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Heat transfer in boilers Heat Engines & Boilers. Combustion chamber calculation Radiation heat...

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Heat transfer in boilers Heat Engines & Boilers
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Heat transfer in boilers

Heat Engines & Boilers

Combustion 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 surfaceConvection 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

T1 = T2

Even in case of different temperatures

T1 T2

Incident radiation

• Absorption a = Ia/ Itotal - absorption coefficienta = 1 - black body

• Reflection r = Ir/ Itotal - reflection coefficientr = 1 - absolute mirror body

• Transmission d = Id/ Itotal - 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*108 [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 ehc

e

hcI

5

2

5

2

0

2

1

12

Radiation emission of black

body

Radiation energy density of black-body -

- Stefan-Boltzman law

• where:

- Stefan-Boltzman constant

E I d Ts

4

0

5 6787 10 8. W / m K2

Flame and fire chamber connectionHeat transfer by means of radiation in between two

bodies are in totally enveloping surface position

Heat transfer by radiation

• where: - Emissivity factor

• A - effective water wall surfaces subject to radiation; [m2]

• Tf - average flame temperatur [K]

• Tw - average wall temperature [K]

[kW] TTAQ4

w

4

ffwr

fw

f w

11 1

1

fw

Emissivity factor variation in real

1. Black body - theoretical maximum2. 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 first

2. Hot flue-gas radiates heat

Adiabatic flame temperature

• Maximal theoretical temperatureof 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, [kgfluegas/kgfuel] considering excess air and flue-gas recirculation

• - cpfg: mean specific heat of flue gas [kJ\kg K]

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

pfgv

in0 cB

Qt

Heat balance in combustion chamber

Qr = Qin - Qfgout

Outlet flugas heat capacity

where:

fgout0pfgv

4w

4ffw TTcBTTA

Q B c tfgout v pfg fgout

fgoutof TTT

Emissivity variation in

case of different

fuels

Flame size variation

Flame size variation

Retention time in fire chamberneeded 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

ccret

where: tret = retention time [s],

Vcc = combustion chamber volume [m3],

Vfg = volume flow of flue gas [m3/s].

,fgV

dV = dt

Adx = dV

dxTV

273A =

V

dV = dt

,fgN

,fgN

Integrated from x=0 to x=xout

fgout

0

fgout0,fgN

ccret T

Tln

TTV

V273t

Summary of combustion 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

Convective 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:

fgfgin fgout2

tt t

wwin wout2

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 cp

• kinematic viscosity • etc.

Heat transfer coefficient calculation

There are several semi empirical equation to determine heat transfer coefficient. For this dimensionless numbers are used. Most commonly used dimensionless numbers:

- Nusselt number: NuL

- Reynolds number Rew L

- Prandtl number Pr a

Explanation of different quantities

Where: - heat transfer coefficient L - specific size - thermal conductivity w - fluid flow velocity - kinematic viscosity

a - temperature conductivity acp

where: - density of the fluid cp - specific heat at constant pressure

Turbulent fluid flow inside tubes

l

25.0

w

43.08.0

Pr

PrPrRe021.0Nu

valid for: 10 5 10 0 6 25004 5 Re . Pr and where: - L specific size - inside tube diameter - t standard temperature - fluid average temperature - Prw - Prandtl number at the wall temperature - l - coefficient against long/diameter ratio

l

dl

d

l

l

1 1 5

50 1 0

.

.

Fluid flow around (between) tubes

Tubes in series arrangement:

25.0

w

33.065.0

Pr

PrPrRe23.0Nu

Tubes in staggered (chequerred) arrangement:

25.0

w

33.06.0

Pr

PrPrRe41.0Nu

valid for: 2 10 2 102 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 tubes = 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/m2K• In case of water flow: 500 < < 2000 W/m2K• In case of steam flow: 100 < < 1000 W/m2K• In case of air or flue gas: 10 < < 200 W/m2K

Heat transmission coefficient Heat transmission coefficient

K][W/m 11

1 2

wi

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 also has to be taken into account.) - thermal conductivity

Convective heat transfer

)(

)(

)(

)(

2

21

1

mWm

WW

Wfgfg

mfg

tt

tt

tt

ttUq

Convective heat transfer modification in case of deposit formation

flue gas side medium side

Transferred heat

lntFUQ dtransferre

where: k - heat transmission coefficient F - heating surface area

tln- logharitmical temperature difference

tt t

t

t

greatest smallest

greatest

smallest

ln

ln

Simple heat balance

Three types of heat quantities have to be equal: Q Q Qfg transferred water steam /

Flue gas heat:

C][ etemperatur 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] ttc BQ

fg

pfg

'v

fgoutfginpfg'vfg

Water/steam:

[kJ/kg]enthalpy am water/ste- h

[kg/s]or water steamof rate flow mass - m :where

[kW] hhmQ

w

w

winwoutwsteam/water

Radiation / Convective heat transfer variation

• Radiation and convective heat transfer has different principal

• Radiation heat transfer is proportional with ~T4

• 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 convective 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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