PROF SEUNG WOOK BAEK DEPARTMENT OF AEROSPACE …procom.kaist.ac.kr/Download/Combustion/Combustion 1.pdfK.K.Kuo, “Principles of Combustion,” Wiley V.R.Kuznetsoz and V.A.Sabelnikov,

COMBUSTION

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

ROOM: Building N7-2 #3304

TELEPHONE : 3714

Cellphone : 010 – 5302 - 5934

swbaek@kaist.ac.kr

http://procom.kaist.ac.kr

TA : Hyunwook Jegal

ROOM: Building N7-2 #2311

wprkfgusdnr@kaist.ac.kr

TA : Kyu-Seop Kim

ROOM: Building N7-2 #1308-4

kswind@kaist.ac.kr

COURSE CODE : AE 410

COURSE NAME : COMBUSTION ENGINEERING

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

GRADING SYSTEM

1 Final Exam

Homeworks

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

CURRENT ISSUES IN COMBUSTION SCIENCE &

TECHNOLOGY

REFERENCES

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

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

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 :

: Universal gas constant R

PROPULSION AND COMBUSTION LABORATORY

energy

: Molecular weight W

: Concentration C

volumeunit

Combustion Engineering

PROPULSION AND COMBUSTION LABORATORY Combustion Engineering

Internal Energy

u : per unit mass

dTTcuuT

0u : Internal energy of formation

Vc : Specific heat

K mass

energy

Enthalpy

TRdTcu

dTTch0

0h : Enthalpy of formation

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

hNeed a convention for and

1) Prescribe a standard state, i.e., 0

T and 0p

2) The formation enthalpy of the chemical elements in their

natural phase at and will be zero. 0

3) , atmp 10

KT 16.2980

0h for, gH

0h gOH

0h sC : 0

Entropy

Let = Entropy at and any temperature . 0s 0

Gibbs Free Energy

Tshf per unit mass basis

0000TshTshf

ln)ln(p

d h v d pT d s d h v d p d s

On a molar basis

pTRFFWf

F : Molar basis

Helmholtz Free Energy

lnR T 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

Mixture of perfect gases ;

cNbOaH

: Density of the mixture

K : Partial density of species K

KY : Mass fraction of species K

KW : Molecular weight of species K

K K jK K j

K K K K K K K K

T 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 K K j j

W C W C K

EQUATION OF STATE

Partial pressure exerted by species K if it occupies

the whole volume at temperature T.

TRCpKK

Dalton’s Law

K K T T

p p R T C C R T C W R T R T

Internal Energy

dTTcuuK

K K K K K VT

u Y u Y u Y c T d T

dTcuu0

0 where

KdTcdTcYdTcY

KK0 00

Enthalpy

dTchh0

0 when is fixed KY

Entropy

TK K K

K K K KT

K K K K

Y cY p

s Y s Y s d T RT W p

css lnln

E n tr o p y in c r e a s e s d u e to m ix in gE n tr o p y th a t a p e r fe c t g a s o f W a n d c

X s o th a t p o s it iv e te r mw o u ld h a v e fo r p a n d T

c YR ps s d T R X

T W p W

ln lnT

c Y p ps s d T R

T W p p

K K K K

W X W X

TRff lnln

Caution ;

When there is reaction p

ln ( ln ln )K K K K

K KK K

Y p Y ppf f R T f R T

W p W p p

Problem for notes

Binary mixture of 422

HeH PHPHPcYcYc

Specification of Composition

p V N R T p V N R T For same

K K K K

p N m W WY

p N m W W

For same P and T, partial volume of species K

K K K K K

V m N W NW W

V m W N W W N

Here, is not so that V KV .

Material Balance for Chemical Reactions

Ex) 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

25NOHCONOHC

Stoichiometric Coefficients: 1188

,2/252

On a mass basis,

)(1831

NOHCONOHC

gmsorlbs

or 15.1 kg of air/ 1 kg of octane

For reactants

0165.052.60

,2065.052.60

X 7769.052.60

21/792/25

0623.01831

: MEAN MOLECULAR WEIGHT OF REACTANTS

3.3052.60

MASS OF PRODUCTS = 1831

)(1831

NOHCONOHC

gmsorlbs

EQUIVALENCE RATIO :

tricstoichiomeoxidizerofmass

fuelofmass

oxidizerofmass

fuelofmass

22222476.32276.322 NOHCONOCH

: 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

: HEAT TRANSFER

(POSITIVE WHEN ADDED TO THE SYSTEM)

: INTERNAL ENERGY

: WORK DONE BY THE SYSTEM

1221EEQ

1: REACTANT STATE

2: PRODUCT STATE

ONLY IMPORTANCE IS , NOT THE ABSOLUTE VALUES.

: REFERENCE OR

BASIC TEMPERATURE

: INTERNAL ENERGY OF REACTION,

DETERMINED IN A BOMB CALORIMETER

11122212EEEEEEEEQ

ncompositiofixed

tabulated

ncompositiofixed

BEEEEE

FOR CONSTANT PRESSURE PROCESS;

VdpdHpdVdEWdEQ

1 2 2 1 2 2 2 1 1 1

B B B B

Q H H H H H H H H

: ENTHALPY OF REACTION

BBBBBBVpVpEH

:INTERNAL ENERGY OF

REACTION AT B

FOR PERFECT GASES;

constpBconstVB

2 1B B BH H H

BBBBBBBTRNTRNTRNVpVp

121122

12NNN BBB

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.

gCOgOsC22

GIVES OFF 94052 cal :exothermic reaction

29 4 0 5 2 /

H ca l g m o le o f C O

HEAT OF FORMATION = 0

29 4 0 5 2 /

fH ca l g m o le o f C O

ALSO A COMBUSTION PROCESS

ENTHALPY OF COMBUSTION 0 0

29 4 0 5 2 /

c fH H ca l g m o le o f C O

2/94052 COofgmolecal

HEAT OF COMBUSTION OF

HEAT OF COMBUSTION

94052)( sCof gcalsC

gNOgOgNEx222

0/8091

NOofgmolecalHNOf

HEATING VALUES; FOR C+O2 REACTION,

BBEH , BECAUSE THERE IS NO WORKS. pdV

IN GENERAL,

HIGHER HEATING VALUES AND LOWER HEATING VALUES

DEPEND ON STATE OF PRODUCTS.

ENDOTHERMIC REACTION

BBBTRNEH

IMPORTANT CASE IS vs. gOH2

OHOH222

IF IS LIQUID,

LHV DIFFERS FROM HHV BY HEAT OF VAPORIZATION.

/32.34 HofgkcalOHHHV

2/9.28

9/602.0 Hofgkcal

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 Book

4. 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 ;

molesHofg 5102

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

22222gNgOHgNgOgH

KgNKgOHHHH

2000),(2000),(222

KgNKgOKgHHHHH

298),(298),(298),(1222

molecal

HHHHKgOHfKKKgOH

7.40535577987.236719630

298),(,29820002000),(22

KgNfKgNHH

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),(

KgNKgOKgH

calQ 76512

TRNHpVHE

etc. ,20009807.15)7.40535(5

552000),(2000),( 22

calcal

TRNHEKgOHKgOH

CALCULATION OF ENTHALPY OF REACTION FROM

THE ENTHALPY OF FORMATION

REACTION ;

ReactantsProductsReaction

nNmMbBaA

AfBfNfMfAofmoleR

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

CALCULATE PER MOLE OF CH4 R

HHHHHgOfgCHflOHfgCOfCHR

8.2129.1732.68205.94

22)()()()(

)(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

dSO: ENTROPY CHANGE OF THE RESERVOIR

dS+dSo: ENTROPY CHANGE OF THE UNIVERSE

0 dSdSO

FROM SYSTEM

1ST LAW sQ dE pdV

0d E p d V T d S

VARIOUS CONSTRAINTS

CASE A ; HOLD E AND V CONSTANT

ISOLATED SYSTEM 0dS

CASE B ; HOLD p AND T CONSTANT

0d E p V T S d H T S d F

GIBBS FREE ENERGY DECREASES

WHEN ; HAVE CHEMICAL EQUILIBRIUM

AT EQUILIBRIUM ;

CASE C ; HOLD V AND T CONSTANT

0 dATSEd

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 1

AT ANY T AND P ;

0ln ppTRFF

K K K K K K

pR Tf f

p pW f F W f R T F R T

BADCbFaFdFcFF

p p p pF F RT

p p p p

01 P a tm

p pF F RT

BADCbFaFdFcFF

0 0 0 0

ln ln ln lnC D A B

C D A B

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

p p p p

pF F R T

NOTE THAT

AT EQUILIBRIUM

DEFINE e q u ilib r iu m c o n s ta n t b a s e d o n p re s s u re

PKTRF ln

)(TgKP

pX m o le fr a c t io n

B Bp p X

C Cp p X

D Dp p X

EFFECT OF T ON EQUILIBRIUM COMPOSITION IS GIVEN IN

EFFECTS OF p ON THE TERM.

FOR THE CASE OF , IE. C + D = A + B

NO PRESSURE EFFECT

EQUILIBRIUM CONSTANT BASED ON CONCENTRATION ;

c d c dc d a b nC D C D

P a b a b

A B A B

X X X XK p p

X X X X

)()( badcn

volumeunit

moleionConcentratC

VALUES OF KP ARE TABULATED FOR SPECIFIC

CHEMICAL REACTION.

CCK C C

p C RT , ETC

n nC D

C pa b

p pK RT K RT

EX) DISSOCIATION OF CO2

1OCOCO 2

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

(2) 22

1COOCO

2 11 / 2

2222 COOCO (3)

CHEMICAL REACTION )(2

222gOgHgOH

2 2 2 2

1 2 1 2

1 2H O H O

H O H O

p p X XK p

2222cObHOaHOH EQUILIBRIUM COMPOSITION

)1(1 O

aHaOaHOH

)1()1(

3 2 1 2

11 .1 4 5 1 0

0137.00137.09863.0 OHOHOH

EQUILIBRIUM

COMPOSITION

EXAMINE LIMITING CONDITIONS

CASE I - LOW TEMPERATURES

; VERY LITTLE DISSOCIATION

LET 1a 1

A) HIGHER PRESSURE ; LOWER ; GREATER

LESS DISSOCIATION

B) HIGHER TEMPERATURE ; HIGHER KP GREATER ;

SMALLER

MORE DISSOCIATION

3 2 1 2

2222cObHOaHOH

)1(1 O

aHaOaHOH

CASE II - HIGH TEMPERATURES ; HIGH DISSOCIATION

A) HIGHER PRESSURE ; HIGHER ; HIGHER

LESS DISSOCIATION

B) HIGHER TEMPERATURE ; HIGHER KP ; LOWER =

MORE DISSOCIATION

3 2 1 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 + e

H : 14 = 4a + 2b + 2d

O : 5 = b + c + 2e

2224245 eCOdHcCOObHaCHOHCH

CObaHbaCObaObHaCH

HHCOOHCH

HHCOOHCO

C H H O

p p 2 2

C O H O

aedcbanT

3 2 7 2

a b a b pK

CObaHbaCObaObHaCH

C O C O

a bp X p p

eEcCaA

dDbBeE

dDcCbBaA ADD (3)

P P Pa b

p pK K K

PRODUCT RULE FOR KP’s

ADIABATIC FLAME TEMPERATURE 0Q

POINT (2) FINAL TEMPERATURE AND H AFTER

A NON-ADIABATIC REACTION

POINT (2i) ISOTHERMAL REACTION

POINT (c) ADIABATIC FLAME TEMPERATURE ; H2=H1

CONSTANT PRESSURE REACTION – GENERAL CASE

iiBbAa

DETERMINE TC FROM H2=H1

H2 DEPENDS ON THE bi WHICH DEPENDS ON Tc WHICH

DEPENDS ON THE bi.

TBTiiiCiC

FOR PERFECT GASES

TO CALCULATE Tc

TPAfTi

TPBfTi

dTCHadTCHb1

HHaHbiiC

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

22222428.08.0 eOdHcCOObHaCOOCH

5.05.06.16.18.0

ObaHbCOaObHaCO

baedcbanT

5.05.04

Dissociation Reactions

1OCOCO 2 2

1 12 2

C O O C O O

C O C O

p p X XK p

1OHOH 2 2 2 2

1 12 2

H O H O

p p X XK p

28.0TOTCHTOTHTCOTOHTCO

HHHeHdHcHbHaCCCCC

Combustion Engineering PROPULSION AND COMBUSTION LABORATORY

Procedure ; assume Tc; Calculate a,b,c,d,e

Substitute 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]

Hco2 HH20

Hco HH2

Ho2 HCH4 Ho2

Tables of Thermodynamic Properties

PROF SEUNG WOOK BAEK DEPARTMENT OF AEROSPACE …procom.kaist.ac.kr/Download/Combustion/Combustion 1.pdfK.K.Kuo, “Principles of Combustion,” Wiley V.R.Kuznetsoz and V.A.Sabelnikov,

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