Heat transfer in boilers

rangebeaverMécanique

22 févr. 2014 (il y a 3 années et 3 mois)

103 vue(s)

Heat transfer in
boilers

Heat Engines & Boilers


Co
mbustion chamber calculation


Radiation heat transfer


Adiabatic flame temperature


Heat transfer in combustion chamber


Retention time in fire chamber


Flame size variation

Heat transfer forms from gas to solid surface

Convection

Radiation

By means of

Fluid flow and
conduction through
boundary layer

Electromagnetic
radiation

Contact in between
gas and solid
surface

Necessary

Not necessary

(even in vacuum)

Depends mainly on

Fluid flow type


and velocity

Temperature difference

raising to the 4th power

Equilibrium state

Q = 0

In case of equal
temperature

T
1

= T
2

Even in case of different
temperatures

T
1



T
2

Incident radiation


Absorption

a = I

a
/ I

total

-

absorption coefficient




a = 1


-

black body


Reflection

r = I

r
/ I

total

-

reflection coefficient




r = 1


-

absolute mirror body


Transmission

d = I

d
/ I

total

-

transmission

coefficient

(diffraction)

d = 1


-

transparent body





a + r + d = 1


-

in each case



Radiation emission of black body

The Planck law with Wien type simplification

Where:

c
-

velocity of light in vacuum

c = 299 792 458


3*10
8

[m/s]

h
-

Planck constant



h = 6.625
*10
-
34



[Js]

k


Boltzmann constant


k = 1,38*10
-
23



[J/K]

kT
hc
kT
hc
e
hc
e
hc
I













5
2
5
2
0
2
1
1
2
Radiation
emission
of black
body

Radiation energy density of black
-
body
-


-

Stefan
-
Boltzman law



where:


-

Stefan
-
Boltzman constant


E
I
d
T
s








4
0




5
6787
10
8
.
W
/
m
K
2

Flame and fire chamber connection

Heat transfer by means of radiation in between two
bodies are in totally enveloping surface position

Heat transfer by radiation


where:



-

Emissivity f
actor









A

-

effective water wall surfaces





subject to radiation; [m
2
]





T
f

-

average flame temperatur [K]





T
w

-

average wall temperature [K]



[kW]

T
T
A
Q
4
w
4
f
fw
r










fw
f
w



1
1
1
1

fw
Emissivity factor variation in real

1.
Black body

-

theoretical maximum

2.
Grey body

-

solid body radiation





emissivity is constant

3.
Color body

-

gas radiation







emissivity is not constant

Combustion process in real

Parallel procedures running at the same time

having dependence on one another:


Chemical reaction


Fluid flow


Heat transfer

Simplification model:

1.
Chemical reaction happens firs
t

2.
Hot flue
-
gas radiates heat

Adiabatic flame temperature


Maximal
theoretical
temperature

of flue
-
gas
without any
heat transfer

Calculation of adiabatic flame temperature


Heat flow into the combustion chamber:





adiabatic flame temperature




where:
-

B: mass flow rate of fuel [ kg/s]



-


v
: specific flue gas amount, [kg
fluegas
/
kg
fuel
]




considering excess air and flue
-
gas recirculation



-

cp
fg
: mean specific heat of flue gas [kJ
\
kg K]

Q
B
H
c
t
c
t
in
i
Lo
pair
hotair
fuel
fuel










pfg
v
in
0
c
B
Q
t




H
eat balance
i
n combustion chamber



Q
r

= Q
in

-

Q
fgout




Outlet flugas heat capacity



where:







fgout
0
pfg
v
4
w
4
f
fw
T
T
c
B
T
T
A












Q
B
c
t
fgout
v
pfg
fgout





fgout
o
f
T
T
T



Emissivity
variation in
case of
different
fuels

Flame size
variation

Flame size variation

Retention time in fire chamber

needed for 99.99% oxidization

Needed temperature [
°
C]

Material

0,5 sec

1 sec

2,0 sec

At retention time

Benzene

880

830

790

Butane

930

900

870

Ethane

1090

990

910

Methane

990

950

920

Tetrachloromethane

1090

990

920

Toluene

1260

1220

1180

Vinyl chloride

770

740

720

Retention time calculation



s

V
V

=

t
fg
cc
ret

where
:

t
ret

= retention time
[s],

V
cc
=
combustion chamber volume
[m
3
],

V
fg
=
volume flow of flue gas
[m
3
/s].

,
fg
V
dV

=

dt





Adx

=

dV


dx
T
V
273A

=

V
dV

=

dt
,
fgN
,
fgN


Integrated from x
=0 to
x=x
out



fgout
0
fgout
0
,
fgN
cc
ret
T
T
ln
T
T
V
V
273
t




Summary

of

c
o
mbustion chamber calculation

You are already familiar with:


Radiation heat transfer


Adiabatic flame temperature


Heat transfer in combustion chamber


Flame size variation


Retention time in fire chamber


Con
vective heat transfer calculation


Definition of convective surfaces


Types and arrangements of convective
heating surfaces


Calculation method


Heat balance


Radiation / Convective heat transfer
variation

Definition


We call “Convective Heating Surfaces”

surfaces which are built in the boiler after the
combustion chamber until the boiler exhaust.

Where heat transfer happens mainly by combustion:


These can be:


-

superheater


-

evaporator


-

water heater (economizer)


-

combustion
air heater


Each heating surface can not be found in every boiler.


Flue
-
gas flow can be inside tubes

Convective
heating
surface
construction


Fluegas is
streaming
around water
tubes

Convective heating surface construction

Typical superheater arrangements

Tube
arrangement

examples


Finned watertube type

heating surface constructions

Heat transfer calculation

Input data:


sizes of the heating surface


construction of the heating surface


built in materials


flue gas
-

inlet temperature



-

inlet pressure





-

mass flow rate


heat absorp.fluid
-

inlet temperature


(water/steam/air)
-

inlet pressure





-

mass flow rate

Iteration process


Outlet temperature of the flue gas and the heat
absorption fluid has to be estimated.

Then average temperatures can be calculated



flue gas:





heat abs.fluid:




fg
fgin
fgout


2
t
t
t
w
win
wout


2
Characteristic features


Knowing the average temperatures you can
determine the characteristic features belonging to
the temperature and pressure both of the flue gas
and the heat abs. fluid, which is needed to the
calculation.

These can be:


density



thermal conductivity




Prandtl number Pr


specific heat c
p


kinematic viscosity




etc.

Heat transfer coefficient calculation


There are several semi empirical equation to determine heat transfer coefficient.


For th
is dimensionless numbers are used.

Most commonly used dimensionless numbers:

-
Nusselt number:
Nu
L





-
Reynolds number
Re


w
L


-
Prandtl number
Pr


a

Explanation of different quant
i
ties

Where:


-

heat transfer coefficient

L
-
specific size




-
thermal conductivity

w
-
fluid flow velocity




-
kinematic viscosity

a
-
temperature conductivity
a
c
p





where:


-
density of the fluid

c
p

-
specific heat at constant pressure

Turbulent fluid flow inside tubes


l
25
.
0
w
43
.
0
8
.
0
Pr
Pr
Pr
Re
021
.
0
Nu
















valid for:
10
5
10
0
6
2500
4
5





Re
.
Pr
and


where:
-
L specific size
-
inside tube diameter


-
t standard temperature
-
fluid average temperature


-
Pr
w


-
Prandtl number at the wall temperature


-


l

-
coefficient against long/diameter ratio


l
d
l
d
l
l











1
1
5
50
1
0


.
.

Fluid flow around (between) tubes


Tubes in series arrangement:























25
.
0
w
33
.
0
65
.
0
Pr
Pr
Pr
Re
23
.
0
Nu

Tubes in staggered (chequerred) arrangement:























25
.
0
w
33
.
0
6
.
0
Pr
Pr
Pr
Re
41
.
0
Nu

valid for:
2
10
2
10
2
5




Re

where:
-
w specific velocity
-
fluid
flow velocity in the narrowest cross
-
section


-




-
coefficient according to the angle including between the

fluid flow and tub
es



= 90°
-



= 1.0



= 10°
-



= 0.56

Heat transfer coefficient in case of water boiling






2
8
0
176
0
7
.
.
.
p
q
[
W
/
m
K
]
2

valid at: 0.2 bar < p < 98 bar






1
27
0
75
.
.
q
e
[
W
/
m
K
]
p
62
2

valid at: 6.0 bar < p < 173 bar


where
-
p
-
saturated pressure [bar]


-
q
-
heat flux
[W/m2]

Ranges of heat transfer coefficients

These are only examples.

According to the surface arrangement you can find

several cases in the literature.

Heat transfer coefficient has different value range at
different types of fluid:


In case of: water boiling: 5000 <



< 20000 W/m
2
K


In case of water flow: 500 <


<


2000 W/m
2
K


In case of steam flow: 100 <


<


1000 W/m
2
K


In case of air or flue gas: 10 <


<


200 W/m
2
K

Heat transmission coefficient


Heat
transmission coefficient



K]
[W/m

1
1
1
2




w
i
i
fg
U






where:

fg

-
flue gas heat transfer coefficient



w

-
water/steam side heat transfer coefficient






-

thickness of the tube or other surface



(In case of soot or scale coating possibility




al
so has to b
e taken
into
account
.)






-
thermal conductivity

Convective heat transfer





















)
(
)
(
)
(
)
(
2
2
1
1
m
W
m
W
W
W
fg
fg
m
fg
t
t
t
t
t
t
t
t
U
q





Convective heat transfer modification in case of
deposit formation

flue gas side




medium side

Transferred heat



ln
t
F
U
Q
d
transferre






where: k
-
heat transmission coefficient

F
-
heating surface area



tln
-
logharitmical temperature difference





t
t
t
t
t
greatest
smallest
greatest
smallest
ln
ln



Simple heat balance

Thr
ee types of heat quantities have to be equal:
Q
Q
Q
fg
transferred
water
steam


/

Flue gas heat:






C]
[

e
temperatur

gas

flue

-

t


K]
[kJ/kg

gas

flue

of

heat

specific
-

c

[kg/s]

fuel

of

rate

flow

mass

specific
-



[kg/s]

fuel

of

rate

flow

mass

-

B

:
where
[kW]

t
t
c

B
Q
fg
pfg
'
v
fgout
fgin
pfg
'
v
fg










Water/steam:




[kJ/kg]
enthalpy

am
water/ste
-

h


[kg/s]
or water

steam
of

rate

flow

mass

-

m

:
where
[kW]

h
h
m
Q
w
w
win
wout
w
steam
/
water







Radiation / Convective heat transfer variation


Radiation and convective heat transfer has different
principal


Radiation heat transfer is proportional with
~
T
4



Convective heat transfer is proportional with velocity


In case of part load operation less fuel is burnt

-

less fuel produce less fluegas


on same cross section gives less velocity

-

combustion reaction temperature remains nearly the same


Consequently radiation/convection heat transfer ratio
increases with power load decrease

Summary

of


c
on
vective heat transfer calculation

You are already familiar with


Definition of convective surfaces


Types and arrangements of convective heating
surfaces


Calculation method


Heat balance


Radiation / Convective heat transfer variation


(
see calculation example
)

Thank You for Your Attention !

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