The Enrichment of Hydro-Carbon Fuel by Aluminum Powder in ...
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All Theses and Dissertations
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
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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 .