 
5
Thermal Efficiency Ideal‐Gas Brayton Cycle
0.8
Argon, =1.7
0.7
Air, =1.4
Thermal Efficiency ()
0.6
0.5
0.4
0.3
Propane, =1.1
0.2
0.1
0
0
5
10
15
20
25
30
35
Compression Ratio (P2/P1)
6
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
th  1 
1
R
 1 
where R  V1 /V2 is the volumetric compression ratio
• This cycle ignores input of new air/fuel mixture, change in composition with combustion, & exhaust of combustion products
7
Thermal Efficiency Ideal‐Gas Otto Cycle
60%
600
50%
500
40%
400
30%
300
20%
200
10%
100
0%
Temperature [°C]
Thermal Efficiency
Inlet Conditions: 25°C & 1.0 bar
=1.3 (typical air+fuel)
0
0
5
10
15
20
25
Volumetric Compression Ratio
8
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
1    1 
th  1   1 

R
     1 
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
9
Thermal Efficiency Ideal‐Gas Diesel Cycle
80%
800
Inlet Conditions: 25°C & 1.0 bar
=1.4 (air)
=3.0
700
60%
600
50%
500
40%
400
30%
300
20%
200
10%
100
0%
Temperature [°C]
Thermal Efficiency
70%
0
0
5
10
15
20
25
Volumetric Compression Ratio
10
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)
11
Gasoline Thermal Efficiency Using Aspen Plus
25
1
100
0.00
B1
FUEL
7
HEATVAL
1
6052
1.00
HIERARCHY
FUELMIX
B2
W-12
W
25
1
384
24
2674
5952
6052
1.00
1.00
6487
1.00
AIR
MIX-HP
116
BURN-1
FLAMEVAL
2A
CMBSTGAS
HIERARCHY
B4
W-34
Temperature (C)
Pressure (bar)
Q-RESID
Molar Flow Rate (kmol/hr)
Vapor Fraction
Duty (kJ/sec)
Q
W
1544
25
7
6487
1
6487
1.00
0.89
LOSTHEAT
Power(kW)
EXHAUST
AMBIENT
• 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 12
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 th 
Wnet W‐TURBIN  W‐PUMP 
Q‐BOILER Qin
13
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
• 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
 Pressure chosen to match common TURBINE inlet pressures – 1500, 1800, & 2400 psig for large power applications
 Very complicated rotating machinery that can have multiple number of stages, multiple entry & extraction points, …
 Real isentropic efficiencies 75 – 90% at optimal flowrates
 Real isentropic efficiencies 70 – 90% at optimal flowrates
• Inefficiency causes temperature rise in water  Mechanical efficiency represents energy loss in drive train  May be designed to exhaust gas phase or water/steam phase (condensing turbine)  Mechanical efficiency represents energy loss in drive train 14
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
th 
W‐TURBIN  W‐PUMP 2789  29

 0.388
Q‐BOILER 7111
15
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
th 
W‐TURBIN  W‐PUMP 2092  36

 0.289
Q‐BOILER 7104
16
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 17
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
th 
 921  2465  34  0.341
 8555  1277 
18
Example Steam Turbine With Reheat
19
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
th 
1306  1414   34  0.336
7986
20
Example Steam Turbine With Heat Recycle
21