r adiation and c ombustion p henomena p rof. s eung w ook b aek d epartment of a erospace e...

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]

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]

http://procom.kaist.ac.kr/

http://procom.kaist.ac.kr/

EXAMPLE

RADIATIVE HEAT TRANSFERPROPULSION AND COMBUSTION LABORATORY

RADIATIVE NON-EQUILIBRIUM

TWO CLOSELY LOCATED PARALLEL

PLATES.

TEMPERATURES ARE & . 11 yT 22 yT

RADIOSITIES

211222111111 , yydFyByEyB b


1

, 1, 2, ,j

N

i i i bi i i j j ij i jAj

B r E r B r dF r r i N

��



VIEW FACTORS

212121 dFdydFdy

232212

212

121

2 Lyy

dydyLdFdy

REFER TO (REF.1 S&H)P.197 Ex 6-2 AND P.297 Ex 7-21



ALSO, BY RECIPROCITY

THEN

232221

122

212

2 Lyy

dydyLdFdy

2

322

21

2222111111 2

1

Lyy

dyyBLyEyB b

2

322

21

1112222222 2

1

Lyy

dyyBLyEyB b

INTEGRAL EQUATIONREF) F.B. Hildebrand Methods of Application Mathematics

232212

212

121

2 Lyy

dydyLdFdy





EX) P.289 Ex 7-18, P.297 Ex 7-21 (REF.1)

FROM

METHODS FOR SOLVING INTEGRAL EQUATIONS P.299

HW#2 [REF.1] P.317 #7-16(a), P.325 #7-40

ibii

i

i

i BEdA

dq

HW#2 [REF.1] P.317 #7-16(a), P.325 #7-40

7-16. (a) What is the effect of a single thin radiation shield on the transfer of energy between two concentric cylinders? Assume the cylinder and shield surfaces are diffuse-gray with emissivities independent of temperature. Both sides of the shield have emissivity , and the inner and outer cylinders have respective emissivities and .

7-40. A cavity having a gray interior surface is uniformly heated electrically and achieves a surface temperature distribution while being exposed to a zero absolute temperature environment, . If the environment is raised to and the heating kept the same, what will the surface temperature distribution be?

< 7-16 > < 7-40 >

s

)(0, STw

S

1 2

0eT eT

COMBINED HEAT TRANSFER



ENERGY BALANCE

EXAMPLE 1

4 4w sg w

T Tk T T

l

1g

What is ? Given W g ST T and T

4 41 2

1 2

1 11

T Tq

A



CASE I) wg TT SMALL

4 4 34w g g w gT T T T T

wggsw TTTTTl

k 34

INTRODUCE , PLANCK NUMBERgg

g PlTk

T

44

swsggwggsw TTTTPTTPTT

REARRANGE AS

g

g

sg

sw

P

P

TT

TT

1

4 4w sg w

T Tk T T

l



CASE II) wg TT

4gsw TTT

l

k 4g

w s g s g gg

TT T T T P T

kT l

g

g

sg

sw

P

P

TT

TT

1 gg

g PlTk

T

44

4 4w sg w

T Tk T T

l



1. CONSERVATION OF MASS

EXAMPLE 2 COUETTE FLOW

)(,0 yuudx

du

2. CONSERVATION OF MOMENTUM )/(,0 lyUudy

d



2 (a). CONSERVATION OF MECHANICAL ENERGY

3. CONSERVATION OF TOTAL

(THERMAL + MECHANICAL) ENERGY

0dy

du

udy

d

dy

dq 0

4. BALANCE OF THERMAL ENERGY

dy

du

dy

dq 0

0 : Momentum eq.d

dy



5. CONSTITUTION

GOVERNING EQUATION

BOUNDARY CONDITIONS

dy

dTkq

dy

du

02

2

2

dy

du

dy

Tdk

TT 0 wTlT

dy

du

dy

dq 0



SOLUTION

NOTE MOMENTUM SOLUTION

ADIABATIC WALL TEMPERATURE

l

y

l

y

k

U

l

yTTTT w 1

2

2

l

yUu

0lydy

dT



EFFECT OF RADIATION ON THE ADIABATIC

WALL TEMPERATURE

21

02a

UT T

l kl

2

ITHOUT ADIATIONW R 2

a

UT T

k

0 Kw

Rw qq

0

11

11

44

ly

a

dy

dTk

TT

02

244

k

UTT

l

kTT aa

2 21 2

1 , 12 2w w

y U y y dT U yT T T T T T

l k l l dy l kl l

0lydy

dT



LINEARIZE

,

HW#3 [REF.1] P.447 #10-2, P.449 #10-12

TTT

TT aa !1

4 344

3 24

2a a

T UT T T T

k l k

2

2

/ 2 1,

1 / 2 1a

a

T TU kT T

P U k P

lkT

TP

/

4 4

02

244

k

UTT

l

kTT aa

2

ITHOUT ADIATIONW R 2

a

UT T

k

HW#3 [REF.1] P.447 #10-2, P.449 #10-12

10-2. A thin two-dimensional fin in vacuum is radiating to outer space, which is assumed at . The base of the fin is at , and the heat loss from the end edge of the fin is negligible. The fin surface is gray with emissivity . Write the differential equation and boundary conditions in dimensionless form for determining the temperature distribution of the fin. (Neglect any radiant interaction with the fin base.) Can you separate variables and indicate the integration necessary to obtain the temperature distribution?

10-12. A copper-constantan thermocouple ( ) is in an inert gas stream at 350K adjacent to a large blackbody surface at 900K. The heat transfer coefficient from the gas to the thermocouple is . Estimate the thermocouple temperature if it is (a) bare (b) surrounded by a single polished aluminum radiation shield in the form of a cylinder open at both ends. The heat transfer coefficient from the gas to both sides of the shield is .

)(xT

15.0

)(25 2 KmW

bTKTe 0

constant.

2

1 :Hint

2

2

2

dx

d

dx

d

dx

d

)(15 2 KmW


GAS RADIATION

READING ASSIGNMENTS CARBON DIOXIDE AND WATER VAPOR FORMED AS

PRODUCTS OF COMBUSTION WERE FOUND TO BE THE SIGNIFICANT EMITTERS AND ABSORBERS OF RADIANT ENERGY (P.514 Fig 12-1, eg : FURNACE, ENGINE, ETC.)

THE ENERGY EMITTED FROM FLAME ; DEPENDS NOT ONLY ON THE GASEOUS EMISSION BUT ALSO ARISES FROM THE HEATED CARBON (SOOT) PARTICLES FORMED WITHIN THE FLAME

TWO DIFFICULTIES• Absorption, emission and scattering occur not only

at system boundaries, but also at some locations within the medium.

• Spectral effects are much more pronounced in gases than for solid surfaces – non-gray. (p.539, Fig.12-10)

ATTENUATION BY EARTH’S ATMOSPHERE OF

INCIDENT SOLAR SPECTRAL ENERGY FLUX


GAS RADIATION

LOW-RESOLUTION SPECTRUM OF

ABSORPTION BANDS FOR VARIOUS GASES


CARBON DIOXIDE GAS AT 830 K, 10 atm, AND FOR PATH LENGTH THROUGH GAS OF 0.388 m.

GAS RADIATION


CARBON DIOXIDE, WATER VAPOR, AND METHANE

GAS RADIATION

PHYSICAL MECHANISMS OF ABSORPTION,

EMISSION AND SCATTERING


ABSORPTION AND EMISSION (P.540, FIG 12-11, P.553, FIG12-16) (REF.1)

BOUND-BOUND ABSORPTION OR EMISSION A photon is absorbed or emitted by an atom or molecule without

ionization or recombination of ions and electrons. Since bound-bound energy changes are associated with specific

energy levels, the absorption and emission coefficients will be sharply peaked functions of frequency in the form of a series of spectral lines – do have a finite width resulting from various broadening effects. The rotational spectral lines superimposed on the vibrational line give a band of closely spaced spectral lines (p.553 Fig.12-16).

At industrial temps the radiation is principally from vibrational and rotational transitions ; at high temps, it is electronic transitions that are important.

GAS RADIATION


Bound-free absorption coefficient is a continuous function of photon energy frequency .

Resulting ion and electron take on any kinetic energy.

Free bound emission produces a continuous spectrum, as the combining particles have any initial kinetic energy.

GAS RADIATION

BOUND FREE ABSORPTION (PHOTOIONIZATION) OR

FREE BOUND EMISSION (PHOTORECOMBINATION)

FREE FREE TRANSITION Since the initial and final free energies can have

any values, a continuous absorption or emission spectrum is produced.

ENERGY STATES AND TRANSITIONS FOR

ATOM OR ION


GAS RADIATION

POTENTIAL ENERGY DIAGRAM AND

TRANSITIONS FOR A DIATOMIC MOLECULE


GAS RADIATION


Scattering – Any encounter between a photon and one or more other particles during which the photon does not lose its entire energy.

Scattering coefficient : The inverse of the mean free path that a photon of wave length will travel before undergoing scattering.

Elastic scattering – photon energy (frequency) unchanged Inelastic scattering - changed

GAS RADIATION

SCATTERING

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