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Realizing Ultra-High-Efficiency Engines:
Understanding Limits
and Overcoming Limitations
Chris F. Edwards
Sankaran Ramakrishnan, Matthew Svrcek, Greg
Roberts, J.R. Heberle, Paul Mobley, Adelaide
Calbry-Muzyka, Rebecca Pass
Advanced Energy Systems Laboratory
Department of Mechanical Engineering
Stanford University
0.1
1.0
10.0
100.0
1600 1700 1800 1900 2000 2100
Time (Years A.D.)
Fir
st-
Law
Eff
icie
ncy (
%)
.
Savery, Newcomen (
Engine Essentials—Outside the Box
• All engines have three essential features– they produce work (by definition)
– they require a resource (1st Law)
– they reject entropy (and therefore energy) to their surroundings (2nd Law)
Engine WorkEnergy
Resource
RejectedEntropy
(Surroundings)
Engine Essentials—Inside the Box
• There are only two types of internal function
– transfers: moving energy around within the box
– transformations: energy rearrangement between storage modes or transfers
WorkEnergy
Resource
RejectedEntropy
Engine Essentials—Transfers and Storage Modes
• There are only four ways to transfer energy:– work (entropy-free transfer of energy)– heat (energy transfer due to DT )– matter (internal and external energy)– radiation (thermal, non-thermal)
• Storage can be of only two types:– radiation (cavity modes/photon density)– matter (sensible, latent, chemical, nuclear, kinetic,
gravitational PE, electrical PE, elastic strain PE, etc.)
The design space of engines is sufficiently small and well-enumerated that it can be analyzed systematically.
The Exergy Limit:
• Obeys 1st Law
• Constrained by 2nd Law • Combine 1st and 2nd law
• Max work iff reversible.
Engine WorkEnergy
Resource
RejectedEntropy
(Surroundings)
Fuel Conversion Efficiency potential (maximum first-law efficiency based on LHV) of most fuels is ~100%.
TransfersTransformations
Destruction
An Exergetic View of Engines
• All engines have four essential features:– they produce work (pure exergy)
– they require an exergetic resource (exergy balance)
– they destroy exergy (2nd Law, zero only in reversible limit)
– they transfer exergy to the environment (zero in limit of all entropy rejected with non-exergetic energy)
Work(Exergy)
ExergeticResource
ExergeticEnergy Transfer
(Environment)
Non-exergeticEnergy Transfers
Spanning Exergy to Engines
Limits are imposed by the resource, environment, and physics governing transfers
and transformations.
Limitations are introduced by the choice of devices and processes—i.e., by the architecture of an engine.
ChemicalResource
RestrainedReaction
Electrostatic Work
Batch Expansion
FlowWork
UnrestrainedReaction
Batch Expansion
Flowing Expansion
Lorentz Work(MHD)
Exergy Classification Architecture Engines
Exergy-to-Architecture Example• Choose a chemical resource (e.g., nat. gas) from which
you wish to extract work by connecting it with a portion of the environment (e.g., the atmosphere).
• Choose unrestrained reaction (e.g., combustion) to transform the chemical energy to sensible energy, and transform that to work (e.g., via flowing expansion).
• Choose an architecture that incorporates use of a steady-flow burner for the first transformation and a gas turbine for the second.
• These two device choices require inclusion of a compressor (pressure difference), that in turn requires an internal transfer of work (turbine to compressor).
ExergyLimit
ClassificationLimits
ArchitecturalLimitations
ArchitecturalRequirements
Using Horlock’s notation, this architecturemight be described as being of the “CBT”
family—Compressor, Burner, Turbine.W
NG
FG(Atm.)
C
B
T T
Air
Optimal Architecture
• Optimal in what sense?– For us, efficiency.
(In exergy terms, minimizing total irreversibility.)– But always as a trade-off with specific work.
(Think carpet plots or Pareto fronts.)
• Subject to what constraints?– Choices of resource, classification, and environment– Device availability (i.e., must actually exist)– Device metrics (e.g., polytropic efficiency)– Device limitations (e.g., temperature cap)
The CBT FamilyOptimal: CB(TB)nT
CB(TB)nT – Efficiency vs. PR
Directed Evolution of Architectures
• Specify resource and environment (Exergy)
• Specify transfers and transformations to be invoked (Classification) and an initial set of devices and system configuration (Architecture)
• Optimize architecture using a combination of analytical and numerical techniques
• Selectively introduce new degrees of freedom(Classification) or new devices (Architecture) and re-optimize.
The CBTX FamilyOptimal: CXinB(TB)nTXout
Effect of Heat ExchangerTemperature Limit
The CBTXI FamilyOptimal: (CI)mXinB(TB)nTXout
Modern Art
Take-Home Messages
• A systematic approach to engine design is possible. It is no longer a matter of inspiration or invention.
• A clear understanding of the limits from physics for energy transfers and transformations is essential. These lead to viewing engine design as an exercise in exergy mgt.
• Intermediaries between (abstract) exergy and (concrete) engines, such as Classification and Architecture can be useful tools in understanding engine design.
• A combination of architecture Optimization and Directed Evolution seems to provide both a systematic and useful path for identifying architectural limitations and thereby providing a path toward ultra-high-efficiency engines.
Commercials(Three posters)
20
Extreme Compression: Initial Results
10 20 30 40 50 60 70 80 90 100
30
40
50
60
70
80
90
Compression Ratio
Eff
icie
ncy
(%
)
First law (per LHV), = 0.35
70-80% first law
Combustion data
Theoretical efficiency with air losses
Low blowby
53%, 20°C walls
Losses in air
experiments
Additional
losses due to
combustion
• Confident we can demonstrate 60% indicated
• Speculate 70% is achievable regeneratively
Diesel #2
Extreme Compression: New Data
• Have demonstrated 60% indicated
• Speculate 70% is achievable regenerativelyDiesel #2
= 0.27–0.30
Combustion in Supercritical Water
0 500 1000 1500 2000 2500300
350
400
450
500
550
600
650
700
750
Products-Specific Enthalpy, kJ/kg-Products
T, K
Combustion Products
Regenerator Cold Streams
MP Desal. & Preheat
MP Brine & Vapor
LP Desal. & Preheat
0 50 100 150 200 250
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Oxygen Exit Pressure, Bar
Energ
y Inte
nsity, M
J/k
g O2
GOX ASU
LOX ASUAir NitrogenOxygen
LOX
Pump
HX 1
LP
MP HP HX 2
High
Press.
Col.
Low
Press.
Col.
SRCCS low-pressure range
AQUIFER BRINEINJECTANT
Lift
Pump
Injection
Pump
COAL
Slurry
Prep.
AIRASU
NITROGEN
MP
Pump
LP
Pump
HP
Pumps
Slurry
Pump
Regenerator
MP Desal.
Products
Stream
To SCWO
System
OxygenLP Desal.
The CBTQ Family
0 0.5 1 1.5-1
-0.5
0
0.5
1
1.5
s-si (kJ/kg
mixK)
h-h
i(M
J/k
gm
ix)
Tcap
1800 K, 0.43, n 20, PR 250:1 poly
0.9
CB(TB)nT
CB(QB)n(TQ)
nT
Relative Merit of Internal, Forward Heat Transfer
Merit of Internal, Backward Heat Transfer
Optimal architecture: CQ(QB)n(TQ)nTQ or CQB(TB)nTQ
All work must be extracted prior to heat transfer
Merit of External, Environmental Heat Transfer—Intercooling
Intercooled Attractor
Experimental Apparatus
33
Operating Space
Combustion Visualization
CR = 30:1 CR = 100:1
#2 Diesel, 1 ms injection duration, finishing at TDC
Diesel-Style CombustionIsooctane, 35:1 CR
0.4 0.5 0.6 0.7 0.8
200
400
600
800
1000
1200
1400
Sp
ecie
s C
on
cen
trat
ion
(p
pm
)
NOx (ppm)
HC (ppmC1)
0.4 0.5 0.6 0.7 0.8
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
So
ot
Sig
nal
(-l
n(I
/I0))
Diesel-Style CombustionIsooctane, 35:1 CR
0.4 0.5 0.6 0.7 0.8-2
0
2
4
6
8
10
12
14
Sp
ecie
s C
on
cen
trat
ion
(%
)
CO2
CO
O2
0.4 0.5 0.6 0.7 0.884
86
88
90
92
94
96
98
100
Co
mb
ust
ion
eff
icie
ncy
(%
)
0 0.5 1 1.5 20
0.1
0.2
0.3
0.4
0.5
Percent CO
So
ot
Sig
nal
(-l
n(I
/I0))
96 97 98 99 100 1010
0.1
0.2
0.3
0.4
0.5
Percent of Fuel Carbon in Gas Emissions
So
ot
Sig
nal
(-l
n(I
/I0))
Diesel-Style CombustionIsooctane, 35:1 CR
50 60 70 80 90 1000
50
100
150
200
CR
Sp
ecie
s C
on
cen
trat
ion
HC (ppmC1)
CO (ppm*10)
Diesel-Style CombustionDiesel #2, = 0.48
30 40 50 60 70 80 90 10095
96
97
98
99
100
Compression ratio
Co
mb
ust
ion
eff
icie
ncy
(%
)
Diesel, = .48
i-Octane, = .48 (interpolated)
Diesel-Style CombustionDiesel #2, = 0.4
50 60 70 80 90 1000
500
1000
1500
2000
2500
CR
NO
x C
on
cen
trat
ion
(p
pm
)
Spanning Exergy to Engines
ChemicalResource
RestrainedReaction
Electrostatic Work
Batch Expansion
FlowWork
UnrestrainedReaction
Batch Expansion
Flowing Expansion
Lorentz Work(MHD)
Exergy Classification Architecture Engines
Engine design is an exercise in exergy management.
Classification and Architecture can be useful intermediates in bridging from exergy to engines.
Chemical Exergy of Some FuelsFuel Chemical Chem. Exergy† DH° Reaction* DG° Reaction* DS° Reaction* Exergy
Species+ Formula MJ per fuel MJ per fuel MJ per fuel kJ/K per fuel to LHV
kmol kg kmol kg kmol kg kmol kg Ratio
Methane CH4 832 51.9 -803 -50.0 -801 -49.9 -5.2 -0.33 1.037
Methanol CH3OH 722 22.5 -676 -21.1 -691 -21.6 50.4 1.57 1.068 Carbon Monoxide CO 275 9.8 -283 -10.1 -254 -9.1 -98.2 -3.51 0.971 Acetylene C2H2 1267 48.7 -1257 -48.3 -1226 -47.1 -104.6 -4.02 1.008 Ethylene C2H4 1361 48.5 -1323 -47.2 -1316 -46.9 -25.2 -0.90 1.029 Ethane C2H6 1497 49.8 -1429 -47.5 -1447 -48.1 60.5 2.01 1.048 Ethanol C2H5OH 1363 29.6 -1278 -27.7 -1313 -28.5 117.7 2.56 1.067 Propylene C3H6 2001 47.6 -1926 -45.8 -1937 -46.0 36.6 0.87 1.039 Propane C3H8 2151 48.8 -2043 -46.3 -2082 -47.2 129.2 2.93 1.053 Butadiene C4H6 2500 46.2 -2410 -44.5 -2421 -44.7 36.9 0.68 1.038 i-Butene C4H8 2644 47.1 -2524 -45.0 -2560 -45.6 120.2 2.14 1.047 i-Butane C4H10 2800 48.2 -2648 -45.6 -2712 -46.7 214.4 3.69 1.058
n-Butane C4H10 2805 48.3 -2657 -45.7 -2717 -46.7 200.0 3.44 1.056 n-Pentane C5H12 3460 48.0 -3272 -45.3 -3353 -46.5 271.3 3.76 1.057 i-Pentane C5H12 3454 47.9 -3265 -45.2 -3347 -46.4 277.0 3.84 1.058 Benzene C6H6 3299 42.2 -3169 -40.6 -3190 -40.8 69.4 0.89 1.041 n-Heptane C7H16 4769 47.6 -4501 -44.9 -4625 -46.2 415.0 4.14 1.060 i-Octane C8H18 5422 47.5 -5100 -44.7 -5259 -46.0 531.4 4.65 1.063 n-Octane C8H18 5424 47.5 -5116 -44.8 -5261 -46.1 487.1 4.26 1.060 Jet-A C12H23 7670 45.8 -7253 -43.4 -7440 -44.5 626.4 3.74 1.057 Hydrogen H2 236 117.2 -242 -120.0 -225 -111.6 -56.2 -27.88 0.977
+All species taken as ideal gases. †Environment taken as: 25°C, 1 bar, 363 ppm CO2, 2% H2O, 20.48% O2, balance N2 .
*Reaction with stoichiometric air at 25°C, 1 bar. All products present as ideal gases, including water.
Fuel Conversion Efficiency potential (maximum first-law efficiency based on LHV) of most fuels is ~100%.
Two Approaches to Reaction
• Unrestrained– Reactants are initially internally restrained, i.e., frozen in chemical
non-equilibrium (e.g. combustion, fuel reforming).
– Internal restraint is released, allowing reaction to proceed.
– Reaction “stops” when equilibrium is achieved or kinetics are so slow as to be negligible (frozen again).
– Inherently irreversible.
• Restrained– Reactants are initially externally restrained, i.e., in chemical
equilibrium (e.g. electrochemistry, solution chemistry).
– External restraints are changed, allowing reaction to proceed.
– Never stops; always dynamically balanced.
– Reversible only in the limit of infinitesimal rate and constrained chemical pathway (chemical reversibility).
Restrained vs. Unrestrained
* After Primus, et al. “Proceedings of International Symposium on Diagnostics and Modeling of Combustion in Reciprocating Engines, (1985) p.529-538.
Restrained (SOFC) Unrestrained (DI Diesel*)
• Efficiency declines with load
• Irreversibility reduced via facile kinetics (reaction and transport)
• Efficiency improves with load
• Irreversibility reduced by reaction at extreme states
Exergy Destruction via Reaction
Stoichiometric propane/air mixture modeled as ideal gases. Includes the effects of variable specific heats, reaction, & dissociation.
47
Restrained/Unrestrained Expansion
maxoutW W maxoutW W
48
Restrained/Unrestrained Reaction
maxoutW W maxoutW W
RestrainedReaction
UnrestrainedReaction
49
Implementing Restrained Reaction
2 2
1 1
0
if is small for a given d
will be small
lost destroyed gen
i i
igen
piston
gen
W X T S
AS d d
T T
dx d
A
T
S
The rate of change of the restraint must be slow compared to the internal relaxation time of the resource in order to be
fully restrained (reversible).
Efficiency Achievable by Compression
* Premixed, stoichiometric, ideal gas i-octane and air, including variable properties, dissociated products, and equilibration during expansion.
100
101
102
0
10
20
30
40
50
60
70
80
max
/0 (Effective Compression Ratio)
Eff
icie
ncy (
per
LH
V,
%)
Otto 1st-Law Limit*
Our Goal
Duratec HE
Prius (engine)
VW TDI HCCI
VW TDI
Sulzer RT-flex
Jumo 205 (1934)
FPEC 2010
Efficiency vs. number of stages
Efficiency vs. equivalence & pressure ratios