6.2 Boiler Design

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6.2 Boiler Design

1. General The purpose of this section is to present some of the problems

encountered in the actual design and to offer approximate solutions.

As a demonstration problem we shall assume that it is desired to findthe efficiency of an oil fired boiler whose plan !iew is shown in "igure 1. Anele!ation !iew would be similar to the boiler shown in "igure 2 except thatthe tube si#e and spacing are different.$ther data will be assumed to be%"urnace waterwalls and roof% & in bare tubes'on!ection section% 2 in tubes on ( in. centers) diamond staggered

arrangement*or+ing pressure% 2,- psig*ater entering% 2-- "Air entering and room temperature%% - "/team lea!ing% saturated0adiation and unaccounted for loss% &$il heating !alue% 1 ),-- Btu per lb$il analysis% ( ') 1& s) 2 /) 1 3"lue gas% 12., '$2 on dry basis) corresponding to 2- excess air'on!ection section% &2 tubes wide) 126 in. between walls

"urnace section% 1 tubes on front wall) sidewalls) and roofs4 waterscreen in path of gases to con!ection #one has tube staggered.5oad% 22)--- lb per hr of steamAn efficiency of ,. will be assumed and calculations will be made to

chec+ this efficiency.

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2. "urnace 'alculations. The first step will be to determine the wall areas and the tube surface. To

simplify the problem) the heat transfer to the floor tubes will be neglectedand the a!erage tube height for the wall will be ta+en as 12 ft. Then thefurnace en!elope surfaces will be as follows%

"ront wall area 7 12 x 1-., 7 126 s8 ft

/ide wall area 7 2 x 12 x 1-.2, 7 2(6 s8 ft0ear wall area 7 12 x , 7 6- s8 ft0oof area 7 1-., x 1-.2, 7 1- s8 ft/creen tube area 7 1291-., : ,; 7 66 s8 ft

The area of the furnace en!elope bac+ed by refractory is 126 < 2(6 < 6- sing cur!e &) the factoris -.?6 and the ad=usted surface us 66 x -.?6 7 6& s8 ft. Then the ad=usted

en!elope surface is (& < 6& 7 ,-- s8 ft.

Before the furnace exit gas furnace can be obtained from "igure () it isnecessary to determine the a!ailable energy. "or simplicity) these losses willbe charged to the furnace.

( ) ( ) ( ) ( )[ ] f abaahaa W CCHt t W QHHV energy Available += 60014910402401 27 ).*hereQ 7 7 the radiation and unaccounted for loss expressed as a decimal)

HHV 7 higher heating !alue of the fuel) Btu per lbW aa 7 actual air) lb per lb fuelt a 7 temperature of air surrounding the boiler) "t ah 7 temperature of the air lea!ing the air heater or entering the burners) "

$bser!e that the e8uation is an expression for the lower heating !alue ofthe fuel with ad=ustments for preheated air) radiation and unaccounted forloss) and the loss due to incomplete combustion.

@t is necessary to use the lower heating !alue of the fuel to determine gastemperatures) since the latent heat of the water !apor from the combustion

of hydrogen in the fuel does not increase gas temperature. Also) it isimpossible for the boiler to condense this !apor and to ma+e use of it toe!aporate water in the tubes. "rom the combustion analysis of the fuel wefind that there is 6., water !apor in the gases by weight and on the wetbasis and there is 1 .1 lb of wet gas per lb of wet gas per lb of fuel. By usingthe higher heating with the assumed boiler efficiency) the fuel consumption isfound to be

( ) hr per lbW f 162250018757001687120100022

==

)...)

And

( ) ( ) ( ) ( )[ ] f abaahaa W CCHt t W QHHV energy Available += 60014910402401

27 ).

W aa 7 1 .1 : 1 7 1 .1H2 7 -.1&C- C ab 7 -. ( : -. (t ah 7 t a 7 - "

(


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( ) ( )( ) ( )( ) ( [ 8084060014130910408080117240030150018 ..)....) +=energy Availablehr per Btuenergy Available 00015027 ))=

Then the a!ailable energy) the abscissa of "igure () is 2 )1,-)--- ,-- 7,()&-- Btu per s8 ft per hr of ad=usted en!elope surface. "rom "igure () thegas temperature lea!ing the water screen and entering the con!ectionsection is 1 - ".

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@n order to determine the sensible energy of the gases lea!ing thefurnace) the !alues of constant pressure instantaneous specific heats areplotted in "igure , by using the flue gas analysis. *ith these data) a cur!e ofsensible energy abo!e - " can be plotted) "igure 6. *hile these cur!es arefor the particular flue gas analysis of this problem) they would not materiallydifferent for many other flue gas analyses.

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"rom "igure 6) the sensible energy of the flue gas lea!ing the waterscreen is ( Btu per lb of gas and the energy transferred in the furnace 9 Q f ;is

hr per BtuQ f 00013013478162211800015027 )).)) ==

The amount of water e!aporated in the waterwalls is 1&)1&?)--- 912-1. :16 ; : 12) -- lb per hr) based on the inlet feedwater temperature.


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The total pro=ected area of the furnace en!elope tubes is%

ft sqlongft diamin

tubesall!ront 541212

318 ==

.

ft sqallslongft diamin

tubesalls"ide 10221212

317 ==

.

ft sqlongft diamin

tubesallar #e 211212

37 ==

.

ft sqlongft diamin

tubes#oof 5412123

18 =

= .

ft sqlongft diamin

tubes"$reen 46251012

318 == .

.

Total pro=ected tube area 7 2 s8 ft

Therefore the radiant heat transfer rate is 1&)1&-)--- 2 7 ( )(-- Btuper 9hr;9s8 ft of pro=ected surface;) or ( )(-- 7 1,)1-- Btu per 9hr;9s8 ftof outside tube surface;.

The assumption of boiler efficiency cannot be chec+ed until thecon!ection surface calculations ha!e been complete.

&. 'on!ection /urface 'alculations@nspection of "igure 1 shows that there are (-1 tubes in the con!ection

#one. Assuming an a!erage tube length of approximately 12., ft to account


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bends) the length of the area will be smaller than the tube length4 ta+e 12 ftas the length of the area. The first con!ection row is , ft , in. long and mustcontain 1 tubes or 16 spaces. The area is

ft sqhighft idthin

spa$es 321212

216 = .

"or the next to the last row) the area is

ft sqhighft idthin

spa$es 141212

27 = .

The a!erage area of 2& s8 ft will be used. A more exact method would be todesign each section separately.

The gas flow is 1622 x 1 .1 7 2?)(-- lb per hr and the density is

ft $u per lb#& '

08080492353

7141440 ..

. ===

Then the mass flow based on the a!erage flow area is

( ) ( )sec.)

sqft per lb( 3560233600

40029=

=

fps(V 4408080

3560

0

0 ... ===

( ) ( ) ( ) ( ) F sqft hr per Btu D

V hU 41.4

12

2

4.491.091.0

31.0

69.0

31.0

69.00

0 =

===

The next step is to estimate the final gas temperature so that the )*&+may be calculated. /ince the furnace was calculated to e!aporate 12) -- lbper hr) the con!ection #one should e!aporate 22)--- : 12) -- 7 ?)&-- lb perhr. Cach pound of flue gases should then transfer to the tubes in thecon!ection #one by radiation and con!ection.

( )lb per Btu328

1181622

0168712019300=

.

..

The energy of the flue gases entering the con!ection #one was calculatedto be ( Btu per lb. Then the energy lea!ing the con!ection #one will be (: &2 7 1,- Btu per lb. "rom "igure 6) this would represent a temperature of6 - ".

This flue gas temperature is too high for an economical steam generatoras it is 26( " abo!e the saturated steam temperature of (-6 ". "or typicalconditions) the exit flue gas temperature should be roughly 1-- abo!e the

saturation temperature.@f the tube temperature is ta+en to be the same as the water temperature

9(-6 ";) in accordance with pre!ious assumptions of negligible resistancethrough the water film and the metal) )*&+ is

! )*&+m 669

406670

4061770

6701770=

==ln

1-


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'on!ection heat transfer ishr per Btu A%Q m$ 0007407669262541400 )). ===

Gases radiate and absorb energy at intermittent wa!e length bands.0adiation in the infrared band from gases has been recogni#ed as importantto the design of some heat transfer apparatus. *hile the radiationconsidered for the furnace is from luminous flames and suspended particles)the con!ection #one radiation is from inacti!e nonluminous gases that are notundergoing a chemical change and that carry !ery little) if any) suspendedsolids.

$f the constituents in the flue gases) carbon dioxide and water !apor arethe only ones that ha!e sufficiently strong radiating characteristics to meritconsideration. /ulfur dioxide and carbon monoxide ha!e strong radiatingtendencies but usually are present in flue gas in such small 8uantities thatthey need not be considered.

The radiation from gases containing carbon dioxide and water !apor maybe approximated by

=

44

10010017230 sggsr

& & AQ .

@n whichQ r 7 heat transfer by radiation from gases) Btu per hr

A 7 outside tube surface area) s8 ft, s 7 tube emissi!ity) -. - for boiler and superheater tubes, g 7 emissi!ity of the gases at temperature Tg& g 7 absolute gas temperature) 0

A 7 emissi!ity of the gases at temperature Ts& s 7 absolute tube surface temperature) 0

*hen the gases are at standard atmosphere) as is the case in nearly allboilers) the gas emissi!ities can be e!aluated 9other assumptions for thesee8uations are that ' $) < ' ) -.& and that & g E& s F 1.2,;

g$gg C +=And s$s C +=

@n which $g 7 emissi!ity of carbon dioxide at temperature & g from "igure . g 7 emissi!ity of water !apor at temperature & g from "igure . $s 7 emissi!ity of carbon dioxide at temperature & s from "igure . g 7 emissi!ity of water !apor at temperature & s from "igure .C 7 correction factor for water !apor emissi!ity from "igure ?.

The a!erage gas temperature may be estimated from the e8uation

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2460 21

t t & mg

+++=

*here m 7 log mean temperature difference between gas and surface) "t and t 2 7 surface temperature at sections where fluid enters and lea!estubes) respecti!ely) ".

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@n the con!ection #one) water is being e!aporated and therefore the tubesurface temperature is constant throughout the #one. This would not be true

for superheaters or economi#ers. Also) it is sufficiently accurate to say thatthe tube surface temperature is the same as the water and steamtemperature within the tube.

$bser!e that the !alues $ and ) shown in "igure and "igure ) areplotted with !alues of ') as parameters. "or each set of cur!es) ' is thepartial pressure of the gas expressed in atmospheres and 5 is the radiantbeam length for the gas) expressed in feet. /ubscripts c and w indicate

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carbon dioxide and water !apor) respecti!ely) as before. alues of ) shouldbe determined from the expressions gi!en in Table 2.

Harameters of ') are also used in "igure ?. This graph accounts for theeffect of the water !apor partial pressure on radiation.

The tube surface temperature for our problem is (-6 " and the mean gas

temperature is#& g 1535406669460 =++=

$r! t g 1075=

Hartial pressure of gases are proportional to the !olumetric analysis of thewet gas. @n this case we ha!e 11.2 carbon dioxide and 1-.( water !apor.

Therefore) e!aluating ) from Table 2 as 2E12 x 2. ) we get

052308212

21120

... ==)' $

And 048608212

21040

...

==)'

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"rom "igure ?) C 7 1.- . "or a temperature t ) of (-6 " and ' ) 7 -.-( 6 . s is -.-6( from "igure . "inding other !alues in similar manner) we get)

s$s C +=

( ) 124008106400550 .... =+=

And

g$gg C +=( ) 104008103900620 .... =+=g

>sing these !alues)

=

44

10010017230 sggsr

& & AQ .

( )( )

=

44

100

8661240

100

15351040800262517230 ....r Q

hr per BtuQ r 0008351 ))= The total energy transferred for the entire boiler is

r $f QQQQ ++=

0008351000740700013013 )))))) ++=Qhr per BtuQ 00070522 ))=

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And the e!aporation is

hr per lb95021016871201

00070522)

..)) =

This shows that the assumed efficiency was correct. owe!er) thetemperature of the gases entering the con!ection #one is low. A moreeconomical unit would ha!e less waterwall surface and more con!ectionsurface to reduce the final flue gas temperature.

$bser!e that the energy transferred by radiation from nonluminous gasesin the con!ection #one amounts to about 2- of the heat transfer in this#one.

(. /econdary /urface

'alculations for surfaces of the con!ection type of superheater)economi#er) and tubular air heater follow the same procedures that wereused for the con!ection #one. Gas) air) and steam film coefficients may bedetermined from Table 1. *ater film coefficients for economi#ers offer onlyto+en resistance to the flow of heat and may be neglected for economi#ers./imilarly) the metal in the tube walls may be disregarded in calculating theheat flow.

3onluminous radiant heat transfer from the water !apor and carbondioxide in the flue gases will amount to a small percentage of the total heattransfer for economi#ers and air preheaters.

"or secondary surface) the flow of water) steam) air) or gas is customarilygi!en as the mass flow in units of pounds per 9hour; 9s8uare feet of flowarea;.

/uperheaters) air heaters) and economi#ers use 2 or 2 1E2 in. $D tubes. These tubes may be placed on approximately & to ? in. centers insuperheaters. The wider spacing is to reduce the possibility of slag bridgingacross the space. *ith either pendent or hori#ontal superheater designs) thetubes are in line and form se!eral passes. Iass gas flows range from 1,-- to&--- lb per 9hr; 9s8 ft; while mass steam flows are from 2--)--- to &--)---lb per 9hr;9s8 ft;. Iass steam flows may be higher) up to --)--- or more) for!ery high temperature superheaters.

Air preheater tubes should ha!e the air on the outside of the tubes topre!ent plugging from soot in the gases. @n this way staggered tubes may beused effecti!ely. The tubes are of either 3o. 12 or 3o. 1( B*G 9-.1-? in. or-.- & in.) respecti!ely; thic+ness and are arranged for at least J in. space

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between tubes. Iass gas flows are from ,--- to 1-)--- and mass air flowsare from &--- to ,--- lb per 9hr; 9s8 ft;.

Cconomi#ers) being of the continuous tube design) are arranged withtubes in line) and there are many water passes. The tubes are on centers that

pro!ide 1 J to 2 in. lanes for gas flow. The spacing parallel to the gas flowranges from 1 to & in. *ater !elocities in the tubes range from & to fps andthe mass flow of gases is about (--- to --- lb per 9hr;9s8 ft;.

,. Assignment

Assume that the pul!eri#ed coal furnace is rectangular in plan and ele!ation!iews. The waterwalls are of & in. tangent tubes. @nclude floor surface 9assume flat)hori#ontal floor; and calculate temperature of the gas lea!ing the furnace) the heattransfer per hour for each s8uare foot of pro=ected surface) the heat release percubic foot of furnace !olume) and the steam produced if the downcomers carrysaturated water.

/team pressure) psia 16,-

"uel) 8uantity) tons per hr (?

Kind @ll.l 'hristian

"urnace) height) ft -

Depth) ft 2

*idth) ft &1

t a) " -

t ah ) " ,,-

0adiation and unaccepted for 1.

Cxcess air) 1?

1

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6.2 Boiler Design