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Prospects for the Development of Low-Exergy-
Loss Chemical Engines
Chris Edwards, Kwee Yan Teh, Shannon Miller,
Matthew Svrcek
Department of Mechanical EngineeringStanford University
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32%32%
The Carnot MisconceptionReversible, Heat,
Isothermal/AdiabaticReversible, Matter, Isothermal
Reversible, Matter, Adiabatic
(Stirling, Ericsson)
(Fuel Cell+Electric Motor)
(I.C. Engines)
Stoichiometric hydrogen/air, To = 300 K
Fuel Cell Polarization Curve
Electrical Current Density i (A/m2)
Ele
ctric
al P
oten
tial φ
(V)
oE
E ReactantPreparationChannel Loss& UtilizationAnode Polar.Cathode Polar.
Ohmic Loss
Mass DiffusionRate Limit
Open Circuit Potential
Delivered Potential
Delivered PowerII
rev
W iW i
φ φη = = =&
& E E
The Carnot Misconception
CarnotReversible, IsothermalReversible,Adiabatic
Poor kinetics (polarization) is the key irreversibility in fuel cells.
PEM Fuel Cell
ImprovedKinetics
The Carnot MisconceptionReversible, Heat,
Isothermal/AdiabaticReversible, Matter, Isothermal
Reversible, Matter, Adiabatic
(Stirling, Ericsson)
(Fuel Cell+Electric Motor)
(I.C. Engines)
Stoichiometric hydrogen/air, To = 300 K
Nat. Gas
Dry Air Flue Gas
Shaft Work
3m
2a 4m2f
1f 1a 5m
1 2 3 4 5 60
10
20
30
40
50
Conversion Device
Exe
rgy
Loss
(%)
Device Key:1-Fuel Compressor2-Air Compressor3-Premixer4-Combustor5-Turbine6-Exhaust
Efficiency (LHV): 42.7Exergy Efficiency: 41.1
200 300 400 500 600 700 80030
35
40
45
50
55
Air-Specific Work (kJ/kg-air)
Firs
t-Law
Effi
cien
cy (%
LH
V)
10
204060
80100
10
20
4065100125
150
10
20
40
65100150
200
1600 K1800 K2000 K
1 2 3 4 5 60
10
20
30
40
Conversion Device
Exe
rgy
Loss
(%)
Device Key:1-Fuel Compressor2-Air Compressor3-Premixer4-Combustor5-Turbine6-Exhaust
Efficiency (LHV): 48.4Exergy Efficiency: 46.5
GT Exergy Loss
The Carnot Misconception
Unrestrained reaction is the key irreversibility in I.C. engines.
CarnotReversible, IsothermalReversible,Adiabatic
Brayton, 50:1Pressure Ratio
EnergyDensity
The Carnot Misconception
CarnotReversible, IsothermalReversible,Adiabatic
In neither case are conclusions based on Carnot of relevance.
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 in the limit of infinitesimal rate and constrained
chemical pathway (chemical reversibility).
Change of Restraints• Removal of an internal restraint generates entropy.
• Entropy generation from a change of external restraintsdepends on the rate wrt internal equilibration processes.
Inherently irreversible(exergy destroyed)
Irreversibility dependsupon the relative rates
t
S InternalRestraintRemoved
Systemstate(s)
1, 1
Systemstate
2
Systemstate notdefined
S=Sgen
U ,V ,Ni
Phase Phase U ,V ,Ni
t
S ExternalRestraintChanged
Systemstate
1
Systemstate
2
U ,V ,Ni
S - SP,0 (kJ/kg
fuel -K)
U-U
P,0
(MJ/
kgfu
el)
P increases
T increases
Reactants (frozen)
Products (with full
dissociation)
Unrestrained Reaction
Stoichiometric propane/air, adiabaticFrozen reactants (no dissociation)Equilibrium products (full dissociation)
Isobars: 0.1, 1, 10, 100 bar Reactant Isotherms: 1000, 2000 KProduct Isotherms: 1000, 2000, 3000 K
log10 (V/VP,0)
Exergy Destruction via Unrestrained Reaction
Stoichiometric propane/air mixture modeled as ideal gases. Isochoric, adiabatic combustion.Includes the effects of variable specific heats, reaction, & dissociation.
Efficiency by Extreme Compression
?
Extreme-Compression Post-Combustion Conditions
Stoichiometric propane/air mixture modeled as ideal gases. Includes the effects of variable specific heats, reaction, & dissociation.
3300K! 1000 bar!
Extreme Compression Concept
• High compression ratio, ~100:1
• Two pistons (balanced forces)
• High speeds, M~0.3 (reduced time for heat transfer)
- air at 300 K, speed of sound ~ 350 m/s 100 m/s
- for reference: 3000 RPM and 90 mm stroke 9 m/s
Proof-of-Concept Apparatus
Modeling the Concept
0 0.05 0.1 0.15 0.2 0.250
2
4
6
8
10
12
Pisto
n Po
sitio
n (m
)
Time (s)
0 0.05 0.1 0.15 0.2 0.25-200
-150
-100
-50
0
50
100
150
Pisto
n Sp
eed
(m/s)
Time (s)
Single piston, w/out combustion, CR 100:1
0 0.05 0.1 0.15 0.2 0.250
0.5
1
1.5
2
2.5
3
Mas
s (kg
)
Time (s)
0 0.05 0.1 0.15 0.2 0.250
100
200
300
400
500
600
Pres
sure
(bar
)
Time (s)
Combustion ChamberDriverReservoir
Junkers Free-Piston Compressor
Van Blarigan/Aichlmayr Linear Alternator Concept
Prototype Schematic
• Specifications:50:1 CR150 m/s max PSnon-combusting
• Testing: Piston ringsPoppet valve jitterPosition sensing
Restrained Reaction• The objective is a reaction architecture that is reversible
in the limit of infinitesimal rate.• Internal restraints are not permitted.
– The fluid is either chemically frozen throughout the process (inert) or in chemical equilibrium.
• External restraints are absolutely required.– Work provides an entropy-free interaction.– Heat provides an entropic interaction.– Matter provides a mixed mode of interaction.
• By varying the external restraints, the reactants may be “reversibly” transformed to products.
A Restrained Chemical Engine
Heat
HumidAir
Water and�Depleted Air
NafionWork
Protons Electrons
Hydrogen
M
2
2, ,
• 2 2
2
Anode:
2gas a nafion a anodeH H e
H H e
μ μ μ+ −
+ −+
= +% %
2 2
2 2, , ,
• 2 2 0.5
2 2 0.5
Cathode: nafion c cathode gas c gas c
O H OH e
H e O H O
μ μ μ μ+ −
+ −+ +
+ + =% %
2 2 2
2 2 2
(
, ,
, , ,
, ,
Chemical Affinity)
,
•
2 0
Nafion connected, open circuit to motor:
.5 2
0.5r overall
nafion anode nafion cathodeH Hgas a cathode gas c anode gas cH O H Oe e
gas a gas c gas cH O O
G
H
μ μ
μ μ μ μ μ
μ μ
+ +
− −
−Δ =−
=
+ + = +
+ −
% %
% %
14442A
( )( )2
2cathode anode
anode cathodee e
F φ φ
μ μ− −
−
= −% %4443 144424443
A Restrained Reaction Engine w/out Electrochemistry?
)()(
),(),(
),(),(
22
22
22
chamberreactionOHcylinderOH
chamberreactionaqOcylindergO
chamberreactionaqHcylindergH
μμμμμμ
===
122 2 2
Gibbs-Duhem: d sdTH O
PH O
vdμ = − ++
10-2
10-1
100
101
102
103
104
105
106
-350
-300
-250
-200
-150
-100
-50
0
50
P/P0
μ (k
J/m
ol)
Chemical Equilibrium, 300K
H2 (kJ/molH2) O2 (kJ/molO2)
H2 + ½ O2 (kJ/molReaction)
Incompressible H2O(l)(kJ/molH2O)
H2 + ½ O2 H2O
Po = 1 bar
Pressure Retarded Osmosis
Sat. NaCl: πο = 380 atm Dead Sea: πo > 500 atm
Osmotic PotentialsΔμosmotic = VA × π0, where VA is the molar volume of pure solvent A,
and π0 is osmotic pressure of the solution wrt A.Assumes: - constant T and VA
- limit process: osmosis proceeds until the solution is infinitely dilute
For liquid water as solvent A, Vwater(l) = 1.8 ×10−5 m3 [mol water (l)]−1
2.5×10 0241 .1.3×10+5H2 + ½O2 → H2O>9.5×10−3>0.9 .>500Dead Sea
7.2×10−30.6 .380Sat. NaCl4.7×10−40.0425Typ. sea water
(eV)Δμosmotic (kJ mol−1)π0 (atm)
Conclusions• Efficiency of simple-cycle engines can be more than
doubled—current exergy efficiencies are less than 50%.• The key to systematically improving engine efficiency
(both simple and compound) is exergy management.• Exergy destruction due to combustion must be reduced.
This can be achieved by positioning of reactants to states of extreme energy density.
• Restrained reaction is possible electrochemically. Reducing irreversibilities due to slow kinetics (reaction and transport) is the key.
• Possibility exists for a non-electrochemical, restrained reactive engine. Making it practical remains a challenge.