Download radiation and combustion phenomena

RADIATION AND COMBUSTION
PHENOMENA



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]





GRADING SYSTEM
Homework (20%), 1 Final Exam (80%)
TEXT : None
REFERENCES…
1. Siegel, R. and Howell, J.R., Thermal radiation heat
transfer, 4th, Taylor&Francis, 2002
2. Sparrow, E.M. and Cess, R.D., Radiation heat transfer,
Brooks/Cole Publishing Company, 1970
3. Michael F. Modest, Radiative Heat transfer, 2nd Academic
Press, 2003
4. M. Quinn Brewster, Thermal Radiative Heat Transfer and
Properties, Wiley-Interscience, 1992
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
OUTLINE…
PART I. RADIATIVE EQUILIBRIUM
PART II. RADIATIVE NON-EQUILIBRIUM
1. ENCLOSURE (SURFACE) RADIATION
2. GAS RADIATION
PART III. RADIATIVE PROPERTIES
PART IV. RADIATION AFFECTED TRANSPORT
PHENOMENA
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
INTRODUCTION
THERMAL RADIATION
Distribution
Conduction
Radiation
Temporal
Spatial
Spatial
Specular
A fundamental difference
between conduction and
radiation is in their
distribution.
Geometry
Explicitly,
PROPULSION AND COMBUSTION LABORATORY
Optics
Quantum
mechanics
RADIATIVE HEAT TRANSFER
INTRODUCTION
 Its importance becomes intensified at high
temperature levels: furnaces, combustion chamber,
rocket nozzle, nuclear power plant, etc.
 No medium required
 With conduction and convection – nonlinear integrodifferential equation : Difficult to solve!!!
 Radiative physical property depends on surface
roughness, material, thickness of coating,
temperature, angle, etc.
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
INTRODUCTION
THEORY OF RADIANT ENERGY PROPAGATION
Classical electromagnetic wave theory
EXCEPTIONS
Spectral distribution of the energy emitted from
a body and the radiative properties of gases explained by only quantum mechanics
[particle(photon) theory]
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
INTRODUCTION
SPECTRUM OF ELECTROMAGNETIC RADIATION
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
INTRODUCTION
SPECTRUM OF ELECTROMAGNETIC RADIATION
NEAR VISIBLE RAY REGION
Wavelength [ ㎛ ]
1000
100
10
1
0.1
Red
PROPULSION AND COMBUSTION LABORATORY
0.4
Visible
Thermal
0.001
Violet
0.7
Infra-red
0.01
Ultraviolet
RADIATIVE HEAT TRANSFER
PART I. RADIATIVE EQUILIBRIUM
A DIRECTIONAL VOLUME
SOLID ANGLE
unit:steradian(sr)
 : azimuthal angle
 : polar angle
d 
R 2 sin  d d
R2
When the sphere with radius R is
projected onto unit sphere,
d   sin  d d
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
TWO MORE DEFINITIONS
Intensity 
Energy
Pr ojected Area  Time  Solid Angle
Energy
Energy Density 
Volume
DIFFERENTIATE WITH RESPECT TO
du dq
c

I
d d

FROM THIS RELATION
1
1
u

Id
du  Id

c
c
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
FOR ISOTROPIC RADIATION AT EQUILIBRIUM
4
u
I,
c
I
u   d
c 
THERMAL
u~I
OPTICS
EdA  qdAn
dAn
dA
projected area

E
emissive power
q
DIVIDE BY dA , DIFFERENTIATE
WITH RESPECT TO 
dE dq  dAn 



d d  dA 
unprojected area
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
E
2
dE
 I cos 
d
I cos  d  : for hemisphere
FOR ISOTROPIC BLACKBODY RADIATION AT EQUILIBRIUM
Eb  I b  cos  d 

 I b  cos   sin  d
 d

PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
 2
Eb  I b
 d  sin  cos  d 
2
0
2
Eb   Ib ,
12
Eb ~ Ib
THERMAL OPTICS
Eb   T 4

Stefan-Boltzmann Law
: Stefan-Boltzmann Constant 5.6696 108 W m2 K 4
THEN,
Eb ~ I b ~ u ~ T 4
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
BLACKBODY
DEFINITION…
An ideal body that allows all the incident radiation to
pass into it ( no reflected energy) and absorbs internally
all the incident radiation ( no transmitted energy) ;
perfect absorber of incident radiation.
PERFECT EMITTER IN EACH DIRECTION AND AT EVERY
WAVE LENGTH
 In equilibrium condition, the blackbody must radiate
exactly as much energy as it absorbs.
 The intensity of radiation from a blackbody is independent
of the direction of emission.
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
SPECTRAL DISTRIBUTION OF
BLACKBODY EMISSIVE POWER
RADIATIVE EQUILIBRIUM
  

v
UNIFORM
USING   cos 

1
1
1
u   Id    d  I sin  d   d  I d ( cos
0
c
c 2
c 2
ISOTROPIC
MATTER
RADIATION
FOR SPHERE
2 1
4 I

I
d


c 1
c
SIMILARLY
P  RT
1
1
2
p   I (n s ) d    I cos2  d 
c
c 4
1
P  u  1 I cos2  sin  d d  2 I 1  2 d 
3
c
c 1

4 I
3c
PROPULSION AND COMBUSTION LABORATORY
1
p u
3
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
Eb ~ I b ~ u ~ T 4
dU  TdS  pdV ,
U  uV
1
udV  Vdu   udV for equilibrium
3
At a higher temperature, the peak
4
udV  Vdu
intensity shifts to a shorter
3
wavelength
du
4 dV

u
3 V
u ~ V 4 3 ~ T 4  V 1 3 ~ T  V 1 3 ~ 
T  const
: Wien’s (DISPLACEMENT) LAW
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
MONOCHROMATIC (SPECTRAL) BLACKBODY EMMISIVE
POWER AT EQUILIBRIUM

Eb   Eb d
0
dEb  Eb d
WITH
Eb  T 4 , T 3dT ~ Eb d
T  const
dT  Td  0
FROM Wien’s LAW
dT ~
T

d
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
3
T
T

1

d  ~ Eb d 
~ T  T 5 d  ~ Eb d 
Eb
 const  f  T 
5
T
E b HAS A MAXIMUM AT WAVELENGTH  max FOR A
GIVEN TEMPERATURE  T  C  2898 m  K
max
3
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
HEMISPHERICAL SPECTRAL EMISSIVE POWER OF
BLACKBODY FOR SEVERAL DIFFERENT TEMPERATURES
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
When radiation travels from one medium into
another, the frequency remains constant while the
wavelength changes because of the change in
propagation velocity.
Wave number :

1

the number of waves per unit length.
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
FROM ORIGIN OF QUANTUM MECHANICS
E b  ,T 
2hc 2

,
5
5
hc
k

T
T
T  e
1


BLACKBODY EMISSION INTO
VACUUM
THE Planck DISTRIBUTION OF THE MONOCHROMATIC
EMISSIVE POWER
WHERE
Planck’s constant :
Boltzmann’s constant :
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
E b  ,T 
2hc 2

5
5
T
T  e hc kT  1


e hc kT  1  hc kT
Eb ( , T ) 2 ck

4
5
T

T
 
FOR T  7.78 105 m  K
THE Rayleigh-Jeans DISTRIBUTION
e hc kT 1  e hc kT
Eb ( , T )
2 hc 2

5 hc k T
5
T
 T  e
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
SPECTRAL DISTRIBUTION OF BLACKBODY
HEMISPHERICAL EMISSIVE POWER
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
CHARACTERISTICS…
1. Energy emitted at all wave lengths increases as
the temperature increases.
2. Peak spectral emissive power shifts toward a
smaller wavelength as the temperature is
increased.
3. Red light becomes visible first as the
temperature is raised – at sufficiently high
temperature, the light emitted becomes white.
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
TEMPERATURE MEASUREMENT
USING 4 WAVELENGTH PYROMETER
Planck’s DISTRIBUTION LAW
E b
2hc 2

,
5
5
hc
k

T
T
T  e
1


E b 
A

5
e
B T

1
1
FOR NON-BLACKBODIES,
E   
1




exp
B

T

1
5
A

PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
THE INTENSITY OF RADIATION MEASURED BY A
PHOTODIODE
A
1
V    5 exp B T   1


a calibration factor including all radiation absorbed
between the emission source and the photodiode
(e.g. windows, optical elements, filter, etc.)
  B  
  1
 exp

Vi  i    jT  

,
Vj  j 5   B  
  1
i exp
  iT  
5
j
FOR GRAY BODIES
PROPULSION AND COMBUSTION LABORATORY
 i   j
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
  B  
FOR NON-GRAY
  1
exp 
5
E i
 i  4    4T  
BODY

,
E 4
  4 5i 
 B  
  1
exp 
  i T  
Vi
 i  i

V 4   4   4
 Ei 


 E 4  b.b
 i
SHOULD DETERMINE Qi  
FOR CALIBRATION
4
USING GRAPHS FOR Vi
 Ei 
 i
V 4
PROPULSION AND COMBUSTION LABORATORY
,
 4
, 

E
  4  b.b
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
EMISSIVITY OF TUNGSTEN RIBBON AS A FUNCTION
OF TEMPERATURE FOR DIFFERENT WAVELENGTH
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
RELATIVE EMISSIVE POWER AS A FUNCTION
OF WAVELENGTH FOR DIFFERENT TEMPERATURES
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER
RADIATIVE EQUILIBRIUM
RELATIVE VOLTAGE OUTPUTS USING TUNGSTEN LAMP
AS A FUNCTION OF TEMPERATURE
DEPENDING ON DIFFERENT CHANNELS AND DIFFERENT SETUP
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER