NBSIR 73-322

(AFAPL-TR-73-37)

FORCED CONVECTION HEAT TRANSFER

TO SUBCRITICAL HELIUM I

Patricia J. Giarrantano

R. C. Hess

M. C. Jones

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

May 1973

Interim Report

Prepared for

AIR FORCE AERO PROPULSION LABORATORY

Air Force Systems Command

Wright-Patterson Air Force Base, Ohio 45433

NBSIR 73-322

(AFAPL-TR-73-37)

FORCED CONVECTION HEAT TRANSFER

TO SUBCRITiCAL HELIOM I

Patricia J. Giarrantano

R. C. Hess

M. C. Jones

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

May 1973

Interim Report

Prepared for

AIR FORCE AERO PROPULSION LABORATORY

Air Force Systems Command

Wright-Patterson Air Force Base, Ohio 45433

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director
NOTICE

When Government drawings, specifications, or other data are used for any purpose

other than in connection with a definitely related Government procurement operation,

the United States Government thereby incurs no responsibility nor any obligation

whatsoever; and the fact that the government may have formulated, furnished, or in

any way supplied the said drawings, specifications, or other data, is not to be regarded

by implication or otherwise as in any manner licensing the holder or any other person

or corporation, or conveying any rights or permission to manufacture, use, or sell any

patented invention that may in any way be related thereto.

Copies of this report should not be returned unless return is required by security

considerations, contractual obligations, or notice on a specific document.

11
FOREWORD

The work described in this report was begun under the

sponsorship of the U.S. Atomic Energy Commission (Contract

Agreement AT(49-2)-n65) as part of the Helium Heat Transfer

program of the National Bureau of Standards begun in 1968.

Previous reports have covered NBS work on heat transfer to

supercritical heltum I, Kapitza conductance, viscosity of

helium I and other thermophysical properties of helium I. This phase of the program was completed under sponsorship

Of the Department of the Air Force, Wright-Patterson Air

Force Base, and was funded with FY-1972 AF Aero Propulsion

Laboratory Director's Funds.

This Technical Report has been reviewed and is approved

for publication.

APPROVED:

iii
CONTENTS

1. INTRODUCTION 1

2. DESCRIPTION OF EXPERIMENTAL APPARATUS AND

MEASUREMENT 1

2. 1 Test Section 2

2. 2 Temperature Measurement 2

2. 3 Pressure and Flow Measurement 7

2. 4 Extraneous Heat Exchange 8

2. 5 Experimental Measurement 8

3. HEAT TRANSFER RESULTS 10

3. 1 Wall Temperature Profiles 10

3. 2 Critical Heat Flux 23

3. 3 Comparison of Modes of Heat Transfer 30

4. PERFORMANCE OF CENTRIFUGAL PUMP WHILE

CIRCULATING LIQUID HELIUM 32

5. CONCLUSIONS 35

6. REFERENCES 36

• FIGURES

Figure 1. Schematic of the boiling heat transfer flow loop 3

Figure 2. Sketch of mounting scheme for carbon resistance

thermometers 4

Figure 3. Wall temperature profile for test section 11

Figure 4. Wall temperature profile for test section 12

Figure 5. Wall temperature profile for test section 13

Figure 6. Wall temperature profile for test section 14

Figure 7. Wall temperature profile for test section 15

Figure 8. Wall temperature profile for test section 16

iv
FIGURES (CONTINUED)

Figure 9. Wall temperature profile for test section 17

Figure 10. Wall temperature profile for test section 18

Figure 11. Heat flux vs temperature difference for station 1 ... 19

Figure 12. Heat flux vs temperature difference for station 10 . . . 20

Figure 13. Comparison of subcritical and supercritical wall

temperature profiles under similar mass velocity

and heat flux conditions 22

Figure 14. Critical heat flux as a function of length to diameter

ratio with pressure and mass velocity as parameters • 25

Figure 15. Heat transfer coefficient as a function of quality with

mass velocity and pressure as parameters 27

Figure 16. Heat transfer coefficient as a function of quality

(comparison of this study's data with that of

reference 4) 29

Figure 17. Comparison of modes of helium heat transfer 31

Figure 18. Pump performance characteristics and flow loop

load line 3 3

Figure 19. Ratio of measured flow rate to flow rate predicted

from centrifugal pump performance characteristics

vs subcooling power 34

V
ABSTRACT

Preliminary results of an experimental investigation

of heat transfer to liquid helium under forced flow

conditions are reported for a 0. 213 cm i. d. x 10 cm

long test section subject to the following range of

operating conditions:

System pressures 1.1 - 2.1 atm

^ Mass velocities 4-64 g/s-cm

Heat fluxes 0 . 04 - 0 . 53 W/cm^

Inlet subcooling 0.03 - 0. 10 K

The effect of the above system parameters on the heat

transfer and critical heat flux is discussed; a comparison of forced convection boiling with other modes of

heat transfer (pool boiling and supercritical) and the

performance of a centrifugal pump used for circulating

the liquid helium are also included in the report.

Key Words: centrifugal pump; critical heat flux;

film boiling; forced convection; heat transfer; helium;

nucleate boiling; subcritical; supercritical.

vi
FORCED CONVECTION HEAT TRANSFER TO

SUBCRITICAL HELIUM I

1. INTRODUCTION

In a previous study by Giarratano, Arp and Smith [l] at the

Cryogenics Division of NBS, Boulder, Colorado, heat transfer

coefficients for forced flow of supercritical helium were measured

and a correlation was developed to predict the heat transfer in this

region. As an extension of that study this report describes the

preliminary experimental results obtained for forced convection

heat transfer in the subcritical region, i. e. , below the critical

pressure 2. 245 atm.* Operation of the centrifugal pump, used for

circulation of helium around the test loop in the subcritical region

will also be discussed.

2. DESCRIPTION OF EXPERIMENTAL APPARATUS

AND MEASUREMENT

A schematic of the boiling heat transfer flow loop is shown in

figure 1. A centrifugal pump, previously described in [2], circu

lates the liquid around the flow loop. To maintain a constant inlet

temperature to the test section, heat is removed from the liquid a

it passes through approximately 13 meters of 0. 32 cm i. d. copper

tubing located in a heat exchanger reservoir of approximately 2. 5

liter capacity. The heat exchanger reservoir is continuously supplied with liquid helium from a storage dewar.

•j" Identification of any materials or their manufacturer by the National

Bureau of Standards in no way implies a recommendation or endorsement by the Bureau. Furthermore, use of other trade names in this

paper is for the sake of clarity and does not in any way imply a recommendation or endorsement by the Bureau.

5 2 * 1 atmosphere = 1. 013 x 10 MN/m .
2. 1 Test Section

The test section is a 0. 213 cm i. d. x 20 cm long stainless

steel tube with a wall thickness of 0. 016 cm. It is resistance

heated along 10 cm of its length (L/D =50). A stainless steelpyrex seal located in the bottom of the loop provides electrical

isolation of the test section. A wire wound preheater upstream

of the test section allows variation of quality at the inlet of the

tube. Accurate measurement of the current and potential drop

across the two heaters is used in the calculation of heat flux.

At the lowest power levels the uncertainty is less than 2%.

2. 2 Temperature Measurement

Outside tube wall temperatures are measured at ten points

along the heated test section length with calibrated carbon

resistance thermometers. A detailed sketch of a thermometer

t and the mounting scheme is shown in figure 2. The thermometers are positioned one cm apart with the first thermometer

located 0. 6 cm from the inlet. Inside wall temperatures are

obtained by calculation of the temperature drop through the tube

wall using the thermal conductivity of stainless steel given by

equation (Al) in the appendix of reference [l]. Bulk fluid temperatures are measured at four points along the flow loop

(upstream of preheater, upstream of test section and two measurements downstream of the test section) with germanium

resistance thermometers. These thermometers are plotted with

vacuum grease in copper wells which are soldered to the tube.

2
3
Electrical Leads Tempered

on Copper Clamp

Copper Clamp

Radiation Shield Thermally

Anchored to Clamp

Carbon Resistance Thermometer

with one Lead Soldered to Clamp

0.0127 cm thick (.005") Mylar

Test Section

Figure 2. 'Sketch of mounting scheme for carbon resistance thermometers.
The carbon resistance thermometers and the germanium

resistance thermometers used in this study were calibrated in a separate apparatus, over the range 4 - 20 K, against three

germanium resistance thermometers (GT 1011, 1027 and 1024),

These three germanium thermometers had been previouslycalibrated against NBS secondary standard germanium thermometers (GT 722 and 734).

In our calibration, over the range 4 - 9 K the agreement

between GT 1011, 1027 and 1024 was within 0. OIK for the

worst case and was generally within 0. 005 K. Above 9 K the

agreement was within 0. 05 K. An average value of the three

germanium thermometer readings was taken to be the true

temperature.

The calibration data for each thermometer were fitted with

a curve of the form

LOG T = r A(N) LOG

with an rms percent error of 0. 300 in temperature or less.

After a period of about six months, and after several

intermittent thermal cycles from room temperature to helium

temperature, three carbon thermometers and two germanium

thermometers were removed from the experimental apparatus

and dip tested in liquid helium (4. 025 K) to check for a shift

in calibration. The carbon resistors were within 0. 1%, 1. 1%,

5
and 1. 2% in temperature of their original calibration while the

germanium thermometers were within 0. 3% and 0. 5%, It should be noted that while this does not represent a calibration

shift for the germanium thermometers^ the error for two of the

carbon resistors lies slightly outside of the 99% confidence

limit of the original calibration (1, e. 3 X rms percent error).

In the two-phase region, since the pressure drop across

the test. section was of the order of a few mm Hg for the data

presented, the intermediate bulk temperatures were taken to

be the saturation temperatures corresponding to the inlet static

pressures. This approximation was within experimental error.

Periodic zero power runs were made to check consistency

among the fourteen thermometers. Agreement between the

four germanium resistance thermometers was within a few

millidegrees while the carbon resistance thermometers showed

a decreasing offset with time when compared to the germanium

resistance thermometer readings. The time constant (of the

order of hours) was too long for it to be practicable to wait.

Since the time of each powered run and each zero power run

was recordedjthis well-defined offset was used to correct the

carbon resistance thermometer readings. This correction

alsb takes care of any shift in calibration of the carbon resistance thermometers. E}xtensive tests on the carbon resistance

thermometers in a separate apparatus (with the thermometers

mounted exactly the same as in the present study) showed that

they are extremely sensitive to irradiation from high temperature sources. It is felt that although substantial effort was

devoted to radiation shielding of the carbon thermometers, the

6
radiation could not be totally eliminated during the period that

the entire apparatus approached temperature equilibrium.

The estimated uncertainty in outside wall temperatures is at

most 0, 05 K. The error in the temperature difference between

the inside wall and the bulk temperature is due to uncertainty

in the thermal conductivity of the stainless steel wall, the wall

thickness, and uncertainty in bulk temperature. This varies

from 26% to 53% below the critical heat flux (see 3. 1) to 0. 3%

above this transition.

2. 3 Pressure and Flow Measurement

Provision was made to measure pressure drop across the

flow orifice, preheater, and test section, and the static test

section inlet pressure using calibrated pressure transducers

and a static Bourdon tube pressure gauge accurate to 0.01 atm

located outside the cryostat at room temperature. Test section pressure drop will be reported in a future report but was

small, generally less than 7 mm Hg.

Since the fluid at the outlet of the preheater was slightly

subcooled for the data presented here, a calorimetric method

determined the flowrate. The calorimetric flowrate was also

used to determine a discharge coefficient for the flow orifice so that the orifice may be used for flow measurement when

calorimetric flow determination is not possible, i. e. , twophase out of the preheater. The discharge coefficient so obtained agrees well with that of an identical orifice section

which was calibrated in a separate apparatus. The accuracy of

the flow rate measurement has not yet been fully evaluated, but

we believe the values based on calorimetry to be accurate to a few percent.

7
2.4 Extraneous Heat Exchange

To minimize heat leak from room temperature to the test

section by conduction, all electrical leads and the thin walled,

0.317 cm diam. stainless steel pressure transmission lines

are thermally anchored to the outside copper surface of the

liquid helium heat exchanger. A length of multifilament

niobium-titanium superconducting wire is used for power leads

between the heat exchanger and the test section and between

the heat exchanger and the preheater. The small diameter and

low thermal conductivity of this wire further minimizes heat

leak due to conduction and joule heating in the leads is eliminated. Error in heat flux due to axial conduction from the ends

is less than 2% for the worst condition. Extraneous heat to and

from the test section is therefore considered negligible. Boiloff from the liquid helium heat exchanger is routed through

coils soldered to the pump housing and the radiation shield.

This arrangement minimizes heat leak from room temperature

via conduction along the pump housing and provides a low temperature radiation shield around the flow loop. The test section portion is further protected from radiation by a copper

shield thermally anchored to the heat exchanger. The evacu-

-7

ated copper enclosure (vacuum less than 10 mm Hg) which is

submerged in a bath of liquid nitrogen provides first stage

radiation shielding from room temperature.

2. 5 Experimental Measurement

For a fixed system pressure, pump speed and quality at

the inlet of the test section, the power to the test section was

varied over a range from zero to that at which a discontinuous

8
rise in the wall temperature occurred at the outlet end of the test

section (critical heat flux). For some of the runs this heat

flux was exceeded causing the discontinuity in wall temperature

to move up the test section. After a change in test section

power, thermometer voltages stabilized generally within a few

seconds and were recorded by a digital voltmeter and automatically punched on paper tape together with all other pertinent voltages and run information.

Since the flow loop is a closed system, as power was

applied it was necessary to vent the system to maintain a constant test pressure, and conversely a decrease in power applied

required adding and condensing gas in the loop to maintain the

pressure.

This procedure was repeated for different pump speeds,

inlet quality and pressure.

During a measurement the temperatures and pressure

were stable to within their accuracy prior to a transition in the

heat transfer mechanism (critical heat flux exceeded). When

a transition occurred, it was accompanied by fluctuations in

temperature (for the wall stations in the transition region) of a rather random frequency, and an amplitude of the order of

0. 5 K. Oscillations in pressure were not noticeable

but this was at least partly accountable for, the pressure transmission line being heavily damped.

One of the goals of the present study is to establish the

repeatability of a measurement in the form, say, of the spread

in wall temperatures which can be expected when the flowrate,

pressure and inlet enthalpy are specified. To date, we do not

9
have sufficient information to establish a day-to-day variability,

but we do have a few figures for the variability observed during

the course of a day's running. Below the critical heat flux this

variability is generally of the order of a few percent of the

excess of wall temperature over bulk temperature, with a

worst value observed of 11%. Above the transition, we do

not have sufficient data at this time to estimate the variability.

HEAT TRANSFER RESULTS

3, 1 Wall Temperature Profiles

Temperature profiles along the wall for subcritical helium

are shown in figures 3 through 10 for pressures from 1. 1 to

2

2. 1 atm and mass velocities from 4. 8 to 63. 6 g/cm . A

typical profile is extremely flat up to some point at which a

sharp rise is observed for the higher heat fluxes. This we

identify, with reference to a vast body of literature on boiling

heat transfer, as indicating a hydrodynamic transition from

wetted-wall, e.g. , nucleate boiling, to dry-wall, e.g. , film

boiling, heat transfer. Thus, at a particular point along the

test section there is a critical heat flux above which the wall

temperature rises quite steeply with heat flux.

Below the critical heat flux, heat transfer is very good as

evidenced by the wall temperatures being nowhere more than

0. 3 K above the bulk fluid temperature. Indeed this behavior

is strongly reminiscent of boiling heat transfer without forced

convection, i, e, , pool boiling. In figures 11 and 12 we plot

the heat flux q against the difference between the wall and

bulk fluid temperatures for the first and last wall thermometers

10
4 6 8 10

LENGTH ALONG TEST SECTION, cm

Figure 3. Wall temperature profile for test sectioru

11
Pressure = 1.1 atm

Mass Velocity = 11.3 g/s cm^

inside Dia. of Test Section = 0.213 cm

q

= 0.257 W/cml

X i Outiet = 0.23

0.247

0.21

7 BULK q

- 0.180

X = 0.15

J I 2 4 6 8

LENGTH IkLDNG TEST SECTION, cm

10

Figure 4. Wall temperature profile for test section.
LENGTH ALONG TEST SECTION, cm

Figure 5. Wall temperature profile for test section.

13
Pressure = 1.2 atm

2 4 6 8 10

LENGTH ALONG TEST SECTION, cm

Figure 6. Wall temperature profile for test section.

14
Pressure = 1.34 atin

Mass Velocity = 63.6 g/s-cm^

Inside Dia. of Test Section = 0.213 cm

2 4 6 8 10

LENGTH ALONG TEST SECTION, cm

Figure 7. Wall temperature profile for test section.

15
Pressure 1.5 atm

Mass Velocity 15.3 g/s cm^

Inside Oia. ot Test Section 0.213 cm

q 0.308 W/cm^

X (a Outlet 0.15

q 0 284

X = 0.13

BULK

q 0.270

X ^ 0.12

2 4 6 8 10

LENGTH ALONG TEST SECTION, cm

Figure 8. Wall temperature profile for test section.

16
18

16

14 —

12

10 —

8

6

4

Pressure = 1.5 atm

Mass Velocity = 7.6 g/s-cm^

Inside Dia. of Test Section = 0.213 cm

2

q

= 0.253 W/cm

X i Outlet = 0.31

/ /q = 0.175

/ / X = 0.19

1 1 1

1 1 1 1 1 1 1

0 2 4 6 8

LENGTH ALONG TEST SECTION, cm

Figure 9. Wall temperature profile for test section.

10

17
LENGTH ALONG TEST SECTION, cm

Figure 10. Wall temperature profile for test section.

18
.01 .05 .1 .5 1 5 10 AT, K

Figure 11, Heat flux vs temperature difference for station 1.

19
AT, K

Figure 12. Heat flux vs temperature difference for station 10.

20
respectively. These are at 3 and 48 tube diameters respectively from the commencement of the heated length of the test

section. We have also plotted as a solid line the nucleate pool

boiling correlation of Kutateladze [7] and indicated at its upper

extremity the critical heat flux for pool boiling given by a second correlation due to Kutateladze [7 ] . As shown for

example by Brentari and Smith [8] these correlations give a good average representation of nucleate pool boiling data for

cryogenic fluids. The present data for forced convection heat

transfer are represented by the first of these correlations

below the critical heat flux as well as any given set of pool

boiling data, which are notorious for their sensitivity to the

precise nature and preparation of the boiling surface, as well

as its heating history (a strong hysteresis effect is often

observed). We conclude that forced convection has had very

little effect on the rate of heat transfer at heat fluxes below

the critical and that the boiling mechanism itself is the primary determinant.

In figure 13 a wall temperature profile for subcritical

helium is compared with one for supercritical helium flowing

at approximately the same mass velocity and the same applied

heat flux. This comparison illustrates well the essential difference between two-phase and single-phase heat transfer;

provided transition is not allowed to occur the boiling phenomenon is extremely effective in holding down the wall temperature.

However, we draw attention to the last wall temperature which,

in the subcritical profile shows a slight increase in temperature indicative of the onset of transition to dry-wall heat transfer. This is seen in figure 9 in a more highly developed stage

21
6.2 I—

5.8 —

5.4 —

,

5.0

4.6

SUBCRITICAl

Pressure = 1.52 atm

G

= 14.3 g/s-cni2

q

= 0.256 W/cni2

CO

4.2

Tbulk

isuicmTicu] ^

Tw«iL

SUPERCRITICAL

Pressure = 4.22 atm

q

= 0.249 W/cmZ

G

= 14.9 g/s-cin2

Tbulk

isupeicriticu]

3.8 —

3.4

0 2 4 6 8

LENGTH ALONG TEST SECTION, cm

10

Figure 13, Comparison of subcritical and supercritical wall temperature profiles

under similar mass velocity and heat flux conditions.

22
at higher heat fluxes. The comparison between heat transfer

in these two pressure regions is discussed further in 3. 3

below.

. 2 Critical Heat Flux

Beyond the critical heat flux the wall temperatures mayrise to quite unacceptable heights, from the point of view of

the cooling of superconductors, as is clearly seen from

figures 3 through 10 and figure 12. It is therefore of great

importance to be able to predict the conditions under which the

transition from wetted-wall to dry-wall heat transfer takes

place. In fact, from this point of view it is almost the only

consideration of importance until the flow rates become

very high, because the wall temperature rises observed in the

wetted-wall region are so small as to be of no concern, and

in the dry-wall region they are generally so large as to preclude

this region from consideration. However, at high flow rates,

as seen in figure 7, the wall temperature excursion appears

to have reached a limit which may be of some practical value

in superconducting technology. Figure 7 gives data for the

highest flow rates obtained in this study, and thus it appears

that at very high flow rates the transition may be kept within

useful bounds.

One of the ultimate goals of this program will be to provide

a means of predicting the transition, that is: given the state of

the fluid at entry to the heated section, i.e., enthalpy and

pressure, the flow rate and the heat flux, we wish to know at

what position downstream the transition will occur. Alternatively, given the state and flow rate, we wish to know the heat

23
flux--the critical heat flux- -at which the transition will occur

at a certain position. Considerably more data than are so far

available from this study will be required. For the present,

however, we shall confine our attention to identifying trends.

The first and most obvious trend is that, for a given

pressure and mass velocity, the critical heat flux is a function

of distance from the inlet to the heated section. In experiments

on heat transfer to subcritical helium under conditions of

natural convection, Johannes and Mollard found that most of

their data could be represented by a single curve when the

critical heat flux was plotted against the distance from the

inlet to the heated section in diameters (the hydraulic or equivalent diameter D is used for rectangular cross sections

e where D = 4 x cross-sectional area/heated perimeter),

e Figure 14 shows this plot with our data points superimposed.

The short channel data of James, et al, , the long channel

data of Keilin, et al, , and the data of Jergel and Stevenson

are also included. Those of Jergel and Stevenson were for a

long channel with a small heater at the inlet. These and the

data of Keilin, et al. , were for forced flow.

The trend shown by Johannes and Mollard is confirmed,

but now also an enhancement with increasing mass velocity is

observed. The point at 2. 1 atm (reduced pressure 0. 93) being

lower even than the curve representing the data of Johannes

and Mollard is not surprising and illustrates a fact familiar

from pool boiling, namely, that the critical flux goes to zero

at the critical pressure in accord with Kutateladze's critical

heat flux correlation.

24
D

/ o G

= 63.6 g/s cii|2 ,P = 1.34 atm

1 G

= 4.8 " ,P =

1.1 "

] G = 11.3 " ,P =

1.1 "

NBS V G = 29.4

" ,P =

1.1 "

Present i o G = 7.3 " ,P =

1.2 "

Study

( • G = 15.3 " ,P =

1.5 "

G

= 8.0 "

, P

=

2.1 "

G

= 10.1 • 12.6 g/s-cm2 .P = 1 Klimenko,

Kovalev (4)

G

= 24.2 - 32.7 , P = 1

-

Jergel and

G

G

G

= 11.9 ",P =

= 9.7 " , P

=

= 6.9 "

, P

=

1 "

1 "

1 "

1.8 atm

lames, Lewis,

Maddock (6)

G not stated, natural circulation,

P = 1 atm assumed

cross sectional area

heated perimeter

Curve representing data given by Johannes [3]

G = 2.2 - 2.96 g/s-cm2 , natural circulation,

P = 1 atm assumed

50 100 150 200 250

RATIO OF LENGTH TO EQUIVALENT DIA., L/De"'

300

Figure 14. Critical heat flux as a function of length to diameter ratio with pressure

and mass velocity as parameters.

25
It is hardly necessary to point out that if the conditions

leading to transition in forced convection heat transfer were

the same as those for pool boiling, then the entire tube would

undergo transition at the same heat flux contrary to figure 14.

It is therefore necessary, in order to properly account for

transition in forced convection heat transfer, to look for either

purely local conditions that change with L/D or to relate the

hydrodynamic condition at a given L/D to the entire set of

conditions upstream. In the search for a local explanation it

is tempting to plot transition data against the local mass fraction of vapor (quality) at a fixed L/D. Since the heat transfer

coefficient (h = q/ AT) is a sensitive indicator of hydrodynamic

conditions, we have plotted this in figure 15 against quality

at L/D = 48. Transition is strongly indicated by a pronounced

maximum. We note the following:

i. As with the critical heat flux, the critical heat transfer

coefficient increases with mass velocity for a given

pressure.

ii. The transition occurs at decreasing qualities for

increasing mass velocity for a given pressure,

iii. For a given quality the heat transfer coefficient generally increases with mass velocity below the transition,

iv. The higher the quality at which transition occurs the

lower the corresponding heat transfer coefficient.

V. For the pressures plotted in figure 15, increasing

pressure has the same effect as increasing mass

velocity. Unfortunately we do not have sufficient data

26
10

5

- I g

!

I

I S atn, Inlet Sybcooing 0.2 K

G

=^ 63.6 1.3 atm, lidet Subcoollni 0.03 K • 6 = 4.8

)

' <A 6 = 11.3 1.1 atn, Inlet Sabcooline 0.03 to 0.1 K

t- fi = 29.4

CM

Sta. 10, L/D = 48

0.1 0.2 X QUALITY

Figure 15. Heat transfer coefficient as a function of quality with mass velocity and

pressure as parameters.

27
at 2, 1 atm to be able to generalize this observation to

near-critical pressures.

vi. In all cases transition occurs while a substantial

fraction of liquid remains.

It is clear that successful correlation of transition observations presents a considerable challenge; there are at least

six interdependent variables involved apart from orientation

effects. These are the critical heat flux, mass velocity, quality,

pressure, diameter, and position along the heated tube or channel.

We know, however, that this correlation must reduce to that

of Kutateladze at low mass flow rates, for then the transition

can be understood as a critical ratio between inertial, interfacial

and buoyancy forces, which was the basis of that correlation.

The development of a suitable correlation will be left to a subsequent phase of this work.

A rather interesting comparison can be made for the present transition results and those of Keilin, et al. , for similar

mass velocities and pressures. These authors report heat

transfer coefficients in flat horizontal coils of copper tubing of

0.45 mm inside diameter at L,/D = 278. In figure 16 the comparison is made with our data at similar mass velocities. The

significant difference is in the quality at which transition apparently takes place. The heat transfer coefficient is also lower

in accordance with trend iv noted above. Altogether, the transition observed by Keilin, et al. , is much weaker than ours; we

find from their report that their wall temperatures were nowhere more than 1 K above bulk fluid temperature even beyond

the transition. It appears that the conditions of transition at

28
5 I1 —

,

Data of Keilefl, Klimenko, and Kovalev

* Data of This Study • G

= 11.3 g/s-cni2 1 -

, , . , „ „

A 11 = 29.4 E/s-cin2 J P = 11 atm, L/D = 48

.05-

.01

.2 .6 X QUALITY

.8 1.0 1.2

Figure 16. Heat transfer coefficient as a function of quality (comparison of this

study's data with that of reference 4).

29
L/ D = 278 are much different from L/D = 48 . There is much

more vapor present; therefore it must travel at higher velocity

and the heat transfer coefficient after transition is not in such

contrast with that before transition, which is the case in our

results

,

. 3 Comparison of Modes of Heat Transfer

In figure 17 the present results of heat flux q as a function

of wall temperature rise AT are plotted for L/D = 48 for

comparison with other modes of heat transfer. We have included calculated values of the nucleate pool boiling correlations

of Kutateladze mentioned above and calculated values of q vs. AT for supercritical helium heat transfer at 3 atm and at

4 5 6

Reynolds numbers of 10 , 10 and 10 . These were computed

from the correlation

developed in reference [ l] which represented the data of that

reference (L/D = 20 and 40) with an rms percent deviation of

8, 5%. Supercritical data obtained in the present work are

represented by this equation to within 10% for most points for

which L/D > 20.

We conclude from this comparison that for heat fluxes

2 between 0.01 and 0.3 W/cm subcritical pressures are preferable to supercritical pressures for equivalent mass velocities

in forced convection. Above these heat fluxes, for the data

presented here supercritical heat transfer is superior to subcritical, which is now in a dry-wall regime and shows very

steep temperature rise for a small heat flux increment.

-0.716

30

PERFORMANCE OF CENTRIFUGAL PUMP WHILE

CIRCULATING LIQUID HELIUM

During the performance of the heat transfer experiments there

was no evidence of vapor binding or instability in the centrifugal

pump provided the loop pressure was above 1. 1 atm. The pump

appeared to perform according to the characteristics shown in

figure 18. These performance curves were determined as described

in reference [2 ] and the load line of the entire flow loop was calculated from standard friction pressure drop equations. It should be

noted that the load line does not change substantially for different

densities in the pump. However, knowledge of the density in the

pump is important in determining the mass flow rate.

In figure 19 the flow rate measured calorimetrically , m , exp

is compared with that derived from the pump characteristics and

the calculated load line, m The density of the liquid was

caic

assumed to be that at the heat exchanger temperature and the

measured loop pressure. The abscissa in figure 19 is the subcooling at inlet measured in watts. For subcritical pressures this is

given by m (-^cat" ~ where H is the enthalpy of saturaexp k3A J. jJ\. i. ted liquid at the loop pressure and H is the actual inlet enthalpy.

For supercritical pressures ^g^-p taken to be the enthalpy

corresponding to loop pressure and the transposed critical temperature. It is seen from the data available that the pump performed to

within ± 15% of its predicted performance at the higher pressures.

The poor performance at 1. 02 and 1. 097 atm is attributed to vapor

formation in the pump due to heat leak down the pump shaft. This

is a special case of cavitation which is entirely dependent on the

installation of the pump. We estimate a heat leak between 0. 8 and

4. 0 watts in the present installation which certainly explains the

32
35

30

25

i 400 r/s

/

377 w f f

Calculated load line @ 4.2 K, / — 1 atm liQ (p= 0 12561 / _ for flow loop -^-...^^^ /

346

300

15

10

Measured characteristics

Calculated characteristics

using pump affinity laws

250

5

r^__r2\ 1^00 -1 \ r- 50 T^-T^T^1

10 15 20 25

3

vol. FLOW RATE, cmVs

Figure 18. Pump performance characteristics and flow loop load line.

33
1.0

0.9

0.3*^

4

O 1.02 atm

1.09

0.7 1.13

1.52

0.5

A

•A

1,77

1.92 "

4.22 "

8 12 16

INLET SUBCOOLING, W

20 24

Figure 19. Ratio of measured flow rate to flow rate predicted from centrifugal

pump performance characteristics vs subcooling power.

34
poor performance at 1 . 02 and 1. 097 atm. However, at higher pressures the pump appeared to perform in spite of the heat leak and

this is not entirely understood,

CONCLUSIONS

i. The usual transition from wetted-wall to dry-wall heat

transfer is observed in heat transfer to subcritical helium I under forced convection,

ii. Below the transition, forced convection has little effect on

heat transfer and the pool boiling correlation of Kutateladze

for the heat flux vs, temperature rise of the wall is sufficient.

iii. Above the transition, the heat transfer coefficient falls off

drastically. For superconductivity applications this will

usually have to be avoided except at mass velocities of the

2

order of 60 g/cm s or higher.

iv. Transition is a function of many variables (see 3.2). More

work will be required to make this a predictable phenomenon,

2

V. At heat fluxes between 0.01 and 0. 3 W/cm , subcritical

heat transfer is superior to supercritical for the same

2

mass velocity. Above about 0. 3 W/cm the reverse is

true,

vi. The centrifugal pump used to circulate the liquid performed

according to the characteristics determined earlier provided that below 1. 1 atm the subcooling power was not less

than about 2 W,

35
REFERENCES

Giarratano, P. J. , Arp, V. D. and Smith, R. V. , Forced

convection heat transfer to supercritical helium, Cryogenics,

JJ^, 385 (1971).

Sixsmith, H. , and Giarratano, P. J. , A miniature centrifugal

pump, Rev. Sci. Inst. 41_, 1570 (1967).

Johannes, C. and Mollard, J. , Nucleate boiling of helium I in

channels simulating the cooling channels of large superconducting magnets, Adv. Cry. Eng. , 1

, 333 (Plenum Press 1972).

Keilin, V. E. , Klimenko, E. D. and Kovalev, I. A. , Apparatus

for measuring hydraulic resistance and heat transfer in the twophase flow of helium, RTS 5062, National Lending Library for

Science and Technology, Boston SPA, Yorkshire (1968).

Jergel, M. and Stevenson, R. , Heat transfer to liquid helium in

narrow channels with laminar and turbulent flow, Applied Phys.

Letters, rz. No. 3, (Aug 1970)

James, G. B. , Lewis K. G. , and Maddock, B. J., Critical

heat fluxes for liquid helium boiling in small channels.

Cryogenics 20, 481 (1970).

Kutateladze, S. S. , Heat transfer in condensation and boiling.

State Sci. and Tech. Pub. of Lit. on Machinery, Moscow

(AEC translation 3770, Tech. Info. Service, Oak Ridge, Tenn. )

Brentari, E. G. and Smith, R. V. , Nucleate and film pool boiling

design correlations for ^22N , H , and He. , Int. Adv. in Cry.

Eng., ljOPart2, 371 (Plenum Press, N. Y. , 1965).

36
FORM NBS-114A ll-7l> U.i. DEPT. OF COMM. 1. PUBLICATION OR RtPOKI NO. «• v»0V » <ICC#»*lOo

BIBLIOGRAPHIC DATA N9.

SHEET NBSIR 73-322

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Forced Convection Heat Transfer to Subcritical Helium I

5* Publication Date May 1973

7. AUTHOR(S)

Patricia J. Giarratano, R. C. Hess and M. C. Jones

S. PerfoTimng Orgaoizatton

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

Boulder, Colorado 80302

lU. Fro)ect/ 1 ask/ Work Unit No* 314532(07)

11. Contract/Grant No. AT(49-2)-1165

MIPR FY 14557200411

12. Sponsoring Organization Name and Address

U. S, Atomic Energy Commission Air Force Aero Propulsion

Headquarters Laboratory

Washington, DC 20545 Wright-Patterson AFB

Ohio 45433

13. Type of Report & Period

C overed Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) Preliminary results of an experimental investigation of heat transfer to liquid

helium under forced flow conditions are reported for a 0. 213 cm i. d. x 10 cm

long test section subject to the following range of operating conditions:

System pressures 1. 1 - 2. 1 atm

Mass velocities 4-64 g/s-cm^

Heat fluxes 0. 04 - 0. 53 W/cm^

Inlet subcooling 0. 03 - 0. 10 K

The effect of the above system parameters on the heat transfer and critical

heat flux is discussed; a comparison of forced convection boiling with other modes

of heat transfer (pool boiling and supercritical) and the performance of a centrifugal pump used for circulating the liquid helium are also included in the report.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Centrifugal pump; critical heat flux; film boiling; forced convection; heat transfer;

helium; nucleate boiling; subcritical; supercritical.

18. AVAILABILITY STATEMENT 19. SECURITY CLASS

(THIS REPORT)

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1. ORIGINATING A C T I V I T Y CCofporsM «u<horJ Cryogenics Division

National Bureau of Standards

Boulder, Colorado 80302

2«. REPORT SECURITY CLASSIFICATION UNCLASSIFIED

26. GROUP

3. REPORT TITLE Forced Convection Heat Transfer to Subcritical Helium I

4. DESCRIPTIVE NOTES (Type of report and Inclusive dates) Final Report

5. AUTHOR(5) (F'ral natrre, middle initial, last name)

Patricia J, Giarratano, R. C. Hess, and M, C. Jones

6. REPOR T DATE

May 1973

7«. TOTAL NO. OF PAGES lyb. NO. OF REFS

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NBSIR 73-322

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this report) AFAPL-TR-73-37

10. DISTRIBUTION STATEMENT

Approved for public release; distribution unlimited.

11. SUPPLEMENTARY NOTES 12. SPONSO RIN G Ml LI T AR Y ACTIVITY Air Force Aero Propulsion Laboratory

Wright-Patterson AFB, OH 45433

13. ABSTRAC T Preliminary results of an experimental investigation of heat transfer to

liquid helium under forced flow conditions are reported for a 0. 213 cm i. d. x

10 cm long test section subject to the following range of operating conditions:

System pressures

Mass velocities

Heat fluxes

Inlet subcooling

1. 1 - 2. 1 atm

4 - 64 g/ s -cm^

0. 04 - 0. 53 W/cm^

0. 03 - 0. 10 K

The effect of the above system parameters on the heat transfer and critical

heat flux is discussed; a comparison of forced convection boiling with other modes

of heat transfer (pool boiling and supercritical) and the performance of a centrifugal pump used for circulating the liquid helium are also included in the report.

DD FORM1 NOV 65 1473 UNCLASSIFIED
UNCLASSIFIED

Security Classification

14. KEY WORDS

LINK A LINK B LINK C ROLE WT ROLE W T ROLE W T

Centrifugal pump

Critical heat flux

Film boiling

Forced convection

Heat transfer

Helium

Nucleate boiling

Subcritical

Supercritical

UNCLASSIFIED

— ^ ^ ^ : /r: