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
QC
Can use any heat source, including solar thermal,
coal, biomass, & nuclear Cold Sink @ TC
• Otto cycle
Approximates the pressure & volume of the
combustion chamber of a spark‐ignited engine
• Diesel cycle Wnet QH QC
th
QH QH
Approximates the pressure & volume of the
combustion chamber of the Diesel engine
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
QH QC TH TC T
th th 1 C
QH 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
1/
TL PL
th 1 1
TH PH
5
Thermal Efficiency Ideal‐Gas Brayton Cycle
0.8
Argon, =1.7
0.7
Air, =1.4
0.6
Thermal Efficiency ()
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
1
th 1 1
where R V1 /V2 is the volumetric compression ratio
R
• 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
Inlet Conditions: 25°C & 1.0 bar
=1.3 (typical air+fuel)
50% 500
40% 400
Thermal Efficiency
Temperature [°C]
30% 300
20% 200
10% 100
0% 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)
70% =3.0 700
60% 600
50% 500
Thermal Efficiency
Temperature [°C]
40% 400
30% 300
20% 200
10% 100
0% 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
7
HEATVAL
FUEL 1
HIERARCHY 6052
FUELMIX 1.00
B2
W
W-12
25 384 2674
1 24 116
5952 6052 6487
1.00 1.00 1.00
BURN-1
FLAMEVAL
AIR MIX-HP 2A CMBSTGAS
HIERARCHY
B4
W
Temperature (C) W-34
Pressure (bar) 1544 25
Molar Flow Rate (kmol/hr) Q-RESID 7 1
Vapor Fraction
6487 6487
Q 1.00 0.89
Duty (kJ/sec)
Power(kW) LOSTHEAT
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
Wnet W‐TURBIN W‐PUMP
th
Qin Q‐BOILER
13
Typical operating parameters
• TURBINE exhaust fully condensed in CONDSR • BOILER increases temperature & changes phase
Outlet saturated liquid (i.e., vapor fraction is zero) or (liquid vapor)
subcooled At minimum, exit at saturated vapor conditions (i.e.,
• No vapor to PUMP to prevent cavitation vapor fraction is one).
Temperature controlled by available cooling media May be superheated to much higher temperature.
• 15 – 35oC (60 – 95oF) typical for cooling water Exit temperature controlled by heat source available
& materials of construction – maximum about 420 –
• 45 – 50oC (110 – 125oF) typical for air cooling 580oC (790 – 1075oF)
Pressure will “float” to match this saturation • Highest temperatures require expensive nickel &
temperature cobalt alloys
• PUMP increases pressure of water to high‐ • Shaft work produced in TURBINE when pressure of
pressure conditions steam let down to CONDSR inlet conditions
Pressure chosen to match common TURBINE inlet Very complicated rotating machinery that can have
pressures – 1500, 1800, & 2400 psig for large power multiple number of stages, multiple entry &
applications extraction points, …
Real isentropic efficiencies 75 – 90% at optimal Real isentropic efficiencies 70 – 90% at optimal
flowrates flowrates
• Inefficiency causes temperature rise in water May be designed to exhaust gas phase or
water/steam phase (condensing turbine)
Mechanical efficiency represents energy loss in drive
train 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
W‐TURBIN W‐PUMP 2789 29
th 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
W‐TURBIN W‐PUMP 2092 36
th 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
