A COMPUTER SIMULATION OF ANAVAL BOILER

Wa! lace Paul Fini

NAVAL POSTGRADUATE SCHOOL

Monterey, California

THESISA COMPUTER SIMULATION OF A

NAVAL BOILER

by

Wallace Paul Fini

September 1978

Thesis Advisor: T. Houlihan

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Wallace Paul Fini

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Naval Postgraduate SchoolMonterey, California 93940

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Navy D-Type BoilerComputer SimulationNaval BoilerCombustion Engineering Type V-2M Boiler

20. ABSTRACT (Continue on ravaraa eldm II neeeeemry end Identity by aloe* number)

A non-linear computer model of a U.S. Navy D-Type

Boiler was developed using lumped parameters. The program

was coded in IBM CSMP-III simulation language. A companion

routine was also coded to permit the user to implement the

DD i j AN^l 1^73 EDITION OP I NOV St IS OBSOLETES/N 0102-014-6601

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UNCLASSIFIEDtuCUQITv gU*gW£ie*TIOM Q> This »<atfin<M r>*tm (aMn<

(20. ABSTRACT Continued)

model for a particular boiler using only readily accessible

data. The model was adapted for a Combustion Engineering

Type V-2M boiler for analysis.

DD Form 1473, 1 Jan 73

5/N 0102-014-6601UNCLASSIFIED

2 *fcu»iTv ctAturiCAvioN o* this *»oer»»>»" o««« £*»•»•*)

Approved for public release; distribution unlimited

A Computer Simulation of aNaval Boiler

by

Wallace Paul -FiniLieutenant Commander, United States Navy

B.S.E.E., Worcester Polytechnic Institute, 1967

Submitted in partial fulfillment of therequirements for the degrees of

MASTER OF SCIENCE IN MECHANICAL ENGINEERING

and

MECHANICAL ENGINEER

from the

NAVAL POSTGRADUATE SCHOOL

September 1978

ABSTRACT

A non-linear computer model of a U.S. Navy D-Type

boiler was developed using lumped parameters. The program

was coded in IBM CSMP-III simulation language. A companion

routine was also coded to permit the user to implement the

model for a particular boiler using only readily accessible

data. The model was adapted for a Combustion Engineering

Type V-2M boiler for analysis.

TABLE OF CONTENTS

I. INTRODUCTION 17

II. DESIGN CONSIDERATIONS 20

A. D-TYPE BOILER 20

B. MODEL FLEXIBILITY 21

C. ASSUMPTIONS 22

III. MODEL ANALYSIS 24

A. GENERAL 24

B. FLUE GAS AND COMBUSTION SYSTEM 24

C. WATER-STEAM CIRCULATION SYSTEM 27

D. WATER-STEAM HEAT TRANSFER 33

1. Risers 33

2. Desuperheater 34

3- Economizer 35

4. Superheater 35

E. PRESSURE DROP CALCULATIONS 36

F. EQUATIONS OF STATE 38

IV. DETERMINATIONS OF CONSTANTS AND INITIALCONDITIONS 39

A. GENERAL 39

B. PROGRAM EQUATIONS 40

C. CIRCULATION BALANCE 47

V. RESULTS AND CONCLUSIONS 51

A. OPEN LOOP RESPONSES 51

B. CONCLUSIONS 54

VI. FIGURES 56

APPENDIX A. INTERFACE PROGRAM LISTING AND SAMPLEOUTPUT 89

LIST OF REFERENCES "

INITIAL DISTRIBUTION LIST 1 Q1

LIST OF FIGURES

1. Simplified Boiler Schematic 56

2. Combustion Engineering Type V-2M Boiler 57

3. Control Volume Arrangement 58

4. Flue Gas and Combustion Schematic 59

5. Basic Circulation System 60

6. Water Level Response to a 10% Increasein Throttle Setting 61

7. Drum Pressure Response to a 10% Increasein Throttle Setting 62

8. Steam Flow Rate Response to a 10% Increasein Throttle Setting 63

9. Main Bank Circulation Response to a10% Increase in Throttle Setting 64

10. Screen Circulation Response to a10% Increase in Throttle Setting 65

11. Riser Exit Quality Response to a

10% Increase in Throttle Setting 66

12. Average Riser Density Response to a10% Increase in Throttle Setting 67

13. Water Level Response to a10% Decrease in Throttle Setting 68

14. Drum Pressure Response to a10% Decrease in Throttle Setting 69

15. Steam Flow Rate Response to a10% Decrease in Throttle Setting 70

16. Main Bank Circulation Response to a

10% Decrease in Throttle Setting 71

17. Screen Circulation Response to a

10% Decrease in Throttle Setting 72

18. Riser Exit Quality Response to a10% Decrease in Throttle Setting 73

19. Average Riser Density Response to a10% Decrease in Throttle Setting 74

20. Water Level Response to a10% Increase in Fuel Flow 75

21. Drum Pressure Response to a10% Increase in Fuel Flow 76

22. Steam Flow Rate Response to a10% Increase in Fuel Flow 77

23. Main Bank Circulation Response to a10% Increase in Fuel Flow 78

24. Screen Circulation Response to a10% Increase in Fuel Flow 79

25. Riser Exit Quality Response to a10% Increase in Fuel Flow 80

26. Average Riser Density Response to a10% Increase in Fuel Flow 81

27. Water Level Response to a10% Decrease in Fuel Flow 82

28. Drum Pressure Response to a10% Decrease in Fuel Flow 83

29. Steam Flow Rate Response to a10% Decrease in Fuel Flow 84

30. Main Bank Circulation Response to a10% Decrease in Fuel Flow 85

31. Screen Circulation Response to a10% Decrease in Fuel Flow 86

32. Riser Exit Quality Response to a10% Decrease in Fuel Flow 87

33. Average Riser Density Response to a10% Decrease in Fuel Flow 88

NOMENCLATURE

English Symbols

2A - Area (ft )

2A, - Drum Downcomer Total Cross Sectional Area (ft )ar

2A, - Header Downcomer Total Cross Sectional Area (ft )

CL S

2AMB - Main Bank Heat Transfer Surface Area (ft )

2A - Main Bank Riser Total Cross Sectional Area (ft )r

2A - Screen Riser Total Cross Sectional Area (ft )s

Be - Becker's Factor

C - A General Constant

Cj, - Specific Heat of Liquid (Btu/lbm/°F)

C - Specific Heat of Tube Metal (Btu/lbm/°F)

C - Specific Heat (Btu/lbm/°F)

C„, - Specific Heat of Flue Gas in the Furnace(Btu/lbm/°F)

CR1 - Specific Heat of Flue Gas at the FurnaceExit (Btu/lbm/°F)

C „ - Specific Heat of Flue Gas at Superheater ExitRZ

(Btu/lbm/°F)

CR , - Specific Heat of Flue Gas at Main Bank Exit(Btu/lbm/°F)

C,

- Constant used in Rohsenow Correlationst

C-,-C. , - Constants Used in Various Equations

d - Diameter (ft)

D, - Sum of the Diameters of the Drum Downcomersdr

(ft)

D, - Sum of the Diameters of the Screen DowncomersdS

(ft)

s

EB

EDI

ED2

ER1

ER2

ER3

ER4

Ewr

EW1

EW2

EW3

EW4

f

Fdr

Fds

Sum of the Diameters of the Main Bank Tubes(ft)

Sum of the Diameters of the Screen Tubes (ft)

Total Heat Input to the Furnace (Btu/sec)

Heat Transferred from the DesuperheatedSteam to the Tubes (Btu/sec)

Heat Transferred from the Superheater Tubesto the Steam (Btu/sec)

Heat Transfer Rate from the Flue Gas to theScreen Tubes (Btu/sec)

Heat Transfer Rate from the Flue Gas to theSuperheater (Btu/sec)

Heat Transfer Rate from the Flue Gas to theMain Bank (Btu/sec)

Heat Transfer Rate from the Flue Gas to theEconomizer (Btu/sec)

Heat Transfer Rate to the Riser Liquid(Btu/sec)

Heat Transfer Rate from the Economizer Tubesto the Feed Water (Btu/sec)

Heat Transfer Rate from the DesuperheaterTubes to the Drum (Btu/sec)

Heat Transfer Rate to the Screen Riser Liquid(Btu/sec)

Heat Transfer Rate to the Main Bank RiserLiquid (Btu/sec)

Friction Factor

Drum Downcomer Friction Factor

Heater Downcomer Friction Factor

Main Bank Riser Friction Factor

Screen Riser Friction Factor

2Acceleration of Gravity - 32.2 ft/sec

Mass Flow Rate (lbm/sec)

10

GB - Fuel Flow Rate (lbm/sec)

GDI - Total Steam Flow Rate from Boiler (lbm/sec)

GD2 - Desuperheated Steam Flow Rate (lbm/sec)

GD3 - Steam Condensing from Vapor to Liquid in theSteam Drum (lbm/sec)

GD4 - Superheated Steam Flow (lbm/sec)

GL - Air Mass Flow Rate (lbm/sec)

GR - Total Flue Gas Flow Rate (lbm/sec)

GS - Screen Riser Circulation Flow Rate (lbm/sec)

Gr - Riser Circulation Flow Rate (lbm/sec)

Gw - Downcomer Circulation Flow Rate (lbm/sec)

GszS - Main Bank Riser Mass Flow Rate (lbm/sec)

Gwr - Drum Downcomer Circulation Flow Rate(lbm/sec)

Gws - Header Downcomer Circulation Flow Rate(lbm/sec)

HD1 - Enthalpy of Saturated Steam (Btu/lbm)

Hfg - Heat of Vaporization (Btu/lbm)

Ho - Heating Value of Fuel Oil (Btu/lbm)

HNB - Non-boiling Height (ft)

HNBR - Main Bank Riser Non-boiling Height (ft)

HNBS - Screen' Riser Non-boiling height (ft)

HW1 - Enthalpy of Saturated Water (Btu/lbm)

HW2 - Enthalpy of Downcomer Liquid (Btu/lbm)

HW3 - Enthalpy of Feed at Economizer Inlet(Btu/lbm)

HW4 - Enthalpy of Feed at Economizer Outlet(Btu/lbm)

HW6 - Enthalpy of Water in Lower Drum (Btu/lbm)

11

Hxr - Effective Height of Main Bank/DrumDowncomer Circuit (ft)

Hxs - Effective Height of Screen/Header DowncomerCircuit (ft)

k - Thermal Conductivity (Btu/hr-ft-°F)

K a general constant

Ks - Equivalent Sand Roughness (in)

KR1-KR4 - Constants Used in the Gas Heat Transfer Equations

2,- Length (ft)

L - Tube Length (ft)

LB - Boiling Length (ft)

Ldr - Total Length of Drum Downcomer Tubes (ft)

Lds - Total Length of Header Downcomer Tubes (ft)

Ldlr - Avg. Length of Drum Downcomer Tubes (ft)

Ldls - Avg. Length of Header Downcomer Tubes (ft)

Lr - Total Length of Main Bank Tubes (ft)

Lrl - Avg. Length of Main Bank Tubes (ft)

Ls - Total Length of Screen Tubes (ft)

Lsl - Avg. Length of Screen Tubes (ft)

LMTD - Log Mean Temperature Difference (°F)

M - Mass (lbm)

MMl - Mass of Screen Tube Metal (lbm)

MM2 - Mass of Superheater Tube Metal (lbm)

MM3 - Mass of Riser Tube Metal (lbm)

MM4 - Mass of Economizer Tube Metal (lbm)

MM5 - Mass of Desuperheater Tube Metal (lbm)

MRl - Mass of Flue Gas in Furnace (lbm)

MWl - Mass of Water in Steam Drum (lbm)

12

P - Pressure (psia)

PD - Pressure of Steam Volume in Steam Drum (psi)

PD1 - Saturation Pressure Corresponding to Enthalpyof Water in the Steam Drum (psi)

PD2 - Pressure at Superheater Outlet (psia)

PD2 - Pressure at Desuperheater Outlet (psia)

Pr - Prandtl Number

Psat - Saturation Pressure (psia)

PWl - Pressure in Water Drum (psi)

PW2 - Pressure in Screen Header (psi)

q - Heat Transfer Rate (Btu/sec)

R - Tube Radius (in)

Ral - Average Density in the Main Bank Risers(lbm/ft 3

)

Ra2 - Average Density in the Screen Risers(lbm/ft 3

)

3RD1 - Density of Saturated Steam (lbm/ft )

Re - Reynolds Number

3RW - Density of Saturated Water (lbm/ft )

RS - Density of Two-Phase Mixture at ScreenOutlet (lbm/ft 3

)

R0 - Density of Two^Phase Mixture at Main BankOutlet (lbm/ft )

t - Time (sec)

T - Temperature (°F)

Tsat - Saturation Temperature (°F)

TD - Temperature of Steam Drum Vapor (°F)

TDl - Temperature of Saturated Steam Correspondingto Drum Enthalpy (°F)

TD2 - Superheater Outlet Temperature (°F)

13

TD3

TM1

TM2

TM3

TM4

TM5

TR1

TR2

TR3

TR4

TR5

TRa2

TRa3

TRa4

TW3

TW4

To

Ub

Um

V

VB

VD1

VENT

VNDR

VR

VS

Desuperheater Outlet Temperature (°F)

Screen Metal Temperature (°F)

- Superheater Metal Temperature (°F)

Main Bank Metal Temperature (°F)

- Economizer Metal Temperature (°F)

Desuperheater Metal Temperature (°F)

Temperature of Flue Gas in Furnace (°F)

Temperature of Flue Gas Leaving Furnace (°F)

Temperature of Flue Gas Leaving Superheater (°F)

Temperature of Flue Gas Leaving Main Bank (°F)

Temperature of Flue Gas Leaving Economizer (°F)

Average Flue Gas Temperature Across theSuperheater (°F)

Average Flue Gas Temperature Across theMain Bank (°F)

Average Flue Gas Temperature Across theEconomizer (°F)

- Feed Inlet Temperature (°F)

Feed Outlet Temperature (°F)

Ambient Temperature

Bubble Rise Velocity (ft/sec)

Mean Velocity (ft/sec)

- Volume (ft3

)

Boiling Volume (ft )

3Volume of Steam in Steam Drum (ft )

Percent Throttle Valve Opening

3Water Drum Volume (ft )

3Mam Riser Bank Fluid Volume (ft )

3Screen Riser Bank Fluid Volume (ft )

14

3v - Specific Volume (ft /lbm)

X - Quality (percent)

X0 - Quality at Main Bank Riser Outlet (percent;

Xs - Quality at Screen Riser Outlet (percent)

Xe - Quality at Riser Exit (percent)

Zl - Drum Downcomer Bend Loss Factor

Z2 - Drum Downcomer Exit Loss Factor

Z3 - Main Bank Riser Bend Loss Factor

Z4 - Main Bank Riser Exit Loss Factor

Z5 - Screen Riser Bend Loss Factor

Z6 - Screen Riser Exit Loss Factor

Z7 - Header Downcomer Bend Loss Factor

Z8 - Header Downcomer Exit Loss Factor

Greek Letters

\i- Viscosity (lbm/ft-sec)

p - Density (lbm/ft )

a - Surface Tension (lbf/ft)

3P n , - Average Density in Superheater (lbm/ft )

Average Density in Desuperheater (lbm/ft )p Da2Average

Subscripts

a Average

£,f Liquid

g Vapor

M,m Metal

15

oo - Far Field Average

r - Main Bank

s - Screen

dr - Drum Downcomer

ds - Header Downcomer

D - Steam

R - Flue Gas

W - Water

16

I. INTRODUCTION

The increasing attractiveness and efficiency of computer-

aided design techniques have established a need for

reasonably accurate computer models of all types of

engineering systems. The design of multivariable control-

lers, in particular, requires the availability of state

information about a system which is not available from

conventional transfer function simulations. A number of

computer models of marine boilers have been proposed

[1,2,3,4]. All of these efforts share one or more of the

following features:

a. Lumped parameters are used.

b. Bubble formation effects with respect to shrink andswell are not modeled.

c. The furnace screen and main riser bank are lumpedtogether as are their respective downcomers [1,3,4].

d. The model is linearized using a Taylor expansionor perturbation technique [3]

.

Use of lumped parameters is dictated by the need to maintain

computational efficiency, particularly when the model is

used in control system design and optimization schemes.

In the past, effects due to vapor formation in the drum

have not been included due to the lack of a suitable model.

A simple model based on the Rohsenow correlation [5] was

developed for use in the current simulation. However, its

contribution to shrink and swell effects was negligible and

17

it was eliminated from the equation set. Regarding the

tube banks, Haraguchi and Akasara [2] split out the various

riser and downcomer loops, including intermediate headers.

Considering the general level of uncertainty inherent in

the correlations used in this model, this appears to be an

excessive degree of complication. A compromise position

was taken in the present effort in that the screen and main

riser bank and their associated downcomers were modeled

separately, but intermediate headers within the screen

circuit were not addressed individually since their configura-

tion varies widely from one boiler to another.

The objective of this thesis was to develop a general,

non-linear model of a Navy boiler for use in simulations

covering the full operating range of the propulsion plant.

However, since a linearized version is normally needed for

multivariable controller design, CENTRL, a computer code

developed locally for use with CSMP models, could be used

to generate linearized state space representations described

by the matrix equations:

This approach would produce linearized representations

covering the entire boiler operating range in a piecewise

18

fashion, rather than attempting to extend the range of

applicability of a single state space or linear model.

Since this author found the notation used in Reference

[1] particularly readable, it was adopted for use in this

document.

19

II. DESIGN CONSIDERATIONS

A. D-TYPE BOILER

The single furnace (D-Type) , uncontrolled-superheat

boiler was chosen as the basis for the model since it is

the predominant design in the current U.S. Navy inventory.

The nominal operating pressures range from 600 to 1200 psi,

and all designs are conceptually similar. A basic schematic

is shown in Figure 1. These boilers are typified by

relatively fast response times for use in high speed

maneuvering vessels. This puts heavy emphasis on properly

designed control systems. Manual control of these boilers

is essentially infeasible except under the most favorable

circumstances, e.g. steady steaming at low speeds. Current

conventional control systems used by the Navy are of the

same generic type with relatively minor customization except

in hardware from one installation to the next. These

designs have been based on analog models intended to provide

reasonable dynamic responses for pressure, water level, and

steam flow which are the only state parameters measured by

conventional controllers. Although these control systems

have in general proven satisfactory, there is some indica-

tion [6] that multivariable control systems can effect

significant improvement in both response time and demands

on auxiliary equipment.

20

A typical boiler of this type, the Combustion Engineering

Type V-2M is shown in Figure 2. The main components of the

boiler are the furnace which is surrounded on all sides

except the floor by screen tubes, the superheater, main

riser banks, economizer, water drum, steam drum, desuper-

heater, downcomers, and screen headers. Navy boilers

do not include air heaters and the only air preheating

which occurs is accomplished by passing the incoming air

over the exhaust stack liner. This procedure generally

produces an air temperature of about 100-130°F for an

ambient of 70°F. In contrast to the boilers used as the

basis for previous models, the desuperheater is located

in the water drum rather than in the steam drum. All of

the steam generated passes through the superheater prior

to being split out as main superheated steam and auxiliary

desuperheated steam.

All of these boilers are of the natural circulation

type. The "throttle valve" was considered to be in the

superheated main steam line.

B. MODEL FLEXIBILITY

The model was designed to be as flexible as possible

to permit its relatively simple adaptation to a particular

boiler. Since the boiler technical manual or equivalent,

the steam and gas tables, and standard engineering hand-

books may be presumed to be available, the model was designed

to utilize data only from these sources for implementation.

21

To convert this input data into the form required by the

model, an interface program was developed to adjust

parameters and determine initial conditions at the operating

point for which the input data were extracted. This

approach was taken to avoid the necessity of redesigning

the model for each operating range or specific boiler

design being considered.

C. ASSUMPTIONS

To permit tractable computation, a number of simplifying

assumptions were made in the formulation of the model;

1. Feed water entering the drum mixes thoroughly with

the drum liquid.

2. No steam generation occurs in the steam drum except

through mass transfer at the water-vapor interface.

3. There is a uniform distribution of heat flux in the

generating tubes

.

4. The mixture of steam and water in the generating

tubes is homogeneous.

5. Quality varies linearly in the generating tubes.

6. Heat losses to the ambient except through the

exhaust gases are neglected.

7. All downcomers and risers in a particular circuit

have the same length as the average length, and the

shapes and diameters are equal. Also the number of

tubes is the same as in the actual boiler.

8. The slip ratio is 1.0 (no slip).

22

Since the feed enters through a long, horizontal feed

pipe, and the drum liquid is in a state of turbulence,

the first assumption is well justified. Although the

second assumption is not strictly correct during transients

when there is a significant change in drum pressure, and

hence saturation temperature, the effect of steam generated

at the drum wall-liquid interface appears to be negligible

based on an analysis of this factor in connection with

this study. The assumption of uniform heat flux is

recommended by Reference [7] as a reasonable alternative

to a stepwise integration over the tube height. The

assumption of a linear change in quality is a consequence

of the assumption of a linear heat load. For a well

designed boiler, heat losses through the casing are small

compared to the total energy generated. The effects of

any such losses will be reflected in small errors in the

computed heat capacities of the gas and in the heat transfer

coefficients. The assumptions regarding tube geometry are

made primarily for computational simplification. The

last assumption regarding slip is not an essential one,

and higher slip ratios could easily be considered if

necessary to the analysis of a particular boiler design.

In addition to these explicitly stated assumptions, those

inherent in the correlations employed in the model formula-

tion are also considered to have been made.

23

III. MODEL ANALYSIS

A. GENERAL

The model was envisioned as an assemblage of control

volumes for which the rates of energy transfer are

described by appropriate equations to obtain the rate of

change of energy storage. The resulting differential

equations were integrated to obtain the "state" of the

system. In this way, the states can be chosen to have

specific physical interpretations. The system is shown

diagrammatically in Figure 3.

The following control volumes were considered in the

model formulation:

1. Riser tube walls

2. Superheater tube walls

3. Economizer mass

4. Desuperheater tube walls

5. Riser fluid (kinetic energy)

6. Riser fluid (thermal energy)

7. Steam drum water volume

8

.

Steam drum steam volume

9. Water drum

10. Furnace

B. FLUE GAS AND COMBUSTION SYSTEM

The flue gas and combustion system is shown schematically

in Figure 4. Heat is carried into the furnace through the

24

sensible heat of the air and fuel, and the heat released

in combustion. Since the fuel-air ratio is relatively

constant, and the fuel and air have relatively constant

inlet temperatures, the sensible heats were lumped with

the heating value of the fuel. The mass flow rate into

the furnace is given by

and the total heat input is

^ft = Gft < Ho .

The heat transfer to the furnace screen is primarily through

radiation, i.e.,

e = wo. S r&t * v^ fit** * w°\i"^Rl Nil

/oo J V /oo

The heat balance for the mass of flue gas in the furnace is

^ ( Met CeiTai ) - Es - E fti - Q^ CuTZl

where the last term represents the heat carried off by the

flue gas. Heat transfer to the remaining tube banks is

primarily through convection. The heat given up by the

flue gas is given by the general relation

^j*s m A Cp AT

25

and the heat transfer to the tubes may be estimated with

the Grimson Correlation [8]

Since the physical properties in the above equation do

not change significantly over the expected range of

temperature variations, the correlation is used in the

form

fW = K G,T (.T. -Tw )

Since the tube geometry is not known in advance, an n = 0.6

was used as a reasonable average for most geometries found

in practice. The equations for the tube banks were:

1. Superheater

EfU = Gg. Caio. (Tr.2. -Tai)

Tc<u» (Tft.*. v Taj") I X..0

26

2 . Main Bank

3. Economizer

The arithmetic average temperature for the gas was used in

the driving potential AT rather than the log mean

temperature differences (LMTD) , because a comparison of

the results obtained for the two methods indicated the

differences were slight for the temperatures involved and

the simpler average was more computationally efficient.

C. WATER-STEAM CIRCULATION SYSTEM

As is shown in Figure 5, the basic circulation system

consists of the steam drum, water drum or header, and the

riser and downcomer tubes. The driving force for circulation

27

is the difference in density between the riser and down-

comer loops. The pressure loss around the circuit balances

this driving force. For the downcomers, the force balance is

^-^*-3»»'-('^^.^^-f?FZr

for the drum downcomers , and

Tki-T^t - fcwj Whs -(Fj5 -jtJs_+Z7*ZB *iJ

6ws

Djs 2Ajf &*

for the screen downcomer.

For the risers, the equations are

**-**. (*fc +i)£&- ^.^^y^V*,* £

+ fcuj*W+fri£* £

2^/e«/ r*/?r

a £c

Ir* J (6/2c

5s4i 6wiTU-*i.(*fc+D3fc^ **sfflt**

£S

J

';/(W V/?sa^ '^i'A

A

for the screen and main bank, respectively. The friction

factors are calculated from [9]

* •C/.7V -Zlcj Rki )_

28

The friction factors for the risers are multiplied by

Becker's factor [10] to account for two-phase effects

Be i + /to7fi .s&Pdi

.9t

The relationship between riser and downcomer mass flow

rates is given by the continuity equation

Gw'Sr

The average density in the risers is found from

j* y = T

From the assumption that the quality varies linearly, the

density may be obtained as a function of i from

fw=v* +

"tt W -/*«•) *tj

Wm6^< L

Regrouping the terms we get

fti)(vf --gj-*UV4s)+-g-V

29

This expression can be integrated in closed form to yield

fuOJi*Lb

XtVfj

4we

"&J.tr v* +Vf TT^3^vb t V4 -fe-H-i^

Combining terms and simplifying finally yields

'H-a L J

From this result, p is obtained asav

j*v = XtVwt

.

V*fw Hwft

An energy balance on the riser tube banks yields the

quality

30

where VB is the boiling volume, and the last term on the

right accounts for heat added in the non-boiling height

to raise the enthalpy to saturated conditions.

The non-boiling height is obtained from

V

where q is the sensible heat added to the liquid in the

non-boiling height, and q, is the total heat input. The

ratio q /q. is given by

rtw-L- tt»i-

The boiling volume is related to the non-boiling height

by

VB =-^^V

With substitution of the appropriate parameters, the above

equations were applied to both circulation loops.

The mass balance of the water in the steam drum is

—r~ = Gro 0-*o) +• Gs (.I-**") +• Gt>3 v&wj* -Giur~GAt

ws

31

and the energy balance is given by

Since all the incoming feed must be passed through the

riser tubes to be heated, an energy balance on the

downcomers gives

— (_ Gruiy- +• Gl*>S ) |4uiJ.

Solving for HW2 , the downcomer enthalpy, we obtain

HiGun.

32

D. WATER-STEAM HEAT TRANSFER

1. Risers

The heat transferred to the riser tubers is used to

bring the incoming flow to saturation conditions in the

non-boiling height, and then generate steam in the remain-

ing portion of the tube. To permit a tractable equation

set, however, the tube walls were assumed to be at a uniform

temperature, and all the heat was assumed to have been

transferred under fully developed flow boiling conditions.

Since the non-boiling height for the main bank was found to

be small, the assumption was reasonable for that circuit.

The non-boiling heights were higher in the screen circuit;

however, the error in temperature introduced was less than

three percent which was deemed an acceptable level. For

fully developed flow boiling, Tong [11] recommends

0. _ ft ?Sq,* Al- 3

Therefore the heat transfer to the risers was given by

Evj3 = £w3 ro\ (-r«,i -lot)

E.v«M = K«H Pol1

*' 1 CTm3 -Tot)3

The tube metal temperatures were obtained from an

energy balance/

33

Mwu C^ -rr- • E Ri- " Eu*3

for the screen, and for the main bank

M*A aC*-Tr" ER3 "" £wjm

2 . Desuperheater

The Dittus-Boelter correlation [12] was used to

determine the heat transfer from the steam to the tubes, i.e.,

8

Eoj. a ^dxGoo. (.LiwrtO

The log mean temperature difference was

Lmtq = (J&v- To 3}

(Tdi. - 1W)_("n>3 -Tws)_

The energy given up by the steam was obtained from

Eot. *» CdxG-oj. (,Toi -T"o3 )

The heat transfer to the water in the drum was

Evul. — VCwx (,lw\y -Tioi)

34

The metal temperature was obtained from the energy balance

qTms

at

3. Economizer

The Dittus-Boelter correlation gives the heat

transfer from the tubes to the water as

EvOi - VCtol Gtul* L*\Ti>

LTVW15 =

In.

The heat absorbed by the water was

4 . Superheater

The heat transfer to the steam was given by

and the heat transferred from the metal in the tubes

was

35

- r '°

L(V\tD a

\n

Tot. — Tqi.

T«y\x -To*,

The metal temperature was found from

I^C*-^-- Bm.-« c»i

E. PRESSURE DROP CALCULATIONS

For turbulent tube flow, the pressure drop is given

by

Now

a? - k v„ ?- -££

'mft?««w

so

AP - * VB -(̂XV

Lumping the constants we get

36

r 7-

A? ^ C

Therefore the pressure drops in the superheater and

desuperheater were given by

70*4

and

"Pbx-^l- C- -^fbaX

The average densities were found from the ideal gas law

under the assumption that the temperature variation can-

be neglected, i.e., density is a function of pressure only.

This assumption is motivated solely by the need for compu-

tational efficiency. It is reasonable for the desuperheater

since the temperature excursions there are small. Although

errors are larger for the superheater density values, they

are still within accuracy overall limits for the model.

The flow through the throttle value was given by

Gtoh - Cj"?^ Ve.*T

37

F. EQUATIONS OF STATE

The following equations, obtained from Reference 113],

were used to determine state properties. Within the range

of pressures for which the model is valid (300-1500 psi)

,

the results were within a few percent of tabular values in

the worst case.

o _. — *-

Y;. k38 - const >4^ + l\3XE-S' I s-t

— V18bE- 8 Te^t

38

IV. DETERMINATION OF CONSTANTS AND INITIAL CONDITIONS

A. GENERAL

For the model to be useful, it should be possible to

obtain the necessary constants and initial conditions from

the data supplied in the boiler Technical Manual augmented

with reasonable engineering estimates and tabular data from

standard handbooks.

The primary items of interest are heat transfer coeffi-

cients and initial conditions such as steam flow rates, inlet

and outlet temperatures, circulation rates, etc. While

some of these were directly obtainable from the boiler

Technical Manual, others such as tube wall temperatures

and riser exit quality were not. Therefore, a program was

developed to permit the user to enter known data elements

from the Technical Manual and other sources, and to obtain

as an output the necessary values for the constants and

initial conditions to ensure static balance at the speci-

fied operating point.

The basic premise under which the program operates

is that the model equations with all derivatives set to

zero form a determinant set with the addition of several

relations which apply under equilibrium conditions. These

relations are:

a. Riser and downcomer mass flow rates in

each circuit are equal.

39

b. Total steam flow from the boiler equals

the incoming feed flow rate.

c. Total heat transfer to the incoming feed

equals the heat transfer to the screen and the

main bank, and the heat removed from the steam

passing through the desuperheater

.

d. The net mass transfer at the steam liquid

interface in the drum is zero.

B. PROGRAM EQUATIONS

The total heat input to the boiler was given by

jE.$ • Ue*T RsLftAst QB^/sec-^) * F*iu>*ce. Volume (.h 2)

If the sensible heats of the oil and air are lumped with

the heating value of the fuel, the heating value is

Bo s E& /Gs

The heat absorbed by the furnace screen at steady state

was calculated from

H.p.1 * FufcHAct HeAT ^fcsoa?W C"Btw Isec -ft*)

40

Since the flue gas temperature and the screen tube wall

temperatures were provided, the heat transfer coefficient

for radiant heat transfer to the screen could be determined

from

This result holds for the conditions reported in the

manufacturers technical manual. Degredation due to age or

fouling must be accounted for through the use of appropriate

correlations.

With the enthalpy of the feed water at the economizer

outlet and the enthalpy of the steam leaving the dry pipe,

and the change in enthalpy of the steam flowing through the

desuperheater , the heat transfer to the main bank was

calculated from

E&5 * Groi (^t>i-^ w4N

)- e^~ Gt>i ^ HSHeuT -HWo.r) .

The metal temperature of the main bank risers were obtained

by calculating the constant

£>kOd — Amb1.1 &X* 10

•

and solving the heat transfer equation

41

Tm3 *^ ECS / K^M ?6i

3f +-TD1

The specific heat of the flue gas passing the main bank

was

and the unknown constant in the gas side heat transfer

relation was determined from

Kc? £fc3 / G^ (Tk«.3 -TV3)

In a similar manner, the specific heat of the furnace

flue gas is

Cat ^ C eo - £<vO / (Sii.Tai

and the water side heat transfer coefficient is

i<u* - £*.!. / T^ 3

(rm -Toi

)

3

m

The heat transferred in the desuperheater was:

42

With this value and the temperature difference the specific

heat of the steam was computed from

Cfci. » Eoi. / G-ol (Tea -~T"&0

The heat transfer coefficient was calculated from the

Dittus-Boelter correlation 111]

*»-K^(i#H'V*

The log mean temperature difference was

almt^ £oy^OJ.^ 62_

and the metal temperature was determined hy

"Tiv\y = Ciai-Qio»^/Cl-«^

where

;

§« <=xp { i-rwTD/^-p^^.-rpj)!

With the metal temperature, the water side heat transfer

constant was obtained from

Ku>0. = Eot / CT(v\s — Tuii )

43

Analysis of the Economizer is more complicated since it is

a multipass heat exchanger with finned tubes. Additionally,

since we are concerned with energy storage within the metal

of the economizer, the internal and external heat transfer

must be considered separately.

The heat transferred was given by the change in enthalpy

of the feed water, i.e.,

E.u/1. a &oi £v4u*4 — Muoi)

The specific heat of the water was

As in the case of the desuperheater , the inside heat

transfer coefficient was calculated from the Dittus-

Boelter correlation as

From this the LMTD was obtained as

44

Finally the metal temperature was determined from

The outside heat transfer constant was

KR4 « Etoi /Gr.'4,

CToAi -T*t)

where

T** 3- Ifea^

The specific heat of the flue gas passing the economizer

was

£-&i = Ewi. / 6r. C > rc-M -Trw}

The superheater heat transfer was obtained from the change

in enthalpy of the steam, i.e.,

E^» 6H(« IHigr . UoO

With this value and the known metal and gas temperatures,

the specific heat of steam, the specific heat of the flue

45

gas passing the superheater, and the inside and outside

heat transfer constants were determined as

where:

and

Cm. = Ebl/GM. CTot-Toi)

Cfti^m Eoi/Ga C t<ii -Taj)

Txn. -Tt»t

'-fe^rl

T«A1 - CTdi +T(ij) /x-o

The superheater and desuperheater pressure drop constants

were evaluated from the known equilibrium pressures as

46

Similarly, the constants used in the calculation of the

average steam densities were obtained from:

c&= (HfM/dktU)

and

c>o* C^*-PfcO JtfL*h,).

Finally the steam value flow constant was computed from

Cj = G&M / (_?0Z fa r)

C. CIRCULATION BALANCE

Since they are not normally provided by the manufacturer,

values for the friction factors, and bend and entrance

loss coefficients must be assumed. The values do not appear

to be particularly critical, and tables found in engineering

handbooks may be used to determine reasonable values for

these parameters.

An iterative procedure must be used to adjust the various

flow values involved to achieve a steady state balance.

Since the riser exit quality for boilers of this type

generally lies in the range of .02 to .04, a starting trial

value for the circulation flow rate may be obtained from:

47

where X is the exit quality, E' is the heat transfer to

the riser, G is the flow rate, and HFG is the heat of

vaporization. With this trial value, the following

balancing procedure is used:

1. Set HW2 (Downcomer Enthalpy) = HW1

2. Calculate HWG = HW2 + ED2/G0"

3. Calculate the riser exit quality:

4. Determine the non-boiling height:

Unto. - V4*fc Cl4u,i - v4coO /(Wtol + X U<3 -Www)

5. Compute the average riser density:

6. Obtain the outlet density:

48

7. Compute the friction factor:

8. Next the riser loss factor is computed:

9. Finally we may calculate G0':

where C100 is the downcomer loss factor.

10. Compare Go" and G0 ' if equal go on, otherwise

update G0

:

Go = &o'-6o + G

and return to step 2.

11. Assume a trial value for Gs (first pass only) .

12. Compute Xs

:

X* = C6-01 - 6-oXc) /C-s

49

13-19 Same as for the main bank, risers. Return to

12 if reiteration necessary.

20. Obtain HW2 ' from:

21. If HW2 1 = HW2 go on, otherwise update HW2

:

and return to step 2.

Upon exit from the iteration loop, equilibrium values

of the flow parameters will have been established. With

these and the previously calculated heat transfer parameters,

the program generates the list of constants and integration

initial conditions required by the dynamic model. The

program listing and a sample output is given in Appendix B.

V. RESULTS AND CONCLUSIONS

A. OPEN LOOP RESPONSES

The output curves for 10% increases and decreases in

throttle valve opening and fuel flow are given in Figures 6-

33. Ramp inputs of approximately 1.5% per second were used

to simulate flexibility test conditions. Only one input

parameter was varied for each run with all others held

constant. The results were similar to those presented in

[3] and [4] insofar as general trends were concerned. Since

the boilers involved were of widely different geometries

and sizes, a quantitative comparison was not possible.

Since CSMP uses only single precision arithmetic packages

and integration algorithms, the high frequency noise in the

outputs is attributable to the roundoff error inherent in

the wide variations in magnitudes of numbers used in the

model, e.g., quality (order of 0.01) and riser mass flow

rate (order of 1000) . In common with the results of [3]

and [4] , the "swell effect" in response to an increase in

throttle opening is negligible. It should be noted that the

swell exhibited in the data of Whalley [3] is more apparent

than real, inasmuch as the scales in his graphs are very

magnified and the rise is actually only 0.01 inches. The

sudden increase in riser mass flow rate shown in [3] is

also not present in the current model.

51

Since "shrink" and "swell" effects are of some concern

to controls designers, an attempt was made to model for

such effects. Four possible causes for the phenomenon

were considered.

1. Homogeneous Nucleation in the Steam Drum Liquid

This effect is caused by a difference between the

saturation temperature corresponding to the actual drum

pressure, and the actual liquid temperature. The super-

heat required for such nucleation is quite high however and

nucleation will occur at the heating surfaces at much lower

superheats. Therefore this was considered to be an unlikely

cause for the effect.

2

.

Nucleate Boiling at the Drum Wall-liquid Interface

The driving force for this phenomenon is also the

temperature difference between the drum surface and the

saturation temperature. Since the temperature difference

will be slight except under large drum pressure excursions,

the impact of this factor should be slight. The Rohsenow

correlation [5] may be solved in terms of a rate of vapor

generation to yield

ii. „ i ^ *I I

3 [U5=M kaV^ [ C» fcf, Pr/1

] V VIt was assumed that the vapor formed would be uniformly

distributed bubbles which would rise to the surface with a

52

velocity given by [14]

ub= iVT§T

which is a conservative estimate since interaction effects

tend to increase the rise velocity. The bubble diameter

is given by [14]

T>- -24* ?~ ,S*

This gives U, as .25 ft/sec. The average liquid depth is

15 inches, so the transit time is ~ 5 seconds. The effect

was modeled crudely by assuming the entrained bubble

mass was 5.0(q/hfg) lbm. The impact of this model on shrink

and swell values was negligible, since no large pressure

excursions were developed.

3. Expansion and Contraction of Varpor Bubbles Entrainedin the Riser Fluid

An attempt was made to model this effect by including

the riser tubes in the control volume used as the basis for

liquid level determination. The equation used was

where Ralx and Ra2x are the average riser densities computed

using the specific volume for the saturated vapor corresponding

53

to drum pressure, while Ral and Ra2 were computed from

the liquid temperature saturation conditions. The

effects were insignificant.

4. Transient Deviation of Riser and Downcomer MassFlow Rates

The small swell effect obtained by Whalley [3]

can be attributed to the temporary increase of riser mass

flow rate over downcomer mass flow rate. The period over

which this imbalance could be sustained is short and would

fail to account for the longer duration of "shrink" and

"swell" effects observed in practice. It may, however

trigger one of the two phase flow instabilities common to

natural circulation loops e.g., flow oscillations [10,13].

The analysis of these effects was not exhaustive, and the

modeling attempts were crude. In the case of the first two,

however, the contribution to swell is probably not signifi-

cant. Modeling difficulties with the latter two effects

precluded any specific conclusions.

B. CONCLUSIONS

As with all simulations, the information available from

the model is extensive. Notably, in this study, main bank

and water-screen circulation values can be separately

evaluated. Hence, the contribution of each of these ele-

ments to overall boiler operational response and efficiency

can be determined.

The model simulates the responses of a Naval boiler

quite well. Unfortunately, open loop data is unavailable

54

for the actual boiler and insufficient information was

available to develop a model of the existing LHA-1 control

system as a basis for comparison studies. As such, however,

the model forms a basis upon which future studies involving

modern control system designs can be established. Moreover,

while considerable refinement of the model is possible,

the advantages of greater accuracy must always be weighed

against increased computation costs. In this regard, the

implementation of more efficient integration algorithms

would be particularly beneficial.

55

, • <] FEED INGDI

TW3HW3

ECONOMIZER

HW4TW4

STEAM

v/ORUM

ORUM .

OOWNCOMER/ /

{>AUX STEAM

FIGURE 1. SIMPLIFIED BOILER SCHEMATIC

56

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TR5

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ER4

FIGURE 4. FLUE GAS AND COMBUSTION SCHEMATIC

59

STEAM DRUM

HNB

WATERDRUM

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APPENDIX A

C ThIS FRCGRAM CALCULATES THE CONSTANTS AND INITIAL CjNCITICNSC FCR a US NAVY D-TYPE pr.ILcP GIVEN THi INPUT DAT* niAINFC PS™C ThE ECILER TECHNICAL MANUAL. STEAM tael'S, ANC STAN3ARC ENGINE^-C !NG HANDBOOKS. THE INPUT TATA AR I ENTERED IN NAVE LIST FORMAT.C NAfELIST DESIGNATIONS AND INPUT NzMCMC* FOLLOWC

CC INCCM:r

C OFFNT CPFftATIKG FC INT (PERCENT ) *

C TCTSTM TOTAL STEAN FLCWILB/HRIC SPFSTM SUPEFHEATEF STEAM FLCW (LB/HR)C CSFSTM DfSUFERHFAT^D STEAP FlCW (IE/HP)C PC«UM DRUM PFESSUcc (PSIG)C SFCT SUPfFHEAT=p CUTLiT TEMPERATL 7C (CEC-F)C SHCP SUPZRHEATE" Ot'TLiT PRESSLRE (PSIG)C CSHCT CESUF-RHEAT-q CUTLET T "MP E R i'U? I <C C C-F)C DSHCP DESUFFPH5AT5P CUTLET FRSSSLP'i (PSIG)C ECCMT ECGNCKIZ C R F?^C INL.ET TcCFSRATLIR = (CcG- c

)

C ECCNOT ECONOMIZER FEEC OUTLET TeMPcRATUR 5: (C C G-F)

C U'TMP AIR INLET "TEMPERATURE TO REGISTERS (FEC-F)C 1ILTMP OIL TEMPERATURE aT BURNER INLET (QEG- C

)

C AI^FLC AIRFLOW RAT = (LP/HR)C 11LFLO CIL FLOW RAT C (LB/HR)C XCSAIP EXC C SS AIP (PERCENT) *

C DRAFT GRAFT LOSS (IN-H20IC TGiSSC FLU C GiS T5r NP r RATURH LEAVING SC^EFN <C n G-F)C TGASSH FLU: GAS T«MP=SATdR= LEAVING SUPERHEATER (CEG-F)C TGASMB FLUE GAS TE^PEFATURE LEAVING MAIN FANK (O^G-F)C TGASEC FLUE GAS TEMPERATURE LEAVING cCGNOMI2"R (DcG-F)C TSCRN SCRF.FN TUBE WALL T EMP~R ATL C E (HEG-F)C TSFhTR SUPEFHEA T ER TUBE WALL TE f- FE F. ATUR' <C

r:G-F)C HPFVOL FEA^ RELEASE (KSTJ/HR/CU FT ojPNACE VCLU'-*E)C FhAS FURNACE HEA T ABSORBTICN (KETU/HR/SQ F

T P40IAKT HMTC ABSORBING AREA)CC NCTE: "PERCEN™ VALUES ARE TO BE LCCGED AS DECIMALS.CC SSCRcENCC 0TL3SC AVERAGE INSIDE DIAMETER OF SCREEN TUBES (IN)C LAVSC AVERAGE LENGTH OF SCREEN TLEE (FT)C NTLBSC NUMBER OF SCREEN TUBESC RHiSSC RADIANT HEAT AESORBING AREA OF FURNACE SCREcN (SC FT)C MASSSC TOTAL WEIGHT of SCREEN TUBES (LB)Cr

C SSPriTRCC AGEASH TOTAL SUPERHEATER HEAT TRANSFER ARFA (SC FT)C MASSSH TOTAL W-IGHT OF SUPERHEATED TUBESCCC StMLbtr

C DTU5M8 AVERAGE INSIDE DIAMETER OF VAIN BANK TUB-!S (IN)C LAVMB AVERAGE: LENGTH PF MAIN BANK TUBE (IN)C NTL6MB NUMBER OG MAIN BANK TUBESC MASSMB TOTAL WEIGHT CG MAIN BANK TUBES (LB)C AREAMfi TOTAL H C AT TRANSFER AREA (SC FT)Cr

C t.ECCNCC DTL3EC INSirr CIAfFTEF OF ECONOMIZER TUB'S(IM)C NPASSE NUMBER OF Tijpg PASSESC NTL2EC NUMBER OF TUBES PER PASSC LTUBEC AVERAGE LENGTH OH ECJNJMIZER TUBE (FT)C MASSEC TCTAL WEIGHT OF ECCNCMIZEF (LE)C

CC $C£SPF

89

cccccccccccccccccc

cccccc

cccr

cc

cccccc

cc

cccccccc

cccccccccccccccccccc

CTLECCLAVDDNTLBCD

SFCRCCR

CTLBFCLAVFDNTL3HD

DMCMCMDMM

DMOL

IECILE"

CSTf-LSTMCfeTPLWTPHNCRHHC«HUTRFIFV

N C 7 E ;

STFEFK

HSFCUTHDSCUTHECINHECCUT1KH2C

( 1)PRH2C(DVSCI-2G( 21KSTM(2 )PRSTM(2)VSCS7M

RSI-GUTPCSCUTRFILE

( 1

NOTES:

AVERAGE DIAf'ETER OF DRUM CCUNCOM-R TLeES (IN)AVERAGE LENGTH OF CRUM OCHNCOMER T UR r (FT)NUMBER OF CPUM DOWNCOM=R TLe=S

AVERAG C IMS1DF CIAMtTER CF FEAC'R CONCCHSfi (IN)AVERAGE LENGTH CF HJ-AD£R CC WNCOMF.R (FT)NUMBER OF HEACER DCWNCOM^RS

CIAMETER OF STEAM CRLN (INILENGTH O c 5TEAM DRUM (FT)CIAMfTSR OF WAT C R DRUM (IN)LENGTH OF WATER DRUM (FT)FZIGFT OF NORMAL WATER LEVEL ABOV" BENCH MARK (FT)HEIGHT OF HEADER (SCREEN) ABOVE BENCH MARK (FT)HEIGHT OF WAT-F. DRUM ABOVE BENCH MA°K (FT)FURNACE VOLUME (CU FT)

CHOICE OF B C NCH MARK IS ARBITRARY

ECONCMIZ1R CUT LET ENTHALPY (BTU/LBM)DESUF rRHEATFR CUTLET ENTHALPY (3TU/LEM)ENTHALPY OF ECONOMIZER. FFEC INLE T (Bfl'/L^M)ENTHALPY OF ECONOMIZER FEEC OUTLET (ETL/LBM)THERMAL CONCUCTIVITY C>= WATER ( S T U/ F R . F"

r. CE G- F )

PRANCTL NUMBER F jR WATcRKINEMATIC VISCCSITY FOR wATER (LBM/Ff-SEC )

THERNAL CONCLiC T I VI TY FOR STEAM ( BTU/HR .FT. C3 G- F)PRANCTL NUMBER FOR STEAMKINEMATIC VISCCSITY FOR STEAM (LB^/FT-JEC)SUPiPHEATER CUTLtT DENSITY (LBM/CU FT)CESUPrRHEATFR CUTLET DENSITt (LBM/CL FT)DENSITY OF FLUE GAS AT TGASSC (LBM/CL FT)

(1) EVALUATED AT AVERAGE ECONOMIZER IcATSR Tc V F ER A tt_ P

'

(2) bVALUATFD AT AVERAGE CE SUPERHEAT ER STEAM T EM F" R ATUR

?

JLCSSESKSCSKSCMKSCCKSCHENTSeENCEMMben:ENTCBENCENTHBEND

CBcDCSCBMBCCDDHD

ROUGHNESS RATICM (SAND EQUIVALENTROUGHNESS FATIC (SAND EQUIVALENT)ROUGHNESS PATIO (SANC EQUIVALENT)ROUGHNESS RATIC (SAND ECLIVALENT)SCREEN T UBE ENTRANCE LDSSSCREEN TUEE BEND LOSS

MAIN BANK FNTPANCE LOSSMAIN BANK EEND LOSS FACTCRCRUM OOWNCCMER ENTRANCE LCSS FAC T ORDRUM DTWNCOcR BEND LCSS FACTORHEADER DOWNC<"Mcp. ENTRANCE LCSS "=AC T OFHEADER DCWNCCMER dENC LOSS FACT1R

) FCR SCREEN TU B'"

3

CF MAIN EANK TUEEFCF DRUM DCKNCCM r

i

FCF F-ADER CCWNCC

IMPLICIT REAL(A-Z)INTEGER I

INTEGER J, K.M.NINTEGER NPASSc

90

DIMENSION T>20< 20),CPASS (20)

CcFINE NAMSLISTS

NAM:1DSK)2TCASNAMEnamenameNAMENA» =NAMENAM :

.

nameSFLRVNAME1KF20NAME

$Bef*CnameNA*Enan:NAMEN4NFNAMENAMENAMENAMENAWE$RW,F

LIST/INCCNDP,=CONIT,ECSF,TGASM3,TLIST/SCREENL!ST/S°hTR/LIST/M'ieANKLIST/EC ON/0LIST/C^SPH/L IST/D^MDCSL 1ST/FORDCRLIST/BOILERCLLIST/THERMO,PRh2C,VSCHLliT/LOSSESME.EN'TDC.BELIST/ INC0N1L1ST/INC0N2L IST/IMC0N3LIST/C0NST1L1S7/C0NST2LIST/CTNST3LIST/CDNST4LIST/CDNST5LIST/CQNST6L 3ST/0UTPLTW1.I-W2, FW2,

/CPPNTCNOT,ACASEC,/DTUBSAPFASH/LTUBfTUBEC,ciuens/CTU3C/DTUBH/CSTMC

,TCTSTMIPTMF.3TSCRN.TCLAVSC,MASSSHE.LAVMBNPASSF,•NTUBOSC ,LAVGOD,LiVHDM T LSTMD

,spnstm,csfstm.,pppum,shct,shcp,csh:t,ilflo,airflq,xcsa!r ,cpaft .tgassc ,

sphtr.frfvcl.^has.ciltcp, ntubsc,ft-assc,masssc

'•s5m6, ap.eane,e:-g,mass c

c

l3DS,AF r ACS,MASSCS

N7U3MB ,N*!NTU3;C ,LTL!,NPASSDtLll,NTU30C, NTUbHDM.DWTRDM.UTRDM, WNCPf»HHORfHiTRCM

/HSHOUT2CKSTM/KSDSC t

NCDD.PN/TRIO.T/HMlOi M/ rRA10,/KR,KS ,

/OORrHN/hXS.M'R/CRl.CC/KR4.Z1/Cll ,C7/ER1 ,EFhk4,HW6

,HfS,PPSKSCNTHD,M10,W10,CPA2KCR ,

8R,C1, VR1A,C,Z2,,CSL2, C P

,HFG

OUT,HTM, VSB,KSDBUJOHT M2D,VROJ,O.G-DlK.DS.APS, 13,VS,VR2.CRZ3,Z4, KWl,3.ER4

ECIN .l-ECOUT,CST"!,K£l-GU'r ,RDSCLT,RFLLEDD,KSCFC,EN T SC,°fN:SC,FMfE,CTM30»TM40,TM50 t GCF.C,GSRCfC>CC,QXSCHW6 ,C-W2,TW3, GL,CE ,GC2 ,GC10, V : KTE»RAl>CfRA2X0fGWFC.GnSCR,LR»CP,LR1,AS,LS,CS»LS1»LCR,ADRS»HNBS iJOS »MM , Mf>2 ,MM3,MM4,MM5 .FX=iNCR, VCP ,L01R, LC1S3tCDltCC2fCWtCM,KCl,KD2tKBltK!S2,KR;,Z5i Z6,Z7,Z8,HW2,GCia,CZ2»C8,C9,C10Kw2,NWE,KW4,HC, -02,GC,GS,XT,XS ,RA1 ,RA2,R0, PS,

RrAD(WRITERFAO(WRITEWFITEREAD(WRITEWRITERtSC(WRITEWRITEREAC(WRITEWRITEREAC(WFITEWRITER£*C(WRITEWPITEREAO(WPITEWRITEREAD(WFITEWRITEREAC(WRITEWRITER£AC(WPITEWPITE

CALCUL

- t

<ec- i

(6(6',

<6(6t- »

(6(65,(6(6c- t

(6UC- T

(c(65,(6(6C- »

<6(65,(6(6c- t

(6(eAT

INC 3,INC

,601,SCRSPHT,601,SPHM"NBA,601,MN3ECON,601,SCODESP,601,DESCRMO,601,DRMHORO,601,HDRBOIL,601,BCITHER,601,ThELCS3,601,LCSICN

N3)CNO)EN))

EEN)R))

TR)NK))

ANK))

)

N)H))

PH)CR))

OCR)CR))

CCR)FR))

LER)MO))

RMO)ES))

SES)CF PRELIMINARY CONSTANTS

PI =3. 1415927G = 22 .2CM*. 11DRAIO^O.O0FA2C=0.OZER1=C.CVENT=CPPNT

91

KF=KSCfBKS=KSCSCKCR=KSCODKCS=KSOhDZ1==N7CCZ2 = BEf>CCDZ3=SN7MBZ4 = BEf*Cf-'B25»SMSCZ6=3ENCSCZ7=:N7FCZE=BEr*DI-DPC1=PCRIM+14.7FM = EX P { 0. 26452 *AL0G< PCD <4.467C6)hFG=9 22.15-C.40 516*FDl+1.717E-0 4*PCl**2FD1 = FV«1+HFGTC1=EXP(.22151*AL0G(PC1)+4.77122)GB=aiLFLC/3600.CGL=AIPFLC/360C.C7F10=7GASSC7P10=7SCRN7P20=7SPhTR7P2=7F107R2=7CASSH7R4=7GASMB7R5=7GAS5CGCl=TCTSTM/3603.0GC1£*CC1*.0001GD4=SFhS7K/2600.0TC2=SFCTPC2=SFCP+14.77C2=DShCTPC2=CSHCP+14.7GC2*CSHSTf/3600.0Th3*EC0NIT7V<4 = ECCNC7EB*HRFVOL*FURVC 1*1000. C/3 600.0E P 1 = FF A:S*RHASSC*1000.C/ 2 600.0LS1=LAVSCLS=MIBSC*LAVSCCS=GJIBSC*NTUBSC/12.CAS = FHCTUBSC**2*NTUBSC/( 4.0*144.0)VS=AS*LAVSCMKlaM/SSSSCft*.2 = f ASSSHLP1=LAVMBIR=N716V3*LAVK3DR«0TLEME*NTUeME/12.0ARaPI*DTUBMB**2*NTUBfB/(4.0*144.0)VP = ARUAVMBK N3 = MSSMBmm4=massecws = *assdsLCR»lAVDD*NTUBOCLDS=LAVHD*MTUBHCCCP»CTUBDD*NTUBC0/12.QDDS = C7LBHD*MUBFD/12.CACR = NTUBDD*tPI* (C7UBDC /2 4 .0 )**2 )

ACS=N7tEHC*<PI*<CTUBFC/24.0)**2)VCR=(PI*DSTKOM**2/(4.0*144) )*LSTMDNVNCR = (P1*CWTRCM**2/(4.C*144) )*LW7R0MFV.2 = FECINFV«4 = FECCITGR-GB *GLRV>=6 3.8-0.01781*TD1 + 1.132E-05*TC1**2-6.786EVF=1/RWVFC=524.0/PCl-.lRD1=1.C/(VF+VFG)PC2=RSFCUTPC3=RCS0UT7hl=TClGW2 =GdNR1=PFLLE*FURV0L

4.219S-C8*PD1**3

08*7C1**3

92

ccc

ccc

cc

cc

ccc

c

c

c

c

cc

c

c

c

c

c

c

c

CZ2=CSTMDM/12.C)*LSTMCN* (1.0/12.0)

CALCULATE LCWER HEATING VALUE OF FUEL CIL

HO=EB/GB

CCNPLTE STOICHICNETRIC AIR/FUEL RATIC

CSL=(1.0-XCSAIR )*GL/GB

RACIATION HEAT TRANSFER COEFFICIENTKFl=EFl/( ((TRIO -«460.0 )/ 100.0 J**4-( (TM K+460. )/ 10C.0)**4 )

CCNPUTE HEAT TRANS CC R TO THE CAIN TL5E BANKeP2=CCl*(HDl-HW4)-GD2*(HSFOUT-H0SOUTI-ERl

COMPUTE MAIN BANK AVERAGE METAL TSMPEFATUR5

KV>4a(l.C/l. 782?C6)*ARE^METN20=(ER3/(KW4*FD1**(4. 0/3.0) ))**(! C/E.0J+TD1

CCNPLTE VAIN BANK GAS SICE FEAT TRANSFERKP3=EP3/((ITP2+TR^)/2.G-TM30)*GR* A .6)CCNPU7E SCREEN EANK WATER SIDE h£AT TSANS C

KW2=£Pl/( (PD1** (4.0/3.0) )*17M10-T01 )**3)HEAT TRANSFER TC THE SUPERHEATER6R2=GC1*(HSHCUT-HD1 )

COEFFICIENT

PR CCEFFICIENT

SUPERKR2 = EHEATER4 = CC^PU

FUCR1= (

suCP1A =

CC1 = EMA

• CP2 = EEC

CR2 = E

SPCh=ERCCNPUCEC1 =

AREAEKU1=A$PRH2CLK1CEXXXX1Tf43 =

KR4 = ESFECIED2MCC2=EDESUPDCSH1HXFRCSPPSTNCONPLLfTDCDETERXXXXCTM50 =

DESUPKW2 = ECESUPKC2 = ESUPERLMTDSKU = ECALCU

HEATERR2/( ((TRANSFCl*(HwIE SPEPNACEEE-ER1FERHEA£R2/(GF2/(GDIN BANP3/(GRCNCMI Z

R4/(GRECIF1C^i / (GDITE AVECTUEECC=NTU3REAEC*** .4C=ER4/1=EXP((Tk3-TR4/(GRFIC HEGC2*(HC2/(GDERHEAT=DTUBDS=(KST**.3TE THES=SC2/MNE T2=EXP((SHGT-ERHFATC2/(TMERHEATC2/(GDHEATERH=(TC2R2/(GQL4TE T

GAS SIDE HEATTR2+TR3)/2.C-TSR TC THE ECOM4-HWE

)

CIFIC HEATS OF

TRANSFER COEFFICIENTP20J*GR**.6)OMIZER

FLUE CAS

*GR))/ ( (TD10-8C.0

)

TER<5*(TP2-TR3) )

1*(TC2-TD1 )

)

KMTR3-TR4)

)

ER(TR4-TR5) )

HEAT FOR WATER*(TW4-TW3) I

RAGE HEAT TRANSFER COEFFICIENT/12.CEC*L1UEEC*PI*C(KH2C/DcCl**l.

EC1*NPASSE8)*.02 3*(4.C/IPI*VSCH2C*NTUBEC))**.8*

(KWHGD1**. 6)(TW4-TW3) /LNTCk4*XXXXll) / (1.**.6*( (TR4+TR5AT OF STEAK ATSHOUT-HDSCLT) )

2*(SH0T-DSHCT)ER ST CAM SICES/12.0M/DCSHl**1.8) *

LCG(HXFHE U(SHOXXXXER W50-TPR S2**.STIE

-TCI1**.HE T

NEANRCS*AESUPFT-DSHC2*DSATEFWl)TEAMC*LMTAN SI)/ALO6*LMTHFOTT

TFMPPEACSPHEATOTJ/LHCT )/SICE

EC)O-XX)/2.AVE

)

HEAT

.023

EPAT)

ER MMTDD(1.0HEAT

XX11)0-TV40) )

RAGE CESUPERHEATER TEMPERATURE

TRANSFER COEFFICIENT

*(4.0*CC2/(PI*VSCSTN*NTUBCS))**.8*

URE CIFFERENCE FCR THE DE SL F ERH E AT ER

ETAL TEfFERATURES)— X X X X " )

TRANSFER COEFFICIENT

SIC = HEAT TRANSFER COEFFICIENTCCS!CE HEAT TG ( (TM20-TDSH)LE VALVE FLCW CCNSTANT

RANSFER CCEFFICIENTCI )/<TN20-TD2) )

93

C11=GC4/(PD2*VENT)SLPERt-cATER QLTL?.T DENSITYce=( fci+pp? )/(r:i+pc2 )

C1C*(FC2*PD3>/<PD2+RD3)RAVSMJRC1+RD2) /2.0RAVCS=(RC2+RJ3l/2.0C7=( FC1-PD2J*RAVSH/GC1**2CS=(PC2-PD3)*RAVCS/GD2**2

CIRCLLATICN SYSTEM CALCULATIONS

CC CCMPUTE LOSS COEFFICIENTS FOR DCWNCCfERSC

FOP* (l.C/tl. 74-2. C*ALCG10 (KSDOO))J**2C100=(FCR*LCR/OCR+Z1*Z2+1.0)/(2.G*ACR**2*RW)FCS=(1.0/(1.74-2.0*ALCG10(KSJhD)))**2C1C1*(FCS*LDS/DDS+Z7+ZE+1.C) / (2.0*ACS**2*RW)

C ITERATIVE PROCECURE FCP BALANCING CIRCULATTCN LCCFSCC SET INITIAL TRIAL VALUESC

GC=2CC.OGS=20C.Ohh2=HH-EC2/G0

CC START FIRST ITERATICN LOOPC1 Fk>6 = Fk2+ED2/GO

XC=( ER3-GO*(hhl-HW6)

)

/(G0*HFG)HXF = t-NCRM-HhTRC^HNeR=HXR*AMAXH (HW1-HW6) »0.0)/( (HWl +XC*HFG)-f-h6 I

LXR=H>R-HNBRRA1= ( (LXP./( XO*VFG) )

i ALCG((XO*VFG)/VF«l."))+RW*HNER)/HXRROl.C/l VF+XO*VFG)FR = ( 1.0/ ( 1.74-2.0*ALOG10(KSDM3J I )**2*< 1.0+16C78 .58* (XO/FC1) **.?fc

1

. PSIMB = (FP.*LR/CR-»1.0)*FAl/(2.0*AR**2*RC-**2)+Z5/(2.CHAR**2*RW) +$Z4/(2.C*AR-*2*RC)GOX=SCRT((RW-RA1J*HXR*G/(C130+PSIMB) )

400 FCRMAT(1H0,G15.5)C IF CHECK VALUE EQUALS INITIAL GUESS, CCNTINU*?; ELS C REITERATE

IF (AeS(GO-G0XI.LT..Ol (GO TO 2GCMGCX-GC) /2.C + G0GC TQ 1

CC START SECONC ITERATICN LOCPC2 CCNTINLE

XS=(GC1-G0*XC)/GSHXS=HNORM-HFCRhNBS*hX$*AMAXl( (HU-HH2) ,0.3)/( lhWl + XS*HFG)-HW2)LXS=HXS-HNBSPA2=((LXS/(XS*VFC)>*ALCG((XS*VFG>/VF+1.0)+RW*FNES)/<HXS)RS=1.C/(VF+XS*V C G)FS=( 1.0/(1. 74-2.C*AL0G10<KSDSC) ) J **2* ( 1.0+16078 .56*

(

XS/FC1 )** .96

)

PSISC = (FS*LS/DS-«1.0)*PA2/(2.0*AS**2*PS**2)+Z5/(2.C*AS**2*Rfc) +

$Z6/(2.C*AS**2*RS)GSXsSCRT({RW-RA2)*HXS*G/(C101+PSISC J J

C IF CHtCK VALUE EQUALS INITIAL GUESS, CONTINUE ELSE REITERATE.IFfABS(GS-GSX) .LT..01JC0 TO 3GSMCiX-GS)/2.04GSGC TC 2

C

C START THIRO ITERATICN LOOPC

2 hk2X=(GW2/(GS + GC) ) * (H Y^-HV,\ ) +HW 1

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4 CCNTINLE

94

CALCULATE INITIAL CCNCITICNS

60C

6C1

GORO =

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WRITEfcfmaWRITEWRITSFCR^AWR ITEWRITEWRITEWRITEWRITEWRITEWRITEWRITSWRITEWRITEWRITEWRITEWRITEWRITEWRITEWRITEWRITEWRITEWRITEWRITEWRITEWRITEWRITEWRITEWRITEWRITESTCPENC

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(6,CONST6)(6,600 )

(6,0LTPUT)(7.INC0N1)(7,INCON2l<7,INCCN3)(7,C0NST1 )

(7,CGNST2)(7, CON ST 3)(7,CCNST4)(7,CC.MST5)(7, CON ST 6)

95

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LIST OF REFERENCES

1. Rydland, K. , Oyvang, K. , and Gloersen, T. C. , "AMathematical Model for Dynamic Analysis of a Boiler,"International Marine and Shipping Conference (IMAS 73)London, England, June 1973.

2. Haraguchi, 0. and Akasaka, N. , "A Mathematical Modelof a Main Boiler for a 60,000 KW Container Ship,"International Marine and Shipping Conference (IMAS73) London, England, June 1973.

3. Whalley, R. , The Control of Marine Propulsion Plant ,

Ph.D. Thesis, University of Manchester, Manchester,England, 1976.

4. Chien, K. L. , and others, "Dynamic Analysis of ABoiler," Transactions of the ASME, V. 80, p. 1809-1819,November, 1958.

5. Rohsenow, W. M. , and P. Griffith, "Correlation ofMaximum Heat Flux Data for Boiling of Saturated Liquids,"AICHE-ASME Heat Transfer Symp., Louisville, Ky., 1955.

6. Miller, M. L. , Multivariable Control of A Marine Boiler ,

Masters Thesis, Naval Postgraduate School, Monterey,Ca., 1978.

7. Babcok and Wilcox Company, Steam , 1972.

8. Grimson, E. D. , "Correlation and Utilization of NewData on Flow Resistance and Heat Transfer for CrossFlow of Gases over Tube Banks," Trans. ASME, Vol. 59,pp. 583-594, 1937.

9. Schlichting, H. , Boundary Layer Theory , 6th ed.

,

McGraw Hill, 1968.

10. Becker, M. , Hernborg, G. and Bode, M. , "An ExperimentalStudy of Pressure Gradients for Flow of Boiling Waterin a Vertical Round Duct," Part II, AktiebolagetAtomenergi, Stockholm, 1964.

11. Tong, L. S., Boiling Heat Transfer and Two Phase Flow ,

p. 118, Wiley, 1965.

12. Dittus, F. W. , and Boelter, L. M. K. , Univ. of Calif.(Berkeley) Pub. Eng. , Vol. 2, P. 443, 1936.

99

13. Oak Ridge National Laboratory Report ORNL-TM-4248ORCON 1: A FORTRAN Code for the Calculation of aSteam Condenser of Circular Cross Section, by J. A.Hafford, July 1973.

14. Hsu, Y. Y. , and Granam, R. W. , Transport Processes inBoiling and Two-Phase Systems , p. 34-39, Hemisphere,1976.

100

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Documentation Center 2

Cameron StationAlexandria, Virginia 22314

2. Library, Code 014 2 2

Naval Postgraduate SchoolMonterey, California 93940

3. Department Chairman, Code 69Mx 2

Department of Mechanical EngineeringNaval Postgraduate SchoolMonterey, California 93940

4. Associate Professor Thomas M. Houlihan, Code 69Hm 5

Department of Mechanical EngineeringNaval Postgraduate SchoolMonterey, California 93940

5. Curricular Officer, Code 34 1Department of Mechanical EngineeringNaval Postgradute SchoolMonterey, California 93940

6. LCDR Wallace P. Fini 2

Commander Naval Forces MariannasFPO San Francisco, California 96601

7. Associate Professor Robert H. Nunn, Code 69Nn 1

Department of Mechanical EngineeringNaval Postgraduate SchoolMonterey, California 93940

101

ThesisF438c.l

: 78908F| ni

A computer simula-tion of a naval boiler,

Thesis

F438c.l

178906

Fini

A computer simula-

tion of a naval boiler.

lhesF438

A computer simulation of a naval boiler.

Hit II HUM II Ml II HI M I '» '

3 2768 002 00159 6

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