AD-A09A 567 NAVAL POSTGRADUATE SCHOOL IED.3 … AD-A09A 567 NAVAL POSTGRADUATE SCHOOL MONTEREY CA ... A method is presented to analyze ... * Projected annual inflation rate for aluminum

AD-A09A 567 NAVAL POSTGRADUATE SCHOOL MONTEREY CA F/B 20/13OPTI M IZATION OF A LOW DELTA T RANKINE POWER SYSTEM. (U)DE C ERCDCAUE

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THESISOPTIMIZATION OF A LOW A T RANKINE

POWER SYSTEM

by

Raymond C. Schaubel

December 1980

Thesis Advisor: R. H. Nunn

Approved for public release; distribution unlimited.

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81 5 04 148

S9Cum1TV CLASSIFICATION OF THIS5 PAGE Ge..1O D ae d' ____________________

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Otmization of a Low AT Rankine Fa aster's hesis,C ;Power System . 11 1980

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Naval Postgraduate SchoolMonterey, California 93940

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17. DIITRIBUTION STATEMENHT (00 Me 81116~ 4111141001 IN Week 0 15. II fV R E I e"If RePO

16. SUPPLEMENTARY NOTES

I(. C V WORS (Conmoe e " wpe #1I .eeeew md e*v or Week inM

OTECRankineCOPES/CONMIN

20. Ainet C? (CS, M Me@" od& of .,eee dd 9~1VU~ 6F 6ee1404e11-. The Ocean Thermal Energy Conversion (OTEC) uses the low

thermal energy potential available from ocean temperaturegradients. A method is presented to analyze such systems and,for this purpose, a comprehensive simulation is developed.The simulation includes parasitic power requirements, losssesdue to interconnecting lines, and heat exchanger pressuredrops. Cost functions are included and numerical optimization

Iis emploed to obtain 2Ljj Alla ~in a~Ainnm~im

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\ BLOCK 20. ABSTRACT (Continued)

The analysis is converted to a computer code and coupled tothe COPES/CONMIN optimization code to facilitate a fully-automated design where the computer makes the designdecisions and perfoymance trade-off studies. The finalproduct is an optimum power system module design for thedesignated net electrical output required and the speci-

4 Lied system and design constraints.

Preliminary results are presented for a range of systempower levels. Optimum designs are obtained and comparedfor systems in which either titanium or aluminum tubes areused in the heat exchangers.

Accer~son Fo r

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unannfounnod

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147#3

Approved for public release; distribution unlimited.

Optimization of a Low AT RankinePower System

by

Raymond C. SchaubelLieutenant Commander, United States NavyB.S., United States Naval Academy

Submitted in partial fulfillment of the

requirements for the degree of

MASTER OF SCIENCE IN MECHANICAL ENGINEERING

from the

NAVAL POSTGRADUATE SCHOOLDecember 1980

Author $

Approved by: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Thesis Advisor

Co -Advisor

Dean of Science and Engineering

3

,-40 4-

ABSTRACT

The Ocean Thermal Energy Conversion (OTEC) uses the low

thermal energy potential available from ocean temperature

gradients. A method is presented to analyze such systems and,

for this purpose, a comprehensive simulation is developed.

The simulation includes parasitic power requirements, losses

due to interconnecting lines, and heat exchanger pressure

drops. Cost functions are included and numerical optimization

is employed to obtain optimal designs based upon minimum cost.

The analysis is converted to a computer code and coupled to

the COPES/CONMIN optimization code to facilitate a fully-

automated design where the computer makes the design decisions

and performance trade-off studies. The final product is an

optimum power system module design for the designated net

electrical output required and the specified system and design

constraints.

Preliminary results are presented for a range of system

power levels. Optimum designs are obtained and compared for

systems in which either titanium or aluminum tubes are used

in the heat exchangers.

4

4

B

TABLE OF CONTENTS

I. INTRODUCTION - 11

A. BACKGROUND -- -i- -------------- 11

B. OBJECTIVES -- ---------------- 13

C. OVERVIEW OF THE OTEC POWER SYSTEMANALYSIS -- ----------------- 14

II. POWER CYCLE DESCRIPTIONS -- ----------- 17

A. INTRODUCTION -- --------------- 17

B. IDEAL OTEC RANKINE CYCLE -- --------- 17

C. ACTUAL OTEC RANKINE CYCLE - -------- 19

III. EVAPORATOR AND MOISTURE SEPARATOR - ------ 22

A. INTRODUCTION -- - - ------------- 22

B. ANALYSIS OF THE EVAPORATOR ANDMOISTURE SEPARATOR -- ------------ 24

IV. PARASITIC LOSSES -- --------------- 62

A. INTRODUCTION -- --------------- 62

B. ANALYSIS OF PARASITIC LOSSES ------------ 65

V. TURBINE AND ELECTRICAL POWER -- --------- 87

A. INTRODUCTION -- --------------- 87

B. ANALYSIS OF THE TURBINE AND ELECTRICALPOWER REQUIREMENTS -- ------------ 89

VI. CONDENSER - ------------------ 93

A. INTRODUCTION -- --------------- 93

B. ANALYSIS OF THE CONDENSER - -------- 94

VII. NUMERICAL OPTIMIZATION - ------------ 117

A. INTRODUCTION - --------------- 117

s

B. COPES/CONMIN - --------------- 118

C. DESIGNATED DESIGN VARIABLES, CONSTRAINTSAND OBJECTIVE FUNCTION - -I--------- 122

VIII. CONCLUSIONS AND RECOMMENDATIONS - -I------ 124

A. CONCLUSIONS - -i-------------- 124

B. RECOMMENDATIONS - -I------------ 126

TABLES - ----------------------- 128

APPENDIX A: SAMPLE INPUT DATA FOR OTEC ANALYSIS - - -150

APPENDIX B: SAMPLE OTEC ANALYSIS OPTIMIZATIONOUTPUT DATA - -------------- 152

APPENDIX C: SAMPLE COPES OPTIMIZATION AND

SENSITIVITY ANALYSIS DATA - ------- 157

NOMENCLATURE AND OTEC ANALYSIS CODE - --------- 160

LIST OF REFERENCES - ----------------- 231

INITIAL DISTRIBUTION LIST - -------------- 233

6

,--t

LIST OF FIGURES

1. Power System Sequential Analysis- ---------- 16

2. Idealized OTEC Rankine Cycle -- ----------- 18

3. Actual OTEC Rankine Cycle- -- ----------- 20

7

LIST OF TABLES

1. OTEC Power System Comparison (Titanium TubedHeat Exchangers) - ----------------- 128

2. OTEC Power System Comparison (Aluminum TubedHeat Exchangers) - ----------------- 134

3. OTEC Heat Exchanger Comparisons (Titanium Tubed)- -140

4. OTEC Heat Exchanger Comparisons (Aluminum Tubed)- -145

I. 8

PARTIAL LIST OF SYMBOLS

A heat transfer surface area

A, tube bundle frontal area

A f free-flow area

C? constant pressure specific heat

diameter

E power

friction factor

F correction to LMTD

mass velocity

acceleration of gravity

conversion factor . 2)

t h specific state point enthalpy

h average heat transfer coefficient

K thermal conductivity

Km mean salt water compressibility

L tube or pipe length

t mass flow rate number

Nt number of heat exchange tubes

Re Reynolds number

P static pressure

9 heat transfer rate

S specific state point entropy

T temperature

LMTD log mean temperature difference

9

i~

LI overall heat transfer coefficient

U specific volume

V velocity

X quality of working fluid

Z elevation

E heat exchange effectiveness

efficiency

density

1- absolute or dynamic viscosity

10

2!

I. INTRODUCTION

A. BACKGROUND

Ocean Thermal Energy Conversion (OTEC) is a concept

using the low thermal energy potential available from the

ocean temperature gradient that exists between warm surface

ocean water and cold water in deep ocean regions.

The idea of converting the stored ocean energy to useful

power originated with French physicist Jacques d'Arsonval in

1881 [Ref. 1]. It was nearly a half-century later that the

technical feasibility of ocean thermal energy conversion

could be demonstrated. In 1926, George Claude used an open

cycle power system to extract heat from surface water for

indirect conversion of the thermal energy of a working fluid.

Operating at a low pressure the working fluid was used to

drive a turbine providing electrical power generation.

Though Claude's limited power system produced only

22 kilowatts of electricity while requiring approximately

80 kilowatts of power to drive its equipment, it stirred

the scientific and research community to consider the

attractiveness of ocean thermal energy conversion [Ref. 2].

Claude called for immediate action on his ocean thermal

power system, because of the Federal Oil Conservation Board's

dire predictions that the United States had only six years

of oil production remaining. Obviously the dire predictions

ascribed to by the Federal Oil Conservation Board did not

11

come true, but the oil crisis of that period heightened

scientific interest in extracting energy from the ocean.

Now, 55 years later, the United States is faced with an

energy crisis because of increasing industrial and social

dependence on foreign petroleum. Dwindling supplies and

erratic price hikes have rekindled interest in ocean thermal

energy conversion, since it utilizes an inexhaustible supply

of fuel.

Currently, the United States Department of Energy is

attempting to develop the necessary technology and demon-

strate the feasibility of large-scale OTEC power systems.

However, there are major engineering development problems

which must be solved before OTEC can be standardized and

become a viable source of electrical power generation.

The single controlling factor which creates troublesome

technical encounters is low thermal power system efficiency

(one to four percent depending upon parasitic power require-

ments). Because the heat energy used by OTEC must be extracted

from a small ocean temperature difference, extremely large

volumes of surface water must pass through a proportionately

sized evaporator to provide sufficient indirect heat energy

tp convert the working fluid into vapor to drive a turbine-

generator for electrical power generation. Concurrently, to

convert the turbine exhaust to a saturated liquid, completing

the closed cycle, a condenser having compatible heat absorp-

tion capacity must be employed.

12

Economic handling of the volume of fluids required for the

heat absorption, expansion, and heat rejection phases of the

cycle requires close scrutiny of evaporator, turbine, condenser,

and pump design to minimize the parasitic losses with respect

to the generated electrical output. Because of the low

thermal efficiency, relative to nuclear or fossil fuel-fired

power plants, the margins for design and operating error in

OTEC plants will be narrow.

With the advent of high-speed computers, numerical

methods for solving these complex engineering problems with

multiple design variables and constraints are now possible.

The case for utilizing an optimizing scheme for not just

one system component, but rather the complete power generation

cycle, can easily be made. In effect, it would serve as a

systems analysis tool, to optimize component design and cost,

relative to a specific electrical output or to enable compari-

son and evaluation of competing OTEC designs.

B. OBJECTIVES

The objectives of this work are to develop a computer

code for the Ocean Thermal Energy Conversion (OTEC) power

system and to couple the analysis to a numerical optimization

code to provide an optimum system design capability, considering

both performance and economics.

This would create an optimum modular design relative to

a specified objective function for a desired net electrical

output, such as a 25 MW (net) power system. Such a design

13

I-

would permit construction of higher capacity power systems

using the optimized modules as substations of the total power

plant. Cost savings, improved plant performance, redundancy,

and reliability could be the immediate beneficiaries of such

a venture.

C. OVERVIEW OF THE OTEC POWER SYSTEM ANALYSIS

To analyze the closed-cycle OTEC power system, the

fundamental relationships of heat transfer, fluid mechanics

and thermodynamics are used to simulate a variety of system

component designs, which form the basis of the power system

algorithm. The scope of this analysis will be limited to

the OTEC power system and sea water systems only. Mooring

systems, power delivery, hull, and cold pipe design will not

be addressed.

The performance analysis will be divided into four

sequential sections as shown in Figure 1, and discussed

in detail in subsequent chapters of this thesis.

Input parameters (design constants) for the power cycle

analysis will include:

Required net electrical output.

Salt water inlet temperature to the evaporatorand condenser.

Length of hot and cold salt water pipes.

Heat exchanger tubing material (aluminum or titanium).

Heat exchanger tube orientation and profile.

Pump mechanical and motor efficiencies.

14

Turbine mechanical efficiency.

Generator mechanical and electrical efficiency.

Biofouling control factor.

* Piping absolute roughness.

* Projected annual inflation rate for aluminum heatexchanger retubing.

15

* - .

EVAPORATOR

PERFORMANCE£

PARASITIC

LOSSES

TURBINE AND

ELECTRICAL POWER

REQUIREMENTS

CONDENSER

PERFORMANCE

Figure 1. Power System Sequential Analysis

16

II. POWER CYCLE DESCRIPTIONS

A. INTRODUCTION

This chapter will provide a brief description of the OTEC

power system. First, looking at the ideal Rankine cycle,

the fundamental thermodynamic concepts will be enumerated.

Then the deviations from the ideal cycle will be presented,

creating the configuration assumed for the present cycle

analysis which will be amplified in detail by follow-on

chapters.

B. IDEAL OTEC RANKINE CYCLE

The closed-cycle OTEC concept is based upon a Rankine

power cycle that is driven by the low thermal energy potential

available from the ocean temperature gradient that exists

between warm surface water and cold deep water in ocean

regions. The power cycle consists of a working fluid circu-

lation pump, evaporator (heat absorption), turbine (expansion),

and condenser (heat rejection), as shown in Figure 2. The

majority of current OTEC designs are based upon ammonia as

the working fluid -- a design decision that is adopted for

this analysis.

Figure 2 also illustrates an ideal OTEC Rankine cycle,

plotted on temperature-entropy coordinates. In the ideal

cycle, the low pressure working fluid (state point 1) is

isentropically pumped to the evaporator operating pressure

(state point 2). The working fluid (ammonia) is then

17

%L -- I

23

EVAPORATO

201n

,- TUBN

NH3 CRC PUP ./

CODNE/-

T/

Figure 2. Idealized OTEC Rankine Cycle

18

converted to a saturated vapor in the evaporator by indirect

heat energy exchange from warm surface ocean water (state

point 3). Mechanical power is generated by isentropic expan-

sion of the saturated ammonia vapor through the turbine

(state point 4).

After exiting the turbine, the wet, low-pressure vapor is

converted to a saturated liquid in the condenser by indirect

heat absorption from cold ocean water (state point 1),

returning the cycle back to the working fluid circulation

pump.

C. ACTUAL OTEC RANKINE CYCLE

In actuality there are numerous deviations from the ideal

cycle which must be considered in this analysis. These are:

(1) Turbine, generator and pump efficiencies.

(2) Pressure drops in evaporator and condenser (tube-side and shellside).

(3) Pressure drop across moisture separator.

(4) Elevation change and frictional losses inpiping: (a) re-flux pump piping, (b) pipingfrom circulation pump to evaporator.

(S) Evaporator outlet quality (85 to 95%).

(6) Moisture separator outlet quality (99 to 99.5%).

The deviations from the ideal Rankine cycle described

above are depicted in the flow diagram and temperature-entropy

plot of Figure 3. In the actual OTEC Rankine cycle, the low

pressure working fluid (state point 1) is pumped up to the

evaporator operating pressure by the ammonia circulation pump

with an adiabatic efficiency (state point 2). The working

19

i2 I

MOISTURESEPARATOR

HOT \~~'EVAPORATOR

WOADWATE

TURIN

RE-FLU PUMP-

2/

T I,

S

Figure 3. Actual OTEC Rankine Cycle

20

fluid (ammonia) is then converted to a wet vapor with an

evaporator outlet quality (85-95%) acting under a shellside

pressure drop (state point 3). Evaporator outlet vapor then

passes through a moisture separator to improve vapor quality

(99-99.5%) creating a pressure drop (state point 4).

Mechanical power is generated by the expansion of the moisture

separator outlet vapor through the turbine with an adiabatic

efficiency (state point 5). After exiting the turbine, the

wet, low pressure vapor is converted to a saturated liquid

in the condenser acting under a shellside pressure drop

(state point 1), returning the cycle to the working fluid

circulation pump.

This figure forms the thermodynamic basis for the OTEC

power system analysis which follows.

21

III. EVAPORATOR AND MOISTURE SEPARATOR

A. INTRODUCTION

Several heat exchanger concepts have been proposed for

closed-cycle OTEC systems. Among these designs are:

• Conventional shell and tube heat exchanger.

• Plate type heat exchanger.

Within these basic concepts, variations in design have

been proposed, including:

Orientation of tubes (horizontal or vertical).

Heat exchanger tube material (i.e., titanium,aluminum).

Method of tube enhancement (i.e., fluted, porouscoatings).

Location of tube enhancement (i.e., internal and/or external).

Location of the vapor separator (i.e., internalor external).

Location of the heat exchangers relative to thesea surface.

Method of biofouling control.

The analysis to be presented for the evaporative heat

exchanger will be based on the following design characteristics:

Single-pass shell and tube heat exchanger.

Internal vapor separator with a gravity drain toevaporator inlet.

Horizontal orientation of tubes with an equi-lateral triangle or square tube profile.

Smooth plain-tube configuration (no enhancements).

I -

Tube material (titanium or aluminum based on a30-year life-cycle criterion).

Biofouling control based upon an achievablefouling factor.

* Heat exchanger centerline located on sea surface.

As an overview of the evaporator-moisture separator

analysis, the following major steps in the algorithm are

listed in order of their execution (numbers in parentheses

refer to equations developed in the subsequent analysis):

Specification of system constants (see I.C.).

Initialization of design variables (D.V.).

Tube length.

SW velocity through hot pipe.

Inner diameter of hot pipe.

Tube outer diameter.

SW velocity through evaporator tubes.

Inner diameter of NH3 piping.

Inner diameter of NH3 re-flux piping.

Tube profile pitch ratio.

Salt water mass flow rate (1).

Total number of tubes (2).

Total heat transfer surface area (3).

* Assume an initial salt water bulk temperature (6), andammonia heat transfer coefficient (9).

Overall heat transfer coefficient (4).

Number of transfer units (11).

Heat exchanger effectiveness (13).

Salt water outlet temperature (15).

23

* Revised bulk temperature (16); iterate with (6).

Amount of heat absorption (17).

Log mean temperature difference (18).

. Film temperature (19).

Initial ammonia mass flow rate (21) without theeffects of moisture separator.

. Initially assume state point 1 thermodynamicproperties are ideal (21).

Thermodynamic pump work (23).

Tube profile, flow parameters across the tubebank (24, etc.).

Tube sheet diameter (30).

Evaporator shellside pressure drop for two phaseflow (33).

* Moisture separator pressure drop (38).

* Properties at state points 3 and 4 (39-41).

Revised ammonia mass flow rate and velocity (50)includes the effects of the moisture separator;iterate with (31).

Revised ammonia heat transfer coefficient (51, etc.);iterate with (9).

Heat exchanger cost analysis.

In the following section, the basic steps summarized

above will be described in detail.

B. ANALYSIS OF THE EVAPORATOR AND MOISTURE SEPARATOR

1. Salt Water Mass Flow rate, m5,.

The salt water mass flow rate through the hot pipe

must be equivalent to the flow rate through the evaporator

(assuming no leakage)

24

12

and A' 1

where A = cross-sectional area of the hot pipe.

V =salt water velocity through hot pipe.

=density of salt water evaluated for an

average hot pipe salt water temperature.

As previously stated, the diameter of the hot

pipe and salt water velocity are among the initializing

conditions of the optimization and will be treated as design

variables.

2. Total Number of Evaporator Tubes,Nt

Using equation (1) , it follows that

1)1Z ' !EL v, N.. (2)4

where =salt water density evaluated at the average

bulk temperature initially assumed as the hot

pipe salt water temperature.

25

d = tube inner diameter.

Nt = the number of tubes required to maintain

the mass flow rate for an average salt water

velocity per tube.

The total number of tubes can be determined by solving

Eq. (2) for N.The diameter of the tube and average salt water

velocity per tube are initialized for the analysis and will

be treated as design variables by the otpimization code.

3. Total Evaporator Heat Transfer Surface Area (Outer),Ac

Having determined the number of evaporator tubes, the

total heat transfer surface area can be determined using

initializing values of outer tube diameter and tube length.

For tubes without extended surfaces

At = i-I , t(3)

As previously, the outer tube diameter and tuLe length

are initializing conditions and will be treated as design

variables.

4. Overall Heat Transfer Coefficient,

The quantity "U" provides a measure of the total

thermal resistance in the flow path, based on either inside

or outside surface area.

This analysis will be based on the value of U for the

outside surface area derived from Eq. (3).

26

Using a resistance analysis, assuming one dimensional

(radial) heat flow,

TS '1W

Tfs"w Tfh Th

f Tnh

TfnTfn3

Tsw ^ Tfs ^ Tw1 Tw2 _ , Tf nh- . Tnh3.

R 1 R 2 R R 4 RS

the overall heat transfer coefficient may be expressed as

A-InC1 /d (4)

-0 haw Ao & K w',h

where = tubeside heat transfer coefficient.

= salt water fouling heat transfer resistance.

K = thermal conductivity of the tube material.

cf0,c = outer and inner tube diameter.

= ammonia fouling heat transfer resistance

(assumed to be negligible).

= outer and inner total fin efficiency (for

plain tube analysis, total fin efficiency

equals 1).

AO = total outer surface area (including fin

and bare tube).

27

AZ = total inner surface area (including fin

and bare tube).'

Az

where Ar,. = total inner fin surface area.

AL= total inner surface area (including fin

and bare tube).

A =total outer fin surface area.

A = total outer surface area (including fin

and bare tube).

= fin efficiency of single interanl fin.

= fin efficiency of single external fin.

a. Tubeside Reynolds Number, hj

Since the heat transfer coefficient correlations

for the evaporator and condenser are dependent on tubeside

flow, Reynolds number must be calculated.

The tube Reynolds number is defined as

R (5)

'Note that this analysis will hereafter consider smoothplain tube configurations only.

28

where / = dynamic viscosity of salt water.

= density of salt water.

Initially, properties are evaluated for

Reynolds numbers greater than 2300 will be indica-

tive of turbulent flow [Ref. 3]. Transition flow was considered

laminar for numerical evaluation.

b. Salt Water Heat Transfer Coefficient, hj

The simple empirical relation proposed by Sieder

and Tate [Ref. 31, expressed as

Nu4 (7)

was used for laminar heat transfer in tubes as defined by

Eq. (5).

Nusselt and Prandtl numbers, M4_1 and P, are

defined as

where/c'.,, and K,. (dynamic viscosity, specific heat,

and thermal conductivity) of salt water are evaluated at salt

water bulk temperature.

29

The effect of the viscosity ratio term in

Eq. (7) ) o.1)

where/I, is salt water viscosity evaluated at tube wall

temperature, is considered negligible and will hereafter be

dropped from the expression of Eq. (7).

Relation (7) is based upon the following assumptions:

fully developed flow in smooth tubes.

* fluid properties are evaluated at the

bulk fluid temperature.

and is valid for the following condition

F', r >10

L

For fully developed turbulent flow in a tube as

defined by Eq. (5), the Dittus-Boelter correlation (Ref. 3]

expressed as

.3 0.4= c~o34=.j Pr(s

was used. Nusselt and Prandtl numbers, Nay and r , are

previously defined by Eq. (9).

Relation (8) is based upon the following assump-

tions:

fully developed flow in smooth tubes.

fluid properties are evaluated at the bulk

fluid temperature

and is valid for the following conditions:

30

- .-

* Prandtl numbers ranging from 0.6 to 100.

. moderate temperature differences betweenthe wall and fluid conditions.

c. Salt Water Fouling Heat Transfer Resistance

In this document, it will be assumed that the

fouling resistance coefficient for tubeside salt water can

be maintained at .00025 (hr it2 F/6UT) using one of the

following techniques:

* Chlorination.

H 4AN Brush System.

Amertap.

Chemical cleaning

Pressure drops associated with cleaning techniques

will not be considered in this analysis. Piping losses will

be a function of tube length, inner diameter, salt water

velocity and the absolute roughness of the tubing design

material only.

d. Ammonia Shellside Heat Transfer Coefficient, NN X

Initially, I will be assumed

since its value cannot be directly calculated during this

phase of the analysis.

Using the thermal resistance expressed as

31

f

an initial value for the overall heat transfer coefficient may

be calculated.

LF = "k(10)

S. NTU-effectiveness Relations

The NTU-effectiveness relationships will be used to

determine the evaporator outlet salt water temperature.

Currently, all salt water properties have been based upon

the initial assumption that

The expression for the number of transfer units (NTU)

which is a measure of the size of the heat exchanger is given

by

TLU = U. At/,,,

where COW! is defined as capacity rate of the single phase

flow in an evaporative or condensing two phase flow regime.

32

t -ilk

Evaporator effectiveness can then be expressed as

~-NrL')

for two phase flow regardless of the flow geometry.

Using the definition of effectiveness

actual heat transferEffectiveness = (13)

maximum possible heat transfer

z A 77iar", 7T1,-TFI (14)

The expression for 6_7-rn,nrepresents the single phase

(salt water) flow and I-_ represents ammonia inlet temperature

to evaporator taken at state point 3A.

6. Evaporator Salt Water Outlet Temperature andBulk Temperature

Using the relationships of Eqs. (12) and (14), the

following expression may be formulated for salt water outlet

temperature

(-T- 7)

33

| IL

Concurrently, a revised evaporator average salt

water temperature can be expressed as

7-UK= ( -t L-7t )/-?(16)

Using the revised value for average salt water

temperature,iterate with equation (1) until the revised and

current values of bulk temperature satisfy a specified

convergence criterion.

-. .Anount of Heat Absorption,C

Using the results of Eq. (16) and (12), the amount of

heat absorption by the evaporator may be expressed as

= -(17)

8. Log Mean Temperature Difference, LMTD

The NTU-effectiveness method can be used to determine

the mean effective temperature difference (LMiD) across the

evaporator (heat exchanger).

Using Eq. (17) and the definition of

Q AL. F LMTI)

with --,O ,

the log mean temperature difference across the evaporator

may be expressed as

34

(-Xrd TTLCL, T(1- (18)

where . = I;,3 evaluated at state point 3.

F = correction factor on LtITD, equal to I for

two phase flow.

9. Film Temperature for Property Evaluation,T4

In order to evaluate the shellside ammonia heat

transfer coefficient, working fluid properties (i.e.,

viscosity, specific heat, etc.) must be evaluated at the film

temperature to validate critical heat transfer expressions.

By modifying the expression in Eq. (10) multiplying

by a single tube outer area, a value for single tube con-

ductance can be expressed as

AA

Subsequently, the average amount of heat transferred

per tube would equate to

where T3 = T ;H evaluated at state point 3.

Again using the resistance analysis in Section 3,

shellside wall temperature may be derived from

35

Knowing shellside wall temperature and the free-stream

temperature, film temperature can be derived from their

arithmetic mean.

T. (1F)

10. Ammonia Mass Flow Rate, ,r. 5

According to first law of thermodynamics for steady

state, steady-flow conditions in the evaporator:

EVAPORATOR (ideal) (hot sw)

01 3 J + 111.~ 3 (20)

from which the ammonia mass flow rate, y. , may be determined

if the enthalpies at state points 2 and 3 are known.

I." we initialize the lower and upper bounds of the

analysis in terms of pressure P and P3? respectively, and

initially assume that a saturated vapor leaves the evaporator,

the following relations may be expressed

36

(21)

where hi = represents enthalpy at state point 1 at

the suction inlet to the working fluid

circulation pump.

13 = represents enthalpy at (ideal)/state point 3

as a saturated vapor.

fI--3 = represent the respective saturation

temperatures.

iL/ = represents the specific volume at state

point 1.

To summarize, the upper and lower pressure bounds of

the system ( Piand P3) will be initialized in the analysis

and treated as design variables by the otpimization code.

Temperature at state point 3 is initially assumed to be a

saturated vapor (ideal T3) ; however, the working fluid is

subject to a shellside pressure drop as it passes across

the evaporator with an outlet quality of 90-95'. Properties

at state point 3 (actual) will be assessed in follow-on

sections.

37

dj

AMMONIA CIRC PUMP

/2

01 Nm3 N 1 2(22)

Assuming steady state, steady-incompressible flow,

the change in kinetic and potential energies, and heat

losses are negligible for isentropic conditions, and the

isentropic pump work can be expressed as

, :~~~~ , (r2 - 5w.) i-- - _

After the isentropic pump work is calculated, the actual

(adiabatic) pump work may be determined using pump efficiency,

VJ , (CP . (23)

Actual outlet enthalpy at state point 2 may be deter-

mined using the results of Eq. (23) with Eq. (22) knowing the

enthalpy at state point 1 from Eq. (21).

Using the results of Eqs. (21) and (22), the mass

flow rate in Eq. (20) may be calculated as the average shell-

side mass flow rate for the working fluid (ammonia).

38

11. Tube Profile, Flow across Tube Bank, and Tube Sheet

Diameter

Since the heat-exchanger arrangements (evaporator

and condenser) involve multiple rows of tubes, the geometric

arrangement of the tube profiles is important in the

determination of the heat transfer coefficient, the tube

sheet diameter and the shell side pressure drop associated

with two-phase flow (homogeneous model) [Ref. 4].

The following geometric arrangements are used:

SP

IN- LINE FLOWS n

where Sn = pitch ratio x outer tube diameter, equal to Sp.

= pitch ratio; the distance between tube centers

with respect to outer tube diameter.

Ar = tube profile area (centerline to centerline)

per tube.

39 (24)

39

OIL-,

sJ~- s n

STAGGERED 30 Sn FLOW

r 2 ,-, (26)

i C o5C0 3o (27)

Therefore, the tube profile area (centerline to centerline)

per tube is equal to

, (28)

The ratio of minimum flow area to the frontal area can be

expressed as

A~~f.i - -_

A5 ri(29)

Using the selected tube profile geometry, either in-

line or staggered, and knowing the required number of tubes

by equation (2), the tube sheet diameter for heat exchanger

design can be assessed as follows:

40

z

4 (30)

where Ts, = tube sheet diameter.

To estimate the sheliside ammonia flow velocity the

following control volume is introduced (ammonia circulation

piping and the top portion of the evaporator).

TY9 BUNML.ERDTi 1

If the mass flow rate remains unchanged across any

boundary (continuity),

Furthermore, if we assume the evaporator has the

means to evenly distribute liquid droplets across the top

of the tube bundle (spray nozzles and baffling), the follow-

ing expressions can be applied to estimate the mean droplet

velocity approaching the bundle:

Let (A /A f I

where percent of tube frontal area which is occupied

by droplets.

The mass flow rates are

41

where Ae = ammonia pipe cross-sectional area.

Vp = average ammonia velocity in the pipe.

Therefore

and since

A

it follows that the average velocity of ammonia through the

circulation pipe is equivalent to the average velocity of

ammonia at the tube frontal area boundary.

ve- v= (31)

Thus the assumption that T'1=Ael/Af is equivalent to

the assumption of constant liquid kinetic energy in the

transition from the pipe exit to the bundle entrance. Con-

sidering the minimum free-flow area for shellside flow passage,

A4 can be derived from Eqs. (29) and (30):

Af: T-s Lt

Aff A f 51, _- ,) (32)

where A = represents the flow frontal area.

- tube length.

42

Using the calculated values of Eqs. (32) and (20),

the mass velocity for the minimum free-flow area can be

expressed

where INIepresents the average ammonia mass flow rate.

12. Pressure Drop of Two-Phase Flow across a Bank ofTubes, zA

This portion of the analysis will use an analytical

model for two-phase pressure drops applicable for a fog or

spray flow pattern occurring at high void fractions -- the

homogeneous model [Ref. 4].

The model asserts that if the pressure drop in the

two-phase flow for a liquid-vapor mixture is relatively small

compared to the absolute pressure, the flow is considered

incompressible. Subsequently, the density of each phase is

practically constant. During the process of phase change,

the phase and velocity distributions are changed, and so is

the momentum of the flow. Therefore, the pressure drop of

a vertical two-phase flow consists of three components:

friction loss, momentum change, and elevation pressure drop

arising from the effects of the gravitational force field.

The local pressure gradient for a two-phase flow

may be expressed as

~iF= (33)2HPfo q Em NiI , MLEvA4TiCA,

43

For a given channel length, Le , the pressure drop

components can be represented by

Z G (34)

ivi.

Z--A

/ P~oi tN 7u in c

and the total pressure drop,AF , is given by the sum ofEvAP

these expressions

where * = single-phase friction factor by Jakob expressed

in Eqs. (35) and (36).

Lc = channel flow length, defined for horizontal

tubed evaporators as Lc--TID (tube sheet

diameter).

P6 = equivalent diameter of flow channel, defined

by = i P 0 j. -Clo.

= mean specific volume defined by

where X = quality of mixture (state point 3).

Vi4 = specific volume of liquid (state point 1).

13 = specific volume of vapor (state point 3).

44

ij

The basic assumptions of the homogeneous model (fog

flow model) [Ref. 4] are:

(1) equal linear velocities of vapor and liquid,

(2) thermodynamic equilibrium between the two

phases, and

(3) a suitably defined single-phase friction factor

is applicable to the two-phase flow.

Using assumption (3) and the correlations by Jakob

[Ref. 3], a suitable single-phase friction factor can be

calculated from previously defined tube profile relationships:

for staggered tube arrangements:

(o ) R (35)

and for in-line tube arrangements:

C- C.4/ c.c.~ J (36(S C414o)/J 0.43 - I.f3 Jc / 5,,

where Reynolds number (max) is determined from the shellside

ammonia flow and the nozzling effect of the tube geometry as

expressed by

where = the ammonia velocity at the tube frontal area

boundary determined by equation (31).

45

S 1

Reynolds number for maximum shellside flow can be

calculated using the following expression

Eq. C37) and tube profile data can then be used to

evaluate the single-phase friction factor, required for

Eq. (34). All other components of the total pressure drop

Eq. (33) can be determined from previously calculated data.

13. Pressure Drop Across the Moisture SeparatorLP,.sFp

This portion of the analysis will simulate the use

of a cyclone separator to improve te evaporator outlet vapor

quality. The flow pattern in a cyclone separator is complex

and simplifying assumptions are inadequate to allow the

calculation of the corresponding pressure drop, which can

vary from 1 to 20 inlet velocity heads [Ref. 5]. Therefore,

the worst case condition will be applied with an approxima-

tion for the fluid flow inlet area to the separator banks.

By approximating the inlet area as a fraction of

the evaporator frontal area

A = C, Id T,

the inlet fluid velocity can then be determined using the

working fluid mass flow rate, Eq. (20).

where /. = density of ammonia at state point 3.

46

i

-S\

Therefore, if the pressure drop across the moisture

separator is equal to 20 times the inlet velocity head,

. (38)

14. Enthalpy at State Points 3 and 4

Since Eq. (33) represents the pressure drop across

the evaporator shellside, the actual pressure at state

point 3 or evaporator outlet may be determined from

where P was previously described as the pressure for a

saturated vapor.

Similarly the actual pressure at state point 4, the

moisture separator outlet, may be expressed as

P~4= P() ., (40)

Operating under the dome of the Temperature-Entropy

diagram, the following properties are defined

h3f (A1v)* Pf33(Njg) hI)P4f(4l)

f13(WV)IjIp 3 (NeV) H.4q~ b 4

47

The subscript sE 'v) representing a revised property

will hereafter be dropped from the expressions in Eq. (41).

Assuming an evaporator outlet quality of 90-95%, and a

moisture separator outlet quality of 99-99.5%, enthalpies

at state points 3 and 4 may be determined using the relation-

ships of Eqs. (41)

i 3 k3T-i-X3 (il31i - h3j)

1 1 1 +X4 ( 1141 114-F) (42)

15. Revised Ammonia Mass Flow Rate and Velocity

Till now, we assumed that the shellside mass flow

rate was given in accordance with the ideal system defined

by Eq. (20); however, in actuality this is not the case.

The diagramatic representation that follows better

illustrates the heat absorption phase of the OTEC power

system and will provide the basis for the analysis and

optimization.

Note, as in the previous control volume analysis,

the following conditions are assumed.

Steady state.

Steady-incompressible flow.

Change in potential and kinetic energies isnegligible.

48

AL-

QI

2 3 MOSTR

EVAPORATOR MSE T SEPARATOR

RE- LUXGRAVITY DRAIN

x PUMPWRIP

Analyzing the moisture separator as a separate

control volume,

3 4MOISTURE 14

If we assume that there is no carry-over of vapor in

the separator drain, then

and X4 -(43)

X3

However, for reasons of flow continuity, the mass

flow rate through the separator drain must be included in

the control volume analysis; therefore

1 3 f t 4 -?- ft I,) (44)

t 49

Substituting Eq. (43) into 41! and solving for *'Th,

the following expression can be derived

• 4 ) , 4

Looking at the evaporator as a separate control

volume,

the energy balance is

Assuming the change in enthalpy across the re-flux

pump and the difference between the separator drain outlet

and evaporator inlet are negligible, the energy balance

becomes

+ 112 t0

-- EVAPoRAO

I"L- - -4 - - - -

iere ,fluid drained from the separator is

assumed to be a saturated liquid.

-urthermore, a :7ass balance of the evaporator control

:oiume can be expressed as

~I! re W&&:C

solving Eq. I f~r tbe mass flow, rate at state

io nt 3 ind substituting into EQ. i h Eq. 3 yielse:foLcwing express-on

in addit ion, a ;iass S Ialance sf: 5toady -s tate, steady - lo ,

:z k~tes : at r h o a - ai , r: ie t tt2 no nt Ta Ind

P

5 n L):. S nd .1 , the rev.-ed mass flow

7'ae a, s-a-e o.n: t mav be determineJ. Concurrentlv, the

S :e\ I &ver:i..e ,im mo ri i eIoc2 iz i.n on ,e tube profile

0cone mv e ie1rmIned fre ( m s v d mat fo rate

"suv. tbe re 'sc1 ammonia ve t a,: t 1 en tric

*ue-'nrot i z,"?ometrrv nd lterat nI L:' r :iq. uil

;7'

an acceptable convergence criterion is achieved provides

the pressure drops across the evaporator and moisture

separator, and the properties at state points 3 and 4 for

a given film temperature. The result is more representative

of the heat absorption phase in the OTEC power cycle than is

the commonly used ideal analysis.

In addition, solving for the revised temperature at

state point 3,

T-3 = Tsar7- (50)

and iterating through Eq. (18) revises the film temperature

and subsequent working fluid properties.

16. Revised Shellside Ammonia Heat Transfer Coefficient

In the search for acceptable correlations to predict

the average evaporative heat transfer coefficient, two analyti-

cal treatments were found that lent themselves to OTEC

power system conditions.

The first of these correlations seeks to predict

thin film evaporation heat transfer coefficient for horizontal

tubes [Ref. 6]. Owens [Ref. 61 uses (1) the similarity

between evaporation and condensation, (2) the correlation

forms of local evaporation heat transfer coefficients for

water on a vertical tube developed by Chun and Seban, and

(3) the dependence of heat transfer on the vertical spacing

of the tubes as was experimentally demonstrated by Liu, to

arrive at the following correlations for non-boiling thin

film evaporation:

52

for laminar flow

H (c4 ) ( )

for turbulent flow

= ~ ( ) ( >Z\~3 I )(52)where ft vertical spacing with respect to tube outer

diameter.

r= tube flow rate per unit length.

The laminar-turbulent transition point is defined

by the intersection of Eqs. (51) and (52)

, ( ~ ,)

The pseudo-Reynolds number for horizontal vertical falling

film evaporation is defined by Ref, 7.

Re- 41

The second correlation combines boiling and evapora-

tion of liquid films on horizontal tubes, applicable for

vertical banks of plain and enhanced tubes [Ref. 8].

53

The overall model for a single tube is expressed as

I j L + 4- C - (53)

L L

where hb Rohsenow pool boiling correlation over the

entire tube length given by

/ -,

with Cs = function of the fluid-surface combination.

= wall temperature minus free stream saturation

temperature.

= surface tension

= heat transfer coefficient in the developing

region.

3 LdI

and h - fully developed heat transfer coefficient given for

laminar flow by

-3 -C.zz

54

-. I

and, for turbulent flow,

•-1/5 0.4 ,d

___ 1 ~' (56)

where L = circumferential length of heated surface.

-< = thermal diffusivity.

L, = developing length around tube circumference.

= flow rate per unit axial length of tube.

To apply Eq. (51) for a vertical bank of tubes, L

is expressed as

The laminar-turbulent transition point is defined by

the intersection of Eqs. (SS) and (56)

As before, the pseudo-Reynolds number is defined by Ref. 7

f~ 4 (S7)

After using Eq. (S7) to establish which flow regime

the system is operating in, the revised heat transfer coeffi-

cient for non-boiling thin film evaporation or nucleate

5S

i ..... IJ',mI i il~i' .il-l I

boiling may be calculated and then iterated with the initial

assumption for the shellside heat transfer coefficient, Eq. (9).

This will have a convergence effect on variables which are

a function of the shellside heat transfer coefficient, moving

them closer to actual OTEC system performance characteristics.

The user should be aware that the predictions for the

OTEC power system using ammonia have been for the case where

no boiling occurs in the film. This condition is dictated

by industrial preference for plain tube heat exchangers to

minimize fouling and the characteristic of ammonia to wet

surfaces well, flooding out nucleation sites. A number of

enhancement techniques have been developed to create

nucleate boiling, including a variety of tube configurations

and surface preparations; however, a preference for them

has not materialized. The nucleate boiling development in

Eq. (51) which would be indicative of tube enhancement is

provided for information only and will not be included in

the optimization or summary of conclusions.

Having described the methods used to predict the

shellside heat transfer coefficient, we can complete this

chapter of the OTEC power system analysis by constructing the

heat exchanger cost analysis.

17. Evaporator Cost Analysis

At the request of TRW, Wyatt Industries, a large

exchanger fabricator, prepared cost estimates for three

different sizes of vertically configured evaporators and

condensers, based upon initial design specifications prepared

56

by TRW. Based upon these estimates, TRW developed sets of

equations that represent the costs of various heat exchanger

component parts for shell diameters ranging from 10-35 ft

and 35-50 ft [Ref. 9].

The following are the TRW evaporator cost ($)

equations as a function of outer tube diameter (inch),

total number of tubes and tube-sheet diameter (ft) for

tube-sheet diameters of 10-35 ft.

Drilling time/tube sheet thickness

' . (. cdL- C. -) (58)

* Thickness of the tube sheet

1: 0S (59)

. Tube sheet labor cost

/4 (60)

* Tube sheet material cost

2.3CTSM q, 45 t fso (61)

* Tube installation cost

0.734 N t- c(62)

• Heat exchanger shell cost

z

1'7 ( Lt + )(T 0 /1~ (63)t1X157

-Ammonia distribution plate and battles cost

D il3 (64)

Bustle, flanges channels and flow plates cost

BFCF = 30es 6o0 ((65)

* Tube material cost

CT-H (EP Lt + EZ) N. - (66)

where ti curve fit of tube cost per foot.

E 2 tube machining cost if required

Heat exchanger head costs

' =5J24 0 (67)tXH

Water inlet, nozzles and supports cost

kAw (68)

Tube welding costs (Titanium tubes)

for Nt 4 3&CGCC.1

= 1441 Nt (a'./1.5-) (69)

C-,= C. g-'7Y7 A t ' 0i.&)

The sum of cost Eqs. (60) through (69) would equal

the cost to fabricate one OTEC evaporator with a tube sheet

diameter of 10-35 feet (all the preceding component costs

have been adjusted for current pricing at a 10% annual rate

of inflation).

58

. . ..

If our analysis is based on a 30-year life-cycle

criterion, no adjustments are necessary to any component

cost equation if titanium tubing is used due to its anti-

corrosive qualities; however, using aluminum tubing (i.e.,

Al-5052), the expense of retubing must be considered to meet

the criterion of a 10-year life cycle for aluminum tubing.

This implies Eq. (61) and (66) must be modified to reflect

the costs of retubing at the 10 and 20-year point in the cycle.

Aluminum tube installation cost

CAL rz ( f* * L)20 (70)

where L = projected inflationary rate (input by customer)

Aluminum tube material cost

0 (71)

For tube sheet diameters of 35-50 ft the following cost

relationships apply [Ref. 9]:

Equations for drilling time/tube sheetthickness (58), thickness of tube sheet (59),and tube material costs remain unchanged.

Tube sheet labor and material cost (titanium)

S 1N. T td (72)

5,014CT r : zq.sG " 66Ts o d (73)

Tube sheet labor and material cost (aluminum)

c.7t q1 0.

1.,61

3Sb , 5-4. 3 T5o &r5 (75)

Tube installation costs

&. N 7 C

3k' 42 J (76)

Heat exchanger shell cost2.06

12.44 (L 4( )t "o (77)

Ammonia distribution plate and baffle costs

1.&2 0,673"P = 1,-8 7~qT5 2.417 Alt d (78)

Bustle, flanges, channels, and flow plate costs

2.12ar< ,= 472. q77 /54) (79)

Heat exchanger head cost

fX4 = 1125,51 7a (80)

Water inlet, nozzles and support cost

1.1

s 745,2 7 F,0 (81)

60

I \-

Tube welding costs (titanium tubes)

for 3 , 1 _,CC,

T 4 73,,/C . (82)

for Nt . 1- 5C C1,03

C*7'V-7A~ (aq./6)

As indicated previously, the cost to fabricate one

OTEC evaporator with a tube sheet diameter 35 to 50 ft is

equal to the sum of component costs Eqs. (72) through (83)

(all the preceding component costs have been adjusted for

current pricing at a 10*) annual rate of inflation).

For an analysis based on a 30-year system life-cycle

criterion, the additional costs for aluminum retubing must

be considered and Eqs. (70) and (71) apply.

61

IV. PARASITIC LOSSES

A. INTRODUCTION

This chapter describes in detail the programming analysis

for parasitic losses which include: (1) pumping and pipe

requirements for both cold and hot salt water systems,

(2) pumping and pipe requirements for the working fluid

(ammonia) circulation and re-flux systems, and (3) turbine

generator losses due to inefficiencies. Hotel requirements

have not been incorporated into the analysis, but could be

included for the final design analysis.

Pumping power requirements will be determined through

the use of the general energy equation between the inlet and

outlet of the system control volume [Ref. 3].

J __ . = v0 + zo + + (Los SE-9

To determine the pumping power W 5 the following effects

will be evaluated:

1. Density head.

2. Friction losses.

Intake piping.

Heat exchanger tubing.

Exit piping (if employed).

3. Thermodynamic pressure head.

4. Elevation head.

62

5. Minor losses.

Intake piping inlet configuration (contraction).

Intake piping screen (obstruction).

Flow through valves, elbows, etc.

Outlet piping (expansion).

Inlet to heat exchanger tubing (contraction).

Outlet from heat exchanger tubing (expansion).

Outlet of exit piping (if employed).

In the above pump head evaluations, the following inputs

are specified:

Pipe lengths (hot, cold, ammonia circulation andre-flux piping).

Inner pipe diameters (initialized and treated as adesign variable by the optimization code).

Absolute roughness corresponding to piping/tubingmaterial (designer specified).

Fluid velocity. (initialized and treated as adesign variable by the optimization code).

Pump mechanical and electrical efficiencies.

As an overview of the parasitic pump loss analysis, the

following major steps in the algorithm are listed in order

of their execution:

Hot pipe salt water pump.

Inlet piping friction losses (86).

Minor piping losses due to inlet screen (87)and plenum design to evaporator core (88).

Evaporator core minor losses (89, 90) andtubeside friction losses.

Total pressure losses (92) and pumpinghead (93).

Pumping power requirements (95).

63

Pump cost analysis (96).

Cold pipe salt water pump.

Initialize cold pipe inner diameter and SWvelocity (design variables).

Minor losses due to inlet ducting (97) andplenum design to condenser core (98).

Inlet piping friction losses (99).

. Condenser core minor losses (100, 101) andtubeside friction losses (103).

Density head (104).

.. Total pressure losses (105).

Pumping power requirement (107).

Pump cost analysis (108).

Ammonia circulation pump.

Piping friction (109) and minor losses due tovalving/elbows (110).

Pressure drop across evaporator shellside (112).

Thermodynamic head (113).

Elevation head (114).

Total pressure losses (115).

Pumping power requirement (116).

Pump cost analysis (118).

Ammonia re-flux pump.

Piping friction (119) and minor losses due tovalving/elbows (120).

Thermodynamic head due to pressure drop ofsaturated liquid ammonia across evaporatorshellside (122).

Elevation head (123).

Total pressure losses (124).

64

. Pumpin; power requirements '1b'

. Pump cost analysis (I .

Parasitic pump 1Dsses.

In the following section, the hasic steps summarized above

will be described in detail.

B. ANALYSIS OF PARASITIC LOSSES

1. Hot Pipe Salt Water Pump, -'e

The pressure losses due to piping friction and

associated minor losses will be determined using the

Darcy-Weisbach correlation [Ref. 10].

K V (83)

where K. describes the resistance coefficient.

V fluid velocity.

(34)

where = friction factor.

L = equivalent length in pipe diameters.

TIn order to determine the friction factor, the pipe

flow Reynolds number must be calculated.

I , ' V, ,) d.

65

•zA

,,here & Q, properties of walt water at the hot pipe

inlet temperature (assumed constant through-

out the pipe).

= salt water velocity and inner pipe diameter

(initialized and treated as design variables

by the optimization code); velocity assumed

constant over pipe length.

Pipe flow Reynolds number greater than 2300 will be

considered turbulent.

for laminar flow

(,4 (S5)

for turbulent flow

."2 (86)i ( .z , .- 74/,<. "

where 6 absolute roughness corresponding to piping material

selected.

Eq. (86) yields a friction factor within one percent

of the Colebrook equation and is valid for the following

conditions [Ref. 9).

66

AIL,_

Considering the resistance coefficient for pipe minor

losses

Assume the inlet duct is the same size as thepipe inner diameter, but it is screened

k'= 1. (S-)

Assume piping enters evaporator through anarea which is abruptly changed [Ref. 11]

2

K ()]

where i~o = evaporator tube sheet diameter (assume tube

sheet diameter is twice as large as the inner

pipe diameter).

Summing the results of Eqs. (84), (S-1, and SS8 to

determine the total resistance coefficient, the pressure

losses due to piping can then be determined using Eq. '83).

If a variety of valves or fittings are to be included

with Eq. (84), Ref. 11 provides a representative listing of

equivalent length-to-pipe-diameter values.

To analyze the pressure drop across the evaporator

tubeside, we again use the Darcy-Weisbach correlation, but

for different design assumptions.

Assume inlets to evaporator tubing are wellrounded [Ref. 11]

67

Assume outlets of evaporator tubing expandto an infinite reservoir (Ref. 10]

SlIC (90)

Using the Reynolds number in the previous chapter,

Eq. (5), the corresponding friction factor Eq. (85) or (86),

and resistance coefficient can be determined

f L~ (91)

where Le,dL = evaporator tube length and inner tube

diameter and are initialized and treated as

design variables by the optimization code.

Summing the results of the resistance coefficient

in Eqs. (89), (90) and (91), the pressure losses due to the

evaporator design may be determined using the Darcy-Weisbach

correlation Eq. (83).

The results of the piping losses and core design

losses are equivalent to the hot pipe salt water pumping

system requirements

r" t p;' 6mVt- D~jSIcjN (92)

converting to pumping head

H, p ./ t (93)

68

Pumping power in terms of horsepower can be determined

using the following expression

- rH(~ (94)tip

where -' pump mechanical efficiency (designer input).

,r1,,=s salt water mass flow rate determined in

previous chapter, Eq. (2).

To equate parasitic pump losses to power input,

Eq. (94) is converted to the motor load requirement in terms

of megawatts electrical.

PHP( j)7PfP< C 1(95)

where - pump motor efficiency (designer input).

Because of the high salt water flow rates and rela-

tively low pumping heads, good engineering design would

dictate the use of axial flow (propeller) type pumps.

Using the algorithm developed by TRW [Ref. 9] from

data provided by Johnston Pump Co., and Process Equipment

Co. (distributors of Ingersoll Rank and Johnston Pumps),

the cost of salt water pumps can be expressed as

L )1 C.1 j X (96)

69

where

, '4

where dc, Vsw = inner hot pipe diameter, salt water velocity

(initialized for analysis and treated as

design variables by the optimization code).

The above algorithm is valid for the following con-

ditions

vertical, wet pit, propeller type pumps withcast iron steel columns with protective epoxycoating, stainless steel shaft and bronzeimpeller.

• pump size from 155,000 through 750,000 GPM

with total dynamic heads of 8 through 12 feet.

Eq. (96) has been adjusted for current pricing at a 10%

annual rate of inflation.

2. Cold Pipe Salt Water Pump.,,

Using Reynolds number

Z V Vs.

where properties of salt water at the cold pipe

inlet temperature (assumed constant through-

out the pipe).

= salt water velocity and inner pipe diameter

(initialized and treated as design variable

by the optimization code), velocity assumed

constant over pipe length.

70

Pipe flow characteristics and friction factor can be identi-

fied. A pumping analysis will be developed for the cold

pipe pump using the Darcy-Weisbach correlation, similar to

the development in the preceding section.

Considering the resistance coefficient for minor pipe

losses

Assume the inlet duct is well rounded [Ref. I1].

K= 0,6, (97)iN(.a-

Assume piping enters condenser through anarea which is abruptly changed [Ref. 10].

where T50 condenser tube sheet diameter (assume tube sheet

diameter is twice as large as the inner pipe

diameter).

Assume one ninety-degree elbow is required

in system [Ref. 11].

L5 0D

Summing the results of Eqs. (84), (97), and (98),

the total resistance coefficient can be expressed as

P L6#L)JtUk ' (99)

71

S---

where Lp = length of cold pipe.

c. = inner diameter of cold pipe.

Pressure losses due to piping can then be determined

using the Darcy-Weisbach, Eq. (83).

In analyzing the pressure drop across the condenser

tubeside, the Darcy-Weisbach correlation is used again, but

for different design assumptions.

. Assume inlets to evaporator tubing are wellrounded.

k C .5' (100)

* Assume outlet of condenser tubing expands toan infinite reservoir.

~ (101)

Defining Reynolds number for condenser tubeside

flow, while assuming

where / properties evaluated at condenser tubeside

bulk temperature (initially assumed equal to

cold pipe inlet temperature).

72

I I

average salt water velocity through

tubing, inner condenser tube diameter (both

are initialized and treated as design

variables by the optimization code).

The corresponding friction factor, Eq. (85) or (86), and

resistance coefficient can be determined

t (103)

where Lt,d , the condenser tube length and inner tube diameter

are initialized and treated as design variables by the optimi-

zation code.

Summing the results of the resistance coefficient

in Eqs. (100), (101), and (103), the pressure losses due to

the condenser design may be determined using the Darcy-Weisbach

correlation, Eq. (83).

A complete analysis of cold pipe losses must also

include the effect of density head and a corresponding increase

in pumping power requirements.

For most engineering problems involving the flow of

liquids through a pipe, where the temperature change in the

pipe is small, the density of the fluid is considered to be

a constant and the fluid is termed "incompressible." However,

the flow problem in OTEC cold pipe systems is unique. We can

continue to assume that there is negligible change in the fluid

temperature, virtually unaffected by the ocean thermal

gradients, because of the system's characteristic high mass

73

flow rates. However, the height of the water column (1500

to 3000 feet) inside the pipe requires the effect of fluid

compressibility to be taken into consideration.

The effect of an increase in density with depth

can be expressed by the integral

'-I

with a density head defined as2

e

Integrating the pressure-density variation, the

density head reduces to [Ref. 12]

H,, zz- F " Li (?e R)L K rM P4

where i( -- mean compressibility of wait water, f(salinity,

temperature and pressure).

reference density at which Km is evaluated.

Considering pressure at any depth obtained from the

integral,

-. e

the density head can be rewritten as follows

2Note that Z is measured as positive upward so that oceandepth values(ZL,,) are negative and (!Z- L)is a positivequantity.

74

Rigorous procedures for calculating the density

profile which is a function of temperature, salinity and

pressure may be found in Ref. 13; however, they will not

be discussed in this document.

For the purposes of simplification, the following

solution technique was developed:

(1) If the liquid in the pipe is taken to have a

constant density with respect to pressure, the compressibility

approaches zero; the density head can then be expressed as

(2) Converting the geometric term for elevation to

an equivalent integral expression

Zee

The reference density is taken to be the inlet value so that

and the density head can be rewritten as follows

(3) Assuming a linear distribution of density with

depth, due to temperature variations, as illustrated below

75

- L-

the following linear expression for density with respect to

depth may be formulated, where Z=O for convenience.

(4) Applying the equation developed in section 3 to

the density head integral above and integrating over the

range of values for sea water depth (z), the following

equation is derived as a linear approximation to the density

variation of sea water with respect to depth

/9

where ,e - curve fit evaluations of density for

specified depths of sea water. Data

extracted from Ref. 14.

The results of the piping losses, core design losses,

and density head are equivalent to the cold pipe salt water

pumping system requirements

76

- *H

Using Eq. (93), Eq. (105) can be converted to a

pumping head. Similarly, pumping power in terms of horse-

power can be determined using Eq. (44).

where

IIITr J,_ (106)

and /O5W = density of salt water evaluated for a

constant inlet temperature.

Vs.k 4;, = cold pipe salt water velocity, and inner

diameter (initialized and treated as design

variables by the optimization code). Note

salt water velocity through cold pipe is

considered to be constant.

Pumping power can then be expressed in terms of

megawatts electrical

P FCP X ~j~A FACTO' (107)

where 7_= pump motor efficiency (designer input).

Using the same arguments for the selection of an

axial flow (impeller type) pump, as used for the hot pipe

salt water pump, the pump cost algorithm developed by TRW

can be applied to the cold pipe salt water pump assuming

77

. . .. .. ... ., " - - !l l I~i am''

a . ......... . " ...

the required conditions are validated.

3f/,,= locc)c. r5 r. !].21,< (1 081

Equation (108) has been adjusted for current pricing at a

10% annual rate of inflation.

3. Ammonia Circulation Pump. ReC

The function of the ammonia circulation pump is to

circulate and lift saturated liquid ammonia from the condenser

hot well at state point 1 and increase its pressure to exceed

the operating conditions in the evaporator at state point 2.

In order to evaluate these characteristics, the

following pumping elements will be included in the analysis:

Piping losses (friction and minor).

Heat exchanger shellside pressure drop.

Thermodynamic pressure head.

Elevation head.

As in the preceding analysis, Reynolds number is used

Fto determine pipe flow characteristics

IV /

where 1 11 = saturated liquid properties of ammonia for

the temperature at state point 1 (assume any

temperature increase from pump work is negligible).

= inner pipe diameter (initialized and treated as

a design variable by the optimization code).

78

" =ammonia flow velocity determined from the pre-

ceding chapter, Eq. (50).

The ammonia pipe friction factor can then be deter-

mined from Eqs. (35) or (86), and the piping friction

resistance coefficient can be expressed as

L (109)

where L = ammonia circulation pipe length (designer input).

Considering the resistance coefficient for minor pipe

losses, assume there are four ninety-degree elbows in the

system

K= 4 L (110)

where - = equivalent length in pipe diameters for a standardp

elbow [Ref. 111.

Summing the results of Eqs. (109) and (110), piping

losses (friction and minor) can be determined using the Darcy-

Weisbach equation (93).

= F,,L,4 V (111)

The heat exchanger shellside pressure drop is also

included in the pumping head requirement because it serves as

a resistance to flow.

/9

Pressure drop across the evaporator shellside was

determined using the two-phase flow model (homogeneous)

expressed by Eq. (33)

AF~P AFRICriON 0 A1 C 4l r_ 'f.j LEVA7FICN (112)

Since the pump is required to lift the working fluid

to a higher elevation and increase its operating pressure,

the following elements must be included in the analysis:

Thermodynamic head

where z F, (113)

represents the difference in thermodynamic

operating pressure between state point 2 and

state point 1.

Elevation head

where Z - (114)

= datum.

. =elevation of the evaporator inlet above

datum (taken to be equal to evaporator

tube sheet diameter plus 25).

represents the lift head required to move the

working fluid to a higher elevation.

80

The results of piping losses (111), evaporator

pressure drop (112), the thermodynamic head (113) and

elevation head (114) are equivalent to the ammonia circulation

pump system requireements.

A ?p~r~ = ~ ~Th~frI ~AL~V4Tj\J(115)

Using Eq. (93) with ammonia properties, Eq. (115)

can be converted to pumping head and finally expressed as

pumping power (horsepower).

I'___ J )(116)

where / =1a = mass flow rate of ammonia determined by

Eq. (20) of the previous chapter.

" tj = pump mechanical efficiency (designer input).

Pumping power can then be expressed in terms of mega-

watts electrical

ffRCc)%: jS CON I~CNip-cc 1

where "'t= pump motor efficiency (designer input).

Because of high pumping head and moderate flow rates,

good engineering design would dictate the use of a single

suction centrifugal flow type pump.

81

Using the algorithm developed by Westinghouse Electric

Co. [Ref. 15] from data provided by Bingham Pump Division,

Portland, Oregon, the cost of the ammonia circulation pump

can be expressed as

=(kI +) 1.21 x , (118)

where M t = mass flow rate of ammonia r)

= specific volume of saturated liquid ammonia

at state point 1 (k'/fb,, J

Eq. (118) has been adjusted for current pricing at a 10',

annual rate of inflation.

4. Ammonia Re-flux PumpPME-_Lux

The function of the re-flux pump is to recycle

ammonia droplets which are not evaporated in the heat absorp-

tion process. Saturated liquid at approximately the heat

exchanger's operating pressure is lifted from the evaporator

d-ain to the ammonia feed inlet, for redistribution as droplets

across the evaporator tube bundle. (Drainage mass flow rate

is assumed to be equal to 30% of the evaporator inlet feed

mass flow rate.)

In order to evaluate these characteristics, the

following pump elements will be analyzed:

Piping losses (friction and minor).

82

Thermodynamic pressure head.

Elevation head.

As in the preceding analysis, Reynolds number is used

to determine pipe flow characteristics

where /-',V = saturated liquid properties of ammonia for the

average pressure across the evaporator.

/i = inner pipe diameter (initialized and treated

as a design variable by the optimization code).

V = ammonia flow velocity determined from the

evaporator drainage mass flow rate assumed

equal to 300 of the evaporator inlet feed mass

flow rate (assume velocity constant throughout

the pipe).

The re-flux pipe friction factor can be determined

from Eqs. (85) or (86), and the piping resistance coefficient

can be expressed as

(119)

where L ammonia re-flux pipe length (designer input).

Once again, considering the resistance coefficient

for minor pipe losses assume there are four ninety-degree

elbows in the system

83

4 -L (120)

where . equivalent length in pipe diameters from a standardD

elbow.

Summing the results of Eqs. (119) and (120), piping

losses (friction and minor) can be determined using the

Darcy-Weisbach, equation (83)

P = A-)[ (121)

In order to determine the thermodynamic pressure

head, the pressure drop across the evaporator for the

saturated ammonia liquid must be analy:ed. Since the

saturated vapor and liquid are in thermodynamic equilibrium,

the results of Eq. (11Z) apply. Therefore

AP P3 - Pa

Therefore, the thermodynamic pressure head is equal

to the pressure drop across the evaporator for the saturated

ammonia liquid.

6 (122)

Finally, the elevation head is equal to the elevation

of the evaporator feed inlet with respect to datum, the

drain outlet.

34

Therefore,

A ,F (123)

where ZI = datum, drain outlet.

Z2 = elevation of the evaporator inlet above datum

(taken to be equal to the evaporator tube

sheet diameter plus 10).

The results of piping losses (121), the thermodynamic

pressure head (122), and elevation head (123) are equivalent

to the ammonia re-flux pump system requirements.

AP =j /3? +-AP -. (124)

As before, using Eq. (93), Eq. (124) can be converted

to a pump head and finally expressed in terms of pumping

power (horsepower).

F/ IR~-LLJ~ ..~~j H(125)

where rf, = drainage mass flow rate.

= pump mechanical efficiency (designer input).

Pumping power can be expressed in terms of megawatts

electrical

, -FL~Ux(l = -u__X LONv ERSlCAi FACT CR (126)

85

-

where T' pump motor efficiency (designer input).

Using the same arguments for the selection of a

centrifugal pump, the pump cost algorithm developed by

Westinghouse can also be applied to the ammonia re-flux

pump.

0 b4 Sx,. 'o'/oo / f, 1 X 1 1 7

where r1] mass flow rate of evaporator drainage ammonia

V4 = specific volume evaluated at the average

evaporator pressure (ft/ib,)

Eq. (127) has been adjusted for current pricing at

a 10% annual rate of inflation.

5. Parasitic Pump Losses

Parasitic pump losses is the summation of electrical

auxiliary pumping requirements (hotel and maintenance loads

not included) determined by Eqs. (95), (107), and (126).

LOs PHP P P ' PC .C PRE-FLUX (128)

86

V. TURBINE AND ELECTRICAL POWER

A. INTRODUCTION

The turbine generator is one of the critical elements

of the OTEC power system. Its energy conversion efficiency

and efficiency of design have a major effect on the overall

system performance. To illustrate this point, Ref. 16

reported that a three-point change in turbine efficiency from

85 to 88% results in a 3.6% increase in gross power, and a 5%

increase in net power developed.

This chapter will describe the analysis to evaluate the

expansion turbine thermodynamic properties and generator

output. The use of these properties will determine the

internal turbine efficiency and outlet quality subject to

design and thermodynamic constraints. The relationship

between the condenser operating pressure (design variable)

and the turbine outlet quality will be used to initialize

the heat rejection characteristics of the condenser.

General literature on turbomachinery designed for OTEC

closed cycle systems indicates that a turbine having the

following characteristics

Double flow, axial inflow,

Four stages of expansion,

Operating at 1800 RPM,

provides the optimum aerodynamic design (Ref. 16]. However,

it is not the intent of this thesis to analyze the geometry

8 7

and performance parameters of the turbine. Turbine geometry

such as

Specific speed and specific diameter,

Wheel diameter,

Rotational speed,

Blade height,

Blade stresses,

should be treated as a separate systems problem using

optimization to improve state-of-the-art design.

Parasitic losses due to the following generator turbine

inefficiencies will be evaluated in this section.

Generator mechanical and electrical.

Turbine mechanical.

As an overview of the turbine-generator analysis, the

following major steps of the algorithm are listed in order

of their execution:

Gross electrical output with no parasitic losses(129).

Enthalpy at state point 5 (130).

Turbine outlet quality (131).

Entropy at state point from a specified outletquality (132).

Quality and enthalpy at state point 5s (133, 134).

Internal (adiabatic) turbine efficiency (135).

Turbine cost analysis (137).

Generator cost analysis (138).

In the following section, the basic steps summarized above

will be described in detail.

88

B. ANALYSIS OF THE TURBINE AND ELECTRICAL POWER REQUIREMENTS

1. Gross Electrical Output and Inefficiency Losses

If the net electrical output required is indicated

by (in terms of megawatts), the gross electrical load at

the turbine shaft can be expressed as

= + KOss (129)

Th-AI )L4AJ

where PLOS = parasitic pump losses determined by Eq. (128).

11TM = turbine mechanical efficiency (designer

input).

= generator mechanical and electrical

efficiency (designer input).

The loss of electrical output due to generator-

turbine inefficiencies is equal to

2. Turbine Efficiency

The power developed across the turbine is

where r = mass flow rate of ammonia given by Eq. (48).

h4= enthalpy at state point 4, Eq. (42).

From this, the enthalpy at state point 5 can be calculated.

If we initialize the operating pressure of the con-

denser in terms of PS, the following relations may be expressed

89

IiP6 (130)

Therefore, it follows that the turbine outlet quality,

XS, can be determined from

Ii +i x~(s-1 (131)

Having established the moisture separator outlet

pressure and temperature, Eqs. (40) and (41), the entropy

at state point 4 can be determined for a known separator

outlet quality (designer input) using the following

relations

S~ ~ ~ -4 -)141 1-454 - S4-f - X ( 54j- S4-) (132)

For isentropic turbine work,

54- S53 (133)

the quality at state point 5s may be determined using the

following relations

+ -' (134)

Having determined the quality at state point 5s, the

enthalpy can now be determined.

90

h~s -4-xs ~~--K (135)

Using the results of Eqs. (41), (130), and (132),

the internal turbine efficiency (adiabatic) can be deter-

mined, expressed by

r (136)

To ensure a realistic selection of internal efficiency,

the following constraints are attached to the optimization

code

* X5 <N

3. Turbine Cost Analysis

The ammonia turbine cost is based on an algorithm

developed by Westinghouse to estimate manufacturing costs

[Ref. 15].

24 2 0 6,,37 /f3/N F (137)

where = gross electrical output in KW.

A4 : 2 (for a double flow turbine).

= flow price factor (1.0 for single-flow, 1.447

for double-flow).

91

The above algorithm is valid for the folowing

conditions:

Double flow, axial inflow.

Multi-stage.

Operating at 1800 RPM.

The generator cost will be based on an algorithm

developed by TRW from data provided by selected manufacturers,

Al .C2 3 b14-J- *C.-J1.I x 1 (138)

and is valid for the following conditions

1800 RPM rotor speed.

• power factor 0.8.

Eqs. (137) and (138) have been adjusted for

current pricing at a 10% annual rate of inflation.

92

Vr. CONDENSER

A. I'TRODUCTION

As indicated in the introduction to Chapter III, several

heat exchanger concepts have been proposed for the closed-

cycle OTEC system, with variations in their design.

The analysis to be presented for the condensing heat

exchanger will be based upon the following design

characteristics:

Single-pass shell and tube heat exchanger.

Horizontal/vertical orientation of tubes with anequilateral triangle or square tube profile.

Smooth plain-tube configuration (no enhancements).

Tube material (titanium or aluminum based on a30-year life-cycle criterion).

Biofouling control based upon an achievable

fouling factor.

Heat exchanger centerline located on sea surface.

As an overview of the condenser analysis, the following

major steps in the algorithm are listed in order of their

execution:

Initialization of design variables (DV).

Tube length.

SW velocity through condenser tubes.

Outer tube diameter.

Tube profile pitch ratio.

Amount of heat rejection (139).

Tubeside bulk temperature (142).

93

Total number of tubes (143).

Log mean temperature difference (144).

Conductance (146).

Number of transfer units (145).

Heat exchanger effectiveness (147).

Initially assume a value for ammonia heattransfer coefficient (151).

Single tube conductance (148).

Average heat rejection per tube (152).

Film temperature (153).

Revised ammonia heat transfer coefficient (154, etc.);iterate with (151).

Tube profile, flow parameters across the tubebank (158, etc.j.

Tube sheet diameter (163).

Condenser shellside pressure drop for two-phaseflow (166).

Revised properties at state point 1 (171, 172);iterate with (21).

Overall heat transfer coefficient (173).

Total heat transfer surface area (174).

Revised condenser tube length (175).

Heat exchanger cost analysis.

In the following section, the basic steps summarized

above will be described in detail.

B. ANALYSIS OF THE CONDENSER

1. Amount of Heat Rejection,Q

Using the calculated value for enthalpy at state

point 5, equation (131) from the previous chapter, the ideal

94

values at state point 1, Eq. (211), and the steady-state mass

flow rate of ammonia, Eq. (S), the amount of heat rejected

by the condenser can be expressed as

N ~ (139)

2. Tubeside Bulk Temperature

As in condenser tubeside Reynolds number, salt

water properties will be evaluated at bulk temperature,

initially assumed equal to the cold pipe inlet temperature.

Using this premise, the -ondenser salt water capacity

rate can be evaluated

(140)

where Up. = specific heat of salt water initially evaluated

at the cold pipe inlet temperature.

, mass flow rate of salt water through the cold

pipe previously evaluated by Eq. (10").

Using the results of iqs. I.39) and (40), and the

known cold pipe inlet temperature, the condenser salt water

outlet temperature may be evaluated from the basic expression

where ] : = condenser salt water outlet and inlet

temperatures, respectively.

Having determined the condenser salt water outlet

temperature. the revised bulk temperature zan be expressed as

95

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MICROCOPY RESOLUlJION HTI T CHARI

N I'll

2

Using the revised condenser bulk temperature and

iterating with Eq. (102) corrects the operating temperature

for salt water properties which are essential to the

analysis.

3. Total Number of Condenser TubesIJt

Since the mass flow rate of salt water through the

cold pipe is equivalent to the mass flow rate through the

condenser, according to the law of continuity,

it follows that the number of condenser tubes for a specified

tube diameter, can be evaluated using the following expression:

4

where = average salt water density evaluated at

bulk temperature.

= inner tube diameter (initialized and treated

as a design variable by the optimization code).

V = average salt water velocity through the con-

denser (initialized and treated as a design

variable by the optimization code).

96

4. Log Mean Temperature Difference,LMTD

Using the result of Eq. (141), the known pipe salt

water inlet temperature, and the inlet temperature of

ammonia evaluated at state point 5, the LMTI) of the condenser

may be expressed as

LMTD 7c. (144)

S. NTU-Effectiveness Relations

The number of transfer units which is a measure of

the condenser size can be determined from the basic

expression

NTU UoA. (14S)

where the conductance (UA.)of the heat exchanger is a

function of the heat absorbed and the LMTD.

c = ( LIA.)L D (146)

The condenser effectiveness can then be expressed as

N- r u )( 1 7

for a two-phase flow, regardless of the flow geometry.

97

6. Single-Tube Conductance, U.A.

Using the resistance analysis derived in Chapter III,

Section 4 for an initialized tube length

L=LL

the heat exchanger conductance for a single tube can be

expressed as

-.dL . L A . (148)

where w = tubeside heat transfer coefficient.

Rfs = salt water fouling heat transfer resistance.

= thermal conductivity of the tube material.

AoAi= total outer and inner tube surface areas

(including fin and bare tube); tube length

is initialized and treated as a design

variable by the optimization code).

= ammonia fouling heat transfer resistance

i, f=

1 *outer and inner total fin efficiency

a. Tubeside Reynolds Number

Since the salt water heat transfer correlation

is dependent on tubeside flow, Reynolds number must be

evaluated P? . o .u VW s,14S

where /O42,- salt water density and viscosity are

evaluated for the fluid's bulk temperature.

98

, inner diameter and average salt water tube

velocity.

Reynolds numbers greater than 2300 will be

indicative of turbulent flow [Ref. 31.

b. Salt Water Heat Transfer Coefficient, h,Once again the empirical relationship proposed

by Sieder and Tate [Ref. 3] will be used for laminar heat

transfer in tubes and as defined by

1/3 113 0.14

Nusselt and Prandtl numbers are defined as

= h w di (149)

cp., 115 (150)

where dynamic viscosity, specific heat, and thermal conduc-

tivity of salt water are evaluated at the salt water bulk

temperature.

The effect of the viscosity ratio in the

Sieder-Tate equation is considered negligible, and will

hereafter be dropped from the expression. The assumptions

and validity condition associated with the Sieder-Tate

equation were stated in Chapter III, Section 4, and will not

be repeated here.

99

. . . ,

For fully developed turbulent flow, again the

Dittus=Boelter correlation [Ref. 3] was used.= 0.8 0.3

c.C23RI

Nusselt and Prandtl numbers are previously

defined by Eqs. (149) and (150). Assumptions and conditions

for validity were stated in Chapter III, Section 4.

c. Salt Water Fouling Heat Transfer Resistance

As indicated previously, it will be

assumed that the foulding resistance for tubeside salt

water can be maintained at .00025(hr.tfF/ATU)

d. Ammonia Shellside Heat Transfer Coefficient,AN 3

Initially, kJ,, will be assumed

h41-- 10oo (BTU/h,.+F) (151)

since its value cannot be directly calculated during this

phase of the analysis.

Using the following single-tube thermal

resistance I

Z= I

7p3 I Ftoid;

Z iTKL

- o,,, d. L

100

;~1'~

an initial value for single tube conductance (outer tube

surface) may be calculated

L.A.= 1

7. Film Temperature for Property Evaluation, Tr

In order to evaluate the shellside ammonia heat

transfer coefficient, working fluid properties must be

evaluated at the film temperature.

This can be accomplished by using the results of the

single tube conductance, the tube side bulk temperature and

the working fluid saturation temperature, expressed in the

following equation for single tube heat transfer rate (average).

( UCA (TS-T8ULK) I)

Again using the resistance analysis as in Chapter III,

the shallside wall temperature may be expressed as

Twz~ = Tax (RI -f- z I+?3)

Knowing the shellside wall temperature and the free-

stream temperature, the film temperature can be derived from

their arithmetic mean

T1VV- Ts- (153)

For purposes of this calculation, saturated tempera-

ture conditions at state point 5 are taken to represent

101

free-stream conditions, when in fact the two-phase process

will experience a pressure drop and a corresponding drop in

temperature.

8. Revised Shellside Ammonia Heat Transfer Coefficient,

This analysis will include correlations for both

horizontal and vertical heat exchangers.

In the horizontal-tubed condenser, Nusselt's

correlation was used as a predictor [Refs. 7 and 17],

for laminar flow

= q(Kf L) (154)

where W - estimate of ammonia mass flow rate across

each tube.

= properties evaluated at film temperature.

L = tube length (initialized and treated as

a design variable by the optimization code).

This correlation is probably conservative, since it

does not consider turbulence due to high vapor velocity

or splashing of condensate [Ref. 7].

For turbulent flow, Nusselt's correlation is increased

by 10% as recommended by Jakob [Ref. 17]

04 L/1 (155)

102

4.j

The laminar-turbulent transition point is defined by

a Reynolds number of 2100, where the pseudo-Reynolds number

for.film-type condensation on horizontal tubes is defined

as [Ref. 7]

where r = mass flow rate of condensate per tube over its

length.

In the vertical tubed condenser, both Nusselt's and

Kirkbride's correlations were used as predictors [Ref. 7].

For laminar flow, Nusselt's correlation is increased

by a factor of 1.28 as recommended by McAdams [Ref. 7]:

P71.~ 747( 4 'jz) () (156)

where r= mass flow rate of condensate per tube over itsdiameter.

For turbulent flow, Kirkbride's correlation is applied

-Z / 0.4

\ 0,.0077 (1S7)

The laminar-turbulent transition point is defined by

a Reynolds number of 1800, where the pseudo-Reynolds number

for film-type condensation on vertical tubes is defined as

[Ref. 7]

103

v '

After using the pseudo-Reynolds number to establish

the flow in which regime the system is operating, the revised

heat transfer coefficient for film-type condensation may be

calculated and then iterated with the initial assumption

for the shellside heat transfer coefficient, Eq. (151).

Once again this will have a convergence effect on variables

in which the shellside heat transfer coefficient is a

function, moving closer to actual OTEC system operating

point characteristics.

9. Tube Profile, Flow across Tube Bank, and TubeSheet Diameter

Since the condenser tube bundle involves multiple

rows of tubes, the geometry of the tube profile arrangement

is important to determine the shellside heat transfer coeffi-

cient, the tube sheet diameter and the shellside pressure

drop associated with the "homogenous" two-phase flow model

[Ref. 4].

Using the same arrangements shown in Chapter III,

Section 2, S

IN-LINE Sn

~,= P~ ~(158)

A=: 5n (159)

104

1IV- b

where Sri = pitch ratio x outer tube diameter.

t = pitch ratio (initialized and treated as a

design variable for the optimization code).

Ap = tube profile area per tube

STAGGERED 30.S FLOW

where

!n -2 Pe, do sim 3c" (160)

5P PR d, cos53c (161)

Ap = Sp(162)

the ratio of minimum flow area to the frontal area can be

expressed as

-- (163)

Using the selected tube profile geometry and know-

ing the number of condenser tubes by Eq. (143), the tube sheet

diameter for the condenser design can be evaluated from the

following expression

i

105 _

NtJA 7 JTFSO2 (164)4

where Tp = Tube sheet diameter.

To analyze the shellside ammonia flow velocity, the

following control volume is introduced (turbine generator

discharge and top portion of the condenser).

I YI'".

Mf

Since the mass flow rate remains unchanged across

any boundary

Furthermore, if we assume the condenser has the

capability to evenly distribute vapor across the tube bundle

(distribution baffles), the following development applies

to the vapor coverage:

Let (Af)V AP

where ?P1 = percent of tube frontal area which is covered

by vapor.

106

where As = condenser inlet cross-sectional area.

V7 = turbine discharge ammonia velocity.

Therefore .vs.

If it follows that the turbine discharge

velocity is equal to the average velocity of ammonia at the

tube frontal area boundary. A determination of the distri-p

bution fraction requires a detailed knowledge of the

design of the turbine/condenser interface. In the absence

of this information it is assumed that

v+ = \15

A similar argument could be presented for a vertical

tubed condenser where turbine discharge is admitted to a

distribution ring that bands the condenser tube bank.

Exhaust vapor would travel radially through the tube bundle

and then collect at the bottom after vertical film-

condensation. I . . .

I Is

Vside S

I I

',-- I

L[__Again, in the absence of a detailed design, it is assumed

thatV',E= vs-

107

Considering the minimum free-flow area for a horizontal

tubed condenser, A~f can be derived using Eq. (163) and the

projected frontal area.

A '~i Lt

Aff= ( Sdr )s. (16S)

where Af = the flow frontal area.

Lt = tube length.

For vertical condensers

A; = 1.s- FROAITAL LGN'6rH OF VAPOR? IkLEF FLOW,

Using the previously calculated value of the ammonia

flow rate and Eq. (165), mass velocity for the minimum free

flow area can be expressed as

Al'1 (166)

10. Pressure Drop of Two-Phase Flow across a Bank of

lubes,/AP

The pressure drop in the two-phase flow condensing

heat exchanger will be determined using the homogeneous

model introduced in Chapter III. The model will consist of

three components -- friction loss, momentum change, and

elevation pressure drop arising from the effects of gravity.

The local pressure drop for a two-phase flow may be

expressed as

108

LM -

C&4 ~ j~iF/CJ ij\JTJH ~ j~A~lI'J(167)

For a given channel length, Lc , the pressure drop

components can be expressed by

F FITO L,: (168)

,1 E&1 rum . (169)

7. Lc (170)

where = single phase friction factor by Jakob expressed

in Eq. (35) or (36).

= mass flow velocity determined from Eq. (166).

LC= channel flow length, defined for horizontal

tubed condensers as LC=TsD (tube sheet

diameter) and for vertical tubed condensers

as Lc=Lt (tube length).

D. = equivalent diameter of flow channel, defined by

- mean specific volume defined by

109

where X = quality of mixture (state point 5).

4 = specific volume of liquid (state point 1)

if = specific volume of vapor (state point 5).

All components of the pressure drop model Eqs. (168, 169,

and 170) can be determined using the preceding information.

11. Revised Properties at State Point 1

Since Eq. (167) represents the pressure drop across

the condenser shellside, the actual pressure at state point 1

or condenser outlet may be determined from

'PI (NeVV) = I - A6 C 0 i (171)

where P, is previously described as the condenser operating

pressure for the ideal cycle.

Operating on the saturated liquid line on the

Temperature-Entropy diagram, the following properties

are defined:

hi EVV hf~pNw Pa~ sr(P (172)

The subscript tNew) representing a revised property

will hereafter be dropped from the expression in Eq. (172).

Until now, we assumed the condenser outlet tempera-

ture and pressure were designed to operate as an ideal system,

without a pressure drop. Therefore, using the revised

temperature at state point 1 and iterating over the range

from Eq. (21) until an acceptable convergence criterion is

achieved, all the preceding variables as function of T,

110

'- 2t

will be reevaluated to complete the closed-loop cycle of the

simulated OTEC power system.

12. Overall Heat Transfer Coefficient, LL

The quantity "U" represents a measure of the total

thermal resistances in the flow path. Therefore, using the

tube conductance expressed in Eq. (148) which is divided by

the outer heat transfer surface area of a single tube, the

overall heat transfer coefficient for the condenser can be

determined.

The thermal resistances are now expressed as

hR,-4 .

R.3 =~I~ La

and the overall heat transfer coefficient for the condenser

may be calculated using

U0 Ri R z 4-R +Fs (173)

I,-- -. ,-

13. Total Condenser Heat Transfer Surface Area,At

Having determined the corrected number of condenser

transfer units (145), salt water capacity rate (140) and

overall heat transfer rate (173), the total condenser heat

transfer area can be calculated from the NTU expression

NTLJ= LJ0 t (174)

14. Revised Condenser Tube Length

Using the total heat transfer surface area calcu-

lated from Eq. (174) and the total number of condenser

tubes (143), the revised condenser tube length can be deter-

mined from the basic expression

A~ N+T J Lt(-v !ep~) (175)

At this time, it is necessary ot iterate the condenser

design until the two values (initial and revised) of the

tube length converge. This iteration may be accomplished by

the COPES routine if the following constraint is defined

Minimization of this difference will cause continual

adjustment of the required tube length, already treated as

a design variable by the optimization code.

112

15. Condenser Heat Exchanger Cost Analysis

As indicated in Chapter III, TRW developed sets of

equations to represent the costs of various heat exchanger

component parts for shall diameters ranging from 10-35 feet

and 35-50 feet [Ref. 9].

The following are the TRW component cost equations

for the condensing heat exchanger. Prior equation reference

numbers will be substituted where equalities exist with the

evaporative heat exchanger component cost expressions.

for tatbe sheet diameter 10-35 feet

Drilling time/tube sheet thickness. (58)

Thickness of the tube sheet. (59)

Tube sheet labor cost. (60)

Tube sheet material cost. (61)

Tube installation cost. (62)

Heat exchanger drill cost. (63)

Ammonia distribution plate and bafflescost.

-X 4 N, T 2,. (176)

• Bustle, flanges, channels and flowplate cost.

2#

=3C f i es"Z e TSO (177)

Tube material cost.

fr L () .C t)N d/1,6 (178)

113

where c1 curve fit of tube material cost

per foot.

= tube machining cost if required.

* Heat exchanger header cost. (67)

• Water inlet, nozzles and support cost.

Tube welding costs (Titanium tubes). (69)

The sum of the preceding costs would equal the cost

to fabricate one OTEC condenser with a tube sheet diameter

of 10-35 feet (all the preceding component costs have been

adjusted for current pricing at a 10% annual rate of

inflation).

If our analysis is based on a 30-year life-cycle

criterion, no adjustments are necessary to any component cost

equation if titanium tubing is selected. However, using

Al 5052-0, the expense of retubing must be considered to meet

the 30-year life-cycle criterion, as in the cast of the

evaporation. For convenience, and possible subsequent

modification, these considerations are repeated here.

Based upon the utility of Al 5052-0, two complete

condenser retubings will be required to meet the basic 30-year

criterion. This implies Eqs. (62) and (178) must be modified

to reflect the costs of retubing at the 10 and 20 year point

in the cycle.

114

Aluminum tube installation cost.

C~4- Lr )i IC (1-) ( (180)

where L = projected annual inflationary

rate (input by customer).

Aluminum tube material cost.

Cq rM~ CrJsit(tL L2 J(11

for tube sheet diameter 35-SO feet.

Drilling time/tube sheet thickness (58)

* Thickness of the tube sheet. (59)

* Tube sheet labor and material costs(titanium). (72, 73)

Tube sheet labor and material costs(aluminum). (74, 75)

Tube installation cost. C76)

Tube material cost. (178)

Heat exchanger shell cost. (77)

Ammonia distribution plate andbaffles cost.

r LpN+ O.qTJ (182)

Bustle, flanges, channels andflow plate.

;.1,f (183)

C FF= 32. e24 T50 Ve 13

Heat exchange head cost.'.43

CJE q3q. zYS (184)

i 15

• Water inlet, nozzles, and supporterscost.

Tube welding cost (titanium tubes). (82)

As indicated previously, the cost to fabricate one

OTEC condenser with a tube sheet diameter of 35 to 50 feet

is equal to the sum of component costs (note, all the

preceding component costs have been adjusted for current

pricing at a 10% annual inflation rate).

For an analysis based on a 30-year life-cycle

criterion, the additional costs for replacing aluminum

tubing must be considered and Eqs. (180) and (181) apply.

116

VII. NUMERICAL OPTIMIZATION

A. INTRODUCTION

Nearly all design processes attempt the minimization or

maximization of some parameter or design objective. For

the design to be acceptable, it must satisfy a set of con-

straints which impose limits or bounds on design parameters.

For the stated problem a computer program can be written

to perform the basic analysis of the proposed design. If

any parameters fall outside the prescribed bounds, the design

engineer changes the parameters and re-runs the program. In

effect, the computer code provides the analysis with the

engineering making the actual design decisions.

A logical extension to the computer-aided approach is a

fully automated design, where the computer also makes the

actual design decisions and performs trade-off studies. The

COPES program provides this automated design and trade-off

capability by the use of the optimization program COPES/CONMIN

[Ref. 18]. COPES is an acronym for Control Program for

Engineering Synthesis, and CONMIN is an acronym for CONstrained

function MINimization. Subsequently, a FORTRAN analysis

program simulating a closed-cycle OTEC power system can be

coupled to the COPES program for automated design, using

some basic programming guidelines [Ref. 18].

117

B. COPES/CONMIN

There are many numerical optimization schemes available

to the engineer. Methods employed by these schemes fall

into four basic categories: random search, sequential

unconstrained minimization, optimality criteria, and direct

constrained optimization. The optimization program,

selected for automated design analysis of the simulated

OTEC power system, is based upon direct constrained

optimization.

Before any discussion of the optimization technique,

basic definitions are summarized for convenient reference

[Ref. 19]:

* Design variables - those parameters which the

optimization program is per-

mitted to change in order to

improve the program.

Objective function - the parameter which is to be

minimized or maximized during

the optimization process.

Inequality constraint - one-sided conditions which

must be satisfied for an

acceptable design.

Equality constraint - condition which must be

equaled for the design to be

acceptable.

118

I *

Side constraints - upper and lower bounds in a

design variable.

Assuming that the FORTRAN analysis program has been

developed and a particular objective function has been

selected, the general optimization problem can be stated

as [Ref. 20]:

Find the vector of design variablesX, to

Minimize FC') (186)

Subject to the constraints:

i,,Nc,; (187)

H ±(0) j=I,NEQ (188)

VL B- 1XVUB L=iNOV (189)

where X = the vector containing the set of independent

design variables.

F(9) = the objective function to be minimized.

j(<) = inequality constraint (NCO4 is the number

of such constraints).

Hj(x) = equality constraint (NEQ is the number

of such constraints).

VL13/VUBL= lower and upper bounds, respectively,

on the design variables.

If all inequalities of Eqs. (187) and (189) are satisfied,

the design is said to be feasible if any constraint is not

satisfied, the design is infeasible. If the objective function

119

is a minimum and the design is feasible, it is said to be

the optimal design.

In order to start the optimization algorithm, the

initial set of design variables,X , must be specified. It

is desirable, but not essential, that the initial design

variables provide a feasible solution. The optimization

algorithm will then proceed in an iterative fashion using

the following relationship

where = the iteration number.

scalar quantity which defines the move in the

search direction.

vector search direction which will reduce

the objective function (useable direction)

without violating constraints (feasible

direction).

To solve this problem, the optimization program

COPES/CONMIN is used (Ref. 18]. CONMIN uses the Fletcher-

Reeves algorithm for locally unconstrained problems [Ref. 20]

and Zoutendijk's method of feasible directions (modified to

improve efficiency and reliability and to deal with designs

which do not initially satisfy all the constraints) for

locally constrained problems [Ref. 21].

However, CONMIN does not handle equality constraints

directly, but rather by means of penalty parameters. To

achieve this, the objective function is augmented as follows

120

[Ref. 19]

haq

(>.K (190)j= I

and the equality condition of Eq. (188) is treated as an in-

equality constraint

The penalty function approach effectively satisfies the

equality constraint while maintaining the rapid convergence

characteristics of the CONMIN program.

The numerical optimization problems of equations (186)

through (190) are very general, allowing for any number of

design variables and constraints. In assessing the value of

optimization, the automated design provides a very attractive

approach to numerical optimization; however, there are both

advantages and limitations to these techniques [Ref. 203.

Advantages:

Reduction in design time.

Systematic design procedure.

Applicable to a wide variety of design variablesand constraints.

Virtually always yields some design improvement.

Not biased by engineering experience.

Requires a minimal amount of man-machine interface.

Limitations:

Computer times may increase dramatically as thenumber of design variables increases. A practicallimit imposed by the current state of the art formost problems is 30 design variables.

121

Optimization techniques have no stored experienceto draw upon; the validity of the result islimited to the validity of the analysis program.

The results of the optimization are as correctas the analysis program is theoretically precise.

Optimization algorithms used here cannot deal withdiscontinuous functions.

* The optimization program will not always obtain aglobal design optimum and may require restartingfrom several different points to acquire reason-able assurance of obtaining the global optimum.

The analysis program must be properly structuredto couple with the COPES/CONMIN optimization code.

C. DESIGNATED DESIGN VARIABLES, CONSTRAINTS AND OBJECTIVE

FUNCTION

To assist in the interpretation of the enclosed OTEC

power system FORTRAN analysis, the following summary identi-

fies the design variables, constraint functions and objective

function used in the analysis and subsequently operated

upon by the COPES/CONMIN optimization code. These parameters

are all contained in a labeled COMMON block in the computer

code, referred to here as "GLOBAL COMON." Specific

GLOBAL COMMON location numbers and upper/lower bounds for

operating parameters summarized below can be located in

Appendix C.

Design Variables

Inner cold pipe diameter

Inner hot pipe diameter

Inner ammonia circ pipe diameter

Inner ammonia re-flux pipe diameter

122

* Evaporator operating pressure

* Condenser operating pressure

Outer condenser tube diameter

Outer evaporator tube diameter

Evaporator tube length

Condenser tube length

* Condenser tube salt water velocity

Cold pipe salt water velocity

Evaporator tube salt water velocity

Hot pipe salt water velocity

* Evaporator tube profile pitch ratio

Condenser tube profile pitch ratio

Constraint Functions

Operating system pressure ratio

Upper temperature bound of ammonia

Lower temperature bound of ammonia

Satisfactory enthalpy at state point 5

Satisfactory quality at state point 5

Satisfactory condenser tube length

Internal turbine efficiency

Evaporator tube sheet diameter

Condenser tube sheet diameter

Objective Function

Cost of major power system components

123

i17%,1 7

VIII. CONCLUSIONS AND RECOMMENDATIONS

A. CONCLUSIONS

1. The use of an analysis code for OTEC power systems

coupled to COPES/CONMIN optimization code provides a power-

ful tool to design an optimum power system for the desired

net electrical output, measured against the objective

function. Such a design could permit construction of higher

capacity systems using the optimized modules as substations

of the total power plant.

2. The analysis code coupled to COPES/CONMIN provides

an excellent vehicle to evaluate proposed designs relative to

a true optimum. Tables 1 through 4 illustrate the result of

preliminary calculations using the analysis code with an

objective function to minimize system cost. From these, the

following conclusions can be drawn concerning horizontally

oriented aluminum (Al-5052) and titanium-tubed heat exchanger

power systems:

a. The cost/KW output is nearly constant over the

range of optimum designs for both titanium and aluminum tube

heat exchangers.

b. During testing for feasible plant designs in

increments of S MW (net) electrical output, it was observed

that a higher megawatt output plant could be achieved with

titanium-tubed heat exchangers than for aluminum (Al-5052).

For titanium-tubed heat exchangers, a 25 MW (net) power

124

WIN771

system is a feasible design; however, aluminum-tubed systems

could not provide a feasible design for the same output.

Titanium tubed plants failed to produce a feasible design

for a 30 MW (net) output power system. In both cases of

infeasible design, the constraint which was consistently

violated was turbine internal efficiency, set at 90% for

current state-of-the-art design.

c. The energy conversion and efficiency of design

of a turbine-generator has a major effect on the overall

system performance as indicated in paragraph b above.

d. The cost/KW output for titanium-tubed heat

exchangers is one third the cost/KW output for aluminum-tubed

heat exchangers using a 30-year life-cycle criterion, with a

10% annual inflation rate and retubing at 10 and 20 year

marks with AL-50S2 tubing.

e. Aluminum-tubed heat exchangers have larger tube

bundle volumes, with volumetric differences between aluminum

and titanium varying from 26.1 to 11.8% for evaporators and

23.2 to 7.4% for condensers over the range of net power

levels considered. In both cases volumetric differences

diminish as the system's net electrical output increases to

20 megawatts.

f. COPES/CONMIN has provided optimum designs for

each incremental output power level. By manipulating the

specified design variables, subject to imposed constraints,

COPES/CONMIN has created designs whose geometry and operating

125

parameters cannot be scaled on the basis of net power output

(10 MW). Therefore, designs for component geometry at

increasing power levels based upon such simplistic scaling

criteria will not achieve an optimum design with respect to

the cost objective function.

B. RECOMMENDATIONS

1. Evaluate additional objective functions including:

a. Minimize heat exchanger volumes.

b. Minimize parasitic power losses.

c. Maximize thermodynamic efficiency.

d. Maximize net electrical output.

2. Perform a sensitivity analysis on power system design

variables to evaluate their influence on component and system

performance. This allows the designer to prioritize system

components which can provide improvement in the objective

function for a corresponding improvement in component design.

3. Considerahle uncertainties are associated with the

expressions used to estimate component performances (two-phase

pressure drops, film coefficients, etc.). The code should be

tested to determine the sensitivity of system design to these

uncertainties.

4. Expand the code to include the use of enhanced heat

transfer techniques and evaluate the influence of increased

piping friction factors on pumping power requirements.

126

wak"-l

5. Evaluate proposed OTEC designs using proposed system

parameter inputs, comparing both the basic analysis and the

optimization output.

6. Select other analytical expressions for heat transfer

coefficients to validate the performance and output of the

existing code.

7. Evaluate the effect of a smaller thermal difference

seen by the power system and its influence on a feasible

design for a specific net electrical output.

8. Evaluate the cost aspects of using variable-pitch

pumps versus fixed-blade for a variable thermal gradient

environment.

9. Evaluate and verify the influence of incremental

improvements (percent) in turbine internal/adiabatic efficiency

with respect to gross and net electrical outputs and compare

with the results reported in Ref. 16.

127

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Z: Z 31 z

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139

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cc 00 cc c0 r-'

00 te 00 N 0 0 0

bn *. 00 0000 N

0) 0 Ln tn 0-~~~~c -,Oi f Ll

-C -f C- 0 -tN

0

3 M 00 t VtnN 00 m~ Vo I- tn uL co

* * 00 LM ~ -d' ' 00 r ,

cc 0 A : .

z4 z

LLn

wL z V) ~ - -

Q >~' ~ -C~

-T z-

144

Ln INFEASIBLE DESIGN

0 _ 0

cc r- Ltn - ~

B~~~ r- \.

r - "T 00 TrCI

0 m 00 \10

0 rq 0.~~ 0 r- . -'

o1 E-. q ' c - ~ N- N

ad CL NJ :mw E- cow~t 0 cc

U4 L- C6- F= ,~ r~ '-' ''

cn U)C uj -go

= -, - c

F- '-~ -~ C.~ ' 1 -5

Ij ~ INFEASIBLE DES16N

Lr. ~ r~ r"

CZ zz ~c ~ *'Ln

< ~~ . *z

uj 00

02 -ILI-

146

l\VE:\SIBLE DUSIGN

~ 2Z ~ -~J~ -~

- - -~ ,z -

r-- ~ -~ -. ~~1

- -

- - -~ -.- ~

-~ -. -J x- -r -

- - - - -

., -

F.

J-.~ -

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- -. - -- -

-

z7

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- I- -~- a-

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- - _ z -~ .1' 7--a. -

- - -~ - - - - z -

-- -a-

- - - .-- -

-a- - .z - - - 7-~ - .7 -

1-I-

INFEASIBLE DESIGNLO~

r - 00 00 , n t

00 0 0 -

Tr - z 00 N- -!T L * n

SLS

00 *r C7 N-n

'S SLU4 =Z J NJ c~~~~*~1 00 rLnL~ U fl c - ~

-, n L^ * n * n -

- -l 00 -,i .!r

U 0 CIA

x -.- -

- ZZ- i

cr -zz

L:4- - C-

o ~ Z ~ ~ - ~ E- E-

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148

INFEASIBLE DESIGNU,

rn 1-4-3

00 -T

U, o . r-0 cct

00'

C) * U, '

00 LnLLn 00 Ln

U, ~ U,

Pe 0u q t) 0ln :O

- ~ - *~-*'~*'~ '0 ~ ~ r* L

U, n

'AnC~L

co~ ~00AL * C-

-n (. !T

rZ~~J~ ) '

-APPENDIX A

SAMPLE INPUT DATA FOR OTEC ANALYSISEVAP0O(ATGFR - r1UgIZUNTAL

TUBE O.C. 1.u 10 ( I NJ) 25,..

TUBE LENGTH -t9.3J0(FT) 12. 1;2 (M)

SW TUBE IEL 6. 0 "00(F T/ S) 1&(m4/S IOPER PRESSJRE L 3 0. 0 00( Lt3F/ 1*2TUBE MATERIAL - T[TAAIU!4

THERM4AL COJND(;04 9.5JOHTUj/Hk.FT.F-) 10.5 j2C ~MCTUBsE PRCF ILE - ST kG._REJ E-,J 1-L.ATEP.L

PITCH AArIG 1. 50

ENH-ANCEM&NT - PLALN TU3E

CO'NENSER - riUKI/L']NT4L

TUBE 0.0. L.JJU(1\fl

TUBE LENuTH 56.5 O(FT) .2l)

SW TUBE iEL ).UJOIFT/S) 1 .3 2H4 A/ S

UPER PREiSUME d).0OjO(L3F/L',q2 I004mA

TUBE 4ATERIAL - TITA,41JM

THERMAL COND(K) 9.5J0(d3TJ/HR.FT.F) 652M.C

TUBE PROFILE - STA7%~RED EJI-LATIL -A

PITCH RATiJ 1.50

ENH-ANCEMENTd - PNAir ru3E

SALT WATERHO iT PIPE

PIPE 1.0. 19. 3 )Q (FT) 5. 333 A)

PIPE LENGJTH 3,.j3.00I(F T)I

SW PIPE VEL 5 )() (F T/ S) 1.372(,4/S)

SW INLET TEMP 8J.QSOCUEV F) 26. a1(UEGY C)

SW SALINlTy 35. (JiUUU

SALT WATER COLD) PIPE

P IPE 1 .0.I). b fb (F T) 5 . y 7,t 4)

PIPE LEN'~GTH 3JJ3.0JOCFT) 4ej (

,W PIPE VEL 5. 5 3J(F T/ S I1SW INLET TEAP '4.0)JD' F) .-- +UGC

SW SALINITY 3i. /0

AMA4ONIA CIAC PIPE

PIPE I.0d. 2.000(FT) 0.61004l)

PIPE LENGTH 15).OCO(FT) -t5.11OC(4I

PLMONIA RE-FLJX PIPE

PIPE 1.0. 2.OOO(FT) 00V4

PIPE LENGTH- 50.0CJ(FT) 15.2'tO (1)

PUAP AND GEN-TURt3 PERFi]RAANCE

EVAP Sw PUM4P

EFFICIENCY M E H 3.U3(pCtf) TC -- 8.))(PCTJ

CONO S" Pu;4P

EFFICIENCY YIECH 35.00(PCT) 4 3TO.J4 98*.JJ(PC T)

AM4MONIA GIrAC PU:IP

£JEt-TURB EFFICIENCIE3

GEN MEt;H&ELECT )o.j(PCT)

TJRB1 MECHI ~ ~ ~ OT

POWER PECUI1&EMENTS

N4ET POWER JJTPJT

151

APPENDIX B

SAMPLE OTEC ANALYSIS OPTIMIZATION OUTPUT DATA

EVAPCRATCR - ?CRILO:4JIAL

HT ABSORi3 Z)5I37o0.(3Tl/HA) 537.6UL('4o)

Sri FLOW 3340Ul~iO.O(LR81/HR) 1515359-.J)( ('%/HR)

S4 TEMP IN 83.OCOtDEG F) 26.-b713E ZC)

sA rEM,' OUT 73. 72-t(0E, F1 23.13j(]E' C?

OPER PRESSJRE 3)b31Lf/~ .-)87(.KPA)

EVAP SAT T&6)' 70.535(JE, F) 21.43 )E. C)

OUTLET TEAl' 7).5L'.(DE F) 21.i,97'JE ; C)

OUTLET QJALITY )2.30(PCT)

NH3 PRESsi DRU-P U).162(L8F/lN2) 1.ii,(KPIX)

TUBE CHAKACTERISTILS

OUTTER 3LA 0.9:)( IN)4 2 4. 13 4)

LENGTH t.132(FT) 12.357(4)

MATERIAL - TITANIUM

TUBE PROFILE - STA-,GERED '-QuI-LAT& AL

PITCH- RATIO 14

ENHANCE4E'd - PLAIN TUcdf

SWr VEL ;CITY 6.02'IFT/S) 1374S

T AALL( SHELLS LJE ) 71.-tob(DElp' Fl I1. 4 C)( JE; C)

IFILM TEMP 70,QCIO(L)EI F) 21.661(3E'A C)

OELTA T iJJLLING 0. 952(DE~p F) '.2(EiC)

L.A. T. 0. 3.757(LE,: F) 3.198J. C)

EVAP EFFECTIVE-4ESS .6

NR OF TRA~NSFER UNITS L.,)Q3

OL HT CUEF b12.97(BTU/HR.FT2.F) LO5'1/~C

r-H~ATEA) il5t.qr(rrjfHR.FT2.F) b336.?1(.4/42.CJ

H(FOULI'46) 3/3,3.TJ/+riJri.FT2,F) 2L5L2.J)( i/42.C)

H41METAL) -+44.i2huTJ/M,4.FT2.F) ~3.~/!0

H(AMMUNIA) -+Qda4(3T/RF2.FI 23215.J)4.*/42.C)

152

AT SuRFACE 5724J5i. J(FT2) 53178.12(-421

TU6E SHEET OIA 27.213(Fr 3.B.A

TJT NR OF 1'J3ES 5+tq

SW PRESS .)R0P 4. Ool (LBF/11\2 ) 3JiKA

,AOISTURE SEPARATOR- INSI DE EVAP SHELL

OPER PRESSUAE 129.935(LBF/IN2) 395.872(KPA)

OUTLET TEMP 7O.333(DEG F) 21.296(JEG C)

OUTLET QUALITY 39.50(PCr)

NH3 PRESS DROP J.416(LBF/I'C2) 2.3ai(&PA)

CO4DENSER - HiU-<t1JNT.NL

T REJECT 1935472346.J(3TJ/HR) it)7.22(41A)

Sw FLOvo 33487L532.J(L3'/HR) 151894363.0(KG/4R)

Sm TEMP IN 4d.0O(DEG F) 4..t-*-(JEG C)

S5i TEMP OUT +6.0550)EG F) 7.iOS(3E-. C)

NH3 FLCW 37337J)a.0oLc3/Hk) 1713514.J(&G/HR)

OPER PRESURE o.151(LBF/IN2) 6)7.731(KPA)

CLJND SAT TE'IP 4:+-.351(DEG F) I.u-t5(JEG3 C)

OUTLET TEMP 49i.23c3(DEG' F) 9.,77(DEG C)

,%H3 PRESS DROP J.206(LOF/1N2) l.-+23(KPA)

TU13E CHARACTERISTICS

OUTTER DIA ).972( IN) 24.o83( 144)

mALL THICK J.2(N .~i :42 1I)

LENGTH >7.'iL6(FT)175J')

MATER~IAL - TITAN[J4

TUBE PROFILE - STAGGERED EQXII-LATERAL

PITCH R~ATIO 1.40

ENHANCEMENT - PLA[4 TUBE

S4 VELOCITY b.017(FT/S) 1.634(14/S)

T 'MALL(SHELLSIOE) '4.331(OEG. F) Q.073(DEG C)

FILM TEMP~ 46.785(DEG F) ).325(JEG C)

LOELTA T C0.140 J.907(DEG F) 0.5O'tIJEG C)

L.M.T.Do 5.683(DE, F) 3. 15 7(OEi C)

CONO EFFECTIVENESS J.b35

NR OF TRANSFER JNLTS 1.0b5

153

C\IL HT Ci)EF -t4.33 ( TJ /HR FT2 F- 2537.11( v/'42.C)

H (FOUL ING) .3792 .J0 TJ /HR. .FT2.F 21531 .7j(4112.C)

H(METAL) .5-J .63 (3TJ/HR .F TZ.F) 2494)41. i'J( r~A2 .C

H(AMMC.NIA) 3 u53 .a5 ( TJ /HR .FT2.F) 17367. o3 ( W/. C I

HT SURFACE 7b219 ).25(FT2) 70d09.69(.42)

TUBE SHEET L)IA 27.1.q4(FT) 9.289('4)

TOT NR OF TUBES 52L79.

SW PRESS JiROV 5. 636 (L3F / 1 NZ 3.o()

SALT WATER HOT PIPE

PIPE 1.0J. 2J.077(FT) o. L.)j(MI)

PIPE LENGTH 3'JO.0'JO(FT) 91 4AA

SW PIPE VEL 4.537(FT/S)1.4L( /3

SW FLOo 334O8I2~iO.0(LBl4/HR) 1515359O4.')(Ku'/H-:)

SW INLET TEMP dO.OJO(DE, F) 26.667(DEG C)

SW SALINITY 35. J/0)J

SW PRESS DROP J.322(LBF/IN42) 2.211(KPA)

SALT WATER COLD PIPE

PIPE 1.0. 13.622(FT) 5.b7o(*A)

PIPE LENGTH 306J.JOO(FT) 14. 4O 0 ( A

SW PIPE VEL 5.334(FT/S) L .62 a( A/ iI

Sfi FLOW 33'td71552..J(LtY4/HR) 1513'q43bd.J(t 6/HR)

SW INLET TE'4P .tO.000(DE3 F) 4.t'i4(DE. C)

SW SALINITY 35. J/OQ'J

SW PRESS DROP O.508(LBF/IN2) 3.301(KPA)

AMMONIA CIRC PIPE

PIPE 1.0. 2.001(FT) J.6LJ(M)

PIPE LENGTH 1.5JOCO(FT) 45. 72 J( 4)

NH3 FLOW 3788708.0(LB4/MiR) 1TI3519.J(( G/HR)

NH3 PRESS DROP 15.033(LBF/1N2) 103.05'JC.PA)

AMMONIA RE-FLJX CIAC PIPE

PIPE 1.0. 2.OOOCFT) 0.bIJ( A)

PIPE LENGTH 5J.DCO(FT) 15.24.J('I)

A'H3 FLOW 113662.0(LdA/HR) 515555.34,(G/HR)

NH3 PRESS OROP 9.874(LBF/1N42) 68.-)71(KPA 1

154

PU AP A 140 G cA JB1 P L NF ,A A. 4C F.

HEAD PK4ESi 3. 8 4 6( T 3 1 Tr(MI

EFFICIENCY AE~ri 3, ). CT) 14,DT J R 98.J)( PCTJi

COND Sw P'UMP

HEAD PRESS 20.753(FT) ?o227( A)

CAPACITY oijell9.Z(GAL/MI:4) 24,j3271.J( LI T/MIN)

EFFICIE-1CY A ECH 3:).JO(PCr) 46 TJrZ 98. J)I( t-C T)

AMMON LA 1 IRC. PUMP

HEAD PR.ESS 2L2.327(FT) b+774

~EFFICIENCY AEC 7 l. )3 ( CT '1 T JR 49 . J( PC T)

AMMONIA iE-FLJX PU-AP

HEAD PRESS 33.UIb(FT) lilA

cApkclry .fjZ. 4(,AL /4 1i) ]4127.1(LIT/MINI

EFFICIENCY IECH 75. JD(PC T)4 MTB,' ~8.J3P~C T)

;EN-TUkB EFFICIENCIES

GEN MECH&ELECT )b.b3(PLT)

TURI3 MECH 9.30(P'OT)

TURB INTERNAL 39.d3(PCT)

TURd OUTLET QUALITY 36.77(PCT)

PQ.4ER rALMULEMENTS

TUR13-GEN GIAOSS 27bc3.3131HP) 2.3(41

EFFICIENiCY LJSSES 0. 5 5 ( Avo)

EVA? Skq PU4P 19o4t. 8 31(HP) 1. 6(40

CONOI Sw PUAP 4 L24. 313 (HP )3. 1,+4 1.vio

NH3 C[RC PUMP 5'.i.714(HP)0.-12(lo

NH3 RE-FLUX PU:4P 2-J.097( HP) .0214

NET POJWER OUTPJT 15.ojU(%4WJ

PERCEAT PARASITIC POnE .5?(PCT)

THEMOYNAMIC LYCLE EFFICIENCY 2.65( PC T)

CJST JF CO.4PC.NE.rS

EVA PC AT OR il 23 6 12. )( DCLL4RS)COND ENSEA 3 6 713 4.J ( DOLLARS)

GENERATOR 3720 5.06 C ) OLLARS IEVAP Sw ?Um4p 6 53 332.94(CUOLLARS)CONJ SW~ PUM4P 5 5 2 29 8.36 (DOLLARS)%Hk3 C.IRC PJ14P )36824.94IJDOLLAIS)NIH3 RE-FLUX PUMP a4443.34(3OLLA.;S)

CPrIM'ul~ COST ZOS-i+921a.J)( )0LLAA')COST PER N'ET Km~ 3jTPUT 1369.951OLLA.ZSI

156

APPENDIX C

SAMPLE COPES OPTIMIZATION AND SENSITIVITY ANALYSIS DATA

$BL'JCK A (rimL: rAROJCC-EA~4 THEiRAAL tNER-Y CONVERSiY14 (OTEC) P3m4 SYST'4SbLUCK 3 (P)uGAM~ CONTRI3L PARA4ETERS)2,I616b

2 16bLSIoL3CK (INTE;ER OPT CC)NT.UL PARAMETRS)5,,),3, 5

5 0 5SBL3CK J (FLLJArI.4G PT OPTr PR2.J P4AAEE3.3

S6LOCjc E ror-' AR Lk &w VA~tDE.3IGI' jij* Lc4 4',40 SliH

16 27 -1.3St3L3CI( F (DE31IJN VARIABLE 3OUi3S,I:4I VALJES S &OALE FrCTC''-'

1. .3+2j*J, 1.J+20

1.3 1.3+231.3 1.0+2)

1.3,1...2+2o11. J+202

d5. Jv,13.J35.3 146.J

J.5,2.53.., 2.53.5 2.5

10.0, 1.3+2013.3 L. 3+2)

IU.3 .. 2313.3 1.0+2j

2.3, lu.32.3 3.

2..),13.32.0 10.3

2.3, 10.32.0 13.0

2.3,13.02.3 10.0

1.-t, 3.31. 3.3

1.',,3.01. 3.J

S6LtJCK G (0 5S1 vN VARIABILE IIDE'4)

it 11 1.

3,3#1.0

3 .

5,,,t 1.J

157

7,7, 1.07 7 1.1

88,.0

13 1 . i

1,9, 1.J1 1.3

15,15, 1. J

11,11,I .0

15 11 ..

12, 12, 1 ..12 12 1.3

14J, 13, 1.0 13 13 1.314,14 ,1 .

14 14 1.315,15,1.3

15 15 1.916, 16,1.3

16 Lb 1.3$5LUCK H (IR 3F CONST.AtNEJ ?trAMET2RSi5 5SbLJCK I (CONSTRAINT IOENT AND BOUNDS)17 17

1.,J.J, 3. ,0. 01. 0.0 3. 0.018,2313 20

C.1 ,3.3, 1.0+20,0.0u.1 3.0 1.0+2) 0.3

21,23 21 230.,0.U, L.0+20,J. 0

0. 0.0 1. J+20 O.J24

24

3). 0.0 9). 0.325,26

25 2610.,,.J,1.0,23,3.O

1j. J.3 1.0+20 .S13LQCK P (SENSITIVITY 05JECTIVES)27,3

27 0l,2,3,4,5,6,7,3,9,LOll, L2,l3, 14,15,16,7,13,19,20,

1 2 3 4 59 Lo 11 12 13

17 L8 I 20 2125 26 27

21 ,22,23,24,2 5,26,2 767

14 15 Lh22 e3 24

SBLOCK Q (SENSITIVITY VARIA6LE 80UNOS)1,0

1 618., 3. ,15., ld.,2J.,25.

13. 10. 15. 18. 20. 25.

2 618.,10.,1. , 13.,20.,25.

13. 1O. 15. 1 J. 20. 25.3,6

158

3 o2. ,0., L. ,2. ,3. ,4.

4 62..,0.5, 1.,2. ,3. ..

2. 0.5 1 . 2. 3. 4.5 6

30. .128. , 29., 130. ,13 1. .132.

L30. 123. 129. 13). 131. 132.6,5d9.*,dl/. , 88. , 9., ) , 9j.

89. 87. 33. 8". 90. 91.7,o77 6

L., .5, .75, .9, .25, L.51. .5 .75 1. 1.25 1.5

8,

1. .5 .75 . 1.25 1.59,5

9 640.,30.,35.,43.,45.,53.40O. 3j. .35. 4j.. 50.10,3

1055. 945. ,50.,55.,60.,o5.55. 4j5. 53. 5.3. 60. 65.1 , 6 L

7.7. 5. 5. 7. 3.12,o

12 64. ,2..3.,4.y5.,6.

2. 3. . 5. 6.13,6

7.,5.,6.,7.,B.,9.1. 5. o. 7'. 3.14,6

I,+ b4.,2.,3.,4.,5.,b.

!. 2 3. ,.5. 6.15,56 15 1I.oo .4,1.5L.o ,l.7,1.8

1.6 1.4 1.5 i. 1.7 1.31696

16 b1 .0, 1.4, 1.59 1 .6, 1 .7, 1. 31.6 1.4 1.5 1.0 1.7 1.3ENt)

159

I-Af-

9 %. - %4.

d -V i2 i.

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-j4 wl- 9.Wt4 - ()-W 0 j ML) 0O'M MLZM NW t*I- cownu ..Ji

cc ~ ~~ ~ ~ z77...- --O 4 u

n -if-) moL 7w WU CCO I-:)U- -0- O 0 cr -0. 9-0-04 I4--- ~-.. -- 4

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LA >4-w --- LNOWUW Z--*W4.JW .W-.i&7- i MCL0.W<XLL .. O.. -AI2120 zoml-Wcw42 0oIn.Lnou(z l< =42 ZI 20z-a tu 4 u.iZZ-a <W ..J00..o -I Ou~ 0>wO~w~zo>..-*%<<WW W..JZa.J-qZw .oww j.

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160

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U. - U. M

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1-t 03 2 ZI-wu :Do Mmz1- ZZZ- *03:_Z WWW M I.-t)0- .- W uj -WLU u = I.- 'r"W -._z2- Ma-W ~ ~ ~ Ui

a (jAn W LMl 0 M-L-Y.r- 0 I-,-4. = ~.ee .-xx--o,-0o-- 7 W-O- T=u.- WU C2:a44U.. Z- LU.U~Z s..-r' --

W-U -O 4'*-Z ZL LW.>4-mUWWWU.. WI_ -- c 0 <1- f44

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LIST OF REFERENCES

1. Office of Technological Assessment, Renewable OceanEnergy Sources, Part 1 OTEC, p. 7, May 1978.

2. Claude, Georges, "Power from Tropical Sea," MechanicalEngineering, v. 52, No. 12, Dec. 1930.

3. Holman, J. P., Heat Transfer, 4th ed., p. 204-223,McGraw-Hill, 1976.

4. Tong, L. S., Boiling Heat Transfer and Two-Phase Flow,p. 76-79, Wiley, 1965.

5. Perry, J. H., and others, Chemical Engineers' Handbook,4th ed., p. 18-82, 83, McGraw Hill, 1969.

6. Owens, W. L., "Correlation of Thin Film EvaporationHeat Transfer Coefficients for Horizontal Tubes,"Proceedings of the Fifth Ocean Thermal Energy ConversionConference, 'Vol 6 of 8, Miami Beach, Florida (February20-22, 1978).

McAdams, W. H., Heat Transmission, 3rd ed., p. 325-343,McGraw-Hill, 1954.

8. Lorenz, J. J. and Yung, D., "Combined Boiling andEvaporation of Liquid Films on Horizontal Tubes,"Proceedings of the Fifth Ocean Thermal Energy ConversionConterence, Vol 6 ot 8, Miami Beach, Florida (February20-22, 1 8).

9. TRW Contract No. EG-77-C-03-1570, OTEC Power SystemDevelopment Utilizing Advanced, High-PertormanceHeat Transfer Techniques, V. 2, p. 1 1-36, 30 Jan 78.

10. Streeter, V. L. and Wylie, E. B., Fluid Mechanics, 7thed., p. 23S-239, McGraw-Hill, 1979.

11. Baumeister, T., and others, Marks' Standard Handbookfor Mechanical Engineers, 8th ed., p. 3-57, 58, McGrawHill, 1978.

12. Metrek Division of the Mitre Corporation Contract No.ET-78-C-01-2854, OTEC Power System Performance Model,by H. Abelson, P. 74-81, August 1978.

231

13. Neuman, G. and Pierson, W. J., Jr., Principles ofPhysical Oceanography, Prentice-Hall, 1966.

14. Sverdrup, H. V., Johnson, M. W., and Fleming, R. H.,The Oceans Their Physics, Chemistry, and GeneralBiology, p. 1053, Prentice-Hall, 1949.

15. Westinghouse Electric Co. Contract No. EG-77-C-03-1569,Ocean Thermal Energy Conversion Power System, Phase 1:Preliminary Design, p. 9-9, 4 Dec 1978.

16. Kostors, C. H. and Vincent, S. P., "PerformanceOptimization of an OTEC Turbine," Proceedings of theSixth Ocean Thermal Energy Conversion Conterence,Vol 1 of 2, Washington, D.C. (June 19-22, 1979).

17. Olsen, H. L., and others, "Preliminary Considerationsfor the Selection of a Working Medium for the SolarSea Power Plant," Proceedings, Solar Sea Power PlantConference and Workshop, June 27-28, 1973.

18. Vanderplaats, G. N., COPES - A User's Manual preparedfor a graduate course on "Automated Design Optimization"presented at the Naval Postgraduate School, Monterey,Calif., March-May 1977.

1). Vanderplaats, G. N., Numerical Optimization Techniquesfor Engineering Design, Class notes for a graduatecourse on "Automated Design Optimization" presentedat the Naval Postgraduate School, Monterey, Calif.,May 1978.

20. Vanderplaats, G. N., "The Computer for Design and Opti-mization," Computing in Applied Mechanics, AMD-Vol. 18,ASME Winter Annual Meeting, New York, Dec. 1976.

21. Vanderplaats, G. N., Method of Feasible Directions,Class notes for a graduate course on "Automated DesignOptimization," presented at the Naval PostgraduateSchool, Monterey, Calif., July 1978.

232

LIM.,

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No. Copies

1. Defense Technical Information Center 2Cameron StationAlexandria, Virginia 22314

2. Library, Code 0142 2Naval Postgraduate SchoolMonterey, California 93940

3. Department Chairman, Code 69Department of Mechanical EngineeringNaval Postgraduate SchoolMonterey, California 93940

4. Assoc. Professor R. H. Nunn, Code 69 Nn 2Department of Mechanical EngineeringNaval Postgraduate SchoolMonterey, California 93940

5. Asst. Professor G. H. Vanderplaats, Code 69 MeDepartment of Mechanical EngineeringNaval Postgraduate SchoolMonterey, California 93940

6. LCDR Raymond C. Schaubel14673 Charter Oak BoulevardSalinas, California 93907

7. Dr. Harvev Abelson IArgonne National LaboratoryWashington OfficeSuite 185400 N. Capitol Street, N.W.Washington, DC 20001

8. Mr. Gene BarsnessOTEC Project ManagerWestinghouse Electric Co.Lester BranchBox 9175Philadelphia, PA 19113

9. Dr. James W. ConnellDirector, Thermal SciencesEnergy Systems DivisionAlfa-Laval Thermal, Inc.South Deerfield, MA 01373

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10. Mr. Bruce E. Dawson 1Foster Wheeler Energy Corp.110 South Orange Ave.Livingston, NJ 07039

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12. Mr. John MichelP.O. Box YBldg. 9204-1Oak Ridge National LaboratoryOak Ridge, Tennessee 37830

13. Mr. Charles RabidartLockheed Missiles and Space Company57-02 150 1P.O. Box 504Sunnyvale, CA 94088

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15. Mr. J. M. ShojiOTEC Project EngineerRocketdyne, Dept. 545-1136633 Canoga AvenueCanoga Park, CA 91304

16. Dr. J. E. SnyderOTEC Project ManagerTRW Defense and Space Systems GroupMail Station 81/1538One Space ParkRedondo Beach, CA 90278

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