Understanding: di The Path to High- Efficiency Chemical Engines Chris F. Edwards Kwee Yan Teh, Shannon Miller, Matthew Svrcek, Sankaran Ramakrishnan, and Adam Simpson Advanced d Energy Systems Laboratory Department of Mechanical Engineering Stanford University
40% 34% >74% of U.S. CO 2 is emitted by engines.
Engines All engines have three essential features: they produce work (by definition) they require a resource (1 st Law) they reject energy to surroundings (2 nd Law) Energy Resource Engine Rejected Energy (surroundings) Work
Efficiency Limits Only four ways to transfer energy: work (entropy free) heat (energy transfer due to ΔT ) matter (internal and external) External: Internal: K.E., gravitational P.E., electrostatic P.E. thermal, chemical, nuclear radiation (not considered d here) It is the combination of energy resource and surroundings that determines the ultimate efficiency i limitation it ti of an engine (exergy).
Classifying Engines by Energy Resource Space Surface Water Lithosphere Atmosphere Geothermal Sun High K.E. Moon Anthrosphere Biosphere Accumulated Resources Hydrosphere Radiation Engines (e.g., PV) Kinetic Engines (e.g., Wind) Heat Engines (e.g., Geo) Gravity Engines (e.g., Hydro) Nuclear Engines (e.g., BWR) Chemical Engines (e.g., ICE)
Chemical Exergy of Some Fuels Fuel Chemical Chem. Exergy ΔH Reaction* ΔG Reaction* ΔS 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 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 CO 2, 2% H 2 O, 20.48% O 2, balance N 2. *Reaction with stoichiometric air at 25 C, 1 bar. All products present as ideal gases, including water. Fuel Conversion Efficiency potential (maximum first-law Fuel Conversion Efficiency potential (maximum first-law efficiency based on LHV) of most fuels is ~100%.
Conversion Efficiency of Engines First-Law Efficiency (%). 100.0 Savery, Newcomen (<0.5%) 50% 10.00 1.0 0.1 1600 1700 1800 1900 2000 2100 Time (Years A.D.) Watt/Boulton Steam Engines Post-Watt Steam Engines Lenoir, Hugon Coal-Gas Engines Otto/Langen Coal-Gas Engines Atkinson, Tangye Coal-Gas Engines Banki Spirits Engine Priestman's Oil Engine Diesel's Oil Engines Automotive SI Engines Truck Diesel Engines Large Bore DI Diesels Steam Turbines Gas Turbine/Steam Turbine Polymer Electrolyte Membrane FC Phosphoric Acid Fuel Cells SOFC/Gas Turbine Aft th t i f d l t bi d l After three centuries of development, combined-cycle efficiency just exceeds 50%, simple-cycle remains below.
Classification & Architecture Classification: Chemical Engines (1) Restrained Reaction Unrestrained Reaction (2) Electrical Work (e.g., SOFC) Mechanical Work (e.g., None) Electrical Work (e.g., MHD) Mechanical Work (e.g., GT) (3) Architecture: the set of components & connections, and the corresponding set of thermodynamic idealizations ations & device limitations that constitute a particular engine.
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 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 * After Primus, et al. Proceedings of International Symposium on Diagnostics and Modeling of Combustion in Reciprocating Engines, (1985) p.529-538.
Work Extraction During Combustion o Otto Cycle Processes Detailed Chemical Kinetics Slider-Crank Piston Profile 2nd Law All complete rxn solutions resulted in increased irreversibility! Conclusions invariant with changes in fuel (methane, methanol, propane), rate, piston profile, etc.
Optimal Control Problems
Optimal Piston Motion Linear system wrt control input q bang-bang g control S gen is minimized when reactions occur at V min The key is to manage the location of the u-v attractor Strategy has no explicit dependence on kinetics (Pontryagin Max. Principle)
Work Extraction During Combustion o Otto Cycle Processes Detailed Chemical Kinetics Slider-Crank Piston Profile u-v attractor states 2nd Law The key to reducing irreversibility in unrestrained reaction (combustion) is to drive the reactants to the highest u state.
Entropy Generation via Reaction Stoichiometric propane/air mixture modeled as ideal gases. Includes the effects of variable specific heats, reaction, & dissociation. Four ways to transfer energy
Efficiency Achievable with Simple- Cycle Extreme Compression First-La aw Effic ciency (% %) 100 80 60 40 CI SI 20 First Law (per LHV) 70-80% First Law Fuel Exergy/LHV 0 10 0 10 1 10 2 Compression Ratio Stoichiometric propane/air
Extreme-Compression Post-Combustion Conditions 3300K! 1000 bar! Must be fast! Must be balanced! Stoichiometric propane/air mixture modeled as ideal gases. Includes the effects of variable specific heats, reaction, & dissociation.
Extreme Compression Concept High compression ratio, ~100:1 Multiple pistons s (balanced a forces, ~unity aspect ratio) 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
Free-Piston Engines Example: Junkers Compressor M. Nakahara and H. Kohama, Junkers High Pressure Air Compressor-A Case of Technology Transfer through the Imperial Japanese Navy, in The 1st international conference on business and technology transfer, 2004.
Van Blarigan/Aichlmayr Linear Alternator Concept
Experimental e Apparatus atus
27 Operating Space
Air Data 500 CR = 99 Isentrope Pressure e (bar) 400 300 200 Compression 100 Expansion 28 10-2 10-1 10 0 Volume (V/V 0 )
Total Losses Over an Air Cycle Losses consist of heat and mass transfer (~50:50). Percentage work lost per LHV Percentage isentropic pressure achieved -8 100 (%) W net /LHV -9-10 -11-12 -13-14 P ak /P isentrop pic (%) pea 95 90 500 bar -15 50 60 70 80 90 100 Compression Ratio 85 40 50 60 70 80 90 100 Compression Ratio 29
Combustion Data at CR = 70 e (bar) 10 2 Air-only Combustion Isentrope ressur P 10 1 10 0 φ = 0.35 10-1 Volume (V/V 0 )
Combustion Visualization CR = 30:1 CR = 100:1 1 ms injection duration, finishing at TDC
First-Law Efficiency: Initial Results 90 80 First law (per LHV), φ = 0.35 70-80% first law Combustion data Eff ficiency (%) 70 60 50 40 30 32 10 20 30 40 50 60 70 80 90 100 Compression Ratio
First-Law Efficiency: Initial Results Eff ficiency (%) 90 80 70 60 50 40 First law (per LHV), φ = 0.35 70-80% first law Combustion data Theoretical efficiency i with air losses Losses in air experiments Additional losses due to combustion 30 33 10 20 30 40 50 60 70 80 90 100 Compression Ratio
First-Law Efficiency: Initial Results Eff ficiency (%) 34 90 80 70 60 50 40 30 First law (per LHV), φ = 0.35 70-80% first law Combustion data Theoretical efficiency with air losses Low blowby Confident we can demonstrate 60% indicated Speculate 70% is achievable regeneratively Losses in air experiments 53%, 20 C walls Additional losses due to combustion 10 20 30 40 50 60 70 80 90 100 Compression Ratio
Simple-Cycle Steady Flow What is the optimal action to be taken (transfer or p ( transformation) at each step in order to minimize S gen?
Challenges w/steady Flow Irreversibility Chemical reaction Reactant t mixing i Rejection of non-equilibrium exhaust Polytropic compression and expansion (Friction, viscous dissipation) Material Limitations Temperature limit Pressure limit
Polytropic work 1 08 0.8 0.6 a a' b b' c' Equilibrium Attractor Trajectory h-h i (MJ J/kg mix ) 04 0.4 0.2 0-0.2-0.4-0.6 Reversible Work Cycle i P i Net Work Out c Irreversible Work Cycle f ' -0.8 f -1-0.5 0 0.5 1 1.5 2 Premixed Reactants, GRI 3.0 Polytropic efficiency -- 0.9 s-s i (kj/kg mix K) i mix P i
Optimal Pressure Ratio Entropy Generatio on (kj/kg K) mix 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 Nonpremixed reactants Polytropic efficiency -- 0.8 Combustion Fluid Friction Total 0 10 0 10 1 10 2 10 3 Pressure Ratio P*
Effect of Polytropic Efficiency Pr ressure Li imit P * (b bar) 3250 10 3 Nonpremixed reactants 3000 2750 10 2 2500 2250 10 1 2000 0 1750 10 0 0.6 0.65 0.7 0.75 0.8 0.85 1500 0.6 0.65 0.7 0.75 0.8 0.85 Polytropic Efficiency η In the absence of material limitations, the pressure ratio of today s engines is well below optimum. Maxim mum Temp perature T max (K)
Temperature Limit h-h i (M MJ/kg mix ) 1.5 1 0.5 0-0.5-1 i Temperature Limit : 1650K c Brayton (18.5:1) CT (40:1) CT(160:1) Attractor (160:1) Attractor (40:1) Decreasing f S gen Increasing work-output Nonpremixed reactants Polytropic efficiency -- 0.9-1.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 s-s i (kj/kg mix K) A temperature-limited, extreme-state cycle gives the optimal simple-cycle GT architecture.
T-Limited Simple-Cycle GT
Next: Regeneration Work, Heat, and Matter with Closure Constraints t and Environmental Interactions ti What is the optimal action to be taken (transfer or transformation) at each step in order to minimize S gen?
Thermodynamic State-SpaceSpace Natural Gas Air, Equivalence Ratio 0.5
Take-Home Messages (1 of 2) Despite three centuries of effort, engine efficiency i remains well below theoretical limits (resource exergy) often by more than a factor of two. Misconceptions about what ultimately limits engine efficiency (e.g., Carnot) are sometimes to blame. Working in the space between the exergy limit and real engines, we have found the ideas of classification and architecture to be useful. Our approach is to use the principles i of optimal control to identify the most efficient architecture for any given set of allowable devices, resources, and environment. For chemical engines, a key to understanding is whether the architecture uses restrained or unrestrained reaction.
Take-Home Messages (2 of 2) Irreversibility in restrained reaction engines can be reduced d by improving kinetics. To date, the only examples of restrained reaction engines are electrochemical (i.e., fuel cells). Irreversibility in unrestrained reaction engines can be reduced by reaction at states of high energy density (extreme-states principle). For simple-cycle engines, we believe that architectures capable of delivering 60% first-law efficiency are possible. For regenerative engines, we believe a systematic approach to identifying optimal architectures can be developed. We speculate that such engines are capable of 70% first-law efficiency. For combined-cycle engines, we speculate that a systematic approach is again possible and can lead to the development of engines with first-law efficiencies i i in excess of 80%.