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

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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

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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

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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

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0.8

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1

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1.2

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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

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0

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1

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s-si (kJ/kg

mixK)

h-h

i(M

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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

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1400

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ecie

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on

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(p

pm

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NOx (ppm)

HC (ppmC1)

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0.25

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0.35

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0.45

So

ot

Sig

nal

(-l

n(I

/I0))

Diesel-Style CombustionIsooctane, 35:1 CR

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Sp

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CO2

CO

O2

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Percent CO

So

ot

Sig

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(-l

n(I

/I0))

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0.5

Percent of Fuel Carbon in Gas Emissions

So

ot

Sig

nal

(-l

n(I

/I0))

Diesel-Style CombustionIsooctane, 35:1 CR

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50

100

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200

CR

Sp

ecie

s C

on

cen

trat

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HC (ppmC1)

CO (ppm*10)

Diesel-Style CombustionDiesel #2, = 0.48

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Compression ratio

Co

mb

ust

ion

eff

icie

ncy

(%

)

Diesel, = .48

i-Octane, = .48 (interpolated)

Diesel-Style CombustionDiesel #2, = 0.4

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500

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CR

NO

x C

on

cen

trat

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(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

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102

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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