Transcript Lecture3 - Propulsion and Combustion Lab.

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]
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



A  p 2KT
3 /2
y A y B exp(E /RT )
C. IGNITION
1) THERMAL IGNITION
EXTERNAL SOURCE OF HEATING
REACTIVE HEAT GENERATION EXCEEDS LOSS RATE
RAPID INCREASE IN REACTION RATE AND TEMPERATURE
2) CHEMICAL CHAIN IGNITION
OCCURS WHEN CHAIN CARRIERS AND CHAIN REACTIONS
ARE INVOLVED.
CAN OCCUR IN ISOTHERMAL CONDITIONS
RADIATION OF PROPER WAVELENGTH CAN GENERATE
CHAIN CARRIERS WHICH RESULT IN IGNITION
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
3) TYPE OF IGNITION
SPONTANEOUS IGNITION OCCURS WHEN
COMBUSTIBLE MIXTURE IS RAISED IN TEMP
E.G. : DIESEL ENGINE CYLINDER
FORCED IGNITION: DUE TO LOCAL ENERGY SOURCESPARK
DETONATION
COLD
FUEL+OXIDIZER
MIXTURE
HIGH T
REGION
PROPULSION AND COMBUSTION LABORATORY
IGNITION AND
COMBUSTION
COMBUSTION ENGINEERING
QUESTIONS :
(1) UNDER WHAT CONDITION DOES IGNITION OCCUR?
(2) WHAT IS “IGNITION DELAY” I.E. TIME BETWEEN
INITIAL TEMPERATURE RISE AND IGNITION?
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
SPONTANEOUS IGNITION
AND IGNITION DELAY
S
T0
V
T
SURFACE AREA: S VOLUME : V
ENERGY CONSERVATION
dT
CV
 Vq  hS (T  T )
dt
A MINIMUM REQUIREMENT FOR SPONTANEOUS IGNITION
0
 A  hS(T  T0 )
  hV
Vq
CONSIDER ADIABATIC SPONTANEOUS IGNITION
CONSIDER A PERFECT GAS , USE   FOR SECOND
ORDER REACTION
P
ρ
(R /W)T
A
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
T T

T T
   Kp [ (T  T )  T ] [ y 

0
1
3 / 2
2
A
1
0
0
Ao
0
[y 
Bo
c(T  T )
 ]
h
1
0
c(T  T ) 1  f
E
(
) ] exp[ 
]
h
f
R (T   (T  T )
1
0
st
st
0
1
0
ENERGY EQUATION
dT
 Vq
dt
3
 
2
P
dT
C (T  T0 )  
C (T  T0 ) (1  f ST )   E 
C
 hKP T 2  y A0 
y

exp  

B0



( R / W )T dt

h

h
f
R
T



 
ST
CV
1
 hKR 
1 f
dT
C (T  T0 )  
C (T  T0 ) 
 E 
2
 PT
yA0 
yB 0 
s  exp  
, s 



dt
CW 
h  
h

 RT 
f
ST
IN TERMS OF DENSITY, 
1
dT
hKR 
C (T  T0 )  
C (T  T0 ) 
 E 
2
 T
yA0 
yB 0 
s  exp  

2



dt
h  
h
CW 

 RT 
2
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
ST
IN GENERAL FORM
dT
t  
T0 r (T )
dT
 r (T )
dt
T
t
1
r (T )
r (T )
Area tig
r (T )
T0
Tig
T1
T
PROPULSION AND COMBUSTION LABORATORY
T0
T1
T
COMBUSTION ENGINEERING
Reactants exhausted
T1
tig
Rapid combustion
T0
t
QUANTITATIVE ANALYSIS
DEFINITION OF tig
T  T0

T1  T0

Tig  T0
T1  T0
 0.1
PROPULSION AND COMBUSTION LABORATORY
FOR INSTANCE
COMBUSTION ENGINEERING
1
dT
hKR 
C (T  T0 )  
C (T  T0 ) 
 E 
2
 T
yA0 
yB 0 
s  exp  

2



dt
h  
h
CW 

 RT 
2
APPROXIMATIONS
hKR 
C (T1  T0 )  
C (T1  T0 ) 
2
T
yA0 
   yB 0 
s 
2

h
h
CW 


2
1
hKR
 1 hKR
2
y
y

PT
y A 0 yB 0  A
2
A0
B0
0
CW
CW
2
 T0
1
2
dT
E 

 A exp  

dt
R
T


ADIABATIC IGNITION DELAY

dT
 r (T )
dt
t

T
T0
dT
r (T )
PROPULSION AND COMBUSTION LABORATORY
E 

r (T )  A exp  

 RT 
COMBUSTION ENGINEERING
E
E


R T R (T0  T  T0 )
IF
T  T0
 1
T0
E
 T  T0 

R T0 1 
T0 

 E 
 E (T  T0 ) 
E
E  T  T0 
E 
1 
  exp 






exp
exp

2


R T R T0 
T0 
 RT 
 R T0 
 R T0

 E  R T0 
  E (Tig  T0 ) 
1


tig  exp 

2
1  exp 

A
R
T
E
R
T



0 
0

2
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
REMARKS)
E
 Ta
R
E (Tig  T0 ) Ta  Tig  T0 

 
2
R T0
T0  T0 
FOR HC’S Ta ~ 20,000K
PROVIDED THAT Ta / T0  1, CHOICE OF Tig, HAS ONLY
A SMALL EFFECT ON tig
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
 E  R T0 
  E (Tig  T0 ) 
1

tig  exp 

2
1  exp 
A
R
T
E
R
T



0 
0

2
Ta
~ 0(1)
T0
T
Tig
Ta
 1
T0
t
 E 
R T0

tig 
exp 
AE
 R T0 
2
A  T0
1
2
Ta
 1
IF
T0
hKR 2
 1 hKR
y A 0 yB 0  PT0 2
y A 0 yB 0
2
CW
CW
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
VARIOUS FORMS FOR
t
ig
ARRHENIUS TERM IS MAIN
FEATURE FOR MOST FUELS.
t
ig
T0  T0 
T0  T0 




Ta
Ta
T A  h / C 
TA  h / C 

exp

exp
2
T0
T0
1 / 2 KR


R
1/ 2
PT0
y A0 y B 0
T0 K   y A0 y B 0
W
W 
tig  p1,  1
COMMENTS
EFFECT OF
dtig
tig
T
dT0

T0
0
;
 Ta 1 
2   
 T0 2 
PROPULSION AND COMBUSTION LABORATORY
Ta
 1,
T0
dtig
dT0
0
COMBUSTION ENGINEERING
 T0 T0

 T h / C 
Ta
ln tig   ln  1a

T0
 PT 2 KR y y 
 0 W A 0 B 0 
Ta
Ta
ln tig  , tig  exp
T0
T0
d (ln tig )
E
 Ta 
R
1


d 
 T0 
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
ln tig
ACTUALLY,
CAN USE THIS GRAPH
TO FIND ACTIVATION
ENERGY
1 / T0
tig
1 / T0
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
TREATMENT OF COMBUSTION WAVES
AS A DISCONTINUITY
STATIONARY COMBUSTION WAVE
ρ1
U1
P1
T1
CHEMICAL REACTION
MASS DIFFUSION
THERMAL CONDUCTION
VISCOUS EFFECTS
REACTANTS
ρ2
U2
P2
T2
PRODUCTS
x
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
ASSUMPTIONS
1) STEADY,ONE DIMENSIONAL FLOW
2) AT FAR-UPSTREAM AND FAR-DOWNSTREAM, IT
BECOMES
(UNIFORM FLOW)
3) NO EXTERNAL FORCES
4) NEGLECT THERMAL AND PRESSURE DIFFUSION
CONSERVATION EQUATIONS
d
MASS dx ( u )  0
 
0
x
1u1   2u2  m1  m2  m  constant
m
= MASS FLOW PER UNIT AREA
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
MOMENTUM : 1-D NAVIER STOKES EQUATION
du
dp d 4 du
ρu

 ( μ
)
dx
dx dx 3 dx
d
d 4 du
(mu  p)  (  )
dx
dx 3 dx
INTEGRATE
2
4 du
(m u p)1  ( μ
)
3 dx 1
du
as
 0 at (1) and (2)
dx
2
 p1  ρ1u1  p2  ρ2u2
2
PROPULSION AND COMBUSTION LABORATORY
2
COMBUSTION ENGINEERING
ENERGY EQUATION
d
u2
d 4 du dqx
u [( h  )]  [u μ ] 
dx
2
dx 3 dx
dx
h INCLUDES THE FORMATION ENERGIES.

qx  Heat Flux Vector  
dT
dx
Heat Conduction
   k VK hK
k
Energy Transport
by Diffusion
dy k
VK : DIFFUSION VELOCITY 
dx
dT dy k
,
and VK  0 AT (1) AND (2)
HOWEVER
dx dx
 qx  0
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
INTEGRATE
2
2
2
u
4 du
2
[m(h  )]  [u  ]  qx 1  0
2 1
3 dx 1
du
and q x  0 AT (1) AND (2)
dx
2
2
u
u
m1  m2
 h1  1  h2  2
2
2
ENERGY h INCLUDES CHEMICAL ENERGY.
T
hk  (h f )k   C pk dT
T0

h   yk hk   yk (h f )k   C pk dT
k
k
PROPULSION AND COMBUSTION LABORATORY
T
T0

COMBUSTION ENGINEERING
ENERGY
u12

y
C
dT


(
y

y
)
(

h
k k1 T0 pk

k1
k2
f )k
2
k
T1
u22
  yk 2  C pk dT 
T0
2
k
T2
LET
T0  0
T1
1
C P1   yk1  CPk dT
0
T1 k
C P2
1

T2
y 
T2
k2
k
PROPULSION AND COMBUSTION LABORATORY
0
CPk dT
COMBUSTION ENGINEERING
LET

Q   ( y  yk 2 )(h0f )k
k
k1
ENERGY EQUATION BECOMES
2
2
u1
u2
C P1T1 
 Q  C P 2T2 
2
2
p1  1u1  p2   2u2
2
2
1u1   2u2  m
COMBINING MASS AND MOMENTUM
p2  p1  1u1 (u1  u 2 )
 1
1 


 u 

 1  2 
2
1
2
1
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
 1
1 
p2  p1   u 




2 
 1
2 2
1 1
1

 Specific volume

p  p1
 2
 ( 1u1 ) 2  m 2
 2  1
p
Slope  m
p
p p
 m
 
2

FINAL STATE(2) ON THIS
LINE
2
1
2
2
1
p1  1u12  p2  2u22
(1)
Rayleigh

PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
p1  1u12  p2  2u22
PERFECT GASES
p
p2
2
2
p1  1 u1  p2 
u2
R1T1
R2T2
a  RT
M
u
a
p1[1  M1 ]  p2[1  M 2 ]
2
OR
p 1  M

p 1  M
2
1
2
1
2
2
PROPULSION AND COMBUSTION LABORATORY
2
c

c
p
v
COMBUSTION ENGINEERING
p 1  M

p 1  M
2
1
(A) SUPPOSE
2
1
2
2
p2  p1
THEN, M 1  M 2
M  1 SUPERSONIC
DETONATION WAVE
1
(B) SUPPOSE
P2  P1
SHOCK INDUCED
REACTION FRONT
THEN, M 1  M 2
M  1 SUBSONIC
DEFLAGRATION WAVE
NOW INTRODUCE ENERGY EQUATION TO CONSIDER HEAT
ADDITION
1
2
2
u1
u2
h1 
 Q  h2 
2
2
PROPULSION AND COMBUSTION LABORATORY
(h ; SENSIBLE ENTHALPY)
COMBUSTION ENGINEERING
p2  p1
 ( 1u1 )2  m2
2  1
1 2
1 2 2 1
1
2
h1  h2  Q  (u2  u1 )  1 u1 ( 2  2 )
2
2
 2 1
1 ( p2  p1 ) 1
1

( 2  2)
2 ( 2  1 ) 1  2

OR
1 ( p2  p1 )
(1   2 )(1   2 )
2 ( 2  1 )
h1  h2  Q 
1
( p1  p2 )(1   2 )
2
Rankine-Hugoniot RELATION
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
h1  h2  Q 
USE
1
( p1  p2 )(1   2 )
2
h  e  p
1
( p1  p2 )(1   2 )  ( p2 2  p11 )
2
1
e1  e2  Q   ( p1  p2 )(1   2 )
2
e1  e2  Q 
OR
ANOTHER FORM OF R-H
EQUATION OF STATE
h  h( p, ) OR e  e( p, )
SAY THAT Q = Constant
DETERMINE THE LOCUS OF ALL POSSIBLE END STATES
FOR GIVEN INITIAL CONDITIONS USING R-H AND
EQUATION OF STATE
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
p
C
STRONG DETONATION
C-J
DETONATION BRANCH
WEAK DETONATION
B
A
PHYSICALLY IMPOSSIBLE
p p
 (  u )
 
2
1
1
2
p
2
1
1
D
1
(1)
WEAK DEFLAGRATION
DEFLAGRATION BRANCH
STRONG DEFLAGRATION
C-J
Hugoniot Curve

1
PROPULSION AND COMBUSTION LABORATORY
E

COMBUSTION ENGINEERING
1
e1  e2  Q   ( p1  p2 )(1   2 )
2
CONSIDER THE Chapman-Jouguet POINTS
AT C-J : Rayleigh LINE IS TANGENT
TO Hugoniot CURVE
dP2
d 2
CJ
P2  P1

 2  1
FOR A SMALL CHANGE NEAR THE C-J POINT
T2 ds2  de2  p2 d 2
FROM R-H RELATION
1
1
de2   ( p1  p2 )d 2  (1   2 )dp 2
2
2
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
dP2
d 2

CJ
P2  P1
 2  1
1
1
T2 ds 2   ( p1  p2 )d 2  (1   2 )dp 2  p2 d 2
2
2
1
1
1
dp2
 d2 [ p1  p2  (1  2 )
]
2
2
2
d2
p p
 
2
T2 ds2  0
2
1
1
NEAR A C-J POINT, ENTROPY CHANGE IS ZERO FOR
A SMALL CHANGE.
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

ENTROPY IS A MAXIMUM OR MINIMUM.
S
2
FOR DEFLAGRATION : C-J POINT IS MAXIMUM S
2
FOR DETONATION
: C-J POINT IS MINIMUM
p
p
(1S)
C-J
(2)
ISENTROPIC
B
A
(1)
(1)

PROPULSION AND COMBUSTION LABORATORY
D
C-J

COMBUSTION ENGINEERING
dP2
d 2

CJ
P2  P1
 2  1
AT C-J POINT : ISENTROPIC PROCESS
dp 2 
dp 2 
2 dp 2 
2 2




2


    2 a2
d 2  s c d (1 /  2 )  s c
d 2  s c
WHERE
a  speed of sound
p2  p1
dp 
 ( 1u1 ) 2    22u22  2     22 a22
 2  1
d 2  s c
 u 2  a2
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
AT C-J POINT : VELOCITY OF BURNT GASES
RELATIVE TO THE WAVE IS SONIC
I.E. M 2  1.0
1-A, CONSTANT VOLUME DETONATION
FROM
P2  P1
 ( 1u1 ) 2  u1  
2  1
1-B, WEAK DETONATION : IMPOSSIBLE
(ENTROPY DECREASES)
1-C, STRONG DETONATION : POSSIBLE
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
1-C-J, COMMON DETONATION
1-D,
CONSTANT PRESSURE DEFLAGRATION
Weak u1 
 0
1-C-J, C-J DEFLAGRATION : NEVER REALIZED
 CHEMICAL KINETICS ARE NOT SO
FAST TO SUPPORT FAST VELOCITY
1-E,
STRONG DEFLAGRATION : IMPOSSIBLE
ENTROPY DECREASES
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
 (M ) APPROACH TO CLASSIFICATION OF COMBUSTION
WAVES
(1)
( 2)
NOW WE’LL ELIMINATE THE THERMODYNAMIC PROPERTIES.
ASSUME PERFECT GASES, C p  Constant,   Constant
AND CONSTANT MOLECULAR WEIGHT
1u1  2u2
FOR MASS
P1
P2
P1M1 P2 M 2
u1 
u2

(1)
RT1
RT2
T1
T2
R IS ELIMINATED, BECAUSE MOLECULAR WEIGHT IS
CONSTANT.
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
FOR MOMENTUM
P1  1u12  P2   2u22
P1[1 M 12 ]  P2 [1 M 22 ]
(2)
FOR ENERGY
u12
u22
C pT1   Q  C pT2 
2
2
u12    1 
Q
u22    1 
 
]
T1[1  
]  T2 [1  
2  RT1  C pT1
2  RT2 
T1[1 
 1
2
M 12 
Q
 1 2
]  T2 [1 
M2 ]
C pT1
2
PROPULSION AND COMBUSTION LABORATORY
(3)
COMBUSTION ENGINEERING
ELIMINATING P2 / P1 & T2 / T1 FROM (1), (2) AND (3)
LET’S
  1 2
Q 
 1 2 
2

M 1
M1 
M
1

M2 


2
2
c
T
p 1
2




(1  M 12 ) 2
(1  M 22 ) 2
2
1
  1 2 
M 1 
M 
2


 (M ) 
(1  M 2 ) 2
2
NOW DEFINE,
SUBSTITUTE,
 (M1 ) 
PROPULSION AND COMBUSTION LABORATORY
Q ( M 1 )
  (M 2 )
  1 2 
c pT1 1 
M1 
2


COMBUSTION ENGINEERING
 (M1 ) 
Q ( M 1 )
  (M 2 )
  1 2 
c pT1 1 
M1 
2


C pT1[1 
 1
2
M 12 ]  C pT01  h01
WHERE,
h01  StagnationEnthalpy, T01  StagnationTemperature
Q
 (M 2 )

1
C pT01  ( M 1 )
 (M ) INCREASES WITH HEAT ADDITION.
C pT01  Q C pT02 T02
 (M 2 )
Q
 1



 ( M1 )
C pT01
C pT01
C pT01 T01
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
  1 2 
M 2 1 
M 
2


 (M ) 
(1  M 2 ) 2
VARIOUS COMBUSTION WAVES
 (M )
d
e.g .
a
CONDENSATION AS A WEAK
e DETONATION,
c
Q
b
a
Q  0, M1  1, M 2  1
Q
a
cw
bw
b c,
STRONG DETONATION
M1  1, M 2  1
M 1
0
a
a
b,
SHOCK WAVE
b
b
c
d,
c
e,
1 .0
e,
M 1
M
C-J DETONATION
M1  1, M 2  1
WEAK DETONATION M1  1, M 2  1
Q0
IMPOSSIBLE
ENTROPY DECREASES
a
e,
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
CHEMICAL KINETICS & TRANSPORT PHENOMENA ARE
NOT SO FAST TO ADD HEAT TO GAS, SO IT DOES NOT
OCCUR.
bw-cw,
b-d,
b-c-e,
M 2  1
WEAK DEFLAGRATION M1  1 ( COMMON
FORM )
M1  1, M 2  1
C-J DEFLAGRATION
STRONG DEFLAGRATION
M 1  1, M 2  1
IMPOSSIBLE: VIOLATE ENTROPY
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
h
M 1
Q
c
b
d
cw
M 1
bw
e
a
Q
M 1
s
HW P393: #29, #30, #32
FANNO CURVE
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING
Homework #2
(from Kanury, P393 #29, #30, #32)
I.
II.
III.
PCI5 decomposes into PCI3 and Cl2 at elevated temperatures. If for PCl5 ⇔ PCI3 +
Cl2 at 250 ℃, Kp is given as 1.78, at what pressure should the system be operated
in order to obtain a 50% decomposition at 250 ℃?
Let C dissociate into A and B according to C ⇔ A + B. If λ is degree of
decomposition and P is total pressure, Kp is a function of λ and P. In other words,
while Kp is a function of temperature T at which the system is operated, so is also P
for obtaining any desired conversion. Eliminating T from the two relations, for any
desired degree of dissociation, Kp can be related to P. If the desired λ is 0.25, find
this relation for the above reaction.
In a vessel containing a mixture of H2, F2 and Cl2, fluorine and chlorine compete with
each other for hydrogen to form HF and HCl by the following reactions:
0.5H2 + 0.5F2
0.5H2 + 0.5Cl2
→ HF
→ HCl
Kp = 15,800
Kp = 51.2
at 3,500K
Are we more likely to observe more HF than HCl or vice versa if the total pressure is
1 atm?