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  1. AME 513Principles of Combustion Paul Ronney Fall 2012

  2. Administrative details • Instructor:  Prof. Paul Ronney Office: OHE 430J Phone: (213) 740-0490 Email:  ronney@usc.edu Website:  http://ronney.usc.edu Office hours: Mondays 1 pm – 4 pm • Teaching assistant:  Ning Liu Office: RRB 207; Lab: RRB 111 Phone: (213) 740-5361 Email:  ningl@usc.edu Office hours: Tuesdays 1 pm – 4 pm • Grader:  ThadaSuksila Email:  suksila@usc.edu • Grading: 30% homework, 30% midterm, 40% final • 7 homework assignments; 10 points per day late penalty; lowest HW grade dropped AME 513 - Fall 2012 - Lecture 1 - Introduction

  3. Administrative details • References • PDR’s lecture notes • Prof. Egolfopoulos’s lecture notes (to be distributed) • Steven R. Turns, An Introduction to Combustion: Concept and Applications, 3rd Edition, 2012http://www.mhprofessional.com/product.php?isbn=0073380199 • Optional supplemental material • Combustion Theory, Forman A Williams, 2nd Edition, Addison-Wesley, 1985 • Combustion, Flames, and Explosions of Gases, Bernard Lewis and Guenther von Elbe, 3rd Edition, Academic Press, 1987 • Combustion, Irvin Glassman and Richard Yetter, 4th Edition, Academic Press, 2008 AME 513 - Fall 2012 - Lecture 1 - Introduction

  4. Tentative course outline • Introduction (1 week) • Building blocks of combustion • Chemical thermodynamics (2 weeks) • Chemical kinetics (3 weeks) • Transport phenomena (1 week) • Combining the building blocks • Conservation equations (1 week) • Premixed flames (3 weeks) • Non-Premixed flames (3 weeks) AME 513 - Fall 2012 - Lecture 1 - Introduction

  5. Helpful handy hints • Download lectures from website before class • Each lecture includes • Outline • Examples • Summary … make use of these resources • Bringing your laptop allows you to add notes & download files from course website as necessary • If you don’t have Powerpoint, you can download a free powerpoint viewer from Microsoft’s website • … but if you don’t have the full Powerpoint and Excel, you won’t be able to open the imbedded Excel spreadsheets • Please ask questions in class - the goal of the lecture is to maintain a 2-way “Socratic” dialogue on the subject of the lecture AME 513 - Fall 2012 - Lecture 1 - Introduction

  6. AME 513Principles of Combustion Lecture 1 Introduction: Why combustion?

  7. Outline • Why study combustion? • What do we want to know? • Types of combustion processes • Premixed • Nonpremixed • Alternatives to combustion for transportation vehicles • Brief history of internal combustion engines • “Bonus” material (on your own…) • Review of thermodynamics • Engineering scrutiny AME 513 - Fall 2012 - Lecture 1 - Introduction

  8. Why study combustion? • > 80% of world energy production results from combustion of fossil fuels • Energy sector accounts for 9% of US Gross Domestic Product • Our continuing habit of burning things and our quest to find more things to burn has resulted in • Economic booms and busts • Political and military conflicts • Global warming (or the need to deny its existence) • Human health issues AME 513 - Fall 2012 - Lecture 1 - Introduction

  9. US energy flow, 2010, units 1015 BTU/yr Each 1015BTU/yr = 33.4 gigawatts http://www.eia.gov/totalenergy/data/annual/diagram1.cfm AME 513 - Fall 2012 - Lecture 1 - Introduction

  10. What do we do with combustion? • Power generation (coal, natural gas) • Transportation (land, air, sea vehicles) • Weapons (rapid production of high-pressure gas) • Heating • Lighting • Cooking (1/3 of the world’s population still uses biomass-fueled open fires) • Hazardous waste & chemical warfare agent destruction • Production of new materials, e.g. nano-materials • (Future?) Portable power, e.g. battery replacement • Unintended / undesired consequences • Fires and explosions (residential, urban, wildland, industrial) • Pollutants – NOx (brown skies, acid rain), CO (poisonous), Unburned HydroCarbons (UHCs, photochemical smog), formaldehyde, particulates, SOx • Global warming from CO2 & other products AME 513 - Fall 2012 - Lecture 1 - Introduction

  11. What do we want to know? • From combustion device • Power (thermal, electrical, shaft, propulsive) • Efficiency (% fuel burned, % fuel converted to power) • Emissions • From combustion process itself • Rates of consumption • Reactants • Intermediates • Rates of formation • Intermediates • Products • Global properties • Rates of flame propagation • Rates of heat generation (more precisely, rate of conversion of chemical enthalpy to thermal enthalpy) • Temperatures • Pressures AME 513 - Fall 2012 - Lecture 1 - Introduction

  12. Why do we need to study combustion? • Chemical thermodynamics only tells us the end states - what happens if we wait “forever and a day” for chemical reaction to occur • We need to know how fast reactions occur • How fast depends on both the inherent rates of reaction and the rates of heat and mass transport to the reaction zone(s) • Chemical reactions + heat & mass transport = combustion • Some reactions occur too slowly to be observed, e.g. 2 NO  N2 + O2 has an adiabatic flame temperature of 2650K but no one has ever made a flame with NO because reaction rates are too slow! • Chemical reaction leads to gradients in temperature, pressure and species concentration • Results in transport of energy, momentum, mass • Combustion is the study of the coupling between thermodynamics, chemical reaction and transport processes AME 513 - Fall 2012 - Lecture 1 - Introduction

  13. Types of combustion • Premixed - reactants are intimately mixed on the molecular scale before combustion is initiated; several flavors • Deflagration • Detonation • Homogeneous reaction • Nonpremixed - reactants mix only at the time of combustion - have to mix first then burn; several flavors • Gas jet (Bic lighter) • Liquid fuel droplet • Liquid fuel jet (e.g. Kuwait oil fire, candle, Diesel engine) • Solid (e.g. coal particle, wood) AME 513 - Fall 2012 - Lecture 1 - Introduction

  14. Deflagrations • Subsonic propagatingfront sustained by conduction of heat from the hot (burned) gases to the cold (unburned) gases which raises the temperature enough that chemical reaction can occur; since chemical reaction rates are very sensitive to temperature, most of the reaction is concentrated in a thin zone near the high-temperature side • May be laminar or turbulent • Temperature increases in “convection-diffusion zone” or “preheat zone” ahead of reaction zone, even though no heat release occurs there, due to balance between convection & diffusion • Reactant concentration decreases in convection-diffusion zone, even though no chemical reaction occurs there, for the same reason • How can we have reaction at the reaction zone even though reactant concentration is low there? (See diagram…) Because reaction rate is much more sensitive to temperature than reactant concentration, so benefit of high T outweighs penalty of low concentration AME 513 - Fall 2012 - Lecture 1 - Introduction

  15. Schematic of deflagration Turbulent premixed flame experiment in a fan-stirred chamber (http://www.mech-eng.leeds.ac.uk/res-group/combustion/activities/Bomb.htm) Flame thickness () ~ /SL ( = thermal diffusivity) AME 513 - Fall 2012 - Lecture 1 - Introduction

  16. Premixed flames - detonation • Supersonic propagating front sustained by heating via shock wave • After shock front, need time (thus distance = time x velocity) before reaction starts to occur (“induction zone”) • After induction zone, chemical reaction & heat release occur • Pressure & temperature behavior coupled strongly with supersonic/subsonic gasdynamics • Ideally only M3 = 1 “Chapman-Jouget detonation” is stable (M = Mach number = Vc; V = velocity, c = sound speed = (RT)1/2 for ideal gas) AME 513 - Fall 2012 - Lecture 1 - Introduction

  17. Premixed flames - homogeneous reaction • Model for knock in premixed-charge engines • Fixed mass (control mass) with uniform (in space) T, P and composition • No “propagation” in space but propagation in time • In laboratory, can heat the chamber to a certain T and measure reaction time, or compress mixture (increases P & T, thus reaction rate) will initiate reaction AME 513 - Fall 2012 - Lecture 1 - Introduction

  18. “Non-premixed” or “diffusion” flames • Reaction zone where fuel & O2 fluxes in stoichiometric proportion • Generally “mixed is burned” - mixing slower than chemical reaction • No inherent propagation rate (flame location determined by stoichiometric location) • No inherent thickness (= mixing layer thickness ~ (/)1/2) ( = strain rate) • Unlike premixed flames with characteristic propagation rate SL and thickness  ~ /SL that are almost independent of  Candle Kuwait Oil fire Forest fire Diesel engine AME 513 - Fall 2012 - Lecture 1 - Introduction

  19.  ≈ ()1/2 AME 513 - Fall 2012 - Lecture 1 - Introduction

  20. Diesel engine combustion • Two extremes • Droplet combustion - vaporization of droplets is slow, so droplets burn as individuals • Gas-jet flame - vaporization of droplets is so fast, there is effectively a jet of fuel vapor rather than individual droplets • Reality is in between, but in Diesels usually closer to the gas jet “with extras” – regions of premixed combustion Flynn, P.F, R.P. Durrett, G.L. Hunter, A.O. zur Loye, O.C. Akinyemi, J.E. Dec, C.K. Westbrook, SAE Paper No. 1999-01-0509. AME 513 - Fall 2012 - Lecture 1 - Introduction

  21. Alternative #1 - external combustion • Examples: steam engine, Stirling cycle engine • Use any fuel as the heat source • Use any working fluid (high , e.g. helium, provides better efficiency) • Heat transfer, gasoline engine • Heat transfer per unit area (q/A) = k(dT/dx) • Turbulent mixture inside engine: k ≈ 100 kno turbulence ≈ 2.5 W/mK • dT/dx ≈ T/x ≈ 1500K / 0.02 m • q/A ≈ 187,500 W/m2 • Combustion: q/A = YfQRST = (10 kg/m3) x 0.067 x (4.5 x 107 J/kg) x 2 m/s = 60,300,000 W/m2 - 321x higher! • CONCLUSION: HEAT TRANSFER IS TOO SLOW!!! • That’s why 10 large gas turbine engines ≈ large (1 gigawatt) coal-fueled electric power plant k = gas thermal conductivity, T = temperature, x = distance,  = density, Yf = fuel mass fraction, QR = fuel heating value, ST = turbulent flame speed in engine AME 513 - Fall 2012 - Lecture 1 - Introduction

  22. Alternative #2 - Electric Vehicles (EVs) • Why not generate electricity in a large central power plant and distribute to charge batteries to power electric motors? • Chevy Volt Li-ion battery – 10.3 kW-hours usable capacity, 435 pounds = 1.88 x 105 J/kg • Gasoline (and other hydrocarbons): 4.3 x 107 J/kg • Even at 30% efficiency (gasoline) vs. 90% (batteries), gasoline has 76 times higher energy/weight than batteries! • 1 gallon of gasoline ≈ 457 pounds of batteries for same energy delivered to the wheels • Other issues with electric vehicles • "Zero emissions” ??? - EVs exportpollution • 50% of US electricity is by produced via coal at 40% efficiency – virtually no reduction in CO2 emissions • Battery replacement cost ≈ $8000 ≈ 80,000 miles of gasoline driving (@ $3.50/gal, 35 mpg) • Environmental cost of battery materials • Possible advantage: make smaller, lighter, more streamlined cars acceptable to consumers AME 513 - Fall 2012 - Lecture 1 - Introduction

  23. “Zero emission” electric vehicles AME 513 - Fall 2012 - Lecture 1 - Introduction

  24. Ballard HY-80 “Fuel cell engine” (power/wt = 0.19 hp/lb) 48% efficient (fuel to electricity) MUST use hydrogen (from where? H2 is an energy carrier, not a fuel) Requires large amounts of platinum catalyst - extremely expensive Does NOT include electric drive system (≈ 0.40 hp/lb thus fuel cell + motor at ≈ 90% electrical to mechanical efficiency) Overall system: 0.13 hp/lb at 43% efficiency (hydrogen) Conventional engine: ≈ 0.5 hp/lb at 30% efficiency (gasoline) Conclusion: fuel cell engines are only marginally more efficient, much heavier for the same power, and require hydrogen which is very difficult and potentially dangerous to store on a vehicle Prediction: even if we had an unlimited free source of hydrogen and a perfect way of storing it on a vehicle, we would still burn it, not use it in a fuel cell Alternative #3 - Hydrogen fuel cell AME 513 - Fall 2012 - Lecture 1 - Introduction

  25. Hydrogen storage • Hydrogen is a great fuel • High energy density (1.2 x 108 J/kg, ≈ 3x hydrocarbons) • Much faster reaction rates than hydrocarbons (≈ 10 - 100x at same T) • Excellent electrochemical properties in fuel cells • But how to store it??? • Cryogenic (very cold, -424˚F) liquid, low density (14x lower than water) • Compressed gas: weight of tank ≈ 15x greater than weight of fuel • Borohydride solutions • NaBH4 + 2H2O  NaBO2 (Borax) + 3H2 • (mass solution)/(mass fuel) ≈ 9.25 • Palladium - Pd/H = 164 by weight • Carbon nanotubes - many claims, few facts… • Long-chain hydrocarbon (CH2)x: (Mass C)/(mass H) = 6, plus C atoms add 94.1 kcal of energy release to 57.8 for H2! • MORAL: By far the best way to store hydrogen is to attach it to carbon atoms and make hydrocarbons, even if you’re not going to use the carbon as fuel! AME 513 - Fall 2012 - Lecture 1 - Introduction

  26. Alternative #4 - solar • Arizona, high noon, mid summer: solar flux ≈ 1000 W/m2 • Gasoline engine, 20 mi/gal, 60 mi/hr, thermal power = (60 mi/hr / 20 mi/gal) x (6 lb/gal) x (kg / 2.2 lb) x (4.3 x 107 J/kg) x (hr / 3600 sec) = 97 kilowatts • Need ≈ 100 m2 collector ≈ 32 ft x 32 ft - lots of air drag, what about underpasses, nighttime, bad weather, northern/southern latitudes, etc.? Do you want to drive one of these every day (but never at night?) AME 513 - Fall 2012 - Lecture 1 - Introduction

  27. Alternative #4 - solar • Ivanpah solar thermal electric generating station • 400 MW maximum power, ≈ 48 MW annual average (small compared to coal or nuclear, 1,000 MW) • 3 towers, each 460 ft tall • 6 mi2, 17,000 mirrors • $2.2 billion = $46/watt vs. $2/watt for conventional coal or natural gas power plants AME 513 - Fall 2012 - Lecture 1 - Introduction

  28. Alternative #5 - biofuels • Essentially solar energy – “free” (?) • Barely energy-positive; requires energy for planting, fertilizing, harvesting, fermenting, distilling • Very land-inefficient compared to other forms of solar energy – life forms convert < 1% of sun’s energy into combustible material • Currently 3 subsidies on US bio-ethanol vehicle fuel: • 45¢/gal (≈ 67¢/gal gasoline) tax credit to refines • 54¢/gal tariff on sugar-based ethanol imports • Requirement for 10% ethanol in gasoline • Displaces other plants – not necessarily “carbon neutral” • Uses other resources - arable land, water – that might otherwise be used to grow food or provide biodiversity (e.g. in tropical rain forests) AME 513 - Fall 2012 - Lecture 1 - Introduction

  29. Alternative #6 - nuclear • High energy density • U235fission: 8.2 x 1013 J/kg ≈ 2 million x hydrocarbons! • Radioactive decay much less, but still much higher than hydrocarbon fuel • Carbon neutral • Not practical for vehicles but… Ford Nucleon concept car (1958) AME 513 - Fall 2012 - Lecture 1 - Introduction

  30. Edison2 vehicle • http://www.edison2.com • Won X-prize competition for 4-passenger vehicles (110 MPG) • Key features - Very low weight (830 lb), very aerodynamic, very low rolling resistance • Engine: 1 cylinder, 40 hp, 250 cc, turbocharged ICE • Ethanol fuel (high octane rating, allows high compression ratio thus high efficiency) • Rear engine placement reduces air drag due to radiator • Beat electric vehicles despite unfair advantage in US EPA MPG equivalency: 33.7 kW-hr electrical energy = 1 gal, same as raw energy content of gasoline (44 x 106 MJ/kg) – doesn’t account for fuel burned to create the electrical energy! AME 513 - Fall 2012 - Lecture 1 - Introduction

  31. History of automotive engines • 1859 - oil discovered at Drake’s Well, Titusville, Pennsylvania (20 barrels per day) - 40 year supply • 1876 - premixed-charge 4-stroke engine – Nikolaus Otto • 1st “practical” ICE • 4-stroke, overhead valve, crankshaft • Power: 2 hp; Weight: 1250 pounds; fuel: coal gas (CO + H2) • Comp. ratio = 4 (knock limited), 14% efficiency (theory 38%) • Today CR = 9 (still knock limited), 30% efficiency (theory 55%) • In 136 years, the main efficiency improvement is due to better fuel AME 513 - Fall 2012 - Lecture 1 - Introduction

  32. History of automotive engines • 1897 - nonpremixed-charge engine - Diesel - higher efficiency due to • Higher CR (no knocking) • No throttling loss - use fuel/air ratio to control power • 1901 - Spindletop Dome, east Texas - Lucas #1 gusher produces 100,000 barrels per day - ensures that “2nd Industrial Revolution” will be fueled by oil, not coal or wood - 40 year supply • 1921 - tetraethyl lead anti-knock additive discovered at General Motors • Enabled higher CR (thus more power, better efficiency) in Otto-type engines AME 513 - Fall 2012 - Lecture 1 - Introduction

  33. History of automotive engines • 1938 – oil discovered at Dammam, Saudi Arabia (40 year supply) • 1952 - A. J. Haagen-Smit, Caltech NO + UHC + O2 + sunlightNO2 + O3 (from exhaust) (brown) (irritating) (UHC = unburned hydrocarbons) • 1960s - emissions regulations • Detroit won’t believe it • Initial stop-gap measures - lean mixture, EGR, retard spark • Poor performance & fuel economy • 1973 & 1979 - energy crises due to Middle East turmoil • Detroit takes a bath, Asian and European imports increase AME 513 - Fall 2012 - Lecture 1 - Introduction

  34. History of automotive engines • 1975 - Catalytic converters, unleaded fuel • More “aromatics” (e.g., benzene) in gasoline - high octane but carcinogenic, soot-producing • 1980s - Microcomputer control of engines • Tailor operation for best emissions, efficiency, ... • 1990s - Reformulated gasoline • Reduced need for aromatics, cleaner (?) • ... but higher cost, lower miles per gallon • Then we found that MTBE pollutes groundwater!!! • Alternative “oxygenated” fuel additive - ethanol - very attractive to powerful senators from farm states AME 513 - Fall 2012 - Lecture 1 - Introduction

  35. History of automotive engines • 2000’s - hybrid vehicles • Use small gasoline engine operating at maximum power (most efficient way to operate) or turned off if not needed • Use generator/batteries/motors to make/store/use surplus power from gasoline engine • Plug-in hybrid: half-way between conventional hybrid and electric vehicle • 2 benefits to car manufacturers: win-win • Consumers will pay a premium for hybrids • Helps to meet fleet-average standards for efficiency & emissions • Do fuel savings justify extra cost? Consumer Reports study: only 1 of 7 hybrids tested showed a cost benefit over a 5 year ownership if tax incentives were removed • Dolly Parton: “You wouldn’t believe how much it costs to look this cheap” • Paul Ronney: “You wouldn’t believe how much energy some people spend to save a little fuel” • 2010 and beyond • ??? AME 513 - Fall 2012 - Lecture 1 - Introduction

  36. Practical alternatives to the status quo • Conservation! • Combined cycles: use hot exhaust from internal combustion engine to heat water for conventional steam cycle - can achieve > 60% efficiency but not practical for vehicles - too much added volume & weight • Natural gas • 4x cheaper than electricity, 2x cheaper than gasoline or diesel for same energy • Somewhat cleaner than gasoline or diesel, but no environmental silver bullet • Low energy storage density - 4x lower than gasoline or diesel AME 513 - Fall 2012 - Lecture 1 - Introduction

  37. Practical alternatives to the status quo • Fischer-Tropsch fuels - liquid hydrocarbons from coal or natural gas • Coal or NG + O2 CO + H2  liquid fuel • Competitive with ≈ $100/barrel oil • Cleaner than gasoline or diesel • … but using coal increases greenhouse gases! Coal : oil : natural gas = 2 : 1.5 : 1 • Could use biomass (e.g. agricultural waste) instead of coal or natural gas as “energy feedstock” • But really, there is no way to decide what the next step is until it is decided whether there will be a tax on CO2 emissions • Personal opinion: most important problems are (in order of priority) • Global warming • Energy independence • Environment AME 513 - Fall 2012 - Lecture 1 - Introduction

  38. Summary - Lecture 1 • Combustion is the interaction of thermodynamics, chemical reaction and heat/mass/momentum transport, but which is/are most important depends on the situation • Combustion is ubiquitous in our everyday lives and will continue to be for our lifetimes • Many advantages of fossil fuels over other energy sources • Cheap (?), plentiful (?), clean (?) • Energy/weight of fuel itself • Power/weight of engines • Materials costs (e.g. compared to fuel cells) • The most important distinction between flames is premixed vs. non-premixed, i.e. whether the reactants are mixed before combustion AME 513 - Fall 2012 - Lecture 1 - Introduction

  39. Discussion point Our current energy economy, based primarily on fossil fuel usage, evolved because it was the cheapest system. Is it possible that it’s also the most environmentally responsible (or “least environmentally irresponsible”) system? AME 513 - Fall 2012 - Lecture 1 - Introduction

  40. Review of thermodynamics (1) • 1st Law of Thermodynamics (conservation of energy) - “you can’t win” • 2nd Law of Thermodynamics - “you can’t break even” • Equation of state (usually ideal gas law) - “you can’t even choose the game” AME 513 - Fall 2012 - Lecture 1 - Introduction

  41. Review of thermodynamics (2) • 1st Law of Thermodynamics for a control mass, i.e. a fixed mass of material (but generally changing volume) dE = Q - W E = energy contained by the mass - a property of the mass Q = heat transfer to the mass W = work transfer to or from the mass (see below) d vs.  = path-independent vs. path-dependent quantity • Control mass form useful for fixed mass, e.g. gas in a piston/cylinder • Each term has units of Joules • Work transfer is generally defined as positive if out of the control mass, in which case - sign applies, i.e. dE = Q - W; If work is defined as positive into system then dE = Q + W • Heat and work are NOT properties of the mass, they are energy transfers to/from the mass; a mass does not contain heat or work but it does contain energy (E) AME 513 - Fall 2012 - Lecture 1 - Introduction

  42. Review of thermo (3) - heat & work • Heat and work transfer depend on the path, but the internal energy of a substance at a given state doesn’t depend on how you got to that state; for example, simple compressible substances exchange work with their surroundings according to W = + PdV (+ if work is defined as positive out of control mass) • For example in the figure below, paths A & B have different ∫ PdV and thus different work transfers, even though the initial state 1 and final state 2 are the same for both AME 513 - Fall 2012 - Lecture 1 - Introduction

  43. Review of thermo (4) - heat & work • What is the difference between heat and work? Why do we need to consider them separately? • Heat transfer is disorganized energy transfer on the microscopic (molecular) scale and has entropy transfer associated with it • Work transfer is organized energy transfer which may be at either the microscopic scale or macroscopic scale and has no entropy transfer associated with it • The energy of the substance (E) consists of • Macroscopic kinetic energy (KE = 1/2 mV2) • Macroscopic potential energy (PE = mgz) • Microscopic internal energy (U) (which consists of both kinetic (thermal) and potential (chemical bonding) energy, but we lump them together since we can’t see it them separately, only their effect at macroscopic scales • If PE is due to elevation change (z) and work transfer is only PdV work, then the first law can be written as dU + mVdV + mgdz = Q - PdV V = velocity, V = volume, m = mass, g = gravity AME 513 - Fall 2012 - Lecture 1 - Introduction

  44. Review of thermo (5) - types of energy AME 513 - Fall 2012 - Lecture 1 - Introduction

  45. Review of thermo (6) - 1st law for CV • 1st Law of Thermodynamics for a control volume, a fixed volume in space that may have mass flowing in or out (opposite of control mass, which has fixed mass but possibly changing volume): • E = energy within control volume = U + KE + PE as before • = rates of heat & work transfer in or out (Watts) • Subscript “in” refers to conditions at inlet(s) of mass, “out” to outlet(s) of mass • = mass flow rate in or out of the control volume • h  u + Pv = enthalpy • Note h, u & v are lower case, i.e. per unit mass; h = H/M, u = U/M, V = v/M, etc.; upper case means total for all the mass (not per unit mass) • v = velocity, thus v2/2 is the KE term • g = acceleration of gravity, z = elevation at inlet or outlet, thus gz is the PE term • Control volume form useful for fixed volume device, e.g. gas turbine • Most commonly written as a rate equation (as above) AME 513 - Fall 2012 - Lecture 1 - Introduction

  46. Review of thermo (7) - 1st law for CV • Note that the Control Volume (CV) form of the 1st Law looks almost the same as the Control Mass (CM) form with the addition of (h+ v2/2 + gz) terms that represent the flux of energy in/out of the CV that is carried with the mass flowing in/out of the CV • The only difference between the CV and CM forms that isn’t “obvious” is the replacement of u (internal energy) with h = u + Pv • Where did the extra Pv terms come from? The flow work needed to push mass into the CV or that you get back when mass leaves the CV AME 513 - Fall 2012 - Lecture 1 - Introduction

  47. Review of thermo (8) - steady flow • If the system is steady then by definition • d[ ]/dt = 0 for all [properties], i.e. ECV, MCV, h, v, z • All fluxes, i.e. are constant (not necessarily zero) • Sum of mass flows in = sum of all mass flows out (or for a single-inlet, single-outlet system) (if we didn’t have this condition then the mass of the system, which is a property of the system, would not be constant) • In this case (steady-state, steady flow) the 1st Law for a CV is AME 513 - Fall 2012 - Lecture 1 - Introduction

  48. Review of thermo (9) - conservation of mass • For a control mass m = mass of control mass = constant (wasn’t that easy?) • For a control volume (what accumulates = what goes in - what goes out) AME 513 - Fall 2012 - Lecture 1 - Introduction

  49. Review of thermodynamics (10) - 2nd law • The 2nd Law of Thermdynamics states The entropy (S) of an isolated system always increases or remains the same • By combining • 2nd law • 1st Law • State postulate - for a system of fixed chemical composition, 2 independent properties completely specify the state of the system • The principle that entropy is a property of the system, so is additive “it can be shown” that Tds = du + Pdv Tds = dh - vdP These are called the Gibbs equations, which relate entropy to other thermodynamic properties (e.g. u, P, v, h, T) AME 513 - Fall 2012 - Lecture 1 - Introduction

  50. Review of thermodynamics (11) - 2nd law • From the Gibbs equations, “it can be shown” for a control mass = sign applies for a reversible (idealized; best possible) process > applies if irreversible (reality) T is the temperature on the control mass at the location where the heat is transferred to/from the CM • And for a control volume SCV is the entropy of the control volume; if steady, dSCV/dt = 0 • These equations are the primary way we apply the 2nd law to the energy conversion systems discussed in this class • Work doesn’t appear anywhere near the 2nd law - why? Because there is NO entropy transfer associated with work transfer, whereas there IS entropy transfer associated with heat transfer AME 513 - Fall 2012 - Lecture 1 - Introduction