I

17^312

NBSIR 83-2638

A Commercial Heating Boiler

Transient Analysis Simulation

Model (DEPAB2)

May 1982

Issued January 1983

Prepared for: USA Facilities Engineering Support Agency

MERADCOM, Department of the Army

Ft. Belvoir, Virginia 22060

100

U56

83-2638

1983

NBSIR 83-2638

NATIONAL BUREAU

OF STANDARDS

LIBRARY FEB 2 m3

O&Z'CfCr - 1 Cfc /trO*

A COMMERCIAL HEATING BOILER

TRANSIENT ANALYSIS SIMULATION

MODEL (DEPAB2)

Joseph Chi

HCP Systems

Rockville, Maryland

Lih Chern

David Didion

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Building Technology

Washington, DC 20234

May 1982

Issued January 1983

Prepared for: USA Facilities Engineering Support Agency

MERADCOM, Department of the Army

Ft. Belvoir, Virginia 22060

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

ABSTRACT

This report documents a second generation boiler transient analysis

computer program DEPAB2. DEPAB2 improves the efficiency and accuracy of calculation over the original NBS-developed boiler transient analysis program

DEPAB. DEPAB2 treats in detail the boiler controllers and different modes of

heat transfer (conductive, convective and radiative) which occur in commercial

boilers. It is built upon seven principal subroutines for the controller and

interface flux calculations and 16 auxiliary subroutines for fluid properties,

fuel/air combustion and heat transfer parameters.

Also included in this report is a guide on using DEPAB2. It contains:

(1) input data requirements for DEPAB2 runs, (2) procedures for DEPAB2 runs,

and (3) output data interpretation.

In addition, a worked example is described and discussed in detail to

illustrate: (1) the DEPAB2 runs, (2) quantitative information generated by

DEPAB2, and (3) the use of information from DEPAB2 to calculate boiler

efficiency and examine energy conservation control strategies.

TABLE OF CONTENTS

PAGE

ABSTRACT ii

LIST OF FIGURES iv

1. INTRODUCTION 1

2. BOILER CONTROLLER DYNAMICS AND SUBROUTINE CT 3

3. BOILER THERMAL DYNAMICS AND SUBROUTINES 7

3.1 Math Model and Subroutine SR for Gas/Furnace Heat Flux 10

at On Period

3.2 Math Model and Subroutine LT for Gas/Tube Heat Flux at 11

On Period

3.3 Math Model and Subroutine FG for Off Period Gas/Solid 16

Interface Heat Transfer

3.4 Subroutine DB and SGHT for Water Side Heat Transfer 16

3.5 Subroutine SH for Boiler Shell Heat Loss 19

3.6 Auxiliary Subroutines 22

4. COMMERCIAL BOILER TRANSIENT ANALYSIS COMPUTER PROGRAM DEPAB2 26

5. USER’S GUIDE 33

5.1 DEPAB2 Input Data Code 33

5.2 Running DEPAB2 & DEPAB2 Output Data Code 34

5.3 An Example Simulation 39

6. SUMMARY 55

7. REFERENCES 56

APPENDIX A: 57

INPUT FILE #8 FOR BOILER PARAMETERS

iii
LIST OF FIGURES

Figure Page

No. No.

1 TYPICAL FIRE TUBE BOILER CROSS-SECTION 2

2 LOGICS FOR BOILER CONTROLLERS 4

3 LISTING OF SUBROUTINE CT 6

4 LISTING OF SUBROUTINE SR 12

5 LISTING OF SUBROUTINE LT 15

6 LISTING OF SUBROUTINE FG 17

7 LISTING OF SUBROUTINE DB 20

8 LISTING OF SUBROUTINE SGHT 21

9 LISTING OF SUBROUTINE SH 23

10 SUBROUTINES FOR DEPAB2 25

11 FLOWCHART FOR PROGRAM DEPAB2 27

12 LISTING OF DEPAB2 MAIN PROGRAM 28

13 A SAMPLE FILE 8INPUT DATA FOR BOILER PARAMETERS 35

14 OUTPUT DATA FROM A SAMPLE DEPAB2 RUN 36

15 CONTROL LOGIC FOR A BOILER UNDER INVESTIGATION 40

16 TYPICAL WEATHER AT WASHINGTON, D.C. DURING A HEATING SEASON 41

17 LOAD VERSUS TIME AT A DAY WHOSE OUTDOOR AIR TEMPERATURE IS 42

9.4°C (15°F)

18 DAILY HEATING LOAD VERSUS OUTDOOR AIR TEMPERATURE 43

19 DAILY FUEL CONSUMPTION VERSUS OUTDOOR AIR TEMPERATURE 45

20 DAILY FUEL UTILIZATION EFFICIENCY VERSUS OUTDOOR AIR 46

TEMPERATURE

21 TRANSIENT STEAM TEMPERATURE AT MORNING SETUP 47

22 TRANSIENT STACK GAS TEMPERATURE AT MORNING SETUP 48

23 TRANSIENT STEAM TEMPERATURE AT NIGHT SETBACK 49

24 TRANSIENT STACK GAS TEMPERATURE AT NIGHT SETBACK 50

25 COMPARISON OF HEATING LOAD AND FUEL CONSUMPTION FOR CASES 54

WITH AND WITHOUT SETBACKS

iv
1 . INTRODUCTION

This report documents DEPAB2, a computer program for design and

analysis of commercial heating boilers, which has been developed to include

subroutines for (1) simulating the boiler controllers, (2) calculating combined radiative/convective heat transfer in the boiler furnace, (3) calculating combined radiative/convective heat transfer in the boiler tubes,

(4) calculating off period draft air heat transfer, (5) calculating water

side convective and boiling heat transfer, and (6) calculating boiler shell

heat losses. Section 2 of this report describes a generalized theory of

the boiler controllers and a controller subroutine CT. Elements of boiler

thermodynamics and the boiler thermal flux subroutines, which includes combustion and different modes of heat transfer, are described in section 3.

Also described in section 3 are thermal response equations of the boiler in

lumped parametric form.

The commercial boiler transient analysis computer program is

described in section 4. Detailed listings of DEPAB2 principal subroutines

and the main program are included in the text of this report. Listings of

auxiliary subroutines, which are used to assist with the principal subroutines' calculations, are appended to this report. A user's guide is presented in section 5. This guide includes instructions on input data

preparation, output data interpretation, and running of DEPAB2 on an

EXEC-1108 computer. Also included in section 5 is a worked example to

demonstrate a series of DEPAB2 runs. A set of results from DEPAB2 runs

are discussed in this section to illustrate how DEPAB2 may be used to

facilitate engineers' design of commercial heating boilers for energy

efficiency. Although the simulation program is applicable to both water

tube and fire tube boilers, the development and application to date has been

towards the Scotch type of fire tube boiler shown in Figure 1.
Boiler

shell

Figure
2 . BOILER CONTROLLER DYNAMICS AND SUBROUTINE CT

There are five types of combustion controllers which are in common

use for commercial heating boilers today [1]. These controllers have three

basic logics as shown in figure 2. These three basic logics are represented by: (1) the on/off controller, (2) the high/low/off controller, and

(3) the air/fuel metering controller. Operational principles for these

three types of controllers are as follows:

The On/Off Controller senses the boiler steam pressure (or

temperature) . Fuel/air supply turns on when the boiler pressure (or temperature) drops below a preset value and turns off when it rises above the same

preset value.

The High/Low/Off Controller senses either the steam pressure or

temperature. Air/fuel supply turns on low when the boiler pressure or

temperature drops below a preset point and it turns on high when the boiler

pressure or temperature drops further below another preset point. As

pressure or temperature rises, the sequence reverses.

The Air/Fuel Metering Controller (or the modulating controller) has a

primary feedback element sensing the boiler pressure or temperature. The output

signal from the feedback element is combined with the set point signal and processed by the air/fuel automatic controller. The resultant actuating signal

from the air/fuel automatic controller is used to position the final control

elements for fuel/air flow in proportion to load. There is usually a minimum

firing rate for a boiler burner; so a boiler with an air /fuel metering controller

operates in an on/off mode when the heating load for the boiler is smaller

than the boiler steady-state output at its minimum firing rate.

3
FIGURE

2

lodes

for

generalized

combustion

controllers

TYPE-3:

METERIHC

CONTROLLER V

/

/

1

1

r -

i 7*

s;

° i-—«.

fib

T7

T8

(T3)

fib i Z

o

“5T"

. if!! *

O 1 O

y * /

< cm. <« «0 VI)

H

01M

•J QOH

O i O * H

7* 7 Zb

O SA «; Cl o

ol 6

' 4

1 4

£o

1

I L

* °

r«»

i H co o l N | «M 5 i

i

fib Cm. X 5“ 5 ^ °l

o o o

CM • t *

1 M >0 Sf> r*. r** cc * H

>- (ia io vi)

p*H

1

1

OM 1

1 J

J 1

1

OM

1

1 z

o 4

- if 1

' COH

Cm. -1 - w 1 o o

O fiu Cm. t 1

fib | U. Z

o

o

| o O | O

.. • 1 vO w < Cm.

>*H (il 10 VI)

>

a< CO w a H H

CO < -

H M

M « J

•J a o j a

>* O UJ

CJ CM X H g

* X CO

Cm. O O O at

Cm. Cm. | O Z I < O I

(ml ^ Cm. at < ac a at w

fid H

U3 H <

flu < od X OM M 3 H X O

O J

as -J b. O Cm. CO J z «s cm] bi m a

co < u.

4
Curves of steady-state air and fuel flow rates versus

the boiler pressure or temperature are shown in figure 2 for

boilers with the three different types of controllers

discussed above. In a transient state, instantaneous air/fuel

flow rate (w

&

and w^) may lag behind the steady-state values

(i.e., the RF and RA values read from figure 2). In terms

of the steady-state values and the time lag constant, the

* on and off cycle air/fuel flow rates can be calculated from

the equation:

ft

-t(R-w) (1)

where w is the instantaneous air or fuel flow rate; T the

on or off period air/fuel flow time constant, and R the

steady-state air or fuel flow rate (i.e., the RA or RF value

read from figure 2). Input to the controller is, therefore

the control variable ( i . e . , pr e s sur e or temperature); and

its outputs are the air and fuel flow rates. Time constants

for air/fuel flows and relations of steady state air/fuel

flow rates to the boiler control variable are the controller

parameters. According to the controller dynamics described

above, subroutine CT has been written to calculate the controller

dynamic responses. Figure 2 shows a detailed listing of

subroutine CT.

5
SUBROUTINE CT( ONF, VFUEL. VAIR, VGAS, TSEN,

JCTBL, ICTYPE,TASEN,TAAIR,AIROF,DT)

cC CALCULATE CONTROLLER STATUS

C

COMMON/CONTRL/TBO I L( 8) ,FRGBL(3) ,AIRBL(8)

COMMON/VRITE/IVRITE

TSEN*TSEN+<. DT/TASEN) *( TBL-TSEN)

GOTO( 100,290.300) , ICTYPE

100 IF(ONF. CT. 9.5. AND. TSEN. GE. TB0IL(7) )GOTO110

I F ( ONF . LT. 0 . 3 . AND . TSEN . LE . TBO I L( 6 ) ) GOTO 1 20

GOTO5O0

110 ONF*0.

GOTO5 00

120 ONF* 1

.

VFUEL* FRGBL( 6

)

WAIR= AIRBLt 6)

GOTO600

200 IF(0NF.LT.0.5)G0T0210

IF( ONF . GT. 0 . 3 . AND . ONF . LT. 1 . 5) GOTO220

IF( ONF . GT. 1 . 3) GOT0230

210 IF(TSEN.CT.TB0IL(7) >GOTO500

ONF* 1

.

VFUEL* FRGBL( 7)

WAIR= AIRBL( 7)

GOTO600

220 IF( TSEN. GT. TBOIL( 6) . AND.TSEN.LT.TB0IL(8) )GOTO300

_ IF( TSEN. GE. TBOILt 8) ) GOT0224

IF( TSEN. LE. TBOIL( 6) ) GOT0228

224 ONF=*.

GOTO5O0

228 ONF* 2.

WFUEL= FRGBLC 6

)

VAI R* AIRBLC 6

)

GOTO6O0

230 IF( T3EN.LT. TBOIL( 7) )GOTO500

ONF* 1

.

VFUEL* FRGBL( 7)

VAIR=AIRBL(7>

GOTO6O0

3O0 NP=8

IFC ONF . GT. 0 . 3 ) C0T03 1

0

IF( TSEN. GT. TBO IL( 7) ) GOTO500

ONF* 1

.

VFUEL=TAB1 ( NP . T30IL, FRGBL, TSEN)

VAI R* TAB 1 ( NP , TBO I L, AI RBL , TSEN) GOTO600

310 IF(TSEN.GE.TBOIL(8))GOT0313

ONF* 1

.

VFUEL* TAB 1 ( NP , TBO I L, FRGBL . TSEN)

VAIR* TAB 1 ( NP , TBOIL, AIRBL. TSEN)

GOTO3O0

313 ONF=0.

500 IF<ONF.CT.0.5)GOTO60O

VFUEL* 0

.

VAIR* WAIF.+ ( DT/TAAIR) *< AIROF-VAIR)

600 VGAS* WAIR+VFUEL

RETURN

END

FIGURE 3 LISTING OF SUBROUTINE CT

6
3 BOILER THERMAL DYNAMICS AND SUBROUTINES

The main thermal elements of a boiler are:

Combustion gas and air

Boiler Furnace Wall and Tube Walls

Water and steam

Boiler Shell

With the above elements divided into elementary sections) energy

balance equations can be written. for each finite element:

For Combustion Gas or Draft Air:

dT

I dt F^“)

t, [(Cn W)P (T l‘ T2 )_Q£rw 1 C W g P g 1 4 gW ( 2 )

where W is defined as the mass flow rate (on page 8).

For Boiler Furnace and Tube Walls:

dT

w

dt ( C m) ^gw ^wf^

p w

For Water or Steam

( 3 )

dt

1 (C m)

P f

{[w

f (h r

h

2 )] f *Qwf > ( 4 )

7
For Boiler Shell

dT

± . dt (Cm)

P *

(Qw.- Q ..

) (5)

In the above equations, w is the mass flow rate, t the temperature,

h the specific enthalpy, the specific heat at constant

pressure, t the time, Q the heat transfer rate, and m the mass.

Subscripts 1 and 2 are for the section inlet and output ports,

respectively; and subscripts g, w, f, s, and a are for gas (or

air), solid wall, fluid, boiler shell and ambient air, respectively. A compound suffix indicates an interface condition. For

example, Q indicates .heat transfer rate from the combustion

5 w gas (or draft air) to the boiler furnace (or tube) wall.

Simplication can be made to the above differential

equations to reduce the number of state variables* For the gas

(or air), its heat capacitance can always be neglected.

Equation 2 can then be reduced to an algebraic equation

Q - (C w) (T.-T-) (6)

gw p g 1 2

For the boiler, the water capacitance is commonly larger than

the furnace (or tubes) wall capacitance. To increase calculation efficiency, the wall capacitance can be added to the

water capacitance. Combination of equations 3 and 4 yields

*A state variable is a variable whose first derivative with respect

to time is equal to a linear combination of other variables.

8
a state variable equation for the water temperature:

dT

f

1 dt [ (Cm) +(C m) ] p w pi {[w(h,-h

2 )l + Q gM > ( 7 )

The wall temperature can then be calculated from the equation:

of combustion gas, draft air, furnace wall, and boiler tubes are

no longer state variables. Besides flow rates for the combustion

gas and draft air (see equation 1), temperatures of the boiler

water and shell elements are the other state variables (see

equations 5 and 7). Methods for solving equations 1, 5 & 7 are

readily available; and among the best known are the standard

Euler and Runge-Kutta procedures [2]. However, in a boiler

environment, the heat transfer rate Q needs careful formulation

for individual elements of the boiler in order to insure the

model's validity. Accordingly mathematical models and computer

subroutines for calculating heat fluxes that occur within commercial boilers

have been developed in the following five sections for (1) the

boiler furnace at on period, (2) the boiler tubes at on period,

(3) the boiler furnace and tubes at off period, (4) the water/

tube interface, and (5) the boiler shell.

( 8 )

where A and a are the heat transfer area and coefficient

respectively.

With the above simplifications, temperatures for elements

9
3 . 1 Math Model and Subroutine SR for Gai/Fumace Heat

Flux at On period

Starting from the products of combustion at the adiabatic

flame temperature, the heat flow Q from the combustion gas to the gw ° furnace wall is by radiation and convection. It was determined

from stirred reactor theory [3] that the Q ew value can be

calculated from the equation:

gw

[a

gs (J_^JL

L

\l - K

2a

+ A

* °< T AG

+ V

3 ]. (TAG T

4

) S’ (9)

where A

A

s + a

r

GS

c

s es - 1

for total gas/sink radiative

exchange area

refractory surface area

sink surface area

ratio of A

g to (A

g + A

R

)

S te f an-B o It zmann constant

convective heat transfer coefficient

gas emissivity

sink surface emissivity

0.5 + T

r q) , average furnace gas temperature

where T A p

: adiabatic flame temperature

T„ p

: temperature of exit gas from furnace

10
K * t

s

/ tAg’ rat ^° of the , *- nlc surface to the furnace

gas temperature

The convective heat transfer coefficient, a

c in equation 9, can be

calculated by McAdams' correlation equation [4]:

- 0.8 *0.4

a - 0.023—£-(Re) (Pr

C v

( 10 )

A computer subroutine SR has been written (using the above

equations ) to calculate the gas/furnace wall interface heat flux

at on period. Inputs to SR are the air/fuel flow rates and temperatures at the furnace inlet, and the furnace wall temperature.

Outputs from SR are the gas/wall .interface heat flux, and

temperature of Combustion gas at the furnace outlet. A detailed

listing of subroutine SR is shown in figure 4.

3 . 2 Math Model and Subroutine LT for Gas/Tube Heat Flux

at On Period

Banks or passes of tubes are present in commercial boilers.

These tubes can be divided into elementary sections in the gas flow

direction. For each elementary section, there is a distinctive

11
SUBROUTINE SR< PTOTAL, PC02 . PH20, PS02 , P02 . PN2 , RATT . RWTF , RPTT

,

XHFUEL , CPFUEL , TFTJEL . BTU3K, EXA I R. TA I R,

XFVOL, FSA, FRA, FD I AM, FSEM, TS , Q, TAF , TCE)

C

C *** SIMULATE STIRRED REACTORS

C

COMMON/VRI 7E/ I WRITE

HHV= HTUEL+CPFUEL*( TFUEL-TAIR)

W= l 000 . *BTUHK/HFUEL

HF3 W*HHV

ERR3 0 . 06

1

CP 1 3 8 . 24

CP=0.

PTT= 14 . 7*PT0TAL

IF( I WRITE. LE. DGOTO710

WRITE! 6,904) PTOTAL. PC02 , PH20, PS02 , P02 , PN2 , RATF , RPTF

,

N3FUEL, CPFUEL, TFUEL, BTUHK, EXAIR, TAIR,

SFVOL. FSA, FRA, FD I AM. FSEM

710 CONTINUE

904 FORMAT! /3(6( 1PEI1.3)/) , 1PE11.3)

TRS=TS+459 . 67

TRA=TAIR+439 . 67

TRF=TFUEL+459 . .r*7 W=W*RPTF

VH20= 18. *PH20/( 44 . *PC02+32 . *P02+64 . *PS02+28 . *PIf2>

IF! IVRITE.LE. DG0T0712

WRITE! 6 , 906) WH20

712 CONTINUE

906 FORMAT! 2X, ’ WH20= * , 1PE1 1 . 3)

SIGMA3 ©. 1713E-08

AC=0. 78339316*FDIAM*FDIAM

ALF=9

.

BLF=0

CLF=0 .

• ATOTAL= FSA+FRA

CS= FSA/ATOTAL

AL= 3 . 5*FVOL/ATOTAL

C

C CALCULATE ADIABATIC FLAME TEMPERATURE

C

TAF=TAFF! HHV, RWTF , RPTF , PC02 , PH20 , P02 , PS02

,

8PN2 , CP 1 , TRA, ERR, CP)

IF! IWRITE.LE. DGOTO700

WRITE! 6, 990) TAF

900 FORMAT! 2X, *TAF=’ , 1PE1 1.3)

700 CONTINUE

C

C CALCULATE RADIATIVE HEAT TRANSFER

C

IF! I WRITE. LE. DGOT0766

WRITE! 6, 902)

766 ' CONTINUE

TG2= TAF-300

ITR=©

300 I TR= I TR+

1

TAG=0 . 5*! TAF+TG2)

CPOE= CPF ! TRA, TG2 , PC02 , PH20 , P02 , PS02 , PN2

)

CPAE= CPF ! TC2 , TAF , PC02 , PH20 , P02 , PS02 , PN2

)

CPOA=CPF( TRA, TAF , PC02 , PH20.P02 , PS02, PN2)

1 = 2

TT= TAG-439. 6

7

CALL PRDPR! TT. PC02 . PH20 . P02 . PN2 , PS02 , AMU, AKK)

FIGURE 4 LISTING OF SUBROUTINE SR

12
PR= PRNB! AMU, CPAE, AKK)

RE=RENB! W. AMU, AC , FD I AH)

H= SGHT( RE . ?R. AKK, FD I AM, ALF , BLF , CLF)

GE= GEF( PC02 , PH20 , AL , TAG)

AGS* GS( ATOTAL , CS , GE , FSEPD

TRAT1 0= TRS/TAG

AGS=AGS*! 1

. -TRATIO**3) /( 1

. -TRATI0**4)

AGS= AGS+2 . *FSA*3/( SIGMA*! TAG+TRS)**3)

<i= AGS*S IGMA*! TAG**4-TRS**4)

CPWOE= CPOE*W

CPWOA=CPOA*W

CCOAT= CPWOA*! TAF-TRA) *! HF-CD

CCOE=CPWOE*HF

TGCAL= CCOAT/CCOE+TRA

DTG2= TGCAL-TG2

IF( I WRITE. LE. 1 > G0T0755

WRITE( 6,912) TAF ,TG2, DTG2 , Q, HF

735 CONTINUE

902 FORMAT! 2X, ’TAF’ ,8X, *TG2’ ,8X, ’DTG2’ ,7X, ’d’ , 10X, ’HF’)

912 FORMAT! 3UPE1 1.3))

702 CONTINUE

IF! A£3!DTG2) . LE. 10.) GOTO 100

IF! ITR.GT. 1 ) GOTO200

DTG1 = DTG2 1 TG1=TG2

TG2= TG2+ 100

.

IF! DTG1 . LT.0. )TG2*TG2-200.

GOTO300

200 TG=TG1-DTG1^! TG2-TG1)/! DTG2-DTG1)

IF! ABS!DTG1) . LT. ABS! DTG2) ) GOTO250

DTG1=DTG2

TG1=TG2

250 TG2=TG

GOTO300

100 TGE= TG2-459 . 67

TAF=TAF-459 . 67

RETURN

END

FIGURE 4 (CONTINUED)

13
characteristic that their length in the direction of gas flow is

much greater than the radiative width or height so that net radiative

flux in the gas flow direction may be ignored relative to flux

normal to it. Long-tube analysis [3] can be used to calculate the

radiative heat flux at the gas/tube interface. Equations for longtube analysis, including both the radiative and convective heat

fluxes, have been derived. A calculation sequence is as follows:

a

c a(Re) b (Pr) c <-£-)' , for convective heat transfer

coefficient

(">

a

r for radiative heat transfer

coefficient

( 12 )

a* a 4- a , overall heat transfer coefficient

c r

* ( 13 )

(C

p

v)

g

( VTw)[1-exp(- Aa

C w

P

for gas/tube interface

heat flux

( 14 )

Using the above calculation sequence, a computer subroutine

LT has been written to calculate the gas/tube interface heat flux.

A detailed listing of LT is shown in figure 5.

14
AAAAnAnAAAAAAAAAAAAAAAAAnA

SUBROUTINE LTC TGI ,TS, PTOTAL, PC02 , PH20 , PS02 , PN2 . P02 , WCAS

,

NCSAS . GSVL , GSAC . GSCD , GSA, GSB.GSC, CSE , ft, TGE) *** LONG TUBE REACTORS

INPUT DATA:

TGI GAS INLET TEMPERATURE F

TS WALL SURFACE TEMPERATURE F

PTOTAL

PC02

PH20

PS02

PN2

P02

WGAS

GSAS

GSVL

GSAC

GSCD

GSA

GSB

GSC

GSE

OUTPUT DATA:

ftTGE

TOTAL PRESSURE

MOLE FRACTION FOR C02

MOLE FRACTION FOR H20

MOLE FRACTION FOOR S02

MOLE FRACTION FOR N2

MOLE FRACTION FOR 02

GAS FLOW RATE

SURFACE AREA

VOLUME

FLOW CROSS SECTIONAL AREA

HEAT TRANSFER CHARACTERISTIC DIMENSION

COEFFICIDNT IN NU EXPRESSION

COEFFICIENT IN NU EXPRESSION

COEFFICIENT IN NU EXPRESSION

TUBE SURFACE EMISSIVITY

HEAT TRANSFER RATE

GAS EXIT TEMPERATURE

ATM

LB/HR

SOFT

CUFT

SOFT

FT

BTU/HR

F *** CALCULATION BEGINS:

TAV=0 . 5*( TGI+TGE)

TTGI=TGI+459.67

TTGE3 TGE+459 . 67

CPGAS=CPF( TTG I , TTCE, PC02 . PH20 , P02 , PS02 , PN2)

CALL PRDPR< TAV, PC02 , PH20 , P02 , PN2 , PS02 , AIM, AKSD

PR= PRNB( AMM, CPGAS , AKK)

RE= RENB( WGAS , AMM, GSAC , GSCD)

HC= SGHT( RE , PR, AXK. GSCD, GSA, GSB.GSC)

TGS= 0 . 5*( TAV**4+TS**4)

TGS=TGS**0.25

XL3 © . 33*GSVL/GSAS

PPC02= PC02*PT0TAL

PPH203 PH20*PTOTAL

EMGS=GEF( PPC02 , PPH20, XL, TGS)

SIGMA=0. 1713E-08

HALL3 1 . /GSE+ 1 . /EMGS- 1

.

HALL=4 . *S IGMA*TAV**C/HALL

HALL3 HC+ HALL

CPV= CPGAS*WGAS

ANTU= GSAS*HALL/CPW

Oft3 ( TGI-TS) *( 1 . -EXP< -ANTU) ) TGE3 TGI -Oft

0= CPW*Oft

RETURN

END

FIGURE 5 LISTING OF SUBROUTINE LT

15
3.3 Math Model and Subroutine FG for OFF Period

Cas/Solid Interface Heat Tranafer

During the off period, draft air flows through the boiler

furnace and tubes. Air can be considered to be radiatively transparent; so air/boiler interface heat transfer at the off cycle is

by pure convection. The convective heat transfer coefficient can

be calculated from the equation [3 ]

:

A computer subroutine FG has been written (using the equations

15 and 16) to calculate heat flux at the interface of the draft air

and the boiler furnace or tube wall. A detailed listing of subroutine

FG is shown in figure 6 .

3.4 Subroutines DB and SGHT for Water Side Heat Transfer

« - a (Re)

b

(Pr) c (—£-) (15)

and the interface heat flux can then be calculated from the

equa t ion

Q -(C w) (T.-T ) [ 1 -exp (

gw p g 1 w

r (16)

With h.eat fluxes calculated by the equations discussed

16
nnannnn

nofl

SUBROUTINE FG( QCT.TGS,

%TTB, WAIR, PAIR. TAIR, AC, AS,D,ALF,BLF,CLF) *** OFF-CYCLE GAS/FURNACE HEAT TRANSFER

1=1

RH=0 .

3

PNOW=PAIR

7R=460. +TAIR

CC*(TR/660. )**0.75

CP=0.24

AK*0. 018*CC

AH=0.052*CC

RH=0

.

CALL AIRPR( I, TAIR, PAIR. RE, SH, CP, R, AM, AD

PR=PRNB(AM,CP,AK)

RE= RENB( WAIR, AM, AC , D)

ALPHA2 SGHT( RE, PR, AE. D, ALF , BLF , CLF)

CPV»C?*WAIR

ANTU= ALPHA*AS/CPW

DELT= ( TAIR-TTB) *( 1

. -EXP( -ANTU)

)

TGS* T.A I R-DELT

QGT* CPW*DELT

RETURN

END

FIGURE 6 LISTING OF SUBROUTINE FG

17
immediately above, the furnace and tube wall temperature can now

be calculated from equation 8. The vater/solid interface heat

transfer coefficient in equation 8 can be calculated by either of

the following two equations, depending upon whether the water

temperature is at or below the boiling point temperature corresponding to the boiler pressure:

These two equations will be used in different ranges of water

temperature and give us a better result.

Equation 17 above is a correlation equation for nucleate boiling

obtained by Rohsenow [5], and equation 18 is the familiar equation

for convective heat transfer due to McAdams [ 4 ]. In evaluating

equation 17, the boiling bubble diameter is used to calculate the

(Re)_ and (k/D_) instead of the usual hydraulic diameter which is

D D used to calculate (Re) and (k/D) for equation 18. The following

equation can be used to calculate the bubble diameter D :

(17)

a - 0.023(Re)°* 8 (Pr) 0,4

( -£-) (18)

b

D

y (19)

b

= tpf^t

wher e Y “ water surface tension coefficient

g = gravitational acceleration

water density

18
Pv

* steam density

Subroutines DB and SGHT have been written to calculate

the water side convective and boiling heat transfer coefficients.

Detailed listing of these subroutines are shown in figures 7 and 8.

.

3 . 5 Subroutine SH for Boiler Shell Heat Loss

The heat loss at the boiler shell Q can be calculated from

sa

the equation:

Q

* UA(T,-T ) (20)

s a r a

where U overall heat transfer coefficient

A « shell area

“water temperature

T

& * ambient air temperature

The value of U in the above equation is calculated using the heat

transfer coefficient values for the series of thermal layers

including the water/shell interface, shell wall, and shell/air

interface

:

U = l/(l/a- + 1/a + 1/a ) (21)

fs s sa

19
nnnnnonnnnnon

FUNCTION DB(ROL,ROV, SIGMA) *** CALCULATE NUCLEATION BUBBLE DIAMETER

INPUT DATA:

ROL LIQUID DENSITY

ROV VAPOR DENSITY

SIGMA SURFACE TENSION

OUTPUT DATA:

DB DIAMETER OF BOILING NUCLEATION BUBBLES

DB" SQRT( S IGMA/( ( ROL-ROV) *32. 174))

RETURN

END _ . .

FIGURE 7 LISTING OF SUBROUTINE DB

LB/CUFT

LB/CUFT

LB/FT

FT

20
non

FUNCTION SGHT( RE, PR, AK, D, ALF , BLF , CLF) *** CALCULATE SINGLE-PHASE HET TRANSFER COEFFICIENT

COMMON/WRITE/ I WRITE

IF( I WRITE. LE. 1) GOTO704

WRI TE( 6 , 706 ) RE , PR, AE, D, ALF , BLF , CLF

704 CONTINUE

706 FORMATC /2X, 3HSGHT: /2X, 2ERE.9X, 2HPR, 9X, 2HAK, 9X. I HD/

N4( 1PE 11.3) /2X, 2HALF , 8X, 3HBLF , 8X, 3HCLF/0( 1PEU.3))

TALF= ALF

TBLF-BLF

TCLF*CLF

IF (TALF.GE. l.E-10) GOTO 10

IF (RE.GE.2000.) GOTO 20

TALF«3.66

TBLF=0.

TCLF»0.

GOTO 10

20 TALF* 0.023

TBLF=0.

8

TCLF=0 .

4

10 SGin^TALF*AK*RE**roLF*PR#*TCLF/D

IF( IWRITE.LE. 1)G0T0700

WRITEC 6 , 702) SGHT

700 RETURN

702 FORMAT( /2X, 5HSGHT* , 1PE1 1 . 3)

END ...

FIGURE 8 LISTING OF SUBROUTINE SGHT

21
In this equation, is calculated by McAdams' equation:

a - 0.023(Re) 0,8 (Pr) 0,4

( £-)

f s D

(22)

a is calculated by the wall conductance

s equation

:

k

a *

8 X

(23)

and a „ is calculated by the free convective

sa J equation

a « 0. 29UT/L) 0,25

, for L

3 AT <10 3

s a — (24)

or 0 333 3 3 a = 0.21 (AT) U * JJ

, for L

J AT>10 J

s a (25)

These equations have been used to write a subroutine SH

for calculating the heat loss at the boiler shell. A detailed

listing of subroutine SH is shown in figure 9.

3 . 6 Auxiliary Subroutines

The six subroutines for calculating the boiler heat flux

22
SUBROUTINE SH( tt,TS,TW,TA, UW, AREA, US* AL)

C

G *** CALCULATE SHELL HEAT TRANSFER

C

Rl«i./AIRFHT(TS,TA,AL)

R2M./US

R3* I . /UW

AD= AREA/( R1*>R2+R3)

Q* AU*( TW-TA)

TS*TW-Q*< 1 . /( AREA*( US+UV) ) ) RETURN

END

FIGURE 9 LISTING OF SUBROUTINE SH

23
have been described in the previous 5 subsections.

These six heat flux subroutines together with the controller

subroutine discussed in the previous section form seven

principal subroutines for the commercial boiler transient

analysis computer program DEPAB2. Figure 10 summarizes names

and purposes of these seven principal subroutines. Also

listed in figure 10 are auxiliary subroutines used to

assist with the principal subroutines calculations. It

can be seen in figure 10 that the auxiliary subroutines can

be categorized into three groups of: (1) fluid properties,

(2) fuel/air combustion, and (3) heat transfer parameters.

Detailed listings of these auxiliary subroutines are appended

to this report.

- 24 -
PRINCIPAL SUBROUTINES FOE DEPAB2

BOILER CONTROLLER CT

ON PERIOD FURNACE HEAT TRANSFER SR

ON PERIOD BOILER TUBES HEAT TRANSFER LT

OFF PERIOD DRAFT AIR HEAT TRANSFER FG

FEEDWATER HEATING SGHT

NUCLEATE BOILING HEAT TRANSFER DB

BOILER SHELL HEAT LOSS SH

AUXILIARY SUBROUTINES FOR DEPAB2

FLUID PROPERTIES:

AIR PROPERTIES AIRPR

WATER PROPERTIES H20LQ

STEAM PROPERTIES H20VP

COMBUSTION PRODUCTS p. & k PRDPR

COMBUSTION PRODUCTS C CPF

P

FUEL/AIR COMBUSTION:

PRODUCTS OF COMBUSTION PP

ADIABATIC FLAME TEMPERATURE TAFF

FUEL AIR FLOW RATES GF

AMOUNT OF EXCESS AIR BG

HEAT TRANSFER PARAMETERS:

REYNOLDS NUMBER RENB

PRANDTL NUMBER PRNB

FREE CONVECTION HEAT TRANSFER FOR AIR AIRFHT

GAS RADIATIVE EMISSIVITY GEF

GAS/SINK RADIATIVE EXCHANGE AREA GS

OVERALL HEAT TRANSFER COEFFICIENT OVHT

LOOKUP OF TABULATED DATA TAB!

FIGURE 10 SUBROUTINES FOR DEAPB2

- 25 -
4. COMMERCIAL BOILER TRANSIENT ANALYSIS COMPUTER PROGRAM DEPAB2

One controller subroutine and six heat flux subroutines

described in the previous two sections are merged together to

form DEPAB2. The controller subroutines can be used to

calculate the air/fuel rates and heat flux subroutines

to calculate heat fluxes at different parts of the boiler

(which include the boiler furnace, tubes in sections arid

shell). The transient response of the boiler can then be calculated from equations 6 to 8 (i.e.: equation 6 for outlet

gas temperatures at furnace and tube sections outlets,

equation 7 for boiler water temperatures, and equation 8 for

boiler furnace, tube sections, and shell temperatures).

DEPAB2 start by reading in the boiler parameters,

load schedules, and initial values. It then calculates interface heat fluxes by calling up the principal subroutines

described in the preceding section. Transient time histories

of the boiler temperatures and performance are then calculated.

Finally, overall performance of the boiler over a chosen

duration of simulation is calculated and printed out.

Figure 11 shows a flowchart for DEPAB2; and a detailed

listing of DEPAB2 is shown in figure 12.

- 26 -
FIGURE 11 FLOWCHART FOR DEPAB2

- 27 -
c

C *** PROGRAM HAMEi DEPAB2

C

C aw PURPOCEi SIMULATE LARCE-8CALX BO I LEM

C

c depifx urrcrr nu

c COMMOR/WRITE/IWRITE

C0KH0N/'HTLD/TN1.'*(««) .TIAI08) .TOA! 48) . BDND< 88)

COPMOH/COirTTU^TDOIL! 8) . FRCDLI 3) . A1RBL! 8) DIMEHSIOH TG8!5l) ,TTB!Sl> .TWTtBl) ,OCT!8l) DIMEHSIOH TAUIB8) .TW.I88) ,TAC(88> .TDI188)

,

XTBA( 88) , TBB(8B> .TBC(88) .TBEI88) DOS I* 1,81

TC3! I

) •

.

TTB( TVT< !)#.

acT< i > •

.

IF! I . EG. 3UG0T03

TAS( I

) #.

TVLt TAC( i

) ••

.

‘ TDI!l>*8.

TBA( l) *#. TBB( I) *8. TBC( I)*8.

TBE( :>*o.

VRITE!0.980)

READ! 3. a) I 'WRITE C I HPIJT PTC. DATAi C PTOTAL* 1 • PAIR-PT0TALA14.7

READ< B. a) CAAB. HVDR. OXYC, XHTR, fULP

VRITE1 6 . 99 1 ) GARB. HYDR. OXYC. XHTR, SULT

READ! B. «) STUEL. CPrUEL.TFUEL. BTUHE

WRITE! 6 , 902) HFUEL. CP7UEL. TFUEL , BTUHE

Cc *** IHPUT COirmOL SUBSYSTEM DATA

C

90301* 1 ,

8

TBOIL! I)*8. FRCBL! I)*0. 38 AIRBL! 1)*8. READ! 8. a) ICTYPE

’•RITE! 6.814) ICTYPE

READ! 8, a) TASEH, TAAIR. PRCPL. EXATL. AIBOP

WRITE! 6. 9 13) TASEH, TAAIR. TRCFL. EXATL, AIROP CALL PP! PTOTAL. CARS. HYDR. OXYC. XHTR. SULF < EXATL, HPC02 . PB20 . FS02 , P02 , PN2 . RATT , RPTF . KVTF) FRLTHT*RVTF*! 19B0./HFUEL)

AIR7L*RATFaFRCFL

AIROF* AIR07*AIRFL THA I R* RATF/( I . +EXATU

WRITE! 6. 888) TASEH, TAAIR. FRCTL.AIRTL. DF

GOTO! 21.22. 23) . ICTYPE

21 11*6 12*7 C0T029

22 11*6 12*8 G0T029

23 11*1 12*8 29 WRITE! 6. 9 17) D03 11*11, !2 31 R£AD!8,*)T30TL! I) .FRCBL! I) . AIRBLI I) D032 1 1 .8 WRITE! 6, 883) TBOIL! I) .FRCBL! I) .AIRBLI I) FRCBL! I

) FRCFLaFRCBLI I) AIRBLi I) * AIRFLaAlRBLi I) 32 WRITE! 6. 8«W> TBOIL! I) .FRCBL! I) .AIRBLI I) CC *** HTPUT WATER DATA

C

READ' 8. a) VT06T. TIH. TOUT

VRI TE1 6 . 989 ) WT06T. TI H . TOUT

C

C IHPUT FURHACE DATA

C

FXAD‘ 8. a) FVOL. FSA. FCA. FRA. FDIAH. FSEM

WRITE! 6.994) FVOL. FSA. FCA. FRA. FD I AM. FSEM

READ! 8. a) FHA, FHB. FHC

WRITE! 6 . 923) FHA. FHB. FHC

FIGURE 12 LISTING OF DEPAB2 MAIN PROGRAM

- 28 -
c

c *** INPUT TUR2 DATA

C

READ* 8. *> NT1 ,NT2

WRITE16.923)NT1.NT2

WRITE) 6. 924) x«i L*NTt DO40J-1.2

IDJ.EQ. DC0TD44

K*NT.'*l L*NT2

44 CONTINUE

READ<a.*)TAS<r> .TVL(E) ,TAC)D .TDK D . NTBA) X) . TBB( ID . TBCUO ,TBE(D

VRITE)6.836)TAS) K) , TVL( D . TAC( K) ,TDI) D ,TBA(D ,TBB)

D

VRI TZ< 6 . 802) TBC) D . TBE( K> H»KM

DO40 T-H.L

TAS( I)*TAS(E>

TVLC I ) *TVL) ID TAC) P«TAC)2)

’TDI< I) *TDI ( K) TBA( I)*TBA(K>

TBB( I)*TBD)K)

TBC)I)*TBC(D

44 TBE(I)>TBE(D

C

c m INPUT WATER DATA C

READ) 8. ») STHVL. VTAC. WTCD, VTA.WTB. VTC

VRI TE( 6 . 9 11 ) STHVL, WTAC . WTCD . VTA. VTB . VTC

3T?SCAP*0. 9*STHVL

VTAS«rSA

I*NT2 DO30K* 1 .

I

VTAS»VTAS*TAS(D

54 CONTINUE RLGA-76.92

BLGB*0. 667 BLCC*-0.7 C

c «« INPUT SHELL AND WEIGHT DATA

C

READ< 8. *> SHARE. SHUPT. SHHCT. SHCAP . PNCAP . TBCAP . NTCAF

WRITS) 6. 9

1

2) SHARE. SEUFT. SHHGT, SHCAP . PNCAP, TBCAP. WTCAP

C LOAD SCHEDULING *

144 CONTINUE

WRITE) 6, 9 13) READ) 3 . *) NTI HE

00101*1,60

THIN)I)*0.

HDMD) I

) *0

.

DOl 1

I

s l.NTTHE

WRITE) 6 , 934)

READ) 3 . *) THIN) I) ,TIAC I) ,TOA( I) . HDHIX I) WRITE) 6. 804) THIN) I) ,TIA( I ) , TOA) I) , HDHIX I)

14

11C

C i C INITIAL VALUES C

WRITE) 6.933)

READ) 3 , *> I CYCLE

ynrTPr a lidd)

READ) 5. i) TIME. DT, IPRHT, ICALC TSTART*TIME

WRITE) 6, 1002)

READ) 3 . *) ONF . TSEN, TBL

DO203 I* 1.31 243 TTB)I)*TBL

DPT* •“) . 0 !666667*DT

WRITE) 6, 1003)

READ) 3 , *) TSH.TRW

C

C

c CALCULATION 3ECINS

NCYCLE*

1

TIMCYC*0.

QUDCTC*0.

<1IPCYC*0. QIPNOW*0. ZTANOV* 0

.

FIGURE 12 (CONTINUED)

- 29 -
oronov**.

OIPTOT-O.

OCDTOT*#.

TTAT0T*O.

QTVAT*0.

qsupld*©.

OLOAD* 9

.

osht;

i

. a oEXar*©. oltrt*©.

I START*

0

itprpt*©

rcalc*0

WRITE* 6. 932)

31* IP! ISTAHT.Ea..#. ARD.riHE.LT.0)COTO3©O

RPRRT*0

RCALC*©

I r ( T3TART. LT. 0

.

0—1 ) TIME*#

.

I START* 1 CRDCYC*ORF

VR1TS(6.«32)

WRITE! 6 . 933) TIME. QSTJPLD. OLOAD. QFVAT, OSHELL. OEXHT. OLTRT.

TTCSI 1) , TC3' RT2+ l> . TTB( 1) . TTB< RT2+1) , TBL. TSER,

juaipnov. qcdnow, etarow, oiptot. oudtot, etatot 3M TIME'TIME+DT

RCALC* NC ALC* 1 RPRKT* RPRKT* 1 c

C «* HEAT DEPART) C

TI DA* TAB 1 ( RTIHE. THIR . TIA. TI HE) TODA-TAB 1 ( HTIME . TaiR . TOA. TIMEJ OLOAD* TAB 1 ( RT I HE . THI R . HDMD . TI ME)

IF( 1 WRITE. CE. 1) VRITE!6. 1M1I TIME. TIDA. TODA. OLOAD C

c «*» WATER S STEAM PROPERTIES C

CALL H20LO! TBL. WATRO . WATCP , VATAT. WATAM.

JTVATST. watbd

CALL H20VP! TBL. STHRO, STMCP .STMAE. STMAH. XSTMHFC, STM3T)

OVAT* 0 . 23^ HnJEL»rRCFL

I F ( OVAT. LT . OLOAD ) OVAT*OLOAD

•'MAS* OWAT/STMHTC 3RD I A* DB< WATRO . STMRO , VATST)

PR* PIUTB! WATAM. WATCP . VATAE

REB* HERB! V2AS , WATAM. VTAS . 3BDIA)

REC= RERB! WMAS . WATAM. VTAC . VTCD) BLALF*SCHT! REB. PR. WATAE. BBDI A. BLCA. BLGB. BLCC) CVALF* SCHT' REC . PR. WATAE. VTCD . VTA. VTB , WTC)

IP( [WRITE. CE.

1

> WRITE! 6 , 928) BLALP , CVALF

C

C *** BOILER CORTBOL STATUS C

CALL CT( OPT . VFUEL, VAIR, OCAS . TSER, TTBL. ICTYPE.TASER.TAAIR.AIROF.DT)

IF< I WRITE. CE. l>VRITE!6.»l9)ORF.VPUEL.VAyi, WAS, TSER. TBL

C *** CAS^rURRACE HEAT TRAHSFER

C Cam. BC< BTUHE. EXAIR. HFTIEL, CPFUEL.

RTFCEL. THAIR, VFUEL, VAIR)

IF( I WRITE. CE. 1 ) WRITE! 6 . 92 1 ) BTUHI, EXAIR

IF! wrUEL. CT. 0. 0001) GOTO20

1

CALL FG!QGT! 1) ,TCS( 1) ,TTB! 1) .VAIR. *PAIR. TIDA. FCA. FSA. FDIAM. FRA. FRB, FRO

IF( IWRITE.CE. 1) WRITE! 6 , 922)

IF( I WRITE. CE. 1 > WRITE! 6 , 803) QCT( 1) ,TCS< l) .TIDA COTO202

201 CALL SR< PT0TAL.PC02. PH20. PS02. P02. PR2.RATT , RWTP

,

JtRPTF . HFTJEL. CPFUEL, TFUEL, BTtTHK. EXAIR, TIDA. rVOL.FSA, FRA. XFDIAM. FSEH. TTB( 1) .OCT! 1) ,TCSI.TC8( D)

IF! IWRITE.CE. 1) WRITE! 6. 922)

IF( IWRITE.CE. 1) WRITE! 6.803) QGT! 1) ,TCS( 1) , TC8I 202 CORTIKUE

C

C **» GAS/TUBE HEAT TRARSFER

C D0219 I* 1 , RT2

J* 1+1

I F ( WFDEL. CT. 0 . 000 1 ) COTD203 CALL PC! OCT! J) . TGS( J) , TTB! J) , WAIR.PAIR.TCS* I)

.

JCTAC! I) ,TAS< I) .TDK I) . TBA( I) , TBB< I) .TBC( I))

IFC [WRITE. CE. 1) WRITE! 6 , 920) OCT! J) ,TG6( J) COTO2I0

203 CALL LT(TGS( I) .TTB(J) . PTOTAL. PC02 , PH20 , PS02 , PR2 . P02

,

XWGAS.TAS! i> .TVL( I) , TAC( I) .TDK I) ,TBA( I) , TBB( I) ,TBC( I)

.

XTBE! I) .OCT! J) , TCS( J)

)

IF! IWRITE.CE. 1) WRITE! 6. 803) OCT! J) ,TG8( J) , TC8! I) 210 CORTIRUE

FIGURE 12 (CONTINUED)
cc

C m SHELL HEAT TRANSFER

C CALL PH( OS 'JELL. TSH. TBL. TI DA. CVALF

.

NSHARE . SHCTT , SHHCT)

IF! I WRITE. GE. I) 'rfRITEi 6 • 926) TSH. QSHELL

CC am HEAT BALANCE

C QSUPLB* 100O.*BTUHK

TALF« CVALF* BLALF TBL

1

« TBL

STHVCL* I ./( STMVL*STrSTC)

FVCPR* WATC?*OLOAD*< 1 . /STKHFC) J-NT2+1

QTOTAL-0.

DO220t*l.J

220 QTOTAL* QTOTAL*QGT( I) CTOTAL*SHCAP*FRCAP*TBCAP*WTCAP*ST?CAP

IF( 1VR1TE.GE. 1) WRITE! 6. 929)

IF( I WRITE. CE. I ) WRITE! 6 , 803) TBL. PEL

GCROSi* QTOTAL-ftSHELL OFVAT* FWCPR* ( TBL-TRW)

•ilTET* 'iCROSS-QFWAT

3STEA3»DDT*( OlfETr0' rt * n> DTBL*QSTEAM*( 1 . /CTOTAL)

TBL* TBL*DTBL

PBL*STSATP! TBL)

lF( I WRITE. CE. 1) WRITE! 6, 803) TBL. PBL UA«FSA*TALF

UC*FSA*CVAiJ

TTB! l)*T3L*ftCT! l>a(0.9/UA*0. l/TJC) J*RT2* I DO270I*2.

J

UA*TAS( I-P*TALF

UC*TAS< I- 1 ) *CVALF

TTB! I

) *TBL*ftGTt I ) *( 0 . 9/UA*0 . 1/UC> 27* CONTINUE

IF! IVRITE.CE. I)VRITE!6.930>

IF! I WRITE. CE. 1 ) WRITE! 6.931) TTB

CLTRT* FRLTTT*QSUPLD

CEXHT*ftSUPLD-ftTOTAL-ftLTRT OCDROV* OFVAT+GLOAD

I F ! T I DA. CT . TODA) OUDJTOW* Q0DKOW-0 . 24*WAI RM TIDA-TOOA)

OiPROV»QSUPLD

ETAfIOV.0.

IF! ftSUPLD. LE. • . 000 1 ) GOT0343

ZTAROV-OUDROV*! l./OIP!fOW> 343 COSTINTO

IF! ISTART.LE.0'COTO360

IF! I CYCLE. Eft. 0) GOTO400

IF! RCYCLE. Eft. 1 . AND. ABS! OITF—C5DCYC) . LE. 0.000 1) GOTO40O

IF! RCYCLE. .YE. 1>COTD4IO CRDCYC*ORF „

"CYCLE*

2

410 ftIPCYC*OIPCYC+GIPlTOW*DDT QUBCYC* QUDCYC*ftDDHOW*DDT

TIHCYC*TI3CYC*DT

IF! RCYCLE. Eft. 1)C0T0490

IF! NCYCLE. Eft. 2. AITD . ABS! OKF-CKDCYC) . LE.0.000DCOTO430

IF! RCYCLE. Eft. 3) GOTO430

RCYCLE*

3

CHDCYC*ORF

430 IF! NCYCLE. Eft. 3. AND. ABS! ORF-CKDCYC) . CE. 0.OOO1) G0T0450

GOTO40^

430 ZTACYC*ftUDCYC*! l./ftlPCYC) WRITE! 6 . 936 ) TIHCYC . ftCDCYC, 01 PCYC . ETACYC

RCALC* I CALC 400 CORTIRUE

ftl PTOT* ft I PTOT+ft I PROW*DDT

QUDTOT* OUDTOT+ftCDNOW* DDT

IF! ft I PTOT. LE. 1 . E-30 ) GOT0335

ETATOT* OUDTOT*( I ./ftI PTOT)

GOTO360

355 ETATOT* 0. . 360 CONTINUE

IF! RPRRT.LT. IPRITT) COTOO20

RFRKT=0

WRITE! 6 . 933) TI3E. ftSUPLD. QLOAD , OFWAT. (SHELL . ftEXHT. ftLTRT,

5TTGS! 1) . TCS! RT2+ 1 ) .TTB! 1) . TTB! RT2* 1 ) . TBL.TSEfl. xaiPROw. qudrow. etarow. oiptot. oodtot. etatot

320 IF! I START. Eft. 0) 0OTO3 19

IF! RCALC . LT. ICALC) COTO300

FIGURE 12 (CONTINUED)

- 31 -
WRITE! 6. 988)

READi 3 , *> ICONT

IFC ICONT. GT.O)GOTOl88

881 FORMAT! 1( 1PE11.3)) M2 FORMAT! 2( 1PE1 1.3) ) 8*3 FORMAT! 3! 1 PEI 1.3)) 804 FORMAT! 4! 1PE11.3)) 803 F0RMAT13! 1FE11.3)) 804 FORMAT! 6! 1?E1 1 . 5)

>

M7 FORMAT! 7! 1PE1 1.3)

>

808 FORMAT! 8! 1?E11.3>)

811 FORMAT! 1 1 0 > 981 FORMAT! 2X. CARB’ ,7X. ’HTDR* ,7X, ’OXTC’ ,7X, X’XnTR’ ,7X. ’SULF’/5( 1PE11.3)) 4*2 FORMAT! 2X. HFUEL’ ,8X. ’CPFTJEL’ , 3X. '

T

TUEL ’ ,4X. ’EBTUH’/

*4! 1PE11.3)) 983 FORMAT! 2X. ’ EXAIR’ ,4X. 'TAlR*/2! 1PE11.3))

984 FORMAT! 2X. FVOL’ .7X. ’ FSA’ , 8X. ’ FCA' .8X. TRA’ , 8X, ' FD I AH'

.

S4X. ' FSEM' 1PE11.3)) 984 FORMAT! 2X. ' I WRITE*?*) 987 FORMAT! 2X. ' BTTTHK. EXAIR.TAIR, TEX. TOA»?' ) 988 FORMAT! 2X. ’ lCONTINUE*?*

)

989 FORMAT!2X,3HVn>ST.4X.3HTIR.8X.4HTOOT/3! 1PE11.3))

9 18 FORMAT! 2X. -iHCSAS , 7X. 4HCSVL.7X. 4HCSAC . 7X. 4BCSCD, 7X. 3HGSA, 7X, 3BGSB^

44! 1PE1 1 . 3) /2X. 3HGSC . 8X, 3BCSE/2! 1PEU.3) ) 9 1 1 FORMAT! 2X. 3HSTMVL, 4X. 4HVTAC , 7X. 4HVTCD. 7X. 3HVTA, 7X.3HVTB,

88X. 3HVTC/4! IPE11.3))

9 12 FORMAT! 2X. 3HSH.ARE. 4X. 3HSHUFT. 4X. 3HSHHCT, 6X. 3HSHCAP/

S4( 1PE1 1 . 3) ^2X. 3HFNCAP , 4X. 3HTBCAP . 4X, 3HVTCAP/

43! 1PE11.3)

)

913 FORMAT! /2X. I9HDTIME. TTIME. PRINT*?)

914 FORMAT! /2X.4HTI ME. 7X. 1HQ. I8X. 3HETA, 8X. 4HTCS1/4! 1PE11.3)^2X.

44HTGS:/4< 1PEU.3>^5! 1PEU.3)^2X.

34HTT3:^4( lPEU.3)/'3( 1PEU.3)/2X.

44H3CT:/4< 1PE1 1 . 3)^3! 1PEU.3))

913 FORMAT! 2X. ’ NTIME*?*

)

914 FORMAT! 2X. ’ ICTTPE* *

. 13) 917 FORMAT! 2X. ’T30IL* . 4X. ’ FRGBL* , 4X. ’ AIRBL’

)

918 FORMAT! 2X. ‘ TASEN* ,4X. ’TAAIR* ,4X. ’FRGFL' ,6X. S’EXAFL’ . 4X. ’ A I ROF ’ /5 ( 1PEI1.3)) 919 FORMAT! 2X. ONF’ .8X. VTUEL* .6X. *VAIR* ,7X. *WGAS* ,7X. 4’TSEN’ . 7X, ’ TBL' -'61 1PI11.3) > 928 FORMAT! 2X. 'OCT! 1) • ,3X. ’TCS! 1) */^( 1PEU.3))

921 FORMAT! 2X. ’ KBTUH’ ,4X. * EXAIR' /2! 1PEU.3))

922 FORMAT! 2X. ’CCT* , 8X. 'TCS! OUT) * ,3X, *TC8( IN) •) 923 FORMAT! 2X. ’FNA’ .EX, ' FNB' . 8X. ’FNCV3! 1PE11.3))

924 FORMAT! 2X. TAS’ ,8X. ’TVL’ . 8X. ’TAC’ .8X. ’TDI ' . 8X. 4’T3A’ .ax. TBB , /2X. 'TBC* ,8X. ’THE'

)

923 FORMAT! 2X.-' KT1» '

. I3/2X. ’ NT2* *

, 13) 924 FORMAT! 2X. ’ TSH’ . 8X. ' QSHELL'/2! 1PE1 1 .3)

)

928 FORMAT! 2X. ' BLALF* ,4X. ’CVALF’^2! 1PE11.3)) 929 FORMAT! 2X. 1 TBL ’ . 8X. ’ PBL * ) ' 938 FORMAT! 2X. BOILER TUBE TEMPERATURES i •

)

931 FORMAT! 2X. 8! 4! 1PE1 1 . 3) /) /3! 1PE11.3)) 932 FORMAT! ’ TIME: • /*2X. * QSUPLD* . 3X. 1 QLOAD’ . 4X. * QnfAT* . 6X.

4 ’ QSHELL’ , 3X. ' QEXHT' , 4X, 'GLTTTT'/ 42X. ' TCASFN’ , 3X. ' TGASTB’ ,3X. ' 1TUBFN * ,3X. ’ TTUBTB" ,5X, X ’ TVATER’ . 3X. * TSENSE*

R2X. • QIPNOW’ . 3X. ' QUDNOW* . BX. ’ ETANOV ,8X, 4 ’ QIPTOT’ . 3X, • QCDTOT* . 3X. ’ ETATOT’

)

933 FORMAT!/ IPS 11. 3^4! lPE11.3)/4< IPE11.3)/*! 1PEU.3))

934 F0RMATI2X. 'TMIN.TIA.TOA.HDMD-?’)

938 FORMAT! 2X. ’ ICYCLE*?*

)

934 FORMAT! //2X. 'TIMCYC* ,8X, 'QUDCYC' ,8X. 4'QIPCYC* ,3X. ’ETACYC’/4! 1PE1I.3))

1888 FORMAT! 2X. ’TIME.DT. IPR1TT. I CALC*?’

)

1881 FORMAT! 2X. ‘TIME’ ,7X, TIDA’ ,7X, TODO’ ,7X. ’QLOAD’/

44! 1PEU.3)

)

1882 FORMAT! 2X, ONF.TSEN. TBL* ?*> 1883 FORMAT! 2X. ’ TSn . TRW* 7 ’

)

CALL EXIT

END

FIGURE 12 (CONTINUED)
5. USER'S GUIDE

To assist users of DEPAB2, details of the (1) DEPAB2

input code, and (2) DEPAB2 running procedure and output

code are given in this section. Also included is a worked

example to demonstrate DEPAB2 runs.

5. 1 DEPAB2 Input Data Code

As described in the previous sections, there are three

types of input data for DEPAB2. They are:

(1) boiler parameters,

(2) boiler load status, and

(3) boiler initial conditions.

File 8 is used to enter the type 1 data; and file 5 (terminal

* at interactive mode) is used to enter the type 2 and 3 data.

To assist the user with the preparation of files 8 and

5, the input data code for file 8 is fully interpreted in

appendix A and the data code for File 5 in appendix B.

While a majority of the terminology used in files 8 and 5 are self explanatory, input (ICTYPE*1, 2 or 3) refers

to the generalized controller types shown in figure 2. A

familiarization of the input data code in appendices A and

B can facilitate -the reader’s use of DEPAB2.

- 33 -
5 . 2 Running DEPAB2 &

DEPAB2 Output Data Code

Each run of DEPAB2 includes three major steps. They

are :

(1) Prepare file 8 for the boiler and its

controller parameters,

(2) Enter the boiler operational schedules

and its initial conditions at the terminal

or through file 5, and

(3) Execute DEPAB2 using the execution command.

Figure 13 shows a copy of file 8 which represents a commercially available 400 boiler horsepower fire-tube boiler.

Figure 14 shows a DEPAB2 run using file 8 data.

The terminal input (file 5) of this run can be observed

on the printout shown in figure 14, following echoes of

the input data from file 8. -

After input data for the boiler parameters, operational

schedules, and initial conditions have been read in, DEPAB2 executes the calculations and outputs results in accordance with

the sequence shown in the DEPAB2 flowchart (see figure 2).

Interpretation of the DEPAB2 output data code is given in

appendix C.

- 34 -
I

100 0. 207 >0. 790 > 0*0023 t 0*0016 >0*00

110 23400 r 0 52 » 65 1 16750*

120 3

130 2* >2. » 7 1 6 » 0 « 25 » 0

3

140 220 r 1* >1*

150 224 » 0 9 » 0 * 9

160 228 » » 0 8 r 0 8

170 232* *0.7 >0.7

180 236* f 0 * 6 > 0

6

190 240* » 0 5 » 0 5

200 244 f 0 4 > 0 4

210 250* » 0 4 y 0 4

220 2 * *200* f 2 1 2

230 264 >145.»10.6*21.»3.67»0.8

240 0 023 r 0 3 y 0

4

250 5 1 1

0

260 50

.

1 1 9 * t 0 5

t

0 . 2 1 y 0 023 t 0 8 y 0 4 y 0

8

270 50* y 19 y0.5y0.21y0.023y'0.8y0.4y0.8

280 250 » 18* y 2 6 72 y 0 33 y 0 6 y 0 33

290 380 ,54»r8.*1710» »337. r 1500* 7 7500.

END OF FILE

FIGURE 13 A SAMPLE FILE 8 INPUT DATA FOR BOILER

PARAMETERS

- 35 -
IURITE=?

>0

CARB HYDR OXYG XNTR SULF

2*070-001 7.900-001 2*300-003 1.600-003 000

HFUEL CPFUEL TFUEL . KBTUH

2*340+004

ICTYPE= 3

5.200-001 6*500+001 1.675+004

TASEN TAAIR FRGFL EXAFL AIROF

2*000+000 2.000+000 7.160+002 2.500-001 3.000-001

2*000+000 2.000+000 7*160+002 1 487+004 4*460+003

TBOIL FRGBL AIRBL

2*200+002 1.000+000 1 *000 + 000

2*200+002 7*160+002 1*487+004

2.240+002 9*000-001 9.000-001

2*240+002 6*444+002 1*338+004

2.280+002 8*000-001 8*000-001

2*280+002 5.728+002 1 * 189 + 004

2*320+002 7*000-001 7*000-001

2*320+002 5*012+002 1*041+004

2*360+002 6*000-001 6*000-001

2*360+002 4.296+002 8*921+003

2*400+002 5*000-001 5*000-001

2.400+002 3*580+002 7.434+003 - 2*440+002 4*000-001 4*000-001

2*440+002 2*864+002 5.947+003

2*500+002 4*000-001 4.000-001

2*500+002 2*864+002 5*947+003

WTOST TIN TOUT

2*000+000 2.000+002 2*120+002

FOOL FSA FCA FRA FDI AM

2.640+002 1*450+002 1*060+001 2*100+001 3.670+000

FNA FNB FNC

2*300-002

NT 1 = 5

8.000-001 4*000-001

NT2= 10

TAS TUL TAC TDI TBA

TBC TBE

5*000+001 1*900+001 5 . 000-001 2*100-001 2*300-002

4*000-001 8*000-001

5*000+001 1*900+001 5*000-001 2.100-001 2*300-002

4.000-001 8*000-001

STMUL WTAC WTCD WT A WTB

2*500+002 1.800+001 2*672+000 3*300-001 6*000-001

SHARE SHUFT SHHGT SHCAP

3*800+002 5*400+001 8.000+000 1*710+003

FNCAP TBCAP WTCAP

3*370+002 1*500+003 7*500+003

FIGURE 14 OUTPUT DATA FROM A SAMPLE DEPAB2 RUN

TERMINAL INPUT

ECHOES OF FILE 8

DATA START

FSEM

8 . 000-001

TBB

8 * 000-001

8 * 000-001

WTC

3*300-001

FILE 8 DATA END

- 36 -
N T I M E = ?

>3

TMIN y T I A y TOA y >-60

•

y 7 0 s45,s

-6 000 + 001 7

TM I N y T I A y TOA y >0. y70* y45. fAi

000 7

TMINf TIAfTOAr

> 6 0 y 7 0 y 4 5 y 4

6*000+001 7*

I C YCLE=?

>0

TIME y DT y IF'RNT

additional TERMINAL

H D M D = ?

4170000*

DATA

000+001

HDMD=?

4*500+001 4*170+006

70000*

000+001

H D M D = ?

170000.

4*500+001 4*170+006

000+001 4*500+001 4*170+006

y I C A L C = ?

>~30* y0*5y20y60

ONF y TSEN y TBL = ?

>1 y 240 y 240 y TSH y TRW = ?

>220* y 180*

FIGURE 14 (CONTINUED)

- 37 -
OUTPUT DATA FROM DEPAB2 RUN:

time:

GSUPLD

TGASFN

GIPNOW

QLOAD

TGASTB

GUDNOW

GFWAT

TTUBFN

ETANOW

GSHELL

TTUBTB

GIF-TOT

GEXHT

TWATER

GUDTDT

GLTNT

TSENSE

ETATOT

-2*000+001

8.187+006

2.270+003

8.187+006

4.170+006

4.303+002

4.397+006

2.706+005

7.736+002

5.370-001

5.555+004

3.012+002

.000

4.646+005

2.420+002

000

7.837+005

2.404+002

.000

-1.000+001

8.060+006

2.261+003

8.060+006

4.170+006

4.324+002

4.406+006

2.792+005

7.711+002

5.467-001

5.630+004

3.021+002

000

4.534+005

2.437+002

000

7.715+005

2.408+002

.000

000

7.752+006

2.238+003

7.752+006

4.170+006

4.277+002

4.416+006

2.877+005

7.643+002

5.697-001

5.704+004

2.996+002

000

4 .163 + 005

2.452+002

.000

7.420+005

2.415+002

000

time:

GSUPLD

TGASFN

GIPNOW

QLOAD

TGASTB

GUDNOW

GFWAT

TTUBFN

ETANOW

GSHELL

TTUBTB

GIF-TOT

GEXHT

TWATER

GUDTOT

GLTNT

TSENSE

ETATOT

000

7.752+006

2.238+003

7.752+006

4.170+006

4.277+002

4.416+006

2.877+005

7.643+002

5.697-001

5.704+004

2.996+002

.000

4 .163+005

2.452+002

.000

7.420+005

2.415+002

.000

1 . 000+001

7.365+006

2.206+003

7.365+006

4 .170+006

4.186+002

4.426+006

2.952+005

7.553+002

6.010-001

5.771+004

2.958+002

9.100+005

3.655+005

2.465+002

7.380+005

7.049+005

2.424+002

8.109-001

2.000+001

6.937+006

2.162+003

6.937+006

4 .170+006

4.072+002

4.435+006

3.017+005

7.432+002

6.393-001

5.828+004

2.914+002

1.817+006

3.297+005

2.475+002

1.476+006

6.639+005

2.434+002

8.126-001

3.000+001

6.700+006

2.138+003

6.700+006

4 .170+006

3.966+002

4.441+006

3.068+005

7.375+002

6.629-001

5.875+004

2.886+002

2.721+006

2.967+005

2.485+002

2.214+006

6.413+005

2.445+002

8.137-001

ICONTINUE=?

>0

FIGURE 14 ( CONTINUED)
5.3 An Example Simulation

A series of computer runs for a commercially available

400-HP fire tube boiler are described below. During these runs,

the boiler is assumed to have a type-3 controller. It proportions

the air/fuel input as long as the value for the controlled

variable (i.e., steam temperature in this example) is below a preset value. After the steam temperature rises above this

preset value, the boiler is supplied with a predetermined low

fuel/air input. If the steam temperature rises further above

a second preset value, the boiler fuel supply will be turned off.

Figure 15 shows a control logic for this control scheme.

A DEPAB2 simulation of this boiler under a series of

different operational conditions (i.e., weather, heating load,

night setback, etc.) was made. A sample set of runs using

Washington D.C. weather data, shown in figure 16, is presented

here. The boiler heating load is assumed to be proportional

to the AT of 70°F minus the outdoor air temperature. The boiler

is 20% oversized at the design outdoor temperature of 10°F

for Washington D.C. Figure 17 shows the heating load for this

* boiler under the conditions of with and without night setbacks , respectively, with the outdoor temperature being 15°F. The daily

heating load for this boiler at different outdoor temperatures

is shown in figure 18.

*W it h night setbacks, heating load at night is

assumed to be 40% of that at the day time.

- 39 -
FUEL

FLOW

RATE,

LB/HR

1 ,000

Figure 15 CONTROL LOGIC FOR A BOILER UNDER INVESTIGATION

- 40 -
o o o o o o

in <t cn cs •—

u* ow

06D

H

<

05

ltd 0<X

hiH

asw

<

06O

O

QH

»

O

N0SV3S 9NIIV3H 33d SAVd

- 41 -

FIGURE

16

TYPICAL

WEATHER

AT

WASHINGTON

D.C.

DURING

THE

HEATING

SEASON
HEATING

LOAD

(10

BTU/HR

)

HOURS

FIGURE 17 LOAD VERSUS TIME FOR A DAY WHOSE OUTDOOR AIR TEMPERATURE

IS 1 5°F

- 42 -
250

o

r*

o o o o o

o m o m

cm •—

o

lO

o

m

o

*3-

O

on

o

CM

to O

to

to»

H

*<

tou

to£

toH

tow

C

too

o

a

H

»

O

9

( Ava/nia 0l) CIV01 0NIIV3H

FIGURE

18

DAILY

HEATING

LOAD

VERSUS

OUTDOOR

AIR

TEMPERATURE
Results of DEPAB2 runs for the 400-HP boiler under

the weather and operational conditions described

above are summarized in figures 19 and 20, where the daily

fuel consumption rate and the daily efficiency values are

plotted versus the outdoor temperatures, respectively. These

results were obtained from simulation of the boiler for a period of 24 hours at each weather and load condition.

Besides the overall performance values as shown in

figures 19 and 20, transient performance of the boiler

can also be observed from the DEPAB2 runs. For the heating

load with night setbacks shown in figure 17 and the outdoor

temperature being at 15°F, transient steam and stack gas

temperatures of the boiler with a 6 a.m. setup are plotted

versus time in figures 21 and 22, respectively; and the

corresponding temperatures at a 6 p.m. setback

are plotted versus time in figures 23 and 24, respectively.

44
250
- 46 -

FIGURE

20

DAILY

FUEL

UTILIZATION

EFFICIENCY

VERSUS

OUTDOOR

AIR

TEMPERATURE
280

§

vO

U~l

vO

o

vO

CM o

CM o

CMCM o

o

CM

<o

m

o

VO

o

O CO

• • Cti vo »

o

x

m

m

m

©

inm

in

<}-

in

O

in

a c

‘ anruvaadHai wvaxs

- 47 -

FIGURE

21

TRANSIENT

STEAM

TEMPERATURE

AT

MORNING

SETUP

(FOR

OUTDOOR

AIR

TEMPERATURE

EQUAL

TO

15°F)
009

o

CM

iD

in

vO

O

ID

inO

VO

o

o• • vD

m

inm

o

m

m

m

in

o

*3-

in

i 0 ‘aamvaadwax svo aovis

C/J 06»

O

X

FIGURE

22

TRANSIENT

STACK

GAS

TEMPERATURE

AT

MORNING

SETUP

(OUTDOOR

AIR

TEMPERATURE

EQUAL

TO

15°F)
280

o

CM

00

m

• • oo

o

00

m

o

oo

O

o

00

m

m

o

m

m

p»

o

a 0 ‘anniYHadwax wvais

CO

OSo

s

co

CMw

02P

O

i-< Cb

- 49 -

TRANSIENT

STEAM

TEMPERATURE

AT

NIGHT

SETBACK

(FOR

OUTDOOR

AIR

TEMPERATURE

AT

15°

F

\
600

- 50 -

FIGURE

24

TRANSIENT

STACK

GAS

TEMPERATURE

AT

NIGHT

SETBACK

(FOR

OUTDOOR

AIR

TEMPERATURE

AT

15°F)
1

Results from DEPAB2 runs can be used in a variety of

ways. For example, results on daily fuel consumption rates

(see figure 19) obtained for the example boiler under the

D.C. weather and prescribed load conditions can be used

to calculate the boiler seasonal performance. The first

four columns of tables 1 and 2 show data read from figures

! 16, 18 and 19 for the boiler operating with and without

setback, respectively. With these data, the boiler annual

load, fuel consumption, and efficiency values can be calculated

in a straightforward manner as shown in the remainders of

tables 1 and 2. These resultant performance values are also

shown in figure 25 for easy comparison. Reduction in annual

boiler load and fuel consumption through night setbacks are

seen to be 30.5% and 28.6%, respectively.

I

I

!

- 51 -
p oo r* 00 Mt CM H oo p-» CM o o 0a • • • • • • vO

C") ON •O •— oo NO £ OES o NO m CM

a- NO CN r* ON

m CM * 0k 0k 0% 0k 0k •J z M |—4 — cn m cn § pa u*H CM ON 00 o r»- NO CM

O CM >o m NO CM *—1 cn CM CM m O o • 0k • • • • • • • — DC cn P- 00 ON o CM m NO CM >• <r ON CM 0— O' •o in a 0k cn NO 00 CM P— f— <r cn a z 0k < M O 03 CM Mf cn •— cn NO j >* P— B00 o O o

NO 00 «—

m CM in NO o 0k • • CM in ON

CM oo cn • • • ON m CM r*

J a*

td <

*" ON

m P P

u* *** PH

OO o o o

NO ON «o

m ON o CM o • • 0 p— NO CM *—1 o CM cn • • p • • NO cn o *o Mt On o a- *— *— r«* *o < < o a

HZ m cn IT\ ON ON cn 0* 0* wr_3 cn cn NO cn NO «o

^0

fid

w

a

os • • • • • • aa

>4 00 o NO cn NO in

a

CM «o «o CM •—

a

p

03 2 H

H

am

a

a >* < 03 a a NO NO z o o aM

v-*' V-#'

aM

a

a

a • < a a

CU o a

a s a a

DU

J

H

m

mm in

mm 5 2

CM cn >o

m NO £ £ DZ m b o o z a o H H <
"1

H

p

m sO Os Os st «»

u

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m 00 rs. so o © e • • • • • z vD o m CO oo CO H

04 oo CM in o fa Os

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m o m o St Z «% Ok * Ok 0k a z CM st 00 in CM OS g

fa

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fa

aaMo a © H fa OS o CM CM St CO •4- CM CQ vO fa 1^. CM o St o *— *— CM < • • e • • • • • • fa 'd- co 1— 00 •d- oo o Os Pu > •— st o O CM CM 00 o cn A Os 00 Os fa r- CO CO Os z | zt—1 n _

Ok co

«% fa

Ok StOk •* os•* CM

aua

os hJ X «— CM z • < CM s ©

os :<

g o ,0u pa CM CM CO fa m OS Pu a

\0 f— sO fa os Os OS .a © e • • • o • a *— co CM . fa rs *— Pu 'Pu CM rs CM n* CO o J

fap

CM CM f—

a< cn

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fa o a

U1

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B

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O rs in o fa fa fa •a

fa co o CM oo CM o • • • • • • pu o

Os Os 00 fa CO *— O' z

CM ooO fa . CM .M

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<5 o a o a M

fa

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CO

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^k Z a o

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W O' <;

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fa co CO fa CO fa St >< U3 < E-* * • • • © • 04 u a >* 00 o fa CO fa in g g

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CM •4- St CM «—

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H« s

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C fa vO sO z Cu

a

© o o a 2 o 3 W u CO z M a a U4 • < a a. • o a a P-i CM s a f*4 a sz

fa

in

«*• 25 35 45 55 65

Ho io azz aa

ca

M

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53 -
100 % K

COCO S H

H S cowH«<Oi«Sco 3: M H Z O Z H tnWHoQ<OMw ZowH

PuXZ

COZoozwz

Cl4

H

r*• CT\ vO

Oo Z M

H Z COWHPQCOZcO Z M H Z O Z H UUHPSCU^cO

O<OZozwH<WX oz<zH

co

CaJ CO<o

PSo

pHzo

t-t H

cuZX

coZouZwz

p.Qz<QCoZozMH<wz

pHozo

coM

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Nosvas ONixvaH/nxa ,oi o m

CMW

OSzo
6 SUMMARY

.

A computer program DEPAB2 has been developed. DEPAB2

Improves efficiency and accuracy of calculation over the original

NBS-developed boiler transient analysis program DEPAB [6,7], It

adds a detailed boiler controller subroutine and combined radiative/

convective and bo il ing / c onv ec t iv e heat transfer subroutines

necessary to accurately simulate commercial boilers. To increase

calculation efficiency, thermal dynamic responses for each elementary section of the boiler is represented by a single state

variable element. A commercial boiler commonly in use today can

usually be analyzed by dividing it into 12 sections (although

DEPAB2 allows users to choose from 3 to 62); one for the boiler

furnace, ten for boiler tubes and one for the boiler shell. The

solution to this 12 state variable dynamic system (with 12 differential equations and 24 algebraic equations) was found to require

only 14 seconds on the EXEC-1108 CPU for each 1 real-time hour.
REFERENCES

[1] "Combustion Equipment and Related Facilities for NonResidential Heating Boilers." National Research Council,

TR-51 , 1966.

[2] Hildebrand, F. B., "Introduction to Numerical Analysis,"

McGraw-Hill Book Co., New York, N.Y., 1956.

[3] Hottel. H. C., and Sarofim, A. F., "Radiative Heat Transfer,"

McGraw-Hill Book Co., New York, N.Y., 1967

[4] McAdams, W. H., "Heat Transmission, "McGraw-Hill Book Co.,

New York , N . Y . , 1954 .

[5] Rohsenow, W. M., "A Method of Correlating Heat Transfer for

Surface Boiling of Liquids," ASME Trans., Vol 73, 1951.

[6] Chi. J., "Computer Simulation of Fossil-Fuel-Fired Boilers,"

Proceedings of the Conference on Improving Efficiency and

Performance of HVAC Equipment and Systems for Commercial

and Industrial Buildings , Purdue University, April 1976.

[7] Chi, J., "Seasonal Operating Performance of Gas-Fired

Hydronic Heating Systems with Certain Energy-Saving

Features',’ International Seminar of Heat Transfer in

Buildings, Dubrovnik, Yugoslavia, 1977.

- 56 -
APPENDIX A:

INPUT FILE #8 FOR BOILER PARAMETERS
DEPAB2 INPUT DATA CODE (FILE 8.)

Line 1

Line 2

Line 3

Line 4

Line 5

Line 6

: CARB, HYDR, OXYG , XNTR, SULF

*CARB “ atomic fraction of carbon in fuel, . *HYDR ° atomic fraction of hydrogen in fuel, . *OXYG = atomic fraction of oxygen in fuel, . *XNTR = atomic fraction of nitrogen in fuel, . *SULF = atomic fraction of sulfur in fuel, .

: HFUEL , CPFUEL, TFUEL , BTUHK

*HFUEL = fuel higher heating value, Btu/lb.

*CPFUEL = fuel specific heat at constant pressure, Btu/lb/F.

TFUEL * fuel temperature, °F.

*BTUHK « boiler full load capacity, KBTUH

.

: ICTYPE

ICTYPE “ 1, boiler with on/off control, . 2, boiler with high/low/off control, . 3, boiler with air/fuel modulation or melting

control ,

.

: TASEN, TAIR, FRGFL , EXAFL, AIROF

*TASEN * sensor time constant, minutes.

*TAAIR = time constant for decay of the off cycle air flow

rate , minutes

.

*FRGFL = full load fuel firing rate, lb/hr.

*EXAFL = excess air at full load (fraction), . *AIROF = minimum air flow rate at off cycle in fraction

of the full load air flow rate, .

: TBOIL( 1 )

, FRGBL( 1 ) , AIRBL(I)

IF ICTYPE =3:

*TB0IL(1) = steam temperature, F.

*FRGBL ( 1 ) “ boiler firing rate in fraction of the full

load firing rate, . *AIRBL( 1 ) = boiler air flow rate in fraction of the full

load air flow rate, . (NOT REQUIRED, IF ICTYPE"! OR 2)

: TBOIL ( 2 ) , FRGBL ( 2 ) , AIRBL( 2

)

SAME AS LINE 5 WITH TBOIL INCREASING.

- 58 -
Line 7

Line 8

Line 9

Line 1

Line 1

: TBOIL ( 3 ) , FRGBL(3 ) , AIRBL ( 3

)

SAME AS LINE 6 WITH TBOIL INCREASING.

: TBOIL(4), FRGBL ( 4 ) , AIRBL ( 4

)

SAME AS LINE 7 WITH TBOIL INCREASING.

: TBOIL (4 ) , FRGBL ( 4 ) , AIRBL ( 4

)

SAME AS LINE 8 WITH TBOIL INCREASING.

0 : TBOIL ( 6 ) , FRGBL ( 6 ) , AIRBL ( 6

)

IF ICTYPE NOT REQUIRED.

IF ICTYPE

*TBOIL ( 6

)

*FRGBL ( 6

*AIRBL: 6)

“2 : = steam temperature at which high firing turns on,F.

= high firing rate in fraction of full firing

ra te , . = air flow rate in fraction of full load air flow

ra t e , .

IF ICTYPE * 3:

SAME AS LINE 11 WITH TBOIL INCREASING.

1 : TBOIL ( 7 ) , FRGBL ( 7 ) , AIRBL ( 7

)

* IF I CTYPE= 1

:

*TB0IL(7) = steam temperature at which fuel supply turns

on, F

.

*FRGBL(7) * firing rate in fraction of full load firing

ra te , . *AIRBL(7) = air flow rate in fraction of full load air

flow rate , .

IF ICTYPE=2

:

*TB0IL(7) * steam temperatu

off and low fir

*FRGBL ( 7 ) * low firing rate

rate , . *AIRBL ( 7 ) * air flow rate a load air flow r

IF ICTYPE *3:

SAME AS LINE 10 WITH TBOIL

re at which high

ing turns on, F.

in fraction of

t low firing in

a te , .

INCREASING

.

firing turns

full load firing

fraction of full

- 59 -
Line 12 : TB0IL(8), FRGBL ( 8 ) , AIRBL ( 8

)

Line 1

Line 1

Line 1

Line 1

Line 1

FOR ICTYPE® 1 , 2 or 3

:

*TBOIL(8) * steam temperature at which fuel supply turns

off

*FRGBL(8) = FRGBL 7) *AIRBL ( 8 ) “ AIRBL( 7

)

3 : WTOST, TIN, TOUT

NOT IN USE AT PRESENT, I.E.

*WTOST any value, . *TIN ® any value,

TOUT ® any value,

4 : FVOL , FSA , FCA , FRA, FDIAM , FSEM

*FVOL

*FSA

*FCA

*FRA

*FDIAM

*FSEM

furnace volume, ft . ^ furnace surface area, ft . furnace air flow cross sectional area,

furnace refractory area, ft . furnace hydraulic diameter, ft.

furnace surface radiative emissivity,-

5 : FNA , FNB , FNC

*FNA“r=a, Sand y in

*FMB

|

Nu =a ( RE ) ® ( PR)

FNC -J

6 : NT 1 , NT2

*NT1 = number of tube segments of the first type, . *NT2 = total number of tube segments,

7 : TAS(1)

TBC ( 1

)

*TAS ( 1

)

*TVL ( 1 *TAC ( i)

*TDI ( 1

)

*TBA( 1

)

*TBB( 1

TVL ( 1 ) , TAC(l), TDI ( 1 ) , TBA( 1 ) , TBB ( 1 )

,

TBE(1)

= surface area for first segment of tubes, ft . = gas volume associated with first segment of

tubes , f t^

.

= gas flow cross sectional area for the first

segment of tubes, ft . = hydraulic diameter for the first segment of

tubes, ft.

= a value in Nu equal to a(re) P (Pr) T

, for the

first segment of tube,---

* B value in Nu equal to ct(Re) P (pr)Y for the first

segment of tubes, .

- 60 -
*TBC(1) * y value in Nu equal to a (Re) (Pr)Y for the first

segment of tubes, . TBEi.l) « radiative emissivity for the first segment of

tubes , .

Line 18 : TAS (NT 1 + 1 )

, TVL(NT 1 + 1 ) , TAC(NT1+1), TDI(NT1+1), TBA(NT 1 + 1 ) TBB ( NT1 + 1 ) ,TBC(NT1 + 1 ) , TBE (NT 1 + 1

)

SAME AS LINE 17 BUT FOR THE (NT1+1)TH SEGMENT OF TUBES.

Line 19 : STMVL , WTAC , WTCD, WTA , WTB , WTC

3 STMVL = steam space volume, ft.

WTAC = water flow cross sectional area, ft^.

WTCD = water flow hydraulic diameter, ft

WTA—*i— = a, 6 and Y value in

WTB I Nu equal to <x(Re)®(Pr) Y

*WTC for the water side heat transfer

Line 20 : SHARE, SHUFT, SHHGT , SHCAP , FNCAP , TBCAP , WTCAP

SHARE = boiler shell surface area, ft^.

SHUFT = boiler shell U-factor value, Btu/ft /F.

SHHGT = boiler shell height, ft.

SHCAP = boiler shell thermal capacitance, Btu/F.

FNCAP = furnace thermal capacitance, Btu/F.

TBCAP - tubes thermal capacitance, Btu/F.

WTCAP = water thermal capacitance, Btu/F.
APPENDIX B:

INPUT FILE #5 FOR OPERATIONAL SCHEDULES AND INITIAL

CONDITIONS

62 -
DEPAB2 INPUT DATA AT TERMINAL (FILE 5.)

Line 1 : IWRITE

* IWRITE * 0, for minimum output, . 1, for medium output, . 2, for maximum output at debuging,

Line 2 : NTIME

*NTIME = number of time schedules to be set minimum

equal to 2 and maximum equal to 60, .

Line 3

Line 4

Line 5

Line 6

TMIN , TIA, TOA, HDMD

*TMIN time schedule, minutes.

*TIA = indoor air temperature, F.

*T0A = outdoor air temperature, F.

*HDMD = heat demand, Btu/hr.

NOTE:

This line is repeated NTIME times.

ICTYPE

*ICTYPE 0, for continuous simulation,

1, for calculating the boiler's cyclic

performance ,

.

TIME, DT, IPRNT , ICALC

*TIME

*DT

* IPRNT

*ICALC

starting time, minutes,

calculation time increment, minutes,

number of DT ' s between successive printed

output ,

. number of DT's to end the calculation, .

ONF, TSEN, TBL

*0NF * 0., start at off cycle, . 1., start at on cycle,

*TSEN = sensor temperature at start, F.

*TBL = steam temperature at start, F.
Line 7 : TSH, TRW

*TSH * boiler shell surface temperature at start, F.

*TRW “ return water temperature, F.

- 64 -
APPENDIX C:

DEPAB2 OUTPUT DATA CODE
DEPAB2 OUTPUT DATA CODE

TIME

QSUPLD

QLOAD

QFWAT

QSHELL

QEXHT

QLTNT

TGASFN

TGASTB

TTUBFN

TTUBTB

TWATER

TSENSE

QIPNOW

QUDNOW

ETANOW

QIPTOT

QUDTOT

ETATOT

time, minutes

heat supplies, Btu/hr v heat load, Btu/hr

feedwater heat, Btu/hr

shell heat loss, Btu/hr

exhaust gas sinsible heat loss, Btu/hr

exhaust gas latent heat loss, Btu/hr

temperature of gas at furnace exit, F

temperature of gas at tube exit, °F

furnace wall temperature, °F

tube. wall temperature, °F

o water temperature, F

o sonsor temperature, F

instantaneous heat input rate, Btu/hr

instantaneous heat utilization rate, Btu/hr

instantaneous boiler efficiency value, Ratio

cumulative heat input, Btu

cumulative heat utilized, Btu

cumulative boiler efficiency. Ratio

ADDITIONAL OUTPUT FOR CYCLIC OPERATION OF BOILERS:

TIMCYC * cycling time, minutes/cycle

QUDCYC = heat utilized per cycle, Btu/cycle

QIPCYC = heat input per cycle, Btu/cycle

ETACYC * cycle efficiency, Ratio

- 66 -
APPENDIX D:

LISTING OF AUXILIARY SUBROUTINES

- 67 -
ooono

SUBROUTINE AIRPR! I,T,PATM,RH, W,CP,R. AM, AX) *** CALCULATE AIR PROPERTIES

*** IF 1=1: RELATIVE HUMIDITY GIVEN

*** IF 1=2: SPECIFIC HUMIDITY GIVER

COMMON/WRITE/ I WRITE

IF( I.EQ. 1) GOTO 100

P=W*PATM/(0.622+V)

100 CONTINUE

TR=T+460.

Z= 1000. /TR

I F ( TR. GE . 492 . ) GOTO 1

0

PSAT= EXP! 0 . O3940*Z**3-0 . 2755*Z*Z- 10.43 1*Z+ 19 . 509)

GOTO30

10 IF( TR. GE. 672. ) GOTO20 • PSAT=EXP( 0 . 17829*Z*Z*Z- l . 6896*Z*Z-5 . 0988*Z+ 13.4353)

GOTO30

20 PSAT=EXP!0.71692*Z**4-4.01506*Z**3+7.5568*Z*Z-14.2131*Z+16.8255)

30 1F( I.EO. DGOTO110

RH= P/PSAT

110 CONTINUE

IF( RH. GE. 0 . 0000 1 ) COT040

V=0.

GOTO50

40 PV=RH*PSAT

Wi-0 . 622*PV/< PATM-P.W)

50 CONTINUE

CP= 0 . 2478786-0 . 4204563E-04*TR+0 . 5767857E-07*TR**2

% -0. 14930 36E-10*TR**3

CP= ( CP+0 . 444*V> /( 1 . +V)

R= ( 53 . 344-85 . 76*W) /< 1 . +W)

AM* 5 . 5029E-03+8 . 7 1 57E-05*TR-2 . 9464E-08*TR**2

% +6 . 250E- 12*TR**3 • AK= -2 . 853E-04+3 . 268E-05*TR-8 . 253E-09*TR*TR

% + 1 . 239E- 12*TR**3

IF( IWRITE.LE. DGOTO700

WRITE! 6 , 70 1 ) T, PATH, RH, W, CP , R, AM, AK

70 1 FORMAT! /2X, ’ T* . 3X, * PATH’ ,5X, *RH’ ,7X, ,8X, *CP* , *7X, * R’ , 8X, ’AM* .7X, ’ AK’ /B( 1PE9. D)

700 CONTINUE

RETURN

END

- 68 -
ftfioooooofinnnofiftfiftfiofto

non

- SUBROUTINE H20LQ( T, RO, CP . AK, AM. ST, BT) *** CALCULATE WATER PROPERTIES

DIMENSION X(5) , A(5,6) ,B(6) , CC6)

INPUT DATA:

T TEMPERATURE F

X( I) , 1=1,3 T, INDEPENDENT VARIABLE F

A( I, 1) , 1=1,3 DENSITY LB/CUFT

A( 1,2) , 1=1,5 SPECIFIC HEAT BTU/LB/F

A( 1,3) , 1= 1,5 THERMAL CONDUCTIVITY BTU/FT-HRA( 1,4) ,1=1,5 DYNAMIC VISCOSITY LB/FT-HR

A( 1,5) , 1=1,5 SURFACE TENSION LB/FT

A( 1.6) , 1=1,5 EXPANSION COEFFICIENT 1/R

OUTPUT DATA:

RO DENSITY LB/CUFT

CP SPECIFIC HEAT BTU/LB-F

AS THERMAL CONDUCTIVITY BTU/FT-HR

AM DYNAMIC VISCOSITY LB/FT-HR

ST SURFACE TENSION LB/FT

BT EXPANSION COEFFICIENT 1/R

DATA NP/3/

DATA X/32. ,60. , 100. ,200. ,500./

DATA A/62.4,62.3,62.0,60.1,49.,

XI. 01. 1.00, 1.00. 1.00, 1. 19,0.319,0.340,0.364,0.394,0.349,

X4. 33, 2. 71, 1.65.0.74,0.26,4. 18E-03,3.97E-03,3.67E-03,

X2.94E-03, 1. 18E-03, -4. E-3 , 8. E-3 , 2. E-4, 4. E-4, l.E-3/

DO100J= 1,6

DO 100 1= 1 ,

5

B< I)=A( I, J)

C(J)=TAB1(NP,X,B,T)

100 CONTINUE

RO=C( 1)

CP=C( 2)

AK= C( 3

)

AM=C(4)

ST= C C 5

)

BT=C( 6)

RETURN

END

- 69 -
ooooftfioofiflnftftflftfiftoooooonofi

non

SUBROUTINE H20VPC T, RO , CP , AK, AM, HFG. BT) *** CALCULATE STEAM PROPERTIES

DIMENSION X( 5) , A( 3 , 6 ) , B( 6) , C( 6)

INPUT DATA: *** CALCULATE STEAM PROPERTIES

INPUT DATA:

T TEMPERATURE F

X( I) , 1=1,3 T, INDEPENDENT VARIABLE F

AC I, 1) , 1=1,5 DENSITY LB/CUFT

AC 1,2) . 1=1.5 SPECIFIC HEAT BTU/LB/F

AC 1,3) , 1=1,5 THERMAL CONDUCTIVITY BTU/FT-HRAC 1,4) , 1=1,3 DYNAMIC VISCOSITY LB/FT-HR

AC 1,5) , 1=1,3 HEAT OF VAPORIZATION BTU/LB

AC 1,6) ,1=1,3 EXPANSION COEFFICIENT 1/R

OUTPUT DATA:

RO DENSITY LB/CUFT

CP SPECIFIC HEAT BTU/LBF

AK THERMAL COONDUCTIVITY BTU/FT-HR

AM DYNAMIC VISCOSITY LB/FT-HR

HFG HEAT OF VAPORIZATION BTU/LB

BT EXPANSION CNEFDICHENT 1/R

DATA NP/5/

DATA X/32. , 100. ,200. ,300. ,300./

DATA A/3 . 03E-4, 2. 85E-3 ,2. 97E-2, 0 . 153,1.48,

SO. 44, 0.4488, 0.479 1,0. 5508, 0.968,

£0.01,0.0116,0.0 140 ,0.0 172 , 0 . 030$

.

£0. 0192, 0.0229, 0.0283, 0.033 1,0. 0427,

551075.3, 1037. 1,977.9,910.0,714.3,

552 . 03E-3 , 1 . 79E-3 , 1 . 32E-3 ,1.3 16E-3 , 1 . 042E-3/

DO100J= 1 ,

6

DO 100 I s 1 ,

3

B( I ) = AC I, J)

C( J)=TAB1CNP,X.B,T)

100 CONTINUE

RO=C( 1)

CP=C( 2)

AK=CC 3)

AM=C( 4)

HFG=C( 3)

BT=CC 6)

RETURN

END
SUBROUTINE PRDP3(T,PC02,PH20,P02,PN2,PS02,

XAMK.AKK)

G

C *** CALCULATE VISCOSITY AND CONDUCTIVITY OF PRODUCTS

C

DIMENSION X( 11) . A( ID ,B( 11) ,AM(5) ,AK(5)

DATA X/-10. ,260. ,440. ,620. .806. , 1070.

,

% 1520 . ,2420. ,3140. ,3500. ,4160./

DATA A/0.0387,0.0553,0.0646,0.073.0.0806,0.0911,

*0. 1062.O. 1320,0. 1500,0. 1583,0. 1710/

DATA B/0 . 0 1 287 , 0 . O 1 944 , 0 . 02333 , 0 . 02692 , 0 . 03022

,

X0. 03483, 0.04 173, 0.05348, 0.06 12, 0.0646, 0.0709/

DATA AK/0 . 889 , 0 . 685 , 1. 123,0.964,0.889/

DATA AK'O. 925, 0.906, 1.037,0.983,0.925/

NP= 1

1

AMM= PC02*AM( 1 ) +PH2C*Att( 2) +P02*AM( 3 ) +

_ 7!?N2*AM< 4) +PS02*AM( 5)

AKK= PC02*AK( 1 ) +PH20*AKC 2) +P02*AK( 3) + %PN2*AK( 4) +PS02*AX( 5)

AMM= AMM*TAB1 < NP , X, A, T)

AKK=AKK*TAB 1 ( NP . X, B, T)

RETURN

END

- 71 -
non

non

non

FUNCTI OR CPF (Tl ,T2, PC02 , PH20 , P02 , PS02 , PR2

)

C

C *** INPUT: (Tl) TEMPERATURE, DEC R, ( T2)

C TEMPERATURE, DEG R. (PC02) NO. MOLES C02.

C (PH20) NO. HOLES H20, (P02) NO. MOLES 02,

C ( PS02) NO. HOLES S02, (PN2) NO. MOLES N2

C

C *** OUTPUT: (CP) SPECIFIC HEAT OF PROD,

C BTU/LB-DZG R

C WHERE CPF IS THE SPECIFIC HEAT FUNCTION

C

DIMENSION C( 6 ,2)

DIMENSION A( 30 ; , B( 30) , AA( 30) , BB( 30)

DATA A/4. 2497678, -6 . 9 12652E-3 .3. 1602134E-5.-2.9715432E-8,

39 . 5 10358E- 12,2.1791,1. 0378 1 15E-2 , - 1 . 0733938E-5 , 6 . 3459 175E-9 , - 1 . 628

3070 IE- 12 , 4 . 1563016, - 1 . 7244334E-3 . 5 . 69823 16E-6 , -4 . 3930044E-9 , 1 . 4233

3654E- 12,3.6916148.-1. 3032S52E-3 , 2 . 6503 1 E-6 , -9 . 768834E- 10,-9. 977223

34E- 14,3.71 89946 , -2 . 5 1 67288E-3 , 8 . 5837353E-6 , -8 . 29987 16E-9 , 2 . 7082 1 8E

X- 1 2 , 3 . 2257 132,5. 655 1207E-3 , -2 . 497O208E-7 , -4 . 2206766E-9 ,2.1 392733E312/

DATA 3/1. 1795744, 1 .0950594E-2,-4.062213E-6,7. 1370281E-10,

3-4 . 7490353E- 14,4.4 129266 , 3 . 1922896E-3 , - 1 . 297823E-6 , 2 . 4 147446E- 10

3,1. 6742986E— 14

,

2. 6707532 ,3.03171 15E-3 , -8. 535 157E-7 , 1 . 1790853E- 10

,

3-6. 1973568E- 15, 2. 8345761, 1.5976316E-3.-6.2566254E-7, 1. 1315849E310,-7. 689707E- 15,3. 5976 129,7. 8 145603E-4 , -2 . 238667E-7 , 4 . 2490 159E

3- 1 1

, -3 . 346O204E- 15,5. 198245 1 , 2. 0595095E-3 , -8 . 6254450E-7

,

31. 6636523E- 10,-1. 1847837E-14/ *** MODIFY A AND B FROM K UNITS TO R UNITS

DO 10 1=1,6

• M=5*( 1-1)

DO 10 J= 1 ,5

JJ=MfJ

AA( JJ)=A(JJ)/( 1.8**(J— 1)>

BB( JJ)=B( JJ)/( 1.8**( J-D)

10 CONTINUE

*** DETERMINE TEMP RANGE OF Tl AND T2

IF(T1.GT. 18O0. ) GO TO 25

IF(T2.GT. 1800. )G0 TO 15 *** Tl AND T2 ARE LESS THAN 1800 R

DO 20 1= 1 ,6

20 C( I, 1)=0.

DO 30 1=1,6

M=5*( 1-1)

DO 35 J= 1 ,3

JJ=M*-J

C(I,1)=C(I,1) +AA( JJ) *( T2**J-T1**J) /J

35 CONTINUE

C( I, 1)=C( I, l)*t.98726/(T2-Tl)

30 CONTINUE

CPF=(PC02«C(2, 1) +PH20#C( 3, 1>+PN2*C(4, 1)

3-*-P02*C(5, 1>+PS02*C(6, 1 ) ) / ( PC02*44

.

3+PH20* 1 8. +PN2*28 . +P02*32 . +PS02*64 .

)

GO TO 99
oftflft

n

non

o

noon

G

15 CONTINUE

*** T1 IS LESS THAU 1800 R AM) T2 IS

GREATER THAR 1800 R

TM= 1800.

DO 22 1=1.6

DO 22 J= 1 ,

2

22 C( I. J)*0.

DO 32 1=1,6

m= 3*( i-n

DO 37 J* 1 ,

5

JJ=M+J

C( I, 1)*C( 1, 1)+AA( JJ)*(T»M!J-T15McJ)/'J

C( 1 , 2) *C( I,2)+BB< JJ)^T2**J-TTPc*J)/'J

37 CONTI ROE

C( I, 1) = <C( 1, 1)+C( 1,2) ) * 1 . 98726/( T2-T1

)

32 CONTINOE

CPF=(PC02*C(2, 1)+PH20*C(3, 1)+PN2*C(4, l)

%+P02*C( 5,1) +PS02*C( 6 . 1 ) ) /( PC02*44

.

%-t-PH2G* 1 8 . +PN2*28 . +P02*32 . +PS02*64 .

>

GO TO 09

25 CONTINUE

IF(T2.LT. 1300. )GO TO 53 *** T1 AND T2 ARE GREATER THAN 1800 R

TM= 1800.

DO 21 1=1,6

DO 21 J= 1,2

21 C( I, J)=0.

DO 31 1=1,6

M=5*< 1-1)

DO 36 J* 1,5

JJ=M+J

C( I,2)=C( I,2)+BB( JJ)*<T2**J-T1**J)/J

36 CONTINUE

C( 1,2) =C( I,2)*1.98726/(T2-Tl)

31 CONTINUE

CPF= ( ?C02*C( 2 , 2) +PH20*C( 3 , 2) +PN2*C( 4, 2)

X+P02*C( 3 , 2) +PS02*C( 6 , 2) ) ( PC02*44.

X+PH20* 1 8 . + PN2*28 . +P02*32 . +PS02*64 . ) GO TO 99

* 35 CONTINUE

*** T1 IS GREATER THAN 1800 R AND T2

IS LESS THAN 1800 R

C

TM= 18O0 •> DO 24 1=1,6

DO 24 J= 1,2

24 C( I,J)*0.

DO 34 1=1,6

M=5*< 1-1)

DO 39 J= 1 ,

5

C( 1 , 1 > =C( I . 1) +AA( JJ) *( TM**J-T2**J) yj

C( I,2)=C( I,2)+BB< JJ'>»(T1**J-T?»*J)/J

39 CONTINUE „ ___

C( I,1)=(C(I,1)+C( 1 , 2) ) * l • 98726/( T1-T2)

34 CONTINUE v CPF=(PC02*C(2, 1)+PH20*C(3, 1>+PN2*C(4, 1)

X+P02*C( 5,1) +PS02*C< 6 , 1 ) ) /( PC02*44

.

X+PH20* 18. +PN2*28 . +P02*32 . +PS02*64 . )

99 CONTINUE

RETURN

END

- 73 -
non

nrirt

rtr>o

SUBROUTINE PP( PTOTAL, CARB. HYDR. OXYG, XNTR, SULF , EXAIR,

*PC02 , PH20 . ?S02 , P02 , PN2 , RATF , RPTF , RVIT)

G

C *** INPUT: (CARB) NO. MOLES CARBON, ( HYDR) NO. MOLES

C HYDROGEN, (OXYG) NO. MOLES OXYGEN, ( XNTR) NO. MOLES

C NITROGEN, (SULF) NO. MOLES SULFUR, (EXAIR) EXCESS AIR

C

C *** OUTPUT: ( PPC02) PARTIAL PRES C02, ATM, ( PPH20)

C PARTIAL PRES H20, ATM, ( AFRTT) THEORETICAL AIR FUEL

C RATIO, (PC02) NO. MOLES C02, ( PH20) NO. MOLES H20, (P02)

C NO. MOLES 02, (PS02) NO. MOLES S02, (PN2) NO. MOLES N2.

C ( UPRD) UNIT PARTIAL PRES OF PRODUCTS, LB PROD/LB FUEL

C

C *** MOLES OF » AND N REQD TO BE ADDED

C

R00=2 . *CARB+0 . 5*HYDR+2 . *SULF-OXYG

RN0=3.76^R00

*** MOLES OF C02, H20, 02, S02 AND N2 IN PRODUCTS

PC02= CARB

PH2O=0.5*HYDR

PO2=O.3*R0t>*EXAIR

?S02=SULF

PN2=0 . 5*XNTR+0 . 3*RN0*C 1 . +EXAIR) *** NT OF FUEL, AIR AND PRODUCTS

VTF= 12 . SCARB+HYDR+ 16 . *OXYG+ 14 . *XNTR+32. *SULF

VTA= ( 16 . *F.00+ 14 . *RNO) *( 1 . +EXAIR)

VTP= ( 44 . *PC02+ 1 8 . *PH20+32 . *P02+64 . *PS02+28 . *PN2)

WrW= 18. *PH20

*** COMPUTE PPC02, PPH20, AFRTT AND UPRD

AMULT= PTOTAL/( PC02+PH2O+P02+PS02+PN2)

PC02= PC02*AMULT

PH20=?H20*AMULT

PS02=PS02*AMULT

?02= P02*AMULT

PN2=PN2*AMULT

RATF= VTA/WF

RPTF= 'WTP/WTF

RVTF= VTV/VTF

RETURN

END

- 74 -
FUNCTION TAFF( HHV, RWTF , UPRD , PC02 , PH20, P02

,

%?S02,?N2,CP1,T0,PC,C?)

C

C *** INPUT: (HHV) HIGHER HTG VALUE, BTU/LB FUEL,

C (UPRD) UNIT PARTIAL PRES OF PROD, LB PROD/

C LB FUEL. ( PC02) NO. MOLES C02, (PH20) NO. MOLES

C H20, (P02) NO. MOLES 02, (PS02) NO. MOLES S02,

C ( PN2) NO. MOLES N2, (CPI) INITIAL GUESS OF SPECIF HT OF PROD,

C BTU/LB-DEG R, (TO) BASE TEMP, DEG R, (PC) PERCENT CHANGE

C IN ACCURACY RE3D BETWEEN TWO SUCCESSIVE VALUES OF TAF

C

C *** OUTPUT: (TAF) ADIABATIC FLAME TEMP, DEG R,

C WHERE TAFF IS THE ADIABATIC FLAME TEMP FUNCTION

C

HW=HHV- 1050 . *RVTF

TAF 1 * HW/UPRD/CP 1 +T0

6 CP=CTF(TAF1 ,T0,PCO2,PH2O,PO2,PSO2,PN2)

TAF2= HW/UPRD/CP+TO

T= ABS( ( TAF 1 -TAF2) /TAF 1

)

TAF 1=TAF2

IF( T. GT. PC) GO TO 6

TAFF =TAF

1

C

RETURN

END
ooftnfioorifiririnnoon

SUBROUTI NE GF ( BTUHK. HFUEL , CPFUEL, TFUEL , TAIR, RATF , RPTF

,

XVFUEL , WAIR, WGAS

)

*** CALCULATE BOILER FUEI^AIR FFLOW

INPUT DATA:

BTUHK K3TUH INPUT RATE

HFUEL FUEL HEATING VALUE, BTU/LB

CPFUEL FUEL SPECIFIC HEAT, BTU/LB/

F

RAT? MASS RATIO OF AIR TO FUEL,

RPTF MASS RATIO OF PRODUCT TO FUEL,

TFUEL FUEL TEMPERATURE, F

TAIR AIR TEMPERATURE, F

OUTPUT DATA:

WFUEL FUEL FLOW RATE, LB/HR

WAIR AIR FLOW RATE, LB/HR

WGAS TOTAL GAS FLOW RATE, LB/HR

COMMON/WRITE/ I WRITE

IF( I WRITE. EGL 2) WRITE! 6, 702) BTUHK, HFUEL, CPFUEL, RATF, RPTF

702 FORMAT! /2X. 33GF : /2X, 5HBTUHK, 6X. 5HHFUEL

,

5t6X, 6HCPFUEL , 5X, 4HRATF , 7X. 4HRPTF/5 ( 1PE 1 1 . 3 ) ) HHV= HFUEL+CPFUEL*! TFUEL-TAIR)

VFUEL= 1000 . £BTUHK/HFUEL

WAIR= RATF*WFUEL

WGAS= RPTF*VFUEL

WRITE! 6, 7 10) TFUEL, TAIR, WFUEL, WAIR, WGAS

710 FORMAT! 2X. oHTFUEL, 6X, 4HTAIR, 7X. 5HWFUEL, 6X, 4HVAIR, 7X, 4HWGAS/

%5 ! 1PE 11.3)

)

RETURN

END

- 76 -
SUBROUTINE BG< BTUHK, EXAIR, HFUEL, CPFUEL,

STFUEL, THAIR, WFUEL, WAIR) *** BOILER AIR, FUEL AND KBTUH INPUT

I FIWFUEL. GT. 0.0001) GOTO 100

BTUHK= 0

.

EXAI R= 0

.

GOTO2O0

100 BTUHK=0.001*WUEL*(HFUEL+CPFUEL*(TFUEL-77.))

RATI 0= WAI R/VFUEL

CBA I R= RATI O/THAI

R

EXAI R= CBA I R- 1

.

200 RETURN

END

- 77 -
non

FUNCTION RENB! AMAS, AMU, AC,D) *** CLACULATE REYNOLDS NUMBER

COMMON/WRITE/ 1 WRITE

IF! IWRITE.LE. DGOTO704

WRITE! 6, 706) AMAS, AMO, AC, D

704 CONTINUE

706 FORMAT! /2X, 5HRENB : /2X, 4HAMAS , 7X, 3HAMU, 8X, 2HAC , 9X,

% 1HD/4! 1PE11.3))

G= AMAS/AC

RENB=G*D/AMU

IF( IWRITE.LE. DGOTO700

WRITE! 6 , 702) RENB

700 RETURN

702 FORMAT! /2X, 5HRENB=, 1PE1 1.3)

END

- 78 -
ftftO

FUNCTION PRNB( AMU, CP , AK) *** CALCULATE PRANDTL NUMBER.

COMMON/WRITE/ I WRITE

IF( I WRITE. LE. 1)GOTO704

WRITE! 6, 706) AMU, CP, AK

704 CONTINUE

706 FORMAT( /2X, 5HPRNB: /2X, 3HAMU, 8X, 2HCP , 9X, 2HAK/

«3! 1PEU.3))

PRRB= AMU*C?/AX

IF( I WRITE. LE. 1 ) GOTO70O

WRITE( 6 , 702) PRN3

700 RETURN

702 FORMAT! /2X. 5HPRNB= , 1PE1 1.3)

END

- 79 -
OOftOOftOCiOftO

FUNCTION AIRFHT(T1,T2,AL)

*** CALCULATE AIRS IDE FREE CONVECTION HEAT TRANSFER COEFFICIENT

INPUT DATA:

Tl SURFACE TEMPERATURE F

T2 AIR TEMPERATURE F

AL CHARACTERISTIC LENGTH FT

OUTPUT DATA:

AIRFHT AIR FREE CONVECTION HT TRANCFER COEFF BTU/SQFT-HR-F

DT=ABS( Tl-T2>~,

^ VI

GG= ( AL**3 . ) xAJj

IF( GG. GT. 1 . E3) GOTOIOO

AIRFHT= O . 29*( DT/AL) **0 . 23

GOTO200

100 AIRFHT=0.21*(DT**0.3333)

200 RETURN

END

- 80 -
non

nnannnnflAna

FUNCTION GEF( PPC02 , PPH20, XL, TG) *** INPUT: (PPC02) PARTIAL PRES C02, ATM, ( PPH20)

PARTIAL PRES H20, ATM, (XL) LENGTH OF COMBUSTION

CHAMBER, FT, (TG) RADIATING GAS TEMP, DEG R

*** OUTPUT: (GE) GAS EMISSIVITY

WHERE GEF IS THE GAS EMISSIVITY FUNCTION

*** SELECT GAS EMISSIVITY CONSTANTS

Cl AND C2

XX= ( PPC02+PPH20) *XL

IF(XX. GT. .2) GO TO 4

Cl =404.

9

C2=9. 62

GO TO 6

4 C 1 = 237

.

COs A 4

6 CONTINUE

*** COMPUTE GAS EMISSIVITY

GEF= XX**C2*C 1 /TG

RETURN

END

- 81 -
non

FUNCTION GS(AT,CS,GE,SE) *** CALCULATE GAS/SINK EXCHANCE AREA

GS= 1 . /SE+ 1 . /( CS*GE) -J

.

GS=AT/GS

RETURN

END

- 82 -
FUNCTION 0VH7< I , AO, AP, AF , AI , ALFO, ALF I , TP , AX, FEE)

C

c *** CALCULATE OVERALL HEAT TRANSFER COEFFICIENT

C *** l»is OUTSIDE SURFACE

G *** 1=2: INSIDE SURFACE

C *** 1=3: OVERALL

C

COMMON/WRITE/ I WRITE

IF( I WRITE. LE. 1 ) G0T0704

WRITE( 6 , 706 ) I , AO , AP , AF , AI , ALFO, ALF I , TP , AK, FEE

704 CONTINUE

706 /2X’ 5H0VET: /2X, 1HI , 2X, 2HA0, 9X, 2HAP , 9X, 2HAF , 9X, N2HAI/I3, 4! IPEl 1 . 3) /2X, 4HALF0, 7X, 4HALFI ,7X,2HTP,9X, X2HAK, 9X, 3HFEE/5 ( 1PE 11.3))

’ ’ AA=AO*TP/! AP*A30

IF (I.EO.2) GOTO 10

ALF= A0/( ALFO*( AO-AF*( 1

. -FEE) )

)

ALF= ALF+0 . 5*AA

IF ( I.Ett. 1) GOTO 100

ALF= ALF+0 . 3*AA+A0/! AI*ALF I

)

GOTO 100

10 ALF=AI*TP/(2.*AP*AK)+1./ALFI

100 0VHT=1./ALF

IF( I WRITE. LE. 1 ) GOTO700

WRITE! 6 , 702) OVHT

700 RETURN

702 FORMAT! /2X. 3H0VHT= , 1PE 1 1 . 3)

END

- 83 -
oftooooonoftftftfto

FUNCTION TAB1 ( HP , X, Y, Xl

)

*** PURPOSE : PROM TABULATED Y VS X VALLLES

TO DETERMINE Y(X1) VALUE

*** WRITTEN BY: JOSEPH CHI *** INPUT/OUTPUT LIST:

NP NUMBER OP DATA POINTS

X DATA POINT INDEPENDENT VARIABLES

Y DATA POINT DEPENDENT VARIABLES

TAB! OUTPUT DEPENDENT VARIABLE

XI INPUT INDEPENDENT VARIABLE

DIMENSION X(NP).Y(NP)

C *** SET OUT OF. RANGE Yl(Xl) VALUES

XMIN=X( 1)

XMAX=X(NP)

IF( Xl . GT. XMIN) GOTO10

Y1 = Y( 1)

GOTO ICO

10 IF( Xl . LT. XMAX) G0T020

Yl = Y(NP)

GOTO lOO

C *** IFTPOLATE FOR Yl(Xl) VALUE

20 I s 1 40 IF (Xl.GT.XC I))GOTO30

BXT=X( I)-Xi 1-1)

DYT=Y( I)-YCI-1>

RDXT= l . /DXT

DY0DX=DYT*RDXT

DX=X1-X( 1-1)

Yl*Yt I- l) +DJC*DYODX

GOTO 100

30 1*1+1

G0T040

100 TAB1* Y1

RETURN

END

80PEB20

- 84 -
AAA

FUNCTION STSATT(PG)

CALCULATE STEAM SATURATION T FROM P

DATA AG.BG.CG.DG, EG, FC, AA,BB,TFR/90. 41838,

+- 1604 1 . 134 , - 10 . 48695 , 0 . 004683 1.0. 270452

,

+1179.51, 132. ,570. ,459.67/

IF( PG. LE. 0) G0T0999

PL0G= ALOG( PG)

TR= 0 . 43429448*AA*PLOG+BB

DO 1 0 1 TR= 1,30

TRO=TR

C=ALOG( ABS( FG-TRO)

)

F= AG+BG/TRO+CG*ALOG( TRO) +DG*TRO+EG*< ( FG-TRO) *C/TRQ> -PLOG

FT= “BG/TR0**2+CG/TR0+DG

IF( ABS< EG) . GE. 1 . E-20) FT=FT-EG*C 1 . /TRO+FG*C/TRO**2

)

TR=TRO-F/FT

IF( ABS(TR-TRO) .LE.0.O5)GOTO20

10 CONTINUE

999 WRITE! 6, 100)

100 FORMAT! 5X, ’ ERROR IN CALLING -STSATT- ’

)

RETURN

20 STSATT= TR-TFR

RETURN

END

- 85 -
SUBROUTINE ROGT?( ROC, TG, PC)

CALCULATE T AND P FROM SATURATION VAPOR DENSITY

DIMENSION RO( 2 1 ) , T( 21

)

DATA RO/0 . 00058679 , 0 . 002857 14,0.01031 034 ,0.01 992032

,

+0 . 029 73536,0. 0373 1 343 , 0 . 043 19634,0.051 38362 ,0.061 24824

,

+0 . 0723273 , 9 . 0849762 1.0.11 560694 , 0 . 1543 1174,0. 20329333

,

+0 . 2637 1 306 . 9 . 33772374 , 0 . 427533 13,0. 53587697 , 0 . 908 1 8273

,

+ 1 . 47907 11,3. 7353248/

DATA T/50. , 190. , 150. , 180. ,200. ,212. .220. ,230. ,240.

,

0230. ,260. ,280. ,300. ,320. ,340. ,360. ,380. ,400.

,

+450. .300. ,600./

NP3 21

TG= TAB 1 ( NP , PO , T, ROG)

PG=STSATP< TG)

RETURN

END

- 86 -
nnn

FUNCTION STSATP(TG)

CALCULATE STEAM SATURATION PRESSURE FROM TEMPERATURE

DATA AG,BG,CG,DG,EG,FG,EEP,TC,TFR/90.41858,

+- 1604 1.139,-10. 48695 , 0 . 604683 1,0. 270452

,

+ 1 179 . 5 1 ,2.7182818, 1165. 11,459.67/

T=TG+TFR

IFC T. GT. TC) G0TQ999

C=ALOG( ABSf'FG-T) ) STSAT?=EEP**< AG+BG/T+CG*ALOG( T) +DG*T+EG*C*( ( FG-T) /T)

)

RETURN

999 WRITE(6, 100)

100 FORMAT( 5X, ’ ERROR IN CALLING -STSATP- * ) RETURN

END

- 87 -
nnn

FUNCTION 3GDP< AMAS, V.RE, AF.BF.D, AC.AL) *** CALCULATES SINGLE-PHASE PRESSURE DROP

COMMON/WRITE/ I WRITE

IF( I WRITE. LE. 1 ) GOTO704

WRITE! 6, 706) AMAS, V.RE, AF.BF.D, AC.AL

704 CONTINUE

706 FORMAT! /2X. 3HSGDP : /2X, 4HAMAS , 7X, 1HV, 10X.2HRE,9X.

X2HAF/4! 1PE11.3)/2X,2HBF,9X, 1HD, 10X.2HAC,9X,2HAL/

J?4( 1PEI1.3)

)

AAT= 0 . 046

BBT=0 .

2

AAL= 16.

3BL= 1

.

G= AMAS/AC

TALF=AF

TBLF=BF

IF (TALF.GT. 0.00003) GOTO 10

IF (RE.GT.2000.) GOTO 20

TALF= AAL

TBLF=-BBL

GOTO 10

20 TALF= AAT

TBLF=-BBT

10 F=TALF*RE**TBLF

SGDP= ( 3 . 330868E- 1 1 ) *F*V*AL*G*C/D

IFC I WRITE. LE. DGOTO700

WRITE! 6 , 702) SGDP

700 RETURN

702 FORMAT! /2X, 5HSGDP» , 1PE1 1.3)

end —

- 88 -
non

SUBROUTINE WATPR( TV, WATRO , WATK, WATM, WATHFC, WATCP) *** CALCULATE WATER PROPERTIES

COMMON/WRITE/IWRITE

DIMENSION ARO(S) , AK(5) , AM(5) , AEFG(3)

DATA ARO/O. 11647E03.-O.4O054E00.0. 10815E-02,

S-0 . 12387E-03 , 0 . 49002E-09/

DATA AK/-0 . 27694E00 . 0 . 43215E-03 , 0 . 49008E-05

,

*-0 . 886 1 3E-08 , 0 . 4 1 387E- 1 1 DATA AM/0 . 79424E03 , -0 . 47389E0 1,0. 10622E-0 1

,

- %-0. 104 16E-04 , 0. 37690E-08/

DATA AHFG.'0 .3151 4E04 . -0 . 13714E02, 0.35945E-01

,

%-0 . 43525E-04 , 0 . 19695E-07/

IF( I WRITE. LE. 1 ) GOTO706

WRITE(6,710)TW

706 CONTINUE

710 FORMAT! /2X, 9HWATPR: TW= , 1PE1 1 . 3)

TFR=439 . 67

• TWR= TW+TFR

WATRO=0.

WATK= 0

.

WATM=0.

WATRFG=0.

IF( TV. LE. 32. ) GOTO 100

DO 10I= 1,5

J= 1-1

AA=TWR**J

WATRO= WATRO+ARO! I)*AA

VATK= WATK+AK( I ) *AA

WATM= WATM+- AM( I ) *AA

10 WATHFG= WATEFG+AEFG! I>*AA

WATC?= 1

.

GOTO200

100 WATRO= 19.

WATK= 0 . 82

WATM= 1 . E25

WATHFG=1219.

WATCP=0. 46

200 IF( I WRITE. LE. DGOTO700

WRITE! 6 , 702) TV, WATRO, WATK, WATM, WATHFG, WATCP

700 RETURN

702 FORMAT! 2X, 2HTW, 9X, 5HWATRO , 6X, 4HWATK, 7X,

X4HWATM, 7X, oHWATHFG, 5X, 3HWATCP/6! 1PE1 1 . 3)

)

END

- 89 -
NBS-114A <REv- 2-«o) U.S. DEPT. OF COMM. 2. Performing Organ. Report NoJ 3. Publication Date BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

4. TITLE AND SUBTITLE

A COMMERCIAL HEATING BOILER TRANSIENT ANALYSIS SIMULATION MODEL (DEPAB2)

5. AUTHOR(S)

Joseph Chi and David Didion

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

Hf ASHINGTON, D.C. 20234

7. Contract/Grant No.

S. Type of Report & Period Covered

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. Stole. ZIP)

Department of Energy

Washington, D.C. 20585

10.

SUPPLEMENTARY NOTES

I

| Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here) This report documents a second generation boiler transient analysis computer

program DEPAB2. It treats in detail the boiler controllers and different modes

of heat transfer (which include conductive, convective and radiative) in the boiler

environment; and it is built upon 7 principal subroutines for the controller and

interface flux calculations and 16 auxiliary subroutines for fluid properties, fuel/

air combustion and heat transfer parameters.

Also included is a guide on using DEPAB2. Included are:

(1) Input data requirements for DEPAB2 runs,

(2) Procedures for DEPAB2 runs, and

(3) Output data interpretation.

In addition, a worked example is described and discussed in detail to illustrate:

(1) the DEPAB2 rims, (2) quantitative information generated by DEPAB2 runs, and (3) use of information from DEPAB2 runs to design energy conservation strategies.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

Boilers; computer model; energy conservation; fire tube boilers; heat transfer

L

13. AVAILABILITY

( y | Unlimited

rj For Official Distribution. Do Not Release to NTIS

[ | Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

[y~~| Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

15. Price

USCOMM-DC 8043-P80