Pertanika 8(1), 3 3 - 4 2 (1985)

Heat Inleak along the Neck ofLiquid Nitrogen Containers

ABDUL HALIM SHAARIPhysics Department,

Faculty of Science and Environment Studies,Universiti Pertanian Malaysia,Serdang, Selangor, Malaysia.

Key words: Heat inleak; neck; liquid nitrogen containers.

ABSTRAK

Pengukuran profil suhu telah dibuat di sepanjang leher keluli nirkarat sebuah dewa kommer-sial 25 liter untuk penyimpanan nitrogen cecair. Pengukuran juga telah dibuat untuk profil suhulapisan sempadan gas efluen. Kebocoran haba ke dalam bekas nitrogen cecair, terutamanya adalahdisebabkan oleh pengkonduksian haba melalui dinding leher dan proses edaran semula wap. Kedua-kedua sumber ini menyumbangkan sebanyak 80% daripada jumlah kebocoran haba. Pengkonduk-sian haba melalui pepejal adalah kerana ukuran leher pendek dan dengan demikian nilai pen-dinginan dari gas efluen yang sejuk tidak digunakan dengan sepenuhnya. Proses edaran semula wapadalah disebabkan olehfluksjisim balikan daripada gas panas ke dalam bekas cecair.

ABSTRACT

Measurements have been made of the temperature profile along the stainless steel neck of a 25litre commercial dewar for the storage of liquid nitrogen. The temperature profile of the boundarylayer of the effluent gas was also measured. The major heat inleak into the liquid nitrogen bath is dueto the solid heat conduction down the neck wall and to the vapour recirculation process. These twosources contributed about 80% of the total heat inleak. The solid heat conduction was due to the factthat the neck was short and as such the refrigerative value of the cold effluent gas was not fully utilis-ed. The vapour recirculation process is due to the reverse mass flux of the warmer gas into the bath.

INTRODUCTION

A minimum rate of heat transfers into thecryogenic liquid is the principal criterion for thedesign of a cryogenic vessel. The following causesof heat flow into the liquid should be considered(Hoare et al, 1961). These are:

a. Heat inleak via insulating materials andresidual gas in the vacuum space;

b. Conduction along the neck of the dewar;

c Radiation through the neck aperture;

d. Conduction through supporting materials;if any, crossing the vacuum space;

e. Thermosyphon phenomena (convection) inthe interior ullage of the dewar.

In the 25-litre commercial dewar, "multi-layer insulations" are used in combination with avacuum housing. The use of multilayer insula-tions, so called because of its alternating layers ofhighly reflective material and low thermal con-ductivity spacer, has very much reduced the totalheat inleak into the cryogen (Scurlock and Saull,1976).

However, the other main share of heatadmitted to the cryogen in the dewar is throughthe neck. This heat conduction is called a heat

ABDUL HALIM SHAARI

short and is the subject of this paper (Shaari,1977). In order to estimate the amount of heatshort-circuited through the neck, measurementsof temperature profiles along the neck wall andboil-off rates were made.

THEORETICAL MODEL

An analysis to calculate the dewar depthnecessary to reduce the liquid boil-off rate to agiven value can also be used to calculate thetemperature profile in the dewar (Henry, 1951;Crooks, 1969). The model is illustrated in Fig. LIt assumes that the inner spherical shell of thedewar may be regarded as an isothermal body attemperature T , the temperature at whichnitrogen boils at the existing pressure. Heatexchange between the effluent gas and the neckwall is perfect. Convection, conduction andabsorption of radiation are considered negligiblein the gas phase of the neck column.

An amount of heat per unit time, Q, flow-ing down the neck wall would pass a contour,where the temperature is T, into a region wherethe temperature is T-dT. As it does so, anamount of heat dQis relinquished into the risinggas. The heat lost is equal to the heat required towarm the gas through the temperature intervaldT. If the specific heat of the effluent gas isdenoted by C and if m is the mass flow rate of

p

the gas, then at any height of the wall at tem-perature T.

CpdT (1)

where Q,ois the power at the base of the neck, i.e.atx = 0.°

Within the wall of the neck, the rate of heattransfer is given by a typical Fourier heat con-duction equation,

dTK(T) A - = Q •+ m J C dT

T Pm I (2)

lem can be simplified by assuming that (Scott,1959),

K(T) = K + a ( T - T ) (3)

where K is the thermal conductivity at the coldend of the neck and a is the average rate ofincrease of thermal conductivity of the wallmaterial between 77K and 300K. Substitutingequation (3) into (2) and assuming that thespecific heat of gas is constant at constant pres-sure, then the position coordinate is given by

x(T) =- * /

T

T

K + a(T - T ) dT(4)

Q, + (T - T )

Thus at JC = L, where L is the neck lengthandT = T we have,

(5)

a ( T , - T o ) + K o - a O

In

L x JJ

M

L,

< * . T >

where K(T) is the thermal conductivity of thedewar material and A is the cross-sectional areaof the wall. The practical solution of the prob- Fig. 1. Model for analysing heat inleak along the neck.

34 PERTANIKA VOL. 8 NO. 1, 1985

HEAT INLEAK ALONG THE NECK OF LIQUID NITROGEN CONTAINERS

Since the thermal conductivities of mostalloys used for the neck tube are rather complexfunctions of temperature, equation (5) is validfor a smaller interval of length in which the con-dition of linearity in K(T) holds.

However, if the heat exchange between theeffluent gas and the wall of the neck is zero, thenit can be shown that,

( • K - a T o ) ( T 1 - T o ) + l .2

(6)

Both equations (5) and (6) were obtained attwo extreme conditions. However, in practice,perfect heat transfer between the wall and thegas is never achieved. But one should not under-estimate the cooling effect of the gas evolved. Assuch, the heat current reaching the liquid bathwill have a value somewhere in between the twovalues calculated for the two extreme conditions.

EXPERIMENTAL

The apparatus used is shown schematicallyin Fig. 2. The dewar used was a 25 litre com-mercial dewar whose outer vessel is made frommild steel while the inner vessel is a 25-litrecopper vessel, with the snubber tube at the neckremoved so as to enable the thermocouples to befixed along the outer diameter of the neck(length 13 cm; thickness 0.046 cm).

Eleven thermocouples made from manga-nin-constantan wires were stationed at variouspoints along the wall of the neck, facing thevacuum space as shown in Fig. 3. To ensuregood thermal contact with the wall, the ther-mocouples junctions were all covered with apiece of aluminium foil and glued to the wall.All the thermocouple wires were each woundaround the neck several times and anchored atthe top of the neck.

In order to obtain an estimate of the radia-tion heat flux entering the neck through thevacuum space, the wall of the neck was wrappedwith six layers of aluminium foil, 12.0 m in

thin wattedstainlesssteel tube thermocouples

multilayerinsulation

liquidnitrogen

> Thermocouples along vapour boundary layer.• Thermocouples along neck wall.® Thermocouples around insulation.

Fig. 2. Schematic drawing of temperature

• Thermocouples along neck wall.® Thermocouples around neck insulation.

Fig. 3. Installation of thermocouples along neck wall.

PERTANIKA VOL. 8 NO. 1, 1985 35

ABDUL HALIM SHAARI

thickness, as a reflective medium. Each layer wasseparated by a ten per cent carbon loaded glassfibre of low thermal conductivity as a spacermaterial. The overall thickness was 0.102 cm.Three thermocouples were then attached to theoutside of the insulation as shown in Fig, 3.Similarly, each thermocouple was wound severaltimes around the insulation and was finallyanchored at the top of the neck as the previouseleven thermocouples.

All the fourteen thermocouples were thenglued together using varnish so as to keep theelectrical insulation intact and thus avoidingshort circuiting the wires during bake-outprocess. These wires were then taken out of thevacuum space through a lead connector fixed atthe outer vessel of the dewar, as shown in Fig. 2.

In order to measure the temperature pro-files of the boundary layer of the vapour in theneck column, ten thermocouples were stationedat various points along the wall of the neckfacing the rising vapour with the junctions jutt-ing out perpendicularly, about 1.5 mm into thevapour column (See Fig. 3).

Having installed all the thermouples, thetest dewar was assembled under commercial con-ditions as shown in Table 1.

During assembly of the dewar, the fine ther-mocouple wires were handled carefully. Beforewelding the inner vessel to the outer vessel, thethermocouples from the neck were all threadedout through leads in the glass-to-metal seal. Thepassage, through which the wires were drawnout, was sealed from inside with araldite. Thetest dewar was then leak tested and baked at120°C.

The temperature profiles were observed atdifferent liquid levels and with different massflowrates. In order to check the dependence oftemperature profiles on the evaporation rates ofthe gas, an electrical heater assembly (whichsomewhat increased the thermal conductiondown the neck) was installed, and measurementsof evaporation rate as a function of power dis-sipation were made. The temperatures were alsomeasured when the exit of the neck was pluggedwith a commercial plug.

RESULTS AND DISCUSSION

Interpretation of Temperature Profiles

A series of temperature profiles weremeasured. Typical results are as shown in Fig. 4.The graphs show that the temperature at the-baseof the neck varies with the depth of the liquidnitrogen in the dewar. Hence, it can be deducedthat the inner vessel is not in isothermal equili-brium with the liquid bath. In Run 1 and 2 (Fig4), the mass flow rate was higher than thenormal boil-off rate. This could be due to thefact that the funnelling of radiation down theneck tube affects the boil-off of the liquid. How-ever, as the depth of the liquid decreases, thefunnelling of radiation down the neck wasminimised by the cold effluent gas and much ofit was absorbed before reaching the liquid bathThus, the boil-off was due to the heat inleak; vianeck wall; through multilayer insulation and dueto the thermosyphon process.

In theory, the heat exchange between thewall and the vapour is assumed perfect. However, in practice, the assumption fails becausethe wall and the vapour are not in thermal equilibrium. This could be seen in Fig. 5, where the

Number of layerof insulation

30

Insulationthickness

(mm)

26.6

TABLE 1Details of test Dewar

Spacermaterial

Glass-fibre paper(GFG 3)

Wrappingtechnique

Swissroll

Other particulars

No Snubber tube

36 PERTANIKA VOL. 8 NO. 1, 1985

HEAT INLEAK ALONG THE NECK OF LIQUID NITROGEN CONTAINERS

TEMPERATURE. *K

• Run 1 - Level of LIN• Run 2 - Level of LIND Run 3 - Level of LIN0 Run 4 - Level of LIN3 Run 5 - Level of LIN0 Run 6 - Level of LIN

12.5 cm below exit.15 cm below exit.23.5 cm below exit.34.5 cm below exit.41.5 cm below exit.43.5 cm below exit.

Fig, 4. Temperature profiles along the neck (withconstant mass flow of effluent gas).

temperatures of the wall are much higher thanthose of the gas. At a lower flowrate, the diffe-rence in the temperatures is fairly constant. At ahigher flow rate, the temperature difference be-tween the wall and the vapour increases, asillustrated in Fig. 6. This shows that a perfectheat exchange is likely to be approached at lowflow rates of a gas. As seen in Fig. 5, measure-ments of the vapour temperature were extendeddown into the liquid level. It is obvious that asthe flowrate increases, a much lower verticaltemperature gradient is observed at the regionclose to the liquid surface.

tooTEMPERATUtE ,

• Run 1 — Wall temperature,. No heat input.• Run 2 — Vapour temperature down to liquid

level. No heat input.• Run 3 — Wall temperature. Heat input 1.2 W.O Run 4 — Vapour temperature down to liquid

level. Heat input 1.2 W.O Run 5 — Wall temperature. Heat input 3.6 W.K Run 6 — Vapour temperature down to liquid

level. Heat input 3.6 W.(Level of LIN ~ 32 cm below exit.)

Fig. 5. Temperature profiles of the wall and thevapour.

Measurements of the temperature profilesacross the neck are as shown in Fig, 7. Oneobvious result is that there is a marked tempera-ture difference between the wall and the effluentgas and this temperature difference increasestowards the neck aperture. The temperatureprofile is fairly stratified except towards theupper part of the neck where the warm gas mixesbefore exiting towards the aperture. At the lowerpart of the neck column, the temperature of theboundary layer is 'lower than that of the bulktemperature of the gas. However, the boundarylayer suffers progressive thinning towards the

PERTANIKA VOL. 8 NO. 1, 1985

ABDUL HALIM SHAARI

6 12

TEMPERATURE DIFFERENCE. *K

• No heat input.• Heat input 1.92 W.® Heat input 3.6 W.

Fig. 6. Temperature difference between the walland the vapour versus height of the wall.

28O

25O<

* 22O

iB 19O(

13O -

lOOi

11 cm

4 5 cm

3 5 cm

2-5 cm

• - ^ j — —

—o—

—-o

-o

— ^

2 1 0 1 2

LENGTH ACROSS THE NECK, cm

Fig. 7. Temperature profile across the neck(Level of LIN *+* 32 cm. Below exit).

upper part of the neck column and as such thetemperature of the boundary layer is fairly equalto the bulk temperature of the gas. This is due tothe rapid thermosyphon circulation as wasobserved by the cryogenic group at SouthamptonUniversity, where a thorough programme oncomplex flows in cryogenic vapour column isbeing carried out.

Calculation of Heat Inleak

Scott (1959) has shown that, assumingperfect' heat exchange between cold vapour andneck wall, it is possible to calculate the minimumheat in inleak Q , through the neck wall by

using equation (5). Applying this equation toRun 1 in Fig. 4} a value of 0.6 watt is obtainedfor Q . Results of Run were used here becausethe base of the neck was at the liquid bath tem-perature, while the other end was at ambienttemperature. From the slope of temperatureprofile of the wall, Q w a s found to be 0.85 watt.The difference in the two values clearly impliesthat the heat exchange between the wall and theneck is not perfect. However, if the cooling effectof the cold vapour is neglected then by usingequation (6), a maximum value of heat inleakvia neck wall into liquid nitrogen was found tobe 1.6 watts. Thus, the value of heat inleak viathe wall of the neck, for a practical dewar falls

38 PERTANIKA VOL. 8 NO. 1, 1985

HEAT INLEAK ALONG THE NECK OF LIQUID NITROGEN CONTAINERS

i.

D experiment® calculated fr,om theory for perfect heat exchange.• calculated from theory for zero heat exchange.

Fig. 8. Comparison of temperature profiles betweentheory and experimental.

between the two extreme values. This is illustrat-ed in Fig. 8. The detailed calculation of heatfluxes is summarised in Table 2. It was foundthat Qo decreased as the external heater powerincreased, i.e. as the mass flowrate of the gasincreased, Obviously, as the heat conductedalong the inner wall, much of it was absorbed bythe rising gas.

Measurements of the temperature gradientalong the outer layer of the insulation of the wallof the neck enabled us to calculate the radiationheat flux along the neck. The results are shownin Table 3. It was found that an average value of0.1 watt leaked via the wall of the neck by radia-tion.

Heat flux due to the vapour recirculation,Q,v, in the vapour space was found to be another

major source of heat inleak. At this stage it couldnot be measured directly. However, the radia-tion heat flux into the vessel, via multilayerinsulations could be calculated using theequation (Vance, 1962),

- T , ) (7)

where K = effective mean thermal conduc-tivity of the insulation.

= 0.5 /iWcm ' R 1 ,

A = area of the inner vessel covered bythe multilayer insulation

= 4.135 X 103cm2

t = thickness of multilayer insulation= 2.66 cm.

T i, T 2 = temperature at two extremes,

Thus, the heat flux due to vapour recircula-tion is estimated as,

(8)

where,Q,T = total heat flux

QE = heater power

Q,o = solid heat conduction to the baseof the neck.

Q,R = radiative heat flux along the neck.

Q i = heat inleak via multilayer insula-tion.

In column 7 of Table 2, the figures show theestimated values of the vapour recirculation heatflux. To a fair degree, it is found that it is afunction of the boil off rate of the gas. Thisagrees with the flow visualisation work atSouthampton, which indicates that the recir-culation of vapour in the neck is a function ofboil-off rate and temperature gradient andcould lead to a heat flux of the order of 0.1 to 1watt.

CONCLUSION

The data presented here give a clear pictureof typical temperature profiles in a 25-litre com-

PERTANIKA VOL. 8 NO. 1, 1985 39

O

TABLE 2Heat fluxes via dewar neck and other sources

Depth or levelof the below

neck aperture(cm)

12.51523.53234.53841.543.5323232343838

Total heat fluxin to liquid

nitrogenQ,T(watt)

1.7831.7831.6261.6261.6261.6261.6261.6261.9422.89

5.1193.4682.5435.274

Externalheat powerQ,E(watt)

000000000.31.23.61.920.953.79

Net Heat Flux

Q,T-Q. (watt)

1.7831.7831.6261.6261.6261.6261.6261.6261.6421.6091.5191.5481.5931.474

Heat fluxinto Lin via

neck conductionQo(watt)

0.8430.854

—0.821

———

—0.5910.223

——

Heat fluxinto ullage

space

—1.117

—1.0751.2221.0841.1131.141

——

1.131.1651.014

Heat flux dueto vapour

recirculation

dv=QT-QE-

(5 cases)

0.640.629

_0.505

—————

0.7180.996

_——

Heat flux dueto conduction

& recirculation(5 cases)

1.4831.483

—1.326

———-

1.3091.219

—_—

wo

>

O • Heat flux by radiation in the neck column (See Table 3 - 0 . 1 watt)Q • Heat flux through multilayer insulation ( = 0.2 watt)

TABLE 3Heat fluxes by radiation along neck

Level of liquid Temperature of outer layer of insulation around dewar neck,nitrogen in the measured at positions above the neck base at ...

dewar (cm) (°K)1.5 cm 4.7 cm 5.6 cm

Mass Flowrates ofthe nitrogen gasm(gs "^XlO "3

8.9488.9488.1598.1598.1598.1598.1598.1599.746

14.09725.6917.40412.71726.468

Heat flux by radiationalong the neck

(W)

0.1130.10.0850.0780.0780.0750.0730.0710.0850.1020.1290.1090,0970.121

v 12.5 206.2 251.0 262.4Sj 15.0 208.8 252.8 264.8

23.5 211.6 253.9 265.332.0 214.8 255.9 267.0

< 34.5 215.5 256.6 267.6r 38.0 219.6 258.1 269.0«> 41.5 221.7 258.5 269.2p 43.5 223.5 259.7 270.3

32.0 217.6 257.3 267.8«g 32.0 213.5 253.7 264.4

32.0 208.8 248.8 260.034.0 210.6 250.5 261.638.0 212.2 251.7 262.538.0 207.9 247.9 259.2

ABDUL HALIM SHAARI

mercial dewer. Analysis of the heat fluxes intothe dewar shows that;

i. Conduction along the neck wall 0.85 W

ii. Multilayer insulation 0.18 W

in. Radiation into the neck 0.10 W

iv. Vapour recirculation process 0.64 W

The total heat inleak is 1.77 W.

In analysing the temperature profile alongthe neck, the model used simply breaks downdue to the fact that there is no thermal equili-brium between the evolved gas and the wall ofthe neck. However, it would probably fit a longnecked dewar such as a helium storage vessel.

Finally it is suggested that the neck wallgeometry of the 25 litre dewar be modified so asto achieve lower boil-off rates by reducing solidconduction and vapour recirculation.

ACKNOWLEDGEMENT

This study is part of a project supported bythe University of Southampton and the BritishOxygen Company, Cryoproducts Division,Crawley, England. The author wishes to thankAssociate Professor Dr. Mohd. Yusof Sulaiman,the Deputy Dean of the Faculty of Science and

Environmental Studies, Universiti PertanianMalaysia, for reading the paper.

REFERENCES

CROOKS, M.J. (1969): Temperature Profiles inExperimental Dewars. Cryogenics. 9: 3 2 -35.

HENRY, W.E. (1951): A Finite Difference Treat-ment of a Helium Cryostat design problem./ Appl. Phys. 22: 1439.

HOARE, F.E., JACKSON, L.C. and KURTI, N.

(1961): Experimental Cryophysis. Butter-worth, London.

SCOTT, R.B. (1959): Cryogenic Engineering. D.Van Nostrand Company Inc. Princeton. J.Jersey.

SCURLOCK, R.G. and SAULL, B. (1976): Deve-lopment of Multilayer Insulation withThermal Conductivities below 0.1 Wcm ~1K"1. Cryogenics. 16:303-311.

SHARI, A. HALIM. (1977): Temperature Profilesalong the Neck of Liquid Nitrogen Con-tainers. Unpublished M. Sc. Project Dis-sertation. Southampton University.

W A N C E . R . W . and DUKE, W.M. (1962): AppliedCryogenic Engineering. John Wiley andSons. New York, London.

(Received 9July, 1984)

42 PERTANIKA VOL. 8 NO. 1, 1985