AME 436. Energy and Propulsion. Lecture 2 Fuels, chemical thermodynamics (thru 1st Law; 2nd Law next lecture)

Transcription

1 AME 436 Eergy ad Propulsio Lecture 2 Fuels, chemical thermodyamics (thru 1st Law; 2d Law ext lecture Outlie! Fuels - hydrocarbos, alteratives! Balacig chemical reactios! Stoichiometry! Lea & rich mixtures! Mass ad mole fractios! hemical thermodyamics!!!! Why? 1st Law of Thermodyamics applied to a chemically reactig system eatig value of fuels Flame temperature 2 1

2 Fuels! Usually we employ hydrocarbo fuels, alcohols or hydroge burig i air, though other possibilities iclude O, N 3, S 2, 2 S, etc.! For rocket fuels that do ot bur air, may possible oxidizers exist - ASTE 470 discusses these - AME 436 focuses o airbreathig devices! Why hydrocarbos?! May are liquids - high desity, easy to trasport ad store (compared to gases, e.g. 4, easy to feed ito egie (compared to solids! Lots of it i the earth (ofte the wrog places! Relatively o-toxic fuel ad combustio products! Relatively low explosio hazards 3 Air! Why air?! Because it's free, of course (well, ot really whe you thik of all the moey we ve spet to clea up air! Air 0.21 O N 2 (1 mole of air or 1 O N 2 (4.77 moles of air! Note for air, the average molecular mass is 0.21 Mole O 2 Mole total 32g O Mole N 2 Mole O 2 Mole total 28g N 2 Mole N g Mole total thus the gas costat (uiversal gas costat / mole. wt. (8.314 J/moleK / ( kg/mole 287 J/kgK! Also 1% argo, up to a few % water vapor depedig o the relative humidity, trace amouts of other gases, but we ll usually assume just O 2 ad N 2 4 2

3 ydrocarbos! Alkaes - sigle bods betwee carbos - 2+2, e.g. 4, 2 6 methae ethae! Olefis or alkees - oe or more double bods betwee carbos ethee or ethylee propee or propylee! Alkyes - oe or more triple bods betwee carbos - very reactive, higher heatig value tha alkaes or alkees propae 1, 3 butadiee ethye or acetylee 5 ydrocarbos! Aromatics - oe or more rig structures bezee toluee apthalee! Alcohols - cotai oe or more O groups O O methaol ethaol 6 3

4 Biofuels! Alcohols - produced by fermetatio of food crops (sugars or starches or cellulose (much more difficult, ot adustrial process yet! Biodiesel - covert vegetable oil or aimal fat (which have very high viscosity ito alkyl esters (lower viscosity through "trasesterificatio" with alcohol Methyl lioleate Geeric ester structure (R ay orgaic radical, e.g. 2 5 Ethyl stearate Methaol + triglyceride Glycerol+ alkyl ester Trasesterificatio process 7 Practical fuels! All practical fuels are BLENDS of hydrocarbos ad other compouds! What distiguishes oe fuel from aother?! Flash poit - temperature above which fuel vapor pressure is flammable whe mixed with air! Distillatio curve - temp. rage over which molecules evaporate! Relative amouts of alkaes vs. alkees vs. aromatics vs. alcohols! Amout of impurities, e.g. sulfur! Structure of molecules - affects octae umber (Lecture

5 Gasolie - typical compositio Paraffis alkaes Bezee Toluee J. Burri et al., Fuel, Vol. 83, pp ( Practical fuels - properties! Values NOT uique because! Real fuels are a mixture of may molecules, compositio varies! Differet testig methods & defiitios Property Jet-A Diesel Gasolie Ethaol Natural gas eatig value (MJ/kg Flash poit ( (T at which vapor makes flammable mixture i air Vapor pressure (at 100 F (psi Freezig poit ( Autoigitio temperature ( (T at which fuel-air mixture will igite spotaeously without spark or flame Desity (at 15 (kg/m More ifo:

6 Stoichiometry! Balacig of chemical reactios with "kow" (assumed products! Example: methae ( 4 i air (O N a(o N 2 b O 2 + c 2 O + d N 2 (how do we kow this kow this set of products is reasoable? From 2d Law, to be discussed i Lecture 3 oservatio of atoms: atoms: 4 (1 + O2 (0 + N2 (0 O2 (b + 2O (0 + N2 (0 atoms: 4 (4 + O2 (0 + N2 (0 O2 (0 + 2O (2c + N2 (0 O atoms: 4 (0 + O2 (2a + N2 (0 O2 (2b + 2O (c + N2 (0 N atoms: 4 (0 + O2 (0 + N2 (3.77*2a O2 (0 + 2O (0 + N2 (2d Solve: a 2, b 1, c 2, d (O N 2 1 O O N 2 or i geeral x y + (x + y/4(o N 2 x O 2 + (y/2 2 O (x + y/4n 2 11 Stoichiometry! The previous page shows a special case where there is just eough fuel to combie with all of the air, leavig o excess fuel or O 2 ureacted; this is called a stoichiometric mixture! I geeral, mixtures will have excess air (lea mixture or excess fuel (rich mixture! The aalysis assumed air O N 2 ; for lower or higher % O 2 i the atmosphere, the umbers would chage accordigly 12 6

7 Stoichiometry! Fuel mass fractio (f f fuel mass total mass M fuel fuel 1 (12x +1y fuel M fuel + O2 M O2 + N2 M N2 1 (12x +1y + (x + y 4 ( umber of moles of species i, molecular mass of species i For the specific case of stoichiometric methae-air (x 1, y 4, f ; a lea/rich mixture would have lower/higher f! For stoichiometric mixtures, f is similar for most hydrocarbos but depeds o the / ratio x/y, e.g.! f for 4 (methae - lowest possible / ratio! f for 6 6 (bezee or 2 2 (acetylee - high / ratio! Fuel mole fractio X f fuel moles X f total moles fuel 1 fuel + O2 + N2 1+ (x + y 4 which varies a lot depedig o x ad y (i.e., much smaller for big molecules with large x ad y 13 Stoichiometry! Fuel-to-air ratio (FAR fuel mass FAR air mass fuel mass total mass - fuel mass (fuel mass/(total mass 1 - (fuel mass/(total mass f 1 - f ad air-to-fuel ratio (AFR 1/(FAR! Note also f FAR/(1+FAR! Equivalece ratio (φ φ FAR (actual mixture FAR (stoichiometric mixture φ < 1: lea mixture; φ > 1: rich mixture! What if we assume more products, e.g. 4 +?(O N 2? O 2 +? 2 O +? N 2 +? O I this case we have 4 atom costraits (1 each for,, O, ad N atoms but 5 ukows (5 questio marks - how to solve? Need chemical equilibrium (Lecture 3 to decide how much ad O are i the form of O 2 vs. O 14 7

8 hemical thermodyamics - itro! Besides eedig to kow how to balace chemical reactios, we eed to determie how much iteral eergy or ethalpy is released by such reactios ad what the fial state (temperature, pressure, mole fractios of each species will be! What is highest temperature flame? 2 + O 2 at φ 1? Nope, T 3079K at 1 atm for reactats at K! Probably the highest is diacetylitrile + ozoe 4 N 2 + (4/3O 3 4 O + N 2 T 5516K at 1 atm for reactats at K! Why should it? The 2 + O 2 system has much more eergy release per uit mass of reactats, but still a much lower flame temperature 15 hemical thermodyamics - itro! The reasos that the product is NOT just 2 O, i.e. we do't get 2 + (1/2O 2 2 O but rather 2 + (1/2O O O O O i.e. the water dissociates ito the other species (how do we kow how much of the other species? Wait for Lecture 3! Dissociatio does 2 thigs that reduce flame temp.! More moles of products to soak up eergy (1.22 vs. 1.00! Eergy required to break -O- bods to make the other species! igher pressures reduce dissociatio - Le hatelier's priciple: Whe a system at equilibrium is subjected to a stress, the system shifts toward a ew equilibrium coditio so as to reduce the stress (more pressure, less space, system respods by reducig umber of moles of gas to reduce pressure 16 8

9 hemical thermodyamics - itro! Actually, evef we somehow avoided dissociatio, the 2 - O 2 flame would be oly 4998K - still ot have as high a flame temp. as the weird 4 N 2 flame! Why? 2 O is a triatomic molecule - more degrees of freedom (DOFs (i.e. vibratio, rotatio tha diatomic gases; each DOF adds to the molecule's ability to store eergy! So why is the 4 N 2 - O 3 flame so hot?! O 3 decomposes exothermically to (3/2O 2! O ad N 2 are diatomic gases - fewer DOFs! O ad N 2 are very stable eve at 5500K - almost o dissociatio 17 hemical thermodyamics - goals! Give aitial state of a mixture (temperature, pressure, compositio, ad a assumed process (costat pressure, volume, or etropy, usually, fid the fial state of the mixture! Three commo processes i egie aalysis! ompressio» Usually costat etropy (isetropic» Low P / high V to high P / low V» Usually P or V ratio prescribed» Usually compositio assumed "froze" - if it reacted before compressio, you would t get ay work out!! ombustio» Usually costat P or V assumed» ompositio MUST chage (obviously! Expasio» Opposite of compressio» May assume froze (o chage durig expasio or equilibrium compositio (mixture shifts to ew compositio after expasio 18 9

10 hemical thermodyamics - assumptios! Ideal gases - ote may "flavors" of the ideal gas law PV RT PV mrt Pv RT P ρrt P pressure (N/m 2 ; V volume (m 3 ; umber of moles of gas R uiversal gas costat (8.314 J/moleK; T temperature (K m mass of gas (kg; R mass-specific gas costat R/M M gas molecular mass (kg/mole; v V/m specific volume (m 3 /kg ρ 1/v desity (kg/m 3! Adiabatic! Kietic ad potetial eergy egligible! Mass is coserved! ombustio process is costat P or V (costat T or s combustio is't very iterestig!! ompressio/expasios reversible & adiabatic ( isetropic, ds 0 19 hemical thermodyamics - 1st Law! 1st Law of thermodyamics (coservatio of eergy, cotrol mass: de δq - δw! E U + PE + KE U U! δw PdV for a simple compressible substace; also assume adiabatic (δq 0! ombie: du + PdV 0! ostat pressure: add VdP 0 term! du + PdV + VdP 0 d(u+pv 0 d 0! reactats products! Recall h /m (m mass, thus h reactats h products! ostat volume: PdV 0! du + PdV 0 d(u 0! U reactats U products, thus u reactats u products! h u + Pv, thus (h - Pv reactats (h - Pv products! Most property tables report h ot u, so h - Pv form is useful! h or u must iclude BOT thermal ad chemical cotributios! 20 10

11 hemical thermodyamics - 1st Law! Ethalpy of a mixture (sum of thermal ad chemical terms (1! hi (2 h! i ethalpy of i per mole of i [ h(t! h! + Δ h! o ( (o subscripts umber of species; umber of moles of i [! h(t! h ethalpy per mole of i to raise i from K to T (thermal ethalpy Δ h! o ethalpy of formatio per mole of i at K & 1 atm, i.e. ethalpy chage from formatio of i from its elemets i their stadard state (chemical ethalpy Note Δ h! o 0 for elemets i their stadard state, e.g. O 2 (gas, (solid (3 m mass of mixture ; molecular mass of i ombie (1 (3 to obtai o ( h [ h(t! h! + Δ h! m 21 hemical thermodyamics - 1st Law! Note we ca also write h as follows o ( h [ h(t! h! + Δ h! m [ h(t! h! + Δ h! o T ( T Moles of i T Total moles of all gases Mole fractio of i X i h m u U m PV m h o ( X i [ h (T h + Δ X i mrt m h RT! Use boxed expressios for h & u with h costat (for costat P combustio or u costat (for costat V combustio 22 11

12 hemical thermodyamics - 1st Law! Examples of tabulated data o h(t - h, Δh f, etc. (double-click table to ope Excel spreadsheet with all data for O, O, O 2,, O 2,, O, 2 O, 2, N 2, NO at 200K K O Molecular weight g/mole Δh f o (kj/mole O 2 Molecular weight g/mole Δh o f (kj/mole O 2 Molecular weight g/mole Δh o f (kj/mole T s h-h_ K J/mole-K kj/mole T s h-h_ K J/mole-K kj/mole T s h-h_ K J/mole-K kj/mole hemical thermodyamics - 1st Law! Example: what are h ad u for a O-O 2 -O 2 mixture at 10 atm & 2500K with X O , X O , X O ? h Pressure does't affect h or u but T does; from the tables: M O ; M O ; M O kg/mole Δh o f,o h o ( X i [ h (T h + Δ h 3784 kj kg R R M ; M R 8.314J molek ; Δh o f,o2 X i J kg X i u h RT ; Δh o f,o kj /mole [ h (2500 h ] O ; [ h (2500 h ] O ; [ h (2500 h ] O kj /mole ( ( ( kj /mole ( ( ( kg/mole kg ( ( ( mole kg 209.2J mole kgk J kg 209.2J kgk (2500K J 106 kg 24 12

13 hemical thermodyamics - 1st Law! Fial pressure (for costat volume combustio PV mrt, R R ; R uiversal gas costat J/moleK M Total mass i M (for mixture Total moles X i Total ostat volume combustio : V costat, m costat ombie : P products P reactats (products T products T reactats i 25 hemical thermodyamics - heatig value! ostat-pressure eergy coservatio equatio (o heat trasfer, o work trasfer other tha PdV work h reactats [ h (T h + Δ h o ( h products (products [ h (T h + Δ h o ( (products Deomiator m costat, separate chemical ad thermal terms: ( ([ h (T h [ h (T h (products! This scary-lookig boxed equatios simply coservatio of eergy for a chemically reactig mixture at costat pressure! Term o left-had side is the egative of the total thermal ethalpy chage per uit mass of mixture; term o the right-had side is the chemical ethalpy chage per uit mass of mixture 26 (products Δh o Δ (products o h 13

14 hemical thermo - heatig value! By defiitio, P ( h/ T P! For adeal gas, h h(t oly, thus P dh/dt or dh P dt! If P is costat, the for the thermal ethalpy h 2 - h 1 P (T 2 - T 1 m P (T 2 - T 1 /m! For a combustio process i which all of the ethalpy release by chemical reactio goes ito thermal ethalpy (i.e. temperature icrease i the gas, the term o the left-had side of the boxed equatio o page 26 ca be writte as ( ([ h (T h [ h (T h P (products m P (T reactats T products m where is the costat-pressure specific heat averaged (somehow over all species ad averaged betwee the product ad reactat temperatures 27 hemical thermo - heatig value! Term o right-had side of boxed equatio o page 26 ca be rewritte as (products fuel Δ h o Δ (products o h Δ h o Δ o fuel f M fuel M fuel fuel M fuel i! Last term is the chemical ethalpy chage per uit mass of fuel; defie this as -Q R, where Q R is the fuel's heatig value (products Δh o Δ o h Q R fuel M fuel! For our stereotypical hydrocarbos, assumig O 2, 2 O ad N 2 as the oly combustio products, this ca be writte as Q R x Δh f,o 2 o o + (y 2 Δh f,2 O o 1 Δh f, fuel 1 M fuel o (x + y 4Δh f,o2 h 28 14

15 hemical thermo - flame temperature! Now write the boxed equatio o page 26 (coservatio of eergy for combustio at costat pressure oce agai: ( ([ h (T h [ h (T h (products m! We've show that the left-had side P (T reactats T products m ad the right-had side -fq R ; combiig these we obtai T products T reactats + fq R / P! This is our simplest estimate of the adiabatic flame temperature (T products, usually we write this as based o aitial temperature (T reactats, usually writte as T thus (products Δh o Δ o h T + fq R / P (costat pressure combustio, T-averaged P 29 hemical thermo - flame temperature! This aalysis has assumed that there is eough O 2 to bur all the fuel, which is true for lea mixtures oly; i geeral we ca write T + f burable Q R P where for lea mixtures, f burable is just f (fuel mass fractio whereas for rich mixtures, with some algebra it ca be show that # 1 f & f burable f stoichiometric % ( $ 1 f stoichiometric ' thus i geeral we ca write T + f Q R P (if f f stoichiometric % 1 f ( T + f stoichiometric ' * Q R (if f f stoichiometric & 1 f stoichiometric P 30 15

16 hemical thermo - flame temperature! For costat-volume combustio (istead of costat P, everythig is the same except u cost, ot h cost, thus the term o the left-had side of the boxed equatio o page 29 must be re-writte as $ ([ h (T h ' $ (products & (PV reactats [ h (T h ' & ( (PV products % ( % ( The extra PV terms ( mrt for adeal gas adds a extra mr(t products -T reactats term, thus which meas that (agai, T products ; T reactats T m P (T products T reactats m P (T products T reactats mr(t products T reactats m m ( P R(T products T reactats v (T products T reactats T + fq R / v (costat volume combustio, T-averaged P which is the same as for costat-pressure combustio except for the v istead of P 31 hemical thermo - flame temperature! The costat-volume adiabatic flame (product temperature o the previous page is oly valid for lea or stoichiometric mixtures; as with costat-pressure for rich mixtures we eed to cosider how much fuel ca be bured, leadig to T + f Q R v (if f < f stoichiometric $ 1 f ' T + f stoichiometric & Q R (if f > f % 1 f stoichiometric ( stoichiometric v! Note that the ratio of adiabatic temperature rise due to combustio for costat pressure vs. costat volume is ( T costat v P γ ( T costat P V P! Oe ca determie by workig backwards from a detailed aalysis; for stoichiometric 4 -air, f 0.055, Q R 50 x 10 6 J/kg, costatpressure combustio, 2226K for T 300K, thus P 1429 J/kgK (for other stoichiometries or other fuels, the effective P will be somewhat but ot drastically differet 32 16

17 Example of heatig value! Iso-octae/air mixture: ( Δ h! o f, kj / mole (O N 2 8 O O *3.77 N 2 (products Δ h! o Δ! o h Q R fuel M fuel 8Δ h! o f,o2 + 9Δ h! o f, 2O +12.5(3.77Δ h! o ( f,n 2 1Δ h! o f, Δ h! o f,o (3.77Δ h! o f,n 2 ( 1M 818 ( ( 1( ( (3.77(0 8 moles( kj/mole + 9( (3.77(0 (1 mole(0.114 kg/mole 44,500 kj/kg 4.45 x 10 7 J/kg 33 Fuel properties Fuel eatig value, Q R (J/kg f at stoichiometric Gasolie 43 x Methae 50 x Methaol 20 x Ethaol 27 x oal 34 x Paper 17 x Fruit Loops 16 x 10 6 Probably about the same as paper ydroge 120 x U 235 fissio 83,140,000 x Pu 239 fissio 83,610,000 x fusio 339,000,000 x : 3 1 :

18 ommets o heatig value! eatig values are usually computed assumig all O 2, 2 O, N N 2, S SO 2, etc.! If oe assumes liquid water, the result is called the higher heatig value; if oe (more realistically, as we have bee doig assumes gaseous water, the result is called the lower heatig value! Most hydrocarbos have similar Q R ( x 10 7 J/kg sice the same - ad - bods are beig broke ad same -O ad -O bods are beig made! Foods similar - o a dry weight basis, about same Q R for all! Fruit Loops ad Shredded Wheat have same "heatig value" (110 kcal/oz 1.6 x 10 7 J/kg although Fruit Loops mostly sugar, Shredded Wheat has oe (the above does ot costitute a commercial edorsemet! Fats slightly higher tha starches or sugars! Foods with (o-digestible fiber lower 35 ommets o heatig value! Acetylee higher (4.8 x 10 7 J/kg because of triple bod! Methae somewhat higher (5.0 x 10 7 J/kg because of high / ratio! 2 MU higher (12.0 x 10 7 J/kg because o "heavy" atoms! Alcohols lower (2.0 x 10 7 J/kg for methaol, 3 O because of "useless" O atoms - add mass but o ethalpy release 36 18

19 Example of adiabatic flame temperature! Leaso-octae/air mixture, equivalece ratio φ 0.8, iitial temperature T 300K, average P 1400 J/kgK, average v 1100 J/kgK: Stoichiometric: (O N 2 8 O O *3.77 N 2 φ FAR (actual mixture, φ 0.8 FAR (stoichiometric mixture, φ 1 f /(1 f φ 0.8 φ f φ 1 /(1 f φ 1 f φ 1 fuel M fuel (1 mole 8 18 (0.114 kg/mole (1 mole 8 18 (0.114 kg/mole + (12.5 mole O 2 (0.032 kg/mole + (12.5 * 3.77 mole N 2 (0.028 kg/mole FAR φ 1 f φ 1 /(1 f φ /( φ 0.8 : f /(1 f φ 0.8 φ f φ T + fq R / P 300K + ( ( J /kg /(1400J /kgk 1906K (cost. P T + fq R / V 300K + ( ( J /kg /(1100J /kgk 2345K (cost. V 37 Summary - Lecture 2! May fuels, e.g. hydrocarbos, whe chemically reacted with a oxidizer, e.g. O 2, release large amouts of eergy or ethalpy! This chemical eergy or ethalpy is coverted ito thermal eergy or ethalpy, thus i a combustio process the product temperature is much higher tha the reactat temperature! Oly 2 priciples are required to compute flame temperatures! oservatio of each type of atom! oversatio of eergy (sum of chemical + thermal but the resultig equatios required to accout for chages i compositio ad eergy ca look formidable! Key thermodyamic properties of a fuel are its heatig value Q R ad its stoichiometric fuel mass fractio f stoichiometric! Key property of a fuel/air mixture is its equivalece ratio (φ! A simplified aalysis leads to T + fq R / P (costat pressure T + fq R / V (costat volume 38 19