Library, N.W. Bldg

NOV 1 1965

^ecUnical vtete 92c. 3/7

BOILING HEAT TRANSFER FOR OXYGEN, NITROGEN,

HYDROGEN, AND HELIUM

E,G. BRENTARI, P. J. GIARRATANO, AND R.V.SMITH

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards is a principal focal point in the Federal Government for assuring

maximum application of the physical and engineering sciences to the advancement of technology in industry and commerce. Its responsibilities include development and maintenance of the national stand- ards of measurement, and the provisions of means for making measurements consistent with those

standards; determination of physical constants and properties of materials; development of methods

for testing materials, mechanisms, and structures, and making such tests as may be necessary, particularly for government agencies; cooperation in the establishment of standard practices for incorporation in codes and specifications; advisory service to government agencies on scientific and technical

problems; invention and development of devices to serve special needs of the Government; assistance

to industry, business, and consumers in the development and acceptance of commercial standards and

simplified trade practice recommendations; administration of programs in cooperation with United

States business groups and standards organizations for the development of international standards of

practice; and maintenance of a clearinghouse for the collection and dissemination of scientific, technical, and engineering information. The scope of the Bureau's activities is suggested in the following

listing of its four Institutes and their organizational units. Institute for Basic Standards. Applied Mathematics. Electricity. Metrology. Mechanics. Heat. Atomic Physics. Physical Chemistry. Laboratory Astrophysics.* Radiation Physics. Radio Standards

Laboratory:* Radio Standards Physics; Radio Standards Engineering. Office of Standard Reference

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* Located at Boulder, Colorado 80301. ** Located at 5285 Port Royal Road, Springfield, Virginia 22171.
NATIONAL BUREAU OF STANDARDS

*€ecltnical ^ote 3/7

ISSUED September 20, 1965

BOILING HEAT TRANSFER FOR OXYGEN,

NITROGEN, HYDROGEN, AND HELIUM

E. G. Brentari, P. J. Giarratano, and R. V. Smith

Institute for Materials Research

National Bureau of Standards

Boulder, Colorado

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, IJ. S. Government Printing Office Washington, D.C. 20402

Price: 60?
FOREWORD

This Technical Note represents a collection of several essentially separate works some of which have been reported in less detail elsewhere (see Advances in Cryogenic Engineering, Volumes

10 and 11). It may be well to specifically identify the contributions of the various authors. The first author did a major portion of the work on pool boiling, section 2. The second author was the major

contributor to forced convection, section 3, and the properties, section 6. The third author made

some contributions to all sections and wrote section 4 on boiling variables. Also special credit is due

to Mrs. Dorothy Johnson who assisted in the final editing and the typing of several drafts of the manuscript.

The work in section 3 was partially supported by NASA Contract R-45, and that assistance is gratefully acknowledged.

11
CONTENTS

PAGE

FOREWORD ii ABSTRACT 1

1. INTRODUCTION 1

Z. NUCLEATE AND FILM POOL BOILING DESIGN CORRELATIONS FOR O , N , H AND he 1

Z. 1 . Presentation of experimental data 1 Table Z. 1 Experimental oxygen pool boiling systems 6 Table Z. Z Experimental nitrogen pool boiling systems 7 Table 2. 3 Experimental hydrogen pool boiling systems 9 Table Z.4 Experimental helium pool boiling systems 10

Z. Z. Presentation of predictive nucleate correlations 16

Z. 3. Presentation of predictive film correlations 17 Z.4. Conclusions - pool boiling 19

3. FORCED CONVECTION BOILING ZZ

3.1. Introduction ZZ 3.1.1. Boiling regimes 2Z

3.1.2. Transition points ZZ 3.1.2.1. Bubble inception ZZ

3. l.Z.Z. Transition to film boiling ZZ 3.1.3. Predictive expressions Z3

3.2. Experimental data 23

3.3. Correlations Z3 3.3.1. Film boiling Z3 Table 3. 1 Data used by this study 24

Table 3.2 Data considered but not used 25

3.3.2. Film boiling - Nusselt number ratio vs x( quality) 29 3.3.3. Film boiling - superposition 34

3.3.4. Nucleate boiling - superposition 36

3. 3. 5. Burnout or transition point 39

3.4. Discussion of correlations and results 43

3.4.1. X and x correlations without boiling number 43

Table 3.3 Summary of results 44

3. 4. Z. X and x correlations with boiling number 5Z

tt B 3.4.3. vonGlahn correlation 5Z 3.4.4. Film boiling superposition 54

3.4.5. Nucleate boiling correlations 54

3. 4. 6. Burnout 54

3.5. Conclusions . 54

iii
4. BOILING VARIABLES 56

4. 1. Saturation fluid properties (pressure) 56

4.2. Subcooling 56

4.3. External force field (gravity) 57

4.4. Surface orientation and size 62

4.5. Surface condition 62

4.5.1. Surface history 62

4. 5. 2. Surface temperature variations 62

4.5.3. Surface roughness 63

4.6. Surface-fluid chemical composition 63

5. SUMMARY AND CONCLUSIONS 63

6. PROPERTIES DATA AND X CURVES 64

7. NOMENCLATURE Ill

8. LITERATURE REFERENCES - - 115

IV
Boiling Heat Transfer for Oxygen, Nitrogen, Hydrogen, and Helium

E. G. Brentari, P, J. Giarratano, and R. V. Smith

This study has been conducted to provide an orderly examination of the information relative to boiling heat transfer for four cryogenic fluids. The general approach has been to examine experimental data with respect to the predictive correlations which would appear to have probable success and which would be likely to be used by design engineers. These correlations were graphically and

statistically compared. The results are discussed, and when it appears a best or acceptable recommendation can be made, computation aids for designers are included. These aids are in the form of graphical presentations for preliminary studies and equations for computer studies. The authors

have also indicated the apparent limits for the use of these correlations, when possible. The effect

of many variables which would often be significant are not included in the predictive correlations.

The influence of these variables is discussed in a separate section on boiling variables.

Keywords: boiling, cryogenic, film, forced-convection, free-convection, helium, hydrogen, nitrogen,

nucleate, oxygen

1. Introduction

Although the boiling phenomenon has been studied for at least a hundred years and has been the subject of many papers, it is not well understood. All this work has not been a failure, however,

even though complete understanding has not been achieved. From a designer's point of view, the predictive expressions have become increasingly more reliable but also more abundant. The purpose of

this study is to test these predictive expressions with the available experimental data in order that a

better choice of expression can be made.

2. Nucleate and Film Pool Boiling Design Correlations

for O , N , H , and He

The purposes of this section are to present the available cryogenic pool boiling heat transfer

data from the literature and selectively to evaluate and present the best available predictive correlations as functions of significant system parameters for use by the cryogenic design engineer. The

basic approach was to search the literature to gather experimental cryogenic boiling data which were

then compared with existing correlations evaluated for the cryogenic fluids. In presenting the data, effects of heating surface geometry, finish, and material were not discriminated from each other.

From these correlations, the ones which best appeared to describe the data were selected for presentation in the cryogenic range. Generally, the selected correlations fell within the spread of the

experimental data and thus should provide engineering utility for many design studies.

2.1. Presentation of Experimental Data

The experimental data for oxygen, nitrogen, hydrogen, and helium are respectively presented

by figures 2.1, 2.2, 2.3, and 2.4, for one atmosphere, with the exception of the nucleate regime for helium, which is shown at 1/2 atmosphere because more data were available at that pressure. The

correlations appear to describe the data adequately, but the general correlations show a tendency to be slightly lower than the visual average of the data. The circles represent the maximum experimental nucleate pool boiling heat fluxes. No minimum film boiling data were found for the cryogenic

range.

In general, the widths of the bands of data indicate the spread of each respective investigator

under constant experimental conditions. However, this is not true for the oxygen and nitrogen nucleate boiling data of Lyon [ 1964 ] and Lyon, et al. [ 1964 ] . These deceptively wide bands are due

to his careful investigations of extensive ranges of heater geometries, orientations, and surfaces.

As previously stated, there is no discriminiation between these effects in this paper. Tables 2.1 - 2.4 summarize by fluid the experimental systems shown in the figures.
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14
AT,(°K)

FIGURE 2.. 9

Comparison of Elevated Pressure Data with the General Kutateladze Correlation

15
2.2. Presentation of Predictive Nucleate Correlations

One experimental difficulty which could contribute significantly to the experimental scatter is that of accurately measuring AT. These inaccuracies would then introduce large fluctuations in — for the higher heat fluxes, when compared to the correlations where AT is cubed. It should be

noted that the correlations and experimental data as presented were evaluated at a standard gravitational acceleration of 980 cm/ sec .

For the nucleate pool boiling regime, the general nucleate heat transfer correlation and the maximum nucleate heat transfer correlation of Kutateladze [1952] were selected. Empirical evidence

indicates that the nucleate heat transfer flux is approximately a function of AT cubed at one atmosphere. Other correlations which were functions of AT raised to powers from 2. 5 to 3. 3 were those of Rohsenow [1952] , McNelly [1953] , Gilmour [1958] , Tolubinskii [1959] , Labountzov [i960] , Michenko [i960] , and a second correlation by Kutateladze [1952] . All of these were compared with

the experimental data.

In his text on condensation and boiling, Kutateladze [1952] developed a set of basic equations

from basic fluid flow considerations which described the nucleate pool boiling phenomena and by

applying similarity considerations to these equations he produced a set of dimensionless groups.

Groups of negligible influence were eliminated, and the remaining variables were formulated into

groups which could be evaluated from available theoretical and experimental property data. This is shown below as (2.1).

K,.„, / „ vl/2 , r ('!/A)„.„,(C) l P l/ „ 1/2 0.6 —) =3.25 ( io)- 4

r *ucl

;

*'* i (-g-) 1 gP. ' L Xp k. \ gp, / J Nucl

k

i (2.1)

Wf a , 3/2

]

- 125

r p i

- 7 Uj' ^gPjg / -I L(a gPi )r72-J

Finally, these groups in (2. 1) were rearranged into the conventional form of heat flux as a function of

difference between the wall and the saturated liquid temperature. Since all the properties were functions of the saturation pressure, a family of pressure curves was generated for each fluid on a

digital computer and compared with the elevated pressure data of Lyon, et al. [1964] , Roubeau

[i960] , Class, et al. [i960] , and Graham, et al. [1965] . These curves appear as the pressure

dependent lines in the nucleate boiling regime of figures 2.5, 2.6, 2.7, and 2.8. Figure 2.9 shows

a representative sample of dimensionless elevated pressure data as a function of AT to illustrate

general agreement or deviation from (2. 1). As the heat flux is increased, a point is reached where any increase in AT will decrease the

total heat flux. This nucleate boiling limit is known as the maximum or peak nucleate boiling heat

transfer flux. It is of interest to designers since heat fluxes are markedly reduced at this point and

fluxes greater than this maximum will occur only in the film boiling region at relatively high values

of AT. It is also of interest to researchers because some of the boiling variables appear to be negligible at this point, making the data more reproducible. The exact mechanism of this transition

remains controversial, but the maximum flux is associated with the inception of transition from

nucleate to film boiling. However, the correlations generally in use which predict the maximum heat

flux are of similar form, being functions of fluid properties only and not being dependent on AT.

Kutateladze [1952] proposed that the maximum heat flux occurs when the stability of the liquid

films penetrating the two-phase boundary layer is destroyed. From this analysis, his maximum

nucleate pool boiling correlation is

(q/A) Max.Nucl. K> {2Z)

1/2, , ,1/4 1 \p agAp ) v v

16
A value of K = 0. 16 was chosen as the numerical average of the values presented in his text. Also,

he recommended this value when the exact evaluation of the constant was unknown. More recently,

Zuber, et al. [1959] have also developed a correlation based on a hydrodynamic analysis similar to that of Kutateladze. After negligible groups were eliminated, their expression was essentially the same as (2. 2)

Since the maximum is not a function of AT, the intersection between (2.1) and (2.2) is required

to determine approximate AT values at which the maximum will occur. These are shown in the nucleate regime as the circles in figures 2.5, 2.6, 2.7, and 2.8 and as the horizontal lines in figures 2. 1, 2. 2, 2. 3, and 2. 4. In this respect, Lyon, et al. [1964) indicate that the data begin to deviate from

the maximum correlation predictions above 0. 6 of their critical pressures and that they become

virtually useless above 0.8. Thus, both of the Kutateladze correlations in the nucleate regime are shown only up to 0.6 of critical pressure for their respective fluids, because the general boiling

correlation uses the same parameters as the peak correlation and thus would also appear to be

incorrect at the higher reduced pressures. Figure 2. 10 illustrates the agreement of data from vari- ous investigators with the Kutateladze maximum nucleate boiling correlation, (2. 2), where the dashed

portion indicates pressures exceeding 0.6 of critical. It is of interest to note that the maxima for the predicted peak values occur at a reduced pressure of 0. 3, which is in agreement with experimental

evidence for the non-cryogenic liquids and for the cryogenic data of Lyon, et al. [1964, 1965] and

Roubeau [i960] .

2.3. Presentation of Predictive Film Correlations

For the film pool boiling regime the general film heat transfer correlation of Breen and

Westwater [1962] and the minimum film heat transfer correlations of Linehard and Wong [1963] and

of Berenson [i960] (which is an empirical adjustment of the Zuber, et al. [1959] analysis) were

selected. These correlations were chosen on a basis of empirical agreement with the available data,

theoretical exploration by the respective investigators, and inclusion of previous work. In all, eight

correlations were investigated, some of the major ones being those of Bromley [1950] , Hsu and

Westwater [i960] , Chang [1959] , Berenson [i960] , and Breen and Westwater [1962] .

Breen and Westwater [1962] base their correlation upon the Taylor instability theory by considering the maintenance of the minimum wavelength on the bottom surface of the boiling liquid which

will release vapor bubbles into the liquid from the supporting vapor film. A significant parameter in

this analysis which was neglected by some previous authors is surface tension. Also, for cylinders,

heater diameters up to 1.0 cm play a significant role in film boiling, as opposed to nucleate boiling

where that effect appears negligible. In dimensionless form, the Breen and Westwater correlation is

Film

Cond.

(i^)

1/8

(^f-)

1/4 —o-»(^f-) B H

f kjP

f Apfg

Xi gD A

Pf

For this correlation, X' is an effective heat of vaporization, given by

[X + 0.340(C ) (AT)]

2

X» = 1—E-*. (2.4)

It is of interest to note that this correlation coincides with the Bromley [1950] correlation over the range of diameters from which the Bromley correlation was developed. Figures 2.5, 2.6, 2.7, and

2.8 show this correlation as a function of varying heater diameters at a constant pressure of one atmosphere, only, since the available cryogenic data indicate somewhat contradictory results at elevated pressures.

As the heat flux is decreased, a point is reached where a further decrease in AT will markedly

increase the total heat flux. This film boiling limit is known as the minimum film boiling heat transfer flux. At this point, the transition from film boiling to nucleate boiling occurs, but not

17
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60

40

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EXPERIMENTAL DATA

O Oxygen, Lyon

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Nitrogen, Lyon —

Nitrogen, Roubeau

C ) B Nitrogen, Cowley et al

Ql Nitrogen, Flynn et al

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CD Hydrogen, Class et al © Hydrogen, Roubeau

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FIGURE 2. 10

Comparison of the Maximum Nucleate Heat Transfer Fluxes with the Kutateladze

Maximum Correlation

18
necessarily at the same value of AT as the maximum nucleate boiling flux. However, the correlations

predicting this minimum are again functions of fluid properties only, being independent of AT.

Lienhard and Wong [1963] also utilize Taylor instability theory by considering the critical

surface wavelength that creates surface waves of sufficient amplitude to break down the vapor film and

carry liquid to the heater surface. Their expression, after empirical adjustment to the same units as shown in the nomenclature is

/„\ / Pf X \r 2 SApf 4a l 1/2 /§Apf ? x" 3/4

Film * +

f D (P +p) D

Cond. x t

In essence, (2. 5) is an extension of the Zuber, et al. analysis by Lienhard and Wong [1963] for a flat plate, to account for small diameters. Thus, as D was increased, the Zuber prediction was used as

the absolute minimum heat flux for film boiling. After adjustment by an empirical constant, this is

. gCTAp 1/4

(lJAbs.

= °- l6XPf[——Z-] < 2 ' 6 > Min. (P i +P

f

) Film

Cond.

Since these minima are not functions of AT, the intersections between (2. 3) and either (2. 5) or

(2.6) are required to determine the approximate AT values at which the minima will occur. These are shown in the film regime as the circles in figures 2. 5, 2. 6, 2. 7, and 2. 8 and as the horizontal lines

in figures 2.1, 2. 2, 2. 3, and 2.4. As an example of the other correlations which were investigated,

Figure 2.11 shows the relationships between various nucleate and film correlations with respect to the

body of hydrogen data. A similar analysis was performed for each of the other three fluids. A more

rigorous comparison such as the statistical methods of section 3 was not used because much of the

data were shown in general curves and not reported as data points which are necessary for such a

study. In general, these additional nucleate correlations were taken from Drayer [1965] while the additional film correlations were taken from Richards, et al. [1957] . Also, a recent report by

Seader, et al. [1964] provides an excellent survey of oxygen, nitrogen, and hydrogen pool boiling.

It should be noted that (2. 3), (2. 5), and (2. 6) do not include the heat transfer due to radiation.

These equations predict the film boiling flux by conduction through the vapor film only. However, if ideal radiative transfer is assumed ("black body" emissivity and absorptivity) then heater surface

temperatures of the order of 400 to 425 C K can be tolerated for all of the four fluids without exceeding

5% error from the radiation even if it is neglected in the calculations. Figure 2.12 illustrates the heat flux due to radiation under the "black body" assumptions which would, of course, yield somewhat

larger values than would actually be experienced in practice.

2. 4. Conclusions - Pool Boiling

For nucleate boiling, the correlation of Kutateladze [19 52] appeared to fit the available experimental data best. At higher pressures the agreement was poorer but perhaps acceptable for some

design studies. For film boiling the correlation of Breen and Westwater [1962] was chosen for the best fit of experimental data. At higher pressures there were insufficient experimental data for comparison. For maximum and minimum heat fluxes in the region of transition from nucleate to film

boiling the correlations of Kutateladze [1952] and Lienhard and Wong [1963] were selected for presentation.

It would appear from the rather wide range of experimental data that some variables, such as

surface conditions, orientation, etc. , are missing and others are perhaps not properly taken into account in the correlations. There is a further discussion of some of these variables in section 4. Finally, the predictive correlations mentioned above were evaluated in the figures at one standard

"g" only.

19
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21
3. Forced Convection Boiling

3.1. Introduction

The purpose of this study was to investigate the relative merits of proposed predictive methods

which may be used to determine required design information from data normally available. The

required design information was assumed to be values of heat flux in the nucleate and film boiling

regions and conditions for the transition between the two regions often referred to as the critical or burnout point. It has been assumed that flow rate, quality, fluid properties, and system geometry

data are available or may be determined in most design studies; thus these quantities constitute the independent variables for the equations or correlations presented.

Since both the forced convection and the boiling phenomena when considered separately are

poorly understood, one may expect only broad treatments of a subject involving their interaction

rather than rigorous and specific studies.

3. 1. 1. Boiling Regimes

Some general divisions for the forced convection boiling regions have been proposed, for

example, by Davis [i960] : (1) Region I - The nucleate boiling (wet wall) region where the nucleate boiling contribution is significant, as for low velocity flows.

(2) Region II - The wet wall region where the forced convection effects are more significantly

controlling for high velocity flows.

(3) Region III - The dry wall or liquid deficient region where the heat transfer is through a vapor film to a liquid or two-phase core.

Since almost all of the cryogenic data available were in Region III, most of this study was

oriented toward that region. The data used are entirely hydrogen since these were the only complete

and tabulated cryogenic data available.

3. 1. 2 Transition Points

The transition points from single-phase flow to flow with bubble inception and the transitions

between the three regions previously described are often of prime design interest; studies of these

transition points may produce a better understanding of the phenomena. In this study very few transition data points were found; however, the boiling inception point and the transition between Regions

II and III (burnout) will be briefly discussed.

3. 1.2. 1. Bubble Inception

Bubble inception will be defined as the point of discontinuous slope change of a heat flux vs AT

curve. This change of slope may be attributed to the change in heat transfer mechanism as boiling occurs. For the forced convection case this change of slope may occur for low velocity flow (Region

I) where the boiling effect is not negligible. The only cryogenic fluid data are for pool boiling

[Mikhail 1952, Tuck 1962, Ehricke 1963, Graham, et al. 1965] , and these are discussed in the

Boiling Variables section of this report. It would appear that this inception point is quite sensitive to surface conditions.

3. 1. 2. 2. Transition to Film Boiling

The transition from Region II to Region III may not produce an actual burnout in many cryogenic

systems because, although the solid surface temperature may be markedly increased it may still be

below the temperature for failure conditions for the heated solid surface. This discontinuity in the

heat flux vs AT curve does mark the transition, however, and essentially all work has been for flow

inside conduits.

Most of the analytical studies for the' transition from Region II to Region III use a general

superposition approach[ Levy 1962, Gambill 1963a] since the cryogenic burnout data were for a change

from a wetted wall to a dry wall condition. Gambill [1963b] has prepared an excellent review of the

subject of forced-convection burnout in which he discusses in detail the primary variables which are:

22
(1) Liquid properties.

(2) Velocity past the heated surface.

(3) System pressure [closely related to (1)] . (4) Subcooling or quality.

(5) Local acceleration forces (gravity).

For the case of flow over surfaces, Vliet and Leppert [1962] have reported studies on critical

heat flux for saturated and subcooled water flowing normal to a cylinder. These results showed that the primary variables were (T ,,-T ), velocity, and cylinder diameter,

wall sat

3.1.3. Predictive Expressions

Generally, the predictive expressions fall into two categories:

(1) Correlating a simple or modified Nusselt number ratio with the Martinelli correlating

parameter or a similar term, primarily reflecting quality. The Nusselt number ratio used

is the ratio of the experimental (or actual) Nusselt number to that value obtained by use of a Dittus-Boelter or Sieder-Tate type of equation with either single-phase properties or some modifications involving two-phase properties.

(2) Simple superposition, that is, adding the separately determined pool boiling and forced

convection (without boiling) contributions.

Many other predictive systems have been proposed, but many of them include empirical constants (previously determined for water data), values of which for cryogenic fluids the authors

assumed would not be generally available to designers. (For instance, see Tippets, 1964).

3. 2. Experimental Data

The experimental data considered by this study are shown in table 3. 1. Other experimental

data found are shown in table 3. 2 but were not included in this study because of lack of complete tabulated data which were necessary for calculations, or because of complex system geometry.

None of the experimental data used were culled for experimental accuracy.

3. 3. Correlations

(See Appendix for Nomenclature)

3. 3. 1 Film Boiling - Nusselt No. Ratio vs X..

A X correlation for the film boiling regime or Region III (as proposed by Hendricks, et al. 1961) used in this study was Nu

Nu-f^l =

f(V' <>>"

calc, f, t. p.

where

0.9 ,P 0.5 , u 0. 1

tt =(^) (17) (3

Nu . . . = 0.023 Re°'

8 Pr°*4

(3.3) calc, f, t.p. f, m, t. p. f, v

P, . U D

Re, = f.m.t.p. avg(3<4)

f, m, t.p. Uf v 23
QH

to

to

cqQW

to<aw

pq

i—1 i—i

r-H

rtj ni ai nj

a o• IH •iH o OH u u u Ih « -rH 4-> -J-J +-> +-> (U 4-1 o o o u

ft <$ >> 4)

4) 1—I

41

I-H i-H

ai

H ffiW

W

w

W oo

<V

MH

_ o o o o o o o o h

*" o vD o ° o ° ^ °

rt 3

-^ o o •* +-> „ o a o o 5 -

01

O vO CO xt< o ^ O ro Shfi LTl CM rt in ** o

in 00 i-H

'+j

fl U o

en >-<v

O o o oo o o

0)

H ^ O o o n o o o H to y in °- 2 o ° o ° o o o o w ° -d M •» +j rj o a o *

"*H

n

i-H j H^ 00 LTl in (NJ 00 ^ ko

m

rf 2 > £

t>- CM cm

n ^ r^

O xO

PO r~ * i-H (SJ 1-1 <n 00

CD oo 3 « 41 4) o 0)

tu ^3

O ° a

a

ft

a o

4J

K to

u Z 2 o Z w

i-H

X 3 nj o ,£> 2oo

00

<1 1 ° o o ^ ID ^ o O CM o o o -M H in ^h in r- o -H

01 +J m ,H o

CJ (D t« ~ 00 O 00 • o o ro r-l csj r~ ro r- OJ HH

(D c o d ni

Ai •H .,H Ih so o <u r-1

NucL and

Film cq a £ h cq

01 01 ?H 01 00 r—(

01

Q

4) I—l

0)ft

.2

4-» ^ 3 *>

01 vO1—1 o

i-H o

in oo . h Q

OBao

i-H • a "-

•|H „

to in

in

boc

i-H

ftu

rH

Q 00

<n +j CD

•-H

—

T

ni ° CM*

i-H h-1 r—1i-H ^-T

nJ ° - T i—1 w ^ "fi u o - z u

in o = * -rH 00 o (M N O

r

oi -M i—l o •ih

m o o +j

0) <u

TM

h

a 2 Q

h (v-1 > O

<\J (U «> > 01 s£>

ffiO vO

C3C fl fl S

01

V <p 0) 60 00 00 00 3 O o O

xj "H

M ^ ^H ^

01 XI XI T3 T) X) D <u >. ^ >s >> H 2 X ffi X a S o N

01

it! "3 fi

h o 5 fi '—

1)

-a s*3 xi s

i-Hni

(U

u

O^ -a

oT^ O CI o — a g

XIa

to 5<; - rd I , H «, ,—,

iS S '—i

a»

h

O T3 i-H oo o»

^1 01

m fl

d •-o

1-1 rtj

.in

m

O -H

O ai oi 0^

u o o 2 ill X X

1—t

^i

24
TABLE 3.2 DATA CONSIDERED BUT NOT USED

Source and/or

Author

Test

Medium

Boiling

Region Reason for not using

Dean and Thompson

[1955] Nitrogen Nucleate,

Film, &

Burnout

Geometry

Richards, Robbins,

Jacobs, Holten

[ 1957]

Nitrogen

Hydrogen

Nucleate Geometry

Sydoriak and

Roberts [ 1957]

Nitrogen

Hydrogen

Nucleate Geometry

von Glahn and

Lewis [ 1959]

Nitrogen

Hydrogen

Film and

Burnout

Lack of complete tabulated

data

Hendricks and

Simon [ 1963]

Nitrogen Film Boiling Geometry

Aerojet [ 1963] Hydrogen Film Boiling Geometry

Chi [ 1964] Hydrogen Nucleate

Film

Lack of complete tabulated

data

25
f, v

f, m, t. p. x 1 - x

(3.6)

P

f P,

Uavg=ir^ < 3 - 7 > b c

and p = - (3.8) b x 1 - x

From the definition of the Reynolds number it is apparent that Nu f is a two-phase type of

caxc, i, t. p. Nasselt number which will, however, approach the value of the single gaseous phase Nusselt number

as the quality approaches 1. A variation of the above correlation was also considered. The correlation used was

Nu

Nu-f^ = f<V' (3 ' 9) calc, v, s„ p.

where Nu , = 0.026 Re°'

8 ° Pr°"33

( —

)

(3.10) calc.v, s.p. v, s.p. v \|i /

,P U D

Re = ( V aVg

J (3.11)

v, s.p. \ u

C u

I Pv V

\ and Pr = (^ —

J (3.12) v

Since the heat transfer from the wall is assumed to be through a gaseous film adjacent to the wall for film boiling (Region III), the Reynolds number was defined as a gaseous single-phase

Reynolds number based on the average velocity of the mixture. The Sieder-Tate equation was chosen

and properties of the gas were evaluated at bulk temperatures of the stream, with the exception of

u which is the viscosity of the gas at the temperature of the inner wall. The general form of the

Sieder-Tate equation was taken from Bird, et al. [1962] . The results of plotting (3. 1) and (3.9) are shown in figures 3. 1 and 3. 2 respectively.

Finally, as suggested by Ellerbrock, et al. [1962] , (3. 1) was modified by the use of the dimensionless boiling number in the following manner:

26
x 1

I

1

1 1 O

- -

G) o

r ^

<] <3

_ X

c

_ «*

00o

o

- rX

c

ex

i

CVJ - m

- Q

X

- *ci

II —

3 < /

<1G o

\T O

<3 G V KG

3

b r aQ

o^

li

<H > e

G jq

GtQ) >o O o

O

— —

3

<l , x G#W

~<b

<d

.1 i<l

<-] —<3_ <J^L-Q_

Q.X

H-T" o

oo

3 - r

< 3°

fern

«a

<3

<3 r% 4

< ^ /

o

gP

c9> -

" o

o

Hendricks

et

al

(1961)

Wright

S

Walters

(1959)

n

- T) - q

- - a

a>o

JJ 1 1 1 i-i|

G [D « SI o

o

X

x

>

uu

J3

<u

in

03

0)CO

exo

Eh

on

cuu

•i-i

Q.X

a> 3

O

o

o3

27
4 1 I I 1 1 - - o o 1 4 4 1 < 1 4

loI (X 1 ° 4 GG o - 1 G - - < In 4 O

o- - o ? a • ( Lo IJlo*^ n U

€1 ' © o I 4 G ^I^^o (g 4

[fa °* ,? G

*' i

*o444 - © o $§• $ 4 - - 4 /e CW 

fc^ -

<* Is?

n \m> nr 4 irb n 4

C\J

><c

ex

00oor

-*- c

ofO

C0+

CM

CM

CM

QlX

<u

ii 4 4 Kj, c 1 « I©! 3 4 — - u -

Hendricks

et

al

(1961)

Wright a

Walters

(1959)

CT> lO

CD - - —

- aX7 aCco2 L o

*_

a>o

CJ 1 | I | 1 1 c> < oo >

a)uuV

ft

tnend

CDCOI <u 1—1bCd

-H

</3

<Dd

CuO

•rH

ds '»' °l°3 nM

dxa

on

28
Nu

^2 )(Bo.No.)-°-

40 =f(X

tt ), (3.13)

calc, f, t.p.

where

Bo. No. = ^-£t (3. 14) mix

Examination of the factors involved in the definition of the boiling number leads to the interpretation

of the boiling number as being a ratio of the vapor generation to the mass flow rate in the tube or in a sense an index of the boiling-induced flow normal to the axis relative to the axial flow.

Thus, for a fixed power input to the tube, a large boiling number would indicate well developed

boiling where velocity is not influential and a small boiling number would indicate forced convection

effects are controlling (high velocity).

The results of this plot are shown in figure 3. 3.

3.3.2. Film Boiling-Nusselt Number Ratio vs x(quality)

Since quality appeared to be the controlling parameter in X. . and, perhaps, in the heat transfer

mechanism, (3. 1), (3.9), and (3. 13) were all plotted as a function of quality (f(x)) in place of f(X ). Results of these plots are shown in figures 3. 4, 3. 5, and 3. 6.

Another type of quality correlation proposed in a recent publication by von Glahn [1964] was

also included herein:

Nu

~^S- F = f(XJ (3.15)

where

Nu tp v f v, calc

Nu . = 0.023 Re

0,8 Pr0,4

(3.16)

v, calc v v

DG . Re = ^2i?S ( 3.17) V %

C u P v Pr = —-1 (3.18) v kv

x

f= t^t < 3 - 19)

F =2.0xl0- 10a

i (3)

- l67

( Y ) [l ' 8 - (Xf)a] (0.005)t 1 - (X ^(N f

" 667

(3.20)

tp 1 bo. no.

29
1 1 I 1

i

1 1

01

.01

.1

1

10

100

Xtt

-

'o

4 4 <

1 +->

4

4 /

'

' G

3

en>

o - < i o o

-

4

4jif<ft

<y 6 u

S

"o~ °/*i f5 D

a

4O <j jTj< D

^fb^

4

Pi

•i-H .—1

•rHo

J3

44 j

5°' i CVJ - o 4 C©B oj^^R

4 ><c

4»< Inm

q

i >T

c

«»< <D

CVJr

in

rq

cvi aX

<vn

en

CD -

o B

o +j

* <i^^ o

4 J." 4 Ho

4->

Cti

0)

4 #

8

- - r-H - 1 G -

d

' © 2

0)

en

Hendricks

et

al

(1961)

Wright

8

Walters

(1959) CZ

cd

f)

i o

- ro -

• CO

CD

ClX

c

c

L 3

V 00

-1-1 fa o

1 1 | 1

a> 3

7

<- Z

I 1

© 3 < 1

o

o

C

(:.

>

c)M c>£3 \ri*V •0|D0n| \l>

1

q

dX9i

30
T 1

i

1

i

1 1 -

- -

CVJXc

to

- O —

- X

-

+

o.X

- < ii -

- <;3 <1 <J^ fl\

o

Q

Uou

3

-

53 ^

i << <1

<tf -<l

i Q3 «*'"agS a.

<1 <l ®

<1 ^ftS <j

I <• n

'

- < * -

- 3 GJ^S -

Jo C^

jp\ o <J % a* T> O 3 m

en ^

(

<<J- \L

> \

b

(1961)

Waltei

il

(1959

-

Hendricks

Wright

S

&

Core

etc

iii

i -

- -

1 1 f 1 ! 1

a1

a}U

43

en

en

cu

en

a,

i o

ro

93U

d

GO

• i-t h

a. o X o

a> o 3 3

-z. Z

31
X i 1 i 1 T _

- -

-

cCP -

- X

c

-

•<f^

CD - O

rX

c

lf> — CM ~ |" 9, -

IT) — CO

4 *

4 '/

f

-

4 «« s h* ,

1 4 r aX

««

4? CI ,OG « 4

> 4

0)

ii < 4o l^^L1

1 4

— a. — X — •

3

c o

8 1 K

o

p

« O

o

4 a ' -

c

c

>

>

. £ .<*'<&

1j o

o -

- |fe« f ^ G o

C. * ©a

I

«8 ° o

5 O

i-rt ° n o

9

o ~ CD

-= ^>

co en

CO

4- O

J2 cO o

*- .e "O o> X ^ l

3 | oo

o o

0)

<uo

_L J j. J_ 1 1

c) u 4

o

o

'&% *A

4 0|D0n(y| O

+->

• rH r—

I

d

cr

en

CO

0)

CO i

PH

I 0) 1—

I

GO

fl

• rH «/>

LD

CO

CD

• H

In

0X9

nisi

32
T 1 1 1 1 1 - - -

CVJXC

5)coinOO+ " • X - c

ro+ L ro00

cvi - - - -

Q.X

0>

II -

CLX

<u D7 <cac

«*.

_tc

«. 7 - - 4 - * *

8f) * * *& 1< 5^ o 4 Q^V' o <j3S

p3j 1< o

°?Q

)4

.1 4 i> - « WJD<. J

— -

pa log

bf G - — 81 Irv sq

O*^

a o 1 Lai *l) * 1 V ' o o •

Hendricks

et

a\

(I960 i

Wright a

Walters

(1959) \e GO 0> - L G

<y>

— - __ - o

«>

<voo

±, I J J- 1 1

<. j u 4 z o ^3>ooda

p|boouu

0)CO

end

a)

•Hfa oo

L-.-ON ogV di

y '3103 nisi '

33
l-[

Re

4.2 1 - Re + 5.85 x 10 v n) + - 92

] (3.21)

C-^l (3.22)

Y = Re 1 + 2500

)] (3.23)

C^r) (3.24)

N "y^i-'v1 bo. no. , .1.5

P CT J v i

and (3.25)

{..,[ 1 - (L /D)

J + 0. 13

J- = 0. 13 for L /D> 3. 5 (L /D) + 0.05'

(3.26)

Results for the von Glahn correlation are shown in figure 3.7 for the data of this study.

3. 3. 3. Film Boiling - superposition

A simple superposition correlation was tested with the available cryogenic data. This procedure has been suggested by numerous papers and textbooks. The heat transfer coefficient calculated

from Breen and Westwater' s [1962] film pool boiling correlation (2.3) was added directly to the heat

transfer coefficient calculated from the modified Sieder-Tate single-phase forced convection correlation. That is

h = h + h pred conv film

s.p.v. pool

Soil

(3.27)

where

h =0.026(Re )°' 8

( Pr )°- 33(

U_Z)°- 14 (il)

conv \ v. s.p./ \ v/ \ u

/ \ D/

s. p. v, (3.28)

.(APJ

0. 375

0. 375 _, , kTX V_, 0.250 w ( —[~bld <> >» [

-^

1 [-T7

1

] (AT)

-.250

(3.29)

)ool

>oil D(Ap f

)

34
=f ! 1 1

1 1 -

CSJ -«— - X

- 4 'ar

4

" c OOqi "- 4


 vS 4 rOO o

n ^4 4

1 4

« 4

1«•- X O

O

3 « P

1>4 «

•3 4

i

C\J

1 O

3

O G

c 9?

4

I

4

4-

4

4

1 < 4

- (0 O Wc>^^" < 4 « 1 - - O

TM 4 4 1 -

L ~~ D D X j

II

a.

u a

D W

( 1 c

30

Hendricks

et

al

(1961)

Wright

a

Walters

(

1959)

a.X«

3

I

t

3

>

! o

« l>

> - -

3

i>

i>

1 | 1 1 | 1

c> J <1

X

o

o

o

o

o

ao

• iH

+-> aJ

si •rHUoa

>

0)

o

o

<u

en

04

0)

a

s

r—

o

>

b0

X

+-> (Us

0<

d4j Q|P3'An N

'

dX9nN

35
_X + 0.340(C ), (AT)., 2 *'=[

^

]• (3.29a)

Results of plotting h , vs h are shown in figure 3.8. pred exp

3.3.4. Nucleate Boiling - superposition

Simple superposition (h based on the liquid phase) and the correlations of Chen [1963] and

Kutateladze [1963] were tested for the nucleate boiling region.

The simple superposition correlation is

h j = h + h (3. 30) pred conv nucleate

s. p. £ . pool

boil

where

hconv =0.023(Re

i

)- 8 (Pr

i

)- 4 (4) (3.31)

s.p.-?.

Re, = DG . /u

* (3.31a)

£ mix i

and

1.282 1.750 1.500 w-^w-TfwA ]

<' t»

1 - 500

• pool 0-P ) cr u boil v *

Chen' s correlation is

where

h = (h, )F+ (h, )S, (3.33) pred fc f-z

h

fc =(4) <°- 023> ( Re

i)°'

8

( Pr

i )0 ' 4

(3 ' 34)

ki

' 79 (C)/- 45

p i

- 49

(AT)

- 24

(AP)

- 75 h

f- z

=

<°' °° 122 > P0.5 0.29,0.24 0.24 (3 ' 35)

F = correction factor which is a function of X and accounts for increased convective turbulence due to the presence of vapor.

/ 125

S = correction factor which is a function of Re. F ' and accounts for suppression of bubble growth

due to flow:

36
2.2~

2.0

.8

I .6

I .4

I .2

ON

I .0

.8

.6

o r n \

lendricks

Vright a

^ore et a

et al (IS

Walters ( (1959)

>6I)

1959)

* c

A

O

o

A /

o

A O

4

A /

A

*

Ao

A C

A Go

<£

A J ft 00 A* * *

O */

O Of A

A A

A

A

A

A

A i

** c A n

Z. j,., A -

* o

O

A

Ao

A

A

A O

o

o

/a

A

A

.2 .8 1.0

watts

' ex P cm2 °K

1.2 1.4 1.6

Figure 3.8 h vs h (film boiling superposition correlation)

to pred exp

37
(Re,)

DG . (1-x) mix

Kutateladze' s correlation is

>red

nucleate, n

pool DOll \ h /

1 + conv

s.p.i.

(3.36)

>red

s.p.

nucleate

pool boil

iconv

s.p.i.

:le1ate1 >I Doil nucl

Figure 3.9 Functional dependence of h , on _— according to Kutateladze (1963). pred hconv

s.p.i.

38
h nucleate

r- -J i .. c Pred pOOl DOll , . r. _ - Consider a plot of r-^ vs 7-*- as shown in figure 3.9, conv

s.p.i. convs.p.i.

pred

s.p.

nucleat^

conv

pool boiJ

s.p.i.

As

nucleate

pool Don

1 conv

s.p.i.

- , i.e., for no boiling, where velocity effects are controlling,

pred , , „/ then -r^ = 1 and f = 0. hconv

s.p.i.

As

nucleate, pool DOll

s.p.

i.e., for well developed boiling where velocity effects are

not influential,

then pred

1conv

s.p.i.

nucleate, P°°Ib°fl and f' conv

s.p.i.

A function which satisfies the above criteria is (3. 36). Values of n from 0. 7 to 2. were used in this study in an attempt to correlate the limited data available. Results of plots of h , vs h for pred exp

(3.30), (3.33), and (3. 36) are shown in figures 3. 10, 3.11, and 3. 12, respectively. Figure 3. 12 reflects results when n = 2 in (3. 36), since that value of n produced the best results.

3. 3. 5. Burnout or Transition Point

Since the only burnout data for cryogenic liquids found was that of Lewis, et al. [1962] , this

paper has merely reproduced their curve, showing a comparison of burnout heat flux for cryogenic

liquids with the water correlation of Lowdermilk, et al. [1958] .

Lowdermilk' s correlation is

(q/A)

270 G

0.85

burnout 0. 2, T ,.0.85 ' D (L/D)

1 < < 150

(L/D)

(3.37)

(q/A)

1400 G

0. 5 burnout ^0.2, T ,.0.15 ' D (L/D)

150< < 10000

(L/D)

39
8

o

CME

o

o> 6

a \ Vright S Waiters ( 1959)

LJ

Q

D

P y^

Q '5f

f P

P / m

3

I 2345678 . watts

" e*P cm2°K

Figure 3. 10 h vs h ^ (nucleate boiling superposition correlation)

40
o

ege

o

a>

10

G>i Vright S Walters M959)

9

8

7

6

5

4

D 3

D Q

3 n

2

1 / D

D

D

I 4 5

watts W cm2 °K

Figure 3.11 h , vs h (Chen correlation)

& pred exp

41
10

«o

06

0)

a\Vright 8 Walters ( 1959)

D

-

n

n/

/ &

D

y' D §

rn

D

4 5

watts

J exp cm2 °K

8

Figure 3. 12 h vs h (Kutateladze correlation)

prect exp

42
3.4. Discussion of Correlations and Results

The data used in this study are limited in numbers of points, ranges of fluid properties, and in

experimental systems. Figures 3. 1 through 3.7 illustrate significant differences in the three sets of data considered; furthermore, no attempt was made to cull the data for accuracy. Thus no conclusions regarding the absolute reliability of the correlations are implied; however it is felt that some

general guides are indicated by this comparative study.

Table 3. 3 gives the equations of the best fit curves of the plots given in column 2. The equations were determined using the method of least squares by means of a digital computer. By applying the resulting least squares fit curve equations and the superposition type predictive equations, an hpred was then calculated for each data point. The figures given in column 5 of table 3. 3 are the results of plotting h vs h for each correlation. As a means of comparing the relative success or

failure of all the film boiling correlations and all the nucleate boiling correlations for the data considered, a root mean square fractional deviation, d, of the predicted value, h n , from the — pred

measured value, h , is given in column 7. The d is defined as exp —

where n is the number of data points. If the data population followed a normal distribution pattern,

±d would be the spread within which about 68% of the data occur and ± 2d would be the spread within

which about 95% of the data are found. Even if the distribution varies considerably from a normal

distribution, it is felt that d may be used as a measure of the relative reliability of all the correlations.

Although all results for d were based on the least squares equations shown in columns 4 and 6 of table 3. 3, it is felt that, for the range of X and x shown in figures 3. 1 through 3. 7, there would

be no significant loss of accuracy if the last term in each of the least squares equations is ignored.

This study also performed the aforementioned calculations for h , and d, using Hendricks, pred —

et al. [l96l] data only. These results also are shown in column 7 of table 3. 3. It is interesting to note that in this case the single-phase Reynolds number and superposition systems do not correlate

the data as well as do the correlations of von Glahn and Nu

,T 6XP - f(X ) or f(x). Nu tt' calc, i, t. p. The converse is true when all the data are considered. Furthermore, for Hendricks, et al. [ 196 l] data only, the boiling number correlations are not as effective in reducing the data spread as they are when all data are used.

However, unless specifically stated otherwise, the following remarks are made with reference

to the results obtained when all data [Core, et al. 1959, Wright and Walters, 1959, and Hendricks,

et al. 196l] were used in the calculations of h , and d. pred —

3. 4. 1. X and x Correlations without Boiling Number

tt e

The first four correlations shown in table 3. 3 may be generally considered together. The X

correlations appear to be based on the analogy between heat and momentum transport. This system

has been used extensively [Guerrieri and Talty, 1956; Dengler and Addoms, 1956; Hendricks, et al. 196l] and a further use of the analogy between momentum and mass transport has been proposed and

used[Wicks III, and Dukler, I960] . It would appear, however, for hydrogen that x is the controlling

factor in X and that a correlation with x might be simpler and just as satisfactory. Also, the means

43
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tt 45
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Figure 3. 14 h

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46
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47
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48
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49
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50
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51
of computing Reynolds number varied with the investigators. Hendricks, et al. [ 196 1 ] use a mean

film density with the average velocity of the mixture and the viscosity of the gas evaluated at the mean

,P

£ m t U

av D

film temperature (

'-—'-*— — J anc[ von Glahn [1964] evaluates the Reynolds number using the

f ' V

/ DGmixX

saturated vapor properties and the mass velocity of the mixture ( J

. Since, for film boiling,

u v

the process is visualized as heat transfer through a vapor film to a liquid or liquid-vapor core, it was

P v U^ D

felt that perhaps a single-phase gas Reynolds number ( —) , rather than the two-phase gas

V U v ^ A m t U

av D

\ Reynolds number (

'—'-^ -—J used in the calculation of Nusselt number, might also produce

a successful correlation. All of these considerations (except the von Glahn approach) variously

combined have produced the first four correlations shown in figures 3. 1, 3.2, 3. 4, and 3. 5. The d

values for these correlations indicate that for these data the simpler system of figures 3. 5 and 3. 16 has provided the best correlation. This is not true when the data of Hendricks, et al. [1961] are used

alone. It appears then, that for hydrogen, accuracy is not lost by the use of quality rather than X

as a correlating parameter and may not be lost by use of the single-phase gas at average velocity in

the determination of the calculated Nusselt number.

3.4.2. X and x Correlations with Boiling Number

Several investigators [Schrock and Grossman, 1959; Ellerbrock, et al. , 1962] have found that by use of the boiling number the correlations have been markedly improved. Figure 3. 20, which is Nu

a plot pof — vs X for some of the data of Hendricks, et al. [l96l] shows, for example, Nu , tt

L J ' * ' calc, f, t. p. how the data tend to separate according to boiling number. Thus, as shown in figures 3. 3 and 3. 6, Nu

when the ratio tt is multiplied by (Bo. No.)-0.4, the correlation is improved. The

calc, f, t. p. improvement in d values is quite significant, reducing the data spread by a factor of 3 for all the data

but less for the Hendricks, et al. [ 196 1] data alone. As discussed previously, perhaps an explanation for the effectiveness of the boiling number in the correlation is that this provides a measure of the ratio of the velocity of the vapor formed to the normal stream velocity. It seems quite conceivable

that this ratio would have a considerable effect on the flow pattern and subsequently on the heat transfer coefficient. No plots are shown using the boiling number with the single-phase Nusselt number

ratio as it would have been necessary to make appropriate changes in the exponent on the boiling

number to optimize the correlation using that Nusselt number ratio. A disadvantage of the boiling number correlation for design purposes is that the heat flux must

be known in order to use the correlation.

3. 4. 3 von Glahn Correlation

The value of d for the correlation proposed by von Glahn [1964] is relatively high. The best

equation for this correlation given in table 3. 3 was determined only from figure 3.7, which shows the

data of Hendricks, et al. [l96l] , Wright and Walters [1959] , and Core, et al. [1959] . The data of Core, et al. appear to plot at a reduced slope compared with the data of Hendricks, et al. and Wright

and Walters, von Glahn points out in his report that for 0. 7< Le/D< 3. 5 such a reduced slope was

obtained when the exponent a was taken to be 0. 13. These authors used a = 0. 13 for the data of Core,

et al. The dimension L was not recorded, but figure 4, Appendix I of Core's report indicates an L /D ratio > 3. 5. However, it is conceivable that L, /D for Core' s test section was in fact less than

e e

3. 5 which may account for the reduced slope plot of their data which subsequently would produce a higher d value for von Glahn1 s correlation. For the Hendricks, et al. [l96l] data alone, the von

Glahn correlation compares favorably with the boiling number correlation. Like the boiling number

correlation, the von Glahn correlation requires a knowledge of the heat flux in order to determine F .

52
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53
Another consideration present in the von Glahn correlation is that the correlating parameters were developed using both hydrogen and nitrogen data and further tested for applicability to Freon 113. Since these fluids present wider ranges of property data one might conclude that this correlation may

bemused over a greater range than those developed for hydrogen data only. This would be true,

however, only if the properties data are accounted for properly. It may be open to question whether

or not any of the correlations used in this study have reached that degree of development.

3.4.4. Film Boiling Superposition

The superposition approach is an extremely simple one, and its d value indicates that it is comparable to the other film boiling correlations. Although the results are not included herein an

interesting sidelight came about when Breen and Westwater' s [ 1962 ] film pool boiling equation was

evaluated with saturation vapor properties rather than the film temperature properties for which the

equation was developed. The result was an improved d for the superposition equation,

h , = h + h . Since using the saturation properties reduced the predicted pool boiling flux, pred conv film

s.p.v. pool

boil

it may be that this lower value provided partial correction for the interaction between the forced

convection and boiling heat transfer mechanisms.

Since the superposition approach does not consider any of the interactions of the boiling and

convective heat transfer mechanisms which would appear certain to be present and significant, the

comparable success of this correlation raises the question as to whether or not any of the other film

boiling correlations of this study have properly accounted for such interrelationship.

3.4.5. Nucleate Boiling Correlations

It might be noted here that some researchers have proposed use of the pool boiling equations

alone for the forced convection boiling case. In a review, paper Zuber and Fried [1962] report the

following in this category:

(1) Kutateladze [1949]

(2) Michenko [i960]

(3) Gilmour [ 1958 ] (4) Labountzov [ I960 ] (5) Forster and Grief [1959]

The forced convection contributions for the data of this study, however, were significant and varied; on this basis it is assumed that the use of the boiling component alone would constitute a relatively

poor predictive system.

For the limited data considered, correlations applied for nucleate boiling, Region I and Region

II, appear to be as good as or better than the film boiling correlations.

All three of these predictive equations employ a superposition approach but the correlation of Chen does attempt to account for the interaction of the boiling and convective heat transfer mechanisms by the factors F and S. However, the d values indicate that the simple superposition equation

and Kutateladze' s equation, neither of which attempt to account for these interactions, are just as

successful in correlating the data used in this study. Unfortunately, limited data from only one source (Wright and Walters [1959] ) were available for this comparison.

3.4.6. Burnout

As might be expected and as substantiated by figure 3.21, the burnout correlation of Lowdermilk,

et al. [1958] cannot be applied to cryogenic fluids without modification to the constants and/or

exponents in the predictive equation. Due to lack of other cryogenic fluid burnout data, no attempt was made to determine the necessary modifications.

3. 5. Conclusions

The general conclusions of this study are:

(1) Within the range of fluid property variables and systems of the data of this study, the

boiling number correlation appears to be more successful in predicting heat transfer

54
d

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cr

10

10

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9

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1 1 1 1

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Hydrogen

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Test- section

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D

I0 ( 10' I0 5

G/(L/D)'

\0 l

Figure 3.21 Comparison of maximum critical heat flux for cryogenic

liquids with water correlation of Lowdermilk, et al. (1958)

55
coefficients in the film boiling region (Region III). However, for design purposes, little accuracy is lost by using the simpler systems such as the correlation using the Nusselt

number ratio versus quality. It may be that further simplification, as the use of singlephase properties in determining the Nusselt number (calc) for the correlations vs x and

X , and use of the superposition method will not result in an objectionable loss of accuracy.

The use of all data considered in this report indicates this to be true, but the use of the

Hendricks, et al. [ 196 1] data only does not.

Correlations for the nucleate boiling region (Region I and II) generally are better than

the film boiling correlations, but on the basis of the small number of data points available

for consideration, these results are not considered very significant. The Kutateladze

approach appears to be the better of the nucleate boiling correlations.

(2) The conditions at which properties are to be evaluated and the interrelationship between

boiling and forced convection phenomena is quite different in all of the correlations of this

study. Yet their reliability as evidenced by the d values is generally the same; it would

appear that all systems of approach are lacking in arrangement and treatment of the significant variables.

(3) The predictive quality of the systems of this study does not appear to fall in a respectable

range for correlation, but certainly for a thorough test of the predictive systems more

experimental data are needed. Further work should be in the direction of a more fundamental analytical study of the fluid mechanics and heat transfer phenomena and the acquiring of data from very carefully controlled, experimental systems.

4. Boiling Variables

4. 1. Saturation Fluid Properties (Pressure)

The predictive equation of Kutateladze [1952] for nucleate pool boiling appears to account

generally for the changes in boiling characteristics brought about by pressure changes which, in turn,

change the saturated fluid properties. The increasing steepness of the experimental curves with

pressure, however, is not reflected in the Kutateladze correlation or in other correlations proposed,

as essentially all use a constant exponent for AT. Deviation of the peak flux from predictive expressions at pressures above 0.6 of the critical pressure as shown by Lyon, et al. [1964] would tend to indicate that the general relationships for boiling do not hold at high reduced pressures. This seems

reasonable as the apparent primary factors in pool boiling heat transfer are the stirring and the

vaporization effects and both of these would be greatly diminished as the critical pressure is approached. Graham, et al. [1964] show that at a pressure of 170 psig hydrogen exhibits a nucleate

boiling type of curve over a very short interval and then apparently enters a film boiling regime,

indicating that conventional nucleate boiling behavior does not occur as the critical pressure is approached.

It is not possible to discuss the effect of pressure on pool film boiling because there are

insufficient data for comparison. In the forced-convection correlations considered, the predictions

at higher pressures appeared to be as good as those at one atmosphere.

4. 2. Subcooling

Apparently the temperature difference between the warm surface and the saturated liquid

represents the most significant variable affecting heat flux. Therefore, this temperature difference

is conventionally used in the Leidenfrost plot as shown in figures 2. 1, 2. 2, 2. 3, and 2. 4. It may be

that subcooling effects are rather small, at least, when the subcooling is no larger than roughly the

temperature difference between the wall and saturation necessary to produce burnout. Graham, et al. [1964] have reported hydrogen data at 175 psia which indicate subcooling temperature differences have

a smaller effect on the nucleate boiling curve than temperature differences above saturation. It would seem that a major subcooling effect may occur in the normal film boiling or transition region, as a result of the increased rate of condensation. Vliet and Leppert [1964] report such changes in studies of forced convection boiling on a cylinder with water crossflow.

Most of the predictive expressions which have considered subcooling have been for pool-boiling,

peak-flux studies. Among these are Griffith [1957] , Zuber, et al. [l96l] , and three reported by

56
Gambill [1963a] in his peak flux survey. Results of the latter four are shown in figures 4.1, 4. 2, 4.3, and 4.4. The expressions are:

p 0.923 C

Kutateladze I [1952] F =1.0+0. 040 (^

) \ir) (AT) (4.1) v

Kutateladze II p. 0.800 C

(from Gambill 1963a) F , = 1.0+0. 065 ( —

)

v ' (^-£)(AT) ,. , „ „, sub \p / \ X /v 'sub , 4.2 v

Ivey and Morris P, .0.750 C

(from Gambill 1963a): F , =1.0+0.102( —

)

( _E ) (AT) , , (4.3) sub \p / V X I sub

lr, , , 0.500,, ,0. 125

(C pk) (AP)

Zuber, etal. [l 9 6l] F = 1.0+12.326[ E- >T> sub - < 4" 4> Xp a v

Considerably more work will be required before the effect of subcooling is finally determined. The

general effect, however, should be indicated by these expressions.

4. 3. External Force Field (Gravity)

Because buoyancy forces are significantly present in boiling and are functions, in turn, of some

external force fields (viz. gravity and other accelerations, magnetic and electrostatic fields) one would expect to find the boiling phenomena changing with changes in the force field. Such changes

have been reported, but the influence has been established only generally at this time.

The lack of resolution results from uncertainties in the effect of other boiling variables. As the external force field (gravity) is reduced, the normal density separation pattern is replaced by one in

which the vapor tends to collect as a centrally-located sphere for wetting liquids (most cryogenic

systems). Therefore, system geometry may play a major role in determining the influence of gravity forces on heat flux, since this could influence whether or not vapor will be removed from the

surface.

For the pool nucleate boiling curves, the changes appear small (i.e., in the slope of a Leidenfrost plot) as evidenced by the work of Graham, et al. [1964] and Sherley [1963] except,

perhaps, very near zero gravity. The inception point and the peak flux are, however, markedly

influenced by the force field. Graham, et al. [1964] report that the Leidenfrost curves at one g and

at seven g

1 s separate considerably near the inception point for hydrogen and then tend to become the same curve at higher fluxes and temperature differences.

For the peak flux, (2. 2) shows a one-fourth power gravitational dependence. The works of Usiskin and Siegel [l96l] and Lyon, et al. [1965] using water, indicate the 1/4 power influence may

be generally correct for force fields down to about 1/4 normal gravity, but then the power influence

is substantially reduced.

For film boiling, one might expect larger influences on the boiling phenomena because the interface behavior may change markedly. The data of Graham, et al. [1964] for hydrogen indicate

that changes in the external force field have a greater effect on the film boiling flux. The authors are not aware of any studies which consider the effects of a gravitational force field on forced con- vection boiling. The effect of electric fields have also been investigated by Markels and Durfee [1964]

who found that the peak nucleate boiling heat flux with isopropyl alcohol and water was substantially

57
58
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61
increased under the influence of an electrostatic field. This was attributed to de stabilization of the vapor film by the electrostatic field. Choi [1962] proposed an expression for an effective gravitational

force of the electrostatic field.

4. 4. Surface Orientation and Size

Pool-nucleate boiling is generally regarded as insensitive to system geometry. Several textbook

authors make this observation. The work of Class, et al. [i960] and Lyon [1964] do show significant

variations when changing from horizontal to vertical orientation with no other changes in the system.

Unfortunately, the results of these works are somewhat contradictory regarding orientation effect, so no general conclusions can be drawn. Lyon also reports a significant orientation effect on the peak

heat flux. As mentioned previously, surface orientation with respect to an external force field (gravity) may have a major effect. For example, Lyon [ 1 965] reports marked reductions in helium

boiling fluxes for horizontal surfaces facing downward, where the influence of vapor removal is significant.

Costello, et al. [1964] have reported that for pool boiling burnout heater size is quite signifi- cant. They found that one- sixteenth-inch diameter semi-cylinders burned out at fluxes 2.7 times

greater than for flat plate heaters with no liquid in-flow from the sides. This suggested to the authors

that such difference may be a result of different convective effects for the various heated surfaces.

They show that the convective component may be approximately one-half the total flux in some cases.

4. 5. Surface Condition

While it is known that surface conditions have a significant effect on the boiling phenomena, the

specific influence of any given surface variable is not well understood. Enough data have been

acquired, however, to permit a qualitative discussion of the effect of specific surface variations.

Considered here are surface history, surface temperature variations as affected by the heated

material mass and properties or by the type of heat source, surface roughness, and surface-fluid

interface phenomena as influenced by the surface and fluid chemical composition.

4. 5. 1. Surface History

A heating surface immediately after immersion in liquid will produce a higher heat transfer

coefficient than one which has been immersed for a reasonable period of time [Kutateladze 1952] . This is presumably due to additional nucleation centers provided by factors such as dissolved air and

oxidation of the heating surface. Graham, et al. [1964] reported that for nucleate boiling of hydrogen, boundary layer history has a significant effect on the boiling incipient point. The apparent

incipient point for nucleate boiling occurred at a much lower AT when a boiling run was immediately

repeated rather than begun with a fresh supply of hydrogen surrounding the heating surface; the two

curves then join at higher heat fluxes. The authors speculate that some residue of the thermal layer

remained to change, the incipient point for the succeeding test.

Vliet and Leppert [1964] studied the effect of aging or boiling for a period of time at about half peak flux. They found that with water flowing over a stainless steel tube, aging of about 90 minutes was necessary before reproducible peak fluxes could be obtained. Aging for about one-third that time produced peak fluxes only slightly greater than half the fluxes produced using the longer aging

procedure.

4. 5. 2 Surface Temperature Variations

It is possible that surface temperature differences can occur which may be attributed to the

heater surface and not to the boiling phenomena. Heaters with a small mass per unit of heater

surface such as very thin materials may produce such temperature variations and, subsequently, a lower peak flux. Vliet and Leppert [1964] , however, reported that there were no surface effects down to a thickness of 0. 006 inch for a cylinder with water crossflow.

The source of energy for the heater may also influence surface temperature variations.

Kutateladze [1952] reports that electrically heated surfaces have slightly different heat transfer

characteristics than those heated by vapor condensation, probably because condensation droplets cause surface temperature differences.

62
Of course, the boiling phenomena also produce temperature variations at the surface, and these are reported, for example, by Kutateladze [1952] , Hendricks and Sharp [1964] , and Moore and

Mesler [ 196 1] . Sharp [1964] studied the microlayer film at the base of nucleate bubbles and found

that the flux from this microlayer appeared to vary with k/Vct for the surface material.

4.5.3. Surface Roughness

Rougher surfaces generally produce higher fluxes for the same AT. Mikhail [1952] reported

work with oxygen using nickel surfaces with different roughness values, and his data were similar to others who investigated higher temperature fluids. Rougher surfaces cause incipient nucleate

boiling to occur at a lower AT, and then the h vs AT curves rise abruptly from that point. Thus the rougher surfaces produce markedly higher coefficients for the same AT, in Mikhail' s work as high as

a factor of 4. Lyon [1964] .working with cryogenic and other liquids, indicates, however, that although the nucleate boiling flux curve is changed by roughness, the peak flux does not change.

Surface roughness would be expected to show a much smaller effect in the film boiling region, and

work such as that of Class, et al. [i960] indicate essentially no effect of roughness for film boiling.

Tuck [1962] , in experimental work with hydrogen, found that the AT for inception was less than

0. 1°K for a rough surface but could be as great as 3°K for a surface finished to 1. 25 micro-inch

RMS. The Tuck experiments were at zero gravity condition; however, the results would be expected

to be generally applicable under other gravitational fields, although at or near zero gravity the

inception point seems to be time dependent and that time a function of the gravitational field.

4.6. Surface-Fluid Chemical Composition

The surface chemical effect is often difficult to separate from other surface effects such as

roughness. Wetting characteristics would appear to be a major influence. Cryogenic fluids will wet

almost all surfaces except those with a very low surface energy, illustrated, for example, in a hydrogen study by Good and Ferry [1963] and perhaps further substantiated by the reasonably effective use of a single wetting coefficient in the Rohsenhow [1952] correlation for cryogenic fluids. Lyon

[1964] studied nucleate boiling with oxygen and nitrogen using clean copper and gold surfaces and

surfaces with various chemical films. He found that the different surfaces produced somewhat

different nucleate boiling curves and differences as much as 25% in the peak flux.

Young and Hummel [1964] have shown that higher coefficients in the lower region of the nucleate boiling regime are made possible by providing poorly wetted spots on the metal surface.

Sharp [1964] has studied the microlayer at the base of bubbles and has found that non-wetting surfaces

tend to destabilize the layer. Costello, et al. [1964] found that the burnout heat flux was increased

by a factor of 2. 3 if tap water rather than distilled water was used.

5. Summary and Conclusions

For the pool boiling case, the correlations of Kutateladze [ 1952 ] (nucleate) and Breen and

Westwater [1962] (film) have been indicated as those which apparently have the greatest reliability.

Although agreement with experimental data is not particularly good, the accuracy of the predictive

expressions is perhaps sufficient for many design studies. Maximum nucleate flux data are reasonably well predicted by the Kutateladze [1952] expression.

For the forced convection boiling case, no correlation emerged as distinctly better; however,

several simple predictive schemes are shown to be as accurate as some of the more complex

systems when tested with the limited experimental data available.

For all boiling cases it is questionable as to whether or not the predictive correlations include

all of the significant variables and whether the variables considered reflect their proper influence in the final expression. It would appear that new analytical approaches considering phenomena not included in the present correlations, such as a treatment of the process near the heated wall as reviewed by Zuber [1964] , would be desirable. Recent experimental work indicates that to properly

account for all the variables, more detailed and better controlled experiments are required. This

would be particularly true for surface and geometry effects which are often averaged or neglected and

in detailed studies of the boiling flow pattern or mechanism.

63
6. Properties p Data and X Curves

tt

As an aid to designers, available properties data for hydrogen, nitrogen, oxygen, and helium

and values of X for hydrogen, nitrogen, and oxygen are presented in graphical form in figures 6. 1 through 6. 46. Values of C for the saturated liquid and vapor were not available for all of the cryogenie fluids included in this study. Therefore C at saturation was approximated by

AH Hl ' H

2 P Sat~ AT

~ T l- T

2

'

where H = enthalpy of liquid or vapor at saturation temperature T

H = enthalpy of liquid or vapor at a temperature T slightly higher than T for the vapor and

slightly lower than T for the liquid (all at the same pressure).

Curves obtained in this manner are so indicated on the graph. The values for H , H and corres1 £ ponding temperatures T and T were obtained from NBS Technical Notes or private communications

cited in the bibliography for thermodynamic properties of the various cryogenic fluids included in

this study. Because of uncertainties in the data used in obtaining an equation of state for oxygen in the temperature range greater than 98 "K for liquid [Stewart, Hust, and McCartyl] , the C values for saturated liquid oxygen are not considered reliable above 90°K (or above the corresponding saturation

pressure of 1 atm). Furthermore, it is pointed out that the C values for saturated liquid helium

P were obtained by extrapolation of the data of Lounasmaa [1958] , and the C values may be inaccurate

by as much as 20%. p

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lu cd or ?h

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to. o

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o

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qi/e.u'ainon ao awrnoA oidioaas

o o o o o O o r- to m <3". ro cvj _

d o o' o o" o d o

r~ i i i i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 - d

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cm *

Roder

,

Dil

ler

,

Weber,

and

Goodwin

(1963)

— enO

to - - bo

- TS

LU +j or ctf 00 3 ^ w 5

ft 1

cc m

,n

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<n 6/00* svo ao aiMnnoA oiaioaas

85
VAPOR PRESSURE, psia

100 200 300

220

200

180

160

— 10

40

20

\ u

o

uo — " "140 — O

CO -) < — O

_ _J &-I20 — u. — O

Ld _ 2 LiJ 2

_|I00 => o _l > O

>

o

uL 80 o

c_> U. UJ o a.CO

UJn 60 CO

400

1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1

Strobridge (1962)

-

i

I

-

\

I\ - — ]

[\

\

\

{\\

r\\\\ n Ij" u "'-

^GA§_

0.16

0.14

O -i 0.10

u. -1 o

0.08=) -

_lo

>

o

0.06 U.o

UJ

a. . CO

0.04

0.02

3.5

3.0

2.5 x>

2.0

CO<

o

u.o

UJ

-

1 > p>

o

Ul

1.0 CO

0.5

10 15 20

VAPOR PRESSURE , atm.

25 30

Figure 6.22 Specific volume of saturated gaseous and saturated liquid nitrogen

86
x 10 40i—

36

32

28

to

24

to<

u_ 20

o

>-

</> 16 Z

UJQ

2 —

0>—

75 —

25 —I

x 10 250

225

200

175

to

150

125

CO<

ioo Tnz

UJQ

75

50

25

24 32 40

PRESSURE, atm

Figure 6.23 Density of saturated gaseous and saturated liquid oxygen

87
0.7

0.6

o

b 0.5

O

CO 0.4 2

Id

UJO

<

Ll

IDCO

0.3

Q

LJO

2 0.2

UJ

0.1

Stewart, Germann and McCarty

(1962)

He-3 : <r = 0.2185 dyne/cm, Tc

= 3.33°K

He-4:<r = 0.5308 dyne /cm, Tc =5.20°K

0.4 0.5 0.6 0.7 0.8 0.9

REDUCED TEMPERATURE, T/Tc

Figure 6.24 Surface tension for helium- 3, and helium 4

1.0

88
20

TEMPERATURE, °R

30 40 50 60

3.0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I V

i i 1 Corruccini

(1965)

\\

POINT

2.5 \

s w-NORMAL H 2

1

k. E

o 2.0

v.

\

\v

c

"O PARA H 2 —

2

V

S. O

w 1-5 2

A

UJ

UJ \

<

>

li_ V

i 1.0 CO ^\

N\\i v

0.5

nV

^ v

N\ CRl lUfl POINTL ^^

n

10

xlO

20

10

o

CO

z

UJH

UJo

<

U_

IDCO

18 22 26

TEMPERATURE, °K

30 34

Figure 6.25 Surface tension for normal hydrogen and parahydrogen

89
E

o

c

>*

T3O

COz

UJ

UJo

<

o:

=>CO

60

120 140

TEMPERATURE, °R

160 180 200 220 240

70

1 1 II III III III 1 II III III II

1 1 i \

- -

i McCarty(l 965 a)

10

r>j

8

7

pD

—

R —

—

/I H

*

o

1

o 80 90 100 110 120 130

TEMPERATURE , °K

Figure 6.26 Surface tension of nitrogen

70xl0" 5

60

50 Z

40 2

COz

—I UJ

UJ 30 O

<

u.

tr

CO

20

140

90
140 160 TEMPERATURE , ° R

180 200 220 240 260 280

20

18

E 14 o\

0)c

•>, TJ \Z

CO

l±J O

<

li- ar3

CO

10

1 1 III III III III 1 1 1 III III 1

M c Carty (1965b)

-

•

•-

_

-

-

70 80 90 100 110 120 130

TEMPERATURE , °K

140 150

Figure 6„ 27 Surface tension of oxygen

I 20 x 10

00

80

60

40

O

COz

UJ

LJo

<

u.

or3

CO

20

160

91
CM

X

O

'AiiAiionaNoo u- rug

O) 00 CD

~IVI/\ld3Hl

ro O

rr MM MM MM MM MM MM MM 1 1 1

IT)

o

o

m

o

cd

•3-

o

CO

<fr

O

00

ro

O

—

(X)

OOO

<r

o

LU3

rro

O

ro

O

ID

00

O

COCO

o

00

—

<

LU A CL *c

Li

r- oA

in'OxO

00

o

CD O oCM o

o

o

00 o

U3

o

o

ro

O

00 W

CO o

o

CO O +-> CDCO o

00 o a

co

a o CL) CO

CO ^ ji o COO

- 0)

co

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o

00 <

a: >

UJ

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d

T3 LU £

o h- o

i—

i

cc> a o <L) <nT X!H

oo o

• OJ

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so o h

o

>1 -luo/sudm ' AllAllOnQNOO "IVIAIUBHl

92
28

TEMPERATURE, °R

30 32 34 36

Eu

V) *-o

$

>-" >

o

3

O

z

o

o

tr

i±j i

JO

l ! I | I | I | I ; 1 | 1 |

1 | 1 | - 1 | 1 CO

Cook (1961) -

26

—

pJr\

K *h

l \<y 1<

24

*>*J>

22

15 16 17 18 19 TEMPERATURE, °K

TEMPERATURE, °R

20

xlO'

16

15

— 14

— 13

21

— 4

(

xl(

) 2 A^ 6 8 10

5 = ]- |

i

i 1 J

—

8

s V< 6

o

t V

4

o

oro

3

I00

I-o

3

Q

Z

o

o

"3 £ xlO S

5 X

— 2

12 3 4 5 6

TEMPERATURE, °K

Figure 6.29 Thermal conductivity of gaseous helium from

1.5°K.to 21°K

93
Io

x

r- n _ nig •AiiAiionaNOO -iviaiu3h±

co m ^J: ro cm

oc

LU(r

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(Z

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m

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ro

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0)

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cr

•r-i i—i

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QC >s

CvJ

ro' I-<

rr CJ UJ

a. a ^ O

O UJ u

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au

CD H

CO

CvJ o

CO

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cvj- rT ,

X

O

ro

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CvJ CDCM

<3-

CVJ CvJ o

CvJ 00

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94
200x10

180

o

i Eu

O

3

160

140

120

^r> ioo

o

z>Q

-z. o

o

<

or

UJX

80

60

40

20

100

TEMPERATURE , °R

200 300 400 500 n n n i n i r~r I I TT

-

Scott , Denton , and

Nicholls (1964)

-\ y

> <^y /

;^; <^

t^

/

V

.N<y

-

^

40 80 280

.10

09

08

07 CD

or

o

.1

06

.05 §

04

O

O

03 or

UJX

02

.01

120 160 200 240 320

TEMPERATURE , ° K

Figure 6. 31 Thermal conductivity of gaseous normal hydrogen

95
30

140x10'

1.35

°' 1.30

o

o 1.25

> 1.20 o

Q

O

O

orX

1.15

1. 10

1.05

.00

0.50

TEMPERATURE , °R

35 40 45 50

I I I I I

I I I I I I I II I I

—

Scott , Denton , and

Nicholls (1964)

8.0x10

— 75

i

I00

or

o

i

7.0

— 6.5

>-

o

a

z

o

o

or

UJX

6.0

16 18 20 22 24 26

TEMPERATURE , °K

28 30

Figure 6. 32 Thermal conductivity of saturated liquid normal hydrogen

and saturated liquid parahydrogen

96
100 120 140 TEMPERATURE , °R

160 180 200 220 240 260 280

200x10

180

oEu

>->

o

a

o

o

160

140

120

100

< 80

S

or

LlI X

I- 60

40

20

III 1 1 1 1

1 1 1 11 1 1 1 II III III Ml III

Brewer (1961)

^K.^ ^

„/h.

3>

?*> V'

Critical Point \ C ritical Point

126.16 °K 154.77 °K\^

- - - i

1

0.1

0.10

0.09

0.08

CD

or

o

.1

0.07

o

0.06 Q

z.o

o

0.05

004

0.03

0.02

<

or

UJX

55 65 75 85 95 105 115 125 135 145 155 TEMPERATURE , ° K Figure 6. 33 Thermal conductivity of oxygen and nitrogen saturated liquid

97
150 250 350

TEMPERATURE , 450 550 650 750 850

50x10

I I I I I I I I I I I I I I I I I II I I I I I I I II I I950

45

40

o

i eo

o

5

>->

I-O

IDQ

o

o

or

LUX

35

30

25

20

15

\

-

"- 1 Brewer

(1961)

1

1 1 Q ! ^P=350p_2^^ 3

o

1 | ^ \ ^0,\ * Q \

UJ \

' 1 r)^

< \ or3 \ n I n

»- \ V

r

i

Critical

CO \^

<J Point

I26.I6°K

\ <P

n<P

<ry

\

/\>

\

\

\ T^ ^_

16r

TEMPER ATURE,°R

260 360 T r

I -5 v1 /P = 3500 psi -.

.7,nnn

-2 -8x10

>-H

-&> cc 1- °l %*-

O £ 4 U s

-J £ < i

-2*"

F

140x10 ^

1 ^w, /' 2500

2000

1500

1000

/500

j_ 120^

{;* ioo- D , Q e o-x eo- o - w <l 60-

ITUJ

fE 40-

Oh

0./- ?

/ _ ih

- s£y

III

_ 100 150 200 25C 3Z TEMPERATURE, °K

-

10 —

100 200 300 400

TEMPERATURE , °K

500

Figure 6. 34 Thermal conductivity of nitrogen

28x10

26

,-3

24

22

i

20 m

>

H

18 >

1-o

3

16 Q

o

o

_l 14 <

2

oru

i

i12

98
150 250 350

TEMPERATURE , °R

450 550 650 750 850 950

100 200 300 400 500

TEMPERATURE , °K

Figure 6. 35 Thermal conductivity of oxygen

50xl0"

5 II 1 1 1 1 I 1 I 1 1 II 1 II 1 1 MM II 1 1 MM MM

Q

3

O

_j

\

28xlC

\

\ ^P = 4000^2^-^

\ 1 1 45- Q

UJ

1-<

or3

1-<

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1 -p.n0 — ~ o, 26

oo2^

-

^

f} * ~>

24

40

-<i9

Pritirn 1 /

\ 22

*: — Point - 154.77 °K

1 \

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1 1 \ /&

2oT,

3

1-

OD

E

£ 35

M

1

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1 r '<¥*

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>

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(1 961 )

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3

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Z

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_l

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, ^ 0^ orW 20

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UJ o

CO r- • H

00 >

CVJ CO

• NO

<D CD Vi CM 3

s

^

CJ

CM

c\i

CDro ro

CVJ ro Oro 00

CVJ CDCVJ CVJ

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100
120x10

6

100

u

a>w 80

E

u

>-

CO

o

u

CO

60

40

20

TEMPERATURE, °R

50 100 150 180

i r

J Cook

(1961)

*

^/

4

\ ^

i«

1 \y

9

*

*lExperimental results indicate viscosity

independent of pressure at these

moderate pressures.

Ciirve was drawn thru experimental data

points obtained at different pressures by

different authors as reported by

Cocik (1961)

-4

xlO

250

200

150 >-

CO

O

o

CO

100

50

20 40 60 80

TEMPERATURE, °K

100

Figure 6.37 Viscosity of gaseous helium from 0* to 100 6 K

101
200

200 x

TEMPERATURE, °R

300 400 500

-4

xlO

450

400 v

350 „ >-o

o

300 2

250

200

140 180 220 260

TEMPERATURE, °K

300

Figure 6.38 Viscosity of gaseous helium from I00 e to 300°K

102
JM-U/qi 'A1ISO0SIA o o o o

o o o o 00 N 10 If) o

o

I I I

I I I I I I I I I I

I I I I I I

I I II I I MM

±; o

to

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LlJ c\j Q

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rO

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to —

.if) ^£

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—

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103
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60

125

TEMPERATURE, °R

150 175 200 225

O.OX MJ

Forster (1963)

3.2

2.8

\

\

S 2.4

i I

i \

E

u

>

a. 2.0

W 1.6 O

o

CO>

1.2

0.8

0.4

n

800 x I0

3

700

600

500

400 ooO

CO 300

200

100

70 80 90 100 110 120

TEMPERATURE, °K

Figure 6.40 Viscosity of saturated liquid nitrogen

130

104
TEMPERATURE, °R

200 300 400 500 600 700 800 900

5.5x1 6

4

1 1 1 1 1 1 1 1 u Brewer

( 1961 )

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5.0

13 ]

12 -Jirl

IT1 1 o T1 1 1 4.5 1 1 1

i 1 ° i 1 1 1

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t_ 1 1 \

—

1 1

. \ \ P

1 1

I \ \ ^pr

1 1 1 I \

IPs /

1 11 \

s 8

o&c

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3.5 o

1

1

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->

1 11 \ \

\-

0>

1 1 1 \ 7000 no ' E

1 1 \

08 «_ o 1 1 \ e;nnn ^

o» 3.0

1 1 \ l^^^f- _^__ JO

1 \ RfiOO

"~

>• 1 jUw .07 ^

1- oo<D^

1-

(/> A </> O

2.5 O

(J

idou^ .0b £

>

5-J^^^ >

9f>>0S>

\

Cr

2.0

.05

\ \

-5£1

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V. \ \ V

o

ex \^ ickpet .04

1.5 ?

T

y

W

hr{\ w f .03

°7 1.0 *>S

/ /T

// 02

//

n ^ 100 200 300 400

TEMPERATURE, °K

Figure 6.41 Viscosity of nitrogen

500

105
JM-U/ Ql 'A1IS00SIA

o

oo

CVJ

o

co

o

(VJ

O

CJ

C\J

£T < o '-CVJ

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COO

1 1 1 1 1 1 1 1 1 Mill

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V.

0)

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*-

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cr

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106
TEMPERATURE, °R

200 300 400 500 600 700 800 900

5.5x1 n

4- II 1 i

i i i i 1

Brewer

( I960

\ \ .13

i V

w \

5.0 I

1 \\ 12

1

1 4.5 1 \ .11 \

1 \

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1 0000

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,

i psi

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1 \

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3/

3

O

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1.5

<2r

J * /V &/ .03

1.0

.02

n r

100 200 300 400

TEMPERATURE, °K

Figure 6 43 Viscosity of oxygen

500

107
4 6 8

PRESSURE , atmospheres

10

Figure 6.44 Martinelli-Nelson correlating term ^ as a function of quality

and pressure for H

108
Figure 6. 45

4 8 12 16 20

PRESSURE , atmospheres

Martinelli-Nelson correlating term x

as a function of quality

and pressure for N_

109
10

8

tt

.8

.6

.4

.2

.1 .08

.06

.04

.02

.01

2

**J

n"5 .

.Sii^""^^^

^-£^

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.25

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.59—

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_^-i§2"

^-£2-

0.5 1.0 1.5 2.0

PRESSURE, atmospheres

2.5 3.0

Figure 6. 46 Martinelli-Nelson correlating term X as a function of quality

and pressure for O

110
7. Nomenclature

English Letters

d

D

sub

tp

g

G

h

h

conv

s. p.i.

= specific heat capacity at constant pressure,

joules

g°K

= root mean square fractional deviation, dimensionless

= diameter of cylindrical heater in the film boiling regime for pool boiling, and

inside diameter of tube for forced convection boiling, cm

= multiplying factor for peak heat flux due to subcooling, (q/A) =(q/A) F

sub sat sub

= von Glahn two-phase modification factor, dimensionless

acceleration of gravity, 3- sec

= mass velocity, sec cm

rr- r , r WattS

coefficient of heat transfer, 5—rr-r cm3 c K

1 1 r rr- . Watt S single-phase liquid convective heat transfer coefficient, ? cm °K

watts conv

s. p. v.

fc

= single-phase vapor convective heat transfer coefficient, 3 cm3 K

watts

= forced convection heat transfer coefficient from Chen's correlation, 3 cm3 °K

f-z watt s pool boiling heat transfer coefficient from Chen' s correlation, 3-rrr cnrr °K

film

pool

boil

watts

film pool boiling heat transfer coefficient, 5-777 cmr K

nucleate

pool

boil

nucleate pool r boiling6 heat transfer coefficient, 5-777 cm3 °K

pred

k

L

e

(WD)

, . , , , rr. WattS predicted v heat transfer coefficient, ^ — cm3 °K

thermal conductivity, watts cm°K

sum of distance 1 and unheated upstream hydrodynamic portion of tube, where 1 is the critical length measured from beginning of heated portion of tube to burnout

location, (cm)

critical-length to diameter ratio in Lowdermilk' s burnout correlation,

dimensionle s s m = mass flow rate,

bo. no Nu

Nu

calc, f, t. p.

= von Glahn correlation boiling number, dimensionless

= Nusselt Number, dimensionless

= two-phase calculated Nusselt Number with vapor properties evaluated at the film

T +T. w i temperature , dimensionless

111
Nu = single-phase calculated Nusselt Number with vapor properties evaluated at calc, v, s. p saturation conditions, dimensionless

Nu , = calculated Nusselt Number with vapor properties evaluated at saturation conditions,

v, calc . dimensionless

dynes P = pressure of the boiling system, —-—5—

r crrr Pr = Prandtl number, dimensionless

q watts A

Re

f, m t. P

Re,

£

Re

'i

Re

V

Re

v, s

.

P.

rate of heat transfer per unit area,

= two-phase Reynolds number based on the average velocity of the mixture and with

vapor viscosity evaluated at mean film conditions, dimensionless

= two-phase Reynolds number based on the average velocity of the mixture and with

liquid viscosity evaluated at bulk saturation conditions, dimensionless

- single-phase Reynolds number based on the average velocity of the mixture and with

liquid viscosity evaluated at bulk saturation conditions, dimensionless

- two-phase Reynolds number based on the average velocity of the mixture and with

vapor viscosity evaluated at bulk saturation conditions, dimensionless

= single-phase Reynolds number based on the average velocity of the mixture and

with vapor viscosity evaluated at bulk saturation conditions, dimensionless

AT = T - T„, °K w £' cm U = averag e fluid velocity,

avg sec

gvapor . x = quality, *

, dimensionless

g . mixture

x = thermodynamic fluid quality at burnout location, dimensionless

x = quality in film boiling regime, dimensionless

X = film boiling vaporization parameter, dimensionless

112
Greek Letters

Oj, p.y, r

x

X'

C P thermal diffusivity, , , dimensionless

k von Glahn film boiling correlation parameters, dimensionless

joules

latent heat-of vaporization at saturation,

"effective" latent heat of vaporization, defined by equation 2. 4, joules

Newtonian coefficient of viscosity, cm sec.

= density,

A Pf

f, m, t. p.

AP v

a

Abs.

Min.

Film

Cond.

avg

b

exp

for f, v

£ f cm3

- two-phase mean film density, —2-gFilm

Cond.

Max

Nucl.

Min.

Film

Cond.

mix

Nucl.

sat sub

t.p. v

dynes

cm

i v cm3

surface tension between the liquid and its own vapor, evaluated at T.,

Martinelli parameter, dimensionless *

Subscripts

indicates heat transfer conditions at the absolute minimum value theoretically

possible for film pool boiling. (Some authors call this the second critical.)

average

indicates bulk property

indicates the subscripted h or Nu is the experimental value

indicates that the subscripted vapor property is to be evaluated at the vapor film

temperature, (1/2) (T + T.) w £ indicates heat transfer conditions, by conduction only through the vapor film, for film pool boiling

indicates that the subscripted liquid property is to be evaluated at the saturation

temperature of the boiling fluid indicates heat transfer conditions at the maximum value possible for nucleate pool

boiling. (Some authors call this the first critical, or burnout.)

indicates heat transfer conditions at the minimum value correlated for film pool

boiling. (Some authors call this the second critical.)

mixture

indicates heat transfer conditions for nucleate pool boiling

saturation conditions

subcooling

indicates two phase

indicates that the subscripted vapor property is to be evaluated at the saturation

temperature of the boiling fluid

113
indicates that the subscripted property is to be evaluated at the temperature of the

heater surface

114
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