c ombustion p rof. s eung w ook b aek d epartment of a erospace e ngineering, kaist, in korea r oom...

COMBUSTION

PROF. SEUNG WOOK BAEK DEPARTMENT OF AEROSPACE ENGINEERING, KAIST, IN KOREA

ROOM: Building N7-2 #3304 TELEPHONE : 3714 Cellphone : 010 – 5302 - 5934 [email protected] http://procom.kaist.ac.kr

TA : Bonchan Gu ROOM: Building N7-2 # 3315 TELEPHONE : 3754 Cellphone : 010 – 3823 - 7775 [email protected]

PROF. SEUNG WOOK BAEK DEPARTMENT OF AEROSPACE ENGINEERING, KAIST, IN KOREA

ROOM: Building N7-2 #3304 TELEPHONE : 3714 Cellphone : 010 – 5302 - 5934 [email protected] http://procom.kaist.ac.kr

TA : Bonchan Gu ROOM: Building N7-2 # 3315 TELEPHONE : 3754 Cellphone : 010 – 3823 - 7775 [email protected]

COURSE CODE : MAE 415

COURSE NAME : COMBUSTION ENGINEERING

PROFESSOR : SEUNG WOOK BAEK (Rm #3304, Ext. 3714)

GRADING SYSTEM

1 Final Exam ( June 11th, 2015 )

Homework

SYLLABUS (1/4)

How to efficiently mix fuel and oxidizer Convection and diffusion

How to efficiently burn fuel and oxidizer: energy saving

How to reduce pollutant emission such as CO,CO2 and NOx

How to improve safety and reduce impact on environment

To develop green, sustainable and alternative energy

ISSUES IN COMBUSTION SCIENCE

REFERENCES

F.A.Williams, “Combustion Theory,” Addison Wesley, 2nd Ed.

D.B.Spalding, “Combustion and Mass Transfer,” Pergamon

Press

I.Glassman, “Combustion,” Academic Press, 2nd Ed.

M.Kanury, “Introduction to Combustion Phenomena,” Gordon

and Breach Science Publishers

P.A.Libby and F.A.Williams (Editors), “Turbulent Reacting

Flows,” Springer Verlag

L.A.Kennedy (Editor), “Turbulent Combustion,” Progress in

Astronautics and Aeronautics, Vol.58

SYLLABUS (2/4)

K.K.Kuo, “Principles of Combustion,” Wiley

V.R.Kuznetsoz and V.A.Sabelnikov, “Turbulence and

Combustion,” Hemisphere Publishing Corporation

JOURNALS

Combustion and Flame

Combustion Science and Technology

Symposium (International) on Combustion

Combustion Theory and Modeling

AIAA Journal

Progress in Energy and Combustion Science

SYLLABUS (3/4)

Combustion, Explosion and Shock Waves

Progress in Astronautics and Aeronautics

Fire Safety Journal

International Journal of Heat and Mass Transfer

Journal of Heat Transfer

Journal of Thermophysics and Heat Transfer

Journal of Propulsion and Power

SYLLABUS (4/4)

Thermochemistry

Combustion- high temperature, moderate or high pressure, perfect gas, real gas effects for high pressure environment

Thermodynamic properties of a single perfect gas

Equation of state :

TRCTW

Rp

: Universal gas constant R

PROPULSION AND COMBUSTION LABORATORY

Kmole

energy

: Molecular weight W

mole

mass

: Concentration C

volumeunit

mole

Combustion Engineering

PROPULSION AND COMBUSTION LABORATORY Combustion Engineering

Internal Energy

u : per unit mass

dTTcuuT

T V0

0

0u : Internal energy of formation

Vc : Specific heat

K mass

energy

Enthalpy

W

TRdTcu

W

TRu

puh

T

T V 0

0or

W

TR

W

TRdT

W

Rc

W

TRuh

T

T P

00

00

= T

T P dTTch0

0

0h : Enthalpy of formation



Only change in or is important (not the absolute level)h

0u0hNeed a convention for and

1) Prescribe a standard state, i.e., 0T and 0p

2) The formation enthalpy of the chemical elements in their natural phase at and will be zero.

0T 0p

3) , atmp 10 KT 16.2980

0h for, gH 2 : 00 h gOH 2 : 00 h sC : 00 h

gN 2 : 00 h lH 2 : 00 h

u


Entropy

T

T

P

p

p

W

RdT

T

css

00

0 ln

Let = Entropy at and any temperature .0s 0p T

0

0 lnp

p

W

Rss

Gibbs Free Energy

Tshf per unit mass basis

0000 TshTshf 0

0

0

0 ln)ln(p

p

W

TRf

p

p

W

RsThf

p

dp

W

R

T

dhds

dh vdpTds dh vdp ds

T T


On a molar basis

0

0 lnp

pTRFFWf

F : Molar basis

Helmholtz Free Energy

Tsua

0

0

lnRT p

f fW p


TC : Total number of moles per unit volume

KC : Total number of moles of species K per unit volume

KX : Mole fraction of species K

K

KT CCT

KK C

CX

KKX 1

Mixture of perfect gases ;

222 cNbOaH


: Density of the mixture

K : Partial density of species K

KY : Mass fraction of species K

KW : Molecular weight of species K

K

KKK

K CW

K

KY ,

1K

KY

KKK

KK Y

WWC


jK KT K

K K jK K j

YYC C

W W W

K

/, Y

/K K K K K K K K

KT j j j j j j

j j j

C Y W W C W XX

C Y W W C W X

W : Mean molecular weight of the mixture

K

jjj

jjj

K K

KK

KK WYWY

W

YW

XWW/

1

/

K K K j jK K j

W C W C KKK

KK Y

WWC

KKK

KK

K

KK

K WXW

YW

W

Y

W1)(,

1

EQUATION OF STATE

Partial pressure exerted by species K if it occupiesthe whole volume at temperature T.

TRCp KK


Dalton’s Law

K K T TK K

p p RT C C RT C WRT RT but

,KT

K K

YC

W W

K K

K TW

R

W

YTRp

Internal Energy

K

KKYuu


T

T VKK dTTcuuK

00

0

0K

T

K K K K K VTK K

u Y u Y u Y c T dT

T

T V dTcuu0

0 where K

KK uYu00

T

TK

T

T VVK

T

T VK

K dTcdTcYdTcYKK

0 00

K

VKV KcYc


Enthalpy

K

KK hYh

T

T P dTchh0

0 when is fixed KY

K

KK hYh00

KPKP K

cYc

Entropy

K

KK sYs


T

T

K

K

PKK p

p

W

RdT

T

css K

00

0

ln

00

0

lnKK PT

K K KK K K K T

K K K K

Y cY p

s Y s Y s dT RT W p

K

K

K

KT

T

P

p

p

p

p

W

YRdT

T

cs

00 lnln

0


T

T

P

p

p

W

RdT

T

css

00

0 ln

K

KK

KT

T

P XW

YR

p

p

W

RdT

T

css lnln

00

0

00

0

1

ln ln

PK

TP K

KTK K

Entropy increases due to mixingEntropy that a perfect gas of W and cX so that positive termwould have for p and T

c YR ps s dT R X

T W p W

K

KK fYf0

0 lnp

p

W

TRff K

KKK

0

0 lnp

p

W

YTRff K

K K

K


00

0

ln lnT

P K K

TK K

c Y p ps s dT R

T W p p

lnK KK

RX X

W

KY K K K K

j jj

W X W X

W X W

K

K

K

K XW

YTR

p

p

W

TRff lnln

0

0

p

KP T

hc

K

Caution ;

When there is reaction p

P T

hc

K

KK hYhp

K

KK

p

K

KK

p T

Yh

T

hY

T

h

p

K

KK

p

P T

Yh

T

hc


K

KKXX

W

TRln

0 0

0 0

ln (ln ln )K K K K

K KK K

Y p Y ppf f RT f RT

W p W p p

KK

K

XYW W

Problem for notes

Binary mixture of 422 HeH

,1

2

2

2

2

H

HH Y

YX

2

2

1

1

H

H

He Y

YX

,12 HeH YY

HeH PHPHPcYcYc

2221

Specification of Composition

,TRnVp KK TRnpV T For same TV ,


jj

j

K

K

K

WYW

Y

X

KK

KKKK

W

WY

Wm

Wm

n

n

p

p

/

/

,TW

RmpV

KKK T

W

RmpV

For same P and T, partial volume of species K

T

K

KT

KK

K

KK

n

n

W

W

Wn

Wn

W

W

m

m

V

V

Here, is not so thatV KV .KK Y

m

m


Material Balance for Chemical ReactionsEx) Combustion of Octane with Air

Air: 2222

176.379.021.0 Oof mole perNof molesNO Molecular Weight: 298.282879.03221.0

For complete combustion (stoichiometric)

22222188 21

79

2

2598

21

79

2

25

2

25NOHCONOHC

Stoichiometric Coefficients: 1188 HC

,2/252O

21

79

2

252 N


On a mass basis,

2821

79

2

25

2

189

2

448

2

)(1831

2821

79

2

25

2

322

25

2

114

188 21

79

2

2598

21

79

2

25

2

25

NOHCONOHC

gmsorlbs

or 15.1 kg of air/ 1 kg of octane

For reactants

0165.052.60

1

21

79

2

25

2

251

1188

HCX

,2065.052.60

2/252

OX 7769.052.60

21/792/252

NX



0623.01831

114188

HCY

W

: MEAN MOLECULAR WEIGHT OF REACTANTS

3.3052.60

1831

MASS OF PRODUCTS = 1831

125.0

2179

225

98

82

CO

X RP nn

2821

79

2

25

2

189

2

448

2

)(1831

2821

79

2

25

2

322

25

2

114

188 21

79

2

2598

21

79

2

25

2

25

NOHCONOHC

gmsorlbs


EQUIVALENCE RATIO :

tricstoichiomeoxidizerofmass

fuelofmass

oxidizerofmassfuelofmass

FOR 1

222224 76.32276.322 NOHCONOCH


1

1

1

: STOICHIOMETRIC

: FUEL LEAN

: FUEL RICH

FOR 9.0 224 76.3229.0 NOCH

FOR 1 differentCH 4

ENERGY Eq. FOR CHEMICAL REACTION

CONSTANT VOLUME SYSTEM – NO MOTION


1st LAW : WdEQ

Q

dE

W

: HEAT TRANSFER

(POSITIVE WHEN ADDED TO THE SYSTEM)

: INTERNAL ENERGY

: WORK DONE BY THE SYSTEM

1221 EEQ 1: REACTANT STATE

2: PRODUCT STATE

ONLY IMPORTANCE IS , NOT THE ABSOLUTE VALUES.


E

BT

C25: REFERENCE OR BASIC TEMPERATURE

BE: INTERNAL ENERGY OF REACTION, DETERMINED IN A BOMB CALORIMETER


11122212 EEEEEEEEQ BBBB

ncompositiofixed

B

tabulated

B

ncompositiofixed

B EEEEE

11

22

FOR CONSTANT PRESSURE PROCESS;

VdpdHpdVdEWdEQ

1 2 2 1 2 2 2 1 1 1

B

B B B B

H

Q H H H H H H H H


BH

BE

: ENTHALPY OF REACTION

BBBBBB VpVpEH 1122

:INTERNAL ENERGY OF

REACTION AT BTFOR PERFECT GASES;

constpBconstVB EE

2 1B B BH H H


BBBBBBB TRnTRnTRnVpVp 121122

12 nnn BBB TRnEH

2 2 1 1

2 1 2 2 2 1 1 1

B B B B B B

B B B B

H E p V p V

Q H H H H H H H H

ENTHALPY OF FORMATION AND ENTHALPY OF COMBUSTION

ENTHALPY OF FORMATION -THAT CHANGE OF ENTHALPY WHICH OCCURS WHEN A COMPOUND IS FORMED FROM THE ELEMENTS, WHICH ARE IN THEIR STABLE STATE, AT SAME STANDARD TEMPERATURE AND PRESSURE.


gCOgOsC 22 GIVES OFF 94052 cal :exothermic reaction

2

0294052 /f CO

H cal gmole of CO

HEAT OF FORMATION =0

294052 /fH cal gmole of CO ALSO A COMBUSTION PROCESS

ENTHALPY OF COMBUSTION 0 0

294052 /c fH H cal gmole of CO

2/94052 COofgmolecal

HEAT OF COMBUSTION OF

HEAT OF COMBUSTION

)(/12

94052)( sCof gcalsC


gNOgOgNEx 2222

1)

20 /8091

2NOofgmolecalH

NOf

HEATING VALUES; FOR C+O2 REACTION,

BB EH ,BECAUSE THERE IS NO WORKS.pdV

IN GENERAL,

HIGHER HEATING VALUES AND LOWER HEATING VALUES DEPEND ON STATE OF PRODUCTS.

BB EH

ENDOTHERMIC REACTION

BBB TRnEH


IMPORTANT CASE IS vs. gOH 2 lOH 2

OHOH 222 2

1

IF IS LIQUID,

LHV DIFFERS FROM HHV BY HEAT OF VAPORIZATION.

OH 2 22 /32.34 HofgkcalOHHHV

22

22 /9.28

9/602.0 Hofgkcal

Hofg

OHofgOHofgkcalHHVLHV


REFERENCES FOR THERMOCHEMICAL DATA

1. NBS, “Tables of Selected Values of Chemical Thermal Properties”, Circular Letter 500

2. JANAF Thermo-Chemical Tables (1993)3. Penner’s Book4. Van Wylen & Sonntag (SI units)5. CHEMKIN: Software package for the analysis of gas-

phase chemical and plasma kinetics (2000)

EXAMPLE

10g OF H2 (g) BURN IN AIR (=1) AT CONSTANT

PRESSURE. INITIAL TEMPERATURE IS 298K AND FINAL TEMPERATURE IS 2000K SO THAT H2O IS GASEOUS. CALCULATE THE HEAT LIBERATED ;


12 HHQ

molesHofg 5102

)(4.9)(5)()76.3(2

5)(

2

5)(5 22222 gNgOHgNgOgH

KgNKgOH HHH 2000),(2000),(2 224.95

KgNKgOKgH HHHH 298),(298),(298),(1 2224.9

2

55

molecal

HHHH KgOHfKKKgOH

7.40535577987.236719630

298),(,29820002000),( 22

KgNfKgN HH 298),(,2000),( 22

3.20728.15494


MINUS INDICATES THAT HEAT WAS

TRANSFERRED OUT OF THE SYSTEM. IN OTHER

WORDS, THE FLAME TEMPERATURE, IF ADIABATIC,

WOULD BE HIGHER THAN 2000 K.

IF THE PROBLEM WERE AT CONSTANT VOLUME,

0298),(298),(298),( 222 KgNKgOKgH HHH

calQ 76512

12 EEQ TRnHpVHE

etc. calcal

TRnHEKgOHKgOH

,20009807.15)7.40535(5

552000),(2000),( 22


CALCULATION OF ENTHALPY OF REACTION FROM

THE ENTHALPY OF FORMATION

REACTION ;

ReactantsProductsReaction

RfPfR HHH

nNmMbBaA

Na

nM

a

mB

a

bA ro

AfBfNfMfAofmoleR HH

a

bH

a

nH

a

mH


EX) GASEOUS CH4 + O2 REACT TO YIELD H2O(l)+CO2(g).

CALCULATE PER MOLE OF CH4 RH

kcal

HHHHHgOfgCHflOHfgCOfCHR

8.2129.1732.68205.94

22)()()()( 24224

)(2)()(2)(2224

lOHgCOgOgCH

EXOTHERMIC PER MOLE OF CH4


CONSIDER A CHEMICAL SYSTEM OF CONSTANT MASS

EITHER HOMOGENEOUS OR HETEROGENEOUS IN

MECHANICAL AND THERMAL EQUILIBRIUM BUT NOT IN

CHEMICAL EQUILIBRIUM. THE SYSTEM IS IN CONTACT

WITH A RESERVOIR AT TEMPERATURE T AND

UNDERGOES AN INFINITESIMAL IRREVERSIBLE

EXCHANGE OF HEAT, Q, TO THE RESERVOIR. PROCESS

MAY INVOLVE CHEMICAL REACTION AND TRANSPORT

BETWEEN PHASES.


FROM SYSTEM

dS: ENTROPY CHANGE OF THE SYSTEM

sQQ

0 dST

Qs

dSO: ENTROPY CHANGE OF THE RESERVOIR

dS+dSo: ENTROPY CHANGE OF THE UNIVERSE

0 dSdSO

T

QdS

O

0 dS

T

Q


FROM SYSTEM

1ST LAW sQ dE pdV

0 dST

Qs

0dE pdV TdS VARIOUS CONSTRAINTS

CASE A ; HOLD E AND V CONSTANT

ISOLATED SYSTEM0dS

CASE B ; HOLD p AND T CONSTANT

0d E pV TS d H TS dF GIBBS FREE ENERGY DECREASES


WHEN ; HAVE CHEMICAL EQUILIBRIUM

AT EQUILIBRIUM ;

0, TPF

CASE C ; HOLD V AND T CONSTANT

0 dATSEd

0, TVA

-


EQUILBRIUM OF A MIXTURE OF PERFECT GASES

UNDERGOING CHEMICAL REACTION

CONSIDER THE REACTION,

dDcCbBaA WE KNOW GIBBS FREE ENERGY FOR

AND ANY TEMPERATURE T PER MOLE.

AF atmP 10

AT ANY T AND P ;

0ln ppTRFF AAA

0ln ppTRFF BBB

, ETC

AF

0

0

0 0

0 0

ln

ln ln

KK K

K

K KK K K K K K

pRTf f

W p

p pW f F W f RT F RT

p p


LET

BADC bFaFdFcFF

0 0

0 0

lnc d

C Da b

A B

p p p pF F RT

p p p p

0 1 P atm

lnc dC Da bA B

p pF F RT

p p

BADC bFaFdFcFF

0 0 0 0

ln ln ln lnC D A BC D A B

p p p pc F RT d F RT a F RT b F RT

p p p p

0

0

ln KK K

pF F RT

p


NOTE THAT

AT EQUILIBRIUM

DEFINE equilibrium constant based on pressurec dC D

P a bA B

p pK

p p

0F

PKTRF ln

TRFP eK

)(TfF

)(TgKP A

A

pX mole fraction

p

B Bp pX C Cp pX D Dp pX


EFFECT OF T ON EQUILIBRIUM COMPOSITION IS GIVEN IN Kp

EFFECTS OF p ON THE TERM.

FOR THE CASE OF , IE. C + D = A + BNO PRESSURE EFFECT

EQUILIBRIUM CONSTANT BASED ON CONCENTRATION ;

WHERE

( )c d c d

c d a b nC D C DP a b a b

A B A B

X X X XK p p

X X X X

)()( badcn

np

0n

CK

volumeunit

moleionConcentratC


VALUES OF KP ARE TABULATED FOR SPECIFIC

CHEMICAL REACTION.

bB

aA

dD

cC

C CC

CCK C Cp C RT , ETC

c d n nC D

C pa bA B

p pK RT K RT

p p

EX) DISSOCIATION OF CO2

22 2

1OCOCO 2

2

1 2

1CO O

PCO

p pK

p (1)


EX) 100% WATER VAPOR, INITIALLY AT 1 atm AND

2200 K DISSOCIATES INTO H2 (g) AND O2 (g).

ASSUMING PERFECT GASES THROUGHOUT,

DETERMINE THE EQUILIBRIUM COMPOSITION

EQUILIBRIUM COMPOSITION

(2)222

1COOCO 2

2

1

2 11/2

COP P

CO O

pK K

p p

22 22 COOCO (3) 212

2

3

2

2 POCO

COP K

pp

pK


CHEMICAL REACTION )(2

1)()(

222gOgHgOH

2 2 2 2

2 2

1 2 1 21 2H O H O

PH O H O

p p X XK p

p X

2222 cObHOaHOH EQUILIBRIUM COMPOSITION

caO

baH

21:

222:

2)1(

1

ac

ab

2222 2

)1(1 O

aHaOaHOH

2

3

2

)1()1(

aaaanT


2

31

2 aa

X H

2

32

1

2 a

a

X O

2

32 aa

X OH

1 2

1 2

11 23 3

2 2 ,

32

P

aaa a

K pa

a

3 2 1 23

1 2

11.145 10

3P

a PK

a a

2222 2

0137.00137.09863.0 OHOHOH

EQUILIBRIUM

COMPOSITION


EXAMINE LIMITING CONDITIONS

CASE I - LOW TEMPERATURES

; VERY LITTLE DISSOCIATION

LET 1a 1

21

2123

2

PKP

32

312

PKP

OR

A) HIGHER PRESSURE ; LOWER ; GREATER LESS DISSOCIATION

B) HIGHER TEMPERATURE ; HIGHER KP GREATER ; SMALLER MORE DISSOCIATION

a

a

3 2 1 2

1 2

1

3P

a pK

a a

2222 cObHOaHOH

2222 2

)1(1 O

aHaOaHOH


CASE II - HIGH TEMPERATURES ; HIGH DISSOCIATION

OR

A) HIGHER PRESSURE ; HIGHER ; HIGHER LESS DISSOCIATION

B) HIGHER TEMPERATURE ; HIGHER KP ; LOWER = MORE DISSOCIATION

a 1

21

21

3P

KP PK

P 1

3

21

a

a

3 2 1 2

1 2

1

3P

a pK

a a

2222 2

)1(1 O

aHaOaHOH


EQUILIBRIUM WHEN SIMULTANEOUS REACTIONS

OCCURRING

THE NUMBER OF INDEPENDENT REACTIONS, WHICH MUST BE CONSIDERED IN EQUILIBRIUM CALCULATIONS, IS EQUAL TO THE LEAST NUMBER OF EQUATIONS WHICH INCLUDE ANY REACTANT AND PRODUCT WHICH ARE PRESENT TO AN APPRECIABLE DEGREE IN THE EQUILIBRIUM MIXTURE.

EX) CALCULATE THE COMPOSITION OF THE EQUILIBRIUM

MIXTURE OBTAINED WHEN 5 MOLES OF STEAM, H2O

(g) REACT WITH 1 MOLE OF CH4 AT ELEVATED

TEMPERATURE AND SOME ARBITRARY PRESSURE


MECHANISM FOR REACTION ;2 ACTUAL REACTIONS ARE ;

C : 1 = a + c + eH : 14 = 4a + 2b + 2dO : 5 = b + c + 2e

2224245 eCOdHcCOObHaCHOHCH

2224

24

42723

5

CObaHbaCObaObHaCH

OHCH


03 224 RHHCOOHCH

0222 RHHCOOHCO

(1)

(2)

2

4 2

3

1CO H

PCH H O

p pK

p p 2 2

2

2CO H

PCO H O

p pK

p p

aedcbanT 28

3 2

1 2

3 2 7 2

8 2P

a b a b pK

ab a

bba

babaKP

23

2742

2224

24

42723

5

CObaHbaCObaObHaCH

OHCH

3 2

8 2.

CO CO

a bp X p p

aetc


(1)

(2)

eEcCaA dDbBeE

dDcCbBaA ADD (3)

1

c eC E

P aA

p pK

p 2

dD

P e bE B

pK

p p 3 1 2

c dC D

P P Pa bA B

p pK K K

p p

PRODUCT RULE FOR KP’s


ADIABATIC FLAME TEMPERATURE 0Q

POINT (2) FINAL TEMPERATURE AND H AFTER A NON-ADIABATIC REACTION

POINT (2i) ISOTHERMAL REACTIONPOINT (c) ADIABATIC FLAME TEMPERATURE ; H2=H1


CONSTANT PRESSURE REACTION – GENERAL CASE

0Q

P

n

iii

R

m

iii BbAa

DETERMINE TC FROM H2=H1

H2 DEPENDS ON THE bi WHICH DEPENDS ON Tc WHICH

DEPENDS ON THE bi.

m

iTATi

n

iTBTi iiCiC

HaHb1,,,,


FOR PERFECT GASES

WHERE

TO CALCULATE Tc

m

i

T

T PAfTi

n

i

T

T PBfTiBi

C

BiCdTCHadTCHb

1

1,,

r

m

iAfTi

n

iBfTi

HHaHbiiC

1,,

1. ASSUME TC FOR GIVEN PRESSURE

2. CALCULATE THE bi FROM THE KP’s

3. SUBSTITUTE INTO H2=H1

4. ITERATE UNTIL H2=H1


CALCULATE THE ADIABATIC FLAME TEMPERATURE

OF A = 0.8 METHANE – O2 MIXTURE AT p = 10 atm,

TAKING INTO ACCOUNT THE DISSOCIATION OF CO2

AND H2O

2 UNKNOWNS

OHCOOCH2224

220.1

222224 28.08.0 eOdHcCOObHaCOOCH

2222

24

5.05.06.16.18.0

28.0

ObaHbCOaObHaCO

OCH

baedcbanT 5.05.04

TCO n

aX

2

TO n

eX

2etc.

Dissociation Reactions

22 2

1OCOCO 2 2

2 2

1 12 2

12

1CO O CO O

PCO CO

p p X XK p

p X

222 2

1OHOH 2 2 2 2

2 2

1 12 2

12

2H O H O

PH O H O

p p X XK p

p X

12 HH

12142222

28.0TOTCHTOTHTCOTOHTCO HHHeHdHcHbHa

CCCCC

Combustion EngineeringPROPULSION AND COMBUSTION LABORATORY

Procedure ; assume Tc; Calculate a,b,c,d,eSubstitute into H2=H1 (from Energy Equation)

If Tc=3000K


a[-94.05 kcal/mole + 38.94-2.24]+b[-57.8+32.16-2.37]

+c[-26.42+24.43-2.07]+d[0+23.19-2.02]

+e[0+25.52-2.07] = 0.8[-17.89]+2[0]

Hco2HH20

Hco HH2

Ho2 HCH4 Ho2


Tables of Thermodynamic Properties

c ombustion p rof. s eung w ook b aek d epartment of a erospace e ngineering, kaist, in korea r oom...

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