Boiling on a finned tube and a finned tube bundle

Int. J. Hea' Mills Tram/a. Printed in Great Britain

Vo!. 26. No.6. pp.

8~9,859.

198J

OOI7,9JIO.83/0608~9-11SOJ.OO 0

Pergamon Press Ltd.

BOILING ON A FINNED TUBE AND A FINNED TUBE BUNDLE E. HAHNE and 1. MOLLER* Institut fur Thermodynamik und Warmetechnik, Universitat Stuttgart, PO Box 80 II 40,0-7000 Stuttgart 80, F.R.G.

(ReceiL'ed 28 May 1982) Abstract-Anexperimentalinvestigation wascarricd out in a 151dm? container in R l Lat saturationstate of 1 bar and 23.3cC. The heat transfer coefficients measured on a single tube in the container resembled approximately results for the case that only one tube is heated within an in-line 18 tube bundle. For a twin tube arrangement, the heat transfer coefficient of the upper tube is up to 80% higher than that of the lower tube. The heat transfer curve of this upper tube represents quite well the heat transfer coefficientsof tubes enclosed in the bundle. Only for the bottom and top tubes of the bundle differences do occur. The possibility to obtain tube bundle data, at least to some extent, by much simpler twin-tube or triple-tube experiments would facilitate experimental investigations.

I'\O;\IEr\CLATURE

A, C, d, h, k, L,

Q,

q, S,

reported in ref. [20] especially in contributions by

Bergles; Yilrnaz, Palen and J. Taborek; Stephan and

surface area; constant; diameter; mean heat transfer coefficient; thermal conductivity; length; heat flow; heat flow density, Q/A ; tube pitch.

Mitrovic, For the range of parameters, there still are comparatively few experimental results for finned tube bundles; certainly not enough for widely applicable correlations to be made. The experiments, however, are quite delicate to perform and require a considerable amount of apparatus. The present aim is to investigate (and provide additional experimental results on) the extent to which the data for single or twin tubes are applicable to bundle heat transfer results. For this purpose, heat transfer coefficients are measured on a single tube, on two tubes positioned vertically above each other, and on an inline bundle consisting of 6 horizontal rows of 3 tubes each.

Greek symbol 9, . temperature, Subscripts w, wall; 0, outside; i, inside; v, vapour; I, liquid; /I, number of tube, row; m, mean.

2. EXPERIi\IENTAL SET·UP

The experiments were performed in R 11 (CFCI 3 , rnonofluorotrichloromethane) at a pressure of about 1 bar and a saturation temperature around 23°C. The finned heater tubes were made of copper to the dimensions given in Fig. 1. All 18 tubes were produced identically and came from the same production batch.] The mean surface roughness of the tube was R p = 0.3 11m. Each tube could be heated separately with an internal electric heater (3000 W at 220 V). The heated length was 260 ± 6 mm (according to the manufacturer). In order to equalize differences in the electric heater temperature, a copper filler tube was fitted inside the finned tube and then expanded. The electric heater was soldered into the filler tube. The homogeneous soldering contact and the pressure fit was checked by cutting a sample tube on a lathe. The ends of the tubes were insulated with Teflon shrouds. The tubes were arranged in a rectangular container in three experimental variations as shown in Fig. 2. In

1. INTRODUCTION

INMODERN tube bundle evaporators, especially those in refrigeration machinery, finned tubes are widely used. The performance of fins in various shapes for boiling heat transfer has been investigated in [1-7]. The behaviour of single finned tubes and effects of their geometric parameters are presented in [8-10]. In experiments with bundles offinned tubes [11-16] it was shown that convection currents induce a remarkable enhancement in boiling heat transfer. Heat transfer results differ due to tube geometries and bundle geometries. Based on a comparison of experiments of [13, 15, 16], heat transfer correlations were worked out [17-19]. In the recent efforts to produce more efficient heat transfer equipment, special kinds of "enhanced tubes" have been developed with experimental results

* Present address: Fichtner, Beratende Ingeaieure, 0-7000 Stuttgart 1, F.R.G. 849

t The finned tubes were produced and prepared for measurements by Wieland-Werke AG, Metallwerke, Ulm(Donau), F.R.G. The authors gratefully acknowledge this valuable support.

E,

850

finned tube diameter root diameter inner diameter

HAHl-o"E

and J.

dF = 18.9 mm d. = 15.9 mm d, '= 13.9 mm

fin pi tch

h t

1.5 mm 1.35 mm

mean fin th ickness

b

0.4 mm

fin height

MUllER

heater diameter dH Rp mean surface roughness (DIN4762) total sur f ace area (tu be) unf inned surfacearea (tube)

1. finned tube 2. filler tube

3. heating element

8.5 mm

OJ IJm

'!l= 3.18

r---- - - - 270 - -- - - - - 1 f inned length

1 t

6

YiW3V'S 4

.-t--.__ ._ I

-

ff

L - - .f.--- . I

!

.

3~lo-l---50--L-50-l-50~o.i-3 1

3 S 2 6 I '4 location of t her mocouples .

FIG. I. Finned tube heater geometry.

1 - - - - - 370 - - - - 1

rh vapourI outlet

<::. I

600

fluidreflaw single -tubeI

bjJ

twin -tube-

s = 2dR = 37.8mm

bundle- arrangement

C

thermocouple location

FIG. 2. Finned tube arrangements and thermocouple locations inside the test vessel.

Boiling on a finned tube and a finned tube bundle

order to prevent lateral flow, and to simulate a fraction of a larger tube bundle, the 18 tubes were placed between glass plates, their upper ends extend out of the fluid by about 70mm in order to help prevent splashing. Additional plates were inserted for the same reason. The container was made from stainless steel and measured 680 x 600 x 370 mm. Three sides (the 680 x 600 mm front and back, and one 370 x 600 mm side) were equipped with glass covers to allow observation. The vapour produced in the test vessel was condensed ina separate, controllable condenser and fed back through a thermostatic pre-heater into the test vessel. The entire test apparatus was set up in a temperature-controlled compartment with air temperatures adjusted to the saturation temperature inside the vessel.

Fluid and vapour temperatures are measured at the locations shown in Fig. 2. In twin-tube and bundlearrangements, the thermocouples inside the respective upper tubes were used to determine the temperature of the approaching liquid 81" (II indicates on-flow to tube or row 2,3, ...). When these tubes were used for temperature measurement they were not electrically heated, of course. As an example, excess temperatures

/18 = 8)-8. and

/18 = 812-8. for the twin-tube arrangement are shown in Fig. 3. 3.2..Pressure The saturation pressure is measured above the liquid level with a pressure gauge of class OJ within the range 0-1.5 bar.

3. l\IEASUREl\IEl'o'TS

3.1. Temperatures Temperatures were measured with coated Philips NiCr-Ni thermocouples (O.S mm O. diameter). The heater inside wall temperatures were taken at six different points along the heater length and around the circumference as shown in Fig. 1. The outside wall temperatures (around dJ were calculated from

8"0

=

8"'i-(2~L) In ~:.

3.3. Heating rate All tubes could be heated separately. Their heating power was measured individually with a power meter of class OJ. 4. EXPERIMEl'oTAL PROCEDURE

Special precautions were taken in order to provide reproducible results: the carefully cleaned vessel was flushed several times with R 11, evacuated and filled; all tubes after careful cleaning were placed in the vessel and heated for at least 50 h (at q = 4 X 104 W m - 2); all boiling experiments were performed under decreasing heat flow densities. In all experiments, the saturation pressure was kept at an average of P. = 1.000±0.005

(I)

The arithmetic mean of six outside wall temperatures was taken as the representative wall temperature 8.,. The difference between 8., and the temperature of the saturated vapour above the liquid, 8" is

/18 = 8.,-8•.

~

1,4

~ 1,2

PI

II

10

d?'
....

~If~v

0.8

~

0

L.. QI

a.

~

J

'\l

0

QI

X

I

27.11.78} upper tube 7. 1.79

0.4

_

~

-

I r>

/~12 -.;)v

h..h vy,

<>. . r- t'Clb

0

0,2

l-D" ~

~

0'"

"'0

I

~

l~

~I- ~v

itu

meosurements.q increasin9,',Q decreasing

2

4

6 8 10 3

2

-

1

1-..:=

0

0

-

Rp = 0,3 pm ; q2 = 0

~

6~hydrostatic= 0,45 K

W

sr ~v=~s

~~2 ~ s

~I

= 1bar = 37,8mm

Ps s

<=

e12

If\....

VI VI

u

I

27. 11. 78} liquid 7. 1.79

0 ~Boiling

/

0.6

E

0

f

I

d?

R~n

I

Natural Convection

851

6 8 10 4

4

Heat flow density

q1

~

~ Q-

2

4

6

W/m 2

FIG.3.Temperature differencesbetween liquid and saturated vapour as a function of heat flowdensity q1 of the lower tube.

852

E.

HAH!'<'E

and J.

bar at a saturation temperature of 8. = 23.31°C. The measurements were repeated at intervals of several months or 1 year.

to row. The same kind of temperature distributions are obtained when the lower two or three rows are heated. This is shown in Fig. 5 for a heat flow density of 4. ;= 4 = 104 W m- 2 • For comparison the distribution of the excess temperature according to the hydrostatic head /18hydrost31ic is given for the various tube positions. Some agreement with the data measured is reached only around rows 4 and 5.

5. EVALUATION OF EXPERIMEl''TAL DATA

5.1. Temperature distribution in the liquid The temperature in the liquid is not homogeneous. For twin-tubes, Fig. 3 shows the excess temperature in various places of the vessel versus the heat flow density of the lower tube. For natural convection conditions, the temperature 8. (of the liquid approaching the lower tube 1) is only slightly above the vapour temperature. It increases to values amounting to /18 = 0.2 K for most of the boiling region. With fully developed boiling at 4 = 104 W m - 2 the excess temperature drops to zero (the deviations into the negative range of Fig. 3 are probably due to subcooled condensate hitting the lower thermocouple). The temperatures of the liquid approaching tube 2, i.e. 812 , are quite different from 81 : in the natural convection regime there is a steep rise, for incipient boiling a decline is followed by a constant excess temperature. This excess temperature agrees very well with the theoretical excess temperature of /18 = 0.45 K obtained from the hydrostatic head above tube 2. Again, for fully developed boiling !18 drops to zero. The temperature distribution within an I8-tube bundle, with the bottom row heated, is shown in Fig. 4. The excess temperatures range from 0.7 to 0.5 and gradually decrease with increasing heat flowdensity 41' Because ofmixing and heat losses, as one would expect, the excess temperatures decrease upwards from row

1.0 ::s::

0.9

I

- "

MOLLER

5.2. Reference temperature and characteristic difference In boiling it is customary to use 'the difference between the heater wall temperature and the saturation temperature of the fluid as the driving potential for heat transfer. In the tube bundle the theoretical saturation temperature changes from one tube row to the next and does not agree with the actually measured values. These latter values indicate a liquid subcooling around rows I and 2 and a superheating around rows 5 and 6. In natural convection the on-flow temperature is considered characteristic to form the temperature difference for the heat transfer coefficient. In our experiments these on-flow temperatures were measured when the tube hit by the approaching fluid was not heated. If the tube is heated, the increased onflow might cause changes in the on-flow temperature, so that our data of the unheated case may deviate from such of the heated case. At any rate, approaching-flow temperatures are difficult to measure and control. The simplest reference temperature to obtain is the vapour temperature above the liquid level: as long as the vapour pressure is kept constant, it does not vary. A comparison between various tube arrangements is quite easy, but specific local results might be camouflaged. It was tried to correlate results on the

I

1--3s-

m r I

i?

0.8

-

I

.= 0.7

r-"

d? II

d?
0.6

f-

0.5 -

U'l U'l


x

w.

OJ

L s

0<1>·

~~

CD 000 000 000

•••

5 5

n.

4

3 2 1

0

,

",.-1

,

VJ

I

I I

v

I~

R11. Ps =1bar

f-

s=2dR=37.8mm • healed tube

~

~lra'N2

~ ~I

r--v- ~~

'V

-

r-o- N

~~

,3 f - -

~ ~~

5

0.2 ..

2

4

6 8 10 3

2

Heat flow density FIG.

4

q1

6 8 10 4

2

4 W/m 2

4. Excess temperature in the bundle as a function of heat /low density.

6 8 105

Boiling on a finned tube and a finned. tube bundle

853

1.1 sr

1.0

I

::<::

0.9 e-

c!?

0006 0005 0004 0003 0002 0001

0.8

.= 0.7

c!?

II

II

~ 0.6 OJ

L..

.2 0.5

e Q)

Cl.

E

0.4

OJ

t-

V'> V'>

OJ

Q)

U

x

UJ

0.2 0.1 0 30

20 15 Height of liquid level

25

10

o

5 em

FIG. 5. Excess temperature in the tube bundle.

basis of each of the above mentioned temperatures, 9. local> 9 1n and 9.; best results were obtained with 9vTherefore the characteristic temperature difference is taken as

with

11

3000 <

(2) with the heat flow {2, the total transfer area Atotal of the finned tube, the mean wall temperature 9 w •m obtained from six local temperatures (section 3.1), and the vapour temperature 9•. The correlation of heat transfer coefficient and heat flow density is presented as usual in the simple form

11 = Clj".

(3)

6. RESULTS

6.1. Single tube In Fig. 6, the heat transfer coefficient is plotted against the heat flow density. Various regions of the boiling curve can be discerned. (a) The transition region between natural convection and incipient boiling for 700 <

q < 3000 W m - 2

qO.64.

(4a)

q < 20000 W m- 2

with

11 5.3. Heat transfer coefficients and correlations From measured data the mean heat transfer coefficient is calculated using

2.27

(b) A region of moderate nucleate boiling for

~9 = 9 wall- 9.apour'

(Any other differences may be obtained from Figs. 3-5.)

=

=

0.697 qO.79.

(4b)

(c) The region offully developed nucleate boiling for

q> 20000 W m"? with

h = 8.53

qO.54.

(4c)

Visual observation reveals that all spaces between the fins are filled with vapour in the fully developed boiling regime. In moderate boiling, a number offin interspaces remains without vapour production. Thus in this latter regime, the effect of convection appears still influential and the activation of new nuclei helps towards a steeper increase in heat transfer than in the fully developed boiling where the off-flow of additional vapour is hampered by the fins. 6.2. Twin-tubes The simplest case ofa tube-bundle evaporator can be seen in two tubes positioned one above the other. Results for this case are presented in Fig. 7. The heat transfer curve for the lower tube 1 exhibits little difference to the single tube curve: The single tube curve yields lower heat transfer coefficients in the region of

E. HAHNE and J. MULLER

854

:.::

5.10 1 4

I

~

...

n

E

I

==

2

s

Rp:0.3 prn

run B 12 78 o 31. 1.79 to. 30 1. 7B sr 22. 1. 78

.c::

101 C '" 8 'u E: 6

'" u

R11,p :1bar

110

o

0

4

L..

~ co

e""

I I

2

d

I I

'"

:::

10 1

10 1

8

Z 4 8 101 Heat flow density Q

10~

6 8 10'

2 W/m 1

FIG. 6. Heat transfer coefficient on a single finned tube vs heat flow density.

low heat flow densities where the heat transfer is convection-controlled. The increased agitation by a recirculatory flow inside of the test vessel may be the cause of the somewhat higher heat transfer coefficient on the lower tube of the twin-tube arrangement. The enhanced heat transfer coefficients from the upper tube 2, clearly exhibit the effectof approaching flow. Higher heat transfer coefficients are observed throughout the moderate boiling region where a convection-controlled regime prevails. Differences in heat transfer coefficients between the lower and the upper tube vanish with fully developed boiling.

6.3. Tube-bundle 6.3.1. Separately heated middle tubes. Within the 18tube bundle only the middle tubes in each row were heated here and only one at a time; results of this variation are shown in Fig. 8. For each tube, approximately the same relation h - q is obtained regardless of the position within the bundle. A closer scrutiny reveals the heat transfer coefficients of tubes 1 and 5 as being higher than those oftube 2,in most cases. 6.3.2. Simultaneously heated middle tubes. For the case that all middle tubes are heated simultaneously

5.10 3 .---.-----.-----r---,--_.__---,------r-r--r:;r-~--r---rT_.____.__7I I I I I /

4-

I

2

I

:~

r

c:

x:

c:: OJ

·u OJ

1'0

R11, Ps: 1bar s : 2 dR: : 37. 8 mm

8 I-6 r

a u

0

0

Run 2711 78} 7 1. 79 upper tube

~ 2;.1~: ~n

lower lube

/

1/

1/

/V /.~ r / I/~J~ 5P / x:: y / . / / p / ~ /

(Duppe::Jbe

I

103

/

\

/ /

/V

»,/ ~7 (Dlower lube

2

2

4

6 810 3

2

4

6 810 4

Heat flow density Q,=Q2=q

2 4 2 W1m

FIG. 7. Heat transfer coefficient h. as a function of heat flow density for the two tube arrangement (til

= til = til.

Boiling on a finned tube and a finned tube bundle ~

E

510 3 4

3, 5

r Q- 0 -Q 6 'L 0- 0 0 5

2

a 0 a 4 a e a 3 a e a 2 o e a 1

c:

.c: OJ

u

..... OJ

0 U L-

~

103

8 6

6

4

e

0

.....0

"

o

til C

l::

5

r7i

3=

..... c

855

2

R1'. PI = 1bar 5 = 2dR = 37.8mm separately heated tube

c o o

tube 6 tube 5 lube 4 lube 3 tube 2 tube 1

OJ

:::c

4 6 8 10 3 2 4 Heat flow density qn

2

6 8 10 4

6 8 10 5

2 4 2 W1m

FIG. 8. Heat transfer coefficient h. for middle tubes heated separately in a bundle arrangement.

with the same heat flow density, the results are shown in Fig. 9. Due to increased convection flows, now the heat transfer is enhanced: the highest heat transfer coefficientsare obtained in the top row, thelowestin the bottom row. In the convection-controlled regime, the increase can be I00%; with fully developed boiling the various curves merge. As one would expect, the heat transfer is better than on separately heated tubes. 6.3.3. All tubes heated. These results, given in Fig. to, are similar to those of the simultaneously heated middle tubes with respect to their overall tendency. In detail: in the region oflower heat flowdensities where convection has its effects, the heat transfer coefficients are

~

5-103 4

3=

2

c:

C OJ

'w ..... OJ

0

OJ

3

10 8 6

m ,'9

~""'-

\;

/1 I I

oeo 3 a eo 2 oe01

I

I

I /

4

Rll. p. = , bar s=2d R=37.8mm • healed tube a unhealed lube

til

c 0

..... .....0

AND CORRELATIONS

As shown in Section 6, the heat transfer coefficients from identical tubes in a bundle vary with tube position and heating arrangement. When the effect of heating

U L-

CO~IPARISON

6 s '.<;) 5 oeo 4

.s:

.....

7.

3s

E

--

somewhat higher when all tubes are heated. At high heat flow densities, no clear difference in the heat transfer coefficients is 0 bserved between the case tha tall tubes were heated or only middle tubes were heated. It should be noted that heat transfer coefficients were calculated with temperatures measured on each middle tube only. So location effects within a horizontal row were not distinguished.

L-

2

OJ

:::c

10 2

10 2

2

4

6 8 103

2

Heat flow density

4

6 8 10 4

qn

FIG. 9. Heat transfer coefficient h. for simultaneously heated middle tubes (41

2

4

6 8 105

W/m 2

= 42 = ... 4.; 11=

1,2, ... ,6).

856

E. HAHNE and J. MULLER

::.::

--:s: E

S·103 4 2

f-

" .L

r-- 35-5

II!

l-

I

I

c

4 3 l 1

.c:

c

ClJ

'w

= ClJ

0

10 3 r8 6 e-

ClJ

4

'-

c a

= a

R11

• heated tUbe/

'-

2

ClJ

....!:'rA ~~

V .:

1/

-if/ ~ ~ r/ty ~/ 1/1/

/

So2d R' =37.8mm

Vi

/

y ~,0 VI/ lube P = 1bar __ 6", ~ ~~/ /

u '-

6

r- ~ /

jY

• •• 5 • • tp ••• ••• ••• • ••

5

~~ ~ ~/p'

~1

y

~

1/1/ V

i

4

6 8

//

V

i

/ 2

6 8 10 4

4

2

:s: .c:

4

Z I-

000 4

0003 000 2

000 000 000 •••

6 S 4 3

••• 2

••• 2

••• 1

••• 1

-- - - --6 0

--sr

D

Rl1. p. = 1 bar.

c

¥-f--

0.0 0.0 0.0 0.0 0.0

6 S 4 3 2 1

oeo

-o

• healed lube

5

••• ••• ••• •••

6 S 4-

3

••• 2 ••• 1

- 0- -

= 37.8mm ~

ClJ

'w 10 3 ClJ 8 0 u

'-

~

(/)

c a L-

a

ClJ

=

K,r:

cuv

~

~~IP. 7--- upper

5

)~oY--

4

= '" ti.).

I

~f---

sr I

6 000 S 000 4 0003

••• 1

4

WIm l

between and around the lower and upper twin-tube results. In Fig. 12 the heat transfer coefficient h 2 obtained on the middle tube in row 2 (second from bottom) in five different heater arrangements is given. Here the results split up into an upper and lower curve which both follow quite well the twin-tube results. The upper curve represents test data with other tubes heated in addition to tube 2 and again indicates the effect of enhanced flow agitation. The lower curve represents data for a separately heated tube 2. Results for tubes 3,4 and 5 are quite similar to those shown in Fig. 12.

arrangement is compared for differently located tubes and also comparison is made to the simplest form of a tube bundle (the twin-tubes) the following results are obtained: In Fig. 11, the heat transfer coefficient h. on the middle tube 1 (bottom row) is presented as measured in six different heating arrangements. The amazing result is, that this heat transfer coefficient when obtained in a test with only tube 1 heated and 17 dummy tubes around, is about the same as when all 18 tubes are heated. Compared to experiments on twintubes, the heat transfer coefficient h. fits tolerably

000 5

I

[/

FIG. 10. Heat transfer coefficient h. for all tubes heated (ti. = til

0005 000 4 000 3 000 2 0.0 1

'/

/

/

Heat flow density Qn

E

;~""

//

10 3

10 4 I I I 8 I- ' f - ¥-'" """ 5 000 000 6 000 6

/

/

",,/

/

/

/

/

/<'separately heated' V'/ middle tubes /

,///

/

/

/

/

",y

S.

iJ

~

lower

,DP~ 'Y'

I

lube

V

<,z

Z ~

z

b-'~

4

,~

./

6 8 10 3

Z

Heat flow density

4

ql

6 8 10 4

Z WI ml

FIG. 11. Heat transfer coefficient h. for different heating arrangements (ti. = .,.

4

6 8 10 5

= ti.).

Boiling on a finned tube and a finned tube bundle

000 000 000 000 0.0 000

E

--2 u

0)

8 CO)

Vi c

o

5 ~

, Z 1

000 6 000 5 000 l000 ,

••• Z ••• 1

n

o R11.

Ds = lbar

s = 37.8 mm • heated lube

10 r--~~~:':'---I--l----J--~c4~~--+---+---I----+---1 8 6 3

4

,w

c-

o 0) ::r:

o

o

I----

c

-~

6

~upper

\pl?'..J! twin tube <[)"I/ r-----'ower

2

~I

2

FIG.

4

I

10 3

6 8 2 Heat flow density

10 4 8 ;:-

6 4

-

oeo 6

oeo 6

000 5 000 4 000 l

0.0 5

2

0.0 Z oeo 1

ooo

000 1

-

2

c

0)

~ 10 3 0)

o

u

CO)

Ul

c

E:

~

=

8 6

4

2

-

4

W1m 2

o eo

o eo

From the results gained on separately heated finned tubes within the bundle arrangement (Fig. 8) the following correlation was obtained: Itsingle

It-

3

••• 6 ••• 5 ••• 4

••• 3 ••• 2

I

• heated tube

s= 37.8mm

0

V'>

II

I I

I 2

I

to

I I

co /' / ~ Il

<"o?O

ll~/~

~IT~ 4

oY2vi

••• 1

0

Ps = 1 bar.

40 •73 5 •

6 8 10 3

(5)

For the mean heat transfer coefficient of the entire bundle arrangement (Fig. 10) the experimental results

------n 0 Ru.

= 1.331

'J

Sf- f -

1- f--f-

2

12. Heat transfer coefficient h 2 for different heating arrangements (til = . . . q,,).

In Fig. 13 the heat transfer coefficient 1t 6 is presented as measured on the middle tube 6 in the top row. In this case only the results of the separately heated tube 6 are somewhat. comparable to the lower twin-tube results. The bundle results differ considerably. If this is attributed to a lack of flow hindrance above the top row, it could be concluded that such a boundary effect would disappear with a seventh row above the sixth.

E

857

0

/'

Il

~~~ p~!l- I IlYI

VI

I 7." upper I twin tube n/

/

I

I----Iower

I 2

Heat flow density Q6

4

6 8 10

I 4

2

4

W/m 2

FIG. 13. Heat transfer coefficient h6 for different heating arrangements (q6 =

... qn)'

E. HAHNE and J. MOLLER

858

can be correlated by hbundle

Both correlations x 103 W m- 2 •

= 10.0

qO.53.

hold

for

(6) 103 < q < 40

8.

9. 8. CONCLUSION

The result that heat transfer coefficients of finned tubes in a bundle do agree tolerably well with those obtained by a simple twin-tube arrangement is promising as experimental expense is decreased considerably. It must be said, however, that this result is so far only proven for an in-line tube arrangement with one quadratic pitch of s = 2dR • Acknowledgement-This investigation was carried out with the support of the Deutsche Forschungsgemeinschaft. The authors gratefully acknowledge this. REFERENCES

1. K. W. Haley and J. W. Westwater, Heattransfer from a fin to a boiling liquid, Chern.Engng Sci. 20, 711 (196?). 2. K. W. Haley and J. W. Westwater, Boiling heat transfer from single fins, Proc. 3rd Int. Heat Transfer Conf, Vol. 3, pp. 245-253 (1966). 3. D. L. Bondurant and J. W. Westwater, Performance of transverse fins for boiling heat transfer, Chern. Engng Progr. Symp. Ser. 67, 30-37 (1971). 4. G. J. Klein and J. W. Westwater, Heat transfer from multiple spines to boiling liquids, A.I.Ch.E. Jl 17, 10501056 (1971). 5. D.R.Cash,G.J.KleinandJ. W. Westwater, Approximate optimum fin design for boiling heat transfer, J. Heat Transfer 93,19-24 (1971). 6. Chien-Cheng Shih and J. W. Westwater, Use of coatings of low thermal conductivity to improve fins used in boiling liquids, Int. J. Heat Mass Transfer 15,1965-1968 (1972). 7. Chien-Cheng Shih and J. W. Westwater, Spheres,

10.

11. 12.

13.

14.

15.

16.

17.

18.

19.

20.

hemispheres and discs as high-performance fins for boiling heat transfer, Int. J. Ileat Mass Transfer 17, 125133 (1974). D. Gorenflo, Zum Wiirmeiibergang bei der Blasenverdarnpfung an Rippenrohren, Diss, TH, Karlsruhe (1966). H. H. Schroth, Ein Beitrag zur Verdampfung an iiberfluteten Glatt- und Rippenrohren, Luft- u. Kiiltetechnik 4, 212-218 (1968). D. Gorenflo, Wiirmeiibergang bei Blasensieden, Filmsieden und einphasiger freier Konvektion in einem gro13cn Druckbereich, in Abhandlungen d. Deutschen Klilte- u. Klimatechn., Vereins Nr. 22. C. F. Miiller, Karlsruhe (1977). W. Jones, Cooler and condenser heat transfer with low pressure Freon refrigerant, Refr. Engng 49, 413 (1941). D. B. Robinson and D. L. Katz, Effect of vapor agitation on boiling coefficients, Chern. Engng Progr. 6, 317-324 (1951). J. E. Myers and D. L. Katz, Boiling coefficients outside horizontal plain and finned tubes, Refr. Engng 60, 56-59 (1952). J. E. Myers and D. L. Katz, Boiling coefficients outside horizontal tubes, Chern.Engng Progr. Symp. Ser. 49, 107114 (1953). P. Heimbach, Wiirmeiibergangskoeffizienten fiir die Verdampfung von R 22 und R 13 an einem iiberfluteten Rippenrohrbiindel, Linde, Ber. Tech. lViss. 29, 33-42 (1971). G. N. Danilova and V. A. Dyundin, Heat transfer with Freons R 12 and R 22 boiling at bundles offinned tubes, Heat Transfer, Sotiet Res. 4, 48-54 (1972). B. Slipcevic und A. Schiitz, Zum Wiirmeiibergang beim Sieden von Kiiltemitte!n, Verfahrenstechnik 9, 578-581 (1975). B. Slipcevic, Uber den Wiirmeiibergang beim Blasensieden von Kiiltemitteln an Rippenrohrbiindeln, Klima Kiilte-lnq. 17, 127-134 (1975). B.Slipcevic, Wiirmeiibergang bei der Blasenverdampfung von Kiiltemitteln an glatten und berippten Rohrbiindeln, Klima. Kiilte-Inq. 17, 279-286 (1975). R. L. Webb et al. (eds.), Adrances in Enhanced Heat Transfer-1981, HTD-Vol. 18. ASME, New York (1981).

EBULLITION COMMENCANTE SUR UN TUBE AILETE ET UNE GRAPPE DE TUBES AILETES Resume-Uneetudeexperimentaleportesurun reservoir-de 151drn? contenant du R-ll, al'etat de saturation de 1 bar et 23,JOC. Les coefficients de transfert thermique mesures sur un tube unique dans Ie reservoir ressemblent approximativernent au cas OU un seul tube est chauffe dans un faisceau en ligne de 18 tubes. Pour un arrangement adeux tubes, Iecoefficient de transfert thermique sur Ie tube superieur estjusqu'a 80% plus grand que celui du tube inferieur, La courbe de transfert thermique pour ce tube superieur represente bien les coefficients de transfert des tubes al'interieur de la grappe. Seules apparaissent des differences pour les tubes a la base et au sommet de la grappe. La possibilite d'obtenir des donnees sur la grappe du tube-s-jusqu'a une certaine limite-par des experiences plus simples sur deux ou trois tubes, devrait faciliter les recherches experirnentales.

SIEDEN AN EINEM RIPPENROHR UND EINEM RIPPENROHRBDNDEL Zusammenfassung- Versuche wurden in einem Behiilter von 151 drrr' Inhalt in R 11 beim Siittigungszustand (1 bar; 23,3°q durchgefiihrt. Die an einem Einze!rohr gemessenen Wiirmeiibergangskoeffizienten folgen angeniihertjenen, die fiir ein separat beheiztes Rohr in einem Biinde! aus 18 fluchtend angeordneten Rohren erhalten wurden. Bei einer Zwei-Rohr Anordnung liegt der Wiirmeiibergangskoeffizient des oberen Rohres bis zu 80% iiber dem des unteren Rohres. Der Verlauf des Wiirmeiibergangskoeffizienten dieses oberen Rohres gibt gut den Verlauf der Koeffizienten fiir Rohre innerhalb des beheizten Biindels wieder. Nur fiir die untersten und obersten Rohre zeigen sich Unterschiede. Die Moglichkeit, Ergebnisse fiir Rohrbiinde!-zumindest angeniihert-durch Versuche mit vie! einfacheren Zwei- oder Drei-Rohr Anordnungen zu erhalten, wiirde experimentelle Untersuchungen sehr erleichtern.

Boiling on a finned tube and a finned tube bundle B03HHKHOBEHHE KI1nEHHJI HA OPEEPEHHOt} TPYEE H nY4KE OPEEPEHHbIX TPYE

AHHOT3I\HH-npOBeJleIlO axcnepasreuransace accnencsaane xanenns B cocyne 061>e~IO~1 151 JI~13, HaCblllleHHbl~1 lPpeOIlO~I·II, npu JlaBJleHlII1 I 6ap II rexmeparype 23,3'C. 311a'le1l1l1l K03lPqlllUlleHTa rennonepeuoca. nO.1Y'IeHHble lL1l1 onnoii noveureunon B cocyn Tpy6bl. npnvepao cosnanarm C peaynsrarassn 113~lepellllii B TO~I cnysae, xorna narpeaanacs TO.1bKO onna Tpy6a BHYTpll xopunopnoro nyxxa 113 18 Tpy6. JlJlll CIICTe~lbl 113 JlBYX 'rpyfi K03lPlPIlUllellT TenJlOnepeHoca eepxneii rpytis: npnxrcpno na 80% nsnue, '1e~1 lL111 HIIJKHeii. Kpnsaa rennonepeaoca lL1l1 nepxueil Tpy6bl JlOBOJlbllO xopouro onacuaaer ziaunste no K03tjllP1lUllellTa~1 TenJlOnepelloca nns Tpy6 B nysxe. Paannxna lIa6J1IOJla1OTClI TOJlbKO JlJllI IIIlJKHeii Il aepxneii Tpy6 nysxa. B03~IOJKIIOCTb nonysenua XOTli 6bI npll6J1I1JKellllblX nannux JlJllI nyxxa Tpy6 na OCHOBe npOCTbIX 3KcnepIIMeHTOB C CIlCTe~la~1II 113 JlBYX IlTpex Tpy6 6YJleT cnocoficraoaart, 60,1eeycneunroxiy npcaenemuo nansuetiunrx axcnepnxrenransIIbIX nccnenosaunti.

3anO.1HeHHO~1

859