Soo Whan Ahn, Experimental Studies on Heat Transfer in the Annuli with Corrugated Inner Tubes, KSME International Journal Vol. 17 No. 8, pp. 1226~ 1233, 2003

7/21/2019 Soo Whan Ahn, Experimental Studies on Heat Transfer in the Annuli with Corrugated Inner Tubes, KSME Internatio

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1 2 2 6 K S M E International Jou rna l Vol . 17 No. 8, pp. 122 6~ 1233, 2003

E x p e r i m e n t a l S t u d i e s o n H e a t T r a n s fe r in th e A n n u l i w i t h

C o r r u g a t e d I n n er T u b e s

S o o W h a n A h n *

Sc ho ol o f M e c ha ni c a l and Ae rospa c e Engine er ing , G . ve ongsang N at i ona l Uni v e rsi tL

Ins t it u t e o f M a r i ne Indus t ry , 445 l npy o ng-d ong , Tongy ong , Gy o ngn am 650-160 , K ore a

E x p e r i m e n t a l h e a t t r a n s f e r d a t a f o r s i n g l e - p h a s e w a t e r f l o w i n t h e a n n u l i w i t h c o r r u g a t e d

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

a r e c o n s i d e r e d . F o r w a t e r fl o w r at e in 1 , 7 0 0 < R e < 1 3,0 00 r e g i m e , d a t a f o r N u s s e l t n u m b e r s a r e

p r e s e n t e d T h e r e s u l t s s h o w s i g n i f i c a n t e f fe c ts o f b o t h t h e p i t c h t o t r o u g h h e i g h t r a t i o ( P / e )

a n d th e r a d i u s r a ti o ( r * ) . A s

P / e

b e c o m e s c l o s e r t o 8 in t h e ra n g e b e l o w t h e r a d i u s r a t i o ( r * )

o f 0 .5 , N u s s e l t n u m b e r s i n cr e as e H o w e v e r , N u s s e l t n u m b e r s d e c r e a s e i n t h e r a n g e a b o v e t h e

r a d i u s r a t i o ( r * ) o f 0 .5 b e c a u s e fl o w r e a t t a c h m e n t p o s i t i o n b e c o m e s f a r t h e r i n t h e n a r r o w e r

c l e a r a n c e

K e y W o r d s : H e a t T r a n s f er C o ef fi c ie n t , C o r r u g a t e d A n n u l a r T u b e , P a r a l l e l F l o w , T u r b u l e n t

F l o w . L M T D ( L o g - M e a n T e m p e r a t u r e D i f fe r en c e)

N o m e n c l a t u r e

A H e a t t r a n s f e r a r e a [ m z ]

C p S p e c i f ic h e a t [ k J / k g K ]

D b B o r e d i a m e t e r [ m ]

D e E n v e l o p e d i a m e t e r [ m ]

D h A n n u l u s h y d r a u l i c d i a m e t er , ( D o ~ - D v o )

[ m ]

Doi

I n n e r d i a m e t e r o f t h e o u t e r s m o o t h t u b e

I m ]

D v i : V o l u m e - b a s e d c o r r u g a t e d t u b e i n n e r d i -

a m e t e r [ m ]

Dvo V o l u m e - b a s e d c o r r u g a t e d t u b e o u t e r d i -

a m e t e r [ m ]

e C o r r u g a t i o n d e p t h ,

( D e - D b ) / 2

[ m ]

e * N o n d i m e n s i o n a l c o r r u g a t i o n d e p t h , e / D v o

[m]

F r i c t i o n f a c t o r , 2 A P D h / p V 2 L

H e a t t r a n s fe r c o e f f i c ie n t [ W / m ~ K ]

T h e r m a l co n d u c t iv i t y [ W / m K ]

T u b e l e n g t h [ m ]

f

h :

k :

L :

*

E-m ail : swahn @gaechuk.gsnu.ac.kr

T E L : +82 55-640 3125:FA X: +82 55 640 3128

School of Mechanical and Aerospace Engineering.

Gyeongsang National University, Institute of Marine

Industry, 445 lnpyo ng-d ong , Tongyong, Gyongnam 650

-160, Korea. (Manuscript R eceived F ebruary 10, 2001;

Revised May 22, 2002)

N : N u m b e r o f c o r r u g a t i o n s t ar ts

N u : N u s s e l t n u m b e r , h D h / k

P

p *

P F

Q

R

R e

F*

T

U

V

V o l

0

O*

C o r r u g a t i o n p i t c h [ m ] , p r e s s u r e [ P a ]

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

P / D v o

[ m ]

P r a n d t l n u m b e r , , u C p / k

H e a t d u t y [ W ]

H e a t t ra n s f e r r e s i st a n c e [ K / W ]

: R e y n o l d s n u m b e r .

D h V / v

: A n n u l u s r a d i u s r a t i o , D v o / D o i

: T e m p e r a t u r e [ K ]

: O v e r a l l h e a t t r a n s f e r c o e f fi c i en t [ W / m 2 K ]

F l o w v e l o ci t y [ m / s ]

: V o l u m e [ m 3]

: C o r r u g a t i o n h e l i x a n g l e , t a n - t (~rD, ,o/NP)

[ ]

: N o n d i m e n s i o n a l c o r r u g a t i o n h e li x a n g l e ,

~ / 9 0

S u b s c r i p t s

a : A n n u l u s

s ; S m o o t h a n n u l u s

i ; I n n e r t u b e . i n l e t

c i : I n l e t a t c o l d s i d e

c o : O u t l e t a t c o l d s i d e

h i : I n l e t a t th e h o t s i d e


2/8

E x p e r i m e n t a l S t u d i e s o n H e a t T r a n s f e r i n t h e A n n u l i w h C o r r u g a t e d I n n e r T u b e s

1227

h o

: Outlet at the hot side

s : Smooth

t : Tube

t o t : Total

w : Wall

r : Corrugate d

1 . I n t r o d u c t i o n

The convective heat transfer coefficients may be

increased by artificially roughened surfaces, inlet

vortex generators, vibration of the surface, appli-

cation of electrostatic fields, and modification of

the duct cross section and surface. Many of these

techniques increase the heat transfer coefficient

through a change in flow patterns. In the recent

past, some attention has been given to heat trans-

fer augumentation by means of spiral flutes, gro-

oves, and ridges on heat exchanger tubes (Marto

et al., 1979). The spirally fluted or corrugated

tube is believed to enhance the convective heat

transfer by introducing swirl into the bulk flow

and/or periodic disruption of the boundary layer

at the tube surface due to repeated changes in

the geometry. Several geometric parameters such

as the inner diameter, envelope diameter, ridge,

pitch, shape, and the number of starts, must be

specified to define a corrugated or fluted enhanc-

ed geometry completely. These dimensions are

shown in Fig. 1. A change in any of these dimen-

sions affects the flow and heat transfer charac-

teristics of the tube. A survey of heat transfer and

friction factor studies for spirally fluted tubing

was also conducted by Bergles (1980). For la-

minar internal heat transfer in heating, 200 per-

cent increases in the heat transfer coefficient and

friction factor were reported. For turbulent inter-

nal flow, several studies were quoted with im-

provements of up to 400 percent above the plain

tube heat transfer coefficients, but the pressure

drop was as much as 10 times higher than for

plain tubes. Heat transfer and pressure drop for

tubes with single- and multiple- helix internal

ridging were investigated by Withers (1980a, b).

An empirical correlation for friction factor in

terms of the Reynolds number, Re and a set of

adjustable constants was proposed. Nakayama

F l u te d o r c o r r u g a t e d t u b e s

i

Fig. 1 Details of test section

et al. (1983) performed an experimental investi-

gation of heat transfer enhancement for water

flowing through spirally ribbed tubes in a turbu-

lent regime. They postulated that at low helix

angles, the flow near the wall follows the rib

profiles, while at high helix angles, it crosses the

ribs. At intermediate angles, the flow changes

from swirl-dominate flow to cross-over flow.

Garimella and Christensen (1995a, b) and Gari-

mella (1990) also addressed the hyd rod yna mic

and heat transfer aspects of the annuli with

spirally fluted inner tubes in counterflow. Flow

mechanisms and pressure drop measurements

were used to propose the friction factor cor-

relations. These flu ted -an nul us friction factor

correlations can be used to develop the Nusselt

number correlations in conjunction with heat

transfer data. While some research has been done

by previous investigators on the spirally fluted

enhanced geometries, there are deficiencies in un-

derstanding of heat transfer at spirally corrugated

geometries. The objective of the present study

is to experimentally investigate the heat transfer

characteristics of annuli formed by placing a

spirally corrugated tube inside a smooth outer

tube in parallel flow.

2 . E x p e r i m e n t a l A p p a r a t u s a n d D a t a

R e d u c t i o n

Six spirally corrugated tubes, one fluted tube,

and three smooth tubes for benchmarking pur-

pose, selected to achieve an adequate variation in

all the relevant geometric variables, were used for


3/8

1228

Soo Whan Ahn

T a b l e 1 T e s t m a t r i x fo r t e m p e r a t u r e m e a s u r e m e n t s

Ob

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[ a m ] [ m m ]

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D~o I p

[ m m ] [ m m ]

9.28 2

9.12 5

12.39 6

12.53 10

12.31 10

15.48 7

15.57 10

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Ds

: O r i g i n a l s m o o t h t u b e d i a m e t e r

Dvo :

V o l u m e - b a s e d g r o o v e d t u b e o u t e r d i a m e t e r

g : N u m b e r o f f l u te o r c o r r u g a t i o n s t a r ts

S : S m o o t h t u b e

T : S p i r a l l y c o r r u g a t e d t u b e

N ~ v * e *

I 0 .368 0 .022

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9

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E n v e l o p e d a i m e t e r

D v i V o l u m e - b a s e d g r o o v e d t u b e i n n e r d i a m e t e r

P F l u t e o r c o r r u g a t i o n p i t c h

Dol

I n n e r d i a m e t e r o f o u te r s m o o t h t u b e

SZ~.l

S p i r a l l y f l u t e d t u b e

t h e h e a t t r a n s f e r t es t. E a c h t u b e w a s p l a c e d i n a

s m o o t h o u t e r t u b e, w h i c h e n a b l e d t h e te s ti n g o f

a n n u l i w i t h d i f f e r e n t r a d i u s r a t i o s h o w n i n F i g . 1 .

A m a t r i x o f a ll th e a n n u l i f o r w h i c h h e a t t r a n s f e r

t e st s w e r e c o n d u c t e d i s p r e s e n t e d i n T a b l e 1. A

s c h e m a t i c o f th e f l o w l o o p a n d t es t s e c t i o n s i s

p r e s e n t e d i n F i g . 2. C i t y w a t e r w a s s u p p l i e d t o a

s e t tl i n g t a n k e q u i p p e d w i t h a n o v e r f l o w l in e . In

t h i s t a n k , a n y d i s s o l v e d a i r e s c a p e d t o t h e a t m o s -

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

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

a c h i e v e t h e o b j e c t i v e o f t h i s s tu d y , a t es t r ig t h a t

a l l o w e d t e s t in g o v e r a w i d e r a n g e o f f l o w r a t e s

w a s r e q u i r e d . I t i s e s s e n t i a l t h a t t h e t e m p e r a t u r e

c h a n g e s i n th e i n d i v i d u a l f l u i d s t re a m s , a n d t h e

a p p r o a c h t e m p e r a t u r e d i f f e re n c e s u se d f o r c a l c u -

l a t i o n o f L M T D s , a r e l ar g e e n o u g h t o m i n i m i z e

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

t r ic h e a t i n g f r o m t h e t u b e s i d e o r t h e t u b e w a l l

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

v o l u t e d c o r r u g a t e d t u b e g e o m e t ry . S t e a m c o n d e n -

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

f o r l a m i n a r f l o w a t th e a n n u l i s i de , th e l o w f l o w

r a t e c a u s e d t h e co l d f l u i d t o a p p r o a c h t h e h o t s i de

t e m p e r a t u r e w i t h i n a v e r y sh o r t d i s ta n c e . T h e r e -

f o re , a s u b s t a n t i a l p a r t o f t h e h e a t e x c h a n g e r d o e s

n o t c o n t r i b u t e t o h e a t t r a n s f e r b u t i s e r r o n e o u s l y

,,T ~, c.--

.,.J.,,r

F i g . 2 S c h e m a t i c d i a g r a m o f e x p e r i m e n t a l s e t u p

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

N e a r t h e o u t le t o f a n n u l u s s i d e, t h e w a t e r c o u l d

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

s i n g l e p h a s e f l u id s t r e a m s i n b o t h t u b e s w a s

s u i t ab l e . L a m i n a r a n d t u r b u l e n t h e a t t r a n s f e r t e st s

w i t h r e a s o n a b l e t e m p e r a t u r e c h a n g e s i n t h e re -

s p e c t i v e s t r e a m s , a s w e l l a s b e t w e e n t h e h o t a n d

c o l d s i de , c a n b e p e r f o r m e d b y u s in g s i n g l e - p h a s e

w a t e r o n b o t h s i d e s o f t h e h e a t e x c h a n g e r . A n

a p p r o p r i a t e l y c o n t r o l l e d t u b e - s i d e i n l e t t e m p e r a -

t u r e a n d m a s s f l o w r a te w o u l d p r o v i d e a h i g h


4/8

Experimental Studies on Heat Transfer in the Annuli with Corrugated Inner Tubes 1229

e n o u g h r a ti o o f ht/ha w i t h o u t c a u s i n g a n e x c e s -

s i v e t e m p e r a t u r e r i s e i n t h e a n n u l i f l u i d . A s t h e

a n n u l u s - s i d e f l o w r a t e i s i n c r e a s e d t o a c h i e v e th e

t u r b u l e n t Re v a l u e s , t h e t u b e - s i d e f l o w r a t e c a n

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

t u b e - s i d e h e a t t r a n s f e r c o e f f i c i e n t (h t ) /annulus-

s i d e h e a t tr a n s f e r c o e f f i c i e n t ( h a ) . C o n s i d e r i n g

t h e s e f a ct o r s, t h is m e t h o d is c h o s e n f o r c o n d u c t i n g

t h e h e a t t r a n s f e r t e s t s . T h i s m e t h o d d o e s , h o w e v e r ,

r e q u i r e a m e a n s o f c a l c u l a t i n g

ht

w i t h a n a c c u r a -

c y t h a t d e p e n d s o n t h e s p e c i f i c v a l u e o f

ht/ha

in

q u e s t i o n . A c o l d w a t e r s u p p l y l i n e a n d a s u p p l y

o f h o t w a t e r w e r e u s e d f o r t h e t es t s. T h e c i t y w a t e r

l i n e w a s s p l i t i n t o t w o d i f f e r e n t s t r e a m s . O n e

s t r e a m w a s u s e d a s th e c o l d w a t e r i n l e t to t h e

a n n u l u s s i d e o f t h e te s t s e c t io n . T h e o t h e r s t r e a m

w a s h e a t e d b y a n e l e c tr i c a l h e a t e r ( C a r t r i d g e

t y p e, 5 k W ) t o p r o v i d e t h e d e s i r e d f l o w r a t e o f

h o t w a t e r a t th e r e q u i r e d i n l et t e m p e r a t u r e . T h e

h o t w a t e r p a s se d t h r o u g h t h e h e a t e x c h a n g e r a n d

e x i te d t o t h e d r a in . C o l d w a t e r f r o m t h e o u t l e t o f

t es t s e c t io n w a s s u p p l i e d t o t h e c o m b i n a t i o n o f

c o n t r o l v a l v e s , f r o m w h i c h it f l o w e d t h r o u g h a

f l o w m e t e r o f c u m u l a t i v e t y pe .

T h e m e a s u r e d f l o w r a te w a s u s e d to c a l c u l a t e

t h e h e a t d u t y i n t h e h e a t e x c h a n g e r a n d t h e a n -

n u l u s R e . T h e c o l d w a t e r f lo w e d t h r o u g h t h e

p a r a l l e l f l o w h e a t - e x c h a n g e r t es t s e c t io n a n d

e x i t e d t o th e d r a i n . T h e t e s t s e c t i o n c o n s i s t e d o f a

1 . 8 - m - l o n g h e a t e x c h a n g e r , i n s u l a t ed o n t h e o u t -

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

s m o o t h o u t e r t ub e . W e m e a s u r e d t h e i n le t a n d

o u t l e t t e m p e r a t u r e s o f t h e t u b e s i d e a n d s h e l l s i d e

f o r o v e r a l l e n e r g y b a l a n c e b y a d a t a a c q u i s i t i o n

s y st em . T h e r m o c o u p l e p o r ts ( f or K - t y p e t h e r m o -

c o u p l e s ) w e r e a l s o p r o v i d e d a t 3 0 c m a n d 1 50 c m

f r o m t h e e n d s o f t h e i n n e r tu b e . N u m e r i c a l v a l u e s

a n d g r a p h s o f t e m p e r a t u r e s a s a f u n c t i o n o f t i m e

w e r e d i s p l a y e d a n d r e c o r d e d o n a c o m p u t e r t o

a l l o w c o n f i r m a t i o n o f t h e s t e a d y s ta te . D u r i n g t h e

t es ts , t h e r a ti o o f t u b e - s i d e t o a n n u l u s - s i d e f l o w

w a s k e p t a t a b o u t f iv e w h e n e v e r f e a s ib l e . B e c a u s e

t h e a n n u l u s - s i d e f l o w a r e a w a s ty p i c a l l y l a rg e r

t h a n t h a t o f t h e t u b e s i de , t h is r a t i o o f m a s s - f l o w

r a t e s r e s u l te d i n h i g h e r r a t i o o f h e a t t r a n s f e r

r e s is t a nc e s . T h i s c o n t r o l s t r a te g y h e l p e d i n m i n i -

m i z i n g t h e s en s i t iv i t y o f t h e d e d u c e d a n n u l u s - s i d e

h e a t t r a n s f e r c o e f f i c i e n t (h ,~ ) v a l u e s t o e r r o r s i n

t h e t u b e - s i d e c o r r e l at i o n s . T h e R e y n o l d s n u m b e r

w a s c a l c u l a t e d f r o m t h e m e a s u r e d f l o w r a te b a s e d

o n t h e h y d r a u l i c d i a m e t e r , D h . T h e f l o w v e lo c i t y

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

a r ea . I t s h o u l d b e n o t e d t h a t th e c o r r u g a t e d t u b e

d i d n o t h a v e a c i r c u l a r c r o s s s e c t i o n : t h e r e f o r e ,

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

s e c t i o n a l a r e a o f t h e c o r r u g a t e d t u b e s w a s c a l -

c u l a t e d f r o m t h e v o l u m e o f w a t e r r e q u i r e d t o fi ll

a g iv e n l e n g t h o f tu b i n g a s f o l l o w s :

4 V o l

D ' = V / a ' L C I)

T h e v o l u m e t r i c o u t s i d e d i a m e t e r ,

Dvo,

w h i c h i s

t h e q u a n t i t y o f i n t e r e s t f o r t h e a n n u l u s s i d e , i s

c a l c u l a t e d b y a d d i n g t w i c e th e tu b e t h i c k n e s s t o

D,,~. T h e h e a t d u t i e s o f t h e t w o f l ui d s t r e a m s

w e r e c a l c u l a t e d f r o m t h e f l o w r a t es a n d t h e te m -

p e r a t u r e c h a n g e s i n t h e re s p e c t i v e s t r e a m s f r o m

t h e i n le t t o t h e o u tl e t. T h e d i s c r e p a n c y b e t w e e n

Q a a n d @ t w a s l es s th a n 6 ~ o e v e n a t t h e w o r s t

s i t u a t i o n . T h e o v e r a l l h e a t t r a n s f e r c o e f f i c i e n t

UAtot

w a s c a l c u l a t e d a s f o l l o w s :

Qto~

i2)

UA tot - L M TDtot

( Tho- - Too) - ( T h ,- Tci i

L M T D - - l n [ ( T h o _ T o ) / ( T h i _ T c i ) i

(3)

w h e r e

L M T D

m e a n s t h e l o g m e a n t e m p e r a t u r e

d i f f e r e n c e i n p a r a l l e l f l o w . T h e s u b s c r i p t s tot

r e p r e s e n t s t h e t o t a l h e a l e x c h a n g e r , i n a d d i t i o n ,

h i a n d

ho

r e f e r t o t h e i n l e t a n d o u t l e t a t t h e h o t

f l u i d s a n d c i a n d

co

r e f e r t o t h e i n l e t a n d o u t l e t

a t t h e c o l d f l u i d s , r e s p e c t i v e l y . H e a t d u t i e s ,

LMTDs, a n d UAs a r e a l s o c a l c u l a t e d b y u s i n g

t h e e q u a t i o n s s h o w n a b o v e f o r t h is f u l ly d e-

v e l o p e d h e a t e x c h a n g e r s f o r e a c h d a t a p o i n t f o r

a ll t h e a n n u l i. T h e o v e ra l l U v a l u e ( U A / ~ r D o o L )

i s c o m p r i s e d o f th e c o n d u c t a n c e o f th e t u b e s i d e ,

t h e t u b e w a l l, a n d t h e a n n u l u s s id e . T u b e s i d e

f l o w is a l w a y s m a i n t a i n e d i n t h e t u r b u l e n t r e g i m e ,

a n d t h e c o r r e s p o n d i n g t u b e - s i d e N u f o r

R e

> 7 0 0

i s g i v e n b y R a v i g u r u r a j a n a n d B e r g l e s ( 1 9 85 ) a s

f o l l o w s :


5/8

1230

Soo Whan Ahn

NusNur ( 1+ [.~ 64ReO.O~ O.mp,_ o.zl ( O,)O.~pr_O.o~]r) (4)

In the correlation heat transfer data for smooth

tubes, several investigators have used an eq uatio n

that incorporated the corresponding friction fac-

tor. One such example is the Petukhov and Popov

correlation (1963). Because the Nusselt numbers

for fluted annuli showed a departure from la-

minar behaviour at Reynolds numbers as low as

700, it was assumed that such an approach would

be applicable for 700


6/8

E x p e r i m e n t a l S t u d i e s o n H e a t T r a n s f e r in t h e A n n u l i w i t h C o r r u g a t e d In n e r T u b e s 1231

3 0 0

2 0 0

_ P r = 6 . 8

- : : : , , :So,t,-:=o. vvl

= : S 0 ~ { r = 0 . 4 9 6 )

- , t* ~ . . ,, : So .~ (r = 0 . 6 : 2 7 )

: E ( l . ( 1 1 )

( r ' = 0 . , 1 9 6 )

o ~ - o , : : c : G a r i m e l l a & C h r i s t . e n s e n

( 1 9 9 5 ) ( r ' = 0 . 5 4 7 )

. . - ~1

, ~ - ~ a .-

l l ~ )O 0 ' - , 0 0 0 9 0 ~ 0 0 ' 1 3 t ; O 0

R e

F i g . 3 N u s s e l t n u m b e r s f o r s m o o t h a n n u l i

F i g u r e 4 s h o w s t h e v a r i a t i o n s o f N u s s e l t n u m -

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

t u be s , T u a n d T ~ z . T h e N u s s e h n u m b e r s i n T u

o f p i t c h to t r o u g h h e i g h t r a t i o ( P / e ) = 1 0 a r e

s o m e w h a t h i g h e r t h a n i n T ~z o f 1 2 .5 . T h i s p h e n o -

m e n a h a v e s i m i l a r te n d e n c i e s to L a w n ' s r e s u l ts

( 19 7 4 ) t h a t N u s s e l t n u m b e r s b e c o m e h i g h e st

a r o u n d P / e = 8 a n d l o w e r a t t h e s i t u a t i o n f a r t h e r

a w a y f r o m

P / e = 8 .

T h i s f e a t u r e i s i n a l i n e w i t h

W i l k i e ( 1 9 6 6 ) a n d A h n e t a l. ( 1 9 94 ) s h o w i n g

t h a t t h e h i g h e s t h e a t t r a n s f e r o c c u r s w h e n t h e

r o u g h n e s s p i tc h a n d f lo w r e a t t a c h m e n t a r e e q u a l .

W e d e r i v e d t h e e m p i r i c a l c o r r e l a t i o n s f o r t h e

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

f o l l o w s ;

r * < 0 . 5 :

Nua= (0.115Pr+0.1987) (-4.94652

X

10-TRe2+0.026896Re-36.25)

12)

x [O.0211(P/e12-0.528 P/e) +3.742]r *-~

.m

z

3 0 0

2 0 0

P r = 6 . 8

o o o , : . o : S 0 t ( s m o o t h a n n u l i )

i l O E ~ O , T I I

W 1

E q . ( 1 2 ) : . "

S o l i d l i n e :T ~ x . '

D a s h e d l in e : T ~ 2 . -

I

10 0 D ~ - C : ]

I

' - e~ , ' ~ C ,

O C '

I

6 ~ Y

t~'00

. , o o o 3 0 ; 0 1 : 3 o ~

l

R e

F i g . 4 N u s s e lt n u m b e r s f o r c o r r u g a te d a n n u l i , T n

a n d T l 2

2oo i

z r

~.o,: c ,o > : S 0 ~ ( s m o o t h a n n u l i

:300 iu ~'~'-- ~ : ' l 'a

* * * ' ~ :Ta a

, o e o o : S T z l ( f l u t e d t r i b e

Eq.{ l:e):

~. S o l i d l i n e :'l'~ .~

I 1 ) a s h e d l i n e : ' f : , ~

. . . . i

P r = 6 . 8

/ / , .

@ ~ . /

L~- ~.

t 0 0 L o r j J

0 ~ E J - ~ . ' ,? ; ~[ '

t ~ ~o},o - - . ~ 0 : o o --~ 13ooo

R e

Fig. 5 Nus sel [ nu mbe rs for corrugated and fluted

annuli, Tzl, T22 a nd ST21

r * > 0 . 5 :

Nu ~= (0.115Pr+0.1987) (7.268x lO-SRe2+O.OIO54Re+ 5.3)

x [0.028I P/e) +0.4991 *-s5 (1 3)

T h e s o l i d a n d d a s h e d l i n e s i n d i c a t e th e d a t a

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

a n d T l 2 . T h e e m p i r i c a l c o r r e l a t i o n s p r o v i d e a

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

m e n t a l da t a. T h e N u s s e l t n u m b e r s in th e a n n u l i

w i t h c o r r u g a t e d c o r e t u b e s o f T21 a n d T 2 2 , a n d

w i t h s p i r a l l y f l u t e d c o r e t u b e o f S T2 ~ a r e s h o w n

i n F i g . 5 . T h e v a l u e s i n ST21 are m u c h h i g h e r

t h a n i n T21 a n d T 2 2. T h i s e f f ec t m i g h t b e c a u s e d b y

t h e f a c t t h a t t h e t r o u g h , c o r r e s p o n d i n g t o t h e

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

h i g h e r . N u s s e l t n u m b e r s f o r T3 1 a n d T 3z a r e i n -

d i c a t e d i n F i g . 6 . C a r e f u l i n s p e c t i o n o f th i s f i g u r e

f u r t h e r s h o w s t h a t , b e i n g d i f f e r e n t fr o m F i g s . 4

a n d 5 , t h e h e a t t r a n s f e r i n T3 2 h a v i n g p i t c h t o

t r o u g h h e i g h t r a t i o

( P / e )

o f 1 4 . 2 i s h i g h e r t h a n

i n T m h a v i n g P / e o f 1 0. T h i s f e a t u r e i s a t t r i b u t e d


7/8

1232 S o o W h a n A h n

7

Documents

Soo Whan Ahn, Experimental Studies on Heat Transfer in the Annuli with Corrugated Inner Tubes, KSME International Journal Vol. 17 No. 8, pp. 1226~ 1233, 2003