Pool-Boiling Heat Transfer in Liquid Nitrogen - J-Stage

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An experimental study was conducted on pool-boiling heat transfer from an electrically heated horizontal wire to saturated liquid nitrogen at atmospheric ...
Journal

of NUCLEAR SCIENCE and TECHNOLOGY, 18[7], pp. 501-513

Pool-Boiling

Heat

Transfer

(July 1981) .

in Liquid

501

Nitrogen*

Muneo KIDA, YoshihiroKIKUCHI:OsamuTAKAHASHI and

Department

Itaru

of Nuclear

MICHIYOSHI

Engineering,

Received

December

Kyoto University**

26,

1980

An experimental study was conducted on pool-boiling heat transfer from an electrically heated horizontal wire to saturated liquid nitrogen at atmospheric pressure. Experimental results of heat transfer characteristics in both nucleate- and film-boiling regimes, critical heat flux and minimum heat flux were analyzed and compared with various correlations. In addition, photography was used to obtain information concerning the vapor-bubble and vapor-film behaviors around the heating wire. These data of microcharacteristics were utilized for evaluating theoretical models of nucleate-boiling mechanism proposed by other investigators. Transient conduction to the relatively cold (saturated) liquid , which came into the space vacated by the departing bubble and contacted with the heating surface, was found to be important for high heat transfer rates associated with nucleate boiling. KEYWORDS: liquid boiling, bubble size, mum heat flux

nitrogen, heat transfer, pool boiling, nucleate boiling, film bubble frequency, nucleation sites, critical heat flux, mini-

I. In

recent

years

exceptionally for liquid

helium nitrogen,

needed

for

during

boiling,

at

for to

fundamental

room

cryogenic

cryogenic

is important

boiling

been

only

departing

bubbles

and

the

to

the

heat

examine

the liquid

obtained

on

heat

emphasis

on

the

formation

transfer

in nucleate

therefore, to

frequency

of

bubble

boiling,

the and

on

* Orally presented at 1980 Fall Meetings ** Yoshida , Sakyo-ku, Kyoto 606.

from

in

both

nucleation

vapor

in the

of At . Energy

25 -

of

are

paper

and

sites pattern

Soc.

of

Japan

for have

film

and

the

in film

(Sep.

studies

for

under-

with

boiling.

1980).

of

some

conducted

horizontal

frequency

heat size

deriving been

the

the

wire

experimental

boiling,

of

boiling

i.e.

important

the

between

Most

boiling,

heated

gives

are

espe-

Extensive

necessary

electrically

usually

transfer,

world(1).

are

by

which

difference

experiments

nucleate

flow

heat

boiling.

which

and

This

of

-

out

convection)

systems,

of

been

developed

by cryogens,

temperature gives

present an

pressure.

the

surfaces

macrocharacteristics

boiling

transfer

number

of

has

being

or forced

high-vacuum

large often

carried

the

temperature now

a knowledge

formation,

need,

low are

(pool

microcharacteristics

during

characteristics

in

the

on

heat

size,

been

investigate

this

cooling

extremely liquid

of

instance,

cooling

liquids

data

meet

of

pressures

limited

at atmospheric

transfer bubble

have,

To

pool-boiling nitrogen

the

a cryogenic

mechanism

formulations.

saturated

since

and

conducted

are

transfer

these

use

for

The

low

of

There

heat

magnets. very

experiments.

transfer.

standing

such

making

types

nucleonics

temperature

have

fields magnets,

Several

produce

storage

liquid

studies

technical

reactor.

proposed is used

and

cially

past

are

of

superconducting

fusion

In dealing

a solid

growth

Large

a Tokamak-type

liquid

of

the

rapid.

INTRODUCTION

to

results particular of

bubble

502

J. Nucl. Sci. Technol.,

II. Figure of

a

EXPERIMENTAL

1 shows

a schematic

double-walled

and

the

outer

gen,

from

walls

room

insulator outer

wall

for

in an

keep

and

the

inner

apparatus

diameter. wall,

A gap which

which

consisted

between

contained

the liquid

inner nitro-

Two

on

vapor-film

experimental

in inner

the

condition. the

side

records

of

behaviors

in

photographic

the

AND PROCEDURE

thermal

to

provided

of 90 mm

to isolate A

adiabatic were

of

evacuated

equipped

obtaining

vapor-bubble liquid

was

was

windows*

wall

diagram

chamber

temperature.

also

glass

glass

APPARATUS

nitrogen. The

heater

platinum diameters

of

connected

by

acrylic

an

izontally

to electrical

nitrogen.

direct

current

potential

the

two

was

placed surface

of

The

wire

heated

by

a shunt

power

a

measured

leads

60 mm

area

thus

wire

I was

apart, being

was

annealed

at approximately

of

1,000K and then cleaned chamber

liquid

nitrogen,

ually

heated

flux by

runs

was

control

heat

system,

in a film boiling

condition,

as shown

in Fig. 2.

film boil-

After

in, the

input power

further

increased

value.

Upon attaining

condition,

the

cooled down the

V and * For heat

heat

heat

wire

to zero flux.

the

the prescribed was,

transfer into

in turn, decreasing

through

The

resistance

leakage

was

up to a prescribed

by gradually

power

mum

apparatus

grad-

resulting

ing had set

Experimental

filled with

the wire power

1

the

with acetone.

was

up to the critical

the

of Fig.

set

the

means

(0.125 O).

to each

After

the 60 pD

in mm.

by

Prior wire

system. between

diameter

measured

hor-

specially

control

V was

D is the

resistor

was

from

transfer

current

supported

free

drop

mm2 where

leads

1.0 mm.

and

supplied

heat

Wire

to

the

electrical

effective

0.1

under

transistorized

The

smooth

length.

from

structure

liquid

a pure,

in

varied

150 mm

designed

was

60 mm

were

It was

The

element

wire

R(=V/I)

experiments liquid

a mini-

potential

drop of

, however, nitrogen.

Fig. another

2

Regimes

chamber

without

- 26 -

in boiling windows

heat was

transfer used

to minimize

Vol. 18, No. 7 (July 1981)

the

wire

were

503

measured

at the saturation

continuously

. During the runs, the liquid nitrogen corresponding to the atmospheric pressure .

temperature

was maintained

The power was readily calculated : W=VI. The mean temperature Tw of the wire obtained from the curve T(R)(2) , which was previously confirmed by measuring R at some different temperatures using a current of very low intensity . Because of the relatively was

high

thermal

conductivity

temperature 0.19 K and

gradient

lower

wire

than

and

the

in the cross the average

diameter

boiling diagram

of

the

was no appreciable temperature being

a condition

: heat

flux

of

2.4 x 105 Wm-2

AND DISCUSSIONS

Transfer

present

heat

flux

nucleate

and DTs

temperature

temperature

contains

wire , there surface

actual

on a log (q) i's. log (DTs)

wall

the saturation also

the

plotted

; q is the

excess

under

RESULTS Heat

3 shows

data

of the

of 0.5 mm.

Nucleate-boiling

Figure

diameter

; for instance,

temperature

III. 1.

small

section

other

the

Tw above

Ts.

The

figure

experimental

results

published to date(3)~(11). Complete agreement is lacking among the results since the nature of the surface has an important influence

on nucleate

other

things.

above-mentioned been and cause

the The

was

general solid

dicates

in

derived

organic

form,

after

data, would

of data. in the

figure

correlation(12)

for nucleate

and various by the

of taking

line drawn

Kutateladze's

variations

measurement

scatter

the

has yet

to this,

method

uncertainties

among

explains

successfully,

In addition

geometry,

process, which

effects

found.

in system

boiling

No theory,

boiling

liquids

in-

which of

water

and is represented

rearrangement,

Fig.

3

Nucleate-boiling

heat

transfer

( 1) where r

is the

the

surface

tion

due

are 2.

The

thermal

latent

conductivity, m

heat

subscripts l equation

the

of

vaporization,

and

v signify

represents

the

viscosity,

P the values

Cp the

pressure

pertaining

present

data

specific

and g

the

heat,

to liquid

and

well

although

fairly

a

acceleravapor, the

scattered. Critical 4

plots

scattered

the

Kutateladze's

Figure The

k the

hfg

to gravity.

respectively. data

density,

tension,

Heat

Flux

shows

reveal slightly.

the that This

effect the

of

CHF tendency

heater

diameter

increases

with

is

similar

liquid(13)~(15). - 27 -

D on increasing to

the

the

critical

heat

flux

(CHF) qmax-

diameter

although

the

data

experimental

results

of

ordinary

are

504

J. Nucl.

For

comparison,

tion(12)

is also

teladze

was

that

the

matter

indicated

in the

probably

critical

of

the

heat

flux

the

to

Kuta-

point

condition

From

final

figure.

equation

out was

stability

surface.

analysis,

correla-

first

hydrodynamic

horizontal

in the

Kutateladze's

Sci. Technol.,

on

a

a flat

the

dimensional

can

be

written

form

(2) where

B

is

Kutateladze between for

that

this

constant

0.19,

with

0.16 as average,

organics

0.16

of

CHF

boiling

Eq. ( 2 ).

theoretical

data

of

both

flat

on

cylinders

in

constant.

and

sets

horizontal

proportionality

found 0.13

several

and

a

(wires). The

line in the

varied

both plates

The

Effect

of heater

except

range

in Fig.

4 was

for D=0.1

of +-20%.

mm,

For

obtained agree

D-=0.1 mm,

fall below the line. This suggests a dependency of CHF on the heater Kutateladze et al.(16) found that Eq. ( 2 ) could be used to correlate data

for

and

horizontal

the

physical

cylinders

properties

heat

diameter flux

and

values,

scattering

4

on critical

solid line drawn

measured data

Fig.

water

if B could of the liquid.

vary

with

This

the

diameter

dependency

by

fairly

letting well

however,

diameter. pool-boiling by the

the

diameter

by

dimensionless

the

Laplace

diameter characteristic

of

the

heater,

length,

CHF

(or wire) relation

B=f (D*), where D*,

the

the plots

of the cylinder

is expressed

B=

with

(3) is

obtained

by

dividing

the

heater

or

(4) Figure

5 is a plot of Eq. ( 3 ) for the

present relations

experimental predicted

et a1.(16) also

Rao

indicated

results. CorKutateladze

by

& Andrews(17)

in this

teladze

et al. proposed

curve

for

14 sets

and 6 organics, over

wide

pressure, smooth

ranges

fitted

of water

were

lines drawn

Applying

in the figure

of the

Rao & Andrews

horizontal derived

and

kinds of surfaces. spread

a hydrodynamic

for

obtained

of diameter

represent the band these data. model

the best

and with different metallic heater

The broken

ity

Kuta-

of data

which

are

figure.

in

stabil-

Fig.

5

cylinders,

Generalized

plot

of dimensionless

the follow-

portionality - 28 -

of CHF heater

constant

B

data

showing

diameter

effect

D* on pro-

Vol. 18, No. 7 (July 1981)

ing

505

correlation

q max/qmaxF= 0.805/D*(D*2i+2)3/4, where

D*i is the

CHF

recommended

dimensionless

(5)

diameter

of vapor -liquid interface. rmax F is the well-known by Zuber(18) for infinite flat plates and is given by the following equa -

tion : (6)

which, except for the dashed line drawn in The proportional range of the present

coefficient , is identical to Eq. ( 2 ) derived by Kutateladze. A dot-andthe figure was obtained by letting D*i= D* in Eq . ( 5 ). constant B increases generally with increasing heater diameter in the heater diameter . Fairly good agreement is observed between the

present data and both correlations within the spread range of data. 3. Film-boiling Heat Transfer Film boiling as a cooling process has not had wide commercial applications because of the high surface temperatures. In cryogenic systems, however, a knowledge of film boiling is particularly important since the extremely large temperature difference between a equipment surface and a cryogenic liquid often causes film boiling during cooling down from the room temperature. Figure of

6 shows

film-boiling

heater

diameters.

excess

of the

saturation

the experimental

heat

transfer

The

wall

abscissa

the heat transfer As DTS

coefficient

increases,

In this

lower DTs

boiling

regimes

and the

various

is DTs,

the

above

the

temperature

temperature

results

for

ordinate

given

h first decreases region, exist

h,

by q/DTs. sharply.

nucleate-

and film-

simultaneously

along

the heating

wire, as clarified

later

by Photo.

1 (c).

boiling

more

dominant

Film

becomes

with increasing DTs, the

heat

transfer

higher DTs

region

is established

and extremely where

h increases

ing DTs.

For a given DTs,

solid

lines drawn

relations For

film is

boiling,

from

frictional

forces

arrived based

at on

increaswith and the the cor-

and Breen Fig.

respectively.

given,

radiation

are

by Bromley(19)

& Westwater(20), model

broken

in the figure

obtained

exists,

with

h decreases

The

the

film boiling boiling

slightly

diameter.

In

stable

and no nucleate

however, increasing

degrades

characteristics.

as

that the

the

molecular

on

compared vapor

heating the

following

with

is surface

vapor

film

equation

conduction

nucleate

generated

alone

at

through flowing

the on

representing : - —29—-

boiling, the

Film

By of

convective

a

transfer

well-known

interface

film.

outside the

boilingheat

a reasonably

liquid-vapor

vapor the

6

by

balancing horizontal heat

transfer

physical

conduction the

buoyant

tube,

and and

Bromley

coefficient

hc

506

J. Nucl. Sci. Technol.,

(7) where the

all

physical

properties

of

the

vapor

are

evaluated

at

the

average

temperature

of

film. Bromley

heat

also

suggested

an

expression

which

included

the

radiative

contribution

hr

to

transfer

h=hc+ 0.75 hr, for

hc>hr*.

He estimated

the

magnitude

of

hr

(8)

from

the

relation

(9) which

is the

equation

for net heat

In Eq. ( 9 ) e. is the Boltzmann

emissivity

transfer

by

of heating

radiation

surface, a

( 7 ) can be rearranged

where

into the dimensionless

parallel

of liquid

plates.

and k

Stefan-

the

subscript

the

diameter

for

isopropanol

Breen

D means

of

cylindrical

wires

(10)

NuD=hD/kv,

(11)

Ra*D=D3rv„(rl-rv)gCpv/(kvmv),

(12)

to

Freon-113,

large

tubes,

than

Rayleigh

numbers,

the

analyzed

and

rather

form

Nusselt

and

results

of

3)+0.4.

(13)

modified

Rayleigh

numbers

are

based

on

heater.

& Westwater

preferred

that

generalized

NuD=0.62(Ra*Dt')1/4,

t'=hfg/(CpvDT

fine

infinite

absorptivity

constant.

Equation

Here

between

the

the

the that

and diameter

were

concluded as

several

obtained

the

that

investigators,

on the

horizontal critical

characteristic

including cylinders

wavelength lc

length

in

the

their ranging

was Nusselt

own, from

sometimes

and

modified

where

(14)

They also found that, depending on the value of the dimensionless ratio lc/D, the boiling characteristics for a horizontal heater fell into three different regimes. However, they succeeded in correlating the data in all three by the equation Nulc=(0.59+0.069lc/D)(Ra*lct")1/4,

(15)

t"=[hfg /(CpvDTs)+0.34]2.

(16)

where

This

correlating

expression

All the measured and

agree

better

0.1 mm.

Similar

liquids.

For

* In total

the

tendency

present

heat

with

such

is obviously

values

cases

experiments

are higher

the

empirical

the

vapor

with

small

film thickness

radiative

contribution

transfer. -

form

of Eq. (10).

the calculated

correlation

was observed the

a modified than

30 -

of Breen diameter

results wires

is comparable was

of

Bromley's

& Westwater,

estimated

for water to the

equation

except and

wire

to be less

for

common

diameter

than

D=

20%

, as of the

Vol. 18, No. 7 (July 1981)

507

suggested by Bromley. The Bromley's model is not applicable for this physical situation. In the higher DTs region wave motion or turbulent flow is further observed, especially due to the intermittent release of bubbles from the vapor film, which is not considered in Bromley's model where the vapor-liquid interface is assumed to be completely smooth, i. e. no capillary nor standing waves existing. Figure 7 shows the generalized plots of film-boiling heat transfer data in the dimensionless form. The abscissa is lc/ D and the ordinate Nulc/(Ra*lct")1/4. The figure contains other experimental results(19)(20)(28)~(32)of water, organics and cryogenic liquids. The height of the bar indicated on the data does not mean the uncertainty range of the measured values, but the spread of each measurements.

Fig.

Correlations

7

predicted

Generalized

plot

of film-boiling

heat

by Bromley and Breen & Westwater

figure. In the region lc/D8, however,

transfer

are also indicated

in this

is observed between the experimental the measured values are higher than

the Bromley's prediction (broken line) and lower than the empirical correlation of Breen & Westwater (solid line). The plots diverge increasingly from the theoretical curves with increasing lc/D, i. e. with decreasing wire diameter. A dot-and-dashed line then gives a best fit for the data and is represented by the following equation : Nulc=(0.75+0.032lc/ 4. The minimum

Minimum transition heat

flux

Heat from

D)(Ra*lct")1-4.

(17)

Flux film boiling

q ruin (see Fig. 2).

to nucleate The

boiling

minimum -

31 -

occurs

heat

flux

at a heat

flux known

is normally

of

lesser

as the im-

508

J. Nucl.

portance

than

nucleate

boiling

lessens

the

need

to predict

loading

the

transition

Figure

on

In the

present

mum

heat

the

immediately

were

existing

The

minimum

on

increasing

large

the

data

at

the

transition

flux

correlations

and

of

this

&

Wong(21)

by

Berenson(22)

in

the

of

since

heat

many

the

transition

temperature

fluids , however, to nucleate

transition in

point

surface

transfer

and

one encounters boiling occurs

coefficient

applications

to then a at

during

the

.

mini-

moment partial

no

vapor

of heating

theoretical

Lienhard

data.

wire.

qmin decreases

In

the

design

flux

i.e.

diameter.

boiling

Technol.,

heater

from

boiling,

since changes

of

high

reduction In cryogenic

for

heat

the surface

heat

the

cylinders

the

flux

effect

taken

to nucleate

film

shown

the

with

system.

considered

minimum

before

boiling

the

The

experiments flux

in fluid a marked

heat

be

shows

on

flux

minimum

must

8

diameter

flat

heat

produces

temperatures.

boiling

film

critical

generally

thermal

operating

by

the

Sci.

with

figure

are

also

predicted

for

horizontal

for horizontal

plates. The

by the bules

film

boiling

steady at

formation

the

element.

to

the

and

release

Zuber(18)

Taylor

transition-

and

from

horizontal

a flat

following

is characterized

liquid-over-vapor

a heating apply

regime

over

was

first

the

instability

film-boiling

relation

of bub-

interface

heat

plate. for

theory

the

Fig.

to

8

Effect of heater diameter on minimum heat flux

transfer

Based

on

minimum

the

heat

analysis

flux

of

with

Zuber

film

boiling

, Berenson had determined the on a horizontal flat plate ,

(18) Accounting instability ing

for

of

the

correlation

the

effect

interface

of

for

surface

tension

a horizontal

in the

cylinder

traverse

, Lienhard

direction

upon

& Wong

the

Taylor

the

follow-

derived

:

(19) Although dominant

a partial at

theoretical 5.

curve

The

liquid

the

predicted

knowledge frequencies

mechanism

limited

film

in

boiling,

from

size

during of data

nitrogen

bubbles for

nucleate

growth

boiling. has

correlation

cryogenic

to examine

coexisting

measured

Lienhard

bubble

boiling,

is important

ordinary studied

liquids. the

of

of

rates,

For been

the

with

values & Wong

film

agree

boiling

well

with

, is the

.

Boiling

microcharacteristics and

boiling

experiments, the

of

of

i.e.

present

Microcharacteristics

departure

ture

qmin

liquids by

many

This

led

size

and

the

- 32 -

i. e. departure for

that

wet

the

heating

investigators(23). present

frequency

sizes

understanding

authors in saturated

of vapor

bubbles

the

transfer

heat

surface There

to carry pool

, the are

out boiling

depar-

, however, a study on .

,

Vol. 18, No. 7 (July 1981)

Photograph

509

1 (a) shows a typical

photograph of vapor bubble behavior on the heating wire (D=0.5 mm) during nucleate boiling. Small bubbles of 0.43 mm in average diameter stream forth from many nucleation sites on the wire. The number of nucleation sites is 9.55 x 105 m-2. The frequency of bubble formation is approximately 90 Hz which was determined from the photographic records taken by the high-speed camera. In film boiling, however, a film of vapor is always formed on the heating wire, as shown in Photo. 1 (b). Waves are observed along the top of the wire, and the crest-to-crest average distance for the waves on the top of the wire is 7.2 mm, a value close to the critical wavelength lc=6.6 mm. Larger bubbles of 3.6 mm in average diameter are released from the top of the wire. A decrease of heat flux produces a partial film boiling where film boiling and nucleate boiling exist simultaneously along the heating wire, as shown in Photo. 1 (c). From the above-mentioned observations, vapor bubbles or vapor films in liquid nitrogen are found to

Photo.

1

Bubble boiling

and film behavior in liquid nitrogen

during

behave quite similarly to those in noncryogens. Figure 9 shows the effect of changes in heat flux q on the number of nucleation sites per unit area of the heating surface n, the frequency of bubble formation f and the diameter of departing bubble d0 for the wire diameter of 0.5 and 1.0 mm. With the rise in heat flux the number of nucleation sites and the bubble diameter increase in the nucleateboiling regime, and film boiling produces much larger bubbles. In this figure are also shown the theoretical values of Fritz(24) and the empirical correlation of Verkin & Kirichenko(25) in nucleate boiling. Fritz considered a balance between buoyancy and surface tension forces to derive the expression

for departure

diameter (20)

where b

is the

conditions

appears

bubble to

contact be nearly

angle. constant

For at

most 45d. - 33 -

situations,

the

value

of b

under

dynamic

510

J. Nucl. Sci, Technol.,

Verkin & Kirichenko found that for 12 sets of data obtained on water, organics and 4 cryogenic liquids over the wide ranges of pressure and subcooling, both the diameter of departing bubbles and the frequency of bubble formation were correlated well with the reduced pressure P/ Pc, where Pc is the critical pressure. Applying their correlation to the present experimental condition (P/Pc = 3.0 x 10-2),d0=0.46 mm and f=100 Hz are obtained. It can be seen from the figure that the measured values of bubble diameter fall below the theoretical line derived from Fritz's equation, but agree fairly well with the correlation of Verkin & Kirichenko although the data are scattered. The microcharacteristics have often been used in deriving heat transfer correlations for saturated nucleate boiling*. Several correlations are based on one or more (simultaneous) contributions of the following mechanisms : (1)

Transient conduction to the relatively cold (saturated) liquid that comes into the space vacated by the departure of the bubble.

(2) Evaporation of a liquid microlayer the base of a growing bubble. (3)

Circulation of liquid in vicinity on vapor-liquid interface.

The

third

mechanism

was

Fig.

at

to cause

years, and on the analogy of heat transfer derived an equation of the following type

Effect

of heat

flux on number

bubble

the

high

due to thermocapillarity heat

transfer

in single-phase turbulent for nucleate pool-boiling

rates

effects for

Nub

liquid

Prandtl

is

the number

Rohsenow(26)

boiling

Nusselt

; A, m1 and

defined

a bubble

number, m2 are

Reb

the

boiling

Reynolds

number

and

Reynolds

number

by

the

* In the

present

was

evaluated

experiments

by liquid

the

(22) from

the

was -

maintained 34 -

heating

(23)

equation

nitrogen

the

relation

Nub=qd0/(DTski). flux

Prl

constants.

where Gb=(p/6)d30rvfn, the average mass velocity of vapor receding surface. He also defined the Nusselt number in Eq. (21) by the equation

heat

have

(21)

Reb=Gbd0/mt,

The

many

flow, investigators heat transfer

Nub=A(Reb)m1(Prl)m2, where

of

nucleation sites, frequency of bubble formation and bubble diameter in nucleate boiling

of a growing

thought

9

at saturation

temperature

.

Vol.

18, No. 7 (July

1981)

511

qnb=(p/6)hfg A different Their

nucleate-boiling

analysis

from

the

space

is based

heating

vacated

with

the

they

obtained

heating

on

surface by

the

heating

transfer

first

mechanism

is transient

departure

surface the

heat the

at

final

equation

correlation

the

bubble

After

the

the

to

the

of

the

and

(24)

was

that

conduction

of Tw

d30 rvfn

the

liquid

by Mikic

of

mode Ts

superheated

formulation

average

derived

significant

and

which layer

heat

.

transfer

comes

into

the

, and then contacts of related terms

integration

nucleate-boiling

& Rohsenow(27) of

heat

flux

over

the

,

whole

surface,

qnb=2(pkl rlCpl

f)1/2 d20nDTs.

(25)

Figure 10 shows a comparison of measured total heat flux q with nucleate-boiling heat flux qnb predicted by Eqs . (24) and (25). In the calculation of qnb,the measured values were applied to f, d0, n and DTs. line indicates a relation qne=q .

The solid

The measured values of q are much higher than the predicted values of qnb by Rohsenow's correlation, but agree well with the correlation of Mikic & Rohsenow. This means that the transient conduction to the relatively cold (saturated) liquid, which comes into the space vacated by the departure of the bubble, is dominant in the high heat transfer rates associated with nucleate boiling.

Fig.

10

Comparison of nucleate-boiling flux with total heat flux

heat

IV . CONCLUSIONS Saturated

pool-boiling

experiments

were

conducted

with an electrically

heated

wire in liquid nitrogen at atmospheric pressure. The wire diameter ranged 1.0 mm. In each run the heater power was gradually increased and decreased designed wire

power

were

control

measured

Comparison conclusions :

system.

during

Changes

boiling.

of the experimental

in the

Bubble results

potential

behaviors with

various

(1)

Nucleate-boiling heat Kutateladze's correlation,

(2)

The critical heat flux tends to be higher with ured values agree fairly well with the theoretical and

(3)

transfer characteristics although the data are

drop

and

the

were also recorded correlations

can be scattered.

increasing wire values predicted

from 0.1 to by a specially

resistance

of

the

on the photo-film.

yielded

represented

horizontal

the fairly

following well

by

diameter. The measby Kutateladze et al.

Rao & Andrews.

The diameter of departing bubble (0.3~0.9 mm) and the frequency tion (approximately 90 Hz) agree fairly well with the correlations chenko

for nucleate

to the cold

(saturated)

boiling. liquid

The

present

is much

more - 35 -

data

suggest

responsible

that

the

of bubble formaof Verkin & Kiritransient

conduction

for the high heat transfer

rates

512

J. Nucl. Sci. Technol.,

associated (4)

with

nucleate

boiling.

In film boiling the heat transfer coefficient decreases with increasing The measured values are higher than Bromley's correlation and agree the correlation of Breen & Westwater. servations that the turbulent wave the

(5)

heat flux measured

more

detailed

studies

are

knowledge

of

formation,

Transient

will

In order based

to on

the

the boiling

as cooling

boiling

required

about

microcharacteristics

such

This is suggested by the photographic obmotion of vapor film is caused along the top of

for film boiling decreases with values are in good agreement

predicted by Lienhard & Wong. The foregoing observations in liquid

bubble

diameter. well with

wire.

The minimum diameter. The

much

wire fairly

down

present

nucleate

rate occurs

in many

transient

steady-state

the bubble

in an

the

boiling

size

of

departing

and

the

number

Rapid

strength boiling

boiling

as

of

to those

analytically

film

accident

applications.

affect

need

of

are similar and

and

including

growth

significantly fill this

both

boiling,

also

nitrogen

experimentally

the increase of the wire with the theoretical values

of

well

as

temperature structures

experiments

in

cryogenic

in noncryogens, order

, of nucleation

change

some

the

the

especially

the

frequency sites .

of

normal

during

but

obtain

liquids,

bubbles

during

to

such

operations, transient

, which is important for are scheduled for coming

safety. years

,

experiments.

[NOMENCLATURE] A: B: Cp: D: Di: D* :

Proportionality constant in Eq. (21) Proportionality constant in Eq. ( 2 ) Specific heat Diameter of cylindrical heater Interfacial diameter of vapor film Dimensionless diameter of cylindrical heater, defined by Eq. ( 4 ) D*i : Same as D*, except that characteristic length is taken as Di d0 : Diameter of departing bubble f : Frequency of bubble formation g : Acceleration due to gravity h: Total heat transfer coefficient hc: Convective (based on molecular conduction) heat transfer coefficient hfg : Latent heat of vaporization hr : Radiation heat transfer coefficient I: Electric current flowing wire k: Thermal conductivity m 1, m2:Constant exponents in Eq. (21) n : Number of nucleation sites per unit area of heating surface Nub : Boiling Nusselt number, defined by Eq. (23) NuD: Nusselt number based on diameter of cylindrical heater, defined by Eq. (11) Nulc: Same as NuD, except that characteristic length is taken as lc P: Static pressure in liquid at boiling surface Pc: Critical pressure - 36 -

Pr: q: qmax.: axF : qmin,: qnb: R: Ra*D: Ra*lc: Reb: T: Ts: Tw.: Ts:

V: W: : : ' : ": : c:

Prandtl number (=Cpm/k) Total heat flux Critical heat flux Critical heat flux qm for horizontal flat plate, defined by Eq. ( 6 ) Minimum heat flux Nucleate-boiling heat flux Electric resistance of wire Modified Rayleigh number, defined by Eq. (12) Same as Ra*D, except that characteristic length is taken as lc Boiling Reynolds number, defined by Eq. (22) Temperature (K) Saturation temperature (K) Temperature of heating surface (K) Excess of temperature of heating D surface above saturation temperature (= Tw-Ts) Potential drop of wire Input power (= VI) a Thermal radiative absorptivity of liquid b Bubble contact angle Dimensionless heat t parameter , defined by Eq. (13) Dimensionless t heat parameter , defined by Eq. (16) k Stefan-Boltzmann constant, 5.669 x 10-6 Win-2 K-4 Critical wavelength,l defined by Eq. (14)

m

Vol. 18, No. 7 (July 1981)

513

: Viscosity r : 'Density s : Surface tension

(Subscripts) l : Liquid,

v:

Vapor

REFERENCES

(1) See, for instance, FROST, W. : "Heat Transfer at Low Temperatures" , (1975), Plenum Press, N ew York. (2) "Dennetsu Kogaku Shiryo", (3rd Ed.), (in Japanese), (1975), Japan Soc . Mech. Engrs., Tokyo. (3) LYON, D. N.: Int. J. Heat Mass Transfer, 7[10], 1097 (1964). (4) ROUBEAU, P. : Proc. 10th Int. Congress of Cryogen and Ref rigent, Copenhagen , 1959, Vol. 1, 49 (1960 ), Pergamon Press, Oxford. (5) COWLEY, C. W., et al.: Ind. Eng. Chem. Process Design Develop., 1[2], 81 (1962) . (6) FLYNN, T. M., et al.: "Advances in Cryogenic Engineering", Vol. 7, 539 (1962), Plenum Press , N ew York. (7) HASELDEN, G. G., PETERS, J. I. : Trans. Inst. Chem. Engrs., 27, 201 (1949). (8) WEIL, L., LACAZE, A.: Acad. Sci., Paris, 230[1], 186 (1950). (9) FRITZ, J. J., JOHNSON, H. L. : Rev. Sci. Instrum., 21[5], 416 (1950). (10) MERTE, H., CLARK, J. A. : Trans. ASME, J. Heat Transfer, Ser. C, 86, 351 (1964). (11) TAMAKI, E., WAKISAKA, N. : Liquid nitrogen boiling experiments, Preprint 7th Japan Nat . Heat Transfer Symp., (in Japanese), 73 (1970). (12) KUTATELADZE, S. S. : AEC-tr-3770, (1959). (13) SUN, K. H., LIENHARD, J. H. : Int. J. Heat Mass Transfer, 13, 1425 (1973). (14) BERNATH, L.: Chem. Eng. Progr. Symp. Ser., 56, 95 (1960). (15) IVEY, G. H., MORRIS, D. J. : Proc. 3rd Int. Heat Transfer Conf., Chicago, 1966, Vol. 3, 129 (1966). (16) KUTATELADZE, S. S., et al.: Teplofiz. Vys. Temp., 5, 841 (1967). (17) RAO, P. K. M., ANDREWS, D. G.: Proc. 6th Int. Heat Transfer Conf., Toronto, 1978, Vol. 1. 227 (1978). (18) ZUBER, N.: AECU-4439, (1959). (19) BROMLEY, L. A.: Chem. Eng. Progr., 46[5], 221 (1950). (20) BREEN, B. P., WESTWATER, J. W. : ibid., 56[7], 67 (1962). (21) LIENHARD, J. H., WONG, P. T. Y. : Trans. ASME, J. Heat Transfer, Ser. C, 88, 220 (1964). (22) BERENSON, P. J. : Transition-boiling heat transfer from a horizontal surface, Heat Transfer Lab. Tech. Rept. No. 17, (1960), M. I. T. (23) See, for instance, "Futto Netsudentatsu", (in Japanese), (1964), Japan Soc. Mech. Engrs., Tokyo. (24) FRITZ, W. : Phys. Z., 36[11], 379 (1935). (25) VERKIN, B. I., KIRICHENKO, Yu. A.: Proc. 7th Int. Cryogenic Eng. Conf., London, 1978, 505 (1978), IPC Sci. Technol. Press, Gildford. (26) ROHSENOW, W. M.: Trans. ASME, J. Heat Transfer, Ser. C, 74, 969 (1952). (27) MIKIC, B. B., ROHSENOW, W. M.: ibid., 91, 245 (1969). (28) INAI, N. : Film-boiling heat transfer in liquid helium, Preprint 14th Japan Nat, Heat Transfer Symp., (in Japanese), 133 (1977). (29) FREDERKING, T. H. K.: Amer. Inst. Chem. Engrs. J., 4, 403 (1959). (30) NUKIYAMA, S.: J. Japan Soc. Mech. Engrs., 37, 367 (1934). (31) MCADAMS, W. H., et al.: Chem. Eng. Progr., 44, 639 (1948). 32) BANCHERO, J. T., et al.: ibid., 51[17], 21 (1955). (

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