ame 513 principles of combustion paul ronney fall 2012

AME 513

Principles of Combustion

Paul RonneyFall 2012

2AME 513 - Fall 2012 - Lecture 1 - Introduction

Administrative details Instructor: Prof. Paul Ronney

Office: OHE 430JPhone: (213) 740-0490Email: [email protected]: http://ronney.usc.eduOffice hours: Mondays 1 pm – 4 pm

Teaching assistant: Ning LiuOffice: RRB 207; Lab: RRB 111Phone: (213) 740-5361 Email: [email protected] hours: Tuesdays 1 pm – 4 pm

Grader: Thada SuksilaEmail: [email protected]

Grading: 30% homework, 30% midterm, 40% final 7 homework assignments; 10 points per day late penalty;

lowest HW grade dropped


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

http://www.mhprofessional.com/product.php?isbn=0073380199




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)


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

http://www.microsoft.com/downloads/details.aspx?familyid=048dc840-14e1-467d-8dca-19d2a8fd7485&displaylang=en

AME 513

Principles of Combustion

Lecture 1Introduction: Why combustion?


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


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


US energy flow, 2010, units 1015 BTU/yr

Each 1015 BTU/yr = 33.4 gigawatts

http://www.eia.gov/totalenergy/data/annual/diagram1.cfm


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


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


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


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)

Type Chemical reaction

Heat / mass transport

Momentum transport

Thermo-dynamics

Deflagration ✔ ✔ ✗ ✔

Detonation ✗ ✗ ✔ ✔

Homogeneous reaction ✔ ✗ ✗ ✔

Nonpremixed flames ✗ ✔ ✗ ✗


Deflagrations

Subsonic propagating front 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


Turbulent premixed flame experiment in a fan-stirred chamber (http://www.mech-eng.leeds.ac.uk/res-group/combustion/activities/Bomb.htm)

Schematic of deflagration

Flame thickness () ~ /SL

( = thermal diffusivity)




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)


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


Candle

Forest fireKuwait Oil fireDiesel engine

“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


≈ ()1/2


Diesel engine combustion

Two extremesDroplet combustion - vaporization of droplets is slow, so droplets burn

as individualsGas-jet flame - vaporization of droplets is so fast, there is effectively a jet

of fuel vapor rather than individual dropletsReality 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.

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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

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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 export pollution 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 consumersAME 513 - Fall 2012 - Lecture 1 - Introduction

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“Zero emission” electric vehicles


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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


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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!


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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

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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


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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 foodor provide biodiversity (e.g. in tropical rain forests)


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Alternative #6 - nuclear High energy density

U235 fission: 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)


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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!


http://www.edison2.com/

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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


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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


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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


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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


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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

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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


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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



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

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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?



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”


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 massQ = heat transfer to the massW = 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)


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


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


Review of thermo (5) - types of energy


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)


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


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


Review of thermo (9) - conservation of mass

For a control massm = mass of control mass = constant (wasn’t that easy?)

For a control volume

(what accumulates = what goes in - what goes out)


Review of thermodynamics (10) - 2nd law

The 2nd Law of Thermdynamics statesThe 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 + PdvTds = dh - vdP

These are called the Gibbs equations, which relate entropy to other thermodynamic properties (e.g. u, P, v, h, T)


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


Review of thermo (12) - equations of state

We’ll only consider 2 equations of state in this course Ideal gas - P = RT (P = pressure, = 1/v = density, T = temperature

(absolute), R = gas constant = /Mmix, = universal gas constant (8.314 J/mole-K), Mmix = molecular weight of gas mixture)

Incompressible fluid - = constant Definition of specific heats (any substance)

For ideal gases - h = h(T) and u = u(T) only (h and u depend only on temperature, not pressure, volume, etc.), thus for ideal gases

From dh = CPdT, du = CvdT, the Gibbs equations and P = RT we can show that (again for an ideal gas only)


Review of thermo (13) - isentropic relations

Recall from the 2nd Law, dS ≥ Q/T If a process is reversible dS = Q/T, and if furthermore the process

is adiabatic Q = 0 thus dS = 0 or S2 - S1 = 0 (isentropic process) then the previous relations for S2 - S1 can be written as

Isentropic processes are our favorite model for compression and expansion in engines

But remember these relations are valid only for Ideal gas Constant specific heats (CP, CV) (note that since for an ideal gas CP = Cv

+ R and R is a constant, if any of CP, Cv and = CP/Cv are constant then the other two must be constant also)

Reversible adiabatic (thus isentropic) process(Still very useful despite all these restrictions…)


“Engineering scrutiny” 1. Smoke test

See http://ronney.usc.edu/AME101F011/AME101-F11-LectureNotes.pdf (Chapters 2 & 3) for more details

Equivalent in building electronics: turn the power switch on and see if it smokes

For analysis: check the units - this will catch 90% of your mistakes

Example: I just derived the ideal gas law as Pv = R/T, obviously units are wrong

Other rules Anything inside a square root, cube root, etc. must have units

that is a square (e.g. m2/sec2) or cube, etc. Anything inside a log, exponent, trigonometric function, etc.,

must be dimensionless Any two quantities that are added together must have the

same units

http://ronney.usc.edu/AME101F010/AME101-F10-LectureNotes.pdf


“Engineering scrutiny” 2. Function test

Equivalent in building electronics: does the device do what it was designed it to do, e.g. the red light blinks when I flip switch on, the bell rings when I push the button, etc.

For analysis: does the result gives sensible predictions? Determine if sign (+ or -) of result is reasonable, e.g. if

predicted absolute temperature is –72 K, obviously it’s wrong Determine whether what happens to y as x goes up or down

is reasonable or not. For example, in the ideal gas law, Pv = RT: At fixed v, as T increases then P increases – reasonable At fixed T, as v increases then P decreases – reasonable Etc.


“Engineering scrutiny” 2. Function test

Determine what happens in the limit where x goes to special values, e.g. 0, 1, ∞ as appropriate

Example: entropy change (S2 - S1) of an ideal gas

For T2 = T1 and P2 = P1 (no change in state) then S2 – S1 = 0 or S2 = S1

Limit of S2 = S1, the allowable changes in state are

which is the isentropic relation for ideal gas with constant specific heats


“Engineering scrutiny” 3. Performance test

Equivalent in building electronics: how fast, how accurate, etc. is the device

For analysis: how accurate is the result? Need to compare result to something else, e.g. a

“careful” experiment, more sophisticated analysis, trusted published result, etc.

Example, I derived the ideal gas law and predicted Pv = 7RT - passes smoke and function tests, but fails the performance test miserably (by a factor of 7)

ame 513 principles of combustion paul ronney fall 2012

Documents

lecture slide

study combustion

introduction outline

egolfopouloss lecture

types of combustion

introduction us energy

week premixed flames

course website