Transcript RADIATION AND COMBUSTION PHENOMENA

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]





SYLLABUS (1/4)

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
ISSUES IN COMBUSTION SCIENCE

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
SYLLABUS (2/4)
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REFERENCES

F.A.Williams, “Combustion Theory,” Addison Wesley, 2nd Ed.

D.B.Spalding, “Combustion and Mass Transfer,” Pergamon
Press
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I.Glassman, “Combustion,” Academic Press, 2nd Ed.
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M.Kanury, “Introduction to Combustion Phenomena,” Gordon
and Breach Science Publishers
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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 (3/4)
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K.K.Kuo, “Principles of Combustion,” Wiley
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V.R.Kuznetsoz and V.A.Sabelnikov, “Turbulence and
Combustion,” Hemisphere Publishing Corporation
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JOURNALS

Combustion and Flame

Combustion Science and Technology

Symposium (International) on Combustion

Combustion Theory and Modeling
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AIAA Journal
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Progress in Energy and Combustion Science
SYLLABUS (4/4)
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Combustion, Explosion and Shock Waves
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Progress in Astronautics and Aeronautics
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Fire Safety Journal
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International Journal of Heat and Mass Transfer

Journal of Heat Transfer

Journal of Thermophysics and Heat Transfer

Journal of Propulsion and Power
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 :
p
R
T  CR T
W
R : Universal gas constant
W
C
 energy 
 m ole K 


 m ass
: Molecular weight  m ole
: Concentration  m ole 
 unit volum e
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
Internal Energy
u : per unit mass
u  u0   cV T dT
T
T0
u0 : Internal energy of formation
 energy 
cV : Specific heat 

 m ass K 
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
Enthalpy
p
T
RT
RT
hu u
 u 0   cV dT 
T0

W
W
or

RT  T 
R
R T R T0
h   u0  0   T  cP  dT 

W 
W
W
W


0
= h0 
T

T0
c P T dT
h0 : Enthalpy of formation
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
Only change in
u or h
is important (not the absolute level)
 Need a convention for h0 and u0
1) Prescribe a standard state, i.e.,
T0 and p0
2) The formation enthalpy of the chemical elements in their
natural phase at T0 and p0 will be zero.
3) p0  1 atm , T0  298.16 K
h0 for, H 2 g  : h0  0
N 2 g  : h0  0
H 2 Og  : h0  0
C s  : h0  0
H 2 l  : h0  0
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
Tds  dh  vdp ds 
dh vdp

T
T
Entropy
dh R dp
T c
R
p
ds 

s  s0   P dT  ln
T0 T
T W p
W p0
Let s 0 = Entropy at p0 and any temperature T .
s  s0 
R
p
ln
W p0
Gibbs Free Energy
f  h  Ts per unit mass basis
R
p
RT
p
f  h  T ( s 0  ln )  f 0 
ln
W p0
W
p0
f 0  h0  Ts 0  h  Ts 0
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
f  f0
RT
p
ln
W
p0
On a molar basis
Wf  F  F 0  R T ln
p
p0
F : Molar basis
Helmholtz Free Energy
a  u  Ts
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
Mixture of perfect gases ;
aH2  bO2  cN2 
CT : Total number of moles per unit volume
C K : Total number of moles of species K per unit volume
X K : Mole fraction of species K
CK
XK 
CT   C K
XK 1

CT
K
K
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
 : Density of the mixture
 K : Partial density of species K
YK : Mass fraction of species K
W K : Molecular weight of species K
    K  WK C K
K
YK 
K
 ,
K
CK 
WK
K
Y
K
1
K


WK
PROPULSION AND COMBUSTION LABORATORY
YK
Combustion Engineering
   K  WK CK  Wj C j
K
K
CK 
j
K
WK


WK
YK
K
Yj
YK
CT   CK  
 
 
WK
K
K WK
j Wj
XK 
CK
Y / WK
 K
,
CT  Y j / W j
YK 
j
K
W C
W X
 K K  K K
 W j C j W j X j
j
j
W : Mean molecular weight of the mixture
YK
WK

WK
1
K
W   WK X K 

K
Y j / W j Y j / W j
j
PROPULSION AND COMBUSTION LABORATORY
j
Combustion Engineering
1
YK

,
K
WK
W
YK 1
W  (
)   X KWK
K W
K
K
EQUATION OF STATE
p K  CK R T
Partial pressure exerted by species K if it occupies
the whole volume at temperature T.
PROPULSION AND COMBUSTION LABORATORY
Dalton’s Law
p   pK  RT  CK  CT RT  CTWRT   RT
but
K
K
CT 

W
 
K
p  R T 
K
YK
,
WK
YK
R

T
WK
W
Internal Energy
u   u K YK
K
PROPULSION AND COMBUSTION LABORATORY
u K  u K0   cVK T dT
T
T0
u   YK uK  YK uK0   YK  cVK T dT
T
K
T
u  u0   cV dT
where u 0   YK u K0
T0
Y 
K
T
T0
K
cVK dT 
T0
K
 Y
K
T
T0
K
cVK dT 
K
cV   YK cVK
K
PROPULSION AND COMBUSTION LABORATORY

T
T0
cV dT
Enthalpy
h   YK hK
K
T
h  h0   c P dT when YK is fixed
T0
h0   YK hK0
K
c P   YK c PK
K
Entropy
s   YK s K
K
PROPULSION AND COMBUSTION LABORATORY
cP
R
p
s  s0  
dT  ln
T0 T
W p0
T
T
s K  s K0  
c PK
pK
R
dT 
ln
T
WK p0
T0
s   YK sK   YK sK0  
K
K
T
Y c
K PK
K
cP
YK
 s0  
dT  R 
T0 T
K WK
T
T
T0
YK
pK
dT  R 
ln
p0
K WK
 pK
p
 ln 
ln
p0 
 p
PROPULSION AND COMBUSTION LABORATORY
cP
YK
s  s0  
dT  R 
T0 T
K WK
T
 pK
p
 ln 
ln
p0 
 p
YK 
WK X K
W X
 K K
W j X j W
cP
Y
R
p
dT 
ln
 R  K ln X K
T0 T
W
p0
K WK
cP
YK
R
p
dT 
ln
 R
ln X K
T
W
p0
K WK
j
T
s  s0  
s  s0  
T
T0
Entropy that a perfect gas of W and cP
would have for p and T
Entropy increases due to mixing
X K 1 so that positive term
f  YK f K
R T pK
ln
WK
p0
fK  fK 
0
K
f  f 0  RT 
K
YK
p
ln K
WK
p0
PROPULSION AND COMBUSTION LABORATORY
R

W
X
K
K
ln X K
YK
f  f 0  RT 
K
XK
W
YK
p
Y
p
p
ln K  f 0  RT  K (ln
 ln K )
WK
p0
p0
p
K WK
RT p
Y
ln  R T  K ln X K
K W
W
p0
K
hK 
Caution ; c PK  T 
p
f  f0
RT
K X K ln X K
W
h 
cP 
When there is reaction

T  p
h 
hK 
YK 
h   YK hK
   YK
   hK

K
K
T  p
T  p
T  p
K
cP 
WK

h 
Y 
   hK K 
T  p K
T  p
PROPULSION AND COMBUSTION LABORATORY
Problem for notes
Binary mixture of
Y
K
X 
K
W
Y

W
X H2
K
j
H 2 2  He4
2YH 2
1 Y

, X 
1 Y
YH 2  1
H2
He
H2
j
j
1  YH2  YHe ,
c  Y c  1 Y c
P
H2
PH 2
H2
PHe
Specification of Composition
p K V  nK R T ,
pV  nT R T For same
PROPULSION AND COMBUSTION LABORATORY
V ,T
p K nK mK / WK
W


 YK
p
n
m /W
WK
For same P and T, partial volume of species K
R
R
pV

m
T
pVK  mK
T,
W
WK
V K m K W n K WK W n K





V
m WK nT W WK nT
mK
 YK .
Here, V is not VK so that
m
PROPULSION AND COMBUSTION LABORATORY
Material Balance for Chemical Reactions
Ex) Combustion of Octane with Air
Air: 0.21O  0.79N  3.76 moles of N per 1 mole of O
Molecular Weight: 0.21  32  0.79  28  28.8  29
For complete combustion (stoichiometric)
2
2
2
25
25 79
25 79
C8 H 18  O2   N 2  8CO2  9 H 2 O   N 2
2
2 21
2 21
Stoichiometric Coefficients: C8 H18  1
O  25 / 2,
2
N2 
PROPULSION AND COMBUSTION LABORATORY
25 79

2 21
2
On a mass basis,
25
25 79
25 79
C8 H 18 
O2 

N 2  8CO2  9 H 2 O 

N2
 

2
2
21
2
21
 

844
918
114
25
32
2
25 79
 28
2 21



1831 lbs ( or gms )
or 15.1 kg of air/ 1 kg of octane
For reactants
1
1
X C8 H18 

 0.0165
25 25 79 60.52
1


2
2 21
25 / 2
25 / 2  79 / 21
X O2 
 0.2065 , X N 2 
 0.7769
60.52
60.52
PROPULSION AND COMBUSTION LABORATORY
25 79
 28
2 21
25
25 79
25 79
C8 H 18 
O2 

N 2  8CO2  9 H 2 O 

N2







2 
2 
21
2 
21




844
918
114
25
32
2
25 79
 28
2 21



25 79
 28
2 21
1831 lbs ( or gms )
YC8 H18 
114
 0.0623
1831
W 
1831
 30.3
60.52
: MEAN MOLECULAR WEIGHT OF REACTANTS
MASS OF PRODUCTS = 1831
X
CO2
8

 0.125
25 79
89 
2 21
PROPULSION AND COMBUSTION LABORATORY
nP  nR
EQUIVALENCE RATIO :

mass of fuel
mass of oxidizer

 mass of fuel 


 mass of oxidizer 
FOR
 1
stoichiome tric
CH 4  2O2  2  3.76N2  CO2  2H 2O  2  3.76N2
PROPULSION AND COMBUSTION LABORATORY
  1 : STOICHIOMETRIC
  1 : FUEL LEAN
  1 : FUEL RICH
FOR   0.9 0.9CH 4  2O2  2  3.76N2    
CH 4      different
FOR   1
ENERGY Eq. FOR CHEMICAL REACTION
CONSTANT VOLUME SYSTEM – NO MOTION
PROPULSION AND COMBUSTION LABORATORY
1st LAW :
Q  dE  W
Q : HEAT TRANSFER
(POSITIVE WHEN ADDED TO THE SYSTEM)
dE : INTERNAL ENERGY
W : WORK DONE BY THE SYSTEM
1
Q2  E2  E1
1: REACTANT STATE
2: PRODUCT STATE
PROPULSION AND COMBUSTION LABORATORY
ONLY IMPORTANCE IS  E, NOT THE ABSOLUTE VALUES.
TB
: REFERENCE OR
BASIC TEMPERATURE 25 C
E B
: INTERNAL ENERGY OF REACTION,
DETERMINED IN A BOMB CALORIMETER
PROPULSION AND COMBUSTION LABORATORY
Q  E2  E1  E2  E2 B  E2 B  E1B  E1B  E1


  E2  E2 B   
E

E

E
B
1
1
B

  

fixed composition
tabulated
fixed composition
FOR CONSTANT PRESSURE PROCESS;
Q  dE  W  dE  pdV  dH  Vdp
1
Q2  H 2  H1   H 2  H 2 B    H 2 B  H1B    H1  H1B 
H B
PROPULSION AND COMBUSTION LABORATORY
H B  H 2 B  H1B
H B : ENTHALPY OF REACTION
H B  EB  p2 BV2 B  p1BV1B
E B :INTERNAL ENERGY
REACTION AT
OF
TB
FOR PERFECT GASES;
EB V const  EB  pconst
PROPULSION AND COMBUSTION LABORATORY
Q  H 2  H1   H 2  H 2 B  
 H 2 B  H1B 
  H1  H1B 
H B EB  p2 BV2 B  p1 BV1 B
p2 BV2 B  p1BV1B  n2 R TB  n1 R TB  nR TB
n  n2  n1
H B  EB  nR TB
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.
PROPULSION AND COMBUSTION LABORATORY
Cs   O2 g   CO2 g 
 H 
0
f CO
2
GIVES OFF 94052 cal :exothermic reaction
 94052 cal / gmole of CO2
HEAT OF FORMATION = H 0f  94052 cal / gmole of CO2
ALSO A COMBUSTION PROCESS
ENTHALPY OF COMBUSTION
Hc0  H 0f  94052 cal / gmole o
 94052cal / gmoleof CO2
HEAT OF COMBUSTION
HEAT OF COMBUSTION OF
94052
C ( s)  
cal / g of C ( s)
12
PROPULSION AND COMBUSTION LABORATORY
H B  EB  nR TB
ENDOTHERMIC REACTION
Ex )
1
N 2 g   O2 g   NO2  g 
2
H 
0
f NO
2
 8091 cal / gmole of NO2
HEATING VALUES; FOR C+O2 REACTION,
H B  E B
IN GENERAL,
,BECAUSE THERE IS NO
pdV
WORKS.
H B  E B
HIGHER HEATING VALUES AND LOWER HEATING VALUES
DEPEND ON STATE OF PRODUCTS.
PROPULSION AND COMBUSTION LABORATORY
IMPORTANT CASE IS H 2 Og  vs. H 2Ol 
1
H 2  O2  H 2 O
2
IF H 2 O IS LIQUID,
HHV H 2 O  34.32 kcal / g of H 2
LHV DIFFERS FROM HHV BY HEAT OF VAPORIZATION.
LHV  HHV  0.602 kcal / g of H 2 O 
PROPULSION AND COMBUSTION LABORATORY
9 g of H 2 O
 28.9 kcal / g of H 2
g of H 2
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 gasphase 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 ;
PROPULSION AND COMBUSTION LABORATORY
Q  H 2  H1
10g of H  5moles
2
5
5
5H 2 ( g )  O2 ( g )  (3.76) N 2 ( g )  5H 2 O( g )  9.4 N 2 ( g )
2
2
H 2  5H H2O( g ), 2000 K  9.4H N2 ( g ), 2000 K
5
H O2 ( g ), 298 K  9.4 H N 2 ( g ), 298 K
2
 H 2000 K  H 298 K  H f ,H 2O ( g ), 298 K
H1  5H H 2 ( g ), 298 K 
H H 2O ( g ), 2000 K
 19630 2367.7  57798 40535.7 cal
H N2 ( g ),2000 K  15494.8  2072.3  H f ,N2 ( g ), 298 K
PROPULSION AND COMBUSTION LABORATORY
mole
H H2 ( g ),298 K  HO2 ( g ),298 K  H N2 ( g ),298 K  0
Q  76512cal 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,
Q  E2  E1
E  H  pV  H  nRT
5E
H 2O ( g ), 2000 K
 5H
H 2O ( g ), 2000 K
 n RT
 5  (40535 .7)cal  5  1.9807  2000cal , etc.
PROPULSION AND COMBUSTION LABORATORY
CALCULATION OF ENTHALPY OF REACTION FROM
THE ENTHALPY OF FORMATION




H


H


H

f P
f R
R 










Reaction



Products
REACTION ;
H 

Reactants
aA  bB  mM  nN
b
m
n
or A  B  M  N
a
a
a

R mole of A


m
H f
a

M


n
H f
a
PROPULSION AND COMBUSTION LABORATORY

N


b
H f
a
  H 
B

f
A
EX) GASEOUS CH4 + O2 REACT TO YIELD H2O(l)+CO2(g).
CALCULATE H R PER MOLE OF CH4


CH ( g )  2O ( g )  CO ( g )  2H O(l )
4
H 

R CH 4
2

 H f

CO2
2



2

H
f
(g)
2





H
f
H O (l )
2

CH 4



2

H
f
(g)
 94.05  2 68.32   17.9  212.8kcal

O2 ( g )
EXOTHERMIC PER MOLE OF CH4
PROPULSION AND COMBUSTION LABORATORY
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.
PROPULSION AND COMBUSTION LABORATORY
dS: ENTROPY CHANGE OF THE SYSTEM
dSO: ENTROPY CHANGE OF THE RESERVOIR
dS+dSo: ENTROPY CHANGE OF THE UNIVERSE
dS  dS  0
Q
dS 
T
O
O
Q  Q
Q
T
 dS  0
s
FROM SYSTEM

 Qs
T
 dS  0
PROPULSION AND COMBUSTION LABORATORY
1ST LAW
 Qs  dE  pdV
FROM SYSTEM

 Qs
T
 dS  0
dE  pdV  TdS  0
VARIOUS CONSTRAINTS
CASE A ; HOLD E AND V CONSTANT
dS  0 ISOLATED SYSTEM
CASE B ; HOLD p AND T CONSTANT
d  E  pV  TS   d  H  TS   dF  0
GIBBS FREE ENERGY DECREASES
PROPULSION AND COMBUSTION LABORATORY
-
WHEN FP,T  0 ; HAVE CHEMICAL EQUILIBRIUM
CASE C ; HOLD V AND T CONSTANT
d E  TS   dA  0
AT EQUILIBRIUM ; AV ,T  0
PROPULSION AND COMBUSTION LABORATORY
fK  fK 0 
RT pK
ln
WK
p0
WK f K  FK  WK f K
0
pK
pK
0
 RT ln
 FK  RT ln
p0
p0
EQUILBRIUM OF A MIXTURE OF PERFECT GASES
UNDERGOING CHEMICAL REACTION
CONSIDER THE REACTION,
aA  bB 
 cC  dD

WE KNOW GIBBS FREE ENERGY FA
FOR P0  1atm
AND ANY TEMPERATURE T PER MOLE.
FA AT ANY T AND P ;
FA  FA  RT ln pA p0
FB  FB  RT ln pB p0
, ETC
PROPULSION AND COMBUSTION LABORATORY
pK
FK  FK  RT ln
p0
0
F  cFC  dFD  aFA  bFB



p 
p 
p  
p 
 c  FC  RT ln C   d  FD  RT ln D   a  FA  RT ln A   b  FB  RT ln B 
p0 
p0 
p0  
p0 



LET
F   cFC  dFD  aFA  bFB
c
d

p
p
p
p
 C 0   D 0  

F  F  RT ln 
a
b 

  p A p0   pB p0  

P0  1 atm
 pCc pDd 
F  F  RT ln  a b 
 p A pB 
PROPULSION AND COMBUSTION LABORATORY
pCc pDd
DEFINE K P  a b  equilibrium constant based on pressure
pA pB
AT EQUILIBRIUM
F  0
F   RT ln K P
KP  e
F  RT
F   f (T )
K P  g (T )
pA
 X A  mole fraction
NOTE THAT
p
pC  pX C
pD  pX D
pB  pX B
PROPULSION AND COMBUSTION LABORATORY
X Cc X Dd
X Cc X Dd n
 c  d   ( a b )
KP  a b  p 
 a b p
XAXB
XAXB
WHERE n  (c  d )  (a  b)
EFFECT OF T ON EQUILIBRIUM COMPOSITION IS GIVEN IN
Kp
n
EFFECTS OF p ON THE p TERM.
FOR THE CASE OF n  0 , IE. C + D = A + B
NO PRESSURE EFFECT
EQUILIBRIUM CONSTANT BASED ON CONCENTRATION ; K C
m ole
C  Concentration 
unit volum e
PROPULSION AND COMBUSTION LABORATORY
CCc C Dd
KC  a b
C AC B
pC  CC RT
 
pCc pDd
KC  a b RT
pA pB
n
, ETC
 
 K p RT
n
VALUES OF KP ARE TABULATED FOR SPECIFIC
CHEMICAL REACTION.
EX) DISSOCIATION OF CO2
1
CO2 
 CO  O2
2
K P1 
PROPULSION AND COMBUSTION LABORATORY
pCO pO1 22
pCO2
(1)
1
CO  O2 
 CO2
2
2CO  O2 
 2CO2
KP2 
K P3 
pCO2
pCO pO1/22
2
pCO
2
2
CO
p pO2
  K P1 
1
 K P1 
2
(2)
(3)
EQUILIBRIUM COMPOSITION
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
PROPULSION AND COMBUSTION LABORATORY
CHEMICAL REACTION
KP 
pH 2 pO1 22
pH 2O
1
H 2 O( g ) 
 H 2 ( g )  O2 ( g )
2
12
X H 2 X O2 1 2

p
X H 2O
H 2O  aH2O  bH2  cO2
EQUILIBRIUM COMPOSITION
H : 2  2a  2b
b  1 a
O : 1  a  2c
c  (1  a) 2
(1  a)
O2
2
(1  a) 3  a
nT  a  (1  a) 

2
2
H 2 O  aH 2 O  1  a H 2 
PROPULSION AND COMBUSTION LABORATORY
1 a
 2
3 a
2
1 a
a
X H2 
X
X

O2
H 2O
3 a
3 a
2
2
12

  1 a 
 1 a   2 
 3 a   3 a 
32 12



1 a P

3
2
2




12
KP 

1.145

10
KP 
p
,
12
a
a 3  a 
3 a
2
EQUILIBRIUM
0.0137
H 2 O  0.9863 H 2 O  0.0137 H 2 
O2
COMPOSITION
2
PROPULSION AND COMBUSTION LABORATORY
1 a p

KP 
12
a 3  a 
32
12
H 2O  aH2O  bH2  cO2
H 2 O  aH 2 O  1  a H 2 
(1  a)
O2
2
EXAMINE LIMITING CONDITIONS
CASE I - LOW TEMPERATURES
; VERY LITTLE DISSOCIATION
  1
LET a  1  
13
 3 2 P1 2
2
 
23
KP 


K
OR


P
12
2
 P
A) HIGHER PRESSURE ; LOWER  ; GREATER a
LESS DISSOCIATION
B) HIGHER TEMPERATURE ; HIGHER KP GREATER  ;
SMALLER a
MORE DISSOCIATION
PROPULSION AND COMBUSTION LABORATORY
KP 
1  a 
32
p1 2
a 3  a 
12
(1  a)
H 2 O  aH 2 O  1  a H 2 
O2
2
CASE II - HIGH TEMPERATURES ; HIGH DISSOCIATION
a 
  1
12
12
P
KP  1 2
3
OR
1
P
   
KP
3
A) HIGHER PRESSURE ; HIGHER  ; HIGHER a
LESS DISSOCIATION
B) HIGHER TEMPERATURE ; HIGHER KP ; LOWER  =
MORE DISSOCIATION
PROPULSION AND COMBUSTION LABORATORY
a
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
PROPULSION AND COMBUSTION LABORATORY
CH 4  5H 2O  aCH4  bH2O  cCO  dH2  eCO2
C: 1 =a+c+e
H : 14 = 4a + 2b + 2d
O : 5 = b + c + 2e
CH 4  5H 2O 
aCH4  bH2O   3  2a  bCO  7  2a  bH 2  4  a  bCO2
MECHANISM FOR REACTION ;
2 ACTUAL REACTIONS ARE ;
PROPULSION AND COMBUSTION LABORATORY
CH 4  5H 2O 
aCH4  bH2O   3  2a  bCO  7  2a  bH 2  4  a  bCO2
CH 4  H 2O 
 CO  3H 2 H R  0
CO  H 2O 
 CO 2  H 2 H R  0
K P1 
pCO pH3 2
(2)
KP2 
pCH 4 pH 2O
nT  a  b  c  d  e  8  2a
3  2a  b  7  2a  b 

K P1 
2
ab  8  2a 

4  a  b 7  2a  b 
K P2 
 3  2a  bb
(1)
3
PROPULSION AND COMBUSTION LABORATORY
p
2
pCO2 pH 2
pCO pH 2O
pCO  X CO p 
etc.
3  2a  b
p
8  2a
PRODUCT RULE FOR KP’s
aA
 cC  eE
(1)
eE  bB 
 dD
ADD
(2)
(3)
aA  bB 
 cC  dD
pCc pEe
K P1 
p Aa
KP2
pDd
 e b
pE pB
PROPULSION AND COMBUSTION LABORATORY
K P3
pCc pDd
 a b  K P1  K P 2
pA pB
ADIABATIC FLAME TEMPERATURE
Q  0
POINT (2) FINAL TEMPERATURE AND H AFTER
A NON-ADIABATIC REACTION
POINT (2i) ISOTHERMAL REACTION
POINT (c) ADIABATIC FLAME TEMPERATURE ; H2=H1
PROPULSION AND COMBUSTION LABORATORY
CONSTANT PRESSURE REACTION – GENERAL CASE
m
n
a A  b B
i
i
i
i
i


i


R
P
DETERMINE TC FROM H2=H1
Q  0
H2 DEPENDS ON THE bi WHICH DEPENDS ON Tc WHICH
DEPENDS ON THE bi.
n
b
i ,TC
m
H Bi ,TC   ai ,Ti H Ai ,T1
i
PROPULSION AND COMBUSTION LABORATORY
i
FOR PERFECT GASES

n
i bi,TC  H


f B
i
  C P dT    ai ,T1  H f
 i

TB
 
i
m

C
i
i
1
i
TO CALCULATE Tc
1.
2.
3.
4.
C P dT 

TB
T1
Ai






b

H

a

H


H
 i ,T
 i ,T
f B
f A
r
n
WHERE

m
TC
ASSUME TC FOR GIVEN PRESSURE
CALCULATE THE bi FROM THE KP’s
SUBSTITUTE INTO H2=H1
ITERATE UNTIL H2=H1
PROPULSION AND COMBUSTION LABORATORY
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
  1.0 CH  2O 
CO  2H O
  0.8 0.8CH 4  2O2 
 aCO2  bH2O  cCO  dH2  eO2
0.8CH 4  2O2 

4
2
2
2
aCO2  bH2O  0.8  a CO  1.6  bH 2  1.6  0.5a  0.5bO2
2 UNKNOWNS
nT  a  b  c  d  e  4  0.5a  0.5b
PROPULSION AND COMBUSTION LABORATORY
X CO2 
a
nT
X O2 
e
nT
etc.
Dissociation Reactions
1
1
CO2  CO  O2
2
K P1 

a H CO2

TC

H 2  H1
 b H H 2O

TC
pCO pO2
KP2 

 cH CO TC  d H H 2
PROPULSION AND COMBUSTION LABORATORY

TC
2
pH 2 pO2
pH 2O

 e H O2

X CO X O22

pCO2
1
1
H 2 O  H 2  O2
2
1
2
TC
X CO2
p
1
2
1

X H 2 X O22
X H 2O

 0.8 H CH 4
p

1
T1
2

 2 H O2
Combustion Engineering

T1
Procedure ; assume Tc; Calculate a,b,c,d,e
Substitute into H2=H1 (from Energy Equation)
If Tc=3000K
HH 0
Hco
a[-94.05 kcal/mole + 38.94-2.24]+b[-57.8+32.16-2.37]
Hco
HH
+c[-26.42+24.43-2.07]+d[0+23.19-2.02]
Ho
HCH4
Ho
+e[0+25.52-2.07] = 0.8[-17.89]+2[0]
2
2
2
2
PROPULSION AND COMBUSTION LABORATORY
2
Combustion Engineering
Tables of Thermodynamic Properties
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering
PROPULSION AND COMBUSTION LABORATORY
Combustion Engineering