This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
COMBUSTION
PROF. SEUNG WOOK BAEK DEPARTMENT OF AEROSPACE ENGINEERING, KAIST, IN KOREA
BE: INTERNAL ENERGY OF REACTION, DETERMINED IN A BOMB CALORIMETER
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
BH
BE
: ENTHALPY OF REACTION
BBBBBB VpVpEH 1122
:INTERNAL ENERGY OF
REACTION AT BTFOR PERFECT GASES;
constpBconstVB EE
2 1B B BH H H
PROPULSION AND COMBUSTION LABORATORY
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.
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
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 ;
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
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
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
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
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
WHEN ; HAVE CHEMICAL EQUILIBRIUM
AT EQUILIBRIUM ;
0, TPF
CASE C ; HOLD V AND T CONSTANT
0 dATSEd
0, TVA
-
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
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)
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
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
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
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
(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
PROPULSION AND COMBUSTION LABORATORY
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
PROPULSION AND COMBUSTION LABORATORY
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,,,,
PROPULSION AND COMBUSTION LABORATORY
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
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
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
Combustion EngineeringPROPULSION AND COMBUSTION LABORATORY