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1968-5

The Enrichment of Hydro-Carbon Fuel byAluminum Powder in an Open-Hearth FurnaceRick Sung-tao LeeBrigham Young University - Provo

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BYU ScholarsArchive CitationLee, Rick Sung-tao, "The Enrichment of Hydro-Carbon Fuel by Aluminum Powder in an Open-Hearth Furnace" (1968). All Thesesand Dissertations. 7144.https://scholarsarchive.byu.edu/etd/7144

0 2

[ r /X

T H E E N R IC H M E N T OF H Y D R O -C A R B O N F U E L

BY A LU M IN U M PO W D ER IN ANr) /

O P E N - H E A R T H F U R N A C E . ✓ ^V

A T h e s i s

P r e s e n t e d to the

D e p a r t m e n t of M e c h a n i c a l E n g i n e e r i n g

B r i g h a m Young U n i v e r s i t y

In P a r t i a l F u l f i l l m e n t

of the R e q u i r e m e n t s f o r the Degree-

M a s t e r of S c i e n c e

by

R i c k S u n g - t a o L e e

May, 1968

This t h e s i s , by Rick S ung- tao L e e , is a c c e p t e d in i t s p r e s e n t

form by the D epar tm en t o f M e c h a n ic a l Engineer ing of Brigham Young

U n iv e r s i ty a s s a t i s fy in g the t h e s i s req u i rem en t for the deg ree of

M a s t e r of S c i e n c e .

Jan u a ry 1968

Typed by N ancy D, Gardner

DEDICATION

To My Parents

ACKNOWLEDGMENT

The au thor w i s h e s to e x p r e s s h i s a p p re c ia t io n

to Dr. John N . Cannon for his c o u n s e l in g and a d v i c e .

The t e a c h in g s of the f acu l ty members of th e M e c h a n ic a l

Engineer ing .Department are a l so much a p p r e c i a t e d .

TABLE OF CONTENTSPage

APPROVALS------------------------------------------------------------------------------------- i i

ACKNOWLEDGMENT---------------------------------------------------------------------- iv

LIST OF TABLES----------------------------------------------------------------------------- v i i

LIST OF FIGURES--------------------------- v i i i

NOMENCLATURE--------------------------------------------------------------------------- ix

CHAPTER

I. INTRODUCTION------------------------------------------------------------------- 1

O b j e c t i v e s ---------------------------------------------------------------------- 2Background---------------------------------------------------------------------- 2

II . ANALYTICAL METHODS FOR ESTIMATING OPEN-HEARTHFURNACE HEAT TRANSFER----------------------------------------------------- 4

A ssu m p t io n s ---------------------------------------------------------------------- 5Time Required for a H e a t --------------------------------------------------- 6A d iaba t ic Flame Tempera ture-------------------------------------------- 9Film C o ef f ic ien t for C o n v ec t iv e H ea t T ran s fe r ----------------- 9Total E m iss iv i ty for Radiative H ea t T rans fe r------------------ 11N o n -d im e n s io n a l i z e d Method U se d in Es t im a t ing the Costs! 3Summary of Assumptions M a d e i n This S tudy-------------------- 13

III. RESULTS--------------------------------------------------------------------------------- 15

Time Required Per H e a t ----------------------------------------------------- 16C o s t R a t io s ----------------------------------------------------------------------- 18Ef f ic iency of the Fu rnace -------------------------------------------------- 31

IV. DISCUSSION OF RESULTS----------------------------------------------------- 32

On C o s t --------------------------------------------------------------------------- 33On E f f ic iency ------------------------------------------------------------------ 35

V. CONCLUSION AND RECOMMENDATIONS----------------------------- 37

C o n c l u s i o n s --------------------------------- 38Recom m enda t ions -------------------------------------------------------------- 39

v

Page

APPENDICES----------------------------------------------------------------------------------- 40

I . COMPUTER PROGRAM I (C a lcu la t ion of Pe rcen tag eW eig h t o f F u e ls ) ------------------------------------------------------------ 41

II. COMPUTER PROGRAM II (To Find an Upper Bound of hand for a S tandard H e a t ) -------------------------------------- 42

III . COMPUTER PROGRAM III (To Find the Time for a H e a t ) - - 44

IV. TABLE I . SETS OF CORRESPONDING VALUES OF h ande # FOR A STANDARD HEAT-------------------------------------------- 4 6

V. TABLE II. PERCENTAGE WEIGHT, ADIABATIC FLAMETEMPERATURE, TOTAL EMISSIVITY OF FUELS-------------- 4 7

VI. PLATE: THREE-DIMENSIONAL ADIABATIC FLAMETEMPERATURE PHOTOGRAPH-------------------------------------------- 50

VII. - X I . FIGURES OF ADIABATIC FLAME TEMPERATURE FOR0% AL, 257cAL, 507cAL, 757cAL, AND 100%AL--------------------5 1 -5 5

XII. DERIVATION OF FORMULAS FOR CALCULATING THEEFFICIEN CIES---------------------------------------------------------------------- 5 6

LIST OF REFERENCES------------------------------------------------------------------------- 58

ABSTRACT

vi

LIST OF TABLES

TABLE Page

1. Time Per H e a t ------------------------------------------------------------------ 17

2 . C o s t R a t io s ' a n d E f f i c i e n c i e s ------------------------------------------- 19

3 . C o s t Ratios and E f f i c i e n c i e s --------------------------------------------- 21

4 . Se ts of C or re spond ing Values of h and for aS tandard H e a t -------------------------------------------------------------- 46

5. P e rc e n tag e W e ig h t o f Fue ls , Adiabatic Flame Tempera ture ,Total Ern iss iv i ty ----------------------------------------------------------- 47

LIST OF FIGURES

Figure Page

1. Step In c r e a s e of the Bath Tempera ture and the TimeRequired for a H e a t --------------------------------------------------- 7

2 . Adjus tment of h for a g iv e n v a lu e o f ---------------------- 11

3 . ^ - T e m p e r a t u r e of Suspend ing P a r t i c le s in a F lam e— 12

4 . , C o s t Ratio (a)---------------------------------------------------------------- 23

5 . C o s t Ratio (b)--------------------------------------------------------- 24

6. C o s t Ratio (c)---------------------------------------------------------------- 25

7 . C o s t Ratio (d)---------------------------------------------------------------- 2 6

8. C o s t Ratio (e)---------------------------------------------------------------- 2 7

9 . C o s t Ratio (f)---------------------------------------------------------------- 2 8

10. C o s t Ratio (g)---------------------------------------------------------------- 2 9

11. C o s t Ratio (h)---------------------------------------------------------------- 30

12. A d iaba t ic Flame Tempera ture for 0% AL-------------------------- 51

13. A d iaba t ic FlameTemperature for 25% AL------------------------- 52

14. Ad iaba t ic Flame Tempera ture for 50% AL------------------------ 53

15. Ad iaba t ic Flame Tempera ture for 75% AL------------------------ 54

16. A d iaba t ic Flame Tempera ture for 100% AL----------------------- 55

v i i i

NOMENCLATURE

A: Area over which c o n v e c t iv e h e a t t r a n s f e r t a k e s p la c e

AL: Aluminum

%AL: Percen t aluminum

Cp: C o n s ta n t p r e s su re s p e c i f i c h e a t o f s t e e l

COST w/AL: C o s t with Aluminum en r ichm en t

COST w/oAL: C o s t w i thou t aluminum en r ichm en t

F/A: Fuel' a i r ra t io

FrH l : Firing ra te for a s tan d a rd h e a t

FrH2: Firing ra te with AL enr ichm ent

FrA: Firing ra te o f AL

ga l : ga l lo n s

h : film c o e f f i c i en t for c o n v e c t iv e h e a t t r a n s fe r

h: r e p r e s e n ta t i v e film c o e f f i c i en t

H / C : h y d ro -ca rb o n fue l

lb s : pounds

m: m a ss o f molten s t e e l in a v e r ag e cube

Min: Time requ ired per h e a t , in minu tes

q: h e a t t r an s fe r r a te

Qin: H e a t energy r e l e a s e d from fuel

Q out:

Q H / C :

H e a t t rans fe r red to the s t e e l

H e a t energy r e l e a s e d from H /C fuel

ix

Q H / C :

Q AL: H e a t energy r e l e a s e d from aluminum powder

Adiabat ic Flame tem pera tu re

Bath t e m p e ra tu re , or the a v e r a g e ba th t em pera tu re during the t ime in t e rv a l A t , w h ich c a n be t a k e n to be Tb l + Tlb2

Bath tem pera tu re a t the b eg inn ing of the t ime in te rv a l A t

Bath tem pera tu re a t the end of the t ime in te rv a l A t

Tapping tem pera tu re w h ich i s t a k en to be (1600°C or 3372°R, See Ref. 1, p . 133)

t: t ime in t e rv a l

e :

3- •

? :

e m is s iv i ty of the flame

S te fa n -B o l tz m a n n 's C o n s t a n t

form fac to rA H ea t t r a n s fe r re d to s t e e l

e f f i c i e n cy of furnace H ea t r e l e a s e d from fue l

x

CHAPTER I

INTRODUCTION

CHAPTER I

INTRODUCTION

O bjec t ive

The o b je c t iv e of th is t h e s i s w as to s tudy th e o r e t i c a l l y the

en r ichm en t of hydroca rbon fue ls w i th aluminum powder for an

o p e n - h e a r t h f u r n ac e .

The eco n o m ics of such an en r ichm ent program w a s s tu d i e d to

ob ta in n o n -d im e n s io n a l i z e d r e s u l t s . The q u e s t i o n o f fur ther s tudy

of aluminum en r ich m en t w as to be exam ined .

Background

There a re two types of o p e n - h e a r t h f u r n ac e , b a s i c type and

a c id ty p e , depend ing on the l ining of the fu rnace w a l l s . The func t ion

of the o p e n - h e a r t h fu rnace is to conver t v a r io u s ty p es of fen 'ous

m a te r i a l s in to f in i sh e d s t e e l of g iven com pos i t ion and q u a l i t y . The

p r o c e s s e s occu r in g in the furnace can be c o n s id e r e d as a s e q u e n c e

invo lv ing m e l t ing , re f in ing and d e o x id a t io n . With som e ty p e s o f l iq u id -

m eta l c h a r g e , the melt ing s t a g e i s not p r e s e n t , bu t re f in ing and

d e o x id a t io n in va ry ing d e g re e s a re fundam enta l f e a tu re s of the p r o c e s s .

In the o p e n - h e a r t h fu r n a c e , the g a s e o u s fue l and the a i r are

p re h e a te d before entry to the fu rnace by the ou tgo ing p roduc ts o f

c o m b u s t io n . Thus ve ry s u b s t a n t i a l fue l eco n o m ics are a c c o m p l i s h e d .

- 3 -

A lso , i t i s p o s s i b l e to o b ta in h ig h e r f lame tem pera tu re than i s the

c a s e w i th o u t th is p re h e a t in g .

O ne of the most important problems in o p e n - h e a r t h s t ee lm ak in g

i s th a t of the t r a n s fe r of h e a t from the burning fue l to the m e ta l l i c

c h a r g e . This f ac to r has a g re a t in f lu en c e upon the d e s ig n of the

modern f u r n ac e . Various fuels h a v e b e e n t r ied and u s e d w i th va ry ing

d e g r e e s o f s u c c e s s . The a d v an ta g e of l iqu id fue ls l i e s p r inc ipa l ly in

the f a s t e r fir ing ra te p o s s i b l e , thus more en e rg y can be l ibe ra ted in

a g iv e n t i m e .

There a re many a d v a n ta g e s in reduc ing the t ime per h e a t . The

ove rh ead in ope ra t ing the fu rnace can be g re a t ly r e d u c e d . The p roduc ­

tion in a g iv en period of t ime c a n be i n c r e a s e d , thus a q u ic k e r r e s p o n s e

to chang ing demand for s t e e l c a n be made. But the o v e ra l l c o s t r e d u c ­

tion d e p e n d s on the fuel u s e d and the t ime thus s a v e d .

\

CHAPTER II

ANALYTICAL METHODS FOR ESTIMATING

OPEN-HEARTH FURNACE HEAT TRANSFER

CHAPTER II

ANALYTICAL METHODS FOR ESTIMATING OPEN-HEARTH FURNACE HEAT TRANSFER

Assum pt ions

The com plex i ty o f w h a t i s h a p p en in g in the o p e n - h e a r t h furnace

makes i t d i f f i cu l t to a n a ly z e the a c t u a l s i t u a t io n by k eep in g t r a c k o f the

e x a c t f lu id m e c h a n ic s and h e a t t r an s fe r p r o c e s s e s in o p e ra t io n e v e r y ­

w h e r e . The co n d i t io n s w i th in the fu rnace v a ry from poin t to po in t

making i t n e c e s s a r y to know a g r e a t d e a l a b o u t the fu rnace lo c a l c o n d i ­

t i o n s . With c e r t a in a s s u m p t i o n s , a n a l y s i s c an b e made if we would

a c c o u n t for the lo c a l c ond i t ions by some a v e r ag e or r e p r e s e n t a t i v e

l o c a l c o n d i t io n . This average or r e p r e s e n t a t i v e cond i t io n could be

thought to app ly to an "Average Cube" in a "S tandard B a th ."

U nder s to ic h io m e t r i c z e r o - p e r c e n t a luminum en r ichm en t c o n d i ­

t i o n , i t t a k e s approx im a te ly e igh t hours for a 2 0 0 - to n o p e n - h e a r t h

fu rnace to c o m p le te a h e a t . This e i g h t - h o u r h e a t for a 2 0 0 - to n

c a p a c i t y o p e n - h e a r t h w i l l be c a l l e d the "S tandard Heat" in th i s t h e s i s .

The ba th o f molten s t e e l in a "S tanda rd Heat" i s d e f in e d a s "S tanda rd

Bath" h e r e . Fur thermore , a r e c t a n g u la r cube of mol ten s t e e l w i th the

d im e n s io n of 12" x 12" x 1 6 . 3 " * in the "S tandard Bath" is c a l l e d an

"Average Cube" in th is t h e s i s . The co nd i t ion of th is "Average Cube"

i s made r e p r e s e n t a t i v e o f the w h o le b a th .

The f i r s t two f ig u r e s , 12" x 12", are c h o s e n to make the "Average Cube" to h a v e a f ace of u n i t a rea of one s q u a r e foot. The third f igure 1 6 .3 " i s the dep th of a furnace of 20.0 tons c a p a c i t y .

- 6 -

Time Required for a H e a t

The h e a t t r an s fe r red from the c o m b u s t io n p roduc ts to the charge

in c lu d e s c o n v e c t iv e h e a t t r an s fe r and r a d i a t i o n h e a t t r a n s fe r , w h ich c a n

b e e x p r e s s e d by the fo llowing ra te e q u a t io n :

q = hA (Taf - Tfa) + 6 e $ h (Ta f4 - Tb4)---------- (1)

Assuming th a t the fir ing r a t e is s u c h th a t th e re is no s ig n i f i c a n t

drop in flame tem pera tu re during the h e a t t r a n s f e r p r o c e s s , then the

a d ia b a t i c f lame tem pera tu re in the above e q u a t io n i s f ixed for a s p e c i f i c

2F/A and p e rc en t a luminum. The a rea A is f ixed to b e 1 ft . by the

a s s u m p t io n of the a v e r ag e c u b e . H o w ev e r , the b a th tem pera ture is

a lw ay s r i s in g a s the s t e e lm a k in g p r o c e s s g o e s o n . H e n c e , the above

e q u a t io n can on ly d e s c r i b e the h e a t t r a n s f e r s i t u a t i o n a t a sp e c i f i c

i n s t a n t .

Assuming th a t the b a th t em pera tu re i n c r e a s e s s t e p by s t e p ,

w i th ve ry sm a l l t ime in t e rv a l for e a c h s t e p , the t ime requ ired for a

h e a t c a n be found w h e n the ba th tem pera tu re r e a c h e s the tapp ing tem­

pe ra tu re as shown in Fig . 1.

- 7 -

Fig. 1— Step in c r e a s e of the ba th tem pera tu re and t ime requ i red for a h e a t .

If the t ime in t e rv a l i s A t , an energy b a l a n c e on the "Average Cube"

g iv e s :M Cp (T - T )

b^ b l _ 4 4-------- = h (Ta f - Tb ) + & (T_c - T )-

A t

If we deno te :

M Cp

af (2 )

C = A t

C^ = h , w here a ba r o ve rhead means r e p r e s e n t a t i v e v a lu e

c3 = Si§then e q u a t io n (2) b e co m e s :

C 1 <Tb2 - V " C 2 'Ta f + C 3 [ TJ - < i f -

w here is t a k e n a s the a v e r ag e ba th t em p e ra tu re during t ime A t .

(3)

2

- 8 -

Equat ion (3) i s a fourth order n o n l in e a r polynomia l in Tb2

For the f i r s t s t e p - i n c r e a s e o f the b a th t em pe ra tu re T , the i n i t i a lb

b a th tem pe ra tu re i s e q u a l to the co ld c h a r g e t e m p e ra tu re , which

i s 530°R a t room tem p era tu re . For l a t e r s t e p s , the i n i t i a l ba th

t em pera tu re a t the beginning of the i n t e rv a l A t i s the f ina l b a th tem ­

pe ra tu re a t the end of the p rev ious s t e p . It is r e c o g n ize d th a t any

true o p e n - h e a r t h ba th does not s t a r t a t 530° R, a s m o l ten pig iron is

o f ten a d d e d , but for pu rp o ses of un i fo rm ity , 530°R w i l l be u s e d for

c a l c u l a t i n g p u r p o s e s .

After expand ing the above equa t ion and r e g ro u p in g , w e g e t the

fo l lowing :

W here

Tb 2 4 + K3Tb 2 3 + K 2Tb22 + K l Tb 2 - K = 0

[(C!

K1 - 4Tb l 3 +

K2 = 6Tb i 2

K3 = 4Tb l

C 2 ) Tb l Tb I 4 +

C 3 2

------------- (4)

C 2T £ + C 3 Tj 4]

The above polynomia l c a n be s o lv ed by com pu te r (see Appendix II,

III), app ly ing the Method of Fa lse P o s i t io n .

Let F (T) = T4 + K3 T3 + K2 T2 + - K

t h e n , the i t e ra t io n formula i s :

Tb2 = Tb l U t 22) - T22 F (Tb l )

F (T22) - F (T ) b l

- 9 -

W h ere T ^ i s a lw ay s r i s in g a s the s t e p - i n c r e a s e o f b a th tem ­

pe ra tu re g o e s o n , u n t i l i t r e a c h e s the tapp ing t e m p e ra tu re . The to ta l

t ime r e q u i r e d , t h a t is the sum m at ion of the t ime for a l l i n t e r v a l s ,

i s the t ime for a h e a t .

A d iaba t ic Flame Tempera ture

The a d i a b a t i c f lame tem pera tu res w ere c a l c u l a t e d v ia a com pute r

program p rep a red by NASA. The method for com pute r c a l c u l a t i o n is

d e s c r ib e d in d e t a i l iii NASA TN. D -132 (Ref. l ) . The c a l c u l a t i o n s for

the input d a ta w e re a c c o m p l i s h e d w i th th e aid of Compute r Program I

(see Appendix I) . The r e p r e s e n t a t i v e fue l w a s taken to be C cH 0 , w i tho o

a s p e c i f i c g rav i ty of 0 .9 8 6 1 and a ne t h e a t in g v a lu e of 14 4 ,9 0 0 B tu /g a l .

Tabular r e s u l t s of the c a l c u l a t i o n s for a d i a b a t i c f lame tem pera tu res

and the p e rc e n ta g e w e ig h t o f fue ls c a n be found in Appendix V. The

f igu res and a pho tograph of a d i a b a t i c f lame te m p e ra tu re s for v a r io u s

p e r c e n ta g e s aluminum c an be found in Appendix VI to XI.

Film C o e f f i c i en t for C o n v e c t iv e H e a t Transfer

Very few a n a l y t i c a l s t u d i e s h a v e b e en made on finding the c o n ­

v e c t i v e fi lm c o e f f i c i e n t w h ich can be ap p l ie d to the o p e n - h e a r t h h e a t

t r a n s fe r p rob lem . The c o n v e c t iv e h e a t t r a n s f e r in an op en hea r th is

s im i la r to an impinging j e t d i r e c te d t a n g e n t i a l l y o v e r a f l a t p l a t e .

Zerbe and Selva (Ref. 3) had i n v e s t i g a t e d a true w a l l j e t w h e re the

i n i t i a l j e t t em pera tu re w a s g re a t e r than the am b ien t . They found an

em p i r ica l e q u a t io n for the c o e f f i c i e n t of h e a t t r a n s fe r to a f l a t s u r f a ce

from a p lane h e a t e d a i r j e t d i r e c t e d t a n g e n t i a l l y to the s u r f a c e . But

- 10 -

t h e i r eq u a t io n c a n be app l ied on ly to h e a t t r a n s fe r prob lems o f s u c h

a na tu re tha t the h e a t t rans fe r r a t e is s im i la r to t h a t requ i red for an

a i r c r a f t - w in d s h ie ld fog p re v e n t io n . As a r e s u l t , i t i s ou t of p l a c e to

ap p ly th e i r e q u a t i o n to an open h ea r th w h e re the h e a t t r a n s fe r r a te is

much la rger . M y e r s , Schauer , and E u s t i s h a v e done some work in

finding the film c o e f f ic ien t for c o n v e c t iv e h e a t t r a n s fe r for p lane tu rbu len t

w a l l j e t s . (Ref. 4 , 5 . ) But d i f f i cu l t i e s w e re e n co u n te re d w h en th is au thor

t r ied to in t e g r a t e the lo c a l film c o e f f i c i e n t o v e r the w ho le ba th to g e t the

av e rag e v a l u e of h .

Thus , th e film c o e f f ic ien t c an n o t be e a s i l y o b ta in e d from the

a n a l y t i c a l work a v a i l a b l e . But, w ith the in form at ion for a "S tandard

Heat" of e ig h t h o u r s , we can work b ack w a rd s to g e t a l imit ing v a l u e of the

c o n v e c t iv e film c o e f f ic ien t for th is s t a n d a r d h e a t a n d , t h u s , a s e r i e s of

v a l u e s in b e tw e e n .

W e a s s u m e tha t t h e s e film c o e f f i c i e n t s c a n b e ap p l ie d to the c a s e s

w i th aluminum e n r ich m en t . That is to w a y , w e a re a ssu m in g th a t the

v a l u e o f h does no t va ry s ig n i f i c a n t ly as a r e s u l t of aluminum e n r i c h ­

m en t , bu t is more a func t ion of g a s c o m p o s i t io n , h i s a l so tem pera tu re

d e p e n d e n t , bu t too l i t t le is known of th is phenom enon to u s e s u c h a

c o r re c t io n h e r e .

For zero p e rc en t aluminum and s to ic h io m e t r i c c o m b u s t io n , the

t ime requ i red for a 2 0 0 - to n ba th to r e a c h the tapp ing tem pera tu re from

it s i n i t i a l ch a rg e tem pera tu re is a s s u m e d to b e e ig h t h o u r s . W ith th is

a s s u m p t io n , we c a n a d ju s t the v a lu e of h (or in e q . 3) for a g iv e n

v a l u e o f u n t i l the t ime req u i red for the b a th t em pe ra tu re to r e a c h

- l i ­

the tapp ing tem pera tu re is e x a c t ly e igh t hours (see Fig. 2) . G iven a

s e r i e s of v a lu e s o f (for Cg in e q . 3) , w e g e t a s e r i e s of c o r r e s ­

ponding v a l u e s of "n th a t would make e igh t hours per h e a t .

W e can s e e from Appendix TV tha t w h en g e t s sm a l l e r and

s m a l l e r , h d o e s no t change much . This g iv e s us an upper bound for h .

Time

Total E m iss iv i ty for R adia t ive H e a t Transfer

B ecause of the t iny s u s p e n d e d p a r t i c l e s of a luminum ox ide in

the com bus t ion p r o d u c t s , the t o t a l e m is s iv i ty of the flame is g rea t ly

i n c r e a s e d . Ref. 2 prov ides a method w hereby e m is s iv i ty of m e ta l ized

flame c an be e s t i m a t e d . The l iquid p h a se o f t h e s e p a r t i c l e s h a s a much

la rger to t a l e m is s iv i ty than tha t o f the so l id p h a s e , as can be s e e n from

Fig. 3. The formula for c a l c u l a t i n g the number of p a r t i c l e s per s q u a r e ? ! x M f

foot i s : N l = ~ -— ------— £189 .2 x l 0 12J

Alu

min

um p

arti

cle

clou

d em

issi

vity

(T

otal

)- 12 -

Tempera ture (°R)

Fig. 3 — Temp, of s u sp e n d in g p a r t i c l e s in a f lame (Ref. 2)

- 1 3 -

V/here i is the i th component p a r t i c l e s , n i s the number of k inds of

p a r t i c l e s , M pi is the m olecu lar w e ig h t o f the i th com ponen t p a r t i c l e s ,*

and X j is the mole f rac t ion of the i th com ponen t p a r t i c l e . The to ta l

e m is s iv i ty c a l c u l a t e d for e ach aluminum en r ichm en t p e rc en t c a s e is

p r e s e n te d in Table II.

N o n -D im e n s io n a l i z e d Method U s e d in E s t im a t ing the C o s t s

A n o n - d im e n s io n a l i z e d method is u s e d in g e t t in g r e l a t i v e c o s t s

in o rde r to make the r e s u l t g e n e r a l so th a t i t w ould not be r e s t r i c t e d to

any s p e c i f i c fu rn ac e . This n o n - d im e n s io n a l i z e d method c a n a l s o red u ce

the e f fe c t s o f some v a r i a b l e s not in c lu d e d , which may be a par t o f both the

m e ta l i z e d a n d H / C only c a s e s . H e n c e , a c o s t ra t io i s u s e d . The ra t io is

t a k e n to be th e c o s t w ith aluminum en r ichm en t to the c o s t of a s tan d a rd h e a t .

So far a l l the c a lc u l a t i o n s are b a s e d on a fu rnace c a p a c i t y o f 2 00

t o n s , but the ra t io ing procedure e l im in a te s th is v a r i a b l e . As a c o n s e q u e n c e ,

the op t im a l F/A and %AL s t a y the sam e for fu rn aces of any c a p a c i t y .

The c o s t ra t io can be c a l c u l a t e d from the following equa t ion :

COST W/AL =COST W/oAL

(hrs . Per Heat) [(Overhead C os t ) + (Cost of H /C ) (Fr H2 ) + (Cost o f AL)(Fr^jf ( h r s . Per Standard Heat) [(Overhead C o s t ) + (C o s t o f H /C ) (FrH^)J~

w here F,-a c an be found from = (i - %AL) / %ALm ~ F p r

Summary o f Assumptions M ade in This Study

It is a s s u m e d tha t ( l) the whole ba th of m ol ten s t e e l is u nde r v io le n t

ag i ta t io n ; c o n s e q u e n t ly the ba th tem pera tu re i s e v e n th roughout . This is *

* This i s an e x t e n s io n of the d a ta in Ref. 2 in th a t i t is a s s u m e d th a t a l l p a r t i c l e s a c t s im i la r to ALgO a t h igh t e m p e ra tu re .

O

- 1 4 -

a im o s t the a c t u a l c a s e . H e n c e , i t is a good a s s u m p t i o n . As a r e s u l t ,

the cond i t io n o f the w h o le ba th c a n be r e p r e s e n t e d by a n a v e r ag e b lock

of molten s t e e l , w i th a s id e of u n i t a rea fac ing th e f lam e , and is c a l l e d

a "S tan d a rd Cube ;" (2) the v a lu e s o f h and 6 ? u s e d r e p r e s e n t a v e r ag e

v a l u e s ove r the s u r f a c e of the ba th ; (3) the c o n v e c t iv e film c o e f f i c i e n t s

found from the " e i g h t - h o u r s t a n d a r d hea t" c a n be a p p l i e d to the c a s e s

w i th a luminum e n r i c h m e n t . That is to s a y , the v a l u e o f IT d o e s not va ry

s ig n i f i c a n t ly w i th v a ry in g a d i a b a t i c f lame tem pe ra tu res for each c a s e ,

or p a r t i c l e load ing ; (4) the ba th t em pera tu re r i s e can be r e p r e s e n te d by

in f in i te ly many sm a l l s t e p s ; (5) the fir ing ra te is s u ch th a t there is no

s i g n i f i c a n t drop in flame tem pera tu re during the h e a t t r a n s fe r p r o c e s s .

CHAPTER III

RESULTS

CHAPTER III

RESULTS

Time Required Per H e a t

The following r e s u l t s a re o b ta in e d b a s e d on a fu rnace

c a p a c i t y of 2 00 t o n s . The c a s e for an in t e rm e d ia te v a l u e of

h = 0 .2 0 0 a s w e l l a s for h = 0 .2 5 9 (the upper bound) a re c a l c u l a t e d

for co m p ar i so n .

- 1 7 -

TABLE 3

TIME PER HEAT (IN MINUTES)

0%AL

25%AL

50°/cAL

75°/cAL

F/A h = 0 .259 h = 0 .2 0 0 h = 0 .2 5 9 h = 0 .2 0 0e $ = 0 .001 0 .0 1 6 3

0 .0 7 484 4810 .1 0 868 891

0 .0 8 60 .1 5

91' 342

96396

399573

385579

0 .0 7 284 325 523 5240 .11 55 57 327 3020 .1 5 42 44 308 2790 .2 0 49 50 332 3080 .3 0 257 294 457 4500 .32 2 69 308 483 4800 .3 6 323 370 587 5940 .5 399 454 762 781

0 .0 9 79 82 405 3920 .1 5 5 15 15 255 2160 .2 5 11 11 228 1850 .3 5 58 60 366 3470 .4 5 54 56 367 3480 .5 0 53 55 368 3500 .7 0 50 51 371 3530 .7 5 34 35 361 341

0 .1 56 58 361 3410 .261 6 6 179 1270 .3 3 6 6 181 1290 . 4 6 6 189 1380 . 5 10 10 234 1920 . 7 36 37 330 306

o oo 34 35 328 304

100%AL

- 1 8 -

C o s t Ratios

The c o s t r a t io s in th is Thes is is d e f in ed a s the c o s t w i th aluminum

en r ichm en t to the c o s t w i thout aluminum en r ich m en t .

The c o s t r a t io s c a l c u l a t e d co r re spond ing to two v a l u e s o f h , 0 .2 0 0

and 0 . 2 5 9 , with = l for 100%AL c a s e and = ̂ for o th e r c a s e s .FrA Fr H 2

The c o s t o f H /C fuel oil is ta k en to be 0 . 0 0 9 do l la r s pe r l b . and th a t of the

aluminum is ta k en to be 0 .393 do l la r s pe r lb . and 0 .6 6 d o l la r s per lb . which

are com m erc ia l la rge quan t i ty p r i c e s . The e igh t s e t s o f r e s u l t s are p r e s e n te d

as fo llows (their g raphs are p lo t ted in Fig. 9 through Fig. 16).

The e f f i c i e n cy of the furnace is de f ined on p. 31.

h . Film C o ef f . C o s t of AL (per l b .) ( :3 ? ,Em iss iv i ty

0 .2 0 0 0 .393

0 .2 5 9 0 .393

0 .2 0 0 0 .6 6

0 .2 5 9 0 .6 6

0 .2 0 0 0 .393 0 .0 1 6 3

0 .2 5 9 0 .393 0 .0 0 1

0 .2 0 0 0 .6 6 0 .0 1 6 3

0 .2 5 9 0 .6 6 0 .001

TABLE 4

COST RATIOS AND EFFICIENCIES

( FrHl = 1, COST OF AL = 0 .393 d o l l a r s per l b . )T ^H2

0%AL

25°/cAL

FixedVariab le

E m is -s i v i t y

€ # = 0 . 0 0 1 € # = 0 .0 1 6 3

FilmC o e f f . h = 0 .2 5 9 h=0 .200 h = 0 .259 h = 0 . 200

C o s t C o s t C o s t C o s tF/A Ratios Eff ic iency Ratios Eff ic iency Rat ios Eff ic iency Rat ios Eff ic iency

0 .0 7 0 .3 5 8 0 .3 5 90 .1 0 0 .1 9 9 0 .1 9 4

0 .0 8 6 2 .3 6 0 .342 2 . 2 8 0 .3 5 4 0 .5 3 6 1 . 5 0 . 5 6 8 1 .420 .1 5 3 .3 9 0 .2 3 8 3 .42 0 .2 3 6 2 .0 2 0 . 3 9 9 2 . 3 4 0 .344

0 .0 7 7 .0 5 0 .185 7 .1 0 .1 8 4 3 .8 5 0 .3 3 9 4 .4 1 0 .2 9 60 .11 4 .4 3 0 .2 9 5 4 .1 0 .3 1 9 0 . 7 4 5 1 .2 5 0 .7 7 3 1 .6 90 .1 5 4 .1 7 0 .313 3 .7 8 0 .3 4 5 0 . 5 7 2 . 3 0 . 5 9 6 2 .1 90 .2 0 4 . 5 0 .2 9 4 . 1 7 0 .3 1 3 0 .6 6 4 1 .9 7 0 .6 7 7 1 .930 .3 0 6 .2 0 .211 6.1 0 .2 1 4 3 . 4 8 0 .3 7 5 3 .9 8 0 .3 2 80 .32 6 .55 0 .2 0 6 .51 0 .2 0 1 3 .6 5 0 .3 5 8 4 . 1 7 0 .3130 .3 6 7 .9 6 0 .164 8 .0 5 0 .1 6 3 4 . 3 8 0 . 2 9 8 5 .01 0 .2 60 .5 0 10 .3 0 .1 2 7 1 0 .6 0 .1 2 3 5 .4 1 0 .2 4 2 6 .1 5 . 0 .212

50%AL

TABLE 4 '— C o n tin u ed

E m is -s i v i t y

FixedVar iab lee $ = 0 .0 0 1 £&-= 0 .0163

Film C o e f f .

h = 0 .259 h = 0 .200 "h = 0 .259 h = 0 200

C o s t C o s t C o s t C o s tF/A Rat ios Eff ic iency Ratios Eff ic iency Rat ios E f f ic iency Rat ios E f f ic iency

7 5%AL 0 . 0 9 1 4 .8 0 .1 2 6 14 .3 0 .1 3 2 . 8 8 0 . 6 4 5 3 . 0 0 .6 2 10 . 1 5 5 9 .3 0 .2 7 .88 0 .2 3 6 0 . 5 4 7 3 . 4 0 . 5 4 8 3 . 40 . 2 5 8 .3 1 0 .224 6 .75 0 .2 7 6 0 .401 4 . 6 4 0 . 4 4 . 6 40 . 3 5 1 3 .3 5 0 .1 3 9 1 2 .7 0 .1 4 7 2 .12 0 . 8 8 2 . 1 9 0 .8 50 . 4 5 1 3 .4 0 .139 1 2 .7 0 . 1 4 7 1 .9 7 0 .9 4 5 2 . 0 5 0 .9 10 . 5 0 1 3 .4 2 0 .1 3 9 1 2 .8 0 .1 4 6 1 .9 3 5 0 .9 6 2 2 .0 1 0 .9 2 70 . 7 0 1 3 .5 5 0 .1 3 8 12 .9 0 .1 4 5 1 .8 2 5 1 .02 1 .8 6 1 .00 . 7 5 1 3 .2 0 .141 12 .45 0 .1 5 1 .2 4 1 . 5 1 .2 8 1 .4 6

100°/AL 0 . 1 0 4 . 8 0 .601 4 .5 4 0 . 6 3 6 0 .7 4 5 3 . 8 8 0 .7 7 1 3 . 7 40 .2 6 1 2 . 3 8 1 .21 1 .69 1 .71 0 .0 7 9 8 3 6 .2 0 .0 7 9 8 3 6 .20 .3 3 2 .4 1 1 .2 1.72 1 .6 8 0 .0 7 9 8 3 6 . 2 0 .0 7 9 8 3 6 .20 . 4 2 .5 2 1 .1 5 1 .84 1 . 57 0 .0 7 9 8 3 6 . 2 0 .0 7 9 8 3 6 .20 . 5 3 .1 1 0 .9 2 8 2 .55 1 .1 3 0 .1 3 3 21 . 7 0 .1 3 3 2 1 .70 . 7 4 . 3 9 0 .6 5 8 4 .0 7 0 .71 0 .4 7 9 6 .0 3 0 .4 9 2 5 . 8 60 . 8 4 . 3 6 0 .662 4 .0 5 0 .7 1 5 0 .4 5 2 6 .3 9 0 . 4 6 5 6 .2

TABLE 5

COST RATIOS AND EFFICIENCIES

Fr H ~~rH

COST OF AL = 0 .6 6 d o l l a r s per l b .)

0%AL

2 5°/cAL

50°/cAL

E m is -s iv i t y

Fixed Variableeg= o.001 € ^ = 0 . 0 1 6 3Film ___ ___ — —

C o e f f . h = 0. 259 h = 0 .2 0 0 h = 0 .259 h = 0 .200

C o s t C o s t C o s t C o s tF/A Rat ios Eff ic iency Ratios Eff ic iency Rat ios Eff ic iency Rat ios Eff ic iency

0 .0 7 0 .3 5 8 0 .3590 .1 0 0 .1 9 9 0 .194

0 .0 8 6 3 .4 9 0 .3 4 2 3 .2 8 0 .354 0 .7 7 4 1 . 5 0 . 8 1 6 1 .420 .1 5 . 4 . 8 7 0 .2 3 8 4 .92 0 .2 3 6 2 . 9 0 0 . 3 9 9 3 . 3 7 0 .344

0 .0 7 1 1 .3 5 0 .1 8 5 11 .1 0 .184 6 .1 6 0 .3 3 9 7 .0 5 0 .2 9 60 .11 7 .1 0 .2 9 5 6 .44 0 .319 1 .1 9 2 1 .2 5 1 . 2 4 1 .6 90 .1 5 6 .7 0 .3 1 3 5 .93 0 .345 0 .9 1 1 2 . 3 0 . 9 5 5 2 .1 90 .2 0 7 .2 0 .2 9 6 .55 0 .313 1 .0 6 2 1 .9 7 1 . 0 8 5 1 .930 .3 0 9 .9 2 0 .2 1 1 9 .5 6 0 .2 1 4 5 .5 7 0 .3 7 5 6 . 3 8 0 .3 2 80 .3 2 10 .5 0 .2 0 10 .2 0 .201 5 .8 3 0 .3 5 8 6 . 6 8 0 .3130 .3 6 1 2 .7 0 .1 6 4 .12 .6 0 .163 7 . 0 0 .2 9 8 8 . 0 3 0 .2 60 .5 0 1 6 .6 0 .1 2 7 16 .9 0 .123 8 .6 5 0 .2 4 2 9 . 8 5 0 .212

TABLE 5 — C o n tin u e d

Em is-s iv i ty

FixedVariable

£ # = 0 . 0 0 1 <E#= 0 .0163

FilmC o e f f . H = 0 . 2 5 9 h = 0 .200 h = 0. 259 h = 0. 200

C o s t C o s t C o s t C o s tF/A Rat ios E f f ic iency Rat ios Ef f ic iency Ratios Eff ic iency Ratios E f f ic iency

75%AL 0 .09 2 4 .3 0 .1 2 6 2 3 . 5 0 .13 4 .7 4 - 0 .6 4 5 4 .9 2 0 .6210 .155 1 5 .6 0 .2 1 2 .9 6 0 .2 3 6 0 .9 3 . 4 0 . 9 3 .40 .25 1 3 .7 0 .2 2 4 1 0 .8 0 .276 0 .6 6 4 . 6 4 0 .6 6 4 . 6 40 .35 2 1 . 9 0 .1 3 9 2 0 . 9 0 .147 3 .4 8 0 .8 8 3 . 6 0 .8 50 .45 2 2 . 0 0 .1 3 9 2 0 . 9 0 .147 3 .2 4 0 .9 4 5 3 .3 6 0 .910 .50 2 2 .1 0 .1 3 9 2 1 . 0 0 .146 3 .1 8 0 .962 3 . 3 0 .9 2 70 .70 2 2 .3 0 .1 3 8 2 1 .2 0 .145 3 . 0 1 .02 3 .0 6 1 .00 .75 2 1 . 7 0 .1 4 1 2 0 . 5 0 .1 5 2 .0 4 1 .5 2 . 1 1 .4 6

100°/cAL 0 .10 7 .6 5 0 .6 0 1 7 .23 0 .636 1 .188 3 .8 8 1 .23 3 .7 40 .261 3 .8 1 .21 2 . 6 9 1.71 0 .1 2 7 3 6 .2 0 .1 2 7 3 6 .20 .33 3 .8 4 1 .2 2 . 7 4 1 .6 8 0 .1 2 7 3 6 .2 0 .1 2 7 3 6 .20 .4 4 . 0 1 .1 5 2 . 9 2 1 .57 0 .1 2 7 3 6 .2 0 .1 2 7 3 6 .20 .5 4 . 9 6 0 .9 2 8 4 . 0 7 1 .13 0 .212 2 1 .7 0 .212 2 1 . 70 .7 7 .0 0 .6 5 8 6 .5 0 .71 0 .763 6 .0 3 0 .7 8 5 5 .8 60 .8 6 .9 5 0 .6 6 2 6 .4 5 0 .715 0 .721 6 .3 9 0 .7 4 2 6 .2

-22-

COST RATIO

Fig. 9. — C o s t r a t i o s ( h = 0 . 2 59 , C o s t of AL = 0 .6 6 D o l l a r s / l b . )

COST RATIO

Fig. 1 0 . — C o s t r a t i o s (h = 0 . 2 5 9 , C o s t o f AL = 0 .6 6 D o l l a r s / l b .)

-24

-

CO ST RATIO

.1 .2 .3 .4 .5 . 6 .7 .8 .9 F/A

Fig . i l . — C o s t r a t i o s (h = 0 . 2 0 0 , C o s t of AL = 0 .6 6 D o l l a r s / l b . )

COST RATIO

Fig. 1 2 . — C o s t r a t io s (h = 0 .2 0 0 , C o s t o f AL = .393 D o l l a r s / l b .)

COST RATIO

ito•-JI

F ig . 1 3 . — C o s t ra tios ("H - 0 . 2 5 9 , C o s t of AL = 0 .3 9 3 D o l l a r s / l b . , = 0.001)

COST RATIO

COST RATIO25

iN>coI

15

14

13

12

11

10

9

8

7

6

5

4

r>O

2

1

Fig. 16 — C o s t r a t io s ( h = 0 . 2 0 0 , 0 . 0 1 6 3 , P o s t of AL = 0 .3 9 3 D o l l a r s / l b . )

-31 -

Ef f ic iency o f the Furnace

The e f f i c i e n cy of the fu rnace is de f ined in th i s t h e s i s as the

ra t io of the h e a t t rans fe r red to the s t e e l to the h e a t energy r e l e a s e d

from the fue l . The fo llowing formulas a re de r ived from the de f in i t ion

to e x p e d i t e the c a l c u l a t i o n o f e f f i c i e n c y . (See Appendix XII.)

for 0°/cAL: ^ = 173___________Time requ i red Per H eat (Min.)

for 25%AL: ^ - 136 .5________Time R e q . Per H e a t (Min.)

for 50°/cAL: ^ = ______________ 9 6 .4______________Time Req. Per H e a t (Min.)

for 75%AL: ^ = 5H0_________Time Req. Per H e a t (Min.)

for 100%AL: ^ = 217___________Time Req. Per H e a t (Min.)

The r e s u l t s of c a l c u l a t i o n a re p r e s e n te d in Tab les 4 and 5.

CHAPTER IV

DISCUSSION OF RESULTS

CHAPTER IV

DISCUSSION OF RESULTS

On C o s t

The e ig h t s e t s of c o s t r a t io s in Table 4 a re p lo t ted in F ig s . 9

through 16 . Compar ison b e tw ee n the f igures shows tha t F ig s . 9

through 12 (with v a r i a b le em is s iv i ty ) are s im i la r in s h a p e . The sam e

is true for F ig s . 13 through 16 (with fixed e m is s iv i ty ) .

The in f luence of film c o e f f i c i e n t on the c o s t r a t io s is a lm os t

n i l for h igh e m is s iv i ty c a s e s , a s c an be s e e n by compar ing Figs . 9

and 11 or F ig s . 10 and 12. For low e m is s iv i ty c a s e s , the film

c o e f f i c i e n t d o es have some e f f e c t on the c o s t r a t i o s , a l though no t a

g r e a t d e a l . H e n c e , our a s su m p t io n tha t the h found by co n s id e r in g the

"S tandard Heat" c a n be app l ied to aluminum en r ich m en t c a s e s c a n be

j u s t i f i e d in terms of "e f fec t on the end r e s u l t . "

The c o s t of aluminum h a s a much more e v id e n t e f fec t on the

c o s t r a t i o s than the fi lm c o e f f i c i e n t a s c an be s e e n by compar ing

F ig s . 9 and 10 or F ig s . 11 and 12.

F ig s . 13 through 16 are b a s e d on c o n s t a n t v a l u e s of c o r r e sp o n d ­

ing to the two limi ts o f h in Table I. These f igu res are u s e d on ly for

co m p ar i so n to find out the in f lu e n c e o f e m is s iv i ty on c o s t r a t io s .

The graphs of th is t h e s i s g ive v a l u a b l e c l u e s on the F/A ra t io s .

Between 0 .05 and 0 . 3 , the l o w e s t c o s t r a t io s can be found (see F igs . 9 -1 2 ) .

- 3 4 -

By compar ing the cu rves for 2 5%AI, and 75%AL, i t c a n be s e e n

th a t they h a v e abou t the sam e minimum v a l u e s . S ince i t is much e a s i e r

to h a n d le the aluminum s lurry for the 25%AL c a s e , i t shou ld b e u s ed

i n s t e a d of the one for 75%AL, ev en if the c o s t ra t ios for the former

would be a l i t t l e b i t h ighe r . Also the AL O s l a g hand l ing problem6 J

would be r e l i e v e d .

For the c a s e o f 100%AL, a lm o s t a l l the c o s t ra t io s f a l l u n d e r 1

(see F ig s . 9 - 12). The lo w e s t c o s t reg ion l i e s b e tw e e n F/A = 0 .2 5 and

F/A = 0 . 5 , w h e re the c o s t i s a round o n e - t e n t h of t h a t for a "S tanda rd H e a t . "

For m os t AL enr ichm ent c a s e s , d i f f i c u l t i e s may a r i s e b e c a u s e

the t ime for a h e a t becomes so shor t tha t th e h igh flame tem pera tu re

w i l l c a u s e a su d d en h e a t - u p o f the w h o le fu rnace th a t the furnace

s t ru c tu re w i l l b e u n a b le to s u s t a i n the s u d d e n i n c r e a s e of t em pera tu re

and the la rge q u a n t i t i e s of h e a t r e l e a s e d . As a c o n s e q u e n c e , a fu rnace

w i l l h a v e to be r e - d e s i g n e d to s u i t the AL en r ich m en t s c h e m e .

Assuming the opera t ing c o s t of a s in g le fu rnace on "S tandard H ea t"

5b a s i s i s approx im a te ly 180 .00 do l la r s pe r h o u r , then 1 5 .8 x 10 do l la r s is

r equ i red for a con t inu ing ope ra t io n o f ten fu rn ac es for a y e a r . If the c o s t

w i th AL en r ich m en t is o n e - h a l f th a t o f a "S tandard H e a t , " then w e can

s a v e approx im a te ly 0 . 8 mil l ion do l la r s a y e a r on the s t e e l - m a k i n g

p r o c e s s for s u ch an o p e n - h e a r t h s e t u p . Assuming the a d d i t io n a l

e x p e n s e e n su e d to hand le the AL as a r e s u l t o f th i s en r ich m en t sch e m e

- 3 5 -

i s 0 . 4 mil l ion d o l l a r s , i . e . , o n e - h a l f of w h a t we h ave s a v e d , w e s t i l l

s a v e a ne t amount of approx im a te ly 0 . 4 mil l ion d o l la r s a y e a r . W ith th is

p ro s p e c t in theo ry , w i th o u t c o n s id e r in g the e f f i c i e n cy of the fu r n a c e ,

fu r ther s tudy into th is aluminum en r ich m en t s c h e m e is w e l l w o r t h w h i l e .

On Ef f ic iency

E f f ic iency a s d e f ined is r e a l l y a c h e c k on Assumption 5. If

the e f f ic ie n cy e x c e e d s 1, i t m eans th a t the h e a t ene rgy r e l e a s e d from

the fue l i s far l e s s th a n the h e a t energy requ i red to h e a t up the b a th .

This is b e c a u s e the fi r ing ra te is no t h igh e n o u g h . As a r e s u l t , the

a d i a b a t i c f lame tem pera tu re would not rem a in c o n s t a n t a s a s s u m e d .

If the e f f i c i e n c y i s in the ne ighborhood of 0 . 2 , i t w i l l be a s su m e d

th a t the drop of a d i a b a t i c f lame tem pera tu re w i l l b e sm a l l enough so

t h a t Assumption 5 w i l l be a c h i e v e d . R ea l i s t i c e f f i c i e n c i e s a p p e a r to be

around .2 - .3 a s in d ic a te d by the %AL f igures of Table 4.

The p roduc t o f c o s t ra t io and e f f i c i e n c y g ive some in d ic a t io n

o f the f e a s i b i l i t y o f m e ta l au g m en ta t io n . For e x am p le , the e f f i c i e n cy

c an a lw ays be r ed u ced by leng then ing the fir ing t im e , bu t th is i n c r e a s e s

the c o s t p ro p o r t io n a l ly . H e n c e , the p roduc t o f c o s t ra t io and e f f ic ien cy

m ust be b e lo w 1 to be a t t r a c t i v e for fu r ther i n v e s t i g a t i o n . The one point

by the c a l c u l a t i o n m ethods u s e d , tha t is b e lo w 1, i s t h a t o f 50%AL at

F/A = 0 . 1 1 . W hi le i t is p o s s i b l e th a t o th e r po in ts may be of i n t e r e s t ,

the c a l c u l a t i o n method u s e d h e re , while c a p a b le of bounding the

p roblem, are not c a p a b l e of s p e c i f i c s o lu t io n . I t sh o u ld be further no ted

th a t the p roduc t of e f f i c i e n cy and c o s t ra t io for the 0%AL is b e tw e e n 0 .2

- 3 6 -

and 0 . 3 6 . This s u g g e s t s tha t e v e n the 50%AL, F/A = 0 .1 1 point

may no t be a t t r a c t i v e enough .

Fur ther exam ina t ion of Tables 4 and 5 po in ts ou t th e s i g n i f i ­

c a n t e f f e c t of e m is s iv i ty on the p rob lem . W ith e m is s iv i ty fixed (but

low) m os t of the energy is locked in the g a s and i s d i s c a r d e d ou t of

the s t a c k . With h igh e m is s iv i ty , energy l e a v e s the g a s so rap id ly

th a t the ga s is coo led w e l l be low a r a d i a t i v e h e a t t r a n s fe r l e v e l . It

i s th is e m is s iv i ty tempera ture phenomenon th a t o r ig in a l ly m ade the

m e ta l augm en ta t ion s y s t e m look a t t r a c t i v e , as it provided a means

w h e reb y the energy of the com bus ted gas c a n be more rap id ly t r a n s ­

f e r r e d to the s t e e l , thus reduc ing the t ime for a h e a t .

CHAPTER V

CONCLUSIONS AND RECOMMENDATIONS

CHAPTER V

CONCLUSIONS AND RECOMMENDATIONS

C o n c lu s io n s

1. The upper bound for f ilm c o e f f i c i e n t is 0 .2 5 9 for the c a s e s

of "S tandard H e a t . "

2 . For h igh e m i s s i v i t i e s , the in f lu e n c e of c o n v e c t iv e film c o ­

e f f i c i e n t on the c o s t r a t i o s is n e g l i g i b l e .

3 . The c o s t of aluminum h as a much g re a t e r e f fec t on the c o s t

r a t io s than tha t of the film c o e f f i c i e n t .

4 . The fu rnace h a s to be r e - d e s i g n e d for m os t o f the AL

en r ichm en t c a s e s w h ic h are e c o n o m ic a l . The fu rnace e f f ic ie n cy is

the l o w e s t for the c a s e s of 100%AL en r ic h m en t .

5 . There i s not much d i f f e r en c e b e tw ee n the e f f i c i e n c i e s for

d i f f e ren t f ixed e m is s iv i ty c a s e s .

6. The c h o ic e b e tw e e n f ixed e m is s iv i ty and v a r i a b l e e m is s iv i ty

h a s a prominent e f fe c t on e f f i c i e n c y .

7 . In th eo ry , the AL en r ichm en t s c h e m e , w i th c a lc u l a t i o n s

employed here in th is t h e s i s , i s no t f e a s i b l e on the e co n o m ica l s id e

e x c e p t n ea r the poin t w here F/A = 0 . 1 1 , w i th 50%AL en r ichm en t .

- 3 9 -

Recommendations

Further s tu d y in to th is AL en r ichm en t s c h e m e is probably

w o r th w h i le . These s tu d i e s shou ld p re fe rab ly be made around the

po in t w here F/A = 0 . 1 1 , w ith 50%AI. en r ichm en t .

APPENDICES

-41

APPENDIX I

COMPUTER PROGRAM I

CALCULATION OF PERCENTAGE WEIGHT OF FUELS

1 J1052 DIMENSION FA(105), AL(l 05) ,C (105), H(l 05) ,STOIAF(105), STOIFA(lOS),

1WHC(105), SAL(105) ,WAL(105) ,S 0 2 (105) ,SN2 (105) ,SWQ2 (105) ,SWN2 (105), 2EXCESS (105) ,W 0 2 (105) ,WN2 (105), TOTALW(l 05) , PERFIC (105), PERAL (105), 3PER02 (105), PERN2 (105)

3 READ (5,2) (C (I ) , H (I) ,AL(I) , FA (I), 1=1,105)10 2 FORMAT (4F10 .6)11 DO 200 1=1, J12 C (I )= 5 .013 H ( l ) - 8 .014 STOIAF(l)=(3. 84*AL(I)«14. 3 * (1 0 0 .0 - A L ( l ) ) ) / 1 0 0 .015 STOIFA(l) = i . 0/STOIAF(I)16 IF (AL(I). NE. 100.0) GO TO 5021 WHC (l )=0 .022 50 IF (AL(I).EQ. 100.0) GO TO 11125 WHC (I)=12 .01 *C(I}+1 . 008*H (I)26 SAL(I) = ((AL(I))/100.0)*$AIHC(I))/(2 6 .98*(1 .0-AL(I) /100.0))27 111 IF (AL(I).NE. 100.0) GO TO 22232 SAL (I)= 2 .033 222 WAL(l)=26. 98*SAL(l)34 IF (AL(I).EQ. 100.0) GO TO 25037 S 02 (I)=(3. 0*SAL(l)+4.0*C ( l )+ H ( l ) ) /4 .040 250 IF (AL(I).NE. 100.0) GOTO 2 7043 S02 (l) = (3 . 0*SAL(l)) /4.044 270 S N 2 ( l j= 3 .76*302(1)45 SW02(I)=3 2.0*302(1)46 SWN2 (l)=2 8 .016*SN2 (I)47 EXCESS (l)=STOIFA(I)/FA(I)50 W 0 2 (l)=SW02 (I) *EXCESS (I)51 WN2 (l)=SWN2 (I) *EXCESS (l)52 TOTALW(l)=WHC (I)+WAL(I)+W02 (I)+WN2 (I)53 PERHC (I) = 10 0 . 0 *(WHC (l)/TOTALW (l))54 PERAL(l)=l 0 0 . 0*(WAL(l)/TOTALW(l))55 PER02 ( I )= l0 0 .0 *(W02 (l)/TOTALW(l))56 PERN2 (l)=100.0*(WN2 (l)/TOTALW(l))57 200 CONTINUE61 K=J-162 DO 333 1=1, K ,263 7 FORMAT (2 (2OX, 1HC, IX, FI 1 . 6 , 4X, 1 1HPERCENT H / C , F 1 1 . 6 ) / ,

1 2 (2OX, 1HH, IX, FI 1 . 6 , 4X, 1OHPERCENT AL, IX, FI 1 . 6 ) / ,22 (19X, 2HAL, IX ,FI 1 . 6 , 4X, 1 0HPERCENT 02 , IX, FI 1 . 6 ) / ,32 (18X, 3HF/A, 1 X ,F 1 1 ,6 ,4 X , 10HPERCENT N2 , IX, FI 1 . 6 ) / / )

64 333 WRITE (6 ,7 )C ( l ) , PERHC (I) , C ( I + l ) , PERHC (I+l)., H (I ) , PERAL (I),1H (1+1), PERAL (1+1), AL (I), PER02 (I), AL ( I+ l ) , PERO 2 (1+1), FA (I),2 PERN2 (I), FA ( I+ l) , PERN2 (I+l)

66 STOP67 END

134

11 101314 20162425 302631 35323334 40354041 504243444546

4750 5551 6052555661 7062 7563666770 80737475 85

- 4 2 -

APPENDIX II

COMPUTER PROGRAM II

TO FIND AN UPPER BOUND OF h AND W FOR A STANDARD HEAT

DIMENSION AL( 5), FA( 5), TF( 5) ,TT( 5)C 3 = 4 . 9E-13READ(5,10) (AL(M),FA(M),TF(M),M=1 ,L)FORMAT (3F I 0 .3 )t t (i )=t f (i )TF(I)=1. 8*TF(I)T 2 2 - 3 3 7 2 .0INTERV-5G 3 = C 3 - 0 . 01E-13IF ( C 3 .L E .0 .0 ) GO TO 908C 2 = 1 .0C C C = 0 .4LLL=0M=1IF (C 2 .L E .0 .0 ) GO TO 900TB1=530.0DO 250 J = l , 100C l - 1 4 . 6 8CK3=4. 0*TB1CK2=6. 0*(TBl)**2)C K l = 4 .0 * ( T B l * * 3 ) + 1 6 .0 * ( C 2 / 2 .0 + C l ) / C 3CK =16 .0*((C 1-C 2 /2 .0 )*T B1-C3*(TB 1**4) /16 .0+C 2*TF (M )+C 3*(TF (M )**4) ) /

1C3 TB2 =T2 2 DO 100 N = 1 ,2 DO 85 L=1,2 IF (L .EQ.2) GO TO 70 T=TB1IF (L.EQ. 1) GO TO 75 T=TB2F=(T**4)+CK3 *(T**3)+CK2 *(T**2)+CK1 *T-CKIF(L.EQ. 2) GO TO 80X1=TFX1=FIF (L.EQ. 1) GO TO 85X2=TFX2-FCONTINUE

- 4 3 -

77 X3 = (X1*FX2-X2 *FX1)/(FX2-FX1)100 T=X3101 IF (N. EQ.2) GO TO 89104 X4=X3105 89 f =T**4+CK3*(T**3)+CKZ*(T**2)+CK1*T-CK106 IF (F .G T .0 .0 ) GO TO 95111 TB1=X3112 95 IF (F .L T .0 .0 ) GO TO 100115 TB2=X3116 100 CONTINUE1 2 0 . IF (ABS(X4~T).GE.0.0l) GO TO 55123 101 IF (X3-T22) 2 4 0 ,2 0 0 ,2 0 0124 240 TB1-X3125 IF (J .LT.97) GO TO 250130 IF (LLL.EQ.l) GO TO 248133 C C C = C C C / 2 .0134 248 C2=C2+CCC135 LLL=1136 GO TO 40137 250 CONTINUE141 200 IF (J. EG. 97) GO TO 206144 IF (LLL.EQ.2) GO TO 2 04147 C C C = C C C / 2 .0150 204 C 2 - C 2 - C C C151 LLL-2152 GO TO 40153 206 KTIME=J*INTERV154 WRITE ( 6 , 300)TB1155 300 FORMAT ( / / / . 10X, 10HFINAL T E M P ,F 1 0 .3 / )156 500 FORMAT ( / , 10X, 1OHPERCENT AL, F 7 . 2 / , 1 OX, 3H F /A , F 6 . 3 / , 1 OX, 23H

ADIABATIC 1 FLAME TEMP (K), F 8 . 2 / , 3 OX, 3H(R), F 8 . 2 / , I OX, 15H TAPPING TEMP (R), F 8 . 2 / , 2 10X, 35HTIME REQUIRED TO REACH TAPPING TEM P,I4 , 1X ,4H M IN . , / )

157 WRITE (6 ,600) C 3 ,C 2160 600 FORMAT ( / , 1 OX,4 8HPREDICTED FILM COEFFICIENT FOR RADIATION

COEFF. = , 1E11 . 3 , 2X, 7HIS-------- , F10 .3)161 GO TO 30162 900 WRITE (6,905) C3163 905 FORMAT C/ ,10X,26HC2 IS . LE . ZERO, ADJUST C3 = , E 1 1 . 2 , 2X, 24H

AND TRY A1 GAIN AS FOLLOWS/)164 GO TO 30165 908 STOP166 END

- 4 4 -

APPENDIX III

COMPUTER PROGRAM III

TO FIND THE TIME FOR A HEAT

CCcc

123

10 10 11 1213 201516 17 2021 502223242526 2730

3132 5533 6034 37 4043 7044 7545505152 805556

THIS IS TO FIND THE TIME REQUIRED TO RAISE THE BATH TEMPERA­TURE TO ITS FINAL TEMPERATURE, FOR VARIOUS COMBINATIONS OF F/A AND PERCENTAGE AL. THIS IS FOR ( e § ) = 0 .0163 AND FILM C O EFFICIEN TS. 2 00. THE TIME INTERVAL IS TAKEN TO BE 1 MIN.

L=27DIMENSION AL(100), FA (100), TF(l00) , TT(l 00)READ (5,10) (AL(M),FA(M),TF(M),M=1,L)FORMAT (3F I 0 .3 )DO 2 0 1=1, L TT(I)=TF(I)TF(I)=1. 8*TF(l)T22=3372 .0 INTERV=1 DO 800 M = 1 , L TB1+530.0 DO 250 J=1,1000 C l = 7 3 .4 C 2 = 0 .200 C 3 = 0 . 465E-12 C K 3 - 4 . 0*TB1 CK2=6. 0*(TB1 **2)CK1=4. 0 *(TB1 **3)+l 6 .0 * ( C 2 / 2 . 0+C 1) /C3C K =16 .0*( (C1-C2/2 .0 )*TB1-C3*(TB1**4) /16 .0+C2*TF(M )+C3*(TF(M )* * 4 ) ) / l C 3TB2=T22DO 100 N = 1 ,2DO 85 L=1,2IF (L .EQ.2) GO TO 70T=TB1IF (L .E Q . l ) GO TO 75 T=TB2F=(T**4)+CK3*(T**3)+CK2*(T**2)+CK1*T-CK IF (L .EQ.2) GO TO 80 XI = T FX1=FIF (L .E Q . l ) GO TO 85X2=TFX2=F

57 356162636667 89 707374 95 77

100 100 102105 101106 240107 250 111 200 112113 300114 800 116 500

117 908 120

CONTINUEX3=(X1*FX2-X2 *FX1)/(FX2-FX1)T-X3IF (N .EQ.2) GO TO 89 X4 = X3F=t **4+CK3*(T**3)+CK2 *(T**2)+CK1 *T-CKIF ( F .G T .0 .0 ) GO TO 95TB1=X3IF (F .L T .0 .0 ) GO TO 100TB2 = X3CONTINUEIF (ABS(X4-T).GE.0.0l) GO TO 55IF (X3-T22) 2 4 0 , 2 0 0 , 2 0 0TB1 = X3CONTINUEKTIME=J*INTERVWRITE (6,300) TB1FORMAT ( / , 10X, 1 OH FINAL TEMP, FI 0 .3 )WRITE ( 6 , 500)AL (M), FA (M), TT(M), TF(M), T2 2 , KTIME FORMAT ( / , 10X, 1OHPERCENT AL, F 7 . 2 / , 1 OX, 3H F /A , F 6 . 3 / , 1 OX, 23HADIABATIC 1 FLAME TEMP (K) , F 8 . 2 / , 30X, 3H(R) , F 8 . 2 / , 10X, 15HTAPPING TEMP(R), F 8 . 2 / , 2 10X, 35HTIME REQUIRED TO REACH TAPPING TEMP, 14, IX, 4HMIN . , / / )STOPEND

- 4 6 -

APPENDIX IV

TABLE 1

SETS OF CORRESPONDING VALUES OF h AND 6 & FOR A STANDARD HEAT

(BASED ON 200 TONS FURNACE CAPACITY) *

: 6 3 h

0.000000C001 0 .262

0 .00001 0 .2 62

0 .0001 0 .2 62

0 .0 0 1 * 0 .2 5 9 *

0 .0 0 7 0 .2 3 4

0 .0 0 8 7 7 0 .2 2 8

0 .0 1 6 3 0 .2 0 0

*Underl ined h v a lu e were t a k en a s the upper bound for c o n v e c t iv e film coe f f ic ien t for gas e m i s s i v i t i e s tha t a re sm a l l u n l e s s m e ta l ized au gm en ta t ion i s u s e d in the f u e l .

APPENDIX V

TABLE 2

PERCENTAGE WEIGHT, ADIABATIC FLAME TEMPERATURE ANDTOTAL EMISSIVITY

0% AL

F/A% W e ig h t 0 .0 1 0 .0 5 0 . 0 7 0 .1 0 0 .1 5 0 .2 0 0 .3 0 .4 0 . 5 0 . 6 0 . 7

c 5 h 8 1 . 0 4 . 8 6 . 5 9 .1 1 3 .2 1 6 .8 2 3 .4 2 8 .7 3 3 . 5 3 7 .7 4 1 .3

AL - - - - - - - - - - -

o 2 2 3 . 0 2 2 .2 2 1 . 8 2 1 .2 2 0 .2 1 9 .4 17 .9 16 .6 1 5 .5 14 .5 13 .7

n 2 7 6 .0 7 3 . 0 7 1 .7 6 9 .7 6 6 .6 6 3 .8 5 8 .7 5 4 .7 5 1 . 0 4 7 .8 4 5 .0

Ta f (K) 6 7 9 .5 7 1851 .79 2 2 1 2 .7 6 1947 .55 1365 .42 1 0 3 0 .8 7 9 5 6 .2 6 909 .55 876 . 37 8 4 0 .5 7 81 0 .1 7

TotalEm iss iv i ty

TABLE 2 Con t inued

2 5% AL

F/A % Weiqht. 0 .0 2 0 .05 0 .0 8 6 0 .1 5 0 .2 5 0 .3 5 0 .4 0 . 4 5 0 .5

C 5H8 1 .5 0 .0 5 5 .9 9 . 8 4 1 2 .6 19 .5 2 1 .5 2 3 .2 2 5 .1

AL 0 .5 1 .2 2 . 0 3 . 2 6 4 .2 6 .5 7 .2 7 . 8 8 .4

o 2 2 2 .9 2 2 .2 2 1 .5 2 0 . 3 1 9 .4 17 .3 1 6 .6 1 6 .0 15 .5

n 2 75.1 7 3 .0 7 0 .6 6 6 .6 6 3 .8 5 6 .7 5 4 .7 5 3 .0 5 1 .0

T a f ® 9 9 0 .1 7 17 9 4 .3 0 2 3 70 .51 2 1 0 7 .0 5 1802 .61 1731 .69 1 7 29 .23 1729 .92 -

TotalE m iss iv i ty - 0 .21 0 . 0 5 - - - - -

50% AL

F/A% W eig h t 0 .0 2 0 .07 0 .11 0 . 1 5 0 .2 0 .0 3 0 .3 2 0 . 3 6 0 .4 0 .5 0 .6

C 5H 8 1 .0 3 .3 5 . 0 6 .6 8 .4 11 .7 12 .2 1 3 .4 14 .5 1 6 .8 19 .0

AL 1 .0 3 .3 5 .0 6 .6 8 .4 11 .7 12 .2 1 3 .4 14 .5 1 6 .8 1 9 .0

0 2 2 2 .8 2 1 .8 2 1 . 0 2 0 .2 1 9 .4 17 .9 1 7 .6 17 .1 16 .5 1 5 .4 14 .5

n 2 75.2 7 1 .6 6 9 .0 6 6 . 6 6 3 .8 5 8 .7 5 8 .0 56 .1 5 4 .5 5 1 .0 4 7 .5

Taf(K) 9 5 5 .5 7 2 1 6 0 .4 7 2 5 7 9 .1 4 2 6 5 2 .4 6 25 5 9 .0 2 2 2 5 5 .4 8 2 2 1 3 .6 8 2 0 9 3 .8 4 - 1 984 .29 -

TotalE m iss iv i ty “ 0 .0 6 0 .2 6 0 .3 1 0 .31 0 .0 5 2 0 .0 5 5 0 .061 - 0 .072 -

TABLE 2 — C o n t in u ed

75% AL

F/A % W e ig h t 0 .0 2 0 .0 9 0 .155 0 .2 5 0 .3 5 0 .4 5 0 .5 0 .7 0 .7 5 0 . 8

C 5H8 0 . 5 2 . 0 3 .3 5 .0 6 .5 7 .7 8 .4 10.3 1 0 .8 1 1 .2

AL 1 .5 6 .3 10.1 15.1 1 9 .6 2 3 .5 2 5 .2 3 1 .0 3 2 .3 3 3 . 5

° 2 2 2 . 8 2 1 .3 2 0 .2 1 8 .6 1 7 .2 1 6 .0 1 5 .4 ' 13 .7 13 .1 1 2 . 8

n 2 7 5 .2 7 0 .4 6 6 .4 61 .3 5 6 . 7 5 2 .8 ■51.0 4 5 .0 4 3 .8 4 2 . 5

Ta f (K) 9 1 9 .5 8 2 3 5 5 .1 0 2 9 1 8 .0 6 3 0 9 9 .2 8 2 4 5 3 .3 6 2 450 .71 2 4 4 6 .5 9 2 4 3 9 .3 8 2 4 6 8 .7 0 -

TotalE m is s iv i ty - 0 .2 6 0 .64 0 .7 4 0 .3 1 0 .3 4 0 .3 5 0 .3 8 0 .5 5 -

i

100% ALC D1

F/A % W e ig h t 0 .0 2 0 .1 0 .261 0 .3 3 0 . 4 0 .5 0 .7 0 .8 0 .9 1 . 0 1 .3

C 5H8 - - - - - - - - - -

AL 2 . 5 9 .3 2 0 . 8 2 5 .0 2 8 . 8 3 3 .5 4 1 .3 4 4 .6 4 7 .6 5 0 .2 5 6 .7

° 2 2 . 9 2 1 .2 1 8 .5 1 7 .4 1 6 .6 15 .5 1 3 .7 1 2 .9 12 .2 1 1 . 6 10 .1

N2 9 4 .6 6 9 .5 6 0 .7 5 7 .6 5 4 . 6 5 1 .0 4 5 . 0 4 2 .5 4 0 .2 3 8 .2 33 .2

Ta f (K) 1009 .13 2 4 68 .09 35 6 5 .0 6 3 5 4 5 .3 3 3 4 5 6 .8 2 30 5 3 .3 4 2 5 6 6 .9 5 2 5 7 2 .6 4 - - -

TotalE m iss iv i ty - 0.31 0 .83 0 .84 0 .8 6 0 .8 2 0 .4 3 0 .4 6 - - -

A P P E N D IX VI P L A T E

T H R E E D IM E N S IO N A L A D IA B A T IC F L A M E T E M P E R A T U R E P H O T O G R A P HF O R A L E N R IC H M E N T S C H E M E

. 1 .2 .3 .4 .5 .6 .7 .8 .9 F/A

APPENDIX VII FIGURE 4

ADIABATIC FLAME TEMPERATURE FOR 0% AL

ICnDO!

F/A

APPENDIX X FIGURE 7 ADIABATIC FLAME TEMPERATURE FOR 75% AL

APPENDIX XI FIGURE 8 ADIABATIC FLAME TEMPERATURE FOR 100% AL

- 5 6 -

APPENDIX XII

DERIVATION OF FORMULAS FOR CALCULATING THE EFFICIENCIES

H e a t t r an s f erred to th e s t e e l (Q out) E f f ic iency = H e a t energy r e l e a s e d from fue l (Q in)

For a fu rnace of 2 00 to ns c a p a c i t y , the h e a t t r a n s fe r re d to the

s t e e l i s (200 x 2000 x 0 .11 x (3372-530)] BTU = 1 .25 x 1 08 BTU.

Assume the fir ing ra te o f H /C is 300 g a l . / h r . (or 2520 l b s . / h r . ) ,

w h ich i s the c a s e for an o p e n -h e a r t h fu rnace in p r a c t i c e . Also , a s s u m e

the fir ing ra te of AL is the s a m e . The h e a t of c o m b u s t io n for AL is

1 3 ,6 0 0 B T U / lb / , for H /C it is 17 ,22 0 BYU/lb.

Thus , for 0% AL c a s e :

yj 1 .2 5 x 1 0 8 173

For

(17220 x 2520) (Min .) 60

100% AL c a s e :

(Min .)

ft _ 1 .2 5 x 1 0 8 217' (13600 x 2520) (Min.)

60For 25% AL c a s e :

ft _ 1 .25 x 108

i M i n .)

' 17220 x 2520 j 13600 x 2520I 60 60

(Min.)

For 50% AL c a s e :

n 1 .2 5 x 108 96 .4

= 136 .5) (Min.)

f l 7220 + 13600 x 1 7 2520 (Min . ) (Min .)C J 60

For 75% AL c a s e :

7 1 . 2 5 x 1 08 _ 5 1 .0

f l 7 2 2 0 + 13600 x 3 l 2520 (Min.)60

(Min.)

LIST OF REFERENCES

LIST OF REFERENCES

GORDON, SANFORD; ZELEZNIK, FRANK J. , and HUFF, VEARL N."A G en era l M ethod for Automatic C om puta t ion of Equi librium C om pos i t ions and T h e o re t ic a l Rocket Performance of P r o p e l l a n t s . " Lewis Research C e n t e r , NASA TN D-132

WELLER, S. W . " In te rn a l Environment of Solid Rocket N o z z l e s , " RPL-TDR-64-140, P u b l i ca t io n No. U - 2 7 0 9 , W . O . 2104 , Philco C o r p . , July 30, 1964.

ZERBE, J . , and SELVA, J. "An Em pir ica l Equa t ion for theC o e f f i c i e n t o f H e a t Transfer to a F la t Surface From a Plane H ea ted Air Je t D i r e c te d T an g en t ia l ly to the S u r f a c e . " NACA, TN 1070, 1946.

MYERS, G. E . , SCHAUER, J. J. , and EUSTIS, R. H. "The Plane Turbulent W al l J e t , Part I , Jet D eve lopm en t and Fr ic t ion F a c to r , " TRNo . 1, D epar tm en t o f M e c h a n i c a l E n g inee r ing , Stanford U n iv e r s i t y , June 1, 1961.

MYERS, G. E . , SCHAUER, J. J. , and EUSTIS, R. H . "The Plane Turbulent W al l J e t , Part II, H e a t T r an s fe r , " TR N o . 2 , Th e rm o sc ien ces D iv i s io n , D ep ar tm en t of M e c h a n i c a l Eng inee r ing , Stanford U n iv e r s i t y , D e c . 1, 1961.

ABSTRACT

Stud ies w e re made on the en r ic h m en t of h y d ro - c a r b o n fue l by

aluminum powder in an o p e n - h e a r t h f u r n a c e . The r a t io s of the c o s t

for aluminum enr ichment to the c o s t for a s t a n d a rd h e a t w e re computed

for two v a l u e s of film c o e f f i c i e n t , one o f w h ic h i s a n uppe r bound . The

e f f i c i e n c i e s for a l l the c a s e s c o n s id e r e d w ere c a l c u l a t e d .

The r e s u l t s show tha t for the c a l c u l a t i o n s p rocedure fo l lowed in

th is t h e s i s , on ly one p o in t , nam ely w h e re F/A = 0 .1 1 v/i th 50% AL

en r ic h m en t , i s f e a s ib l e to g e t som e e c o n o m ic a l r e s u l t s . Further

s tu d i e s sh o u ld there fore be made around th is po in t .