Ceramic Heat Pipe for High Temperature Heat Recovery

8/4/2019 Ceramic Heat Pipe for High Temperature Heat Recovery

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Heat Recovery Systems V o l . 2 . N o . 2 . p p . 1 8 9 - 1 9 9 , 1 9 8 2 . 0 1 9 8 - 7 5 9 3 8 2 0 2 0 1 8 9 - 1 1 5 0 3 . 0 0 0

P r i n t e d i n G r e a t B r i t a i n P e r g a m o n P r e s s L i d

C E R A M I C H E A T P I P E S F O R

H I G H - T E M P E R A T U R E H E A T R E C O V E R Y

HA L J . S T R U M P F

A i R e s e a r c h M a n u f a c t u r i n g C o m p a n y , 2 5 2 5 W e s t 1 9 0 t h S t r e e t, T o r r a n c e , C A 9 0 5 09 , U .S .A .

A b s t r a c t - - T h i s p a p e r s u m m a r i z e s t h e r e s ul ts o f a c o n c e p t u a l d e si g n s t u d y f o r c e r a m i c h e a t p i p er e c u p e r a t o r s c o n d u c t e d b y t h e A i R e s e a rc h M a n u f a c t u r i n g C o m p a n y , a d i v is i o n o f T h e G a r r e t tC o r p o r a t i o n , f o r t h e U n i v e r s i t y o f C a l i fo r n i a L o s A l a m o s S c ie n t if i c L a b o r a t o r y .

T h e f u n c t i o n o f t h e r e c u p e r a t o r i s to p r e h e a t c o m b u s t i o n a i r w i t h in d u s t r i a l f u rn a c e e x h a u s tg a s e s , t h u s e f fe c t in g a s u b s t a n t i a l f ue l s a v i n g a s c o m p a r e d w i t h u n r e c u p e r a t e d , n o n - p r e h e a t e df u r n a c e s . T h e p r o p o s e d r e c u p e r a t o r s y s t e m c o n s i s t s o f t w o h e a t e x c h a n g e r u n i t s : a h i g h - t e m p e r a -t u r e c e r a m i c h e a t p i p e r e c u p e r a t o r u s i n g s o d i u m a s t h e w o r k i n g fl u id a n d a l o w - t e m p e r a t u r em e t a l l i c p l a te - f in r e c u p e r a t o r . S y s t e m s w e r e d e s i g n e d f o r t h r e e f u r n a c e a p p l i c a ti o n s .

T h e c e r a m i c u n i t c o n s i s t s o f a b u n d l e o f i n d i v i d u a l h e a t p i p e s a c t in g i n c o n c e r t , w i t h a p a r t i t i o ns e p a r a t i n g t h e a i r a n d e x h a u s t g a s f l o w s t r e a m s . T h e o v e r a l l f l o w c o n f i g u r a t i o n i s c o u n t e r f l o w .

T h e m e t a l l i c u n i t i s o f a c r o s s f lo w c o n f i g u r a t i o n , a n d i s s i m i l a r t o A i R e s e a r c h d e s i g n s u s e d f o ro t h e r a p p l i c a t i o n s .P o t e n t i a l fu e l s a v i n g s a r e in t h e 4 0 - 5 0 % r a n g e . C a l c u l a t e d s i m p l e p a y b a c k p e r i o d s , b a s e d o n

p o t e n t i a l fu e l c o s t s a v i n g s a n d e s t i m a t e d s y s t e m c o s t s , a r e l e ss t h a n s i x m o n t h s f o r a l l d e s ig n s ,

e x c l u si v e o f s p e ci fi c r e t r o f i tt i n g a n d h i g h - t e m p e r a t u r e b u r n e r c o s t s .

I N T R O D U C T I O N

A STU DY h a s b e e n c o n d u c t e d b y t h e A i R e s e a r c h M a n u f a c t u r i n g C o m p a n y , a d i v i si o n o f

T h e G a r r e t t C o r p o r a t i o n , f o r t h e U n i v e r s i t y o f C a l i fo r n i a L o s A l a m o s S c i e n ti fi c L a b o r a -

t o r y ( L A S L ) in v e s t ig a t i n g t h e u s e o f h e a t p i p e s m a d e o f c e r a m i c m a t e r i a l f o r t h e r e c o v e r y

o f h e a t f r o m t h e fl u e g a s e s o f h i g h - t e m p e r a t u r e i n d u s t r i a l f u r n a c e s. T h i s w a s t e h e a tr e c o v e r y r e s u l t s i n a r e d u c t i o n i n f u e l c o n s u m p t i o n b y t h e f u r n a c e .

T y p i c a l i n d u s t r i a l f u r n a c e s o p e r a t e w i t h u n h e a t e d c o m b u s t i o n a i r o r l o w - e f f e c t i v e n e s s

r e c u p e r a t i o n . T h u s , a s u b s t a n t i a l p o r t i o n o f t h e fu e l i s r e q u i r e d t o h e a t t h e a i r t o t h e

f u r n a c e o p e r a t i n g t e m p e r a t u r e , w h i c h c a n b e i n t h e 2 0 0 0 ° t o 2 5 0 0 ° F ( 1 1 0 0 ° - 1 4 0 0 ° C )

r a n ge . T h e h o t p r o d u c t s o f c o m b u s t i o n ( fl ue ga s e s) a r e e x h a u s t e d t o t h e a t m o s p h e r e a n d

t h e e n e r g y c o n t e n t l o s t . A m o r e e f f ic i en t a p p r o a c h i s t o p r e h e a t t h e c o m b u s t i o n a i r t o

h i g h t e m p e r a t u r e w i t h th e h o t f l u e g a s e s , t h u s u t i l i zi n g s o m e o f t h e a v a i l a b l e e n e r g y . A

h e a t e x c h a n g e r o r r e c u p e r a t o r c a n b e u s e d t o e f fe c t t h i s e n e r g y t r a n s fe r .

S t a t e - o f - t h e - a r t, h i g h - t e m p e r a t u r e , s t a i n le s s st e e l h e a t e x c h a n g e r s h a v e a m e t a l t e m -

p e r a t u r e l i m i t a t i o n i n t h e 1 4 0 0 ° t o 1 5 0 0 ° F ( 7 6 0 ° - 8 2 0 ° C ) ra n g e . T h u s , t h e h o t g a s i n l e t

t e m p e r a t u r e t o a s t a i n l e s s s t e e l r e c u p e r a t o r i s l i m i t e d t o a b o u t 1 5 5 0 ° F ( 8 4 0 ° C ) . W i t h t h i st e m p e r a t u r e l i m i t a t i o n t h e h o t f u r n a c e g a s e s n e e d t o b e d i l u t e d w i t h c o l d a i r p r i o r t o

r e c u p e r a t i o n . F o r a m a x i m u m g a s t e m p e r a t u r e o f 1 55 0 ° F (8 40 °C ), t h e a ir p r e h e a t t e m -

p e r a t u r e i s e s s e n t i a l l y l i m i t e d t o a b o u t 1 4 0 0 ° F (7 6 0° C ). T h e r e q u i r e d r e c u p e r a t o r w o u l d

h a v e a n e f fe c t i ve n e s s o f a b o u t 0 .9 0 .

T o f u r t h e r i n c r e a s e f u e l s a v i n g s , a i r p r e h e a t t e m p e r a t u r e s m u s t b e i n c r e a s e d a b o v e

1 4 0 0 ° F ( 76 0 °C ). C e r a m i c h e a t e x c h a n g e r s o f f e r t h e p o t e n t i a l f o r p r e h e a t i n g a i r t o w i t h i n

1 5 0 ° - 2 0 0 ° F (8 0 ° - 1 1 0 ° C ) o f t h e f u r n a c e g a s t e m p e r a t u r e , l im i t e d o n l y b y h e a t e x c h a n g e r

s iz e a n d b y h i g h - t e m p e r a t u r e b u r n e r d e v e l o p m e n t . I f a l a r g e r a i r p r e h e a t - t o - fu r n a c e g a s

t e m p e r a t u r e d i f fe r e n c e i s d e s i r e d , a s u b s t a n t i a l r e d u c t i o n i n h e a t e x c h a n g e r e f fe c t iv e n e s si s p o s s i b l e . T h e i n f lu e n c e o f e f fe c t iv e n e s s o n t h e h e a t e x c h a n g e r s i ze i s s u c h t h a t a c e r a m i c

h e a t e x c h a n g e r r e q u i r e d t o h e a t a g i v e n f l o w r a t e o f c o m b u s t i o n a i r t o 1 6 0 0 ° F ( 87 0 °C )

~ vi th 2 1 0 0 ° F ( 11 5 0° C ) g a s i s o n l y a b o u t o n e - t h i r d t h e s i z e o f th e m e t a l l i c h e a t e x c h a n g e r

r e q u i r e d t o h e a t t h e s a m e a i r f l o w r a t e t o 1 4 0 0 ° F ( 7 6 0 °C ) w i t h 1 5 5 0 ° F ( 8 40 ° C ) g a s . T h i s

i l lu s t ra t e s t h e a d v a n t a g e s o f t h e c e r a m i c h e a t e x c h a n g e r a p p r o a c h : i n c re a s e d f ue l sa v i n g s

a r e p r o v i d e d b y a s m a l l e r , l o w e r - e f fe c t i v e n e s s r e c u p e r a t o r .

189H.x.s. 2~2

190 HAL J. SI"RUMPF

REFRACTORYMETAL LINER ANDWICK~

CERAMCENDPLUG

EVAPORATOREND GRAVITY CONDENSERND

Fi g . 1 . C e ra m i c h e a t p i p e s c h e m a t i c .

O n e t y p e o f c e r a m i c h e a t e x c h a n g e r t h a t c a n b e u s e d f o r h e a t r e c o v e r y i s a r e c u p e r a t o r

c o m p o s e d o f c e r a m i c h e a t p ip e s . T h e h e a t p i p e s t h e m s e l v e s a r e l o n g c e r a m i c t u b e s c a s t

w i t h e x t e r n a l r a d i a l fi ns . T h e f i n s a i d i n th e h e a t t r a n s f e r a n d r e d u c e t h e n u m b e r o f p i p e s

r e q u i r e d f o r a p a r t i c u l a r t a s k . T h e i n s i d e o f e a c h p i p e i s c o a t e d w i t h a t h i n r e f r a c t o r y

m e t a l l a y er . T h i s la y e r h a s a d u a l p u r p o s e : t h e m e t a l a c t s a s a w i c k t o t r a n s p o r t t h e h e a t

p i p e w o r k i n g f l u i d a n d a l s o p r o t e c t s t h e c e r a m i c f r o m t h e w o r k i n g fl ui d, w h i c h i s a l i q u i d

m e t a l s u c h a s s o d i u m o r l i t h i u m . T h e s e h e a t p i p e e l e m e n t s a r e b e i n g d e v e l o p e d a t

L A S L [ 1 ] . A s c h e m a t i c o f t h e h e a t p i p e i s s h o w n i n F i g . 1 . N o t i c e t h a t t h e h e a t p i p e i s

t i l t e d t o a i d i n t h e c o n d e n s a t e r e t u r n .

T h e h e a t p i p e s a r e b u n d l e d t o g e t h e r t o f o r m a t u b e b a n k , s i m i l a r i n a p p e a r a n c e t o a

c o n v e n t i o n a l f i n n e d - t u b e h e a t e x c ha n g e r . H o w e v e r , b o t h t h e fl ue g a s a n d t h e c o m b u s t i o n

a i r f l o w o u t s i d e t h e t u b e s , w i t h t h e g a s s tr e a m s s e p a r a t e d b y a p a r t i t i o n . T h e o v e r a l l f l o w

c o n f i g u r a t i o n i s c o u n t e r f l o w . T h e h e a t p i p e w o r k i n g f l ui d t r a n s f e rs h e a t f r o m t h e g a s

s t r e a m t o t h e a i r s t r e a m . T h e a r r a n g e m e n t i s s h o w n i n F i g . 2 . S u c h a h e a t e x c h a n g e r

F ig . 2 . H e a t p i p e h e a t e x c h a n g e r c o n f i g u r a t i o n .

HOT FLUID

C e r a m i c h e a t p i p e s f o r h e a t r e c o v e r y

HOT EXCHANGERt h 1 t h 2

COUPLING FLUID

C PUHP

tc 2 w, COLD EXCHANGER a tc l

COLD FLUID

F i g . 3. L i q u i d - c o u p l e d i n d i r e c t - t r a n s f e r t y p e h e a t e x c h a n g e r s y s t e m u s e d a s a m o d e l f o r t h ea n a l y s i s o f h e a t p i p e r e c u p e r a t o r s .

c o n f i g u r a t i o n h a s a d i s t i n c t s i z e a d v a n t a g e c o m p a r e d t o a c o n v e n t i o n a l a i r - t o - g a s h e a te x c h a n g e r . F o r t h e t u b e s iz e r e q u i r e d f o r t y p i c a l i n d u s t r i a l p r o c e s s e s , t h e t h e r m a l r e s i s t-

a n c e i n s i d e t h e t u b e s i s c o n s i d e r a b l y l a r g e r t h a n t h a t o u t s i d e t h e t u b e s . T h u s , t h e i n s i d es u r f a c e ' c o n t r o l s ' t h e d e s i g n o f c o n v e n t i o n a l u n it s . W i t h h e a t p i p e s , h o w e v e r , b o t h a i r a n dg a s f lo w o v e r t h e l o w e r - r e s i s t a n c e o u t s i d e s u r f ac e , t h u s m a k i n g p o s s i b le a s i g n i fi c a n t siz er e d u c t i o n . T h e h e a t p i p e r e s i s t a n c e i n s i d e t h e t u b e s i s q u i t e s m a l l d u e t o t h e h i g h h e a t

t r a n s f e r c o e f fi c ie n t s a s s o c i a t e d w i t h t h e p h a s e c h a n g e o f t h e h e a t p i p e f l ui d a n d t h e s m a l l

t e m p e r a t u r e c h a n g e b e t w e e n t h e e v a p o r a t o r a n d c o n d e n s e r s e ct io n s . In a d d i t i o n t o t h e

s iz e a d v a n t a g e , t h e h e a t p i p e r e c u p e r a t o r o f fe r s d e c r e a s e d s e a li n g a n d m a n i f o l d in g c o m -

p l e xi ty c o m p a r e d t o a c o n v e n t i o n a l h e a t e x c h a n g e r.

H E A T E X C H A N G E R A N A L Y S I S

C o n t r a r y t o s e v e ra l r e c e n t p r e s e n t a t io n s i n t h e l i te r a t u r e l : 2 , 3 ] a h e a t p i p e r e c u p e r a t o rc a n n o t , i n g e n e r a l , b e c o n s i d e r e d a s i n g l e c o u n t e r f l o w h e a t e x c h a n g e r w i t h a n o v e r a l l

a i r - t o - g a s t h e r m a l r e s i s t a n c e a n d a n o v e r a l l a i r - t o - g a s l o g a r i t h m i c m e a n t e m p e r a t u r e

d i f fe r e n c e ( L M T D ) . T h i s a p p r o a c h n e g l e c t s t h e f a c t th a t t h e h e a t p i p e f lu i d is a t a ne s s e n t i a l l y c o n s t a n t t e m p e r a t u r e i n a n y i n d i v i d u a l h e a t p i p e . B e c a u s e o f t h i s f a c t , t h e

a c t u a l i n t e g r a t e d t e m p e r a t u r e p o t e n t i a l fo r a h e a t p i p e i s s m a l l e r t h a n t h e o v e r a l l L M T D .T h i s i s t r u e e v e n i f t h e t h e r m a l r e s i s t a n c e o n t h e h e a t p i p e s i d e is v a n i s h i n g l y s m a l l. I t i so n l y i n t h e l i m i t o f a l a r g e n u m b e r o f t u b e r o w s i n t h e a i r / g a s f l o w d i r e c t i o n t h a t t h i s

o v e r a ll a p p r o a c h b e c o m e s c o r r e c t.T h e a p p r o a c h u s e d f o r t h e p r e s e n t s t u d y c o n s i d e r s e a c h h e a t p i p e ( i n t h e f lo w d i r e c -

t i o n ) s e p a r a t e l y . I n d e e d , e a c h p i p e i s a s s u m e d t o b e t w o s e p a r a t e h e a t e x c h a n g e r s :g a s - t o - h e a t p i p e f lu i d a n d h e a t p i p e f l u i d - to - a i r . T h i s a p p r o a c h i s s i m i l a r t o t h a t s t u d i e d

b y L o n d o n a n d K a y s C 4l a n d e x p a n d e d u p o n b y E a s t w o o d [ 5 ] f o r l i q u id - c o u p l e di n d i r e c t - t r a n s f e r h e a t e x c h a n g e r s . T h i s c o n f i g u r a t i o n is s h o w n s c h e m a t i c a l l y i n F i g . 3 .T h e s y m b o l s in F i g . 3 a r e l a r g e l y s e l f - e x p l a n a t o r y ; t r e p r e s e n t s t e m p e r a t u r e , q r e p r e s e n t st h e h e a t l o a d ( e q u a l f o r b o t h e x c h a n g e r s ) , a n d C r e p r e s e n t s t h e c a p a c i t y r a t e , w h i c h i s

t h e p r o d u c t o f t h e fl o w r a t e a n d t h e m e a n h e a t c a p a c i ty . F o r t h e h e a t p i pe s c o n s i d e r e di n t h e p r e s e n t s t u d y t h e h o t e x c h a n g e r a n d c o l d e x c h a n g e r r e p r e s e n t r e s p e c ti v e ly t h e g a s

a n d a i r p o r t i o n s o f t h e p i p e . T h e c o u p l i n g f l ui d is t h e s e a l e d h e a t p i p e f lu i d w i t h t h e h e a t

p i p e w i c k i n g s y s t e m a c t i n g a s t h e p u m p .F o r a l i q u i d - c o u p l e d a p p l i c a t i o n , t h e c o u p l i n g f lu i d r e m a i n s i n t h e l iq u i d p h a s e ; h e a t i s

t r a n s f e r re d b y a c h a n g e i n t h e t e m p e r a t u r e o f th i s fl ui d. T h e p u m p i n g r a t e is u s u a l l y

a d j u s t e d s o t h a t t h e c o u p l i n g f l u i d c a p a c i t y r a t e , CL, i s s i m i l a r to t h e a i r a n d g a s c a p a c i t y

ra t e s (Co an d Ch re spec t ive ly ).

192 HAL J. STRUMPF

For the heat pipe application, the heat pipe fluid changes phase and the temperature

change is usually very small; in effect t L l = t L : . This means that the heat pipe fluid

capacity rate, CL, is very large.

A numerical example serves to illustrate the difference between the coupled approach

and the overall resistance approach. Using the nomenclature of Fig. 3, assume the

following temperatures for a particular heat pipe (customary engineering units are used

exclusively in this example): th , = 1500°F, th2 = 1420°F, to, = 1300°F~ tel = 1200°F.These temperatures indicate a capacity rate ratio, C c / C h , of 0.8, which is reasonable for a

recuperator. The thermal conductances (TC) are assumed to be equal for the hot and

cold sides. Using the overall resistance approach, the LMTD is 209.8°F and the overall

thermal conductance, considering only the air- and gas-side resistances, is (0.5) (TC).

Thus, the total heat transferred, q, is (104.9) (TC).

The coupled approach yields for hot side:

1500 -- 1420L MTDh - (1)

1500 - t Lin

1420 - t L

and for the cold side:

1300- 1200LMTD~ - (2)

In t t - - 1200 "

t L -- 1300

Since the thermal conductances are equal, LMTDh = LMTD,. Combining equations

(1) and (2) and solving for the heat pipe fluid temperature yields tL = 1356.5°F and

LM TD = 98.1°F, Thus, q = (98.1) (TC), which is smaller by 7% than the value arrived atusing the overall resistance approach. This error will increase with the fluid temperature

change across a single row of tubes and will decrease with the temperature difference

between the two fluid streams. The error thus will decrease with the total number of

rows in the air/gas flow direction of the recuperator for a given overall temperature differ-

To aid in conducting the study, a detailed heat pipe heat exchanger design computer

program was written. The program performs tube-by-tube heat transfer calculations

based on the indirect-coupled heat exchanger technique described above. At each tube,

the heat balance and thermal conductance equations are solved simultaneously to yield

the outlet conditions. The calculations continue row-by-row through the heat exchanger

until the desired temperature conditions are attained. These heat transfer calculations areiterated with pressure drop calculations, with the heat exchanger frontal area being

varied until both the heat transfer and pressure drop requirements are satisfied. Actually,

calculations need not be performed for every tube in the heat exchanger. Since the overall

recuperator configuration is counterflow, tubes in any given 'no-flow' row operate at

essentially identical conditions. Thus, a row-by-row calculation in the air/gas flow direc-

tion will suffice.

The thermal conductances and pressure drops on the air and gas sides are determined

using correlations for finned tube Colburn modulus and friction factor. Also included are

the resistances associated with the tube wall, the heat pipe fluid phase changes, and the

heat pipe fluid vapor transport. The vapor transport resistance, which is equal to the

fluid temperature change divided by the heat pipe heat load, is related to the pipegeometry and heat pipe fluid properties by the use of the Clausius-Clapeyron equation

and analytical expressions for the vapor flow pressure drop. Local heat pipe fluid proper-

ties are used. The computer program is described and illustrated in more detail in

Strumpf and Miller [6].

C e r a m i c h e a t p i p e s f o r h e a t r e c o v e r y

T a b l e 1 . D e s i g n c o n d i t i o n s t

A p p l i c a t i o n

S te e l A l u m i n u m G l a s ss o a k i n g r e m d t m e l t in g

p i t f u r n a c e f u r n a c e

A i r S i d e

F l o w r a t e , l b / s 5 . 45 6 .5 5 4 . 5 0I n l e t t e m p e r a t u r e , ° F 1 0 0 1 0 0 1 0 0O u t l e t t e m p e r a t u r e , ° F 1 6 00 1 6 00 2 0 0 0I n l e t p r e s s u re , p s i a 1 4 .9 2 1 5 . 16 1 5 .1 6P re s s u re d ro p , i n . H 2 0 6 .1 1 2 . 75 1 2 .7 5

F l u e g a s s i d e

Flo w ra t e , l b /s 5 .75 6 .91 4 .75I n l e t t e m p e r a t u r e , ° F 2 1 25 2 1 0 0 2 5 00I n l e t p r e s s u re , p s i a 1 4 .7 0 1 4 .7 0 1 4 .7 0P r e s s u r e d r o p , i n . H 2 0 8 .7 5 4 0 . 5 0 1 8 .5 0

t Co nv er s io n fac to rs : kg/s = (0 .4536) ( lb /s) ; °C = (°F-32) /(1 .8);k P a = ( 6. 8 95 ) (p s i a ) ; k P a = ( 0 .2 4 9 1 ) ( i n . H 2 0 ) .

D E S I G N C O N S I D E R A T I O N S

T h r e e s p e c if ic i n d u s t r i a l p r o c e s s e s w e r e s e l e c te d fo r t h e s t u d y : a s t e el s o a k i n g p i t, a n

a l u m i n u m r e m e l t f u r n a c e , a n d a g la s s m e l t i n g f u r n a ce . E a c h p r o c e s s i n v o lv e s t h e c o m -b u s t i o n o f f ue l, t h e t r a n s f e r o f s o m e o f t h e r e l e a s e d e n e r g y t o t h e p r o c e s s l o a d , a n d t h e

l o ss o f t h e r e m a i n d e r o f th e e n e r g y a s e x h a u s t e d h i g h - t e m p e r a t u r e fl ue g as . T h e d e s ig nc o n d i t i o n s s p e c i f ie d fo r e a c h p r o c e s s a r e g i v e n in T a b l e 1 .

T h e k e y p a r a m e t e r i s p e r h a p s t h e a i r p r e h e a t ( o ut le t ) t e m p e r a t u r e . S i n c e t h is r e p r e s e n t st h e c o m b u s t i o n a i r t e m p e r a t u r e , t h e b u r n e r s m u s t b e a b l e t o o p e r a t e a t t h i s t e m p e r a t u r e .

T h e 1 6 00 °F ( 87 0 °C ) l e v el w a s s e l e c t e d a s r e p r e s e n t a t i v e o f t h e l i m i t i n c u r r e n t b u r n e r

t echno logy . The 2000°F (1090°C) l eve l was se l ec t ed t o i nves t i ga t e the fue l sav ingsp o s s ib l e w i th a d v a n c e d b u r n e r d e v e l o p m e n t .

I t is r e a d i l y a p p a r e n t t h a t a s i n g l e h e a t p i p e w o r k i n g f l u i d c a n n o t b e u s e d o v e r t h e

e n t i r e t e m p e r a t u r e r a n g e r e q u i r e d to h e a t c o l d a i r t o h i g h t e m p e r a t u r e s . R a t h e r t h a n u s e

d i f f e re n t h e a t p i p e f lu id s , i t w a s d e c i d e d t o u s e a c o n v e n t i o n a l m e t a l l i c h e a t e x c h a n g e r t oh e a t t h e c o m b u s t i o n a i r t o a t e m p e r a t u r e s u f fi c ie n t f o r e f fi c ie n t o p e r a t i o n o f a s in g le -

w o r k i n g f l u i d h e a t p i p e h e a t e x c h a n g e r . S t a t e - o f - t h e - a r t s t a i n l e s s s t e e l h e a t e x c h a n g e r sc a n h a n d l e h o t g a s e s u p t o a b o u t 1 5 00 °F ( 82 0 °C ). A b o v e t h is l e ve l, t h e h e a t p i p e s c a n a l lo p e r a t e u s i n g s o d i u m a s t h e w o r k i n g f lu id .

I t s h o u l d b e p o i n t e d o u t t h a t t h e m e t a l l i c h e a t e x c h a n g e r r e q u i r e d i s o f q u i t e l o we f f e c t i v e n e s s - - m u c h s m a l l e r th a n a u n i t r e q u i r e d t o p r e h e a t a i r t o 1 4 00 °F ( 7 60 °C ) w i th

1 5 00 °F ( 82 0 °C ) g a s . F o r e x a m p l e , t h e m e t a l l i c u n i t r e q u i r e d f o r t h e s t ee l s o a k i n g p i t h e a t sthe co ld a i r t o 835°F (446°C) and has a n e f fec t iveness o f on ly 0 .53 .

W i t h t h is l o w e f f e ct iv e n e s s , a s i n g l e -p a s s c r o s s f l o w c o n f i g u r a t i o n i s a d e q u a t e f o r t h e

m e t a l l ic u n it . T h is i s a m u c h l e ss c o m p l e x a r r a n g e m e n t t h a n t h e c o u n t e r f lo w o r m u l t i-

p a s s c r o s s f l o w c o n f i g u r a t i o n s r e q u i r e d f o r h i g h e r - e f f e ct i v e n e s s h e a t e x c h a n g e r s . A p l a t e -f i n h e a t e x c h a n g e r h a s b e e n s e l e c t e d f o r t h e m e t a l l i c r e c u p e r a t o r . P l a t e - f i n h e a t

e x c h a n g e r s c o n s i s t o f l a y e r s o f c o r r u g a t e d s h e e t s t o c k ( fi ns ) w h i c h a r e s e p a r a t e d b y p l a te s .T h e f i n s , p l a t e s , a n d e d g e b a r s a r e s t a c k e d i n a f i x t u r e a n d b r a z e d t o f o r m a n i n t e g r a t e d

c o r e a s s e m b l y. A l te r n a t e p a s sa g e s f o r m e d b y t h e p l a t e s a n d b a r s a r e a l l o c a te d t o e a c hf lu i d . T h e p a s s a g e s c a n b e a l i g n e d s o t h a t t h e f lo w p a t h s a r e p a r a l l e l (c o u n t e r f l o wa r r a n g e m e n t ) o r p e r p e n d i c u l a r ( c r os s fl o w a r r a n g e m e n t ) . T h e c r o ss f lo w c o n f i g u r a ti o n

s e l e c t e d f o r t h e p r e s e n t d e s i g n i s s h o w n s c h e m a t i c a l l y i n F i g . 4. N o t i c e t h a t t h e f l o w p a t hi s i n t e r r u p t e d b y a f i n o f f s e t . T h i s a i d s i n d i s r u p t i n g t h e f l u i d b o u n d a r y l a y e r a n di n c r e a s e s t h e f l u id h e a t t r a n s f e r c o e f f i c ie n t ( a n d p r e s s u r e d r o p g

T h e a i r a n d g a s f lo w s th r o u g h t h e m e t a l li c r e c u p e r a t o r a r e i n s e ri es w i t h t h o s e t h r o u g ht h e h e a t p i p e u n i t . T h e p r o p o s e d o v e r a l l c o n f i g u r a t i o n i s s h o w n i n F i g . 5 .

194 HAL J. STRUMPF

GASSURFAI

Fig . 4 . Crossflow plate-fin heat exchanger construction.

I n g en e r al , th e m i n i m u m o p e r a t in g t e m p e r a t u r e f o r a l i q u i d - m e t a l h e a t p i p e i s a

func ti on of the axi al he at f l ux. F o r d i ffe re nt tem pe r atur e r ange s a nd he at pi pe s i ze s ,

d i f fe r e nt mod e s of he at tr anspor t ac t as the l i mi t i ng fac tor s . D e pe nd i ng on the c on-

d i t i o n s , t h e h e a t f l o w c o u l d b e l i m i t e d b y v i s c o u s , s o n i c , e n t r a in m e n t , c a p i ll a r y ( w i c k i n g ) ,

o r b o i l i n g c o n s i d e r a t i o n s , a s i n d i c a t e d i n F i g . 6 .

A l l the d e s i gns c onsi d e r e d e ntai l ope r ati on of the he at pi pe s i n a gravi ty-ass i st m od e :i n t h i s m o d e , t h e c a p i l l a r y p u m p i n g r e s t r i c t i o n s d o n o t c o n s t i t u t e l i m i t i n g c o n d i t i o n s f o r

t h e v a l u e s o f h e a t f l u x e s e n c o u n t e r e d i n t h e p r e s e n t s t u d y . T h e e n t r a i n m e n t l i m i t s f o r

HETALLIC

PLATE FIN HEAT PIPESHEAT EXCHANGER (CONDENSING SECTION)

l •FLUE GAS OUT

HEAT PIPES(EVAPORATOR SECTION)

Fig . 5 . Ceram ic heat pipe f lue gas heat recovery sy stem.

Ceramic heat pipes for heat recovery 195

i 7OUS L li~lT

TEMPERATURE

Fig. 6. Axial heat flux limits.

s o d i u m h e a t p i p e s o p e r a t i n g i n a g r a v i t y - a s s i s t m o d e a r e h i g h e r t h a n t h e h e a t f l u x e s

e n c o u n t e r e d i n t h e p r e s e n t d e s i g n s a n d c o u l d b e i n c r e a s e d , i f n e c e s sa r y , t h r o u g h t h e u s eo f c o n d e n s a t e r e t u r n p a s sa g e s. T h e b o i l in g l im i t i s s e l d o m e n c o u n t e r e d w i t h l i qu i d - m e t a lw o r k i n g f lu i d s, e s p e c i a l ly w h e n t h e h e a t t r a n s f e r t o t h e p i p e i s c o n t r o l l e d b y o u t s i d e f il mc o e f f ic i e n ts t y p i c a l o f t h o s e o b t a i n a b l e w i t h e x t e r n a l g a s f lo w s .

F o r t h e t u b e s iz es c o n s i d e r e d i n t h e s t u d y , t h e v is c o u s l im i t i s o v e r r i d d e n b y t h e s o n i cl i m i t a t a t e m p e r a t u r e o f a b o u t l l 0 0 ° F ( 59 0 °C ), w h i c h is w e l l b e l o w a n y h e a t p i p e

o p e r a t i n g t e m p e r a t u r e s . T h u s , t h e o n l y h e a t p i p e p e r f o r m a n c e l i m i t i n g c r i t e r i o n c o n -s i d e r e d i s t h e s o n i c li m i t. T h i s e s t a b l is h e s a n a x i a l h e a t f l ux l im i t f o r t h e c o l d e s t h e a t p i p ed u e t o t h e a t t a i n m e n t o f s o n i c v e lo c i ty b y t h e l o w - d e n s i t y s o d i u m v a p o r .

T h e s e l e c te d c e r a m i c t u b e m a t e r i a l w a s s i l i co n i z e d s i li c o n c a r b id e . T h e r e i s a r e a s o n -

a b l e a m o u n t o f e x p e r i e n c e i n t h e f a b r i c a t i o n o f l o n g , f in n e d t u b e s o f t hi s m a t e r i a l .

T e m p e r a t u r e c a p a b i l i t y is in e x c e s s o f 2 5 0 0 ° F ( 1 37 0 °C ). A s u r v e y o f c e r a m i c fa b r i c a t o r si d e n ti fi e d a m a x i m u m t u b e l e n g t h o f a b o u t 8 f t (2 .4 m ) a s a r e a s o n a b l e p r o d u c t i o n l i m i t.

T h e c e r a m i c f a b r i c a t o r s a l s o i d e n t i f i e d a m a x i m u m f i n p a c k i n g o f 5 f i n s / i n . ( 2 . 0f in s / e ra ) . The f i n s wou ld l i ke ly be t ape red (a s shown in F ig . 1 ) and have an ave rage

t h i c k n e s s o f a b o u t 0 . 0 7 5 i n. ( 1 .9 1 m m ) . A m i n i m u m t u b e w a l l t h i c k n e s s o f 0 . 1 2 5 i n.(3 .18 m m ) was a l so e s t ab l i shed .

T h e l o c a t io n o f t h e p a r t i t io n s e p a r a t i n g t h e a i r a n d g a s s id e s is a n i m p o r t a n t d e s i g nc o n s i d e r a t io n . I n g e n e r a l , h e a t e x c h a n g e r s iz e c a n b e m i n i m i z e d b y b a l a n c i n g t h e a i r a n d

g a s t h e r m a l c o n d u c t a n c e s . F o r h e a t e x c h a n g e r s w i t h s i m i la r c a p a c i ty r a t e s o n e i th e r s i d e

( as i s t h e c a s e f o r t h e p r e s e n t r e c u p e r a t o r ) , t h e r e is a r e l a t i v e ly w i d e r a n g e o f c o n d u c t a n c er a t io s w h i c h r e s u lt in a p p r o x i m a t e l y m i n i m u m s iz e so l u ti o n s. I n d e e d , t h e L o n d o n - K a y s

c r i t e r i o n f o r o p t i m i z i n g a l i q u i d - c o u p l e d i n d i r e c t - t r a n s f e r r e c u p e r a t o r l - 4 ] i s 0 . 7 5<(UA),/(UA)h < 2 . 0 , w h e r e t h e UAs a r e t h e o v e r a ll t h e r m a l c o n d u c t a n c e s .

T h e r m a l c o n d u c t a n c e b a l a n c i n g i s u se f ul fo r n o n - c o n s t r a i n e d a i r - a n d g a s - si d e p re s s-

u r e d r o p s . H o w e v e r , f o r f i x e d p r e s s u r e d r o p s , t h e m i n i m u m s iz e r e c u p e r a t o r is e s s e n t ia l l y

t h a t w h i c h u s e s u p t h e a v a i l a b l e p r e s s u r e d r o p o n b o t h s id e s, r e g a r d l e s s o f t h e t h e r m a lc o n d u c t a n c e r a t i o . F o r t h e d e s i g n c o n d i t i o n s g i v e n in T a b l e 1 , t h e o p t i m a l p a r t i t i o nl o c a t i o n i s a t t h e c e n t e r o f t h e h e a t p i p e f o r t h e s t e e l s o a k i n g p i t a n d g l a s s m e l t i n gf u r n a c e d e s i g n s a n d a t 6 0 % c o n d e n s e r ( a i r - s i d e ) l e n g t h f o r t h e a l u m i n u m r e m e l t f u r n a c e .

SPECIFIC DESIGNS

A d e t a i le d p a r a m e t r i c s t u d y w a s c o n d u c t e d f o r e a c h f u r n a c e a p p l ic a t io n , a t t e m p t i n g t oo p t i m i z e t h e h e a t p i p e h e a t e x c h a n g e r a n d m e t a l l i c r e c u p e r a t o r b y v a r y i n g t h e h e a te x c h a n g e r g e o m e t r ie s . T h e d e v e l o p e d h e a t p i p e d e s i g n c o m p u t e r p r o g r a m a l o n g w i t h a ne x i s t i n g p l a t e - f i n c o m p u t e r p r o g r a m w e r e u s e d . D e t a i l s o f t h e s t u d y a r e n o t p r e s e n t e dh e r e d u e t o s p a c e l i m i t at io n s , b u t c a n b e f o u n d i n S t r u m p f a n d M i l le r [6 ] .

196 HAL J. STRUMPF

T a b l e 2 . H e a t p i p e r e c u p e r a t o r d e s i g n s ~

P a r a m e t e r

S te e l A l u m i n u m G l a s ss o a k i n g r e m e l t m e l t i n g

N u m b e r o f t u b e s 1 8 0 1 7 6 2 2 0T u b e l e n g t h , i n . . 9 6 9 6 9 6Tu b e O D / I D , i n . 1 / 0. 7 5 1 / 0. 7 5 1 / 0. 7 5Fin he ig h t , i n . 0 .25 0 .25 0 .25F i n s p a c i n g , i n . - 1 5 5 5Tra n s v e r s e t u b e s p a c i n g , i n . 1 .5 7 5 1 .5 7 5 1 .5 7 5L o n g i t u d i n a l t u b e s p a c i n g , i n . 1 . 36 4 1 . 36 4 1 . 36 4W e i g h t , l b 1 3 8 1 , 1 3 51 1 6 8 8F r a c t i o n c o n d e n s e r l e n g t h 0 . 5 0 0 .6 0 0 . 5 0Flow l eng th , i n . 8 .32 11 .05 13 .78No -f low l eng th , i n . 47 .99 35 .39 3 5 .40

N u m b e r o f f lo w r o w s 6 8 1 0N u m b e r o f n o - f lo w r o w s 3 0 2 2 22G a s - s i d e p r e s s u re d ro p , i n . H 2 0 5 . 11 5 2 2 . 96 0 6 .8 2 3A i r - s i d e p r e s s u re d ro p , i n . H 2 0 3 . 52 5 7 . 70 7 4 .7 4 7G a s i n l e t t e m p e r a t u r e , ° F 2 1 25 2 1 0 0 2 5 0 0

G a s o u t l e t t e m p e r a t u r e , ° F 1 4 94 1 4 95 1 4 99A i r i n l e t t e m p e r a t u r e , ° F 8 3 5 8 6 9 7 7 8A i r o u t l e t t e m p e r a t u r e , ° F 1 6 00 1 6 00 2 0 0 0

C o n v e r s i o n f a c t o r s : k g = ( 0 .4 5 3 6) ( I b ); m m = ( 0 . 0 39 4 ) (i n . ); k P a = ( 0 .2 4 9 1 )

( in , H20) ; °C = (°F-32) /1 .8 .

T h e h e at e x c h a n g e r s s e l ec t e d w e r e t h o s e r e su l t in g in m i n i m u m c o s t . T h e c o s t a s s u m p -

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

p r e s e n t e d i n T a b l e 2 a n d t h e m e t a l l i c r e c u p e r a t o r d e s i g n s a r e p r e s e n t e d i n T a b l e 3 . T h e

f in n o m e n c l a t u r e i s e x p l a i n e d i n F i g . 7 .

F U E L S A V I N G S

T h e r e d u c t i o n i n f l ue g a s e x h a u s t t e m p e r a t u r e r e s u l t i n g fr o m r e c u p e r a t i o n i m p r o v e s

t h e e f fi c ie n c y o f t h e p r o c e s s a n d s a v e s f u e l T h e l o w e r f u el u s a g e d e c r e a s e s t h e f l u e g a s

f low rate, res u lt in g in a fu rth er red u ct ion in en ergy los s es . T o es t im ate th e fu el s av in gs ,

T a b l e 3 . M e t a l li c r e ~ u p e r a t o r d e s i g n s §

P a r a m e t e r

S te e l A l u m i n u m G l a s ss o a k i n g r e m e l t m e l t i n g

G as- s id e f i n 3R-0 .55-0 .5(0)- 4R-0 .55-0 .5(0) - 4R-0 .55-0 .5(0) -0 . 0 1 0 0 . 0 1 6 0 , 0 1 6

Air -sid e f in 3R-0.55-0.5(0)- 6.5R-0.55-0.5(0)- 3R-0.55-0.5(0)-0.010 0.016 0.010

G a s f l o w l e n g t h , i n. 2 7 -0 2 6 .0 2 0 .0Ai r f l ow l eng th , i n . 31 .0 18 .5 30 .5N u m b e r o f g a s f in l a y e r s 3 0 3 4 2 0N u m b e r o f a i r f i n l a y e r s 3 1 3 5 2 1No -f low l eng th , i n . 35 .04 39 .63 23 .56C o r e w e i g h t , I b 8 1 3 8 6 9 4 9 3M a x i m u m c o r e t e m p e r a t u r e , ° F 1 3 9 2 1 3 98 1 3 75G a s i n l e t t e m p e r a t u r e , ° F 1 4 94 1 4 95 1 4 99G a s o u t l e t t e m p e r a t u r e , ° F 8 9 1 8 5 9 9 4 6

A i r i n l e t t e m p e ra t u r e , ° F 1 0 0 1 0 0 1 0 0A i r o u t l e t t e m p e r a t u r e , ° F 8 3 5 8 6 9 7 7 8G a s - s i d e p r e s s u r e d r o p , i n . H 2 0 3 .5 0 2 1 5 .8 8 6 6 .8 2 3A i r - s i d e p r e s s u re d ro p , i n . H 2 0 2 . 26 7 4 .7 4 7 4 .7 4 7

§ C o n v e r s i o n f a c t o r s : m m = ( 0 . 0 3 9 4 ) ( i n . ); k g - - ( 0 . 4 5 3 6 ) ( Ib ) ; ° C --- ( ° F -3 2 ) / 1 . 8 ; k P a • ( 0 . 2 4 9 1 ) ( i n . H 2 0 ) .

C e r a m i c h e a t p i p e s f o r h e a t r e c o v e r y 1 9 7

DESIGNATION: nR - b - ~ - t

EXAMPLE: 6 .5R-O.550-0 .500(0)-O.016

Fi g . 7 . R e c t a n g u l a r o f f s e t f i n n o m e n c l a t u r e .

r e c u p e r a t e d a n d u n r e c u p e r a t e d f u r n a c e s a r e c o m p a r e d f o r t h e s a m e h e a t l o a d s . T h i s c a nb e d o n e b y c o n s i d e r i n g a h e a t b a l a n c e a r o u n d a f u r n a c e :

Q = W , , C~ , . (T , , - T b ) + I ' V / C p s ( T: - T b ) + I, s A H r - ( I V . + W s ) C p , ( T ¢ - T b ) ( 3)

Q l W s = ( W . I W : ) C , : ( T . - T b ) + C , , ( T s - T ~ ) + A H s - ( i + I ' V : I W : ) C , , . ( T ~ T ~ ) ( 4 )

w h e r e

Q i s t h e f u r n a c e h e a t l o a d , i n c l u d i n g i n s u l a t i o n a n d h e a t l e a k l o s s e s ;

I4 :. i s t h e c o m b u s t i o n a i r f l o w r a t e ;C p . i s t h e c o m b u s t i o n a i r a v e r a g e h e a t c a p a c i t y ;

T . is th e c o m b u s t i o n a i r f u rn a c e i n le t te m p e r a t u r e ;

T b i s t h e b a s e t e m p e r a t u r e a t w h i c h t h e f u e l h e a t i n g v a l u e i s k n o w n ;

W i s th e f u e l f l o w r a t e ;

C ps i s t h e f u e l a v e r a g e h e a t c a p a c i t y ;

T i s t h e f ue l f u r n a c e i n l e t te m p e r a t u r e ;

A H i s t h e fu e l n e t h e a t i n g v a l u e a t T b;

C p . i s t h e f l u e g a s a v e r a g e h e a t c a p a c i t y ;

Tg i s th e f l ue g a s o u t l e t t e m p e r a t u r e .

E q u a t i o n ( 4) c a n b e a p p l i e d s e p a r a t e l y to r e c u p e r a t e d ( s u b sc r ip t r ) a n d u n r e c u p e r a t e d( s u b s c r ip t u ) f u r n a c e s . S in c e t h e f u r n a c e h e a t l o a d i s a s s u m e d t o b e t h e s a m e f o r t h e

r e c u p e r a t e d a n d u n r e c u p e r a t e d c a s e s , d i v i d i n g t h e t w o h e a t b a l a n c e s y i e l d s t h e f u e l

u s a g e r a t i o :

~ , / i , ' v s . =

( ~ / W : ) . C , . . ( T o . - r ~ ) + C , t . ( r : . - r ~ ) + a H : - ( I + W . / ~ ) . C , , . ( T + . - r ~ )

(I , J W f ) , C , . . ( T ~ , - T b ) + C p ., . .( T Ir T ~ ) + A H f - ( ! + W . / W : ) , C , , , , ( T ~ , T ~ ) .

I f i t i s a s s u m e d t h a t t h e f l ue g a s t e m p e r a t u r e a n d t h e a i r -t o - f u e l r a t i o a r e t h e s a m e f o r

t h e r e c u p e r a t e d a n d u n r e c u p e r a t e d c a s e s a n d t h a t t h e f u e l i n l e t t e m p e r a t u r e i s T b ,

e q u a t i o n ( 5 ) c a n b e s i m p l i f i e d t o :

W I , / ~ . = ( W J W ~ ) C p . . (T . . - Tb) + A H - - (1 + W o / W ~ ) C , g ( T g - T b ) (6 )

( W , / W f ) C p ° . . ( T = . - T b ) + A H f - ( I + I / V . / W f ) C t , , ( T g - T b )

19 8 HAL J. STRUMPF

Table 4 . Fuel sav ings i i

P r o b l e m s t at e m e n t

F u e l P e r c e n t a g e C o s tsav ings fue l sav ings ,

l b / s s a v i n g s $ / y

Stee l soak ing p i t , 1600°F a i r p reh ea t 0 .234 43 .8 455 ,600Alu m inum rem el t furnace , 1600°F a i r p reh ea t 0 .277 43 .4 539 ,300Gla ss m el t ing furnace , 2000 °F a i r p reh ea t 0 .333 57 .1 648,300

r! Co nv ers ion facto rs kg /s = (0.4536) f ib/s); °C = (°F-32)/1.8.

Since IVy ,, Wf f W I , T~ ,, Tg, an d T~, a r e a l l ava i l ab le f rom the p rob lem s ta t e m en t s (Tab le 1 ),

s e lec t ion o f a fue l ne t he a t ing va lue i s su f f ic i en t f o r the ca lc u la t io n o f the f ue l sav ings . To

p e r f o r m t h e c a l c u l a t i o n , a n e t h e a t i n g v a l u e o f 20 ,0 0 0 B t u / l b ( 46 ,0 0 0 J / g ) a t 6 0 ° F (1 6 °C )

i s a s s u m e d . T h i s i s a r e p r e s e n t a t i v e v a l u e f o r n a t u r a l g a s e s a n d f u e l o i l s . B a s e d o n t h i s

va lue , the fue l s av ings (WI , - WI , f o r each o f the th r e e p ro ces s e s i s p r es e n ted in Tab l e 4 .

A ls o l i s t ed i s the pe rcen tage f ue l s av ings , de f ined as 100 ( W I . - WI,) /WI. . Th e co s t sav-

i n g s g i v e n i n T a b l e 4 a r e b a s e d o n 1 0 0~ o f u r n a c e u t i l i z a ti o n f o r 8 0 0 0 h / y a n d a fu e l c o s to f $3 .38 /106 BTU ($3 .21 /109 J ) bas ed on f ue l g ro s s hea t ing va lue .

I t c a n b e s e e n f r o m T a b l e 4 t h a t f l u e g a s r e c u p e r a t i o n o f f e r s s u b s t a n t i a l f u e l s a v i n g s

p o t e n ti a l. A d v a n c e d b u r n e r d e v e l o p m e n t m a y b e d e s ir a b l e t o m a x i m i z e t h e b e n e f it s o f

r e c u p e r a t i o n .

E C O N O M I C A N A L Y S I S

E c o n o m i c a n a l y s e s w e r e p e r f o r m e d t o d e t e r m i n e t h e p a y b a c k p e r i o d s f o r f l u e g a s

r e c u p e r a t i o n u s i n g t h e c e r a m i c h e a t p i p e a n d m e t a l l ic h e a t e x c h a n g e r d e s ig n s d e v e l o p e d .

T h e c o s t o f t h e r e c u p e r a t o r s i s o n l y a p o r t i o n o f t he t o t a l h e a t r e c o v e r y s y s te m c o s t . T h e

c o s t a s s u m p t i o n s a r e l i st e d b e l o w ; t h e a s s u m p t i o n s a r e b a s e d o n c e r a m i c v e n d o r i n fo r -m a t i o n , d i r e c t i o n f r o m L A S L , a n d A i R e s e a r c h e x p e r i e n c e o n o t h e r w a s t e h e a t r e c o v e r yin s ta l l a t ions .

1 . Ceram ic he a t p ip es : $2 5 /1b ($55 /kg ) f o r tub e p r od uc t ion ; $67 /1b ($148 /kg ) f o r r e f r ac -

to ry l ine r ; $20 /h f o r hea t p ipe a s s e m bly (2 .5 h pe r tube) .

2 . C e r a m i c e n d s u p p o r t s ( t u b e p la t e s ) a n d c e n t r a l p a r t i t i o n : $ 5 0/1 b ( $ 1 1 0 /k g ) p l u s $ 1 0 0

p a c k i n g c o s t .

3 . M e t a l l i c r e c u p e r a t o r : $ 1 0 / l b ( $ 2 2 /k g ) c o m p l e t e l y f a b r ic a t e d .

4 . A s s e m b l y l a b o r o n - s i t e : $ 1 8 / m a n - h o u r : 4 0 h f o r m e t a l l i c u n i t a n d 0 .5 h p e r h e a t p i p e

t u b e .

5 . T ran s i t ion duc t ing : $50 /f t 2 ($538 /m2) .

6. Ins ula t io n: $20/ft z ($215 /m 2) for 1600 °F (870°C) de s ign s ; $25/ft z ($269/m 2) for 20 00 °F

(1090°C) des igns .

7 . S u p p o r t s t r u c t u r e : $ 2 . 5 0 /i b ($ 5 .5 1 /k g ); w e i g h t e q u a l s o n e - h a l f r e c u p e r a t o r p l u s d u c t -

ing we igh t .

8 . F an s : $400 /a i r hp ($536/kW) .

9 . Co n t ro l s , i n s t rum en ta t ion , e tc . : $5000 / lb /s ($11 ,000 /kg / s ) to t a l f low ( a i r p lu s gas ).1 0. A & E f ee : 1 5 ~ o o f c o s t .

I t s h o u ld b e p o i n t e d o u t t h a t t h e c o s t a n a l y s is d o e s n o t i n c l u d e a n y b u r n e r r e p la c e -

m e n t c o s t s o r c o s t s a s s o c i a t e d w i t h r e t r o f i t t i n g t h e h e a t r e c o v e r y s y s t e m t o a s p e c i f i c

i n s t a l la t i o n . T h e s e c o s t s , i f a n y , a r e s i t e - sp e c i fi c a n d c a n n o t b e r e a d i l y g e n e r a li z e d . T h e

c a l c u l a t e d c o s t s a r e p r e s e n t e d i n T a b l e 5 .B a s e d o n t h e s e c o s t s a n d t h e f u e l s a v i n g s g i v e n i n T a b l e 4 , s i m p l e p a y b a c k p e r i o d s c a n

b e c a l cu l a te d . T h e s i m p l e p a y b a c k p e r i o d is t h e r a t io o f t h e t o t a l s y s t e m c o s t t o t h e f u e l

c o s t s a v in g s . T h e p a y b a c k p e r i o d s a r e 0 . 4 0 y e a r f o r t h e s t e e l s o a k i n g p i t, 0 . 4 4 y e a r f o r t h e

a l u m i n u m r e m e l t fu r n a c e , a n d 0 . 3 0 y e a r fo r t h e g la s s m e l t i n g f u r n a c e . T h e s e p a y b a c k

C e r a m i c h e a t p i p e s f o r h e a t r e c o v e r y 1 9 9

p e r i o d s d o n o t i n c l u d e a n y a l l o w a n c e f o r h i g h - t e m p e r a t u r e b u r n e r o r s p e c if ic r e t r o f i tt i n g

c o s t s . H o w e v e r , e v e n if t h e s e c o s t s e q u a l t h e s y s t e m c o s t s c a l c u l a t e d i n T a b l e 5 , t h e

p a y b a c k p e r i o d s w o u l d a l l s t i l l b e l e s s t h a n o n e y e a r .

T a b l e 5 . C o s t s u m m a r y f o r c e r a m i c h e a t p i p e s y s t e m s ( d o l l a r s )

I t e m

S t e el A l u m i n u m G l a s ss o a k i n g r e m e h m e l t i n g

C e ra m i c h e a t p i p e s 5 3 ,0 0 0 5 1 ,8 0 0 6 4 ,7 0 0C e r a m i c e n d s u p p o r t s a n d c e n t r a l b a f fl e 6 8 0 0 6 7 0 0 8 3 0 0M e t a l l i c r e c u p e r a t o r 8 1 0 0 8 7 0 0 4 9 0 0A s s e m b l y l a b o r

H e a t p i p e s 1 6 0 0 1 6 0 0 2 0 0 0M e t a l l i c r e c u p e r a t o r 7 0 0 7 0 0 7 0 0

T r a n s i t i o n d u c t i n g 7 7 0 0 6 6 0 0 6 6 0 0I n s u l a t i o n 3 1 0 0 2 6 0 0 3 3 00Su p p o r t s t ru c t u re 1 3 ,7 0 0 1 2 ,6 0 0 1 2 , 60 0Fa n s 9 6 0 0 4 9 ,6 0 0 1 7 , 80 0A d d i t i o n a l i t e m s 5 6 ,0 0 0 6 7 ,3 0 0 4 6 ,3 0 0

Su bto t a l 160 ,300 208 ,200 167,200A & E f e e 2 4 0 0 0 3 1 ,2 0 0 2 5 , 10 0

To ta l cos t 184 ,300 239 ,400 192 ,300

A cknow l edgem ent s - - Th i s w o r k w a s s u p p o r t e d b y t h e U n i v e r s i t y o f C a l i f o r n i a L o s A l a m o s S c ie n t if ic L a b o r a -t o r y u n d e r P u r c h a s e O r d e r 4 - L 2 9 - 5 5 5 - O K - I . W . S . M i l le r a n d M . V . G r e e v e n m a d e s i g n if ic a n t c o n t r i b u t i o n s t ot h e s t u d y .

N O M E N C L A T U R E

C = C a p a c i t y r a t eC p = H e a t c a p a c i t y a t c o n s t a n t p r e s s u r eQ = F u r n a c e h e a t lo a dq = H e a t t r a n s f e r r e d

T,t = T e m p e r a t u r e

U A = O v e r a l l t h e r m a l c o n d u c t a n c eW = F l o w r a t e

A H = N e t h e a t i n g v a l u e

Subscripts

a = A i rb = B a s e ( r e f e r e n c e )c = C o l d s i d e

f = Fu e l

g = G a sh = H o t s i d eL = C o u p l i n g f lu i d

r = R e c u p e r a t e du = U n r e c u p e r a t e d

R E F E R E N C E S

1 . E . S. K e d d y a n d W . A . R a n k e n , C e r a m i c p i p e s f o r f u r n a c e h e a t r e c o v er y . Chemical Engineering Progress 7 5 ,

3 5 -3 7 ( D e c . 1 9 7 9 ) .2 . K . T . F e l d m a n a n d D . C . L u , P r e l i m i n a r y d e s i g n s t u d y o f h e a t p i p e h e a t e x c h a n g e r s . 2 n d I n t . H e a t P i p e

C o n f . , B o l o g n a , I t a l y , 4 5 1 -4 6 2 ( 1 9 7 6 ) .3 . Y . W a k i y a m a , K . H a r a d a , S . I n o u e , J . F u j i t a a n d H . S u e m a t s u , Heat Transfer Jap. Res. 7 , 2 3 - 3 9 ( J a n .

1978).

4 . A. F . L o n d o n a n d W . M . K a y s , T h e l i q u i d - c o u p l e d i n d i r e c t - t r a n s f e r r e g e n e r a t o r f o r g a s - t u r b i n e p l a n t s ,Trans. Am. Soc. mech. Enors " /3 , 529-542 (1951) .

5 . J . C. E a s t w o o d , L i q u i d - c o u p l e d i n d i r e c t - t r a n s f e r e x c h a n g e r a p p l i c a t i o n t o t h e d i e s e l e n g i n e . J. Enong Pwr1 0 1 , 5 1 6 - 5 2 3 ( 1 9 7 9 ) .

6 . H . J. S t r u m p f a n d W . S. M i ll e r , C e r a m i c h e a t p i p e r e c u p e r a t o r s t u d y . R e p o r t N o . 7 9 -1 6 48 0 , A i R e s e a r c hM a n u f a c t u r i n g C o m p a n y ( M a y 1 9 8 0) .

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