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Full text of "Marine steam condenser design using numerical optimization."

MARINE STEAM CONDENSER 

DESIGN USING NUMERICAL 

OPTIMIZATION 



17 



Charles Michael Johnson 



Report Number--NPS69-77-002 



NAVAL POSTGRADUATE SCHOOL 

Monterey, California 




THESIS 







MARINE STEAM CONDENSER 

DESIGN USING NUMERICAL 

OPTIMIZATION 










by 












Charles Michael Johnson 










December 


1977 






Thesis 


Adv 


isors : 


Paul J. Marto 
G. N. Vanderp 


laats 



Approved for public release; distribution unlimited 

Prepared for: 

Naval Sea Systems Command 
Washington, D.C. 



T182134 



UNCLASSIFIED 



SECURITY CLASSIFICATION OF THIS PAGE (When Dmim Bntarad) 



REPORT DOCUMENTATION PAGE 



READ INSTRUCTIONS 
BEFORE COMPLETING FORM 



1. REPORT NUMBER 

NPS69-77-002 



2. OOVT ACCESSION NO 



3. RECIPIENT'S CATALOG NUMBER 



4. TITLE (and Subtitle) 

Marine Steam Condenser Design Using 
Numerical Optimization 



S. TYPE OF REPORT A PERIOD COVERED 

Engineer's Thesis; 
December 1977 



6. PERFORMING ORG. REPORT NUMBER 



7. authorc*; 



8. CONTRACT OR GRANT NLMBERf*,) 



Charles Michael Johnson 



9. PERFORMING ORGANIZATION NAME ANO AOORESS 

Naval Postgraduate School 
Monterey, California 93940 



10. PROGRAM ELEMENT, PROJECT TASK 
AREA 4 WORK UNIT NUMBERS 

N0002477-WR74134 



II. CONTROLLING OFFICE NAME AND AOORESS 

Naval Postgraduate School 
Monterey, California 93940 



12. REPORT DATE 

December 1977 



13. NUMBER OF PAGES 

167 



TT MONITORING AGENCY NAME a AOORESSf// dltlarant from Controlling Otflca) 



IS. SECURITY CLASS, (ot thtm riport) 



Unclassified 



I5«. DECLASSIFICATION/ DOWNGRADING 
SCHEDULE 



16. DISTRIBUTION STATEMENT (ot thla Raport) 



Approved for public release; distribution unlimited. 



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18. SUPPLEMENTARY NOTES 



19. KEY WORDS (Contlnua on ravaraa aida It nacaaaary and Idmnttty by block numbar) 

Marine Condenser Design 

Condensers 

Automated Ship Design 



20. ABSTRACT (Conttrma on ravaraa atda it nacaaaary and idantity by block numbar) 

Two separate computer codes were coupled with a constrained 
function minimization code to produce automated marine 
condenser design and optimization programs of vastly different 
complexity. The first program, 0PC0DE1, was developed from 
the Heat Exchange Institute's Standards for Steam Surface 
Condensers (HEI) . The second program, 0PC0DE2, was developed 
from the sophisticated 0RC0N1 , a computer code produced by the 



DD 



FORM 
I JAN 73 



1473 EDITION OF I NOV 68 IS OBSOLETE 

S/N 102-014- 6601 I 

1 



UNCLASSIFIED 



SECURITY CLASSIFICATION OF THIS PAGE (Wnan Data tntarad) 



UNCLASSIFIED 



ft:CU«*lTv CL AiSIFlC*TiQM O * TmiS P>GEfW»n D»«« Enfrml 



(20. ABSTRACT Continued) 

Oak Ridge National Laboratory. CONMIN, the optimization 
program, was developed at the Ames Research Center. 

0PC0DE1 was well verified using main condenser input 
data of an aircraft carrier and a destroyer escort. 
Verification of 0PC0DE2 , using main condenser data of an 
aircraft carrier, was less satisfactory due to the 
conservative nature of flooding effects on the outside film 
heat transfer coefficient used in 0RC0N1 . 

0PC0DE1 is an excellent design tool for the conceptual 
design of a marine condenser. Optimized test cases run with 
0PC0DE1 show that a condenser designed by the HEI method is 
nearly optimum with respect to volume. 

Test cases with 0PC0DE2 show that enhancing the heat 
transfer on the shell-side by 80 percent yields a condenser 
with ten percent less volume than the unenhanced case. 



DD lJan^ 1473 UNCLASSIFIED 



5/N 0102-014-6601 2 $tCu«lT¥ CIAHI'ICAHON 0» T«i$ MBtfW,«, Oin lm.'««) 



Approved for public release; distribution unlimited 



Marine Steam Condenser 

Design Using Numerical 

Optimization 



by 



Charles Michael Johnson 
Lieutenant, United States Navy 
B.S.E., University of South Florida, 1968 



Submitted in partial fulfillment of the 
requirements for the degrees of 



MASTER OF SCIENCE IN MECHANICAL ENGINEERING 

and 
MECHANICAL ENGINEER 

from the 

NAVAL POSTGRADUATE SCHOOL 
December 1977 



ABSTRACT 

Two separate computer codes were coupled with a con- 
strained function minimization code to produce automated 
marine condenser design and optimization programs of vastly 
different complexity. The first program, 0PC0DE1 , was 
developed from the Heat Exchange Institute's Standards for 
Steam Surface Condensers (HEI) . The second program, 0PC0DE2, 
was developed from the sophisticated 0RC0N1 , a computer code 
produced by the Oak Ridge National Laboratory. CONMIN, the 
optimization program, was developed at the Ames Research 
Center. 

0PC0DE1 was well verified using main condenser input data 
of an aircraft carrier and a destroyer escort. Verification 
of 0PC0DE2, using main condenser data of an aircraft carrier, 
was less satisfactory due to the conservative nature of 
flooding effects on the outside film heat transfer coeffi- 
cient used in 0RC0N1 . 

0PC0DE1 is an excellent design tool for the conceptual 
design of a marine condenser. Optimized test cases run with 
0PC0DE1 show that a condenser designed by the HEI method is 
nearly optimum with respect to volume. 

Test cases with 0PC0DE2 show that enhancing the heat 
transfer on the shell-side by 80 percent yields a condenser 
with ten percent less volume than the unenhanced case. 



TABLE OF CONTENTS 

I. INTRODUCTION 15 

A. BACKGROUND 15 

B. METHODOLOGY 16 

C. OBJECTIVES 18 

II. NUMERICAL OPTIMIZATION 20 

A. BACKGROUND 2 

B. CONSTRAINED FUNCTION MINIMIZATION (CONMIN)-- 21 

C. CONTROL PROGRAM FOR ENGINEERING 

SYNTHESIS (COPES) 31 

III. OPTIMIZED CONDENSER DESIGN, VERSION 1 

(OPCODE1) 33 

A. DEVELOPMENT 3 3 

B. OPCODE1 VERIFICATION 36 

C. LIMITATIONS OF OPCODE1 38 

IV. OPTIMIZED CONDENSER DESIGN, VERSION 2 

XOPCODE2) 41 

A. BACKGROUND 41 

B. MODIFICATIONS TO ORCON1 44 

C. OPCODE2 VERIFICATION 48 

D. LIMITATIONS OF OPCODE2 49 

V. RESULTS 50 

A. EXPLANATION OF THE CASE STUDIES 50 

1. Constraint Framework for OPCODE1 50 

2. Design Variable Framework for OPCODE1 -- 55 

3. Constraint Framework for OPCODE2 54 



4. Design Variable Framework for 0PC0DE2 -- 56 

B. CASE STUDIES USING 0PC0DE1 57 

1. Case One - Minimize Pumping Power; 
Rejected Heat Constant 57 

2. Case Two - Minimize Volume; 

Rejected Heat Constant 58 

5. Case Three - Maximize Rejected Heat; 
Pumping Power Constant 59 

4. Case Four - Minimize Volume; Pumping 

Power and Rejected Heat Constant 61 

5. Case Five - Minimize Condenser Length; 
Pumping Power and Rejected Heat 

Constant 63 

6. Case Six - Minimize Pumping Power; 
Condenser Volume and Rejected Heat 
Constant 64 

7. Case Seven - Maximize Rejected Heat; 
Pumping Power Increased by 50 Percent 

and Held Constant 65 

C. CASE STUDIES USING OPCODE2 67 

1. Case Eight - Minimize Volume Using 
Korodense Relation and 14 Percent 
Enhancement 67 

2. Case Nine - Minimize Volume Using 
Korodense Relation and 80 Percent 
Enhancement 68 

3. Case Ten - Minimize Volume Using 
Eissenberg Relation and 14 Percent 
Enhancement 69 

VI. CONCLUSIONS 71 

VII. RECOMMENDATIONS 7 3 

VIII. FIGURES 75 

IX. TABLES 89 

APPENDIX A: DEVELOPMENT OF THE ANAL I Z SUBROUTINE 

FOR 0PC0DE1 104 



APPENDIX B: DEVELOPMENT OF SUPPORTING SUBROUTINES 

FOR OPCODE1 111 

APPENDIX C: USER'S MANUAL FOR OPCODE1 -- 114 

APPENDIX D: SAMPLE OUTPUT FROM OPCODE1 136 

APPENDIX E: OPCODE1 PROGRAM LISTING 147 

BIBLIOGRAPHY 162 

INITIAL DISTRIBUTION LIST 165 



LIST OF FIGURES 



FIGURE 1. 
FIGURE 2. 
FIGURE 3. 
FIGURE 4. 
FIGURE 5. 
FIGURE 6. 
FIGURE 7. 
FIGURE 8. 
FIGURE 9. 

FIGURE 10. 

FIGURE 11. 

FIGURE 12. 
FIGURE 13. 
FIGURE 14. 



Significance of the Constraint 

Thickness (CT) Parameter 75 

Two-Variable Design Space Showing 

the Initial Design at Point A 76 

Two-Variable Design Space Showing 

the First Design Iteration 77 

Two-Variable Design Space Showing 

the Second Design Iteration 78 

Two-Variable Design Space Showing 

the Third Design Iteration 79 

Two-Variable Design Space Showing 

the Fourth Design Iteration 80 

Two-Variable Design Space Showing 

the Fifth Design Iteration 81 

Two-Variable Design Space Showing 

the Need for Optimization Techniques 82 

Two-Variable Design Space Showing 
Relative Minima for a Constrained 
Minimization Problem 83 

Circular Condenser Bundle Designed 

by 0RC0N1 84 

CVA 67 Main Condenser as Modeled 

by ORCON1 and 0PC0DE2 85 

CVA 67 Main Condenser Tube Sheet 86 

Flowchart from ORCON1 87 

Flowchart Showing Modification of 

ORCON1 to OPCODE2 88 



TABLE I 

TABLE II 

TABLE III 

TABLE IV 

TABLE V 

TABLE VI 
TABLE VII 
TABLE VIII 
TABLE IX 
TABLE X 
TABLE XI 
TABLE XII 
TABLE XIII 

TABLE XIV 

TABLE XV 



LIST OF TABLES 

Verification of the CVA 67 Main Condenser 
Design Using OPCODE1 89 

Verification of the DE 1040 Class of 

Main Condenser Using OPCODE1 90 

Verification of the CVA 67 Main Condenser 
Using OPCODE2 91 

Input Parameters Used in OPCODE1 for 

Cases One Through Seven 92 

Initial Design by OPCODE1 for Cases 

One Through Seven 93 

Case One Optimization Results 94 

Case Two Optimization Results 95 

Case Three Optimization Results 96 

Case Four Optimization Results 97 

Case Five Optimization Results 98 

Case Six Optimization Results 99 

Case Seven Optimization Results 100 

Case Eight Initial Design and 

Optimization Results 101 

Case Nine Initial Design and 

Optimization Results 102 

Case Ten Initial Design and 

Optimization Results 103 



NOMENCLATURE 



English Letter Symbols 

? 
At: - tube sheet area/number of tubes , ft /tube 






2 
Atj - heat transfer area, ft 



? 



A- - internal tube area per linear foot, ft "/ft 

? 

A - external tube area per linear foot, ft"/ft 
o 

2 
A_p - flow area for a single tube, ft 

C - coefficient for calculation of overall heat 
transfer coefficient 

D - tube outside diameter, ft 

d - tube inside diameter, ft 

E. - internal heat transfer enhancement factor 

E - external heat transfer enhancement factor 
o 

F(X) - objective function 

F, - average tube flooding factor 

F - tube flooding factor for the n-th tube 
n & 

F, - fouling factor 

F-, - material correction factor 

F, - temperature correction factor 

f - tube-side friction factor 

G - cooling water flow, gpm 

G.(X) - inequality constraint 

g - tube flow factor 

2 
g L - acceleration due to gravity, ft/hr 

7 

g - acceleration due to gravity, ft/sec" 



H, (X) - equality constraint 



10 



h 
h 



h* 
o 



fg 

ICALC 
k 

k 
w 

k v 
L 

LMTD 

m 

N 

NAC 

NCON 

NDV 

n* 

P 
PP 

AP 



ext 



AP 
AP 
AP 



ent 



enthalpy, BTU/lb 

internal film heat transfer coefficient, 
BTU/(hr) (ft 2 ) (°F) 

external film heat transfer coefficient, 
BTU/(hr) (ft 2 ) (°F) 

external film heat transfer coefficient 
corrected for inundation, BTU/ (hr) (f t 2 ) (°F) 

latent heat of condensation, BTU/lb 

control flag for COPES 

tube constant, k = s/g 

fluid conductivity, BTU/ (hr) (f t) (°F) 

wall conductivity, BTU/ (hr) (ft) (°F) 

vapor conductivity, BTU/ (hr) (f t ) (°F) 

tube length, ft 

log mean temperature difference, °F 

mass flow rate, lb/hr 

number of tubes 

number of active constraints 

number of constraints 

number of design variables 

number of tubes in a vertical row above 
the n-th tube 

absolute pressure, psia 

pumping power, ft-lbf/sec 

tube exit loss, ft w.c. 

tube entrance loss, ft w.c. 

sum of all tube-side pressure losses, ft w.c 

internal tube friction loss, ft w.c. 



11 



Q - heat transferred, BTU/hr 

q - iteration number 

R f - fouling resistance, (f t) (hr) (°F) /BTU 

r. - tube inside radius, ft 
1 

r - tube outside radius, ft 
o 

S" - search direction 

2 

s - outside area of tube per linear foot, ft~/ft 

T - temperature, °R 

AT\ M - log mean temperature difference, °F 

t. - cooling water inlet temperature, °F 

t - cooling water outlet temperature, °F 

t - saturation temperature, °F 

t - vapor temperature, °F 

t - wall temperature, °F 

w r ' 

U - uncorrected overall heat transfer coefficient, 
BTU/(hr) (ft 2 ) (°F) 

U - corrected overall heat transfer coefficient, 

c BTU/(hr) (ft 2 ) (°F) 

U. - overall heat transfer coefficient based on 

1 inside tube area, BTU/ (hr) (f t 2 ) (°F) 

V - cooling water velocity, ft/sec 

VLB. - lower side constraint on i-th design variable 
l ° 

VUB . - upper side constraint on i-th design variable 

W - steam flow, lb/hr 

w.c. - water column 

w - weight of cooling water, lb/gal 

X - vector of design variables 



12 



Dimensionless Groups 

Pr - Prandtl number 

Re - Reynolds number 

Greek Letter Symbols 

a* - move parameter in optimization problem 

6 - ratio of A p /A f 

3 - parameter in method of feasible directions 

e - absolute roughness, ft 



push off factor in method of feasible directions 

? 



J 

Pr - fluid absolute viscosity, lb sec/ft 

p - condensate density, lb/ft" 5 

3 

p - sea water density, lb/ft 

^sw 7 ' 

p - vapor density, lb/ft" 3 



ACKNOWLEDGEMENTS 

The author wishes to express his appreciation to 
Professor Paul Marto , Doctor Gary Vanderplaats and 
Professor Paul Pucci for their advice and guidance during 
the development of this project. Without their valuable 
assistance, this thesis could not have been completed. 

The author wishes to thank Sharon Raney , Richard Donat 
and especially Edwin Donnellan, all of the W.R. Church 
Computer Center, for their time and patience in teaching 
an engineer how to use all of the tools available. 

Infinite thanks and grateful appreciation are due my 
wife, Lari, for understanding the project, encouraging 
its completion and making the difficult times bearable. 
iMahalo . 



14 



I. INTRODUCTION 

A. BACKGROUND 

In the last ten years a revolution has swept the marine 
power plant industry that could result in the obsolescence 
of the marine steam power plant. The revolution was caused 
primarily by the use of the gas turbine as an alternative 
to marine, and more recently, to naval propulsion. Gas 
turbines brought about power plants which were more compact, 
lighter, but less fuel efficient than the steam power plants 
which they displaced. 

When compared with the compact gas turbine, the massive 
size and weight of the marine steam power plant, which 
evolved in stride with the behemoth of the power industry, 
the stationary steam power plant, made this means of propul- 
sion less desirable for naval vessels. Therefore, it has 
become imperative for the naval engineering community to 
develop a more efficient, more compact, lighter weight steam 
power plant. 

As steam power plants are durable and they can burn a 
variety of fuels — both essential qualities when considering 
the Navy's combat readiness — they must not be allowed to 
be overdesigned out of existence. To make steam propulsion 
competitive with marine gas turbines, advanced concepts must 
be explored in all areas of steam propulsion. Such concepts 
as pressurized boilers, super critical cycles, enhanced 



15 



condenser tubes, and dropwise condensation must be developed 
further. Above all, overdesign by the use of unnecessary 
safety factors must be curtailed, and the minimum safe design 
must be developed and identified. 

B. METHODOLOGY 

In the United States the most prevalent criterion for the 
design and specification of surface condensers is based on 
the "square root of V" relationship as developed by the Heat 
Exchange Institute (HEI) [1]. Using this method, the overall 
heat transfer coefficient is calculated as a function of the 
square root of the cooling water velocity multiplied by 
correction factors for inlet cooling water temperature, tube 
wall thickness and material, and fouling. 

The HEI method was adopted by the Department of the Navy, 
Bureau of Ships (now Naval Sea Systems Command) for the 
specification of U. S. Navy condensers by issuing Design 
Data Sheet 4601-1 (DDS) [2] in 1953. Henceforth this thesis 
will designate the preceding methodology as the HEI/DDS 
method. 

With the advent of the high speed digital computer, 
numerical methods of solving complex engineering problems 
are now possible. A computer code has been developed to 
calculate the local heat transfer and thermodynamic properties 
of a large surface condenser on a row by row basis. Known as 
ORCON1, this code was developed by Oak Ridge National 
Laboratory (ORNL) under contract to the Office of Saline 



16 



Water during the period from 1968 to 1970 [3] . The program 
was based, in part, on the work performed by Eissenberg [4]. 
Eissenberg's experimental results led to correction factors 
on the basic Nusselt equation to account for inundation 
effects of tubes within a condenser tube bundle. Addi- 
tionally, logic was developed to account for the pressure 
loss caused by the steam's passage through the tube bank 
with the accompanying reduction in saturation temperature; 
the heat resistance due to the presence of a noncondensable 
gas film; heat transfer enhancement factors on both sides of 
the tubes; and other important factors to yield a program 
which could calculate heat flux, overall heat transfer 
coefficient, noncondensable gas concentration, and fifteen 
additional parameters on a local, row by row basis. 

Search [5] has used 0RC0N1 to perform parametric studies 
of an actual naval condenser. Tube enhancement, the high 
velocity flow allowed with titanium tubes, and dropwise 
condensation were investigated. The penalties paid in 
increased pumping power and increased cost were weighed 
against the gains realized with a more compact and with a 
lighter condenser. 

In the open literature there is but one reference [6] 
to coupling a condenser analysis and design program with 
an optimization procedure that is capable of improving a 
given design. 



17 



The case for utilizing an optimizing design scheme for 
the condenser portion of a steam propulsion plant can easily 
be made by re-emphasizing the fact that in order for steam 
propulsion to remain a viable contender when the naval 
vessels of the late 1980's are designed, it must compete 
and succeed in an area that is rapidly being dominated by 
gas turbines. All components of the naval ship's steam 
propulsion plant will have to be critically designed to 
ensure that the minimum design will still perform as and 
when required. 

C. OBJECTIVES 

There were two primary objectives of this thesis. 

The first objective was to develop a computer code based 
on the HEI/DDS method of condenser design, as this method 
is considered the industry standard. Coupling the HEI/DDS 
code with a numerical optimization program yields a complete 
design package. The design package can be used for trade- 
off studies, first cut analysis, and conceptual design. 

The second objective was to couple 0RC0N1 , with its 
capability of varying both internal and external tube 
enhancement factors, with a numerical optimization program 
to produce a more detailed design program. 

These design tools provide the Naval architect and the 
Naval engineer with the means to optimize size, weight, 
design, and cost of the marine steam propulsion plant for 
ships of the 1980's; the enhanced design provides the optimum 



18 



streamlined design of a steam plant resulting in its 
reinstatement and continuance as a viable alternative to 
gas turbine propulsion. 



19 



II. NUMERICAL OPTIMIZATION 

A. BACKGROUND 

Nearly all design problems require either the minimiza- 
tion or maximization of a parameter or function. This 
parameter will be called the problem's objective function 
or design objective [7]. For the design to be acceptable, 
it must satisfy a set of design constraints. For example, 
if an engineer was designing a piping system to achieve the 
minimum in required pumping power, the minimum allowable 
flow delivered would be a meaningful constraint. Likewise 
a constraint that required the inside diameter of the pipe 
to be less than the outside diameter of the pipe would be 
a necessity. 

If the problem could be formulated analytically with a 
great deal of simplicity, the minima or maxima could be 
found by using the methods of differential calculus or the 
calculus of variations. However, these methods would fail 
for all but the very simplest of problems. 

A numerical method that would be satisfactory for rela- 
tively small scale problems would be an iterative solution 
technique. A simple computer program could be written 
containing a series of nested iteration loops that would 
vary the design parameters and solve the problem for a 
variety of values for each of the parameters. For small, 
easily formulated problems, the cost in central processor (CPU) 
time would not be excessive, and this method would be 
satisfactory . 

20 



However, for a serious engineering problem, this method 
quickly becomes too costly to pursue. For example, if the 
engineer had ten design parameters for which he wanted to try 
ten separate values, he would need to make ten billion 
calculations. If each calculation took ten CPU seconds, 
the solution would be available in approximately 3200 years! 
Thus a rational approach to design automation and optimiza- 
tion is obviously needed. 

There are many optimization schemes available to the 
engineer. The various methods fall into three broad cate- 
gories based on the type of problem to be solved: 
unconstrained minimization, solution of constrained problems 
by unconstrained minimization, and direct methods for 
solution of constrained problems [8]. An optimization 
program based on the last method was chosen for this 
research work. 

B. CONSTRAINED FUNCTION MINIMIZATION (CONMIN) 

Vanderplaats [9] developed an optimization program, 

CONMIN, capable of optimizing a very wide class of 

engineering problems. CONMIN is a FORTRAN program, in 

subprogram form, that optimizes a multi-variable function 

subject to a set of inequality constraints. 

Three basic definitions are required [10]: 

Design Variables - Those parameters which the 
optimization program is permitted to change in 
order to improve the design. Design variables 
appear only on the right side of an equation, 
are continuous and have continuous first derivatives. 



21 



Design Constraints - Any parameter which must 
not exceed specified bounds for the design to be 
acceptable. Design constraints may be linear 
or non linear, implicit or explicit, but they 
must be functions of the design variables. 
Design constraints appear only on the left side 
of equations . 

Objective Function - The parameter which is going 
to be minimized or maximized during the optimization 
process. The objective function may also be linear 
or non linear, implicit or explicit, and must be a 
function of the design variables. The objective 
function usually appears on the left side of an 
equation. The only exception is if the objective 
function is also a design variable. 

As can readily be seen by the definitions above, design 
constraints and objective functions are usually 
interchangeable . 

The number of design variables being utilized for an 
optimization is equivalent to the dimension of the design 
space in which the design is being calculated. Thus, if 
an optimization problem has four design variables specified, 
the design will be carried out in four-space. 

Assuming that the optimization process requires the 
minimization of a particular objective function, the general 
optimization problem can be stated as: 

Find the vector of design variables, X, to 

minimize F(X) subject to the constraints 

G. (X) <_ 0.0 , j = l,NCON (1) 

VLB. < X < VUB. , i = 1,NDV . (2) 

In the general problem statement, F (X) is the objective 
function, there are NDV design variables, and NCON constraints 
VLB. and VUB. are the lower bounds and upper bounds respec- 
tively on the i-th design variable. If the inequality 



22 



condition of equation (1) is violated, (G.(X) > 0) , for any 
constraint, that constraint is said to be violated. If the 
equality condition is met, (G.(X) = 0), the constraint is 
active. If the inequality condition is met, (G.(X) < 0), 
the constraint is inactive. Because of the numerical 
problems involved in representing exact zero on a computer 
with a finite number of significant figures, the equality 
condition is represented by a band around the value G. (X) = 
The band is equal to twice the constraint thickness (CT) and 
is shown in Figure 1. Figure 1 is a representation of a 
two-variable design space with the values of G . (X) = 
plotted. In this instance, 



X. 
X, 

For n-space, G.(X) would appear as a hypersurface 
whereas for n = 2, the hypersurface degenerates to a single 
curve that can be easily represented. 

Any design which satisfies the inequalities of 
equations (1) and (2) is referred to as a feasible design. 
If a design violates any of these constraints, it is an 
infeasible design. The minimum feasible design is said to 
be optimal. Note that if it is desired to maximize an 
objective function, the process reduces to minimizing the 
negative of the objective function. 

CONMIN requires an initial vector of design variables, 
X, which may or may not yield a feasible design. If the 



23 



initial design is infeasible, CONMIN moves towards a 
feasible solution with a minimal increase in the objective 
function [9]. The optimization process then proceeds in 
an iterative fashion with the following recursive 
relationship : 

where q is the iteration number and a* is the move parameter, 
a scalar, which defines the distance of travel in the 
direction of search, S. 

The optimization process is divided into two parts. 
The first is the determination of S which will reduce the 
objective function without violating any constraints. The 
second is the determination of the scalar a* so that F(X) 
is minimized in this direction, a new constraint is 
encountered, or a currently active constraint is encountered 
again. 

For the sake of discussion, consider a condenser design 
problem with two design variables, X, and X , where 

X, = condenser tube outside diameter, and 
X~ = tube pitch to diameter ratio. 

The objective function is condenser volume, VOL(X). Assume 

that the tube bundle diameter must be greater than a 

specified value, BD . , and that the cooling water pumping 

power must be less than a specified value, HP . Figure 2 
r r ' max ° 



24 



is a graphical representation of the problem. Note the 
lines of constant objective function, with VOL, (X) > VOL- (X) , 
and the initial design at point (a) . 

It must be reiterated that, while this example assumes 
a feasible initial design, this is not a requirement and 
CONMIN will also optimize when given an infeasible initial 
design. 

The optimization begins by calculating the gradient of 
the objective function by using the finite difference tech- 
nique. A perturbation of 0.01 is applied to each of the 
design variables in a single forward step. The gradient 
vector is therefore 



VF(X) 



VVOL 



3 (VOL) 





Because no constraints are active or violated, the greatest 
improvement in the objective function will be realized by 
moving in the direction of steepest descent so that 



VVOL 



as shown in Figure 3. 

With the value of S now determined, it remains to find 
the move parameter, a*, that will allow the greatest 



25 



improvement in the objective function. A one-dimensional 

search is carried out in the S direction until the value for 

a* is found. This is point (B) on Figure 3. The location 

of point (B) terminates the first design iteration. 

The second design iteration is begun by, once again, 

perturbing X to find VVOL. Instead of moving in the 

direction of steepest descent, however, a new S is found 

by the method of conjugate directions, developed by 

Fletcher and Reeves [11]. With this method, S is calculated 

by the following relationship: 

2 
V F(X) q 
' - V F(X) q + 



gq 



gq-1 



V F(X) 



q-1 



This is shown in Figure 4. 

The advantage of using the Fletcher-Reeves method 

instead of the steepest descent is that convergence to an 

optimum is much faster. With the new search direction, S, 

a search is performed in this direction until a constraint 

is encountered. This occurs at point (c) on Figure 4 at 

the pumping power constraint, thus terminating the second 

design iteration. 

The third design iteration begins with the HP 

& & max 

constraint active at point (cT) on Figure 5. As VVOL is 
found, the gradient of the active constraint is found using 
the information from the same forward finite difference step 

Not only is a new S required that will reduce the 
objective function, but this new S must not violate the 



26 



active constraint. This problem may be solved by the method 
of feasible directions developed by Zoutendijk [12] and 
implemented by Vanderplaats and Moses [13] . 

The finding of a new S has now become a sub-problem 
which is a linear programming problem with a single 
quadratic constraint. This sub-problem [14] is stated as: 

Find a vector S to maximize 3 subject to the constraints 

V F(X) • S + 3 < (3) 



V G. (X) • S + 9 .3 £ j = 1,NAC (4) 



S < 1 (5) 



where, for the case at hand, V F(X) E7V0L,VG.(X) = -VHP, 

and G . (X) = HP - HP. NAC , the number of active constraints, 

j *■ ' max ' ' 

is one in this instance. 

If equation (3) is satisfied and 3 is positive, the 

resulting search direction will reduce the objective function 

and is defined as a usable direction. If equation (4) is 

satisfied and 3 is positive, S is a feasible direction 

because, for a small move in this direction, no constraints 

will be violated. 9. is defined as the push-off factor for 

G. (X) and has the effect of pushing the design away from 

the active constraint. 9- must be zero or positive to 

maintain a feasible design. For 9- = 0, S would be tangent 

to the active constraint. For 9. >> 1.0, S would be 

3 



27 



pushed away from the active constraint and very nearly 

tangent to a line of constant objective function. For 

9. = 1.0, the angle between constant objective function and 

the active constraint would be approximately bisected. If 

the maximum value of 6 obtainable from equations (3) , (4) 

and (5) is zero, then no direction exists which will both 

reduce the objective function and satisfy the constraint, 

and the current design is optimal or is at least a local 

minimum. In this example, a usable and feasible direction 

exists and a one dimensional search leads to point (D) in 

Figure 5 where the minimum bundle diameter, BD . , constraint 
s ' mm' 

is encountered. This ends the third iteration in the 
optimization process. 

The fourth iteration begins as before, with the calcula- 
tion of the gradient of the objective function and the 
active constraint. The sub-problem of equations (3) through 
(5) is again solved for a new S. 

It should be noted that the minimum bundle diameter 

constraint is assumed to be linear; therefore in equation (4) 

the push-off factor, 8., is set to zero allowing S to 

follow the constraint as shown in Figure 6. A one 

dimensional search is again carried out in the new S direction 

until a new constraint is encountered or an active constraint 

is re-encountered. Thus, the activated BD . constraint is 

' mm 

"ridden" until no further design improvement is realized. 
This occurs at point (|) on Figure 6 and the fourth design 
iteration is terminated. 



28 



For the fifth iteration, the same procedure is followed 
and the solution to the sub-problem characterized by 
equations (3) through (5) yields a value of zero for 8. 
Thus, there is no direction that will both reduce the 
objective function and satisfy the constraint and the 
current design at point (E) in Figure 7 is optimal. 

Figure 8 illustrates the value of using optimization 
techniques to solve the design problem. Assume an initial 
design at point (A) such that the minimum tube outside 
diameter is active. A reduction in the tube pitch to 
diameter ratio will yield a design improvement until the 
minimum bundle diameter constraint is encountered at point 
(B) . At this point, neither the pitch to diameter ratio 
nor the outside tube diameter can be reduced independently 
as required to reduce the objective function, without 
violating the active constraints. Only by changing the 
two design variables in a particular manner can the minimum 
value of the objective function at point © be achieved. 

This discussion of the methodology involved with CONMIN 
would not be complete without citing the program's limita- 
tions. The number of design variables (NDV) directly 
affects the computational time required to reach an optimum. 
Since the calculation of the gradient information required 
for each design variable at the beginning of each design 
iteration is found by using a single forward finite difference 
step, requiring a complete pass through the analysis portion 
of the program, there is a subsequent increase in CPU time 



29 



as NDV increases. Also, problems with many design variables 
tend to converge more slowly due to the interaction between 
the design variables and because of the numerical inaccuracy 
(machine related) generated during the optimization process. 
The number of design variables should therefore be kept 
small in order to expedite the optimization process. 
Vanderplaats [7] recommends a practical limit of twenty 
design variables. 

The number of design constraints used is not limited in 
the same manner. Recall that the only time gradient 
information is stored for a constraint is when that constraint 
is active. Therefore, the sheer number of constraints will 
not adversely affect the optimization. 

As can be seen in Figure 9, it is quite possible that 
the optimal design found is actually a relative optimum and 
not a global optimum. This problem can be overcome by 
starting the design with several different initial vectors, 
X, until the same optimal design is repeated. 

Equality constraints of the type 

H k (X) = 

are very difficult to provide for in the general optimization 
scheme [7]. By defining an objective function in which a 
weighting factor multiplies the parameter to be held constant, 
Y, and this product is summed with the parameter to be 
optimized, X, 

objective function = X + weighting factor x Y 



30 



the parameter to be held constant can be forced to the 
appropriate bound. The weighting factor is generally one 
that will keep both terms in the same order of magnitude 
but trial and error is sometimes required. Parameters can 
be held "constant" within to. 5 percent. 

C. CONTROL PROGRAM FOR ENGINEERING SYNTHESIS (COPES) 

Recall that the optimization program, CONMIN, was 
written in subroutine form. Vanderplaats [15] has developed 
a main program to simplify the use of CONMIN and to further 
aid in the design optimization process. 

The user must supply an analysis subroutine with the 
name ANALIZ. ANALIZ, in keeping with general good program- 
ming practice, must have three segments: input, analysis and 
output. Based on the value of a flag from COPES 
(ICALC = 1,2 or 3), ANALIZ performs the proper function. 
Finally, CONMIN and ANALIZ do not communicate directly with 
each other as COPES is the main program. 

COPES is constantly being revised by Vanderplaats to 
better meet the needs of the engineer. 

The COPES program currently provides four specific 
capabilities : 

1. Single analysis - just as if COPES/CONMIN were 
not used. 

2. Optimization - minimization or maximization of a 
multivariable function with limits imposed on other 
functions . 



31 



3. Sensitivity analysis - used to investigate the 
effect of changing one or more design variables 
on one or more calculated functions. 

4. Two-variable function space - provides analyses 
of all specified combinations of two design 
variables . 

This work is concerned only with the application of 
COPES/CONMIN to the optimized design of a marine condenser, 
therefore, items 3 and 4 are included only for completeness. 

If there is no relative or absolute change in the value 
of the objective function for three design iterations, 
the optimum is found and COPES prints the appropriate 
message and terminates the program. If no feasible design 
can be found after ten design iterations, COPES prints the 
appropriate message and terminates the program. 

Experience has shown that most design problems can be 
optimized within 20 design iterations and the maximum number 
of design iterations permitted is defaulted to this value. 
Thus, if the optimum value has not occurred in 20 design 
iterations, COPES will print the appropriate message and 
terminate the procedure. 

COPES has simplified the procedures involved in using a 
sophisticated program such as CONMIN. Thus the engineer is 
freed from the unwanted role of systems analyst and may 
devote his talents to engineering. 



32 



III. OPTIMIZED CONDENSER DESIGN, VERSION 1 (OPCODE1) 

A. DEVELOPMENT 

The Bureau of Ships adopted the Heat Exchange Institute's 
Standards for Steam Surface Condensers [1] by issuing Design 
Data Sheet DPS 4601-1 [2] in October, 1953. The DDS is still 
being used to specify naval condensers. 

The technique involved is based on calculating a value 

of the overall heat transfer coefficient, U , based on the 

' c ' 

cooling water velocity through the condenser tubes, the 
condenser tube wall thickness and material, the tube fouling 
factor, and the cooling water inlet (injection) temperature. 
Knowledge of these parameters and their associated correction 
factors leads to the simple formulation of U 



U = F n F F, C /V 

c 12 3 



The correction factors F, , F- , and F, are tabulated in 

12 o 

references [1] and [2]. Reference [2] specifies a value of 
C = 270 for 0.625 and 0.750 inch outside diameter (o.d.), 
18 Birmingham Wire Gauge (BWG) tubes. A value of C = 263 is 
used for 0.875 and 1.00 inch o.d., 18 BWG tubes. 

Because of the simplicity of the HEI/DDS method of 
condenser design, and since the DDS is still the specifying 
document for naval condensers, the author chose to implement 
the HEI/DDS method for automated design. The combination of 



33 



COPES/CONMIN with the HEI/DDS method was named 0PC0DE1 
(Optimized COndenser DEsign, Version 1 ) . The development of 
0PC0DE1 is presented in Appendices A and B. 

To add greater versatility to the HEI/DDS method, 
algorithms were developed for 0PC0DE1 to calculate a 
circular bundle geometry and the cooling water pumping 
requirement. The circular bundle geometry was designed from 
the long axis out. A central 12 inch diameter void to serve 
as the collection header for noncondensable gasses was 
provided along the bundle's longitudinal axis. Once the 
number of tubes was calculated, the tubes were placed in 
rows concentric to the central void and spaced with a 60 
degree triangular pattern. To simplify the algorithm, and to 
provide continuous functions to COPES/CONMIN, partial tubes 
were permitted in a row and the outermost row was allowed 
to be partially filled. 

The calculation of the mass flow rate of cooling water 
required began the calculation of the sea water (S-W) pressure 
drop and pumping power requirement. 

The S-W pressure drop was divided into a component based 
on the sudden expansion and contraction losses caused by the 
flow entering and exiting the waterboxes; a component based 
on the sudden contraction and expansion losses caused by 
flow from the inlet waterbox into the inlet tube sheet and 
from the outlet tube sheet into the outlet waterbox; and a 
component based on the normal frictional losses associated 
with internal tube flow. 



34 



Reference 1 presents, in graphical form, the pressure 
drops for all the components. The graphical data from 
Figure SF-9 of reference 1 for the calculation of waterbox 
losses was implemented using a systems library interpolating 
subroutine. The S-W velocity in the waterboxes was taken 
as 75 percent of the velocity in the condenser tubes as 
specified in reference 16. 

To simplify the tube-side pressure loss algorithm, the 
friction factor, f, was first calculated by solving the 
transcendental Colebrook equation [17]. Details of the 
solution are provided in Appendix B. An absolute roughness 
of 5 x 10 feet was assumed as representative of drawn 
tubing. With the value of f calculated, the tube-side 
pressure drop, AP , was calculated using the familiar 
Darcy-Weisbach formula [17]: 



AP t - £ & C^O 



The tube sheet entrance and exit losses were calculated 
by utilizing the area ratio technique developed in 
reference 18. With this method, the flow area associated 
with each tube was calculated 



a - tube sheet area 
F number of tubes 



followed by the calculation of the internal flow area for 
an individual tube, Ar and the ratio of the two areas: 



35 



A £ 
6 A ' 



With the value of 8 calculated, the entrance loss was 
calculated with the relation 



2 

AP «. = 0. 5(1.0 - 6 2 ) (-r— ) [feet of water column] 
ent ^ ' ^2g J L J 

& o 



and the exit loss was calculated with the relation 



2 2 
2 V 

AP . = (1.0- 6 ) f* — ) [feet of water column] 
ext 2g L 

*o 



Although the heat transfer calculations performed in 
0PC0DE1 were for a single pass condenser, expansion of the 
program to multiple pass condensers is feasible. To 
simplify this future expansion, the waterbox pressure loss 
was multiplied by the number of tube passes, read as an 
input variable. 

The pumping power was now easily calculated 



PP = N • V • A r * p • P j- ft-lbf j 

f sw L sec J 



The input variables required for the use of 0PC0DE1 
are listed in the User's Manual provided as Appendix C. 

B. 0PC0DE1 VERIFICATION 

It was desirable to verify the performance of 0PC0DE1 
as a predictor of condenser performance by comparison with 



36 



actual experimental data. Complete and accurate data was 

not available, therefore, another method of model verification 

was sought. 

Using the design data from the condenser technical 
manuals for two classes of ships, the CVA 6 7 and the DE 1040, 
an attempt was made to repeat the design of the condensers. 
The two condensers are vastly different in size; the CVA 67 
has a heat transfer area of 16,011 square feet while the 
DE 1040 class condenser has a heat transfer area of 
6600 square feet. 

The results of the design of the CVA 67 by 0PC0DE1 
are tabulated in Table I with the data from the condenser 
technical manual [19] included for comparison. Very close 
agreement was achieved for all parameters except tube-side 
pressure drop. This difference was attributed to the tube 
sheet layout by 0PC0DE1 and the fact that no steam lanes 
were accounted for. The addition of steam lanes would tend 
to increase the tube-side pressure drop since more tube sheet 
area would be unused as tube sites. Thus the entrance and 
exit losses associated with the tube sheets would be greater 
than predicted by 0PC0DE1. 

The results of the design of the DE 1040 class condenser 
by 0PC0DE1 are tabulated in Table II with the data from the 
condenser technical manual [20] included for comparison. 
Excellent correlation was achieved with all parameters within 
three percent of the specifications except for bundle 
diameter and tube-side pressure drop. Since no provision was 



37 



made for the calculation of circumferential steam lanes 
in 0PC0DE1, the bundle diameter calculated was less than 
the prototype. 

Since the DE 1040 condenser has a basically circular 
bundle geometry, close agreement was expected between the 
calculated tube-side pressure drop and the value specified 
in the technical manual. This was not the case. One 
plausible explanation could be that the designers specified 
a large factor of safety for this parameter. 

These results confirm that the designers of the CVA 67 
and the DE 1040 main condensers did, in fact, use the 
HEI/DDS method for the calculation of the heat transfer 
parameters and, with the notable exceptions of tube-side 
pressure drop and bundle diameter, 0PC0DE1 accurately 
predicts these parameters at the full power design point. 

If the limitations imposed on tube-side pressure drop 
and bundle diameter by the exclusion of steam lanes from 
0PC0DE1 are acknowledged, the results received from 0PC0DE1 
can be viewed as a "first cut" analysis. This was the 
original purpose of developing this program. 

C. LIMITATIONS OF 0PC0DE1 

0PC0DE1 is insensitive to shell-side conditions. The 
saturation steam pressure and the saturation steam temperature 
are assumed to remain constant as the steam passes through 
the bundle, whereas the steam flow actually experiences a 
pressure drop with a resulting decrease in saturation 



38 



temperature as the steam passes through each row of tubes. 
As a result, 0PC0DE1 makes no attempt to specify steam 
lanes, either circumferential or radial, since the proper 
design of steam lanes is a strong function of local steam 
pressure . 

0PC0DE1 has no provision for the application of tube 
enhancement factors due to the simple manner in which the 
corrected overall heat transfer coefficient is computed. 
The usual method for the calculation of U- [21] is: 



U- = (6) 

i + \ m Cy^j A. , 

R~ 2¥kT R f A " h~ 

1 W 



where the internal film heat transfer coefficient is given 
by the Colburn form of the convective film heat transfer 
correlation [21] : 



k 
h i = 0.023 (Re)°- 8 (Pr) 1/3 (-^) (7) 



The outside film heat transfer coefficient is given by 
Nusselt's equation [21] corrected for the inundation, or 
condensate rain, effects of upper tubes on lower tubes in 
the bundle by including the factor n* in the denominator, 
where n* is the number of tubes in a vertical row above the 
i-th tube 



39 



0.725 



P (p - P ) g T h r k 
c^ c v^ & L fg c 



U n*D (t 



v 



V 



1/4 



(3) 



With h. and h in the forms given by equations (7) and 

(8), enhancement factors can be applied as multipliers of 

these equations and equation (6) will yield a value for 

the enhanced overall heat transfer coefficient, U.*. 

' i 

None of the foregoing is possible with the HEI/DDS 
based 0PC0DE1. 

Finally, since 0PC0DE1 is insensitive to steam conditions, 
the effect of noncondensable gasses on the heat transfer 
characteristics of the condenser are unknown. 



40 



IV. OPTIMIZED CONDENSER DESIGN, VERSION 2_ (OPCODE2) 

A. BACKGROUND 

In the late 1960's, engineers at the Oak Ridge National 
Laboratory developed a sophisticated computer code under 
contract to the Office of Saline Water. This code, called 
0RC0N1 [3], was generated to aid in the analysis and 
parametric study of large, generally circular steam 
condensers for use in large scale, multistage distillation 
plants for the production of potable water from sea water 
by the flash evaporation process. 

Much of 0RC0N1 was dependent on Eissenberg's research 
work [4] on the effects of condensate rain on the shell- 
side convective heat transfer coefficient. 

The program analyzes a single pass, circular or semi- 
circular condenser, with steam flowing on the shell-side 
of the tubes and variable salinity water flowing on the 
tube-side. An optional, rectangular air cooler bundle is 
provided for, as well as elementary, shell-side baffles. 
The bundle is divided into 30 degree sectors and symmetry 
about the central axis may be employed to reduce computa- 
tional effort. The tubes are placed on a 60 degree equilat- 
eral triangular pattern of concentric rows with the rows 
added from the outermost row to an inner void provided 
along the bundle's longitudinal axis. This serves as a 
collection header for noncondensable gasses prior to passage 
through the air cooler, if specified. The steam is assumed 



to flow radially from the outside of the bundle to the 
central void. Figure 10 shows the ORCON1 model of a steam 
condenser with optional baffles and cooler. 

0RC0N1 proceeds with sector by sector, row by row 
calculations of the following quantities: 

a) Saturation temperature of the steam entering the 
row. 

b) Pressure of the steam plus noncondensable gas 
entering the row. 

c) Steam flow entering the row. 

d) Steam and noncondensable gas velocity at the minimum 
cross section in the row. 

e) The fraction of noncondensable gas by weight. 

f) The overall heat transfer coefficient for the 
average tube in the row. 

g) The steam-side condensing coefficient. 

h) The tube-side heat transfer coefficient. 

i) The shell-side film heat transfer coefficient 

composed of the noncondensable gas film plus the 
condensate film. 

j) The shell-side Reynolds number based on the mass 

flow at the minimum cross sectional area in the row. 

k) The heat flux per square foot of condenser tube. 

1) The shell-side friction factor. 

m) The mass flow rate of steam plus noncondensable gas 
at the minimum cross section in the row. 

n) The cooling water temperature at the inlet end of 
the condenser tube. 

o) The cooling water temperature at the outlet end of 
the condenser tube. 

p) The heat transfer coefficient for the noncondensable 
gas film. 



42 



q) The number of tubes per row. 

r) The cumulative shell-side pressure drop from row 1 
to row n. 

In addition to the above parameters, the area weighted 
overall heat transfer coefficients for the condenser section, 
the cooler section, and the combined condenser are used to 
calculate the "back calculated" log mean temperature 
difference (LMTD) . This value of the LMTD , when compared 
with the LMTD calculated by standard means using the 
saturation steam temperature and the average cooling water 
inlet and exit temperatures, represents the loss in average 
thermal driving force due to pressure drops within the 
bundle . 

The tube internal film heat transfer coefficient is 
calculated by the Colburn equation multiplied by the 
internal enhancement factor 



0.023 (Re) ' 8 (Pr) 1/3 (-/) (E i ) 



The uncorrected external film heat transfer coefficient 
is calculated using the basic Nusselt equation [21]: 



h 



0.725 



7 3 
kc P, 



-i 1/4 



h fg g L 



THT 






(E ) 



(9) 



The value of h calculated in equation (9) is for a 
single tube. Eissenberg [4] corrects for inundation effects 



43 



by first calculating a tube flooding factor using the 
following relation: 



F = 0.6F, + (1 - 0.5647F,)n" - 20 
n d & J 



F_, is an input parameter and is a function of both tube 
spacing to diameter ratio and tube orientation [3,22]. 
The condensate film coefficient for the typical tube in 
the n-th row is then calculated by correcting the value of 
h from equation (9) : 



h *(n) = [nF - (n - 1)F - ]h 
o v J L n J n-l J o 



To model the main condenser of the CVA 67, one quarter 
of the full circular bundle was specified. With two bundle 
quarters placed back to back as shown in Figure 11, the 
steam lanes and tube arrangement closely approximated the 
CVA 67 tube sheet as shown in Figure 12 from reference 19. 

The combination of the COPES/CONMIN optimization package 
with a suitably modified 0RC0N1 produced 0PC0DE2 (Optimized 
COndenser DEsign , Version 2) . 

B. MODIFICATIONS TO 0RC0N1 

The original 0RC0N1 had neither tube-side pressure drop 
calculations nor volumetric calculations. The subroutines 
developed for 0PC0DE1 to calculate the tube-side pressure 
drop and pumping power were installed in 0RC0N1 when 



44 



converting it to 0PC0DE2. An equation for the calculation 
of condenser volume based strictly on the model as developed 
for the CVA 67 main condenser and shown in Figure 10 was 
added to 0RC0N1 . 

The flowchart given in Figure 13 illustrates the 
original program logic for 0RC0N1 . Once all calculations 
were completed, a test for the exit steam fraction was made 
against an input' target value. If the target value was not 
met, and depending on the value of an input flag, either 
the length of the condenser tubes or the quantity of inlet 
steam was varied, and the calculations were repeated until 
the target value and the calculated values agreed. The 
adjustment of tube length or inlet steam was performed in 
subroutine ADJUST. 

It was felt that the quantity of inlet steam was generally 
the value which should drive the entire design of the 
condenser and should therefore remain a constant. 
Similarly, the tube length was a good candidate for inclusion 
in the optimization program as a design variable. For these 
reasons, subroutine ADJUST was removed from 0RC0N1 . 

The original ORCON1 provided logic for multiple data 
runs. This capability was removed since COPES/CONMIN 
requires a "once through" analysis program. Figure 14 shows 
the sections of 0RC0N1 removed during the conversion to 
0PC0DE2. 

Search [5] had previously modified 0RC0N1 so as to 
calculate the shell-side heat transfer coefficient either 



45 



with the original equation from the work of Eissenberg [4] 
or by using the relation specified by the manufacturer of 
Korodense condenser tubes [23]. This facility was left in 
0PC0DE2. 

0RC0N1 was not originally a machine independent program 
as it had been tailored for operation on IBM (International 
Business Machines) equipment. This was not a desirable 
characteristic and programming changes were made to ensure 
that 0RC0N1 was machine independent and that 0PC0DE2 would 
remain machine independent. 

0RC0N1 uses iterative techniques to solve for quantities 
such as condensation rate, steam mass flow rate, and pressure 
drop balance between sectors. The description of subroutine 
ADJUST is an excellent example of such an application. 

CONMIN uses perturbation techniques to calculate the 
gradient information required for each design variable and 
for each active design constraint during an optimization 
iteration . 

Since 0RC0N1 has the capability to make design decisions, 
a perturbation by CONMIN would cause an adjustment by 0RC0N1. 
The two programs therefore worked at cross purposes. 

It was not possible to remove all of these design 
decision points from 0RC0N1 because of the strong coupling 
between the subroutines. The decision was made to remove 
only ADJUST and to leave the other design decision points 
intact . 



46 



This problem affected the choice of parameters that 
could be used as design variables and the range of values 
that the chosen design variable was permitted to assume. 

Another problem area developed because many of the thermo- 
dynamic properties were calculated in 0RC0N1 by subroutines 
that use logarithmic functions to approximate the thermo- 
dynamic curves. If the arguments for these functions take 
on values less than or equal to zero, the function is 
undefined. While constraints could be added as part of the 
optimization process, the computation would stop during the 
pass through the analysis. 

Tests were put before all calculations that involved 
logarithmic evaluation and before all function evaluations 
where the denominator could take on values very close to 
zero. These tests, when activated, would make a "design 
decision" by setting the function to an approximate value 
such as : 

if x <_ 0.0001 , then y = -10.0 
otherwise, y = In x . 
These approximate values would cascade due to the large 
number of times the function was evaluated. Other mathematical 
instabilities also occurred. 

The design variables or the values of the design variables 
that would trigger the original instability were found. The 
tests were removed and the troublesome design variables and/or 
the particular values that would cause the undesirable 
response were avoided. 



47 



C. 0PC0DE2 VERIFICATION 

Verification of 0PC0DE2 as a predictor of condenser 
performance was attempted by inputing the design values 
from the CVA 67 technical manual [19] and comparing the 
condenser designed by 0PC0DE2 with the values given by the 
condenser technical manual [19]. Both the Eissenberg [3] 
and the Korodense [23] relations for tube inundation 
effects were used. 

Because only one half of the condenser is designed by 
0RC0N1 , the quantity of inlet steam and the number of tubes 
specified by reference 19 were halved. 

The program would not accept an inlet steam rate of 
greater than 200,000 pounds per hour (400,000 pounds per hour 
for the entire bundle) . 

Holman [21] states that up to a 20 percent increase in 
heat transfer rate may be realized by the ripples set up in 
the condensate film by steam passing over the film. The 
Korodense literature [23] indicates an enhancement due to 
the same phenomena as less than the 20 percent reported by 
Holman but also shows the enhancement to be a weak function 
of tube location in the bundle. 

An enhancement, due to film ripples, of 14 percent was 
assumed for the current work. 

The results of the verifications using both the Eissenberg 
and the Korodense relations are tabulated in Table III with 
the data from the CVA 67 technical manual [19] included for 



48 



comparison. Both relations yielded unsatisfactory design 
verification and in both cases a very conservative condenser 
was designed. 

All parameters, as calculated by 0PC0DE2, were ten to 
twenty percent less than those from the actual condenser. 
With the removal of subroutine ADJUST, the condenser designed 
by 0PC0DE2 vented in excess of 20 percent of the inlet steam 
without condensing it. 

It is believed that the effects of tube inundation give 
a shell-side film heat transfer coefficient which is too 
conservative as reflected in the reduced value of the overall 
heat transfer coefficient. 

D. LIMITATIONS OF 0PC0DE2 

Because 0RC0N1 has the capability to make design decisions 
and COPES/CONMIN requires a "once through" analysis, the 
coupling of these two programs in 0PC0DE2 created a situation 
where the programs were working against each other. This 
placed a limitation on which parameters could be used as 
design variables and on what range of values these design 
variables could use. 

The condenser designed by 0PC0DE2 was very conservative, 
a condition caused primarily by the conservative value of 
the overall heat transfer coefficient calculated. 

Accepting these limitations, it was felt that 0PC0DE2 
should be further developed and that case studies should be 
performed . 



49 



V. RESULTS 

A. EXPLANATION OF THE CASE STUDIES 

The case studies were devised to best exercise the 
attributes of 0PC0DE1 and 0PC0DE2, and were made as realistic 
as possible so as to simulate the problem of a condenser 
design and specification during the early stages of power 
plant design. Only input parameters that would normally 
be available were used. 

When comparing the results from the different cases, two 
cautions must be kept in mind. First, since all the cases 
involve four to six design variables, the design is taking 
place in a four to six dimensional design space and intuition 
on how an optimized design "should" turn out is not always 
applicable. Secondly, the percentage change referred to in 
each case is calculated based on the initial design for that 
particular case. 

1 . Constraint Framework for 0PC0DE1 

In order to simulate an actual trade off study, the 
constraints for each case study were kept the same, even 
though an unimportant constraint could become active during 
a particular case study. In this way, each case study could 
be directly compared with all others. 

The main condenser for the CVA 67 was to be designed 
with a maximum bundle diameter of ten feet; a terminal 
temperature difference (pinch point) of at least five degrees 



50 



Fahrenheit (°F) but not more than 35°F; a cooling water 
temperature rise of at least five °F, but not more than 20°F; 
and a ratio of tube sheet hole area to tube sheet area 
without the drilled holes of less than 0.36. 

The constraint on bundle diameter was chosen only 
because it is a reasonable value. If more or less vertical 
space was available in a proposed machinery arrangement, the 
diameter constraint would be appropriately changed. The 
lower constraint on pinch point came from reference 1 
which called for a minimum terminal temperature difference 
of five °F. No reference to an upper limit on pinch point 
could be found, but several technical manuals specified 
temperatures in the range of 20°F to 45°F. A value of 35°F 
was therefore chosen as the upper bound on the terminal 
difference . 

Reference 24 states that the difference in temperature 
between the steam and cooling water streams entering the 
condenser, or temperature range, is ordinarily kept to 20°F, 
and that the cooling water temperature rise is usually made 
about five °F less than the temperature range. Since the 
CVA 67 exhausts steam with a saturation temperature of 125°F 
and reference 3 calls for a cooling water injection tempera- 
ture of 75°F, the temperature range used was 50°F and the 
cooling water temperature rise upper limit was 45°F. As 
the guidance given by reference 24 seemed inappropriate and 
since neither reference 1 nor reference 2 specifies limits 
on cooling water temperature rise, the lower limit was 



51 



arbitrarily set at five °F and the upper limit was 
arbitrarily set at 20°F. The amount of tube sheet material 
that can be removed by drilling for the installation of 
tubes is specified at 24 percent of the blank tube sheet 
area by reference 2. Since 0PC0DE1 does not allow for 
steam lanes in the design of a condenser, and since these 
steam lanes would provide blank tube sheet area, the 
24 percent limit was raised to 56 percent. 

To ensure that an unrealistic tube wall thickness 
was not specified, a constraint on the wall thickness was 
added. The wall thickness was calculated from the current 
values of tube outside diameter and tube inside diameter, 
and the constraint applied. Values of wall thickness in 
the range from BWG 24 (0.022 inch) to BWG 12 (0.109 inch) 
were used as the lower and upper constraints. 

In summary, the general design constraints and the 
associated upper and lower bounds were: 

0.022 <_ tube wall thickness (inch) 0.109 

1.0 <_ bundle diameter (feet) <_ 10.0 

5.0 <_ terminal temperature difference (°F) <_ 55.0 

5.0 <_ sea water temperature rise (°F) 20.0 . 

These design constraints and the associated upper and lower 
bounds were used in all of the OPCODE1 test cases except 
where specifically modified. 



52 



2 . Design Variable Framework for 0PC0DE1 

The condenser tube outside and inside diameters 
were used as design variables. The side constraints were 
set to correspond with the values of normally available 
tubes [1] . The tube outside diameter was allowed to vary 
in the range between 0.625 inch and 1.25 inch. The tube 
inside diameter was allowed to vary from 0.407 inch to 
1.206 inch. 

The tube pitch is defined as the center to center 
spacing between tubes. The pitch to diameter ratio (S/D) 
is an accurate measure of how closely packed the tube 
bundle is. Generally accepted S/D ratios lie in the range 
of 1.3 to 1.7. However, to give greater latitude to this 
design variable, and since 0PC0DE1 was insensitive to 
shell-side conditions, the S/D ratio was allowed to vary 
within the range from 1.1 to 3.0. 

There was no guidance available on the range of tube 
lengths that would be applicable to a condenser of this size 
using 0.625 inch tubes. Reference 1 gave a range of 
recommended tube lengths of eight to fourteen feet for 
0.625 inch outside diameter tubes with an upper limit on 
heat transfer surface area of 1000 square feet. In the 
range of the expected heat transfer area of 12,000 to 18,000 
square feet, the recommended tube outside diameters were 
from 0.75 inch to 0.875 inch with tube lengths ranging 
from 16 to 24 feet. Since the lower bound was not considered 
to be as crucial as the upper bound, it was set at one foot. 
The upper bound on tube length was set at 25 feet. 



53 



Cooling water velocity generally ranges from three 
to nine feet per second for all common tube materials 
except titanium which has an upper bound of 15 feet per 
second. 

In summary, the general design variables and the 
associated side constraints were: 

0.625 <_ tube outside diameter (inch) <_ 1.25 

0.407 <_ tube inside diameter (inch) <_ 1.206 

1.1 <_ pitch/diameter ratio 3.0 

1.0 <_ tube length (feet) < 25.0 

3.0 <_ cooling water velocity (feet/second) <_ 9.0 

These design variables and the associated side 
constraints were used in all of the 0PC0DE1 test cases 
except where specifically modified. 

3 . Constraint Framework for 0PC0DE2 

The same constraints that were used for 0PC0DE1 
were used for 0PC0DE2 with several additional constraints 
required due to the physical calculations performed. 

To ensure that the cooler was not designed to be 
wider than the void inside diameter, the ratio of cooler 
width to void diameter had an upper bound of 1.0 and a lower 
bound of 0.1 

As the initial design with 0PC0DE2 vented over 
20 percent of the inlet steam without condensing it, an 



54 



upper bound on the exit steam fraction was set at five 
percent. The lower bound was set to zero. 

Since 0PC0DE2 was attempting to allow for a central 
steam lane, the upper limit on bundle diameter was set at 
12 feet and the lower limit was set at five feet. 

Bundle volume had an upper limit of 1500 cubic 
feet and a lower limit of 100 cubic feet. These limits 
had been used satisfactorily with 0PC0DE1. 

To ensure that the cooler height did not become 
larger than the band of condenser tubes from the outside 
diameter of the bundle to the inner void, the ratio of 
cooler height to tube band width was calculated. This 
ratio had an upper limit of 1.0 and a lower limit of 0.01. 

The pinch point and the sea water temperature rise 
had the same range as was used for 0PC0DE1. 

The tube wall thickness was not used as a design 
constraint in 0PC0DE2 as it had been in 0PC0DE1. Instead 
the tube inside diameter was used, with the lower constraint 
set at 0.407 inches and the upper constraint set at 1.206 
inches to correspond with the values of normally available [1] 

In summary, the general design constraints and the 
associated upper and lower bounds were: 

0.1 <_ cooler width/void diameter <_ 1.0 

0.0 <_ exit steam percentage <_ 5.0 

5.0 < bundle diameter (feet) < 12.0 



55 



100. <_ bundle volume (cubic feet) <_ 1500. 
0.01 <_ cooler height/tube band width <_ 1.0 
0.407 <_ tube inside diameter (inch) <_ 1.206 

5 . <_ terminal temperature difference (°F) <_ 35. 
5.0 <_ sea water temperature rise (°F) <_ 20. 

4 . Design Variable Framework for OPCODE2 

The condenser tube outside diameter and wall 
thickness were used as design variables. The side con- 
straints were set to correspond with the values of normally 
specified tubes [1]. The tube outside diameter had a 
lower side constraint of 0.625 inch and an upper side 
constraint of 1.25 inch. The tube wall had a lower side 
constraint of 0.022 inch and an upper side constraint of 
0.109 inch. 

Tube length had the same side constraints as were 
used for 0PC0DE1. 

The tube pitch to diameter ratio had a lower side 
constraint of 1.4 and an upper side constraint of 2.0. 
This band of allowable values was reduced from that used 
with 0PC0DE1 because of instabilities that developed for 
values of this variable outside of this band. More prob- 
lems occurred at the lower end of the range than at the 
upper end. These problems originated from the tubes coming 
too close together and causing an excessively high steam 
velocity with a subsequent large pressure drop through a 
row of tubes. Since condenser pressure was already low, 



56 



passage through very few rows led to a negative steam 
pressure and thus the computational problems associated with 
the logarithmic calculation of thermodynamic properties 
discussed in Chapter IV. 

The sea water velocity was allowed to vary within 
the range from three feet per second to ten feet per second. 
The upper side constraint was raised from the nine feet 
per second specified in 0PC0DE1 in an attempt to increase 
the mass flow rate of the cooling water and, therefore, the 
heat rejection rate. 

In summary, the general design variables and the 
associated side constraints were: 

5.0 <_ tube length (feet) <_ 25.0 

3.0 <_ sea water velocity (feet per second) 10.0 

0.625 tube outside diameter (inch) <_ 1.25 

0.022 <_ tube wall thickness (inch) <_ 0.109 

1.4 <_ tube pitch/diameter ratio <_ 2.0 

B. CASE STUDIES USING 0PC0DE1 
1 . Case One 

The objective of this test case was to minimize 
the pumping power requirement while holding the heat load 
to the condenser constant. The input parameters are pre- 
sented in Table IV, the' initial design is presented in 
Table V, and the results of the optimization are presented 
in Table VI. 



57 



These results show an 84 percent decrease in pumping 
power with a commensurate 37 percent increase in heat 
transfer surface area, a 55 percent increase in condenser 
volume, and a decrease of 27 percent in overall heat trans- 
fer coefficient. The log mean temperature difference 
remained constant. 

The lower bound on tube wall thickness constraint 
and the upper bound on sea water temperature rise constraint 
were both active. No side constraints were active and no 
constraints were violated. 

The decrease in pumping power is impressive but 
so are the increases in condenser dimensions with the implied 
increases in weight and cost. 
2 . Case Two 

The objective of this test case was to minimize 
condenser volume with the heat load to the condenser held 
constant. The input parameters are presented in Table IV, 
the initial design is presented in Table V, and the results 
of the optimization are presented in Table VII. 

These results show a 15 percent decrease in condenser 
volume with an unexpected 5.0 percent decrease in pumping 
power. This design can be understood by noting that the 
tube wall thickness was reduced from 0.049 inch to 0.022 
inch causing an increase in material correction factor 
from 0.90 to 0.99. This increase was the primary factor 
in increasing the overall heat transfer coefficient 9.9 
percent . 



58 



The lower constraint on tube wall thickness, and 
the upper constraint on tube sheet area ratio were both 
active. In addition, the lower side constraint on tube 
outside diameter and the upper side constraint on sea water 
velocity were both active. There were no violated constraints 
3 . Case Three 

The objective of this case was to maximize the heat 
rejected while holding pumping power constant. Since the 
pumping power is a calculated quantity, the method of com- 
bining pumping power and the heat rejected with an appro- 
priate weighting factor in the objective function was used. 
The objective function was therefore: 

OBJ = QREJ + A * POWER 

and POWER was added as a design constraint with the target 
value of 68836 foot pounds per second as the upper constraint. 
With the weighting factor, A, set at 5600, the pumping 
power was constant within one percent. Turbine exhaust 
steam and auxiliary exhaust steam were both added as design 
variables to provide the driving force to increase the heat 
rejection rate. 

The input parameters are presented in Table IV, 
the initial design is presented in Table V and the results 
of the optimization are presented in Table VIII. 



59 



These results show an 82 percent increase in the 
heat rejection rate with an accompanying 88 percent increase 
in surface area. The log mean temperature difference 
remained constant and the overall heat transfer coefficient 
decreased by 3.7 percent. The condenser volume increased 
by 78 percent and the number of tubes increased by 96 percent 

The upper constraint on pumping power was active, as 
desired, and the upper constraint on the tube sheet area 
ratio was active. There were no violated constraints and 
no active side constraints. 

It should be noted that the turbine exhaust steam 
rate increased by 83 percent, whereas the auxiliary exhaust 
steam rate increased only 1.0 percent. Inspection of the 
component parts of QREJ explains the dominance by the main 
steam rate. The rejected heat was calculated by: 

Q . = m.. c Ah,, + m, c Ah , c + heat from other sources 
x rej MS MS AS AS 

where the subscript MS corresponds to main steam and the 
subscript AS corresponds to auxiliary steam. Heat from 
other sources was assumed constant during the optimization. 
The product nu,^ Ah MC , was several orders of magnitude greater 
than the product m.~ Ah.- and it therefore dominated the 
optimization process as a change in the m MC , design variable 
would yield a greater design improvement than would a like 
change in the m.- design parameter. 



60 



In all probability, the m.~ design variable would 
not begin to make an appreciable move until the niwg design 
variable approached its upper side constraint. This could 
not occur as the m MC , design variable had an unbounded upper 
side constraint. 

No attempt was made to balance the flow of steam 
from the two sources to more evenly distribute the incoming 
heat load. Balancing could be accomplished by appropriately 
scaling the two mass flow rates so they would have approximately 
the same values . 
4 . Case Four 

The objective of this case was to minimize the 
condenser volume while holding pumping power and the rejected 
heat constant. POWER was again included in the objective 
function 

OBJ = VOL + A * POWER 

and as a design constraint with a lower bound of 68836 foot 
pounds per second. The lower bound was the target value 
for pumping power. Trial and error solutions with various 
values of the weighting factor showed that a value of 
A = 0.0 gave a value of POWER which was constant within 
0.5 percent. This was interpreted to mean that the optimi- 
zation would have reduced the objective function further 
if the pumping power constraint was not present and that 



61 



the pumping power lower constraint was therefore always 
active. With the value of this constraint set at the 
target value for constant pumping power, inclusion of POWER 
in the objective function was unnecessary and A = 0.0 was 
appropriate . 

The input parameters are presented in Table IV, 
the initial deisgn is presented in Table V and the results 
of the optimization are presented in Table IX. 

These results show only a 2.0 percent decrease in 
condenser volume. The tube pitch to tube diameter ratio 
remained essentially constant as did the tube outside diameter 
The tube wall thickness increased by 11 percent with an 
accompanying decrease in material correction factor from 
0.90 to 0.88. 

The lower constraint on pumping power was active, 
as discussed above. The upper constraint on sea water 
temperature rise, as well as the upper constraint on tube 
sheet area ratio were active. The upper constraint on sea 
water velocity was the only active side constraint. There 
were no violated constraints. 

The results of this case study indicated that the 
circular bundle prototype was very close to having an opti- 
mum volume within the given design variable and design 
constraint framework. 

Comparison of Cases Two and Four shows that a 
smaller condenser with essentially constant pumping power 



62 



was achieved with Case Two then with Case Four. This 
anomaly can be understood by comparing the constraints 
for the two cases. 

Pumping power was not a constraint for Case Two 
and it was an active constraint for Case Four. Thus, 
the Case Four optimization had to contend with an additional 
constraint whereas, Case Two had more latitude within the 
design space and a better optimum was found. 
5 . Case Five 

The objective of this case was to minimize the 
condenser overall length while holding pumping power and 
the heat rejected constant. Pumping power was included 
in the objective function: 

OBJ = CLOA + A * POWER 

and as a design constraint with a lower bound of 68856 foot 

pounds per second as the target value. With a weighting 

- 4 
factor of 3.526 x 10 , pumping power was held constant 

within 0.5 percent. 

The input parameters are presented in Tabe IV, the 
initial design is presented in Table V and the results of 
the optimization are presented in Table X. 

The overall condenser length was reduced by 28 percent 
The heat transfer area increased by 9.7 percent and the 
overall heat transfer coefficient decreased by 15 percent, 



63 



while the log mean temperature difference increased by 
7.1 percent. The number, 'of tubes increased 96 percent and 
the tube length decreased 44 percent. The tube wall thick- 
ness increased causing a decrease of 14 percent in the 
material correction factor thereby contributing to the 
decrease in overall heat transfer coefficient. 

Accompanying the 23 percent decrease in condenser 
length was a compensating 37 percent increase in bundle 
diameter and an 18 percent increase in condenser volume. 

The lower constraint on pumping power was active, 
as desired. The upper constraints on pinch point and on 
tube sheet area ratio were active. There were no active 
side constraints and no violated constraints. 
6. Case Six 

The objective of this case was to minimize pumping 
power while holding condenser volume and the heat rejected 
constant. For this case, volume was included in the 
objective function: 

OBJ = POWER + A * VOL 

and it was also included as a design constraint with an 
upper bound of 928.8 cubic feet as the target value. The 
usual trial and error procedure with various weighting 
functions was performed and the best results were obtained 
for a weighting factor of -2.5. With this value, condenser 
volume was held constant to within 1.3 percent. 



64 



The input parameters are presented in Table IV, 
the initial design is presented in Table V and the results 
of the optimization are presented in Table XI. 

The pumping power was reduced by 35 percent. The 
log mean temperature difference and the heat transfer area 
remained essentially constant, while the tube wall thickness 
decreased 52 percent causing a ten percent increase in the 
tube material correction factor. The sea water velocity 
was reduced by 16 percent, however, and the overall heat 
transfer coefficient remained essentially constant. There 
were no active constraints, no violated constraints and 
no active side constraints. 

Volume was not forced against its upper constraint 
as planned because the two members of the objective function 
were attempting to move in opposite directions. As power 
was decreased, the volume tended to increase. The negative 
weighting factor helped to turn this process around but 
the optimum was reached before the constraint was activated. 
7 . Case Seven 

English has shown [25] that by placing boundary 
layer fences in front of the injection scoop of a ship, 
the pressure coefficient, and hence pumping power, will 
increase by 68 percent. These boundary layer fences cause 
shedding vortices to form behind them thus pumping water 
from the boundary layer around the ship into the condenser 
intake . 



65 



This case takes advantage of the increase in 
available pumping power by setting pumping power at a 
value 50 percent greater than the normal 68836 foot pounds 
per second, and holding this new value of pumping power 
constant while maximizing the rejected heat. 

The constraints and design variables were set up 
exactly as they were for Case Three with the exception that 
the upper constraint on pumping power was raised to 103,250 
foot pounds per second. POWER was included in the objective 
function as before and a weighting factor of 4095 yielded 
pumping power constant within 0.5 percent. 

The input parameters are presented in Table IV, the 
initial design is presented in Table V and the results 
of the optimization are presented in Table XII. 

The heat rejected was increased by 107 percent. The 
heat transfer area increased by 101 percent, and the log 
mean temperature difference remained constant. The tube 
wall thinned down by 53 percent causing an increase in the 
tube wall material correction factor of ten percent. The 
sea water velocity decreased 15 percent and the overall heat 
transfer coefficient increased 2.5 percent. 

The upper constraints on pumping power and the tube 
sheet area ratio were active. There were no active side 
constraints and no violated constraints. 



66 



C. CASE STUDIES USING 0PC0DE2 
1. Case Eight 

This case was run assuming plain copper-nickel 
tubes with a 14 percent enhancement factor applied to the 
outside film heat transfer coefficient as described in 
Section IV(C) of this work. Steam baffles were specified 
and the inlet steam flow rate was set at 200,000 pounds per 
hour as only one half of a condenser bundle was being simu- 
lated. The Korodense equation from reference [23] was used 
to calculate the correction factor for tube inundation by 
condensate rain. 

The objective of this case was to minimize condenser 
volume. The initial and optimum designs are presented in 
Table XVI. 

The volume was reduced 13 percent and the heat 
transfer area increased 14 percent. The log mean tempera- 
ture difference decreased 5.6 percent, the overall heat 
transfer coefficient increased 11 percent and the heat 
rejected increased 21 percent. The vented steam rate 
decreased 76 percent to five percent of the inlet steam 
flow rate. Finally, pumping power increased 65 percent 
and the sea water flow rate increased 35 percent. 

The upper side constraint on sea water velocity as 
well as the lower side constraints on tube outside diameter, 
tube pitch to diameter ratio and tube wall thickness were 
all active. The upper constraint on vented steam rate 
was active. There were no violated constraints. 



67 



2 . Case Nine 

The objective of this case was to minimize the 
condenser volume when enhanced tubes were specified. 
The initial parameters were the same as those used in 
Case Nine with the exception of the outside enhancement 
factor which was set to 1.8. It was felt that this modest 
enhancement was attainable with the augmented tubes 
currently being manufactured. 

The initial and optimum designs are presented in 
Table XVII. 

Use of enhanced tubes reduced the condenser volume 
by 21 percent. The heat transfer area increased 2.6 per- 
cent, the overall heat transfer coefficient increased 34 
percent, the log mean temperature coefficient decreased 
11 percent and the heat rejected increased 21 percent. The 
vented steam rate decreased 76 percent to five percent of 
the inlet steam flow rate. 

Pumping power increased 52 percent and the cooling 
water flow rate increased 35 percent. Tube length was 
increased by 2.7 percent and the tube inside diameter 
increased ten percent. 

The pumping power calculated was based on smooth 
tubes. The most common augmented condenser tubes use either 
a rope design, a twist design, or internal flow promoters 
to enhance heat transfer. Reilly [26] has found that the 
pressure drop through enhanced tubes is 1.5 to 3.0 times the 
pressure drop through smooth tubes for the same flow conditions 



68 



The upper side constraint on sea water velocity, 
as well as the lower side constraints on tube outside 
diameter, tube pitch to diameter ratio and tube wall 
thickness were all active. The upper constraint on vented 
steam rate was active, and there were no violated constraints. 
3 . Case Ten 

This case was run using the same conditions as 
Case Eight with the exception that the original equation 
from 0RC0N1 was used to correct for tube inundation. Reference 
3 specified a value for the flooding factor, FDAVE , of 
zero for pitch to diameter ratios greater than 1.4. 

This value was used during this run of 0PC0DE2. 
The objective of this case was to minimize the condenser 
volume. The initial and optimum designs are presented in 
Table XVIII. 

A more conservative design was produced with the 
Eissenberg equation than the design produced with the 
Korodense equation. The volume was reduced 5.3 percent and 
the heat transfer area increased 24 percent. The log mean 
temperature difference remained constant, the overall heat 
transfer coefficient increased by 8.9 percent, and the 
heat rejected increased by 33 percent. The vented steam 
rate decreased 83 percent to five percent of the inlet 
steam flow rate. Pumping power increased 75 percent and the 
sea water flow rate increased 35 percent. 

The upper side constraint on sea water velocity, 
as well as the lower side constraints on tube outside 



69 



diameter, tube pitch to diameter ratio and tube wall 
thickness were all active. The upper constraint on vented 
steam rate was active. There were no violated constraints 



70 



VI. CONCLUSIONS 

The intent of this investigation was to couple a 
numerical optimization code with both a simple computer 
code for condenser design based on the HEI/DDS method 
and the more sophisticated 0RC0N1 , and to test the programs 
developed with a variety of test cases to prove their 
viability. The results of these test cases were presented 
in Section V; the resulting conclusions are summarized 
here . 

A. A condenser designed by the HEI/DDS method is very 
near the volumetric optimum in design, as only a 
15 percent decrease in condenser volume was 
realized when volume was optimized using 0PC0DE1. 

B. 0PC0DE1 is an excellent design tool for the concep- 
tual design of a condenser to meet specified con- 
straints such as length, height, and weight. 

C. 0PC0DE1 can optimize a variety of objective func- 
tions, and with some trial and error application 
of weighting factors, equality constraints can 

be met. 

D. 0PC0DE1 will yield an optimum design on which 
experience-based safety factors may be applied. 

E. The ability to enhance tubes and the sensitivity 
of the program to shell-side conditions make the 
ORCONl-based 0PC0DE2 very attractive. 



71 



F. The basic equations and the research applied to 
the development of 0RC0N1 are sound, but a conser- 
vatively-designed condenser results. More baffles 
are required to more closely approximate an actual 
condenser and to aid in reducing the inundation 
effect on interior tubes. 

G. The 0PC0DE2 designed condensers were more conserva- 
tive than those designed by 0PC0DE1. This was 
caused by the detrimental effect on outside film 
coefficient by tube flooding. It is felt that this 
effect could be reduced by the addition of more 
baffles. 



72 



VII. RECOMMENDATIONS 

In addition to the insight that this investigation has 
given into the generation of automated design programs for 
condenser design, it has also generated an awareness of 
this investigation's shortcomings. Presented herein are 
recommendations for improving upon and furthering develop- 
ment of the OPCODE family of condenser design programs. 

A. 0PC0DE1 should be expanded to include the capability 
for multi-pass condenser calculations, geometrical 
options, material costing equations, strength of 
material considerations, and an algorithm to compute 
steam velocity through the rows of tubes to ensure 
that the velocity remains realistic. 

B. Research should be performed to develop enhancement 
factor data for various tube types that can be 
applied to the basic equations used in 0PC0DE1. 

C. 0RC0N1 should be rewritten with the intent of 
applying optimization techniques to the new program, 
and based on the equations and logic developed by 
Eissenberg, Korodense, and other investigators and 
manufactures, with the option to choose the 
desired relationship to be used. 

D. In an effort to reduce the computer time required 
for a run using 0PC0DE2 (typically 55 CPU minutes) , 
an investigation into using 0PC0DE1 as a pre- 
processor in front of a detailed analysis scheme is 
attractive . 



E. Expand 0PC0DE2 to perform calculations for other 
than a circular bundle. 



74 



VIII. FIGURES 



h A 



FEASIBLE 
REGION 
G-<CT 




INFEASIBLE REGION 
Gj> [CT| 



FIGURE 1. Significance of the Constraint Thickness (CT) 
Parameter 



75 



2.2 r- 



2.0 - 



© 1.8 - 



cc 
a: 

LU 

I— 

< 

Q 

IE 
C_3 



CO 



1.6 - 



1.4 - 



1.2 - 



SIDE CONSTRAINT 



CONTOUR OF CONSTANT VOLUME 



1.0 




0.0 



= 



0.2 0.4 0.6 0.8 
TUBE OUTSIDE DIAMETER (INCH) 



FIGURE 2. Two-Variable Design Space Showing the Initial 
Design at Point (A) . 



76 



2.2 



2.0 



1.8 



a: 



£ 1.6 

t— I 
Q 



1.4 



CD 



1.2 



1.0 



SIDE CONSTRAINT 



CONTOUR OF CONSTANT VOLUME 




■OD r=0.18 
> gLL" 



0.0 



0.2 0.4 0.6 0.8 
TUBE OUTSIDE DIAMETER (INCH) 



FIGURE 3. Two-Variable Design Space Showing the First 
Design Iteration 



77 



2.2 i- 



SIDE CONSTRAINT 



CONTOUR OF CONSTANT VOLUME 



2.0 - 



1.8 - 



0£ 



£ 1-6 



O 



1.4 - 



CO 

13 



1.2 - 



1.0 




0.0 



0.2 0.4 0.6 0.8 
TUBE OUTSIDE DIAMETER (INCH) 



FIGURE 4. Two-Variable Design Space Showing the Second 
Design Iteration 



2.2 »- 



SIDE CONSTRAINT 



CONTOUR OF CONSTANT VOLUME 



2.0 - 



1.8 



■< 



!- 1.6 - 



UJ 

< 

(—1 
Q 



~ 4 



CO 



1.2 - 



1.0 




0.0 



0.2 0.4 0.6 
TUBE OUTSIDE DIAMETER (INCH) 



HP -HP =0 
max 



0.8 



FIGURE 5. Two-Variable Design Space Showing the Third 



Design Iteration 



79 



2.2 r- 



2.0 - 



1.8 - 



< 



< 

1—1 
Q 

a: 

o 



CO 



1.6 - 



1.4 - 



1.2 - 



1.0 



SIDE CONSTRAINT 



CONTOUR OF CONSTANT VOLUME 




0.0 



0.2 0.4 0.6 0.8 
TUBE OUTSIDE DIAMETER (INCH) 



FIGURE 6. Two-Variable Design Space Showing the Fourth 



Design Iteration 



80 



2.2 »- 



SIDE CONSTRAINT 



CONTOUR OF CONSTANT VOLUME 



2.0 - 



1.8 - 



< 

en 
cc 

LU 



h 1.6 - 



LU 

< 

Q 

I— 

■""• 1.4 

LU 
OQ 



1.2 



1.0 




0.0 



0.2 0.4 0.6 0.8 
TUBE OUTSIDE DIAMETER (INCH) 



FIGURE 7. Two-Variable Design Space Showing the Fifth 



Design Iteration 



81 



SIDE CONSTRAINT 



2.2 



2.0 



1.8 



< 



UJ 

< 

I— t 
Q 



CD 



1.6 



1.4 



1.2 



1.0 




•OD r=0.18 
J P n 1 i 



0.0 



0.2 0.4 0.6 0.8 
TUBE OUTSIDE DIAMETER (INCH) 



FIGURE 8. Two-Variable Design Space Showing the Need for 
Optimization Techniques 



82 



g(X) = o 



F(X)= CONSTANT 



Y^^b \ 




\c \ 




\ 


^_p\ \ 


^ sXsyysyv 



FIGURE 9. Two-Variable Design Space Showing Relative 

Minima for a Constrained Minimization Problem 



83 



STEAM 
FLOW 



AIR COOLER 




BAFFLE 



0.866-q X D 

BAFFLE 



STEAM 
FLOW 



FIGURE 10. Circular Condenser Bundle Designed by ORCON1 



84 



STEAM IN 




SEA WATER OUT- 



CONDENSATE OUT 



STEAM IN 



JO AIR EJECTOR 



AIR 
COOLER 



TO AIR EJECTOR. 



AIR COOLER 




-TUBE SHEETS— ' 
SECTION 0-0 



FIGURE 11. CVA 67 Main Condenser as Modeled by ORCON1 
and OPCODE2 



85 



£• V. © 



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CALL 
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CALCULATE 

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AFTER 

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■GEj 




FIGURE 13. Flowchart from 0RC0N1 



87 



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REMOVED 




FIGURE 14. Flowchart Showing Modification of 0RC0N1 
to 0PC0DE2 



S8 



IX. TABLES 





TECHNICAL 
MANUAL 


0PC0DE1 


DEVIATION 

m 


2 
Heat transfer area; ft 


16,011 


16,099 


+ 0.55 


Number of tubes 


6,612 


6,648 


+ 0.54 


Bundle diameter; ft 


N/A 


7.26 


- 


Heat rejected; BTU/hr 


4.035X10 8 


4.035xl0 8 


0.00 


Overall heat transfer 
coefficient • 
BTU/(hr) (ft 2 ) C°F) 


635 


637 


+ 0.31 


Log mean temperature 
difference; °F 


39.7 


39.3 


-1.01 


Sea water temperature rise; 

op 


19.9 


19.9 


0.0 


Terminal temperature 
difference; °F 


30.53 


30.2 


-1.08 


Sea water flow rate, gpm 


40,565 


40,645 


+ 0.20 


Tube-side pressure drop; 
f t . w. c . 


16.3 


12.4 


-23.9 



TABLE I. Verification of the CVA 67 Main 
Condenser Design Using 0PC0DE1 



89 





TECHNICAL 
MANUAL 


0PC0DE1 


DEVIATION 

m 


2 
Heat transfer area; ft 


6,600 


6,527 


-l.ii 


Number of tubes 


3,892 


3,850 


-1.08 


Bundle diameter; ft 


5.9 


4.6 


-22.1 


Heat rejected; BTU/hr 


2.05xl0 8 


2.047xl0 8 


-0.15 


Overall heat transfer 
coefficient* 
BTU/(hr) (ftO (°F) 


635 


637 


+ 0.31 


Log mean temperature 
difference; °F 


50.0 


49.2 


-1.6 


Sea water temperature rise; 

op 


16.9 


17.4 


+ 2.96 


Terminal temperature 
difference; °F 


41.9 


41.0 


-2.15 


Sea water flow rate; gpm 


23,900 


23,539 


-1.51 


Tube-side pressure drop; 
ft. w. c. 


11.5 


8.21 


-2S.6 



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O 1 


i.* • 


X 1 


«tl— O 


-i. 1 


— u,— 


** 1 


XI 1— 


1 


-<l 


XI 1 


ujujoc 


-J 1 


-is: 


(J 1 


cj j< 


Z 1 


^_JLU 


D 1 


_)Unc 


to 1 


-Q>«t 





• 


• • 


• 




• 


• • 


•■ 




• 


• • 


• 






• • 


o. 






mm * m 


X 




• 


X, •<_» 




• ♦■ 


iJ - 




• 


fM cC^JTZ. 




• 


* -JJJ'N.UJ 




•*h- *U_ JC 




• 


I-ZQT30 




3 


u.-a_iOw 
*a * 




—J 


iO.oi-0 




J 


X ZU.Z 




•<* 


■-»x— 


— 




aNoa. 


a. 




UJ3ZS 


X 


2 


I >H- — D 


3 


a 


ODdi 


a. 


— 








^ 








< 








X 








ae 








X) 


(J> 


l"»0 


-* 


X 


o 


f^m 


• 


Z 




• • 


o» 


M« 


XI 


li^m 


n 




•u 


— «-r 


-r 


'J3 


CO 


• r\ 


(M 


<£ 


■■\\ 


<r 


"> 


»■« 


o 


aa 




Ck 


■o 






3C 


• 






_) 


u 


» ♦ 




a 




• • 


^ 




• 


• s 


< 


o 


• 


XX 


X) 


Z 


• 


O 


ae 


•a 


• 


•> 


< 




• 


XI •■ 




X 


C3 


/1IO 


X 


UJ 


XI 


'1 


XI 


X 


►-ctuc< 


X 


yt 


1 J 


L ne 


u» 


ii 


ajs • 


Z 


<* 


->_JO. J 


•«» 


CC 


XII— «-0 


X 


h- 


cexiuj_i 


I" 






<-u» 


i« 


>— 


r- 




t— ♦ 


<J 


<1 


-fc E 


«»* 


LU 1 


XI 


1 1 


XII—, 


Z 


X 


Ulwl 


EX. 



o 



> 

0) 
C/} 

CD 

Cu 

U 



< 



100 





INITIAL 
VALUE 


VALUE AT 
OPTIMUM 


CHANGE 


2 
Heat transfer area; ft 


16,008 


18,290 


+ 14 


Number of tubes 


6,612 


6,612 


0.0 


Bundle diameter; ft 


10.23 


8.95 


-13 


Heat rejected; BTU/hr 


3.241xl0 8 


3.916xl0 8 


+ 21 


Overall heat transfer 
coefficient 
BTU/Chr) (ft2) (°F) 


562 


625 


+ 11 


Log mean temperature 
difference; °F 


36 


34 


-5.6 


Sea water temperature 
rise; °F 


15.6 


13.7 


-12 


Terminal temperature 
difference; °F 


25.6 


24.6 


-3.9 


Sea water flow rate; gpm 


40,341 


54,479 


+ 35 


Tube-side pressure drop; 
f t . w. c . 


12.3 


- 


- 


Tube length; ft 


14.8 


16.9 


+ 14 


Tube outside diam. ; in. 


0.625 


0.625 


0.0 


Tube inside diam.; in. 


0. 527 


0. 581 


+ 10 


Tube wall; in. 


0.049 


0.022 


-55 


S-W velocity; fps 


9.0 


10.0 


+ 11 


Pitch/diameter 


1.6 


1.4 


-13 


Exit steam; % of input 


21 


5 


-76 


Pumping power; ft- lb/sec 


55,409 


58,290 


+ 65 


Condenser volume; ft 


775 


678 


-13 

- - — — 



TABLE XIII. Case Eight Initial Design and 
Optimization Results 



101 





INITIAL 
VALUE 


VALUE AT 
OPTIMUM 


CHANGE 

m 


2 
Heat transfer area; ft 


16,008 


16.431 


+ 2.6 


Number of tubes 


6,612 


6,612 


0.0 


Bundle diameter; ft 


10.23 


8.95 


-13 


Heat rejected; BTU/hr 


3.241xl0 8 


3.924xl0 8 


+ 21 


Overall heat transfer 
coefficient,-, 
BTU/Chr) (ft z ) (°F) 


562 


751 


+ 34 


Log mean temperature 
difference; °F 


36 


32 


-11 


Sea water temperature 


15.6 


13.1 


-16 


rise; °F 








Terminal temperature 
difference; °F 


25.6 


21.6 


-16 


Sea water flow rate; gpm 


40,341 


54,479 


+ 35 


Tube-side pressure drop; 
f t . w. c . 


12.5 


- 


- 


Tube length; ft 


14.8 


15.2 


+ 2.7 


Tube outside diam. ; in. 


0.625 


0.625 


0.0 


Tube inside diam.; in. 


0.527 


0. 581 


+ 10 


Tube wall; in. 


0.049 


0.022 


-55 


S-W velocity; fps 


9 


10 


+ 11 


Pitch/diameter 


1.6 


1.4 


-13 


Exit steam; % of input 


21 


5 


-76 


Pumping power; ft- lb/sec 


35,409 


53,674 


+ 52 


Condenser volume; ft -3 


775 


609 


-21 



TABLE XIV. Case Nine Initial Design and 
Optimization Results 



10 





INITIAL 
VALUE 


VALUE AT 
OPTIMUM 


CHANGE 

m 


2 
Heat transfer area; ft 


16,008 


19,808 


+ 24 


Number of tubes 


6,612 


6,612 


0.0 


Bundle diameter; ft 


10.23 


8.95 


-13 


Heat rejected; BTU/hr 


2.937xl0 8 


3.910xl0 8 


+ 33 


Overall heat transfer 
coefficient • 
BTU/(hr) (ft*) (°F) 


505 


550 


+ 8.9 


Log mean temperature 
difference; °F 


56 


36 


0.0 


Sea water temperature 
rise; °F 


14.4 


14.2 


-1.4 


Terminal temperature 
difference; °F 


25.2 


26.3 


+ 4.4 


Sea water flow rate; gpm 


40.341 


54,479 


+ 35 


Tube-side pressure drop; 

f t . w. c . 


12.3 


16.0 


+ 30 


Tube length; ft 


14.8 


18.5 


+ 24 


Tube outside diam. ; in. 


0.625 


0.625 


0.0 


Tube inside diam.; in. 


0.527 


0. 581 


+ 10 


Tube wall; in. 


0.049 


0.022 


+ 11 


S-W velocity; fps 


9 


10 


+ 11 


Pitch/diameter 


1.6 


1.4 


-13 


Exit steam; % of input 


29 


5 


-83 


Pumping power; ft -lb/sec 


35,409 


62,059 


+ 75 


Condenser volume ; ft 


775 


734 


-5.3 



TABLE XV. Case Ten Initial Design and 
Optimization Results 



105 



APPENDIX A 
DEVELOPMENT OF THE ANAL I Z SUBROUTINE FOR OPCODE1 

OPCODE1 was based on the HEI/DDS method of calculation 
of heat transfer and thermodynamic parameters. 

The following equations are used in the design of 
a condenser using the HEI/DDS method. 

U = F,F.,F-C/V (A-l) 

c 1 2 :> 



Q = U c A H AT LM (A- 2) 



Q = W Ah (A- 3) 



Q = 500 G (t Q - t^ (A-4) 



AT LM ■ k -Y ( A - 5 ) 

in (^_ ^i) 

S 

A R = L N s (A-6) 



G = Ng V (A-7) 

k = s/g (A-8) 

The ANAL I Z subroutine of 0PC0DE1 was divided into three 
sections: input, analysis and output. The correct section 



104 



of ANALIZ was entered by testing for the value of ICALC 
that was passed from COPES to ANALIZ. 

When ICALC = 1, the input section of ANALIZ was entered 
and the input variables and problem identification were 
read. The input section had the capability to default the 
latent heat of vaporization to 950 BTU per pound as speci- 
fied by reference [2] and to calculate either the saturation 
temperature or the saturation pressure depending on which 
value was not read in on the data card. 

When COPES set ICALC = 2, the analysis section of 
ANALIZ was entered and the calculation of the outside 
area of a condenser tube per foot of tube length was made: 



? 
ft 
it D [ff-] . 



The rate of flow, in gallons per minute, through a 
condenser tube at a velocity of one foot per second was 
then made : 



Gl = (_j) (d 2 ) (60x7.481) = 448.46(j)d' 



riL_][f t 2 ]r£eC]rgal] = .gaK 
L sec H J L min J L ^T J L min J 



The value of C in equation (A-l) was assumed to be a 
constant 270 when in fact, C was weakly dependent on tube 
outside diameter. With this assumption, the uncorrected 
heat transfer coefficient was calculated as: 



105 



u = c/v [ B T U ] . 

hr-ft .°F 



A call was then made to subroutine MATFAC to find the 
new value of the material correction factor, F2 , based on 
the current value of tube wall thickness. The temperature 
correction factor, F,, was found with the function sub- 
routine TEMFAC. 

The data from Figure 1 of reference [2] was implemented 

in TEMFAC and a value of F„ as a function of injection 

3 J 

temperature was retrieved using subroutine INTRPL, a systems 
supplied interpolator. 

The fouling factor, F, , was set to 0.85 in accordance 
with references land 2 during the input section of ANALIZ. 

The corrected value of the overall heat transfer 
coefficient was calculated: 



U = F 1 F 9 F- U 
c 1 2 j> 



The original form of equation (A-4) was 



Q = 60 W C G (t - t.) 
p ^ o i J 



For sea water, the following value of 60 W C was 

& p 

calculated : 



60 (W C ) s . w = (60) (8.55) (0.94) = 482 



106 



while, for fresh water, 60 W C was calculated as 

P 



60(W C p ) F . w = (60) (8.33) CI. 0) = 500 



Reference [2] recommends the use of 60 W C = 500 in 

P 

keeping with industry standards. This approximation will 
induce an error of approximately one-half percent. 

Be setting equation (A-2) equal to equation (A-4) 
and substituting for values of G, A H and AT TM , the following 
relation was obtained: 



(A-9) 



t 

s 


■ t . 

1 


U L K 


t 

s 


• V ■ 


c 

500 V 



which can be written as : 



t - t . 
si a 

V~^ = e 



where 



U L K 

_ _c 

a " 500 V 



Equation (A-9) was solved for the cooling water outlet 
temperature 



t - t. 
t = t x 



o s a 



107 



The sea water temperature rise and the pinch point were 
calculated, as was the initial temperature difference. All 
the factors were now available for the calculation of the 
logarithmic mean temperature difference, ^Tjw, using 
equation (A- 5) . 

The input heat load was divided into the auxiliary 
steam flow, main steam flow, and heat from other sources. 

The auxiliary and main steam flows were multiplied by 
their respective changes in latent heat, Ah, and summed 
with the heat from other sources to yield the total heat 
input, Q. 

If an input value for Ah is not read in for either 
auxiliary or main steam flow, the default value of 950 BTU 
per pound, specified by reference [2], is used. 

With the value of Q, equation (A-4) was utilized to 
calculate the required flow rate of cooling water, G. With 
the value of G known, the heat transfer area, A„ , was 
found using equations (A-6), (A-7) and (A-8): 



A = L G K 
A H V 



The heat rejected to the cooling water was found by 
using equation (A-2). 

The next portion of ANALIZ was devoted to the calcu- 
lation of bundle geometry. The call to subroutine GEOM 
yielded a condenser design of circular bundle cross section 



108 



with a 12 inch diameter void along the longitudinal center- 
line to serve as a header for the removal of nonconden- 
sable gasses by an air ejector. The rows of tubes were 
filled from the inner void and were concentric to the 
center void. Partial tubes were permitted in order to 
simplify the algorithm and the final, outermost row was 
only partially filled. The bundle radius was calculated 
with no allowance for circumferential steam lanes, since 
it is beyond the capability of the HEI/DDS method to provide 
for steam lanes . 

It was assumed that the waterboxes were hemispherical 
caps on the ends of the cylindrical bundle. The waterboxes 
may not be any deeper than 45 inches [2] and logic was 
included to ensure that this specification was met. 

The ratio of tube sheet material removed for tube 
installation to original undrilled tube sheet area was 
calculated and used as a design constraint during the 
optimization process. Reference [2] requires that the 
ratio calculated must be less than or equal to 0.24 to 
allow for adequate tube sheet strength. 

A hotwell capacity capable of receiving the condensate 
from one minute of full power operation is specified by 
reference [2]. This value was calculated as the product 
of the specific volume of the incoming steam and the 
steam flow rate. 

The calls to subroutines FRIFLAC and PRSDRP found the 
factors required for the calculation of tube side pressure 
drop and pumping power. 



109 



Total condenser volume was the sum of the tube bundle 
volume, the waterbox volume, and the hotwell volume with 
the individual watervoxes treated as spherical caps. 

The final step in the analysis section of subroutine 
ANALIZ was to define the objective function with any 
necessary weighting factors as described in Chapter II. 

COPES repeatedly enters the ANALIZ subroutine with 
ICALC = 2 during the optimization process — often on the 
order of hundreds of times. Therefore, no WRITE statements 
were included in the analysis section. All output was 
performed within the output portion of ANALIZ, a region 
that is entered only when the optimization process is 
terminated and ICALC is set equal to three. 



110 



APPENDIX B 
DEVELOPMENT OF SUPPORTING SUBROUTINES FOR OPCODE1 

In this appendix, the subroutines that were utilized 
during the execution of ANALIZ in OPCODE1 are briefly 
described. 

FRIFAC 

This subroutine iteratively solved the transcendental 
Colebrook equation [17]: 



2.51 + 
/T " ^Re/f 3 



2 log C^= + t^) 



for the value of the internal friction factor for tube 
flow. FRIFAC was valid for the range 

0.01 <_ f <_ 0.10 . 

This method was chosen over the simpler Blasius equation 
because of the inclusion of the desirable dependence on 
the relative roughness, e/d, in the Colebrook equation. 

GEOM 

This subroutine calculated bundle geometry. The 
condenser bundle was assumed to have a 12 inch central void 
along the longitudinal centerline with the rows of tubes 
in concentric rows about the void. The void served as a 



111 



header for the venting of noncondensable gasses. The rows 
were filled from the inside out; partial tubes were permitted 
and the outermost row was unfilled. 

PRSDRP 

This subroutine calculated the cooling water pressure 
drop through the condenser bundle. The development of this 
subroutine was thoroughly discussed in Chapter III and will 
not be repeated here. 

DENSE 

This subroutine calculated the density of water as a 
function of temperature with the relation from reference [27]: 

p = 63.8 - 0.01781 t + 1.132 x 10" 5 t 2 

- 6.786 x 10" 8 t 3 . 

Based on the assumption made for determining the coeffi- 
cient for equation (A-4) in Appendix A, the relation given 
above was used for the sea water as well as the steam and 
condensate densities. 

For the calculation of cooling water density, the 
numerical average of the cooling water injection temperature 
and the cooling water overboard temperature was used. 

PSATFN 

This function subroutine calculated the saturation 
pressure of steam as a function of the saturation temperature, 



112 



in degrees Rankine, using the relation from reference [3]: 

In P s = 14.150119 - 64 f- 562 - S57S l 3 - 21 (B-l) 

s T s 

TEMFAC 

The retrieval of the temperature correction factor, 
F,, was performed in this function subroutine. The data 
presented in Figure SF-2 of reference [1] was implemented 
in tabular form and was retrieved as a function of cooling 
water injection temperature by a call to the library 
supplied interpolation subroutine, INTRPL. 

TSATFN 

This function subroutine calculated the saturation 
temperature as a function of saturation pressure by solving 
equation (B-l) for T . 

MATFAC 

This subroutine retrieved the material correction 
factor, Fy , as a function of wall thickness and tube material 
The data presented in Figure ST-1 of reference [1] was 
in tabular form and was retrieved using the library supplied 
interpolation subroutine, INTRPL. 



113 



APPENDIX C 
USER'S MANUAL FOR OPCODE 1 

This Appendix describes the data cards required for 
the use of 0PC0DE1. A complete optimization run is included 
as Appendix D. 

The data is divided into the COPES/CONMIN program section 
and the HEI/DDS-based condenser design program section. 

The COPES data is segmented into "blocks" for convenience. 
All formats are alphanumeric for TITLE, END, and STOP cards, 
F10 for real data and 110 for integer data. Comment cards 
may be inserted anywhere in the data stack prior to the END 
card and are identified by a dollar sign ($) in column 1. 
The COPES data stack must terminate with an end card 
containing the word "END" in columns 1-3. 

The analysis data is also segmented into blocks for 
convenience and must immediately follow the "END" card. 
No comment cards are permitted and the analysis data stack 
must terminate with the word "STOP" in columns 1-4. 

It should be noted that only the information for using 
OPCODE1 for either a single analysis or for optimization 
is included in this User's Manual. Information pertaining 
to the use of the sensitivity analysis and the two-variable 
function space features of COPES can be found in reference [15] 



114 



DATA BLOCK A 



DESCRIPTION: COPES Title Card 



FORMAT: 20A4 



TITLE CARD 



REMARKS 

1) Program is terminated by the word 'STOP' in columns 1-4 



115 



DATA BLOCK B 



DESCRIPTION: COPES Program Control Parameters 



FORMAT 



7110 



1 


2 


3 


4 


5 


6 


7 


8 


NCALC 


NDV 






IPNPUT 











FIELD 



CONTENTS 



NCALC: Calculation control 

- Read input and stop. Data of blocks 

A-B is required. Remaining data is 
optional . 

1 - One cycle through program. Data of 

blocks A-B is required. Remaining data 
is optional. 

2 - Optimization. Data of blocks A-I is 

required. Remaining data is optional. 

NDV: Number of independent design variables 
in optimization or optimum sensitivity 
study. 

IPNPUT: Input print control 

- Print card images plus formated print 

of input. 

1 - Formated print of input only. 

2 - No print of input. 



REMARKS 

1) Field 1 determines program execution. 

2) Fields 5, 4, 6, 7, and 8 to be left blank for the 
0PC0DE1 application of COPES/CONMIN. 



116 



DATA BLOCK C 



DESCRIPTION: COPES Integer Optimization Control Parameters 



FORMAT: 8110 



1 


2 


3 


4 


5 


6 


7 


8 


IPRINT 


ITMAX 


ICNDIR 


NSCAL 


ITRM 


LINOBJ 


NACMX1 


NFDG 





FIELD 



CONTENTS 






1 




2 




3 




4 
5 


2 


ITMAX: 


3 


ICNDIR 


4 


NSCAL: 



IPRINT: Print control used in optimization program, 
CONMIN. 

No print during optimization. 
Print initial and final optimization 
information . 

Print above plus function value and 
design variable values at each iteration. 
Print above plus constraint values , 
direction vector and move parameter 
at each iteration. 

Print above plust gradient information. 
Print above plus each proposed design 
vector, objective function and constraints 
during the one-dimensional search. 
Maximum number of optimization iterations 
allowed. DEFAULT = 20. 
Conjugate direction restart parameter. 
DEFAULT = NDV+1. 

Scaling parameter. GT.O - Scale design 
variables to order of magnitude one 
every NSCAL iterations. LT . - Scale 
design variables according to scaling 
values input. DEFAULT = No scaling. 
Number of subsequent iterations which 
must satisfy relative or absolute 
convergence criterion before optimization 
process is terminated. DEFAULT = 3. 
Linear objective function identifier. 
If the optimization objective is known 
to be a linear function of the design 
variables, set LINOBJ = 1. 
DEFAULT = Non-Linear. 

NACMX1 : One plus the maximum number of active 
constraints anticipated. 
DEFAULT = NDV+2. 



ITRM: 



LINOBJ 



117 



DATA BLOCK 



C (Continued) 



FIELD 



CONTENTS 

NFDG : Finite difference gradient identifier. 

- All gradient information is computed 

by finite difference. 

1 - Gradient of objective is computed 

analytically. Gradients of constraints 
are computed by finite difference. 

2 - All gradient information is computed 

analytically. 



REMARKS 

1) The value of NSCAL = 5 is suggested and 
ITRM = NACMX1 = should be used. 

2) The value of IPRINT may be reduced when the user is 
familiar with the optimization output. 



118 



DATA BLOCK 



DESCRIPTION 



COPES Floating Point Optimization Program 
Parameters 



FORMAT: 8F10 



1 


2 


3 


4 


5 


6 


7 


8 


FDCH 


FDCHM 


CT 


CTMIN 


CTL 


CTLMIN 


THETA 


PHI 





Note: Two cards of data are read here 



FIELD 



CONTENTS 



1 


FDCH: 


Relative change 
calculating fin 
DEFAULT =0.01 


2 


FDCHM: 


Minimum absolut 
gradient calcul 
DEFAULT = 0.001 


3 


CT: 


Constraint thic 
DEFAULT = -0.1. 


4 


CTMIN: 


Minimum absolut 
in the optimiza 
DEFAULT = 0.004 


5 


CTL: 


Constraint thic 
linear and side 
DEFAULT = -0.01 


6 


CTLMIN: 


Minimum absolut 
in the optimiza 
DEFAULT = 0.001 


7 


THETA: 


Mean value of p 
method of feasi 
DEFAULT =1.0. 


8 


PHI: 


Participation c 
or more constra 
DEFAULT = 5.0. 



in design variables in 
ite difference gradients. 

e step in finite difference 
ations . 

kness parameter. 

e value of CT considered 
tion process. 

kness parameter for 
constraints . 

e value of CTL considered 
tion process . 

ush-off factor in the 
ble directions. 

oefficient, used if one 
ints are violated. 



119 



DATA BLOCK D (Continued) 



FORMAT: 2F10 



1 


2 


■T 


4 


5 


6 


7 


8 


DELFUN 


DABFUN 

















FIELD CONTENTS 

1 DELFUN: Minimum relative change in objective 

function to indicate convergence of 
optimization process. 
DEFAULT = 0.001. 

2 DABFUN: Minimum absolute change in objective 

function to indicate convergence of 
the optimization process. 
DEFAULT = 0.001 times the initial 
objective value. 



120 



DATA BLOCK 



DESCRIPTION 



Total Number of Design Variables, Design 
Objective Identification and Sign on Design 
Obj ective . 



FORMAT: 2110, F10 



1 


9 


3 


4 


5 


6 


7 


8 


NDVTOT 


IOBJ 


SGNOPT 















FIELD 



CONTENTS 



NDVTOT: Total number of variables linked to the 
design variables. NDVTOT must be 
greater than or equal to NDV. This 
option allows two or more parameters 
to be assigned to a single design 
variable. The value of each parameter 
is the value of the design variable 
times a multiplier which may be 
different for each parameter. 
DEFAULT = NDV. 

IOBJ: Global variable number associated with 
objective function in optimization 
or optimum sensitivity analysis. 

SGNOPT: Sign used on objective of optimization 
to identify whether function is to be 
maximized or minimized. +1.0 indicates 
maximization. -1.0 indicates minimization 
DEFAULT = -1.0. 



121 



DATA BLOCK 



DESCRIPTION : Design variable bounds, initial values and 
scaling factors . 



FORMAT: 4F10 



1 


2 


3 


4 


5 


6 


7 


8 


VLB 


VUB 


X 


SCAL 













Note : Read one card for each of the NDV independent design 
variables . 



FIELD 



CONTENTS 



VLB 

VUB 

X 



SCAL 



Lower bound on the design variable. 
Upper bound on the design variable. 
Initial value of the design variable. 
If X is non-zero, this will supercede 
the value initialized by subroutine 
ANAL I Z . 

Design variable scale factor. Not used 
if NSCAL.GE.O in Block C. 



122 



DATA BLOCK G 

DESCRIPTION : Design Variable Identification 

FORMAT: 2110, F10 



1 


2 


3 


4 


5 


6 


7 


8 


NDSGN 


IDSGN 


AMULT 















Note : Read one card for each of the NDVTOT Design Variables 

FIELD CONTENTS 

1 NDSGN: Design variable number associated with 

the variable. 

2 IDSGN: Global variable number associated with 

the variable. 

3 AMULT: Constant multiplier on the variable. 

The value of the variable will be the 
value of the design variable, NDSGN 
times AMULT. 
DEFAULT =1.0. 



123 



DATA BLOCK H 

DESCRIPTION : Number of constrained parameters 

FORMAT: 110 

12 3 4 5 6 



NCONS 



FIELD CONTENTS 



NCONS: Number of constraint sets in the 
optimization problem. 



REMARKS 

1) If two or more adjacent parameters in the Global common 
block have the same limits imposed, these are part of 
the same constraint set. 



124 



DATA BLOCK I 



DESCRIPTION: Constraint Identification and Bounds 



FORMAT: 3110 



1 


2 


3 


4 


5 


6 


7 


8 


ICON 


JCON 


LCON 















Note: Read two cards for each of the NCONS constraint sets 



FIELD CONTENTS 

1 ICON: First Global number corresponding to 

the constraint set. 

2 JCON: Last Global number corresponding to 

the constraint set. 
DEFAULT = ICON. 

3 LCON: Linear constraint identifier for this 

set of constrained variables. 

LCON = 1 indicates linear constraints 

DEFAULT = = Nonlinear constraint. 



125 



DATA BLOCK I (continued) 



FORMAT: 4F10 



1 


2 


3 


4 


5 


6 


7 


8 


BL 


SCAL1 


BU 


SCAL2 













FIELD 



CONTENTS 



BL: Lower bound on the constrained variables 

Value less than -l.OE+15 is assumed 

unbounded. 
SCAL1 : Normalization factor on lower bound. 

DEFAULT = Max of ABS(BL), 0.1. 
BU : Upper bound on the constrained variables 

Value greater than l.OE+15 is assumed 

unbounded. 
SCAL2 : Normalization factor on upper bound. 

DEFAULT = Max of ABS (BU) , 0.1. 



REMARKS 

1) The normalization factor should usually be defaulted. 



126 



DATA BLOCK 



DESCRIPTION: COPES data 'END' card 



FORMAT : 3A1 



END CARD 



END 



FIELD 



CONTENTS 



The word 'END' in columns 1-3 



REMARKS 

1) This card must appear at the end of the COPES data 

2) This ends the COPES input data. 



127 



0PC0DE1 Analysis 

Data for the condenser analysis follows the 'END' 

card in the COPES data deck. If the general design 

capability of COPES/CONMIN is not needed, the condenser 

analysis portion of 0PC0DE1 can be run in a stand-alone 

mode by using the following main program: 

C MAIN PROGRAM FOR STAND-ALONE CONDENSER 
ANALYSIS 

C INPUT SECTION 
ICALC=1 
CALL ANAL I Z (ICALC) 

C EXECUTION SECTION 
ICALC=2 
CALL ANAL I Z (ICALC) 

C OUTPUT SECTION 
ICALC=3 
CALL ANAL I Z (ICALC) 

STOP 
END 



128 



DATA BLOCK AA 

DESCRIPTION : Condenser Analysis Title Card 

FORMAT: 20A4 



TITLE CARD 



129 



DATA BLOCK BB 

DESCRIPTION : Objective Function Weighting Factor 

FORMAT: E12.5 



130 



DATA BLOCK 



CC 



DESCRIPTION: Condenser Tube Input Data 



FORMAT: 6F10, 12 



1 


2 


3 


4 


5 


6 


7 


8 


SDO 


SDI 


XW 


SDD 


ALGTH 


ROUGH 




NPASS 





FIELD 



CONTENTS 



SDO 

SDI 

XW 

SDD 

ALGTH 

ROUGH 

NPASS 



Tube outside diameter; inch. 
Tube inside diameter; inch. 
Tube wall thickness; inch. 
Tube pitch to diameter ratio. 
Tube length, feet. 
Tube inside absolute roughness 
Number of tube passes. 



foot 



151 



BLOCK DD 



DESCRIPTION: Sea Water Information 



FORMAT: 8F10 



1 


2 




4 


5 


6 


7 


8 


VELC 


Tl 

















FIELD CONTENTS 

1 VELC: Sea water velocity in the condenser 

tubes, feet per second. 

2 Tl : Sea water injection temperature, °F 



152 



BLOCK EE 



DESCRIPTION: Inlet Steam and Heat Load Information 



FORMAT: 7F10 



1 


2 


3 


4 


5 


6 


7 


8 


WMS 


HFGMS 


WAS 


HFGAS 


PSAT 


TSAT 


TRNSHT 







FIELD 



CONTENTS 



WMS: Incoming main steam rate, pound per hour 
HFGMS: Latent heat of condensation for main 
steam, BTU per pound. 
WAS: Incoming auxiliary steam rate, pound 
per hour 
HFGAS: Latent heat of condensation for 
auxiliary steam, BTU per pound. 
PSAT: Saturation pressure of incoming steam, 

pounds per square inch absolute. 
TSAT: Saturation temperature of incoming 
steam, degrees Fahrenheit. 
TRNSHT: Heat load from other sources, BTU 
per hour. 



REMARKS 

1) If no value for HFGMS or HFGAS is read in, these 
parameters will default to 950 BTU per pound. 

2) Either PSAT or TSAT is to be specified. 



133 



DATA BLOCK FF 



DESCRIPTION: Tube Material Identification 



FORMAT: 110 



IDMATL 



FIELD 



CONTENTS 



IDMATL: Material 


identification 


following 


tabl 


e . 


TUBE MATERIAL 


CODE 


ADMIRALTY METAL 




1 


ARSENICAL COPPER 




1 


ALUMINUM 




1 


ALUMINUM BRASS 




2 


ALUMINUM BRONZE 




2 


MUNTZ METAL 




2 


90-10 CU-NI 




3 


70-30 CU-NI 




4 


COLD ROLLED LOW 






CARBON STEEL 




5 


STAINLESS STEELS 






TYPE 410/430 




6 


TYPE 304/316 




7 


TYPE 329 




8 


TITANIUM 




9 



from the 



134 



DATA BLOCK GG 



DESCRIPTION: STOP Card 



FORMAT: 4A1 



STOP CARD 



STOP 



FIELD 



CONTENTS 



The word 'STOP' in columns 1-4 



REMARKS 

1) This card must appear at the end of the analysis data 

2) This ends the analysis data. 



135 



APPENDIX D 
SAMPLE OUTPUT FROM OPCODE 1 



CCCCCCC CCCCOQO PPPPPPP EEEEEEE SSSSSSS 

C G P P E S 

C Q P P E S 

C QO PPFPPPP EEEE SSSSSSS 

C OOP E S 

C OOP E S 

CCCCCCC CCOGOOCJ P EEEEEEE SSSSSSS 



C C NTRCL PRCGRAM 

FOR 

ENGINEERING SYNTHESIS 



TITLE 

CVA / CASE ONE /0EJ=PGwER/r1IN: POKER WITH CONSTANT CREJ/ 



136 



CARC IMAGES OF CONTROL DATA 
CARO IMAGE 

1) CVA / CASE LM : /CuJ=PC*ER/hI\: PCkER i»ITH CONSTANT CRFJ/ 

2) 2 b 

31 1 40 5 15 

4) 

5) 

6) 18 -1.0 

7) S TUBE 0.0. . INCHES 
8J C.625 1.25 

9) i TUBE I.O., INCHES 

1C) C.4C7 1.2C6 

11) S PITCh/OIAMETER RATIO 

12) 1.1 3.C 

12) i TUBE LENGTH, FEET 

14) l.C 25. C 

15) S S-W VELOCITY IN TUBES, FPS 

16) 2.0 9.C 

17) 1 1 

18) 2 2 
i<=) 3 6 

20) 4 4 

21) 5 5 
12) 5 

22) $ TUBE WALL THICKNESS, INCHES 

24) 7 7 

25) C.022 0.109 

26) S CCNOENSER DIA.METER, FEET 

27) S 3 

28) 1.0 10.0 

25) J PINCH POINT, F 

30) 12 12 

31) 5.C 35.0 

22) * S-k TEMPERATURE RISE, F • ' 

33) 13 13 

34) 5.0 20.0 

35) $ RATIC OF TLBE HCL E AREA TO TUeE SHEET AREA WITHOUT ORILLEC HOLES 

26) 16 16 

37) C.l 0.36 

36) ENO 



137 



TITLE: 

CVA / CASE ONE /OBJ»PQWgR/MIN: POWER WITH CONSTANT CREJ/ 



CCNTFCL PARAMETERS : 
CALCLLATICN CCNTRCL. 
NUM3ER OF GLOBAL DESIGN VARIABLES, 
NU>eER CF SENSITIVITY VARIABLES, 
NUMBER OF FUNCTIONS IN TwO-SPACE, 
INPUT INFORMATION PRINT COOE, 
SENSITIVITY ^RINT CCCE, 
TWO-SPACE PRINT CODE, 
CEeUG PRINT CCOE, 

CALCULATICN CCNTROL, NCALC 
VALUE MEANING 

1 SINGLE ANALYSIS 

2 OPTIMIZATION 

3 SENSITIVITY 

4 TWC-VARIAolc FLNCTION SPACE 

GLCBAL VARIABLE NUMEtR CF OBJECTIVE = 18 

MULTIPLIER (NEGATIVE INOICATES MINIMIZATION) = -O.IOOOE 01 

CCNMN PARAMETERS I IF ZERO, CQNMIN DEFAULT WILL OVER-RIOE) 



NCALC 


3 


2 


NOV 


3 


5 


NSV 


3 





N2V AR 


3 





IPNPUT 


= 





IPSENS 


3 





IP2VAR 


3 





IPOBG 


S 






IPRINT 
1 


ITMAX 
40 


ICNCIR 



NSCAL 
5 


ITRM 



LINOBJ 



NACMXl 
15 


NFOG 



FOCH 
0.0 




FOCHM 
0.0 




CT 

0.0 




CTMIN 
0.0 




CTL 
0.0 




CTLMIN 
O.C 




THETA 
0.0 




PHI 
0.0 




OELFUN 
0.0 




0A6FUN 
O.C 






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141 



BUNGLE GECHETRY INFORMATION 




ROW NR. RADIUS ( IN. J 


,\R. CF TU 


1 c .JO 


37.70 


2 6.37 


4^.14 


3 7.73 


48.58 


4 S.60 


54.02 


5 5.46 


59. 4o 


6 10.33 


64.51. 


7 11.23 


70.3 5 


8 12.06 


75.79 


9 12.93 


81.23 


1C 12.79 


36.6 7 


11 14.66 


52.11 


12 15.53 


97.55 


13 16.39 


102.59 


14 17.26 


108.44 


15 13.12 


113.88 


16 la. 99 


119.22 


17 19.36 


124. 76 


13 20.72 


120.20 


19 21.59 


lr5.64 


20 22.45 


141.0 8 


21 23.32 


146.5 2 


22 24.15 


151.57 


23 25.05 


157.41 


24 25.92 


162.35 


25 26.78 


163.29 


26 27. o5 


i73.73 


27 2e.52 


179.17 


28 25.36 


184.61 


29 30.25 


190 .0 5 


30 31.11 


195 .50 


31 31.56 


200.94 


32 32.55 


206 .53 


22 23.71 


211.82 


34 34.56 


217.26 


35 35.44 


222.70 


36 st. 31 


223. 14 


37 37.18 


233.56 


38 28.04 


239.03 


39 26.51 


244.47 


40 35.77 


245.91 


41 4C.a4 


255.35 


42 41.51 


260. 79 


*»3 42.37 


266 . 23 


44 43.24 


113.58 



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145 



BUNCLE GEOMETRY INFCPMATICN 



RCW NR. 

1 
2 
3 

4 

3 

6 

7 

8 

9 
10 
11 
12 
13 
14 
15 
16 
17 
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24 
25 
26 
27 
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29 
30 
21 
52 
33 
34 
35 
36 
37 

3e 

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40 
41 
42 
43 
44 
45 
46 
47 
46 
49 
£C 
51 
52 

THE OUTER RCh HAS A PITCH OF 1.19 INCHES, 



HUS (IN.) 


MR. OF TU 


6.00 


21.65 


7. 03 


37.09 


6. 06 


42.53 


9.09 


47.97 


10.13 


53. *1 


11.16 


56.65 


12.19 . 


64.2 9 


13.22 


69.74 


14.25 


75.18 


15.28 


80.62 


16.32 


86. 36 


17.35 


91.50 


18. J8 


96 .94 


19. 41 


102.38 


2C.-*4 


1G7. 62 


21 .47 


113.27 


22.51 


118.71 


23.S4 


124. 15 


24.57 


129.59 


25.60 


U5.03 


26. o2 


140.47 


2 7 .6 6 


145.91 


26.70 


151.35 


29.72 


156. ac 


3C.76 


162.24 


31. ?9 


1&7.68 


52.82 


173.12 


J2.85 


17d.5o 


34.39 


134.00 


35.92 


1?9 .44 


36.95 


194. 83 


37.98 


200.33 


39.01 


20 5.7 7 


40.34 


211.21 


41.08 


21c. 65 


42.11 


222.09 


43.14 


227.53 


44.17 


252.97 


t5.20 


238.41 


46.2; 


243. 65 


47.26 


249.30 


48.30 


254. 74 


49. j3 


260. 18 


5C.36 


265.62 


51.59 


271.0^ 


52.42 


276.50 


53.45 


2?1 .94 


54.49 


267.38 


55.52 


292.63 


5c.55 


29d.27 


57.56 


303. 71 


5 8.61 


309.13 



146 



APPENDIX E 
0PC0DE1 PROGRAM LISTING 



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BIBLIOGRAPHY 



1. Heat Exchange Institute, Standards for Steam Surface 
Condensers , Sixth Edition, 1970. 

2. Department of the Navy, Bureau of Ships, Design Data 
Sheet DDS4601-1 , 15 October 1953. 

3. Oak Ridge National Laboratory Report ORNL-TM-4248 , 
0RC0N1: A FORTRAN Code for the Calculation of a Steam 
Condenser of Circular Cross Section , by J .A. Haf ford , 
July 1973. 

4. Eissenberg, D.M., An Investigation of the Variables 
Affecting Steam Condensation on the Outside of a 
Horizontal Tube Bundle , Ph. D . Thesis , University of 
Tennessee , December 1972 . 

5. Search, H.T., A Feasibility Study of Heat Transfer 
Improvement in Marine Steam Condensers^ MSME Thesis , 
Naval Postgraduate School, December 1977. 

6. Stoecker, W.F., Design of Thermal Systems , McGraw- 
Hill, 1971. 

7. Vanderplaats , G.N., Automated Design Optimization , 
class notes for a graduate course of the same title 
presented at the Naval Postgraduate School, Monterey, 
California, March-May 1977. 

8. Fox, R.L., Optimization Methods for Engineering Design , 
Addison-Wesley, 1971. 

9. NASA Ames Research Center Technical Memorandum NASA 

TM X- 6 2, 282, CONMIN - A FORTRAN Program for Constrained 
Function Minimization User's Manual , by G.N. Vanderplaats , 
August 1973. 

10. Vanderplaats, G.N. and Funs , A.E., "LASTOP - A Computer 
Program for Las er Turret Optimization," NPS Report 

NPS 69-77-0004, Naval Postgraduate School, 1977. 

11. Fletcher, R. and Reeves, CM., "Function Minimization 
by Conjugate Directions," British Computer Journal , 
v. 7, n. 2, p. 149-154, 1964. 

12. Zoutendijk , G.G. , Methods of Feasible Directions , 
Elsevier, Amsterdam, 1960. 



162 



13. Vanderplaats , G.N. and Moses, F. , "Structural 
Optimization by Methods of Feasible Directions," 
Journal of Computers and Structures , v. 3, p. 739-755, 
1973. 

14. Aerodynamic Analysis Requiring Advanced Computers 
NASA SP-347 Part II, Application of Numerical 
Optimization Techniques to Airfoil Design^ by 

G.N. Vanderplaats, R.N. Hicks and E.M. Murmaa , p. 74 9- 
768, March 1975. 

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

16. Harrington, R.L. (ed) , Marine Engineering , p. 477, 
The Society of Naval Architects and Marine Engineers, 
1971. 

17. Baumeister, T. and Marks L.S. (eds) , Standard Handbook 
f or Mechanical Engineers , 7th ed. , Chapter 3, p. 55-67, 
McGraw-Hill, 19677 

18. Crane Company, Technical Paper No. 410 , 1976. 

19. Naval Ship Systems Command 0946-004-7010, Main Condensers 
(CVA 6 7) , January 1969. 

20. Westinghouse Electric Corporation Steam Divisions 
Technical Manual 1440-C72 (NAVSHIPS 346-0268), 6,600 
Square Foot Surface Condenser and Main Air Ejectors , 
May 1964. 

21. Holman, J. P., Heat Transfer , 4th ed. , McGraw-Hill, 1976. 

22. United States Atomic Energy Commission Report 
ORNL-TM- 2972 , Computer Model and Correlations for 
Prediction of Horizontal Tube Condenser Performance 
in Seawater Distillation Plants , by D.M. Eissenberg 
and H.M. Noritake, April 1970. 

23. Universal Oil Products Company Bulletin No. 4020, 
Wolverine Korodense Tube: General Information and 
Heat Transfer Design Notes~ 10 January 1973. 

24. Fraas , A. P. and Ozisik, M.N., Heat Exchanger Design , 
Wiley, 1965. 

25. English, J.W., Hydrodynamic Considerations in the Design 
of Condenser Cooling Water Systems for Large Ships , 
paper presented at the Royal Institution of Naval 
Architects, London, England, 12 April 1973. 



163 



26. Reilly, D.J., An Experimental Investigation of Enhanced 
Heat Transfer on Horizontal Condenser Tubes , MSME 
Thesis, Naval Postgraduate School, March 1978 . 

27. Westinghouse Electric Corporation WAPD-TM-213, 
STDY-3 A Program for the Thermal Analysis of a 
Pressurized Water Nuclear Reactor During Steady-State 
Operation, by Pyle, R. S . , June 1960 . 



164 



INITIAL DISTRIBUTION LIST 

No. Copes 

1. Defense Documentation Center 2 
Cameron Station 

Alexandria, Virginia 22314 

2. Library, Code 0142 2 
Naval Postgraduate School 

Monterey, California 93940 

3. Department Chairman, Code 69 2 
Department of Mechanical Engineering 

Naval Postgraduate School 
Monterey, California 93940 

4. Office of Research Administration, Code 012A 1 
Naval Postgraduate School 

Monterey, California 93940 

5. Professor Paul J. Marto, Code 69Mx 10 
Department of Mechanical Engineering 

Naval Postgraduate School 
Monterey, California 93940 

6. Dr. Gary N. Vanderplaats , Code 1613 5 
David Taylor Naval Ship Research 

and Development Center 
Bethesda, Maryland 20084 

7. Professor Paul Pucci, Code 69Pc 1 
Naval Postgraduate School 

Monterey, California 93940 

8. Lt. Charles M. Johnson 4 
3784 Hyak Way 

Bremerton, Washington 98310 

9. CDR N.P. Nielsen, USN 1 
Naval Sea Systems Command (033) 

2221 Jefferson Davis Hwy , CP#6 
Arlington, Virginia 20360 

10. Mr. Charles Miller 2 

Naval Sea Systems Command (0331) 
2221 Jefferson Davis Hwy, CP#6 
Arlington, Virginia 20360 



165 



11. Mr. Frank Ventriglio 

Naval Sea Systems Command (0331) 
2221 Jefferson Davis Hwy , CP#6 
Arlington, Virginia 20360 

12. Mr. Arthur Chaikin 

Naval Sea Systems Command (0331) 
2221 Jefferson Davis Hwy, CP#6 
Arlington, Virginia 20360 

13. CAPT J. K. Parker, USN 

Naval Sea Systems Command (PMS-301) 
2221 Jefferson David Hwy, CP#6 
Arlington, Virginia 20360 

14. CDR D. W. Barns, USN 

Naval Sea Systems Command (PMS-301. 3) 
2221 Jefferson Davis Hwy, CP#6 
Arlington, Virginia 20360 

15. Mr. Walter Aerni 

Naval Ship Engineering Center (6145) 
Washington, D.C. 20362 

16. Mr. Wayne L. Adamson 

Naval Ship Research § Development Center 

(2761) 
Annapolis, Maryland 21402 

17. Mr. Gil Carlton 

Naval Ship Engineering Center (6723) 
Philadelphia, Pennsylvania 19112 

18. Dr. David Eissenberg 

Oak Ridge National Laboratory 

Post Office Box Y 

Oak Ridge, Tennessee 37830 

19. Mr. Joseph A. Hafford 

Oak Ridge National Laboratory 

Post Office Box Y 

Oak Ridge, Tennessee 37830 

20. Mr. John W. Ward 
Marine Division 

Westinghouse Electric Corporation 

Hendy Avenue 

Sunnyvale, California 94088 

21. Mr. Henry Braun 

De Laval Condenser and Filter Division 
Florence, New Jersey 08518 



166 



22. Miss Eleanor J. Macnair 
Ship Department 
Ministry of Defence 

Director - General Ships , Block B 

Foxhill, Bath, Somerset 

ENGLAND 

23. Mr. Kurt Bredehorst 
NAVSEC 6147D 
Department of the Navy 
Hyattsville, Maryland 02782 



167 



Thesis 173370 

J574 Johnson 

c.l Marine steam conden- 
ser design using nu- 
merical optimization. 



thesJ574 

Marine steam condenser design using nume 




3 2768 002 10788 

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