HEAT EXCHANGER DESIGN FORTHERMAL CYCLE FEASIBILITY EVALUATION

Paul Chandler Jackson

f DUDLEY KNOX LIBRARY1

HAVAL POSTGRADUATE SCHOO

MONTEREY, CALIFORNIA 939

1

HEAT EXCHANGER DESIGN FOR

THERMAL CYCLE FEASIBILITY EVALUATION

by

PAUL CHANDLER JACP^SON

LIEUTENANT (JUNIOR GRADE)

UNITED STATES COAST GUARD

B.S., United States Coast Guard Academy1970

£««

SUBMITTED IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF

OCEAN ENGINEER

AND THE DEGREE OF

MASTER OF SCIENCE IN MECHANICAL ENGINEERING

at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGYJune, 197^

DUDLEY KNOX LIBRARYNAVAL POSTGRADUATE SCHOOLMONTEREY, CALIFORNIA 93940

Heat Exchanger Design for Thermal Cycle Feasibility Evaluation

Paul C. Jackson

"Submitted to the Department of Ocean Engineering on May 10th, 197/1

in partial fulfillment of the requirements for the degrees of

Ocean Engineer and Master of Science in Mechanical Engineering."

ABSTRACT

The general properties of heat exchangers are examined in

this study. Mathematical models are developed for the mechanism

of heat transfer that take place during

1. Evaporation in two-phase flow

2. Condensation

3. Heating or cooling

From these models, computer programs have been developed for the

preliminary designing of the following heat exchanger tynes:

1. Counter-flow cooler with no change of state

2. Counter-flow heater with no change of state

3. Counter-flow condensor

4

.

Counter-flow evaporator with two-phase flow

5. Cross-flow heater

6. Cross-flow cooler

These programs are designed to be used in the examination

of the size requirments for heat exchangers used in the onera-

tion of thermodynamic cycles. The cycles of interest in this

study are ones proposed for the production of useful oower from

sources not conventionally used at present.

-2-

Thesis Supervisor: A. Douglas CarmichaelTitle : Professor of Power Engineering

Thesis Reader : Warren M. RohsenowTitle : Professor of Mechanical Engineering

-3-

ACKNOWLEDGEMENTS

The author wishes to express thanks to Professors A.D. Carmichael

and W.M. Rohsenow for their guidance in the preparation of this thesis

Also the author wishes to thank Bill Mack for the information and

assistance he gave, especially in the preparation of the section on

Material Selection.

_H_

TABLE OF CONTENTS

Page

Tit le Page]_

Abstract 2

Ackowledgements2j

Table of Contents '

5

List of Figuresg

Chapter I . Introductiony

Chapter II . Heat Exchanger Properties -^q

2 . 1 General Properties-, q

2.2 Evaporation Properties 20

2 .

3

Condensation Properties 07

2 . ^ Cooling and Heating i|c

Properties

2.5 Material Selection c-]_

Chapter III. Results 55

Chapter IV. Conclusions gy

Chapter V. Recommendations gg

References gq

Appendix A. Counter-flow Condensing 72Heat Exchanger Program

Appendix B . Counter-flow Evaporation yqHeat Exchanger Program

Appendix C . Counter-flow Heater ggHeat Exchanger Program

Appendix D. Counter-flow Cooler jqqHeat Exchanger Program

(cont. overleaf)

-5-

TABLE OF CONTENTS (cont).Page

Appendix E. Cross-flow Heater Heat 113Exchanger Program

Appendix P. Cross-flow Cooler Heat 124Exchanger Program

Appendix G. Examination of Zener Cycle 13 2*

-5-

LIST OF FIGURES

Title Page

Flow Patterns of Heat Exchangers 13

Comparison of Required Heat Transfer lkArea

Pool Boiling Data 21

Two-phase Flow 2 3

Reynolds Factor 28

Supression Factor 30

Two-phase Frictional Multiplier 33

Dipprey and Sabersky Results 58

Kemery and Cypher Results 58

j Re vs fRe 3 Curve 60

NTU vs e Curve 6

Comparison of Exchanger at Point 62and at point A

Comparison of Exchanger at Point 62and at Point B

Comparison of Exchanger at Point 64and at Point C

Comparison of Exchanger at Point 64and at Point D.

Zener Cycle Condensor Number of 136Tubes vs Length

Zener Cycle Condensor Number of 137Tubes vs Tube Diameter

Zener Cycle Evaporator Number of 138Tubes vs Length

-6-

I. INTRODUCTION

In recent years, many proposals have been made for methods

to produce oower from sources not conventionally used. With the

recent increase in the cost of fossil fuel energy sources, it

can be expected that many such proposals will be forthcoming in

the near future.

One such proposal came from Professor Clarence Zener of

Carnegie-Mellon University ( 1) . This proposed cycle would pro-

duce power utilizing the' temperature gradient in the tropical

areas of the oceans. To do this, a working fluid with a high

vapour pressure is heated by the water at the surface of the

ocean. In the tropics, this is around 25°C. The working fluid,

as a vapor, then drives a turbine to produce power. It is then

condensed back into a liquid by the deep ocean water at a temper-

ature of 5°C.

Hilbert and James Anderson(2) in 1966 proposed a cycle simi-

lar to that of Professor Zener. It relies on the heating of the

ocean surface water by the sun as the means for powering the sys-

tem. In 1966, the cost of such a power source was deemed unrealis-

tic, therefore the project was discontinued. In the light of

the current shortage of energy, this proposal might warrent re-

examination.

Another such proposal came from a husband and wife team.

/Aden and Marjorie Meinel, optical physicists, proposed a differ-

ent way of using the solar energy to produce unsable power(3).

-7-

Their proposed cycle would use solar energy collectors to heat

a liquid metal. This liquid metal would heat the working fluid

which drives a turbine to produce power.

The use of geothermal energy, heat from the earth's in-

terior, as a power source has also been suggested(4) . This

type of heat source would be used in a manner similar to the

warm surface water in the Zener proposal.

All of these proposed cycles require similar machinery.

The heat source is used to heat or evaporate the working fluid.

For this, a heat exchanger is needed. The working fluid then

drives a turbine and is cooled or condensed in another heat ex-

changer. A pump or compressor is used to raise the pressure of

the fluid and the cycle begins again.

The feasibility of these and other such proposals must be

examined. One phase of this examination should be to obtain an

estimation of the size of the equipment necessary for the opera-

tion of the cycle. A major item, both in the performance of the

cycle and the size of the equipment, is the heat exchangers that

are required.

It is proposed that this study be an examination of the re-

quired heat exchangers. This will be carried out by the develop-

ment of a computer program for preliminary design purposes.

General properties of heat exchangers will be examined. Mathe-

matical models will be developed for evaporation, condensation,

heating and cooling heat exchanger design.

The heat exchangers needed for the cycle proposed by

-3-

Professor Zener will be designed in this study. The author

feels that this will be useful for two major reasons. First,

it will serve as an example of how this study and the computer

programs developed can be used. A careful examination of the

Zener proposal can also be useful in determining if it is a

feasible method of producing power.

-9-

II. HEAT EXCHANGER PROPERTIES

2.1 General Properties

2.1.1 Introduction

A heat exchanger is a device used to transfer heat bet-

ween two fluids that are separated by a wall. It is the form

of the separating wall and the flow pattern of the fluids that

distinguish between types of exchangers. This study will examine

shell and tube heat exchangers and tubular cross flow exchangers.

Fins are attached to the walls of some heat exchangers to increase

the heat transfer. The use and effectiveness of fins will also

be examined.

Cost evaluation Is an Important problem in the heat ex-

changer design. A minimum cost, including intitial _cost and the

cost of pumping the fluids, Is generally desired. The alterna-

tives in cost are examined in this study.

2.1.2 Shell and Tube Exchangers

A shell and tube heat exchanger is made up of round tubes

mounted in a cylindrical shell. The axis of the tubes are para-

llel to the shell. Shell and tube exchangers are classified by

the direction of flow of the fluids and by the method of reducing

thermal stress between the tubes and the shell used (5 (page 18-3*0).

Selection of the type of exchanger to be used depends on a variety

of properties including cost, pressures and temperatures.

Fixed-tube-sheet exchanger is the simplest to fabricate and

has the least cost. In this type of heat exchanger the shell and

-10-

and tubes are rigidly held. Because of this method of connec-

tion the thermal stresses are the highest of any type of shell

and tube exchanger. Another disadvantage of fixed-tube-sheet

exchangers is the inability to clean the shell side of the ex-

changer by mechanical means.

To eliminate the high stresses of a fixed-tube-sheet ex-

changer, an exchanger with an Internal floating head can be used.

With this type of exchanger the tubes can be removed for clean-

ing. The cost of an internal floating head exchanger is high

and there is much more of a leaking problem than with a fixed

exchanger. Pot the same job, the two types of exchangers would

have the same size requirements and the design method is the

same.

The most commonly used shell and tube exchanger is the

fixed-tube-sheet type(6). For this study it will be examined.

A factor that has a large effect on the design of a heat

exchanger is the choice of fluid to be passed through the tubes

and that to be passed on the shell side. A number of factors

go into the making of this decision: ( 5(Page 18-35) ).

1. Cleanability. The shell is difficult to clean andtherefore should have the cleanest fluid.

2. . Pressure. It is much easier and cheaper to madetubes to withstand high pressure than the shells.High pressure fluids should oass in the tube.

3. Temperature. Hiph temperature fluids cause highstress. This stress can be more easily allowedfor In the tubes. High temperature fluids shouldpass through the tubes.

k. Quantity. The best design can be obtained when thefluid with the smallest flow rate is Dlaced In the shell

-11-

A counter heat flow exchanger has the flow of the two fluids

in opposite directions. Figure 2.1-1. In most exchangers the

flow is not purely counter flow. In the entrance and exit re-

gions of the exchanger, some cross flow exists. If the exchanger

is more than twice as long as it is wide, this cross flow region

is small and can be disgarded.

Parallel flow exchangers have the flow of both fluids in

the same directions. See Figure 2.1-1. As with the counter

flow exchanger, the end regions have some cross flow which is

disregarded. Parallel flow exchangers require more heat trans-

fer surface area, for the same temperature rise, than counter

flow. SeeFigure 2.1-2. Parallel flow also has the disadvan-

tage, compared to counterflow, ,that the fluid being heated can

only have a temperature rise equal to fifty percent of the hot

fluid temperature at inlet. Counter flow exchangers can, in

the limiting case, have the fluid being heated reach the hot

fluid inlet temperature (7) . For these reasons parallel flow

exchangers will not be further examined in this study.

2.1.3 Cross Flow Exchangers

In a single pass cross flow heat exchanger, the two

fluids move perpendicular to each other. Figure 2.1-1.

Cross flow generally requires more heat transfer area than coun-

ter flow heat exchangers for the same temperature rise. Figure

2.1-1. Cross flow units are used in areas of special application

as the exchanger can be made compact. These exchangers are most

widely used in gas to liquid exchangers v/Ith finned surfaces(8).

(More discussion of fins appears in section 2.1*4).

-12-

flu I A I

T lui'd ^

Parallel Plow

Fl „.;d i

_x

«Fluid 3-

Fiu;d i

->

->

<e

G ounter Plow

Ft^i'd *

Cross Plow

Pigure 2.1-1

Plow Patterns of Heat .Exchangers

"»

-13-

avU<VoM-i

(-1

3CO

f-4

cCWCO

crj

H4->

rtO3C

Cold Fluid Temperature Rise as a Percentage ofHot Fluid Temperature Loss

Figure 2.1-2

Comparison of Required Heat Transfer Area

14

The cross flow heat exchangers examined in this study will

be tubular exchangers. The heating or cooling fluid is passed

through a tube and remains unmixed. The working fluid flows

across the tubes and is allowed to mix.

2.1. A Pinned Surfaces

Fins are extensions of the tubes that increase the heat

transfer surface. They are most effectively used when the heat

transfer is between a liquid and a gas. A rough rule-of-thumb

for the heat transfer surface area of the fin is that the sur-

face area for the gas and liquid should be inversely proportion-

al to the ratio of respective heat transfer coefficient ( 7 (page

182) ). This rule must be slightly modified because the effici-

ency of a fin decreases with an increase in area. If, for ex-

ample, an air-water heat exchanger was desired, the area of the

air side should be 10 to 20 times as large as the water side.

This is caused by the heat transfer coefficient of water being

about 500 Btu/ hr ft °F to 20 Btu/ hr ft °F for air. To make

up this need for different areas, fins would be used on the air

side.

The spacing of fins in a heat exchanger is generally de-

termined by manufacturing limits. The height is limited by the

required flow area. A spacing of from 6 to 15 fins per inch is

the normal range (9).

In the heat exchangers examined in this study, fins are

not used. Cost is an Important factor. The fabrication costs

of fins is much higher than for non-finned tubes. If the fin

•15-

is not either integrally or metallurgucally bonded to the tube,

the fin efficiency may be adversely affected(ll) . This requires

the fins to be soldered or welded to the tubes. This is an ex-

pensive fabrication process. Because fins decrease the flow

area, they increase the required pumping power for the fluids,

increasing the operational costs.

The nature of the fluids used in this study also discourage

the use of fins. In the proposed cycles, the heat transfer is

from a fluid in one phase to a fluid of the same flow or to a

two phase flow. Fin performance in both cases is less than ideal,

If a detailed design of heat exchangers was going to be

carried out, the use of fins should be included. As this study

is a preliminary design to determine feasibility, examination

of fins is not needed.

2.1,5. Cost of Construction

The estimation of cost of a heat exchanger is a diffi-

cult task and is often only a very rough estimate. Many rea-

sons for this exist. Companies that make heat exchangers and

components generally consider cost of both materials and fab-

rication highly proprietry. They are, therefore, quite reluc-

tent to release this data. What available cost data there is,

is a number of years old by the time it is published. With

the current rate of inflation, data as little as six months old

is inaccurate.

Cost of a heat exchanger is sensitive to special require-

ments. A small matter such as rigorous quality control can

-16-

easily double the cost of an exchanger(ll) . The use of spe-

cial materials, unusual size materials, or non-standard shapes

can greatly change the cost of an exchanger. All of these fac-

tors are difficult to include in a cost estimation.

In this study a rough cost is examined. The values are

from 1960(12), and are therefore quite inaccurate. They do serve

to give a method of comparison between different shapes. If two

exchangers are designed to do the same job, examining their com-

paritive costs, the best can be selected, regardless of the ab-

solute accuracy of the numbers themselves.

Two cost factors are examined; the cost of the material

making up the shell, and the tubes, and the cost of fabrication.

The fabrication costs include header joint cost (welding), cost

of drilling of the header sheet, cost of cutting tubes to size

and positioning of the tubes. The cost does not include inspec-

tion, sales costs, and shop overhead(12) . The material costs

are determined on a base size heat exchanger. Corrections are

made to adjust the base size to the particular heat exchanger

desired. The two correction factors used are the Tube Material

Factor and the Tube Length Factor. The tube material correction

takes into account the higher costs associated with the use of

special materials. The correction for tube length decreases

as the length increases. This accounts for the economy of scale.

-17-

where:

and

Cost = CW + CTB

CW = CWV x N

CWV = 3.0 if Dout is less than h in.

CWV = 12/5 * (Dout - .5/12) + 3.0 if Dout is

greater than h in.

CTB - 15 - (AREA - 100) 2

5

x TLF x AREA x TMF

and TLF 1.3 (LENGTH - 8)

10

-18-

NOMENCLATURE

AREA

CTB

cwv

cw

Dout

h

k

L

P

q

T .

AT

TLF

TMF

S'

Heat transfer surface area

Cost of materials to build heat exchanger

Cost of fabrication per tube

Cost of fabrication of heat exchanger

Outer diameter of tubes

Heat transfer coefficient

Thermal conductivity of material

Length

Wetted parameter

Rate of heat transfer

Temperature

Change in temperature

Tube length factor

Tube material factor

Cross sectional area

Subscripts

f

o

With fin

Without fin

-19-

2.2 EVAPORATOR PROPERTIES

2.2.1 Introduction

Boiling heat transfer is the mode of heat transfer that occurs

when a liquid changes phase to a vapor. There are two regimes

of boiling, film boiling and nucleate boiling. The form that

boiling will take in a given circumstance depends on the degree

of superheat of the liquid. Figure 2.2-1 shows typical pool

boiling data(ld). Pool boiling occurs when the heating surface

is submerged beneath the surface of the liquid. In this study

the region of interest is where Tw - Tsat is between 5 and 15

degrees, in the nucleate boiling region.

Nucleation is the formation, growth and motion of bubbles.

For nucleation to occur in a liquid, that liquid must be super-

heated, its temperature raised above the saturation temperature.

The nuclei is formed on a foreign object in the liauid. This

object is usually a cavity on the heating wall but it can be

suspended foreign matter with a non-wetted surfaced 3. page 6).

The bubble grows by heat conduction to the liauid-vapor inter-

face. The size it will become is based on a balance between

buoyant and surface tension forces.

When boiling occurs in a confined region with force convect-

ion present, two-phase flow results. It is this type of boiling

heat transfer that is discussed in this study. A mathematical

model for two-phase evaporation is developed.

-20-

uI

4-1

3

60OJ

V« rH

t± -9 6*.

rf « ofSI 4J iHt-l W (Uo 3.3 £> oS3 *J

•a C0) r-l C •HV os rtc-l G) i-t 60J3 O aj ao fi.O « M C •H3 V rt .H 63 s

P* t-i 3. OCI <-< E •ft O /

6.0 4J < © iH r-f

e e _,_^ PQ -H •H 3 /60 •H 1-) / ^\ fn O o /c «-* / PQ •H /•H •HO / ** /rH o u / s n) /•H M / i-l •H /

g O « / •H "3 /o pq « w / Cn rt /•H 4-> ..-1 / W /4-> o « cm I 4)O u v / I-HV rt ^ / /a> « o / itc r-l 3 / 4->

o U355

25 / V)

CI

Vpta

.1 1.0 10 100

Tw-Tsat °F

Figure 2.2-1

Pool Boiling Data

1000 10000

21

2.2.2. Two-Phase Evaporation

Two-phase flow is a pattern that contains both liquid and

vapor. It occurs when a flow is subject to forced convection

in a confined space, a tube, annul! , parallel plates. The ob-

jective of the designer of a two-phase evaporator is to determine

the heat transfer and the pressure drop characteristics of this

flow7. From this data the size of the required heat exchanger

can be found.

The determination of the desired characteristics can be a

complex task as these two properties are coupled thermodynami-

callyOS, page ^47). A change in the heat transfer changes the

quality of the flow and the flow pattern. This changes the

pressure drop. At the same time a pressure change alters the

quality of the flow and therefore effects the heat transfer

characteristics

.

The flow regimes change as heat is added&o> page 1*0.

Figure 2.2-2. The flow enters as a subcooled liquid. Boiling

will take place at the walls even though the liquid as a whole

is below the saturation temperature. This forms a bubbly flow.

At moderate velocities, greater than 3 feet per second, the

bubbles will be fairly evenly distributed. When the liquid reaches

the saturation point, bulk boiling will occur. As the quality in-

creases the flow becomes annular with a thin layer of liquid on

the walls and a vapor core. In this vapor core will be liquid

droplets that will decrease in amount and size as the quality of

the flow increases. At some point the heated surface will become

-22-

o e £

(rv;% V V*°. i \

' -v I

ct

'. »

EH«sCOEH

I

CMm

cm

bO•H

orHP-H

w

I

O

-23-

dry. This Is called the burnout point. From here on the heat

transfer mechanism changes and must be dealt with in a separate

manner(5, page 13-35).

With the complex flows and the coupling of the heat transfer

and pressure drop properties, many of the solution techniques

depend on a combination of analytical and experimental studies.

A basis for any solution for a two-Dhase problem is the assump-

tion that the flow is fully developed^?, page 48).

2.2.3 Mathematical Model

Two models can be used for two-phase flowQo, page 24). The

•homogenous' model considers the two phase flow as a single phase

with mean fluid properties. This model is also known as the

•friction factor* model. The 'separated flow' model considers

the phases to be segregated into two streams, one liquid and one

of vapor. If the velocity of each of the streams is considered

to be equal, the 'separated flow' model becomes the 'homogenous'

model. As one would expect, the 'homogenous' model is valid for

the flov; of low quality with the separated flow more applicable

for the higher quality annular flow. For the mass flow expected

in this study, G less than 5001bm/ft2 sec , the separated flow

model gives better agreement with experimental dataOo* page 47).

For this mathematical model the 'separated flov;' model will be

used.

The following assumptions are made for the 'separated flow'

model: (21)

(overleaf)

-24-

1. The vapor velocity and liquid velocity are constantbut are not necessarily equal.

2. There is thermodynamic equilibrium between thephases

.

3. Empirical correlations can be used to relate the twophase friction multiplier <$>

2 and the void fraction ato the independent variables of the flow.

It is this third assumption that allows one to separate the

calculation of the heat transfer and the pressure drop. The coup-

ling effect of the properties is taken into account by the empiri-

cal correlations.

To find the heat transfer in two-phase flow, the standard

heat transfer equation q = A UAT is used.

V/here: q = w hfg

Because there is a great deal of variation in the value of U

over the range from a quality, x, of for pure liquid to a quality

of 1 for pure vapor, the heat exchanger is broken into segments

of equal Ax.

To find U: 1=1+1+ Dout - DlnU hh hw kmat

The last term is generally disregarded as kj^t

Dout - Din

is much less than hw and h^.

To find hn , the local heat transfer of the heating fluid,

the following relationships are used: (22)

For Re < 2100

hh =1 - 86 k* " ?V * £hl

Vh5 D ' 5

-25-

For 2100 < Re < 10000

.ll6_kh Prh*"

Dhh = 2 S (Reh »

67 - 125)

For Re > 10000

_ . 023 kh Prh -* Gh - 8

hh -

D » 2 yh« 8

These relationships are empirical equations based on results of

many experiments. Other relationships to find h can be used.

C4 page 192).

To calculate hw , the local heat transfer coefficient for

evaporation, with two-phase flow is a bit more difficult. Chen (23)

postulated that there are two mechanisms which take part in the

heat transfer process for boiling in two-phase flow. One is the

macroconvective mechanism that is associated with bubble nuclea-

tion and growth as takes place in pool boiling. Chen further

postulated that these two mechanisms are additive to their contri-

bution to the total heat transfer. Others have suggested this

idea. RohsenowCfl) in 1952 and BambillO.G) in 1962 both concluded

that the heat transfer effects of boiling and convective flow

when occuring at the same time should be additive.

For the contribution of the macroconvective mechanism, Chen(3,3)

felt that the heat transfer coefficient hmac , should be calcu-

lated in a manner similar to forced convection flow.

(equation overleaf).

-26-

= 0.023 £ Re - 8 Pr-"

This equation is modified to show the effect of the two-phases.

hmac " °- 02 3 Re-^ 8 Prx •" -± FD

where

;

Re 1=

Gw D (1 - x)

"1

p „ CP1 Ml

This leaves the only unknown as F. F is the Reynolds factor and

is a function of X^f

where

:

and

F = (Re/Re!)

Xtt =

.8

'1 - xl .9 .5 f "•

,

y v.lx

J

For experimental data a curve of F vs l/X-^t is plotted. (Figure 2.2-3)

An equation can be empirically derived.

F = 0.15 -i_ + _2-85

Xtt ^tt.1*7 5

The contribution of the microconvective mechanism is derived

from the analysis of Foster and Zuber(3 6) on pool boiling. Foster

and Zuber found:

(equation overleaf)

-27-

Figure 2.2-3

Reynolds Factor

-28-

Nub = 0.0015 (Reb )- 67 Pr x

•"

hb rb

rb is the radius of the bubble and is derived from .bubble buoyancy

and surface tension forces.

Where:rb =

'AT kip 1Cp 1 a

AP

.5 f

U APJ

.25

Forster and Zuber in their analysis disregarded the fact that the

degree of superheat is not constant across the liquid film on the

wall material. For convective flow this is important as the

temperature gradient across this boundary layer is made much

steaper by the flow rate.

Chen (0) then rewrote the Foster and Zuber equation to take

this temperature gradient into account.

hnicm

0.00122 kr" Cpr* 5pjg g"

Am Ak Ap >75 g

O 5 p-^ 29 \'2 " p/-

S is the supression factor and is plotted as a function of

Re = Rei F 1- 25.

The total heat transfer coefficient hw is the sum of hmac

and hmi c . This correlation appears to give better comparison

with experimental data than any other correlations OS', page 126).

The heat transfer coefficient hw cannot be calculated in the

above method for the region that is after the burnout point.

-29-

1.0-

.75-

.5

.25-

f / /

10' 1CT

Re

Figure 2.2-4

Supression. Factor

10<

-30-

For this study it is assumed that burnout will occur at a quality

of .95. For the low amount of superheat expected this appears to

be a reasonable value. For the segiment of the heat exchanger

from quality of .95 to quality of 1, the following should be

used for hw :

1

hw = 0.023 kv Prv-* Qw

D 2yv

8•

Once the value of U is determined, the required heat trans-

fer area can be found for each segment.

Area =W hfF

Ax

U AT

Where

:

:

AT Twall " Tsat

By assuming a geometry of the heat exchanger, the number of tubes

and the diameter of tubes, the length of each segment can be

calculated.

Az = Area/irD n

This completes the heat transfer calculations.

To calculate the frictional pressure drop in two-phase flow,

the Lockhart-Martinelli-Nelson modelUf, 27) will be used. Although

this model was derived for adiabatic flow, it is valid for heated

pipesCS", pa Ge 14-9). The heat exchanger is broken into the

same segment as for the heat transfer calculations. The pressure

drops are then summed for the total.

-31-

The relation of two-phase friction pressure drop to single-

phase friction pressure drop is:

APAz TPF

APAz

*,

Where <J> V2 can be found empirically as is plotted as a function

of Xtt . Figure 2.2-5.

4>v = 1 + 2.85 (Xtt°*522

)

Then

.

AzJtpf

APAz

Where $iz can be found empirically

l - ^L_Xtt

f||]= V x K8

fAP

]<.Azj iVo

WhereAPAz

• 09 Gw y v -2

if Re>2 500

Jlo s p v d1 - 2

AndAP] =

128 Gw liy lf Re<250(Az

Iaz

Jlo g P v D '

A pBy substitution, (=—) can be determined. APW is calculated by

Az ippp

multiplying (f^-) by the length of the segment Az. The sumAz TPF

-32-

100 -t

4e 10-

1.0.01

-T

.1 1.0 lb 100

Figure 2.2-5

Two-Phase Prictional Multiplier

!?-

of the APW is the friction pressure drop in the evaporator.

If this pressure drop is too large to be handled by the

cycle in which the evaporator is to be placed, the geometry of

the evaporator can be changed. Increasing the flow area should

decrease the length and the pressure drop.

This concludes the necessary mathematical model for two-

phase flow evaporators.

31-

NOMENCLATURE

lfg

A

Cp

D

Din

Dout

F

G

g

h

k

n

Nu

P

Pr

APAz

AP

q

r

Re

S

T

AT

Heat transfer surface area

Specific heat at constant pressure

Diameter

Inter diameter of tubes

Outer diameter of tubes

Reynolds number factor

Mass flow velocity

Gravitational constant

Heat transfer coefficient

Latent heat of evaporation

Thermal conductivity

Number of tubes

Nusselt number

Pressure

Prandtl number

Pressure drop per length

Change in pressure

Rate of heat transfer

Radius

Reynolds number

Supression factor

Temperature

Change in temperature

-35-

NOMENCLATURE Ccont,)

X Quality

xtt Martinelli parameter

Ax Change in quality

w Mass flow rate

z Length

X Latent heat of vaporization

V Viscosity

P Density

a Surface tension

* Two-phase frictional multilplier

Subscripts

b Bubble

h Heating fluid

1 liquid

lm Lograthnic mean

mac Macroconvective

mat Material of walls

mic Micro convective

sat Saturation

TPF Two-phase flow

V Vapor

w Working fluid

-36-

2.3 CONDENSATION PROPERTIES

2.3.1 Introduction

Condensation is the removal of heat from a vapor to convert

it into a liquid. This is generally done by using a surface with

its temperature, -Tw , lower than the saturation temperature, Tsat ,

of the vapor. The vapor will condense into a liquid on the colder

surface. The exact nature of this condensation mechanism is not

fully established. It is felt that the condensation begins in

small cavities in the surface much as bubbles are formed in boil-

ing^, page 12-2).

There are two forms of condensation - dropwise and film.

Dropwise condensation occurs on a non-wetting surface. Droplets

form and run down the surface, increasing in size by further

condensation and coalescence. New droplets are formed to take

their place. The heat transfer for dropwise condensation is

from 5 to 50 times that for film condensation (31) . It is diffi-

cult to maintain dropwise condensation for more than a short

period of time without treating the heat transfer surface.

Film condensation occurs when the liquid being formed wets

the surface and establishes a stable film. This type of conden-

sation is the prevalent in commercial condensers. As the heat

transfer rate is lower with film condensation, condens rs are

designed for this form of condensation. If the condensing should

be dropwise for part of the operation of the condenser, it will

perform better than design. In this study, film condensation

-37-

will be examined.

2.3.2 Film Condensation

The first attempt to analyse film condensation was carried

out by Nusselt in 1916. When the stable film is formed, vapor

condenses on the liquid. The condensation takes place at the

liquid-vapor interface because the heat is being transferred

through the liquid. At this interface there is a continual

interchange of molecules being condensed and molecules evapora-

ting, with the net flow condensing.

In his analysis Nusselt made the following assumptions:

CIO, page 31*0.

1. The flow of condensate in the film is laminar.

2. The fluid properties are constant.

3. The condensate temperature distribution is linear.

lj. There are no changes of momentum through the film.

5. The vapor is stationary and there is no shear forceat the liquid-vapor interface.

6. Heat transfer is by conduction only.

These assumptions are important in the later development of the

mathematical model for condensation. The only modification to

these assumptions is in the temperature distribution. The actual

temperature distribution is slightly curved(iO, page 239).

2.3.3 Mathematical Model

In the design of a condensar, the desire is to determine the

required heat transfer area. The rate of heat transfer, a, is

-38-

found by:

q = U AATlm

Where 1

U1 + 1 + Pout - Dinfiw cmat

As v/as done in boiling heat transfer, K ,/Dout - Din can be' mat

disregarded.

q = w hfg

andAT ..

(Tsat -Tcl ) - (Tgat - T c2)fll lni

"

InT , - T ,sat cl

Tsat " Tc2

Where AT]_m is the ' logarithic' mean temperature.

To find the required area, all that needs to be calculated

is the overall heat transfer coefficient, U. The heat transfer

coefficient for the cooling fluid, h c , is found by the following

relations (I'D .

if Rec

< 2100

h c = l,86(Rec

.* Prc

- 5 p ^

if 2100 < Rec

< 10000

= .116 (Rec•"- 125) Pr

(

.67

(cont. overleaf)

•39-

if Re c > 1000

0.023 Kg Pr^ G c' ;

Vc8 D 2

To derive the coefficient of heat transfer for condensation,

hw , one begins with the Nusselt analysis. For condensing on

a verticle plate,

hw = 0.943;p 1 (p 1

- pv ) ki!£fi

1

L]i 1 AT

Where h£ = hf + .68 Cp AT.

The deriviation of this equation is examined in detail in References

5", 31 and /P.

This coefficient must be modified for condensation on a hori-

zontal tube. The relation above is valid with the modification

that g sin is used to replace g. The average value of h for the

tube is found by integrating h from to

hw = 0.728H

\

gp1(p 1

- P^k! 3fij.

Doutyn AT

For a number of tubes in a vertical row, all of the conden-

sate dropping from any tube is assumed to fall on the next lower

tube. This will increase the film thickness of lower tubes and

require a modification in h,,'w •

hw = C1728

Mgp, (p, - p ) k.

!££

n. Dout u-l AT

-40-

nh is the number of tubes in a vertical row. Observations by

Grant and OswentOl) show that the condensate seldom falls from

the upper tube to lower tubes as a continuous sheet. This would

tend to lessen the importance' of having the n^ term.

Two other effects can change the heat transfer coefficient.

These are the presence of noncondensable gas and changes in the

surface geometry.

The presence of even a small quantity of non-condensable

gas in a condensing vapor has a profound effect on the heat

transfer coefficient. The non-condensable gas tends to form at

the liquid-vapor interface. This increases the partical pressure

of the gas at the interface and increases the resistance to heat

transfer. The details of the methods to calculate this effect

are given in References!. In this study, the effects will be

disregarded. In most commercial condensers, ejectors are used

to remove these gases and alleviate the problem.

Changes in the surface geometry of the tubes can greatly

increase the heat transfer coefficient with film condensation.

One of the most premising of these geometry changes is fluting

the tubes. This geometry was first examined by Gregorig(3i)

.

In experiments Gregorig obtained an h for condensing of

8000 Btu/hr. ft 2 °F, a factor of four above what is obtainable

with round tubes. Because of the complex shape of these tubes,

it is difficult to analytically evaluate the heat transfer co-

efficient. Instead, experimental data must be used.

Upon finding h and hw , the overall heat transfer coefficient

-111-

can be found and the required heat transfer surface area

determined. A heat exchanger geometry, tube diameter and number

of tubes is chosen by the designer. The condenser length can

be found from this.

1 = Area/im Dout

The frictional pressure drop of the cooling fluid can be

calculated.

if Re > 2500c

0.046jj

1 G c2

Rec

* 2 D 2g p c

P. =

Din G cV/here Re- =

uM c

if Re„ < 2500c

Pc

= en 1 1 g c:

Rec

Din 2g p c

If this pressure drop is too large for the desired apDlication,

the condenser geometry, tube diameter and number of tubes, can

be changed to decrease the pressure loss.

This concludes the necessary mathematical model for con-

densing on the outside of tubes. Condensing on the inside of tubes

is not often carried out as it involves tv/o-phase flow and is diffi-

cult to analyse.

-42-

NOMENCLATURE

A

Cp

Din

Dout

g

G

h

hfg

k

L

n

nb

Pr

AP

q

Re

T

AT

U

w

II

P

Heat transfer surface area

Specific heat at constant pressure

Inner diameter of tubes

Outer diameter of tubes

Gravitational constant

Mass flow rate w/Area

Heat transfer coefficient

Latent heat of condensation

Thermal conductivity

Length

Number of tubes

Number of tubes in vertical bank

Prandtl number

Change in pressure

Rate of heat transfer

Reynolds number

Temperature

Change in temperature

Overall heat transfer coefficient

Flow rate

Absolute viscosity

Density

Subscripts

c Cooling fluid

-U3-

NOMENCLATURE (cont.)

1 Liquid

lm Logarithmic mean

mat Material of the walls

sat Saturation

v Vapor

Working fluid.w

-l\H-

2.4 Cooling and Heating Properties

2.4.1 Introduction

In this study, the evaluation of the properties of cooling

a working fluid and heating a working fluid in a heat exchanger

are carried out at the same time. Thermodynamically the mechan-

ism of heating and of cooling Is the same. Any differences that

do exist in the relationships will be discussed in the develop-

ment of the mathematical model.

As was noted in section 2.1, counter-flow heat exchangers

and cross-flow heat exchangers will be examined in this study.

The heat transfer mechanisms of both exchanger types are similar

but the approach to the designing of each is different.

The job to be done by these heat exchangers will be to trans-

fer a specific amount of heat from one fluid to another. If the

exchanger is a heater, the working fluid will be the cooler fluid.

For a cooler, the working fluid must be the hotter fluid. The

mass flow rate, w, of both fluids in each type of exchanger will

be specified as will be the inlet and outlet temperatures. This

will be true regardless of the flow pattern of the fluids.

2.4.2 Counter-Flow Heaters and Coolers

The mathematical model for the sizing of counter-flow

heaters and coolers is based on the solving of similtaneous equa-

tions. This is accomplished by setting groups of known constants

equal to a large constant, Kl, K2, K3, etc. The heat transfer

->I5-

area, number of tubes, and the exchanger length will be deter-

mined in terms of these constants. This method is described in

detail in Reference 7.

To make this model valid for both heating and cooling, the

hotter fluid in the exchanger is designated by a subscriot 1 and

the cooler fluid by a subscript 2. In a heater the working fluid

is colder and Is designated by the subscript 2, while for a cooler

the inverse is true. The mathematical relationships are otherwise

identical.

A limiting constraint on the design of a counter-flow ex-

changer is the pumping power required to overcome the friction

pressure loss of the fluid flowing in both the tubes and the

shell. In this design method, this constraint is set by estab-

lishing an allowable pressure drop, AP.

If Re x > 2500

APt ='0.092 v-l

0.2 "\

. g p-j_ J Din

G 1 ' 8 L

1.2

(35)

1.8

AP n = KlL

Din 1.2

If Re, < 25001

r 128 Pl'2

g piRei^J Din

Gl L

1.2

Kl G1

1 - 8 L

Din 1.2

-146-

If Re2

> 2500

P 2 -'0.092 v 2

" G 21 '8 L

g P 2 )Dea 1.2

Po = K2 ^21.8

Dea 1.2

If Re 2< 2500

Po = rl28 y 2' 2

1

1.8

g P 2Re

2* 8

K2G<

i.e

Dea 1.2 Dea l*2

Where: Deq = (1.271 (s/Dout) 2 - 1) Dout (7, page 32*0

This is for square pitch exchangers with s the spacing between

tube centers.

Where: Re 1 - Din (wx/ (it P 1 " 2

)

and Re 2= Deq (w 2/ U Deq

-

2

)

Next the heat transfer coefficient, h, is calculated. (30, page kh2)

If Rei > 10000

hi = 0.023 ki Pri" Gi'!

Ml Din"

K3

Din~

If 2500 < Rej < 10000

'1. .116 ki Prr33

n-i =

Re- 13

Or'

Din"

K3 Gra

Din :

If Rex < 2500

h l =1.86 ki Prr 5 Gy8

Re. Din-

K3Gr'

Din.2

-M7-

If Re 2 > 10000

0.023 k 2 Pr^ G 2-' /t .8

Deq'.2 Deq"

If 2500 < Re2

< 10000

.116 k? Pr ?-33

h 2=

Re 13

£2iDeq

KH02-8

Deq :

If Re2

< 2500

1.86 k 2 Pr2'5 Go"

8

2_ e K4 Sliy 2

8 Re2

3 Dea Deq'

n, A Pi ,, ,, , v KlThen: — (both known) —

—

A ? K2

fGll 1 - 8 fDea^- 2

G 2 Din

By definition G^ - Wt/Ax-i

G 2 v;2/Ax 2

Where Ax is the cross sectional area of the flow.

Axi = tt/1» Din 2 n

Ax 2 = tt/4 Deq 2 n = -n/k Deq Dout n

By substitution

Then

K2 K5

Kl

.33 _K6

w2

Din

-U8-

From solving for AP1/AP2 and G3/G2

21 = K3

h 2 K4'£iV

8

.G2 J

DeqUDin

m K3 fK2 K5]'33

K4 I"Kl

DoutP fclj'2

.Din J UgJK7

by:

The overall heat transfer coefficient can be calculated

1 1_ + 1_ Pout - Din

U cmat

The last term can be disregarded as it is insignificant compared

to the other terms. This equation does not include the effect

on U of scale deposits. For a preliminary design it can be dis-

regarded.

Where

1 m _1_

U h x+ _1_

h 2

1 = _1_

U K3

Din-2

0/

K8 = —XK6 Din'2

KH

K6 Deo"2,

K8 Din'2

of G-

The heat transfer rate

q = A U AT1m

Where A = n Din L

q = n TrDin U L A T,1 lm7' Din 2 n G, Cp, ATl) 1

yl 1

-JI9.

Where AT^_ is the difference between the inlet and outlet tempera-

ture of the hotter fluid and ATlm is the logarithmetic mean

temperature.

ThenL == Cp_Ei G

l Dln= K9

G l Din

^ Tlm u U

1.2 n 1«2L = K9 K8 D-l1 ' 2 G x

Then by substitution of

Into

Gl' 2 =^ K9 ^

Kl L G, -8

AP n = L_Din 1 2

Gi =

kKl K8 K9,

.5

= K10

By definitionG^ = W]_/Axi

Therefore wl n

n =

Gl

TT D-j^

The value of Din and Dout are selected so L can be calculated,

L = K9 K8 Din 1,2 K10

and the heat transfer area can be found. i

A = Din n L

30-

This concludes the necessary calculations for the heat exchanger

design. This design method assumes that:

(1) The specific heat of the fluid, Cp is constant.

(2) The overall heat transfer coefficient is constant.

If these factors are not constant, the design approach is

modified. The above procedures are carried out using average

values of the fluid properties. A value of n and G^ is determined.

The exchanger is then divided into segments such that Cp and U

can be assumed to be constant over the segiment. The design method

is then repeated for each segiment with n and Gi kept constant.

The length is determined for each segiment. These lengths can then

be added to get the overall length of the heat exchanger.

2.4.3 Cross-Flow Heaters and Coolers

In addition to the information about the job to be done

by the heat exchanger noted in section 2.4.1, one must know the

condition of the flow through the exchanger to size a cross-flow

heater or cooler. (3, page 18 - 8l). As stated in section 2.1.3,

for this study it is assumed that the working fluid is flowing

across the tubes and is mixed. This keens the working fluid at

a uniform temperature as it leaves the exchanger.

In the development of the mathematical model, the equation

q = U AAT is again used with a slight modification -

a = U A FAT, mrt :n lmc

(cont. overleaf).

-51-

Where: (T - T ) - (T,_ - T _)^m _ h2 cl hi c2lmc

T T1

In xh2 " cl

T - TXhl Xc2

AT^mc is the logarithmetic mean temperature for counterflow arrange-

ment. This is not the integrated mean temperature ATm . F is then

defined as:

F = ATm/ATlmc (30)

and is a function of e c and Z.

Where: e c is called the effectiveness of the heat exchanger.

ec = T

c2 " Tcl/Thi" T

ci (30)

and T _ tZ = hi h2

ITcl " T

c2

F can be found on tables as a function of Z and e c . F also

varies v/ith the flow pattern, if one or both of the fluids are

mixed. These tables can be found in References 5, 10 and 30.

The value of a can be found from a = v; Cp]_ AT^. All of

these values are known. To find the heat transfer surface area:

A = q/U FATXmc

U can be calculated by the relations for h. and h„ examined

in the section 2.4.2 of this study.

By selecting an exchanger geometry, number of tubes and tube

-52-

diameter, the length of the required exchanger can be determined.

L = Area/TrDin n

The frictional pressure loss is then calculated. The relation-

ships are examined in detail in section 2.4.2 and need not be re-

derived. If the pressure loss is too great, the geometry of the

exchanger can be modified and the length recalculated.

This design method assumes that U is constant throughout

the length of the exchanger. If this is not a valid assumption,

the exchanger can be broken into segiments. The above design

procedure is then used for each segiment with the sum of each

segiment length the total length.

-53-

NOMENCLATURE

A

Ax

Cp

Din

Dout

Deq

F

g

G

h

k

K

L

n

AP

Pr

q

Re

s

Tc

Th

ATin

U

Heat transfer surface area

Cross sectional flow area

Specific heat at constant pressure

Inside diameter of tubes

Outside diameter of tubes

Equivalent diameter for shell side

Mean temperature difference factor

Gravitational constant

Mass velocity

Heat transfer coefficient

Thermal conductivity

Constant

Length

Number of tubes

Frictional nressure drop

Prandtl number

Heat transfer rate

Reynolds number

Tube spacing

Temperature of cooler fluid

Temperature of hotter fluid

Log mean temperature difference

Overall heat transfer coefficient

-5U-

NOMENCLATURE (cont.)

w Mass flow rate

Z Teimoerature coefficient

e c Effectiveness of heat exchanger

y Viscosity of fluid

p Density of fluid

Subscripts

1 Hotter fluid

2 Cooler fluid

mat Tube material

-55-

2.5 Material Selection

2.5.1. Introduction

In the selection of material for the tubes and other

heat transfer surfaces in the heat exchanger, it is desirable

to have the heat transfer coefficient as high as possible.

An increase in the heat transfer at the surface of the material

produces a corresponding increase in U, the overall heat trans-

fer coefficient. This will decrease the reauired heat transfer

surface area as the area proportional to the inverse of U.

This augmentation of the heat transfer can be accomplished

in many ways. The surface of the tubes can be roughened by a

number of methods. The heat transfer surface can be left the

same but the flow disturbed. This increases the heat transfer

by displacement of the fluid or by setting up a vortex flow.

Other methods of augmentation include vibration of the heat

transfer surface, fluid vibration, and the use of electrostatic

fields. Of these methods of increasing the heat transfer, the

best appears to be the roughening of the surface material. The

vibration and electrostatic methods require outside power to

operate and are therefore less attractive. ( 5(page 10-2) ).

2.5.2. Methods of Enhancement

The first method for enhancing the heat transfer to be

seriously considered, was increasing the surface roughness of

the transfer material. The most successful for single-phase

flov; appears to be a method devised by Dipprey and Sabersky (14 )

,

and one developed by Kemeny and Cyphers(15). Dipprey and Sabersky

-56-

produced the roughness by electronically depositing copper on

a rod coated with sand grains. The rod was dissolved leaving

a tube of copper with close-packed sand grains on the inner

surface. This method, for high Prandtl number flow, increases

the h, heat transfer coefficient, by a factor of two. Figure

2.5-1. The Kemeny and Cypher method uses a helical groove in

the material and a helical protrusion from the material. The

grooved surface showed little improvement in the heat transfer.

The helical protrusion did increase the h by up to a factor of

two. Figure 2.5-2. As can be seen from Figures 2.5-1,2, the

effects of the enhanced surfaces decrease with the increase in

the Reynolds number. These methods also show no advantage in

two-phase flow.

In two-phase flow, the heat transfer is increased by pro-

moting nucleate boiling at as low a heat flux as possible.

Young and Hummel(l6) placed spots of teflon on the heated sur-

face. This promoted nucleation as shown in Figure 2.5-3. This

lowered the required level of superheat required to produce

boiling. With an increase of Reynolds number, the effect of the

teflon spots decreases.

The methods of increasing the heat transfer can also in-

clude the use of a smooth surface with a higher k. All of these

methods of Increased heat transfer would be useful in the design

of the heat exchangers for the thermal cvcles . »What Is needed

Is a method of comparison of these Increases heat transfer sur-

faces to unenhanced surfaces.

-57-

2.0,

1.0

h

10' 10"

Re10

Figure 2.5-1

Dippry and Sabersky Results

2.

1.5

i. 4-

.5107

Protrusion

10' 10"

Reo

Pigure 2.5-2

Kenery and Cypher Results

10

-58-

2.5.3 Methods of Comparison

A method of comparison has been developed by Professor

W.M. Rohsenow and others working in the Heat Transfer Lab at

M.I.T. (17). The data on the surfaces is presented based on the

same heat transfer area and tube diameter of equivalent diameter,

f Re 3 is plotted agains-t j Re. Figure 2.5-3.

Where: f Re 3 = P/v 2gp 2 De 3 q/A/V u3

^ * d~ Ah Pr^3 Peaand j Re =

V A/V Cpy

The following are kept constant:

g, p, Deq, A/V, u, Cp, Pr

Therefore:f Re 3 ~ P/V

an(i .. ,. ma t?^ o Ah o/AT,mJ Re % — or •** '—

V V

where P = V.'AP/p

For the same mass flow rate and material properties:

. . ., r AhA h/V "v NTUWCp = -1^-

For any flow arrangement there is one NTU vers e curve (18)

Figure 2.5-4.

Where:u ATrise in cold fluid

Thot in - Tcold in

_ 5 9_

j Re

f Re^

Figure 2.5-3

NTUFigure 2.5-4

-60-

The two materials can now be compared at two points. See

Figure 2.5-3. The mass flow rate, w, the Deq, A/V, Thot in and

^cold in remain constant throughout this comparison.

At point A, tha values of w, V, and Re are the same as at

point 0. This gives the same size and shape heat exchangers with

different surface material. The amount of heat transfer and re-

quired pumping power will be different. These can be plotted as

shown in Figure 2.5-5.

Point B has the same mass flow rate, pumping power required

and volume as point 0. A heat exchanger operating at B will have

the same volume as one at 0, but the shape changes and there is

more heat transfer. This comparison is made in Figure 2.5-6.

If the comparison of the materials is to be made while doing

the same job, point C and point are examined. At these points

the same heat transfer (NTU), mass flow rate and pumping power

occur. The difference is that less volume is needed with materi-

al B (point C). Figure 2.5-7.

Since A/V has been held constant, the area required at point

C is also less. This can be an important comparison if the heat

exchanger needs to be as small as oossible. A cost comparison

can easily be done. As the pumping power is the same, the only

variable cost is the material costs.

Cost n/ Souare foot * A„2 : a = Cr

Cost./ Scuare foot * A.A A

-61-

1.0

Re - Re

Figure 2.5-5Comparison of Exchanger at Point and

at Point A

NTU

"ntu

1.0Re

Figure 2.5-6

Comparison of Exchanger at Point andat Point A

-62-

If Cr is greater than 1, A will be a cheaper material

to use. If, however, Cr is less than 1, B is the cheaper

material.

A fourth comparison can be made at point D. Here the heat

transfer, mass flow rate and the volume are kept constant with

point 0. The shapes differ and the pumping power Is lower.

Figure 2.5-8. If the cost of the required pumping power was

too high with material A, material B could be used to lower it.

-63-

1.0-

1.0 -

D

Re.

Figure 2.5-7

Comparison oi Exchanger at Point andat Point G

ReQ

Figure 2.5-8

Comparison of Exchanger at Point andat Point D

-6h-

NOMENCLATURE

A Heat transfer surface area

Cp Specific heat at constant pressure

Cr Cost ratio

Deq Equivalent diameter

f Friction factor

g Gravitational acceleration

h Local heat transfer coefficient

k Thermal conductivity

NTU Number of exchanger heat transfer units

P Pumping power

AP Change in pressure

Pr Prandtl number

q Rate of heat transfer

Re Reynolds number

AT, Logarithmic mean temperature

V Volume of exchanger

w Mass flow rate

e Exchanger heat transfer effectiveness

Mass density

Absolute viscosity

Subscripts

:

A Material A

B Material B

-65-

III. RESULTS

In this study, the objective use to develop a series of

computer programs to carry out. preliminary design on heat ex-

changers required for thermal cycles. For this development,

general properties of heat exchangers were examined and mathe-

matical models were developed for various modes of heat trans-

fer.

The computer programs were developed and tested. All of

the programs performed as desired except for the cost calcula-

tions and the author feels that they should perform success-

fully in studies of a broad range of inputs. The programs are

explained and written in detail in the Appendix.

Two of the programs were used in detail in an examination

of the proposal made by Prof. Zener. See Aopendix G. The evao-

oration and condensation heat exchanger programs carried out the

desired preliminary design and showed the variety of designs

that can be carried out with these programs.

The Zener proposed cycle was examined to determine its

feasibility. With the use of freon-21 as a working fluid, the

evaporator must have a volume of two billion cubic feet for a

100 Mega-watt power plant. The condenser will have a minimum

size of over three-hundred million cubic feet of volume. More

detailed results are included in Aopendix G.

-66-

IV CONCLUSIONS

The following conclusions can be drawn from the results of

the study.

1. The computer can be a valuable aid in heat exchanger

design work.

2. The cycle proposed by Prof. Zener is not feasible at

the present time.

3. The cost analysis done in this study is very inaccurate.

*J . Although the programs can give a variety of geometrical

arrangements there is no way to compare these arrange-

ments to determine the best.

-67-

V RECOMMENDATIONS

This study appears to the author to be weak in two areas

.

The evaluation of cost is very inaccurate. The problem of opti-

mization was not discussed in this study. A further study of

these two areas xvould be beneficial. As these two areas are

inter-related, they could be examined together.

More examination of the cost of heat exchangers needs to

be carried out. The relationships for cost caluculation deri-

ved in section 2.1 are based in I960 data. This in in itself

is a problem, but also the size of heat exchangers designed is

way beyond the range of validity of these relationships. To

extrapolate to M,000 feet a curve that is valid up to 400 feet

is unrealistic. More up to data values of cost should be de-

termined. Also cost relationships that are valid for large

heat exchangers should be derived. These relationships could

easily be placed in the program.

The programs as written contain no ootimization operations

The programs require a disigner to input various geometric

arrangements and then compare the output to determine wich is

best for his application. With up to data cost relationships,

an optimization operation could be incoroorated into the pro-

grams giving the designer the best heat exchanger within some

specified limit.

-68-

REFERENCES

1. Clarence Zener, "Solar Sea Power", Physics Today , Jan. 1973,pp. 58.

2. J. Hilbert Anderson and Janes H. Anderson Jr., "ThermalPower from Seawater", Mechanical Engineer , April, 1966, pp. 11.

3. Aden Meinel and Majorie Meinel, "Physics Looks at Solar Energy",Physics Today , Feb. 1972, pp. %2 .

i| . Geothermal Energy: A National Proposal for Geothermal ResourceResearch , Battelle Memorial Institute, Seattle Research Center,U. of Washington Press, Seattle, 1972.

5. W.M. Rohsenow and J. P. Hartnett, Handbook of Heat Transfer ,

McGraw-Hill Book Co., New York, 1973.

6. T. Tinker, "Characteristics of Shell and Tube Heat Exchangers"Transactions ASMS , Vol. 80 (1958), pp. 36.

7. A. P. Fraas and M.N. Ozisik, Heat Exchanger Design , John Wileyand Sons Inc., New York, IO65.

8. R.A. Stevens, "Mean Temperature Difference in One, Two, andThree Pass Cross-flow Heat Exchangers." Transactions ASF-IE ,

Vol. 79 (1957), pp. 28.

9. K.A. Gardner, "Efficiency of Extended Surface," TransactionsASME, Vol. 77 (1955), PP. 621.

10. V/.M. Rohsenow and H.Y. Choi, Heat, Mass and Momentum TransferPrentice Hall Inc., Englewood Cliffs, New Jersey, 1961

.

11 K.A. Gardner and T.C. Carnavos, "Thermal Contact Resistancein Finished Tubing", Journal of Heat Transfer , Vol 82 (I960)PP. 279.

12. C.H. Chilton, Cos t Engineering in the Process Industries , McGraw-Hill Book Co.., New York, 1?*0.

13 N.R. Dunteman, A New Look at the Cornetitive P osition of theInverted Cycle Gas Turbine for Waste Heat Ut i lizati o n andOther Aoplica^ions , M.S. Thesis, Mechanical EngineeringDepartment, M.I.T., Cambridge, Mass., 1970

-60-

References (cont).

14

.

D.F. Dippry and R.H. Saberslcy, "Heat and Momentum Transferin Smooth and Rough Tubes at Various Prandtl Numbers",International Journal of Heat and Mass Transfer , Vol 6 (1963)pp. 329.

15. G.A. Kemery and J. A. Cyphers, "Heat Transfer and Pressure Dropin an Annular Gap with Surface Spoilers ", Journal of HeatTransfer , Vol 83 (1961), pp. 189.

~~ ""

16. R.K. Young and R .L. Hummel, "Improved Nucleate Boiling HeatTransfer", Chemical Engineering Progress , Vol 60 (1964) pp. 53.

17. W.M. Rohsenow "Heat Exchanger Comparison - Smooth vs Enhanced",an unpublished paper prepared at M.I.T., June, 1973-

18. W.M. Kays and A.L. London, Compact Heat Exchagers , 2d. ed.

,

The National Press, Palo Alto, Calif. 1955.

19- Tong L.S., Boiling Heat Transfer and Two-Phase Plow , John Wileyand Sons Inc

. , New York, 1965

•

20. Collier, J.C., Convectlve Boiling and Condensation , McGraw-Hill Book Co., London, 1972.

21. Lockhard, R.V,7., and Martinelli, R.C., "Proposed Correlation

of Data for Isothermal Two-Pahse, Two Component Flow in Pipes",Chemical Engineering Progress , Vol 45 > (19^9), PP • 39-

22. Kern, D.Q. and Kraus , A.D. Extended Surface Heat Transfer ,

McGraw Hill Book Co., New York , 1972.

23. Chen, J.C. "A Correlation for Boiling Heat Transfer to Latu-rated Fluids in Convectlve Flow", AS?!E oaoer no. 63-H7-34,May, 1963.

Rohsenow, W.M., "Heat Transfer, A Symposium", EngineeringResearch Institute, U. of Michigan Ann Arbor, 1952.

Gambill, W.R., "Generalized Prediction of Burnout Heat Fluxfor Flowing Sub-Cooled Wetting Liquids", AIChE ^ifth NationalHeat Transfer Conference, Houstan, Texas, 1962.

Forster, H.K. and Zuber, N., "Dynamics of Vapor Bubbles andBoiling Heat Transfer", AIChE Journal , Vol 1 (1055) No 1, pp. 531

Martinelli, R.C., and Nelson, D.3., " prediction of Pressure DrooDuring Forced Circulation Boiling of Water", Transactions ASME ,

Vol. 70 (1948), pp.695.

-70-

References (cont).

28. Levys, "Generalized Correlation of Boiling Heat Transfer",Journal of Heat Transfer , Vol 8l, (1959), pp. 37.

29. Engleberg, K. and Grief, R. , "Heat Transfer to a BoilingLiquid-Mechanism and Correlations", Journal of Heat Transfer ,

Vol 81, (1959) PP. 43.~

"

30. Rohsenow, W.M. ed., Developments in Heat Transfer , MIT Press,Cambridge, Mass., 1964

.

31. Mikic, B.B., "On the Mechanism of Dropwise Condensation",International Journal of Heat and_ Mass Transfer , Vol. 12 (1969)

32. Akers, W.W., Davis S.H. and Crawford, J.E., "Condensation ofa Vapor in the Presence of a Non-Condensing Gas", ChemicalEngineering Progress Symposium Series , Vol 56 (i960)

.

33. Gregorig, R.Z., Echangeurs de Challeur,

3^1. Grant, I.D.R. and Osnet, D.D., "The Effect of Condensate Drain-age on Condensor Performance", N.E.L. Report 350, 1968.

35. Binder, R.C., Fluid Mechanics , Prentice-Hall Inc., EnglewoodCliffs, II. J., 1962.

36. Kays, W.M. and London, A.L., Compact Heat Exchangers , McGrawHill Book Co., New York, 1964.

37. Adams, J. A., and Rogers, D.F., Computer Aided Heat TransferAnalysis, McGraw-Hill Book Co., New York, 1973-

38. McAdams, W.H., Heat Transmission , McGraw-Hill Book Co., NewYork, 1954.

39. Stoeker, W.F., Design of Thermal Systems , McGraw-Hill BookCo., New York, 1971.

10. I.B.M. System/360 and System/370 FORTRAN IV Language, IBMPublication Mo. GC28-6515-8- 1971.

11. FORTRAN User's Guid e, M.I.T. Joint Computer Facility, CivilEngineering and Mechanical Engineering, "Pink Sheete", Jan. 197^

^2. Stuart, P., WATFOR, V/ATFIV, FORTRAN Programming , John Wilg andSons Inc., New York, 1971

-71-

Appendix A - COUNTER-FLOW CONDENSING HEAT EXCHANGER PROGRAM

A.l Instructions for operation and input

This program is written in FORTRAN IV and can be run as is

on the Interdata computer of the Joint Civil and Mechanical

Engineering Computer Facility at M.I.T. With modifications In

the control, input and output cards, this program can be run

on any computer that Is programed to compile FORTRAN IV.

For this program, the input data is broken into two groups.

The first contains four cards, three of which contain properties

of the fluids and the fourth is the number, M, of input sets to

follow. The second group has 2M cards. There are two cards to

a set. The first card serves as an identification card and the

second has the geometric arrangement of the heat exchanger; Din,

Dout, S, N, KMAT, and NB. With this Input arrangement, M varia-

tions of the geometry of the exchanger can be examined using the

same fluid properties.

The input data is punched on the cards as follows:

(1) All values will be In units of lb , hr.

,

feet, Btu, and °F.

(2) All values will be fixed point numbers withdecimal points except the value of H.

(3) No commas are needed to separate the inputvalues

.

CO The input values must be in the nroner col-umns but need not be right or left justified.

(5) All fixed nolnt numbers can have un to 'A (four)digits after the decimal point.

(6) The properties of the fluids, unless specifiedto be at a oarticular point, are average valuesover the length of the exchanger.

-72-

COLUMNS

1—13

TCI

ROWV

1—12

ROC

1—4

Identification name for each geometric variation

53—65

KMAT

14— 26 27—39 40—52 53—65 66—78

TC2 Tw DELHW MKRW ROWL

MUWL KWL KC PRC MUC

13—24 25—36 37—48 49—60

HFG CPC PCI PC2

CARD

1

2

3

4

5

6

I7

:

8

This repeats M times.

The output will appear with the identification_at the top of

a page and the following printed below it.

1—13 14— 26 27—39 40—52

DIN DOUT S N

Same as Card 5

Same as Card 6

66—78

MB

MASS PLOW RATE WORKING FLUIDMASS PLOW RATE COOLING FLUIDNUMBER OF TU5ESINNER DIAMETER OFOUTER DIAMETER OFSPACING OF TUBESLENGTH OF TUBESDROP IN PRESSURE COOLING FLUIDCOMPARITIVE COSTS

?UBES^UBES

For each identification there will be a separate page.

•73-

A. 2 LIST OF VARIABLES

AREA

COST

CPC

CTB

cw

cwv

DELHW

DIN

DLPC

DOUT

DTLM

GC

HC

HFG

HWA

KC

KWL

KMAT

LENGTH

M

Heat transfer surface area in ft 2

Cost of heat exchanger in dollars

Snecific heat at constant pressure of coolingfluid in Btu/lbm °F

Cost of the materials for the tubes and shellin dollars

Fabrication costs in dollars

Fabrication cost per tube in dollars

Change in enthalpy in Btu/lbm

Inner diameter in feet

Frictional pressure drop in cooling fluid inlb/ft 2

Outer diameter of tubes in feet

Log mean temperature difference in °F

Mass flow velocity in lbm/hr. ft. 2

Heat transfer coefficient of cooling fluid inBtu/hr. ft. °F

Latent heat of condensation in Btu/lbm

Average heat transfer coefficient of workingfluid In Btu/hr. ft. 2 °F

Thermal conductivity of cooling fluid inBtu/hr. ft. °F

Thermal conductivity of working fluid as aliquid in Btu/hr. ft. °F

Thermal conductivity of wall material InBtu/hr. ft. °F

Length of heat exchanger in feet

Number of groups of inputs data

-71-

A. 2 LIST OF VARIAELES (cont.)

MFRC

HPRW

MUC

MUWL

N

NB

PCI

PC2

PRC

Q

REC

ROC

ROWL

ROWV

S

TCI

TC2

TW

TLF

TMF

U

Mass flow rate of cooling fluid in lbm/hr.

Mass flow rate of working fluid in lbm/hr.

Viscosity of cooling fluid in lbm/hr. ft.

Viscosity of working fluid as a liquid Inlbm/hr. ft.

Number of tubes

Number of tubes In a verticle row

Inlet pressure of cooling fluid in lb/ft. 2

Outlet pressure of cooling fluid in lb/ft 2

Prandtl number of cooling fluid

Rate of heat transfer in Btu/hr.

Reynolds number of cooling fluid

Density of cooling fluid In lbm/ft.3

Density of working fluid as a liquid in lbm/f t

.

3

Density of working fluid as a vapor in lbm/ft

.

3

Spacing of tubes

Inlet temnerature of cooling fluid in °F

Outlet temperature of cooling fluid In °F

Temperature of working fluid in °F

Tube length factor in dollars/ft.

Tube material factor

Overall heat transfer coefficient in BTU/hr.ft 2 op.

-75-

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-78-

Appendix B - COUNTER-FLOW EVAPORATION HEAT EXCHANGER PROGRAM

B.l Instructions for operation and input

This program Is designed to be run on the Interdata com-

puter of the Joint Civil and Mechanical Engineering Computer

Facility at M.I.T. The program is written in FORTRAN IV and

can be run on any computer that is Drogramed to compile FOR-

TRAN IV. If run on a computer other than the Interdata, some

modification may be required to the control, input and outout

cards

.

The Input data is broken into two sections. The first con-

tains five cards, four contain fluid properties and the fifth

is the number, M, of input sets to follow. The second section

has 2M cards. The first card serves as an identification card

and the second card has the geometric arrangement of the heat

exchanger; DIN, DOUT, S, N, KMAT. With this input arrangement,

M different variations of geometry can be examined using the

same fluid properties.

The input data is punched on cards with the following

format

:

(1) All values will be in units of lbm , hr,feet, Btu, and °F.

(2) All values except M will be fixed pointnumbers and will have decimal noints.M is a floating ooint number.

(3) No commas are needed to separate the inputvalues on a single card.

CO The input values must be in the designatedcolumn but need not be right or left justi-fied.

-79-

(5) AH fixed point numbers can have upto four digits after the decimalpoint. :

(6) The fluid nroperties, unless speci-fied to be at a particular noint,are average values.

CARD

1

2

3

I|

5

6

7

8

9

15- 28 29- 42 43—56 57—72

TH 1 TH 2 TSAT ROWL

MUWL MUVW CPWL KWL

PHI PH2 PW1 PW2

CPH MUH ROH KH

COLUMN

1—14

DELHW

ROWV

MFRU

HFG

1—4

M

Identification name is columns 5 18

1—14

DIN DOUT S N

Same as card 6

Same as card 7

KMAT

This is repaeated M times

The output will appear with the identification name at the

top of the page and the following orlnted below it.

MASS FLOW RATE WORKING FLUIDMASS FLOW RATE HEATING FLUIDNUMBER OF TUBESINKER DIAMETER OP TUBESOUTER DIAMETER OF TUBESSPACING OF TUBES

(cont. overleaf)

-80-

LENGTH OP TUBESDROP IN PRESSURE WORKING FLUIDDROP IN PRESSURE HEATING FLUIDCOMPARITIVE COSTS

For each identification there will be a separate page,

-81-

B.2 LIST OF VARIABLES

AREA

COST

CPH

CPWL

CTB

cw

cwv

DELHW

DELPH

DELPW (1)

DELZ (1)

DELX

DEQ

DIN

DOUT

FXTT

GH

01/

HII

HFG

Heat transfer surface area in ft?

Cost of heat exchanger in dollars

Specific heat at constant pressure of heatingfluid in Btu/lbm °F

Specific heat at constant pressure of workingfluid as a liquid in Btu/lbm °F

Cost of the material for the tubes and shellin dollars

Cost of fabrication in dollars

Fabrication cost per tube In dollars

Change in ethalpy of working fluid in Btu/lbm

Change in pressure of heating fluid In lb/ft?

Frictional nressure drop of working fluidper segiment of exchanger in lb/ft?

Length of each segiment in feet.

Change in quality in each segiment

Equivalent diameter in feet

Inner diameter of tubes in feet

Outer diameter of tubes in feet

Reynolds number factor

Mass flow velocity of heating fluid Inlbj/hr. ft?

Mass flow velocity of working fluid Inlbm/hr. ft.3

Heat transfer coefficient of heating fluid inBtu/hr. ft 2 °F

Latent heat of evanoration in Btu/lb m

-82-

B.2 LIST OP VARIABLES (cont.)

HMAC

HW

IV

KH

KWL

M

HPRH

HFRW

MUH

MUWL

MUVW

N

PHI

PH2

PV/1

PW2

PRWL

REWL

ROH

ROWL

Heat transfer coefficient for macroconventiveeffect in Btu/hr. ft 2

. °F

Heat transfer coefficient for working fluidas a vapor is Btu/hr. ft 2

. °F

Two phase frictional multiplier

Thermal conductivity of heating fluid inBtu/hr. ft. °F

Thermal conductivity of working fluid as aliquid In Btu/hr. ft. °P

Number of groups of innut data

Mass flow rate of heating fluid in lbm/hr.

Mass flow rate of working fluid in lbm/hr.

Viscositv of heating fluid in lbm/hr. ft.

Viscosity of working fluid as a liquid inlbm/hr. ft.

Viscosity of working fluid as a vapor Inlbm/hr. ft.

Number of tubes in exchanger

Inlet pressure of heating fluid in lb/ft 2.

Outlet pressure of heating fluid in lb/ft 2.

Inlet nressure of working fluid in lb/ft 2.

Outlet pressure of working fluid in lb/ft 2.

Pradtl number of working fluid as a liauid

Reynolds number of working fluid as a liquid

Density of heating fluid in lbm/ft3

.

Density of working fluid as a liquid in lbm/ft

83-

B.2 LIST OF VARIABLES (cont).

ROWV Density of working fluid as a vapor In

'ill'lb^/ft 3

.

REH Reynolds number of heating fluid

S Spacing between tubes

TH1 Inlet temperature of heating fluid in °P

TH2 Outlet terroerature of heating fluid in P

TLF Tube length factor

TMF Tube material factor

TSAT Saturation temperature in °F

X Quality

XTT Martinelli parameter

U Overall heat transfer coefficient in Btu/hr. ft

Z Length of heat exchanger in ft.

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-87-

Appendix C. COUNTER FLOW HEATER HEAT EXCHANGER PROGRAM

C.l Instructions for Operation and Input

This Drogram is written in FORTRAN IV and can be run as is

on the Interdata computer of the Joint Civil and Mechanical

Engineering Computer Facility at M.I.T. The program can be run

on any computer facility that is designed with the ability to com-

pile FORTRAN IV. If run on a computer other than the Interdata,

some modifications may be required to the control, input and out-

put cards.

The input data is broken into two sections. The first sec-

tion contains eight input data cards. The first seven of these

cards contain the fluid properties and the eight is the number,

M, of input sets in the second section. The second section has

2M cards. The first card in each of these M sets serves as an

identification card. The second card has the data on the geometric

arrangement of the beat exchanger; DIN, DOUT, and S. With this

input arrangement, M different geometrical arrangements can be ex-

amined using the same fluid nroperties.

The input data is punched on cards as follows:

(1) All values will be in units of lb m , hr.

,

feet, Btu and °F.

(2) All values except M will be fixed pointnumbers and will have a decimal point. M isa floating noint number.

(3) No commas are needed to separate the inputdata on a single card.

-83-

(4) The input values must be in the desig-nated column but need not be right or leftjustified.

(5) All fixed point numbers can have up to 4

(four) digits after the decimal point.

(6) The fluid properties, unless specifiedto be at a particular point, are aver-age values. Any property that the lastfigure of its variable name is a numberis specified to be at that temnerature

.

COLUMN

1—12 13—-24 25—36 37—^8 49— 60

TH2 TW1 TW2

PW1 PW2 MUK

CPW ROH ROW

DCPW1 DCPW2 DCPW3

1—10 11—20 21—30 31—40 41—50 51—60 61—70 71—80

1 MFRW TH1

2 PHI PH2

3 MUW CPK

H KH KW

5 DCPH1 DCPH2 DCPH3 TW3 TH3 DMUV.'l DMUV72 DMUW3

6 DtfUHl DWJH2 DFUH3 DKW1 DKW2 DKW3 DKH1 DKH2

7 DKK3

1—4

DR0W1 DR0W2 DROV/3 DR0H1 DROH2 DROH3

8 M

5 - -18

9 Identification name

1— 12 13—24 25—36

Dili DOUT S

1 Same <is 9

2 Same <as 10

~hls repeats M time:

(cont. overleaf)

-89-

The output will appear with the Identification name at the

top of a page and the following printed below it.

MASS FLOW RATE WORKING FLUIDMASS FLOW RATE HEATING FLUIDNUMBER OF TUBESINNER DIAMETER OF TUBESOUTER DIAMETER OF TUBESSPACING OF TUBESLENGTH OF TUBESDROP IN PRESSURE WORKING FLUIDDROP IN PRESSURE HEATING FLUIDCOMPARITIVE COSTS

For each identification there will be a separate oage.

-90-

LIST OF VARIABLES

AREA

COST

CPH

CPW

CTB

cw

cwv

DIN

DOUT

DEQ

DPH

DPW

DTLM

D 1

D 2

D 3

GH

GW

KH

KW

LENGTH

Heat transfer area in ft 2.

Cost of heat exchanger in dollars

Specific heat at constant pressure of heatingfluid In Btu/lbm °F

SDecific heat at constant pressure of workingfluid in Btu/lbm °F

Cost of materials for shell and tubes in dollars

Fabrication costs in dollars

Fabrication costs per tube in dollars

Inner diameter of tubes In ft.

Outer diameter of tubes in ft.

Equivalent diameter in ft.

Frictional pressure dron in heating fluid inlb/ft 2

.

Frictional pressure droD of working fluid inlb/ft 2

.

Log mean temperature difference in °F

Property at temperature 1

Property

Property

at temperature 2

at temperature 3

Pass flow velocity of heating fluid in lbm/hr. ft 2.

Mass flow velocity of working fluid in lb^/hr. ft 2.

Thermal conductivity of heating fluid InBtu/hr. ft. °^

Thermal conductivity of working fluid inEtu/hr. ft. °F

Length of heat exchanger in ft.

-91-

LIST OP VARIABLES (cont).

MPRH Mass flow rate of heating fluid in lbm/hr

MPRW Mass flow rate of working fluid in lbm/hr.

MUH Viscosity of heating fluid in lbm/hr. ft.

MUW Viscosity of working fluid in lbm/hr. ft.

M Number of input data groups

N Number of tubes

PHI Inlet pressure of heating fluid In lb/ft 2.

PH2 Outlet pressure of heating fluid in lb/ft 2.

PW1 Inlet pressure of working fluid in lb/ft 2.

PW2 Outlet pressure of working fluid in lb/ft 2.

PART Terrroerature ratio

PRH Prandtl number of heating fluid

PRW Prandtl number of working fluid

REH Reynolds number of heating fluid

REW Reynolds number of working fluid

ROH Density of heating fluid in lbn/f

t

3.

ROW Density of working fluid in lb^/ft 3.

S Tube spacing

Till Inlet temperature of heating fluid in op

TH2 Outlet temnerature of heating fluid in °F

TH3 Intermediate temperature of heating fluid in F

pWl Inlet temperature of working fluid in °F

TW2 Outlet temnerature of working fluid in °P

TV/3 Intermediate temperature of working fluid in F

-92-

LIST OF VARIABLES (cont).

TW1 Inlet temperature of working fluid in F

TVJ2 Outlet temperature of working fluid in F

TV/3 Intermediate temperature of working fluid in F

TLF Tube length factor

IMF Tube material factor

XI X9 are grouped constants

XXL XX12 are grouped constants

X (J) Above properties for each segment of exchanger

-93-

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-99-

Appendix D. COUNTER-FLOW COOLER HEAT EXCHANGER PROGRAM

D.l Instructions for Oneration and Inputs

This program is written in PORTRAIT IV and can be run as Is

on the Interdata computer of the Joint Civil and Mechanical 'Engineering

Computer Facility at M.I.T. The program can be run on any com-

puter facility that Is designed to compile FORTRAN IV. If run

on a computer other than the Interdata, some modifications may

be required to the control, input and output cards.

The Input deck Is broken Into two sections. The first con-

tains eight input cards. The first seven cards contain the fluid

properties and the eighth is the number, M, of input sets in the

second section. The second section has 2M cards. The first card

of each set serves as an Identification card. The second card con-

tains the data on the geometric arrangement of the heat exchanger;

DIN, DOUT, and S. With this arrangement of the input data M differ-

ent geometrical arrangement can be examined using the same fluid

properties

.

The innut data Is ounched on cards as follov.'s:

(1) All values will be in units of lb n , hr.,

feet, Etu and °P

(2) All values except M will be fixed pointnumbers and will have a decimal noint.M is a floating point number

(3) No commas are needed to seoarate the innutdata on a sinr.le card

(*0 The input values must be in the desirnatedcolurrn but do not need to be rirht or leftjustified

-100-

EARD

1

2

3

4

5

6

7

10

11

12

(5) All fixed point numbers can have up to1 (four) digits after the decimal point.

(6) The fluid properties, unless specifiedto be that at a particular point, areaverage values. Any nroperty that the lastfigure of its variable name is a number isspecified to be at that temnerature.

COLUMN

1—12 13—21 25—36 37—^8 i| 9— 60

TCI TC2 TW1 TW2 PW1

PW2 PCI PC 2 MFP.V/ MUW

CPW MUC CPC KW KC

ROW ROC DCPW1 DCPVJ2 DCPW3

1—10 11—20 21—30 31—10 11—50 51—60 61 70 71—80

DCPC1 DCPC2 DCPD3 TW3 TC3 DWUV.'l DMUW2 DMUW3

DMUC1 DIOJC2 DMUC3

DKC3 DROW1 DROW2

1 1

M

5 18

Identification name

1—12 13—21 25—36

DIN DOUT S

Same as 9

Same as 10

DKW1

DROW3

DKV/2

DROC1

DKW3

DROW2

DKC1

DROVJ3

DKC2

• nese last tv/o cards are repeated fl times

(cont. overleaf)

-101-

The output will appear with the identification name at

the top of a page and the following printed below it.

MASS PLOW RATE WORKING FLUIDMASS FLOW 'RATE COOLING FLUIDNUMBER OF TUBESINNER DIAMETER OF TUBESOUTER DIAMETER OF TUBESSPACING OF TUBESLENGTH OF TUBESDROP IN PRESSURE WORKING FLUIDDROP IN PRESSURE COOLING FLUIDCOMPARITIVE COST

For each identification name there will be a separate page.

-102-

LIST OP VARIABLES

AREA

CPC

CPW

COST

CTB

CW

CWV

DIN

DOUT

DEQ

DPC

DPW

DTLM

D 1

D 2

D 3

GC

GW

KC

KW

LENGTH

Heat transfer area in ft 2.

Specific heat at constant pressure for coolingfluid in Btu/lbm °F

Soecific heat at constant pressure of workingfluid in Btu/lbm °F

Cost of heat exchanger in dollars

Cost of materials for shell and tubes in dollars

Fabrication costs in dollars

Fabrication costs per tube in dollars

Inner diameter of tubes in ft.

Outer diameter of tubes in ft.

Equivalent diameter in ft.

Frictional pressure drop of cooling fluid inlb/ft 2

.

Frictional pressure drop of working fluid inlb/ft 2

.

Log mean temperature in °F

Property at temperature 1

Property

Property

at temperature 2

at temperature 3

Mass flow velocity of cooling fluid in lbm/hr. ft 2.

Mass flow velocity of working fluid in lb„/hr. ft 2.

Thermal conductivity of cooling fluid inBtu/hr. ft. °F

Thermal conductivity of working fluid inBtu/hr. ft. °F

Length of heat exchanger in ft.

-103-

LIST OF VARIABLES (cont).

M

MPRC

MFRW

MUC

MUW

N

PCI

PC2

PW1

PV/2

PRC

PRW

PART

REC

HEW

ROC

ROW

S

TCI

TC2

TC3

TLF

TMP

Number of inputs data groups

Mass flow rate of cooling fluid in lb /hr.

Mass flow rate of working fluid in lbm/hr.

Viscosity of cooling fluid In lbn/hr. ft.

Viscosity of working fluid in lbm/hr. ft.

Number of tubes in exchanger

Inlet pressure of cooling fluid in lb/ft 2.

Outlet pressure of cooling fluid in lb/ft 2.

Inlet pressure of working fluid in lb/ft 2.

Outlet pressure of working fluid in lb/ft 2.

Prandtl number of cooling fluid

Prandtl number of working fluid

Temperature ratio

Reynolds number of cooling fluid

Reynolds number of working fluid

Density of cooling fluid in lbm/ft3

.

Density of working fluid in lbm/f

t

3.

Spacing of tubes

Inlet temnerature of cooling fluid in °P

Outlet temperature of cooling fluid In °F

Intermediate temperature of cooling fluid in °F

Tube length factor

Tube material factor

-10'!-

LIST OP VARIABLES (cont).

TV/1 Inlet temperature of working fluid in P

TW2 Outlet temperature of working fluid in °F

TW3 Intermediate temperature of working fluid in °F

XI X9 are grouped constants

XXI XX12 are grouped constants

X (J) Above properties for each segment of exchanger

-105-

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-112-

Appendix E. CROSS-PLOW HEATER MEAT EXCHANGER PROGRAM

E.l Instruction for Operation and Inputs

Written In FORTRAN IV, this program is designed to be run

on the Interdata computer of the Joint Civil and Mechanical

Engineering Computer Facility at M.I.T. With modifications in

the control, Input and output cards, this program can be run on

any computer that is designed to compile FORTRAN IV.

The first three cards of the input data are used for proper-

ties of the fluids. Ten cards are then needed to input the ten

bt ten matrix F. The nest card contains a single number, M.

This is the number of geometric arrangements that will be examined.

The input cards that follow are in two card sets. The first of

these contains an Identification name, the second has the data on

geometric arrangement, DIN, DOUT, S, N, and KMAT. With this in-

put arrangement, M different geometric arrangements can be ex-

amined with the same fluid properties.

The input data is punched on the cards as follows:

(1) All values will be in the units oflbm , hr. , feet, Btu, and °F

(2) All values except M will be fixed pointnumbers and will have a decimal point.M is a floatinr point number.

(3) No commas are needed to separate theinput data on a single card.

(*0 The Input values must be in the desig-nated columns but do not need to beright or left Justified.

-113-

(5) All fixed point numbers can have up to4 (four) digits after the decimal point.

(6) The fluid properties are average valuesof these properties over the temperaturerange

.

ARD COLUMN

1—12 13-•2k 25—•36 37—-48 49— 60 61—70

1 MFRW TWH TWC TKH THC PHI

2 PII2 PW1 PW2 CPW CPH MUW

3 MUH KW KH ROH ROW

Cards 4 through 13 contain values of the matrix F

Theses values are Dunched 10 to a card with six columns per value

1—4

14 M

5 18

15 Identification name

1—12 13— 24 25—36 37—48 49— 60

16 Dili DOUT S N KMAT

17 Same as 15

18 Same as 16

These last two cards are repeated M times

The output will appear with the identification name at the

top of a page and the following printed below it:

(cont. overleaf).

-114-

MASS PLOW RATE WORKING FLUIDMASS PLOW RATE HEATING FLUIDNUMBER OF TUBESINNER DIAMETER OF TUBESOUTER DIAMETER OF TUBESSPACING OF TUBESLENGTH OF TUBESDROP IN PRESSURE WORKING FLUIDDROP IN PRESSURE HEATING FLUIDCOHPARITIVE COSTS

For each identification nar.e there will be a separate page

-115-

E.2 LIST OF VARIABLES

AREA

COST

CPH

CPW

CTB

bw

cwv

DIN

DOUT

DLPH*

EC

F

GH

GW

HH

HW

KH

KW

lei;gth

M

MFRH

*DTLM

Keat transfer area in ft .

Cost of exchanger in dollars

Specific heat at constant pressure of heatingfluid in Btu/lbm °F

Specific heat at constant Dressure of workingfluid in Btu/lb °F

m

Cost of materials for shell and tubes in dollars

Fabrication costs in dollars

Fabrication costs per tube in dollars

Inner diareter of tubes in ft.

Outer diameter of tubes in ft.

Frictional pressure dron in lb/ft 2.

Keat exchanger effectiveness

Mean temoerature difference ratio

Mass flow velocity of heating fluid in lbm/hr. ft 2

Mass flow velocity of working fluid in lb /hr. ft?

Keat transfer coefficient of heating fluid inEtu/hr. ft 2

,o^

Keat transfer coefficient of working fluid inBtu/hr. ft 2

. °F

Thermal conductivity of heating fluid inBtu/hr. ft 2

, o^

Thermal conductivity of v;orking fluid inBtu/hr. ft. °F

Length of heat exchanger in ft.

Number of input data grouos

Mass flov; rate of heating fluid in lbrn/hr.

Log mean ternerature difference in °F

-116-

LIST OF VARIABLES (E.2) (cont).

MFRVJ Mass flow rate of working fluid In lbm/hr

MUH Viscosity of heating fluid in lbm/hr. ft.

MUW Viscosity of working fluid in lbm/hr. ft.

N Number of tubes

PHI Inlet pressure of heating fluid in lb/ft 2.

PH2 Outlet pressure of heating fluid in lb/ft 2.

PV/1 • Inlet pressure of working fluid in lb/ft 2.

PK2 Outlet pressure of working fluid in lb/ft 2.

PP.H Prandtl number of heating fluid

PRW Prandtl number of working fluid

Heat transfer rate in Btu/hr.

RE II Reynolds number of heating fluid

FEW Reynolds nuirber of working fluid

ROH Density of heating fluid in lbm/Tt3

.

ROW Density of working fluid in lbn/f

t

3.

S Tube snacing

THC Cooler temperature of heating fluid in °F

THH Hotter temnerature of heating fluid in °F

TVJC Cooler temperature of working fluid in °F

TWH Hotter temperature of working fluid in °F

TLF Tube length factor

TP-T Tube material factor

U Overall heat transfer coefficient in Btu/hr ft 2 °F

Z Temperature coefficient

-117-

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-123-

Appendix F. CROSS-PLOW COOLER HEAT EXCHANGER PROGRAM

P.l Instructions for Operation and Inputs

Written in FORTRAN IV, this program is designed to be run

on the Interdata computer of the Joint Civil and Mechanical

Engineering Computer Facility at M.I.T. With modifications in

the control, input and output cards, this program can be run

on any computer that is designed to compile FORTRAN IV.

The first three cards of the input deck contain Droper-

ties for the fluids. The next ten cards are used to input the

ten by ten matrix F. A single number, M, is placed on the four-

teenth card. This is the number of geometric arrangements that

will be examined. The inout cards that follow are in two card

sets. The first of these two cards contains an identification

name. The second contains the data on the geometrical arrange-

ment of the exchanger, DOUT, DIN, ?, N, and KMAT. With this in-

put arrangement, M different geometric arrangements can be ex-

amined using the same fluid proDerties.

The input data is punched on cards as follows:

(1) All values will be in units of lbm , hr.

,

feet, Btu, and °F

(2) All values except M will have fixed nointnumbers and will have a decimal point.M Is a floating noint number

(3) No commas are needed to separate theinput data on a single card

CO The input values must be in the designatedcolumn but need not be right or left justi-fied

-12'l-

(5) All fixed noint numbers can have ut> to4 (four) digits after the decimal point,

(6) The fluid properties are average valuesaveraged over the temperature range

CARD COLUMN

1—12 13—24 25—36 37—^8 49—60 61—72

1 MPRW TCH TCC TWH TWC PCI

2 PC 2 PW1 PW2 CPW CPC MUC

3 MUW KW KC ROVJ ROC

Cards 4 through 13 contain values of the matrix F

These values are punched 10 to a card with 6 columns per value

1—4

14 M

5 18

15 Identification name

1—12 13—24 25—36 37—48 49—60

16 • DIN DOUT S N KMAT

17 Same as 15

18 Same as 16

These last two cards are repeated M times

The output will appear with the identification name at the

top of a page and the following printed below it:

MASS PLOW RATE WORKING FLUIDMASS FLOW RATE COOLING FLUIDNUMBER OF TUBESINNER DIAMETER OF TUBES

(cont. overleaf)

-125-

OUTER DIAMETER OF TUBESSPACING OF TUBESLENGTH OF TUBESDROP IN PRESSURE WORKING FLUIDDROP IN PRESSURE COOLING FLUIDCOTTARITIVE COSTS

For each identification name there will be a separate nage,

-126-

F.2 LIST OF VARIABLES

AREA

COST

CPC

CPW

CTB

cw

cwv

DIN

DOUT

DLPC

DTLM

EC

F

GC

GW

HC

HW

KC

KW

LENGTH

Heat transfer surface area in ft 2.

Cost of exchanger in dollars

Specific heat at constant pressure of coolingfluid in Btu/lb °Fm

Specific heat at constant pressure of workingfluid in Btu/lbm

ov

Cost of materials for shell and tubes in dollars

Fabrication costs in dollars

Fabrication costs per tube in dollars

Inner diameter of tubes in ft.

Outer diameter of tubes in ft.

Frictional pressure drop of cooling fluid inlb/ft 2

.

Log mean temperature difference In °F

Heat exchanger effectiveness

Mean temperature difference factor

Mass flow velocity of cooling fluid in lb^/hr. ft 2.

Mass flow velocity of working fluid in lb m/hr. ft 2.

Heat transfer coefficient of cooling fluid inBtu/hr. ft 2

. °F

Heat transfer coefficient of working fluid InBtu/hr. ft 2

. °F

Thermal conductivity of cooling fluid InBtu/hr. ft. °F

Thermal conductivity of working fluid inBtu/hr. ft. °F

Length of heat exchanger in ft.

-127-

F.2 LIST OF VARIABLES (cont).

M Number of input data groups

N!FRC Mass flow rate of cooling fluid in lbm/hr.

MFRW Mass flov; rate of working fluid in lbm/hr.

MUC Viscosity of cooling fluid in lbm/ft.

MUW Viscosity of working fluid in lbm/ft.

N Number of tubes

PCI Inlet pressure of cooling fluid in lb/ft 2.

PC2 Outlet pressure of cooling fluid in lb/ft 2

PW1 Inlet pressure of working fluid in lb/ft 2.

PVJ2 Outlet pressure of working fluid in lb/ft 2

PRC Prandtl number of cooling fluid

PRW Prandtl number of working fluid

Q Heat transfer rate in Btu/hr.

REC Reynolds number of cooling fluid

REV/ Reynolds number of working fluid

ROC Density of cooling fluid in lbm/f

t

3.

ROW Density of working fluid in lbm/f

t

3.

S Tube spacing

TCC Cooler temperature of cooling fluid in F

TCH Hotter temperature of cooling fluid in F

TWC Cooler tenroerature of working fluid in F

TWH Hotter temperature of working fluid in °F

TLF Tube length factor

-128-

F.2 LIST OF VARIABLES (cont).

TMF Tube material factor

U Overall heat transfer coefficient in Btu/hr. ft 2. °F

Z Temperature coefficient

-129-

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-133-

Appendix G - EXAMINATION OF THE ZENER CYCLE

G.l Examination

To examine the usefulness of the computer progrmas de-

veloped, the thermal cycle proposed by Prof. Clarence Zener(l)

was examined. The program for designing condensers and the

program for evaporator design were used.

In his proposal, Zener suggests the use of ammonia as

the working fluid. The condensor and the evaporator for this

cycle were designed using ammonia and freon-21 as working fluids

.

Because of its high latent heat of vaporization about 5^0 Btu/lb m ,

ammonia requires a much larger heat exchanger for evaporation

than does freon-21 with a latent heat of vaporization of 102 Btu/lb n<

This difference in size can be seen in figures G-l, G-2 and G-3.

The properties of Zener's proposed cycle, as given In Ref. 1,

were used as InDuts to the computer programs . The allowable

pressure drop over the length of the condenser and evaoorator

was used as a constraint on the size of the exchangers. An

inner diameter of h inch was used as a starting diameter. If

this diameter caused a frictional pressure drop greater than

the allowed pressure droo, the diameter of the tubes was In-

creased and the heat exchanger redesigned.

In the condenser design, two values of the coefficient of

heat transfer for condensation were used. The program was first

run with the coefficient being calculated as discussed In section

-13^-

2.3. The design was then revised using a coefficient of

800 Btu/hr-ft 2 - °F. This is the value thatGregorig( 33) ob-

tained using fluted tubes. This is further discussed in sec-

tion 2.5. Zener in his proposal suggested the use of this tyoe

of surface to increase the heat transfer coefficient.

The two programs were run with the variation mentioned

above and with different geometries. - The size of the heat ex-

changers required for these different arrangements were then

calculated.

G.2 Results

The condensor was sized using different numbers of tubes.

The resultant required length of heat exchanger for each differ-

ent number of tubes are olotted in Figure G-l. As there is a

significant improvement in reducing the size of the required

condensor with the use of Oregorig surfaces, it is that size

that is plotted. Plotted on Figure G-l are the results for

both ammonia and freon-21. The minimum allowable diameter of

the tubes for each given number of tubes is also plotted.

Figure G-2

.

The evaporator was sized In the same manner as the con-

denser. Zener suggests the use of surface enhancement for the

evaporator also. However, with the high mass flow rate surface,

enhancement appears to be of little advantage. The required

length for the evaporator with the use of both ammonia and

freon-21 is plotted in Figure G-3.

-135

1500 -

1250

1000

•p

©

a•H

Si•p

750

5 00

250

25000 50000 75000 100000Number of Tubes

Figure G-l

Zener Cycle Condenser iiumber of Tubes versLength

-136-

6 -

5 -

po

•H

W

EH

O

U<DP©sa

•H

25000 50000 75000Number of Tubes

100000

Figure G-2

Zener Cycle Condenser ifumber of Tubes versTube -Diameter

-137-

1500 •

1250--

100$

Ammonia

-p

<D

©

si-ptoa©J

7 50-

5 00

2 50i

0.75000 100000Number of Tubes

25000 50000

Figure G-3

Zener Cycle Evaporator Number of Tubes versLength

-138-

G.3 Conclusions of the Zener Proposal

The use of ammonia as a working fluid in this cycle apnears

to be totally unrealistic. The minimum size requirement for

the evaporator would amount to over thirty billion cubic feet

with a length of over four thousand feet. The condenser using

fluted tubes would be a great deal smaller, but still is over

one billion cubic feet in total volume.

Freon-21 is a much better working fluid for these heat ex-

changers. The reduction in latent heat required to vaporize

the working fluid reduces the size requirement of the evaoorator.

Still the total volume required for the evaporator is two billion

cubic feet. The condenser for a freon-21 system would be over

three hundred million cubic feet in volume.

The sizes of the above mentioned heat exchangers would

be for production of 100 Mega-watts of electrical power. This

is not an extremely large power plant by today's standards in

terms of power output

.

From a thermodynamic point of view, this cycle is a feasible

one. However, when the size of the required heat exchangers is

taken into account, the cvcle quicklv appears to be unrealistic.

V/ith a temperature difference of only two degrees Centigrade, in

the evaporator, the mass flow rate is so great that the cycle

is unusable.

-139-

AUG7S28 JUN767 6 0CT76

2 2 U 6 5

2 3 8*0

Thesis

J224

1 L3128Jackson

Heat exchanger design

for thermal cycle feasi-

bility evaluation.

1 SPLAY, 7 SEP 74 22U65

AUG7 -! 22865'28 JUN76 It" n•>6 0CT7fi

23860

ThesisJ224

1 C>11J J l^i

JacksonHeat exchanqer design

for thermal cycle feasi-

bility eval uation.

thesJ224

Heat exchanger design for thermal cycle

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