NBSIR 75-823

DO NOT ESMOVE

HELIUM RESEARCH IN SUPPORT OF

SUPERCONDUCTING POWER TRANSMISSION

V.D. Arp, D.E. Daney, N.V.Frederick,

M.C. Jones, P.R. Ludtke, W.R. Parrish and R.L. Powell

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

October 1975

Prepared for : Energy Research and Development Administration

Electrical Energy Systems Division

Washington, D.C. 20545

NBSIR 75-823

HELIUM RESEARCH IN SUPPORT OF

SUPERCONDUCTING POWER TRANSMISSION

V.D. Arp, D.E, Daney, N.V.Frederick,

M.C. Jones, P.R. Ludtke, W.R. Parrish and R.L. Powell

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

October 1975

Prepared for : Energy Research and Development Administration

Electrical Energy Systems Division

Washington, D.C. 20545

U.S. DEPARTMENT OF COMMERCE, Rogers C. B. Morton, Secretary

John K. Tabor, Under Secretary

Dr. Betsy Ancke r-Johnson , Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

CONTENTS

Page

1. INTRODUCTION 1

2. THEORETICAL STUDIES OF COOLING SYSTEM DYNAMICS 1 2.1 Acoustic Oscillations 1 2.1.1 Acoustic Wave Propagation and Reflection in a Flow Channel .... 3 2.1.2 Heat Driven Oscillations 3 2.2 Negative Differential To Flow Resistance 5 2.3 References 5

3. EXPERIMENTAL STUDIES OF COOLING SYSTEM DYNAMICS 6 3.1 Introduction 6 3.2 Pothead Modeling 6 3.3 Expe^-imental 8 3.4 Progress 8 3.5 Nomencalture 14

3.6 References 14

4. HELIUM PRESSURE MEASUREMENTS IN SUPERCONDUCTING POWERLINES 15

4.1 Present Technology 15

4.2 Possibility of Thermodynamic Pressure Measurement . . 16

4.3 Microwave Pressure Transducer 16

4.3.1 Schematic Pressure-Measurement System 18

4.3.2 Cavity Tests . 18

4.3.3 Future Work 21

4.4 References 24

5. TEMPERATURE MEASUREMENT 25 5.1 Introduction 25

5.2 Types of Thermometers 26

5.2.1 Active Electrical-Thermocouples 26

5.2.2 Passive Resistive Electrical 26

5.2.3 Passive Capacitive Electrical 28

5.2.4 Magnetic 28

5.2.5 Fluid 28

5.3 Effects of Electromagnetic Fields 29

5.4 Recommended Program 33

5.4.1 Thermometer Adaptations 33

5.4.2 Signal Processing 36 5.5 Conclusion and Future Plans 38

5.6 References 39

6. IMPURITY PROBLEMS IN SUPERCONDUCTING TRANSMISSION LINES 40

6.1 Introduction ^0

6.2 Accumulation of Impurities • • 40

6.3 Effect of Dispersed Impurities on Voltage Breakdown 44

6.4 Methods to Minimize the Impurity Problem 45

6.4.1 Purification of Helium Supply Gas 45

6.4.2 Purification of Recirculating Helium 46

6.4.3 System Configuration ^ 46

6.5 Conclusions and Recommendations 47 6.6 References

APPENDIX - NEGATIVE DIFFERENTIAL FLOW RESISTANCE IN SUPERCRITICAL HELIUM A-1

iii
LIST OF FIGURES

Figure Page

2.1. Open loop gain in the region of acoustic resonance Vq 2 2.2. Phase angle corresponding to figure 2.1 2 2.3. Phase relationships in heat driven acoustical oscillations .... 4 2.4. System configuration for heat driven acoustical oscillations 4

3.1. Pothead apparatus flow schematic 9 3.2. Pothead assembly drawing 10

3.3. Instrumented pothead without vacuum jacket 11

3.4. Assembled pothead 12

3.5. Pothead temperature profiles 13

4.1. Velocity of sound in helium, and derivatives with respect to pressure

and temperature, for selected pressures and temperatures 17 4.2. UHF oscillator measurement system 19

4.3. 440 MHz resonant cavity pressure sensor 20

4.4. 369 MHz resonant cavity pressure transducer 22 4.5. 1200 MHz resonant cavity pressure transducer 23

5.1. Magnetoresistance of platinum resistors 29

5.2. Magnetoresistance of germanium thermometers 31

5.3. Magnetoresistance of germanium thermometers 31

5.4. Magnetoresistance of carbon resistor thermometers 32

5.5. Magnetoresistance of carbon resistor thermometers 32

5.6. Magnetoresistance of carbon-glass thermometers at 4.2 K 33 5.7. Thermometer encapsulation 35

5.8. Circuit for capacitance thermometers 36

5.9 Methods of signal removal 37

6.1. The size of a sphere of impurity as a function of initial impurity

concentration in the helium and helium capacity in the line 41

6.2. Effect of leak rate and operating time on the size of a sphere of solid air . . 42

6.3. Effect of oil concentration and operating time on the size of a sphere

of frozen oil 43

LIST OF TABLES

Table Page

5.1 : 30

iv
HELIUM RESEARCH IN SUPPORT OF SUPERCONDUCTING

POWER TRANSMISSION

V. D. Arp, D. E. Daney, N. V. Frederick, M. C. Jones,

P. R. Ludtke, W. R. Parrish and R. L. Powell

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

ABSTRACT

This is the first annual report on a program of helium related

research in support of superconducting power transmission. Program

areas reported on are concerned with the dynamics of helium cooling

systems — theoretical aspects of oscillatory behavior and experiments —

and helium related measurements. The latter include pressure measurement, temperature measurement and the problem of impurity levels in

the helium refrigerant.

Key words: Cooling system; cryogenics; helium-cooled electrical

leads; helium impurities; microwave cavities; negative differential

flow resistance; pressure measurement; system dynamics; thermometers.

V

1. INTRODUCTION

This is the first annual report of progress on research in support of superconducting

power transmission carried out at the National Bureau of Standards, Cryogenics Division

under ERDA, Division of Electric Energy Systems, sponsorship. Work was started under

AEG and Dol funding received respectively in September and November 1974, so this first

report covers between 8 and 10 months of work.

In this reporting period the major tasks undertaken were under categories described

by Chapters 2, 3 and 4. These are respectively: i) Theoretical studies of the dynamics of

the helium flow system which incorporates the cable and its terminations. We are concerned

here with the potential for various types of oscillations, and the response to external

perturbations. ii) Experimental studies in relation to system dynamics. We were directed

first to study the stability of cable terminations (potheads) and then to consider the cable

itself. iii) The development of methods of measurement of the helium cooling system parameters in the presence of electromagnetic fields of the power line.

In addition to these major tasks we were also to review and make recommendations on the problem of temperature measurement in the unique environment of a power transmission

cable. The results of this review are given in Chapter 5. Finally, we were to review and

recommend on the problem of impurities in the helium cooling system. This is presented in

Chapter 6.

2. THEORETICAL STUDIES OF COOLING SYSTEM DYNAMICS

2.1 Acoustic Oscillations

In a previous study [1] we had developed a rather general set of equations with which

the dynamics of a helium cooling system could be investigated in the linear limit, i.e.,

small perturbations. These equations were used to investigate local stability about a steady state operating point of heated channels with typical power transmission line

parameters. Computational methods were found which enabled accurate determinations to be

made using the Nyquist plot at frequencies encompassing the density wave instability. However, when used at higher frequencies typical of acoustic resonance the numerical integration

methods failed to produce convergent results in reasonable computation time. We therefore

developed an approximate method whereby the integration could be performed analytically

over a short length of channel where fluid property variation was negligible. Proceeding

in short lengths along the entire channel, the channel transfer function could be rapidly

computed and again the Nyquist ploi of the system open loop transfer function could be

made with any desired accuracy. The approximation basically neglected the fluid velocity

relative to the acoustic velocity and became more accurate the higher the frequency. It was felt to be very adequate for typical transmission line parameters. We stress that this

approximation did not affect the steady state situation about which stability was to be

investigated. Thus the acoustic wave traveling along the channel still encountered the same variation of fluid states as before. We felt this to be a verv realistic calculation.

A typical computation is illustrated in Figures 2.1 and 2.2 where frequency response is

plotted. The open loop gain stays above 1.0, but the phase angle remains below tt thus

guaranteeing stability. Similar results computed for several different transmission lines were also invariably stable, and on this basis we had to conclude that helium cooled

transmission lines would be stable against acoustic resonance. But this raised the

question: why is it possible for acoustic oscillations to occur at all, as for Instance

in the experiments of Thurston and co-workers [2] using hydrogen, and Friedly [3] using

nitrogen? We believe the kev to this question lies in the interaction with the channel

wall.

In the next section we show that the computed stability at acoustic frequencies for

helium-cooled transmission lines is in fact resonable. Following this we attempt to resolve the question raised.
80

60

40

Q.

o

o

LU

O.o

20

10

8

V 1 1 1

1

1 -

1 1 c

1 1 1 1 M 1

1 1 1 1 1 1

P - lU U atm

KI = 20.0

\ KE = 9999.0 - \ N = 50

—

Length - DUUU m

Diam. = 5.0 cm DQ/DZ = 0.400 W/m

M = 138.0 g/s

Resonant Frequency , Z/q

1 1

1

1

1 1 1 1 1 1 1 1 1 tl 6 8 10 20 40 60 80 100 200 400 600 800x10

FREQUENCY, Hz

Figure 2.1 Open loop gain in the region of acoustic resonance v^.

0

20

a> TJ

UJ

_le><

liJ cn<

Q.

-40

-60

-80

T = 6.5 K P = 10 0 atm

KI = 200

KE= 9999.0

N= 50

Length = 5000 m

Diam. = 5.0 cm DQ/DZ = 0400 W/m

M = 138.0 g/s

Resonant Frequency,!/

6 8 10

Figure 2.2

20 40 60 80 100 200 400 600 800x10

FREQUENCY, Hz

Phase angle corresponding to figure 2.1.
2.1.1 Acoustic Wave Propagation and Reflection in a Flow Channel

Starting with the linearized time dependent continuity, energy and momentum equations

developed in fl], if we assume that the mean fluid velocity U is small compared to the

sonic velocity C, terms in dU/9x and U3/9x-can be shown to be small compared to acoustic

frequencies and thus for the dominant Fourier component <jj these may be dropped from the

equations. We also drop terms resulting from interaction with the channel walls which is

always permissible at helium temperatures. The resulting three equations can be used to eliminate perturbations H in enthalpy and U in velocity to give the following wave equation

for the pressure perturbation p.

r2__bi£-I^ l!^ =0- (2.1)

s x~ dx C ot C at

o o — - 2 where b = p(3v/3p) d/dx(p), and C is the thermodynamic speed of sound: C = (3p/5p) , p is the steady state

H pressure and

o

c the steady state

^ density. F = fP/a where

OSf is the

friction factor for steady turbulent flow in the channel, P is the perimeter and a the cross sectional area of this channel. Now friction can certainly not contribute to amplification of an acoustic wave leading to an instability so we may set F to zero. Then,

if we find no mechanism for amplification and instability a finite F will not change things.

Fourier analysis of the above equation with p = exp-(kx-cot) leads to

(2.2)

where the + sign indicates a wave traveling in the +x direction and the - sign the -x direction. For all cases of interest at frequencies near the fundamental acoustical

frequencv, ^ = 2~C /2L, the second term under the radical is much less than the first,

o o Also, b from its definition above is a positive quantity. Thus the wave vector k is that

of a wave traveling at a speed close to C^, amplified in the positive x direction and

attenuated by like amount in the negative x direction.

Consideration of the reflection of acoustic waves at flow restrictions or other

c'nannel discontinuities shows that the reflection coefficient is alwaj^s less than unity.

Then on a complete round trip within the channel a wave can only be damped. We see here

no mechanism for net amplification and therefore no instability at these frequencies, in

accord with our results from accurate numerical computation of stability criteria.

2.1.2 Heat Driven Oscillations

We consider that oscillations at acoustical frequencies when observed in higher tem- perature flow systems are of the heat driven kind. These were explained in the 19th

century by Rayleigh [4] when he noted that "if heat be given to the air at the moment of

greatest condensation (compression) , or be taken from it at the moment of greatest rarefaction, the vibration is encouraged". The ingredients for such a heat driven oscillation

are: i) flow of gas through the channel ii) heat input in a region where, in the standing wave pattern at resonance, all the gas particles are moving in the same direction

iii) a channel wall with a high heat capacity, and iv) thermal diffusion time in the fluid

much less than the period of oscillation. Items i) and ii) establish an axial temperature

gradient in the fluid, the level of which oscillates in the presence of a standing wave.

If the heat input is in the 1/4 wave section of the tube between a pressure node and

antinode or a 1/2 wave section between two pressure antinodes then the phase relationship

of pressure, fluctuating component of velocity, residence time and temperature are as sketched in figure 2.3. Then, if through iii) the wall temperature is essentially constant

the fluctuating component of heat flux seen by the gas is -h6T where h is the heat transfer

coefficient^ and is thus in phase with the pressure as required. In figure 2.4 possible

configurations for heat driven oscillations are given.
(a)

(bl

(c)

t t t t t "XL

I/4 Wave >

I t I 1 I I

TIME

Figure 2.3 Phase relationships in

heat driven acoustical oscillations.

Figure 2.4 System configuration for heat

driven acoustical oscillations.
We have not yet completed the generation of analytical criteria for the stability of

this mode of oscillation, but we believe the circumstances of the experiments of Friedly

and of Thurston support these ideas. Friedly observed acoustic resonance in the tube

between a nitrogen gas reservoir and a flow restriction, case a. The standing wave pattern

for this is a 1/4 wave between the pressure node at the reservoir and the antinode at the

flow restriction which gives unidirectional velocity fluctuaticns as required. Thurston

had reservoirs at each end of his heated tube with flowing hydrogen, i.e., a 1/2 wave

section, case b. But it is significant that acoustic modes were mostly observed when

the first 1/3 alone was heated, and only rarely when the last 2/3 were heated.

The essential difference between the helium-cooled transmission line and the above

cases lies of course in the wall heat capacity. We do not believe that this type of

oscillation is possible at liquid helium temperatures, and thus should not be important

in the transmission line itself. However, helium cooled pot-heads will operate mostly at higher temperatures and have the right configuration, probably a. or c. Whether oscillations

occur or not should depend on the thermal diffusion times from conductor to helium.

2.2 Negative Differential To Flow Resistance

Study begun some time ago on this problem under BNL support is now complete. A paper

has been written on the subject by V. D. Arp and is included in this report as an appendix.

The importance of this study is in two areas. In the first place the existence of negative

differential flov resistance can lead to maldistribution in parallel channel flow. In the

second place, based on high temperature experimental studies, [5] its existence in a flow

channel appears to be a necessary condition for so-called pressure drop oscillations between

a reservoir and the channel.

The results of our study may be briefly summarized as follows:

Necessary and sufficient conditions have been derived for the existence of negative

differential flow resistance. By approximate analysis and then exact numerical calculations

it has been established that for helium the inlet thermodynamic states must be in a fairly restricted region below about 3.5 K and bounded by the two-phase coexistence line.

For single-phase cooling systems it will only occur below about 3 atm pressure, with very

high heat input, short channel lengths and in the absence of exit pressure drop restrictions.

The phenomenon will not arise in helium-cooled superconducting transmission lines.

These conclusions are in accord with calculations performed earlier in the frequency

domain by Nyquist analysis. For negative differential flow resistance the phase lag of the

system should be ~ instead of zero as the frequency goes to zero. This circumstance never

arose with parameters representative of superconducting power transmission.

2.3 References

1. Jones, M. C. and Peterson, R. G. , A study of flow stability in helium cooling systems,

ASME paper no. 74-WA/HT-24.

2. Thurston, R. S. , Thermal-acoustic oscillations induced in forced convection heating

of dense hydrogen, Ph.D. dissertation. University of New Mexico and Los Alamos

Scientific Laboratory Report LA-3543 August 26, 1966.

3. Krishnan, V. S. and Friedly, J. C. , Pressure oscillations in forced convection heating

of gases, paper presented at the International Heat Transfer Conference, Tokyo, 1974.

4. Rayleigh, J. W. S. , The theory of sound , Vol. II, p. 226 (Dover Publications, N.Y. , 1945).

5. Maulbetsch, J. S. and Griffith, P., Prediction of the onset of system induced

instabilities in subcooled boiling. Symposium on Two-Phase Flow Dynamics Vol. I EURATOM Report 4288e, Brussels, 1969.

5
3. EXPERIMENTAL STUDIES OF COOLING SYSTEM DYNAMICS

3.1 Introduction

The purpose of the initial part of this study is to investigate flow stability in

potheads (gas cooled current leads) for superconducting power transmission lines (SPTL)

.

These potheads, which provide the link between the ambient conductor (300 K) and the

superconductor (4 to 10 K) , may be subject to two types of system instability: thermal

runaway instability and oscillatory instability.

Thermal runaway instability occurs when there is strong coupling between the total

pothead flow resistance and the pothead temperature. Under these circumstances, a small

current overload will warm the pothead, which increases the flow resistance and reduces

the coolant flow. Further warming and flow reduction occur until the metallurgical limit

of the conductor is reached and it melts. When an adequate pressure difference is available, the simple solution to this type of system instability is to place a metering valve

(having a flow impedance large relative to that of the pothead) at one end of the pothead.

Temperature feedback control of the metering valve should further increase' the stability

of the system. Because most gas cooled current leads presently in operation are cooled by

liquid helium boil-off gas, they operate with insufficient pressure for a metering valve

system. Superconducting transmission lines, however, will operate at elevated pressure and

are well suited to metering valve control of the pothead flow. Therefore thermal runaway

instability should not be a serious problem for SPTL potheads.

Oscillatory instability, however, could be a serious problem. Helium systems are notorious for so-called thermo-accoustical oscillations in passages connecting ambient and

helium temperatures [1-4], which is precisely the configuration of a pothead. Although

such oscillations have not generally been a problem for boil-off gas cooled current leads,

the danger of such an instability may be much higher for SPTL potheads operating at supercritical pressures. Potheads with inlet temperatures at or below the transposed critical

temperature may be particularly susceptible to instability since the transposed critical

line will be crossed somewhere in the pothead with consequent large volume change.

The detailed objective of this experimental investigation is to map the regions (pres- sure and temperature) of stability for a variety of pothead configurations and operating

conditions (current and flow rate).

3.2 Pothead Modeling . . •

4 Because full scale SPTL ' s are envisioned with operating currents of 10 amps or more, economics dictate testing pothead models rather than full scale prototypes. To assure the validity of these model tests we r.se scaling parameters which are derived

from the differential equations of the pothead. First law analysis gives

('-IA

2

) - Ph (T-e) + 0 (3.1)

for the conductor, and

m ^ = Ph (T-0) (3.2)

for the gas; or assuming

dH = C dH

P equation [3.2] becomes
If we further assume

1) steady state,

2) T - r = constant,

3) that the Wiedeman-Franz-Lorenz Law applies, viz.,

T -

" MT

4) 0* = p, i.e., the thickness of the conductor does not exceed the AC skin depth

5) constant conductor cross-sectional area,

equations (3.1) and (3.3) yield

2 I- ) - ^

1^ + ^ T = 0. (3.4) dx dx A dx ^^2

Or defining a dimensionless length y = x/£, we obtain

^ C m£ . 2p2

k A

Identical dimensionless profiles require that the coefficients in equation (3.5) be

constant , i.e.,

mC i ^ ^1- 2. P , L I «: ^

= constant, and — —— = constant.

As=u~ing use of the same material and fluid in the model and prototype, these conditions

become

^ = constant (3.6)

and

^— = constant (3.7)

A

Y

= constant. (3.8)

If we make the length of the model identical to that of the prototype, then the

requirements for identical axial temperature profiles in the model and prototype are simply

I/A = constant (3.9)

and

m/A = constant. (3.10)

7
In addition to maintaining the same axial temperature distribution in the model pothead, we also wish to maintain dynamic similarity by maintaining the flow impedance dp/du con- stant [5] and to maintain hydrodynamic similarity by maintaining the Reynolds number constant.

For configurations such as multiple strands of braided wire (e.g., Efferson leads [6]),

both dynamic similarity and hydrodynamic similarity are maintained over a wide range of

conductor areas, provided the conductor matrix (wire size and packing density) remain

unchanged. Because exact thermal and dynamic modeling are not always possible, we plan to test pothead models with a range of flow impedances. Thus, the first pothead tested is a hollow tube, which represents the low impedance limit; higher impedance models will follow.

3.3 Experimental

Figure 3.1 is a schematic of the apparatus which provides helium to the model potheads

at temperatures down to 4 K and pressures up to 20 atm. High pressure helium gas passes

through an ambient temperature purifier and is then cooled to 80 K and further purified in

the liquid nitrogen cooled precooler. The helium then flows through a vacuum insulated line

to the pothead dewar where it is further cooled as it passes through a counterflow heat

exchanger. Final temperature control is achieved with the flow splitting valve which directs

up to 100 percent of the flow through a coil immersed in the liquid helium refrigerant bath.

Instead of entering the potheads directly, the helium passes through a 15 liter reservoir

so as to provide a low dynamic flow impedance source.

Currents up to 2000 amps are supplied by a current transformer. Current measurement

is accomplished with a current transformer in combination with a one ohm standard resistor

and a peak voltage detector.

The apparatus is designed so that a variety of potheads may be tested. Conductor diameters in excess of 3 cm and lengths over Im can be accommodated. Figure 3.2 is an assembly drawing of the first pothead model to be tested. The conductor is a 4.76-mm I.D. X 0.25-mm wall x 46-cm long tube of phosphorized copper with a nominal current capacity of

lOOA. Germanium resistance thermometers measure the temperature at the base of the con- ductor and the temperature of the helium coolant. Ten gold (0.07 at. percent iron) vs KP thermocouples, which are referenced to the base of the pothead, measure the conductor

temperature along its length. Current, helium, flow rate, pressure and pressure drop are also measured. Figure 3.3 shows the instrumented pothead before assembly of the vacuum

jacket, and figure 3.4 shows the completely assembled and instrumented pothead ready

for insertion into the apparatus. Because each pothead is assembled as a separate unit,

they may be interchanged with a minimum of effort and down-time.

The second pothead constructed serves as the return current lead and consists of a 45.7 cm length of braided copper wire (192 strands, 34 gauge). The braids lie in the

annular space between a 4.8 mm diameter stainless steel tube and a 3.2 mm diameter micarta*

rod which forces the helium flow into the annulus. Self-regulated helium flow through

this lead is accomplished with a flow control valve actuated by a nitrogen vapor pressure

bulb.

A series of potheads will be tested, and although the design shown in figures 3.2

through 3.4 may never be used in practice, its importance is that it represents the low

pressure drop limit. The second pothead to be instrumented and tested will be of the

braided wire construction described above, and other potheads will be chosen to model

specific potheads proposed by the various SPTL groups as their designs become available.

3.4 Progress

The apparatus, instrumentation, and data reduction program are complete, and an initial

shake down run at helium temperatures has been completed. Only a few minor problems

occurred, and it is anticipated that on the next experimental run (planned for the immediate

future), mapping of the region of stability for the first pothead will begin. Data acquisition and reduction are accomplished by a mini-computer which provides on-line data reduction.

The complete, current temperature profile of the pothead is always available to the operator,

making the control of the experiment, and selection of the correct operating point quite

easy

.

8
9
Terminal post, copper

Phenolic sleeve

\ui Conductor (4 8 mm ID x 0 25 mm wall phosphorized copper)

Thermocouple, Gold (0.07 at % iron)

vs KP (chromel)

Dewar top plate

Thermocouple reference junction

Radiation shield

Terminal post & thermometer block, copper

Germanium thermometer

Dielectric coupling

Helium inlet

Figure 3.2 Pothead assembly drawing.

10
Figure 3.3 Instrumented pothead without vacuum jacket.

11
Figure 3.4 Assembled pothead.

12
An example of the temperature profiles measured during the shake-down run are shown in

figure 3.5. The family of curves are typical of the solutions expected from equation (3.5).

DIMENSIONLESS LENGTH (X/L)

Figure 3.5 Pothead temperature profiles.

13
3.5 Nomenclature

A conductor cross sectional area

C specific heat of the coolant

P

C specific heat of the conductor

s

h heat transfer coefficient

H specific enthalpy of the coolant

I current

k thermal conductivity of the conductor

Z total conductor length

m coolant mass flow rate

p pressure*

P wetted perimeter*

t time

T absolute temperature of the conductor

u coolant velocity

X distance along the conductor.

Greek

p DC resistivity

p* AC resistivity

0 absolute temperature of the coolant.

3.6 References

1. Clement, J. R. and Gaffney, J., Thermal oscillations in low temperature apparatus.

Adv. in Cryogenic Eng., 1, p. 302 (1953).

2. Keesom, W. H., Helium, Elsevier, p. 174, (1942).

3. Scott, R. B. , Cryogenic Engineering, Van Nostrans, p. 247, (1959).

4. Bannister, J. D. , Spontaneous pressure oscillations in tubes connecting liquid helium

reservoirs to 300 K environments, Proceedings IIR Commission I Meeting, Boulder, Colo.

(1966) .

5. Jones, M. C. and Peterson, R. G. , A study of flow stability in helium cooling systems,

ASME paper No. 74-WA/HT-24 (1974).

6. Efferson, K. R., Helium vapor cooled current leads. Rev. Sci. Instr., 38, 12, p. 1776

(1967) .

*Note this nomenclature differs from that in Appendix A.

14
4. HELIUM PRESSURE ^^EASUREMENTS IN SUPERCONDUCTING POWERLINES

Pressure measurements in helium cooling systems may be accomplished in either of two ways, (1) by bringing pressure taps out from the low temperature region to room temperature, where conventional instrumentation may be used, or (2) by placing a transducer at lew temperature, in the helium system, and bringing an electrical signal out to room tem- perature. It is common to experience difficulties with method (1), e.g., the temperature

gradients in the pressure taps promote thermoacoustic oscillations, variable thermal gradients show up as a drift in the output, and lengthy pressure lines may easily reduce the

frequency response to below acceptable limits. The problem with method (2) is that no commercial instrumentation is known which can do the job in the presence of power line fields,

and with a large separation between transducer and readout equipment. Thus, we have been

asked to study and recommend helium pressure measurement systems for use on superconducting power lines.

The operational specifications for such a pressure measurement system were laid out

at a steering committee meeting on Sept. 19, 1974 as follows:

(a) Primary operating ranges of 4-20 K and pressures to 2 x 10^ Pa (20 atmospheres).

It should also be useable during cooldown from room temperature, though possibly at re- duced accuracy.

(b) Overall accuracy of + ^^=, with a precision of + 0.3%, for pressures ranging from

static to 30 Hz pulsations (typical of thermoacoustic oscillators).

(c) Essentially unaffected bj' a.c. electric and magnetic fields of the cable, including both intrinsic calibration effects and eddy current heating.

(d) Measured output must be independent: of spacing, up to 1 kilometer, between the

transducer 'and the recording equipment. J-Iillivolt-level d.c. output voltages would be

essentially unuseable.

(e) If necessary the output signal may ride at the power line voltage (y 10^ kV) with

conversion to ground potential occurring outside of the cryogenic envelope. [This part of

the circuit design has not been very well specified in the superconducting power line

studies to date, and we are actively seeking further input].

4.1 Present Technology

Pressure transducers have been used .in liquid helium research [1], and NASA uses reliable pressure transducers in liquid oxygen and hydrogen spaceflight applications. A

review of pressure transducers for liquid oxygen service has recently been completed by

our laboratory [2]. The main requirements which separate this application for superconducting power line service from the others include maintaining a reliable calibration over long

periods of time in a very "noisy" electromagnetic environment, and operating with a large

separation between the transducer and external readout circuitry. A careful search was made of commercial pressure transducers approved for GSA (Government Services Administration)

purchase, searching for one which in principle should work at helium temperature, have a sensitivity to detect 10'* pascals (1.4 psi) of differential pressure (or better), and produce a signal not easily masked by noise. This search included the following types of

transducers

:

(1) Capacitance transducers, which form one arm of an external bridge circuit. These

can be very accurate in the research laboratory and have been used for helium studies (7).

However, great care with electromagnetic shielding and avoidance of ground loops is required,

and this would be very difficult in a power line environment, especially if conversion

from 10^ kV to ground potential is required. Commercial capacitance gauges often utilize

active circuit elements (transistors) in the transducer to bjijass capacitive effects in

the leads, but these would not work at low temperature. We have not found any gauges of

this type which seem suitable.

15
(2) Transducers using strain-gage sensing elements (often connected in a low tem- perature bridge circuit). These can be compact and reasonably accurate, at least for

higher gage pressures, but it is customarily necessary to measure output signals to millivolt accuracy or better. This would be very difficult with long leads in the presence of

powerline noise. Differential pressure gauges of this type, as would be useable for

venturi flow measurement, are much less common. We have not found any commercial gauges

of this type which seem suitable.

(3) Transducers employing a variable inductance (linearily variable differential

transformer). The magnetic element in these units could be perturbed by the power line

electromagnetic fields, though it is not clear what loss of accuracy would result. Operating and output voltages could be higher than with other types, thus easing the noise rejection problems. We did find one commercial gauge of this type, available in sensitive differential pressure form, operating at 5000 Hz, whose design showed no obvious inconsistency

with liquid helium service. According to the manufacturer, their transducer had not been

used in liquid helium to their knowledge, but one of their models had been operated in

liquid nitrogen at NAL. As it seemed to be the most promising commercial gauge for our purpose, we purchased one for trial. Unfortunately, one of the secondary coils failed when

cooled (slowly) to 76 K, probably because of a rigid, low expansion material used in the

coil construction. We have discontinued this study.

4.2 Possibility of Thermodynamic Pressure Measurement

The pressure in a fluid is a function of two independent parameters, generally taken as the density p and temperature T, through the equation of state P(p,T). Since temperatures

will be measured in the superconducting power line system, it is possible to calculate the

pressure if one other parameter, such as density, could be independently measured. In practice, density is not the logical choice for this approach, since it is generally more

diff icult to measure directly than is pressure itself. However, we would be remiss if we

did not consider other possibilities.

The most promising candidate, in a theoretical sense, is the velocity of sound, c. It can be measured with an ultrasonic technique which should work reasonably well in a power line environment. A gas chromatograph in our laboratory uses an ultrasonic transducer at the output to measure sound velocities to an accuracy dc/c s; 10 ^ (1 ppm) , and

it is reasonable to assume that this accuracy could as well be approached in a low temperature transducer. Thus, by measuring c and T, and feeding this information into an equation

of state P(c,T) (which would have to be developed), one could calculate the pressure in

the system.

A basic limitation on this approach can be deduced from the data in figure 4.1, which

gives

c, (P/c) Oc/9P)^, and (T/c ) ( 3c/ 9T)

p

as a function of pressure and temperature. One can see that the sound velocity is almost

independent of pressure in the ideal gas range, and goes through a minimum along the transposed critical line, so that the useable range for a meter of this type would only be the

dense fluid range, to the left of the transposed critical line in the P-T plane, i.e., in the

operating range for Nb power lines. Within this range, the data indicate that 0.1 to 1%

accuracy in c, combined with 0.5 to 5% accuracy in T, would determine P to 11. Thus,

though reasonable accuracy would be attainable in its dense fluid operating range, it

would not be useable during cooldown or for operation near the transposed critical line,

e.g., for NbsSn power lines.

We conclude that this is not a practical approach for superconducting power lines,

though it may be for other liquid helium applications.

4.3 Microwave Pressure Transducer

C. T. Van Degrift has shown that a microwave cavity can be a very sensitive displacement transducer, and could be the basis for a pressure transducer [3]. Potential

operational advantages for use with superconducting power lines include the following:

16
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17
(a) It can all be made of one metal, thus obtaining a rigid and robust structure and

avoiding the differential thermal contractions associated with composite metal and insulator

structures. Slow drifts in the output signal (for a constant pressure input) should be

completely negligible at operating temperatures below about 20 kelvin. Also, the design

should accommodate an order-of-magnitude overpressure without damage or subsequent calibration

shift, by allowing the flexible diaphragm to contact and be supported by a closely spaced rigid

wall.

(b) It can be made in a self-shielding geometry, so that its operating frequency is

essentially unaffected by external electromagnetic fields or magnetic materials.

(c) The output signa] is a frequency, typically 10® to 10^ Hz, which can be transmitted over long distances and easily filtered from 60 Hz "noise". Also, using radio

techniques, it can be transmitted from high voltage to ground potential, e.g., 345 kV to ground, with comparative ease.

(d) When constructed of a highly conducting material (e.g., copper) and operated at helium temperature, the Q of the cavity should be very high, = lO"*, thus permitting high

resolution to be obtained. If the operating temperature is low enough that a superconducting cavity could be used (T < 7 K), Q's of 10^ or 10^ may be obtainable.

4.3.1 Schematic Pressure-Measurement System

The basic transducer consists of a microwave cavity having one thin wall which deflects

elastically with pressure. The wall deflection causes a change in the natural resonant

frequency of the cavity, which is monitored by external circuitry, as illustrated in

figure 4.2.

The important consideration in the circuit design is that the measured resonant

frequency must be unaffected by the coaxial cable, perhaps 1 kilometer long, connecting

the cavity to the external instruments (shown in figure 4.2 as the length 2-3). At the

microwave frequencies being used, the important parameters of the coaxial cable for this

application are:

(a) The characteristic impedance, Zq, which must be matched at the termination to the cavity; mismatch, or sharp variations in Zq with position (e.g., due to temperature

gradients), will degrade the sensitivity but have negligible effect on the calibration.

(b) Total cable length, £ , which introduces a phase lag into the sensing system

and reduces the high frequency response of the system. In practice, a frequency response

up to 1000 Hz should be attainable using several kilometers of coaxial cable, so that

this is not a significant limitation, and

(c) the total attenuation, a£, in the coaxial cable. If the attenuated signal is

less than the noise at the amplifier input (4) , feedback is lost and the system fails to produce a meaningful output; this length limitation is probably several tens of meters if the coaxial cable is normally conducting (it is quite system-dependent and difficult to estimate accurately) and will be determined experimentally. A 250 meter length of superconducting coaxial cable has been obtained from Furakawa Electric Company in Japan for

testing with our cavities. Its attenuation of high frequency signals is of the order

1 dB/GHz/kilometer , which is so low that cable lengths of many kilometers seem feasible.

4.3.2 Cavity Tests

There are two possible cavity configurations which seem attractive for this application. The first one which we tried is shown in figure 4.3, and consists of a copper cavity

soldered coaxially onto a pipe containing helium. Slight deflections of a thin wall

section of the pipe cause capacitance changes to a close-fitting annular piece. Experimentation with this cavity, which resonated at about 440 MHz, led to problems of difficult

assembly and disassembly, and mechanical construction in general. The advantage of this

geometry is tliat a suitably shaped central channel could probably be used to construct a venturi flowmeter with the same microwave circuit. However, numerous small problems

led to the conclusion that this was just not a good choice for initial experimentation,

where ease of assembly is important.

18
He

3 2

1 ;—IV6

Output 2 He

Output 1

1. UHF Oscillator (Tracking)

2. Directional Coupler

3. Sensor (Resonant Cavity)

4. Amplifier

56

7

Mixer

Ampl if ier

Varactor Tuner for the UHF

Osci 1 1 ator

BASIC SENSOR SYSTEM

The UHF oscillator (1) drives the sensor (3) through the

directional coupler (2) and the long transmission line. The

signal reflected from the sensor is amplified (4) and multiplied

by the reference signal from the UHF oscillator (1). The output,

which is a function of the amplitude and the phase variation of

the reflected signal, is amplified (6) and used to tune the UHF oscillator (1) via the varactor (7).

Figure 4.2. UHF oscillator measurement system.

19
3.81 cm I.D Coupling Loop to Electrical Circuit

He! i um

1 .906 cm O.D.

Sol der

Joint 5.08 cm O.D.

Gap .0076 cm + .0004 cm -I 1- Wall Thickness .0127 + .0008 cm

All dimensions in centimeters.

Figure 4.3. 440 MHz resonant cavity pressure sensor.

20
A different configuration was used in the second cavity, illustrated in figure 4.4,

operating at 369 MHz. The pressure sensing diaphragm is realtively thick, 0.11 cm, giving

high stability and freedom from damage by inadvertant overpressure. The pressure sensing

chamber is easily separated from the microwave cavity, and small clearances in the gap

region are measured and machined with relative ease.

Experiments with this cavity have shown:

(1) The Q of the cavity is about 9000 at helium temperature, using ordinary machining

techniques on copper. This means that we can resolve a diaphragm displacement of about

1.9 X 10 ^ cm, or a pressure change of about 2 x 10 ^ N/cm^(3 x 10 ^ psi)

.

(2) A simple mechanical force on the lip (where the cavity is assembled from two parts)

is not adequate to obtain a high Q, and some sort of soldered contact is necessary.

(3) By far the largest perturbation on system stability comes from thermally-induced

distortions in the coaxial line which couples external instruments to the cavity, with

resultant small variations in impedance matching as the center conductor moves slightly.

To minimize this effect, we have switched from inductive to capacitive coupling between

the coaxial line and the cavity body, and are making other changes in the attachment

of the coaxial lead to the cavity body. Satisfaction with and final testing on an optimum

lead design has not yet been done, but we are confident that this perturbation can be

reduced to insignificance.

At the project review held in Boulder on May 7, 1975, some concern was expressed

about the physical size of the cavities, and we were asked if they could be made smaller.

To accomplish this, one is forced to operate a higher frequency where (a) Q's are lower,

(b) coaxial line losses are higher, and (c) external amplifiers are more noisy. To explore

this, we have built a third cavity designed to operate at 1200 MHz, as illustrated in

figure 4.5. This frequency is chosen as being about the highest frequency for which suitable

amplifiers can be purchased commercially (having come on the market in just the last year

or so). For a given frequency, the mushroom-shaped pillar in the cavity increases the

capacitance, allowing a smaller inductance (cavity volume) to be used; however, it also

increases the path length over which the microwave currents must flow, and hence reduces

the Q. Further, with this design, the total capacitance changes less with diaphragm

displacement than, for example, in the configuration of figure 4.4. The design also

incorporates a capacitive coupling probe of the type developed with the 369 MHz cavity.

The overall size reduction, from about 7 to 2 cm diameter is very significant. Because of

a delay in obtaining a 1200 MHz amplifier, we have not yet tested this device.

4.3.3 Future Work

In order to complete a logical development step, we plan to

(a) further evaluate and improve if necessary the stability of the cavity with

respect to temperature changes and external mechanical stresses induced by the support

mechanism.

(b) evaluate performance as a differential pressure gauge, as well as the absolute

pressure gauge tests to date.

(c) Evaluate effects of long coaxial lead length.

(d) Compare the 369 MHz cavity with the 1200 MHz cavity for the above items

(a) - (c).

(e) Obtain practical experience by installing and operating one in the pothead test apparatus described elsewhere in this report.

In addition, it may be desirable to obtain higher Q's by

21
2.85

I h- 2.500 D H

5.3I9D " ^ 6.35 D

All dimensions in cnn. MATERIAL - Copper

Figure 4.4. 369 MHz resonant cavity pressure transducer.

22
^.635 O.D. Stainless

Steel Tube

218 Drill,

thru

AN dimensions in cm. MATERIAL - Copper

Figure 4.5. 1200 MHz resonant cavity pressure transducer.

23
(f) improved surface-finishing techniques on copper cavities, or

(g) using lead-plated cavities to obtain additional loss reduction from

superconductors

.

These last two items are of lower priority, and will be undertaken only if the above work

items suggest that it would be worth the effort.

4.4 References

1. Wheatley, J. C, New techniques in refrigeration and thermometry, p. 455, Low Temperature Physics-13, Plenum Press, N.Y., 1974.

2. Arvidson, J. M. and Brennan, J. A., ASRDS oxygen technology survey - pressure measurement,

NASA Special Publication.

3. VanDegrift, C. T. , A sensitive displacement transducer using an extremely reentrant

84 MHz cavity oscillator, presented at the 1974 Applied Superconductivity Conference.

24
5. TEMPERATURZ ^lASUREMENT

5.1 introduction

The goals for this part of the program were to make reconnaendations for reasonably

accurate thermometry in superconducting transmission lines. Superconducting lines present

very unusual environments for conventional thermometers. Future designs may call for up to 700 kV a.c. or d.c. for the potential difference between conductors and up to 50 kA current

along the conductors. The electric fields caused by these voltages may be of the order of

20 kV/mm with higher harmonics and ripple fields. The peak magnetic fields will typically

be of the order of 0.1 tesla at the conductor surface in a.c. cables, and no more than 1. tesla for the highest power d.c. cables under consideration. Many types of thermometers

are potentially suitable for instrumentation in the two main modes of operation: 4 to 20 K

under stable conditions or 4 to 300 K during cooldown, (or possibly after a serious system

failure). The types of available thermometers differ radically in the physical phenomena

that they measure and therefore it is expected that they will differ significantly in

their response to high, alternating or static, electric and magnetic fields. The main

five types of thermometers that are potentially suitable are discussed in the next section.

Thermometer measurements can be affected in three different manners by electrical and

magnetic fields. First of all, the fields may directly affect the physical phenomena

being measured, e.g., the magnetoresistance effect in metals or electric field gradient

effect in semiconductors. Second, the thermometer casing may be heated by alternating

fields. This may occur even for fluid thermometers. This effect, if carefully considered,

can be minimized by good design and placement of the thermometer holders. The third

effect is the disturbance of the transducer or instrumentation wire leads by alternating

fields or erratic pulses in nominally static fields.

The themonetry project was divided into three phases for the preliminary studies:

1) literature survej",

2) estimates of probable effects, and

3) recommendations for appropriate experimental tests.

The literature survey revealed, as expected, very little on the effects of O-Zte'r^nat'L-ng magnetic or electric fields or static electric fields. There, however, is a considerable

body of information on the effects of high 3~c.t'^s magnetic fields. Thermometers that are poor in high static magnetic fields, such as some themocouples , will of course also be

poor in alternating fields.

An outline of the present knowledge on the effects of electromagnetic fields on thermometers is given in section 5.3. A summary of the results of a literature search is

given in 5.4. Further development of this program is discussed in section 5.5.

As it was stressed in the Steering Committee meetings, it is very important that the

themonetry project reflect the true needs of the practical transmission line assemblies

and that there be complete compatibility of measurement systems and cable configurations.

The thermometry project is therefore oriented toward the needs of the three main U.S.

efforts on superconducting transmission lines, the programs directed by: Brookhaven

National Laboratory, Linde Div. of Union Carbide, and the Los Alamos Scientific Laboratorj-,

and funded by the Energy Research and Development Administration and the Electric Power

Research Institute. Very thorough re-^iews of those programs have been given by Belanger

[1,2]. Very briefly, a) the LASL line is d.c, the other two a.c, b) the BNL line is

flexible with wrapped tapes, the other two rigid or semi-rigid. These differences lead

immediately to considerable complexity in designing a thermometry" system that can be used

for any one of the transmission lines. An additional complexity is introduced when one wishes to have both fast response time thermometers for diagnostic tests and more stable

ones for operating lines. The various criteria, with some explanations and possible

solutions, are discussed in section 5.4.1.

25
5.2 Types of Thermometers

The five main types of thermometers that were investigated as potentially useful in

these applications were:

1. active electrical - thermocouples,

2. passive resistive electrical - carbon, germanium or

s platinum resistance thermometers, semiconductor diodes, etc.

3. passive capacitive electrical - glass-ceramic capacitors,

4. magnetic - paramagnetic and nmr,

5. fluid - vapor pressure, gas pressure, or acoustic.

5.2.1. Active Electrical-Thermocouples

Richards, et al. [3] have shown that the thermoelectric output voltage is independent

of magnetic fields fluctuations if there is no temperature gradient along the wires that are in a magnetic field. However, it is very unlikely that it would be possible to obtain

those severe restrictions in a working system. Therefore the effects of electromagnetic

fields on thermocouples would have to be considered carefully.

There are very accurate thermocouple calibration tables for all of the thermocouples

commonly used at low temperatures [4,5,6]. However, it is well known theoretically [7],

that there is usually a strong dependence of the thermoelectric voltage, E, on magnetic

field. This effect can be calibrated, and since thermocouple wires are usually very small

and polycrystalline, there would not be a large orientation effect.

There have been recent experiments on the magnetic field dependence of copper-constantan thermocouples [8], though they are not the preferred system for cryogenic usage [4].

There is a positive temperature error of about 2 percent at 20 K, less at higher temperatures. At lower temperatures that couple has so little output that its signal would be

insensitive to thermal fluctuations and possibly masked by electromagnetic noise in the

measuring system.

There is also some data on Au-Fe elements reported by Berman and colleagues [9,10].

The effects are quite complex: at low temperatures (near 1 K) the effect is positive up

to 2.5 T, then negative at higher fields; at higher temperatures the increase in thermoelectric power is monotonic. Sample, et al. [11] have recently measured the effects of

fields on KP vs Au-Fe and TN couples. They show that it is possible to obtain reliable

correction factors for well controlled wires in laboratory systems.

In summary, the effects of electromagnetic fields on thermocouples are quite complex,

calibrations and corrections would be quite difficult to carry out in practice for field

installations.

5.2.2. Passive Resistive Electrical

Platinum resistance thermometers are the most often used accurate thermometers

in much of the whole temperature range. Their properties and methods of utilization have

been well described by an NBS-Gaithersbur g group [13]. However, they have a rapidly decreasing temperature sensitivity at low temperatures making them a poor choice below about

12 K. They also, unfortunately, have a relatively large magnetoresistance . Platinum

thermometers are constructed of high-purity platinum and so their electrical resistance Is governed primarily by scattering from phonons . This scattering mechanism can be highly

affected by electromagnetic fields and it becomes more severe at low temperatures. Curves

derived from the work of Neuringer and Shapira [14] are given in the next section.

Germanium resistance thermometers are also widely used for accurate thermometry at low temperatures. Like platinum thermometers, they also have a large magnetoresistance

effect. Germanium thermometers are fabricated from single crystals of doped, but moderately

pure, material. Because of the technological refinements in semiconductor manufacture, they can be made both reproducible and temperature sensitive. In fact, they have become the

best accurate thermometer in their main temperature range from 2 to 20 K. Because of the

two characteristics of germanium crystals, their sensitivity and crystallinity , they have

26

^ >V.\
both a large magnetoresistance and a significant orientation effect [15]. Values for these

effects are given in the next section.

Because of these characteristics, germanium thermometers are not recommended for use

in practical transmission cables in magnetic fields above 0.1 tesla. However, after

careful calibration, they may be used as reference thermometers in laboratory systems at higher fields.

Semiconductor junction diodes have recently entered the competition as reliable lowtemperature thermometers. Their main advantage is their very wide useful temperature

range, from about 1 to 300 K. They are also quite easy to measure electrically. The diode

utilize the phenomenon that the forward voltage drop of the junction increases with

decreasing temperature if the forward current is kept constant. The voltage is current

sensitive and the polarity of measurement is critical, therefore the current polarity on

the leads must be kept proper and the current must be amplitude regulated (nominally 10 uA)

These are, however, not serious difficulties in instrumentation systems. The Swartz's fl6]

have recently written a review on diode thermometers (as well as on resistance and capacitance thermometers). The p-n diode junctions may be constructed from silicon [17,18],

germanium [19], or GaAs [20,21,16], but only the latter is both available commercially and

has had extensive testing. The effects of magnetic fields have been determined for some

types of Ga As diodes [22] and they are reviewed in the next section. Using optimum conditions of bias current and orientation for the best units, the percentage error in temperature can be made very small.

Because of their favorable characteristics, GaAs or Si p-n junction diodes appear to be one of better possibilities for thermometry in superconducting transmission lines.

Thermistors are also relatively new in low temperature thermometry. The first discussion of their characteristics was given by Schlosser and Munnings [23]. However, they

have not received the recognition accorded other thermometers. They usually have a ex- tremely high temperature sensitivity, but it occurs only over a narrow temperature range.

The same authors have determined the effects of magnetic fields on various types of

thermistors — the effect is usually very small [24]. However, because of the lack of

general usage, the necessity of using different types in different temperature ranges, and

the sometimes-observed anamolous effects, they are not generally recommended for measurements in transmission lines.

Carbon resistance thermometers are very often used as secondary sensors in cryogenic

systems with high magnetic fields [11,12,14,25,26]. They have a good temperature sensitivity, good reproducibility (if handled properly), and small size. Because of the small

size they also have a small heat capacity. Fortunately the magnetoresistance is both

small and very reproducible so that the units can be accurately calibrated without too much effort. They also show a negligible orientation effect.

Several different sizes of carbon resistors have been tested as thermometers. The

47 ohm, 1/4 watt ones from one well-known manufacturer seem to give the best compromise of

temperature sensitivity, reproducibility, and magnetic field dependence.

Results on the magnetoresistance of several sizes of carbon resistors are given in

the next section.

Because of their excellent characteristics, carbon resistors (when specially selected

and handled) would seem to give one of the best thermometry systems available for diagnostic tests. They can probably also be used in practical transmission lines, especially if they have been well encapsulated and calibrated.

Another of the newer thermometers is the carbon-glass (carbon-impregnated porous glass

resistor developed by Lawless [27]. The materials, when encapsulated, are extremely

reproducible, mechanically strong, and interchangeable. They are constructed from a phase-separated alkali-borosilicate glass that has been leached to remove the boron-rich

phase. The porous glass is saturated with a high-purity organic fluid which is then

decomposed thermally. This process leads to filamentary carbon conductors embedded in

27
the porous glass matrix. Because of the lack of clay filler (as with carbon radio resistors)

and the high purity of the carbon, the units are very homogeneous and interchangeable.

Their resistance ratios are high (e.g., 2''^300 ~ 130) but their room temperature re- sistivities are low (e.g., P-^qq ~ 0.7 J^cm) . Recently Swartz, et al. [28] have measured

the magnetoresistive effects in these thermometers and the results are given in the next

section. They show no significant orientation effect [28].

5.2.3. Passive Capacitive Electrical

The glass-ceramic capacitive thermometer developed by Lawless [29,30] has many advantages

that will suit it very well for instrumentation in a transmission line: 1) It is sensitive,

fast in response, and relatively small; 2) it can have a simple electrical readout, either

capacitive variation, or with special circuitry, frequency variation; 3) one unit can

give an unusually sensitive output over the entire cryogenic range; and 4) a virtually

field independent output signal. However, it does suffer from two disadvantages, 1) The

capacitance goes through a maximum between room temperature and helium temperature (typically

at about 80 K) , so that its output is not a unique function of temperature during cooldown.

-2

2) They are occasionally beset with small calibration drifts, ~ 10 K, whose origin is not

completely understood at this time. The SrTiO^ capacitor is fabricated by forming a alumino silicate glass from a melt of SrO and TiO^ refractory oxides dissolved in SiO^

with some Al^O^ additive. If the melt is rapidly quenched, a stable glass-ceramic SrTiO^

is formed after the material is reheated and recrystallized . The dielectric permittivity

of this glass is strongly temperature dependent at low temperatures. The composite capacitor consists of 25 layers, 0.025 mm thick, of glass with 26 layers of Au-Pt separating

them. A platinum can is used for encapsulation. A description of the characteristic

properties of commercial units has been given recently by the Swartz's [16]. In fields up

to 18 tesla, deviations are less than 1 millikelvin [31].

In summary, the SrTiO^ glass-ceramic thermometer is potentially, very promising for use in transmission line thermometry; its output may be read and processed in several ways

and it has a negligible magnetic effect. Commercial units are now available for the simple

kind; intermixed types would have to be fabricated specially.

5.2.4. Magnet ic

Various paramagnetic and nmr thermometers are available for cryogenic use. The

thermometers are too complex in application, often too large, and too sensitive to electromagnetic fields to be useful for practical transmission lines. Rubin [25] has reviewed

their characteristics and properties.

5.2.5. Fluid

Gas thermometers can be quite accurate, but they are slow in response, often bulky,

and difficult to instrument conveniently. Because of their fundamental accuracy, they are often used as a reference thermometer. However, they are not suitable, in general, for

practical systems with confined space or long transducer lines.

Vapor pressure thermometers are extremely sensitive and accurate in their applicable

temperature ranges. However, there is no available thermometric fluid for the main tem- perature ranges of interest for transmission lines, 5-15 kelvin. Therefore they are also

not suitable for use in this application.

The other main fluid type thermometer is the acoustical one. It has been used to develop the basic standard germanium resistance thermometer scale, but its measurement

system is too complex for use in anything but basic standard thermometry.

A brief review of these three fluid thermometers has been given by Rubin [25].

28
0.3 Effects of Electromagnetic Fields

An exhaustive literature search was performed by our Cryogenic Data Center [32] on thermometers in general, and the effects of electromagnetic fields in particular. As

expected, the literature search turned up almost nothing relating to effects of a.c. or

d.c. electric fields on thermometers useful for transmission lines. Several references of one sort or another were found. Most of them referred simply to problems of measuring

resistance thermometers with a.c, rather than d.c, potentiometers or circuits.

There were the same number of references on the effects of magnetic fields, but

most of them weve pertinent to this thermometry project. Those references have been cited

in the previous section and several will be referred to again in the following pages.

First will be shown the magnetoresistance of two types of thermometers that are not

likely to be used in practical transmission lines because they do have a large effect. In figure 5.1 are some semi-quantitative results by Neuringer and Shapira [14] on platinum

thermometers with the magnetic field parallel to the length of the enclosing capsule.

The magnetoresistance ratio is large and temperature dependent. Temperature errors, as shown in Table 5.1, would be several percent at fields of 1 tesla.

65-

4

1

0 lOT

MAGNETIC FIELD

Figure 5.1. Magnetoresistance of platinum resistors.

29
TABLE 5.1

Type of thermometer Temperature AT/T(%) (0-2. 5T)

Platinum ,

< Germanium

Thermistor

Carbon resistor

Carbon impregnated glass

GaAs diode

SrTiO,

20

4.2-20

4.2-20

4.2-20

4.2

4.2

10

20

4.2

20

5-30

<0.05

< 1

2 2-3

1.5-2

0.5-1

not measurable

The second set of curves, figure 5.2, is on germanium with the magnetic field perpendicular to the current and long side of the encapsulation. The results are from Neuringer,

et al. fl5]. Figure 5.3, adopted from the same publication, gives similar curves showing

the orientation effect. In fields of 1 tesla, germanium thermometers show a magnetoresistive effect of several percent, decreasing with increasing temperature. A typical result

is given in Table 5.1.

The magnetoresistive effects in carbon thermometers are considerably smaller [14]. A graph of the effects for 47 Q, 1/4 W Allen-Bradley resistors is given in figure 5.4. For those measurements, the magnetic field was perpendicular to the current in the resistor.

The equivalent curves showing the effect of temperature at different fixed fields are given in figure 5.5. Note that in both curves the magnetoresistance is expressed as a percent change in the resistance. The tabular summary is given in Table 5.1.

The magnetoresistive effect in carbon-impregnated glass is not very large, though it

is about twice that of carbon radio resistors. A curve derived from Lawless' research [27]

is given in figure 5.6.

Summarized results, modified from the ones given by Neuringer and Rubin [26], are given

in Table 5.1, for maximum magnetic fields of 2.5 tesla. Since magnetoresistance is generally

proportional to the square of the magnetic field, the temperature errors at a peak field of

0.1 tesla will be about 1/625 of the listed values; at a peak field of 1 tesla, they will

be about 1/6 of the listed values. On this basis, one may conclude that all thermometers

listed in Table 5.1 would be acceptable in peak fields of 0.1 tesla, though platinum and

germanium thermometers would be only marginally so, becoming unacceptible at the higher

fields

.

30
0

MAGNETIC FIELD

lOT

Figure 5.2. Magnetoresistance of germanium thermometers.

Figure 5.3. Magnetoresistance of germanium thermometers.

31
0 10T

MAGNETIC FIELD

Figure 5.4. Magnetoresistance of carbon resistor thermometers.

0

7

6

5

O 4 <

3

2 ^^^^

1

0 1

- B-2J

1 ~-| 1 —

4 6 8 10 12 14

TEMPERATURE

Figure 5.5. Magnetoresistance of carbon resistor thermometers.

32
3

0 3T

MAGNETIC FIELD

Figure 5.6. Magnetoresistance of carbon-glass thermometers at 4.2 K.

5.4 Recommended Program

Two aspects of the thermometry problem need more careful study at this time:

j) Thermometer adaptation, and

2) Instrumental problems associated with long electrical leads at high voltage in high electromagnetic fields.

5.4.1 Thermometer Adaptations

Although a number of presently existing thermometers seem potentially acceptable for

reliable thermometry in superconducting cables, there remain the problems of encapsulating

various thermometers so that they will fit into prototype superconducting cables. There

is also the strong possibility that much better thermometer systems (e.g., glass-ceramic

capacitors) may be developed at a relatively low cost. At all times the dual needs for

thermometers of two different characteristics must be kept in mind. First, there is a requirement for relatively accurate, thermometers for field and prototype models and later

for utility power transmigslon systems. Second, there is a need for less precise, small,

fast response time (1 millisecond) thermometers that can be used as diagnostic tools in

laboratory research and development. Since the design of transmission lines is not yet

determined (in fact, the options for d.c. or a.c. are not even settled), there must be

considerable flexibility in ascertaining the criteria for a working thermometry system.

33
Thermometer adaptations will require repeated close interaction with the main programs

at Brookhaven, Linda, Los Alamos. The project leader will have to systematize the probable

requirements for thermometry with respect to:

accuracy,

size, •

• • response time,

heat capacity

thermal expansion,

signal output level, and

insensitivity to electric and magnetic fields.

With all those criteria in mind, the physical phenomenon to be probed to determine the

temperature will have to be determined. It is almost certain that no single thermometer

will fit all of the requirements: At least two different thermometers will be required to cover the extremes in response time and accuracy. At a more practical level the following

additional specifications will have to be determined:

Means of attachment of the thermometer to the cable,

size and placement of the signal leads,

thickness and type of thermometer encapsulation and

method of transmitting the signal to a safer environment.

Some preliminary thoughts on the above requirements and specifications can be given:

Accuracy . The diagnostic type thermometers should have an accuracy of about 0.1 K; the

semi-permanent ones, about 0.01 K.

Size . The diagnostic thermometers should be flat, 2-5 ram thick, but their length is not

so critical, 1-3 cm long. The larger thermometers may be as large as 1 cm in diameter,

and again their length is not critical.

Response time . This is a critical property; methods of reducing response time usually

simultaneously reduce the accuracy. Diagnostic thermometers should have a response time

as fast as 1-10 milliseconds; the larger thermometers are slower, say 0.1 to 1 second.

Heat capacity . The property is usually not very adjustable. The diagnostic thermometers

will probably have no significant encapsulation. The thicker encapsulation of permanent

thermometers leads to higher heat capacities, slower responses, better heat transfer, and more self-heating (if the case is in a varying field).

Thermal expansion . The thermal expansion of the thermometer capsule should match that of

the cable part that it is attached to. The material will depend on the cable then, rather

than on the type of response time desired, etc. Thermometers attached to aluminum supports

may have to have different glues or insulating materials from those interwoven into dielectric layers.

Signal output level and insensitivity to fields . These parameters will have to be determined as the project progresses. They will represent a considerable compromise between those

most desirable for instrumentation measurement and the practical requirements of a working

system in a high voltage cable.

Attachment . For most systems a metal-filled epoxy can serve as a suitable glue. For thermometers with metallic encapsulation, soft soldering to metallic parts of the cable will

probably afford the best response times and thermal equivalence.

Size and placement of signal leads . These will depend on the type of thermometer selected.

Both the leads and the thermometers themselves have to be protected so that they will not be ruptured during the field assembly of a complex cable. Very small coaxial cables have

been developed for cryogenic usage. These will be especially useful if a frequency signal

(rather than voltage) is transmitted from the thermometer to the measuring instrumentation.

34
Thermometer encapsulation . Much of the effect caused by the electromagnetic fields can be

shielded by encapsulating the thermometers in a metallic reentrant tube. Because of size

limitations the shielding can probably only be provided for the larger thermometers that are attached to a free surface in the transmission line. The smaller diagnostic thermometers could probably have little or no shielding. The metallic shield can serve several

functions. Both d.c. and a.c. electric fields can be virtually eliminated from the active

thermometer region. If a high permeability nickel alloy is used for the shield encapsulator

,

then much of the d.c. and a.c, magnetic fields can be deflected. The encapsulation

can serve three other functions as well: It can serve as a mechanical attachment (permanent

or removable) for placing a thermometer on various surfaces. The attachment could be made

with epoxies, varnishes, soft-solder, or bolts while the thermometer itself is protected.

The capsule can serve as an isothermal body of large heat-conducting surface area so that

the thermometer can more closely approximate the temperature of the test body. The same

heat conducting surface can serve to help remove any energy generated by self-heating or induced field-dependent heating in the thermometer. And lastly, a properly designed capsule

can serve as an electric field shaping conductor that will help to prevent voltage breakdown that could be caused by the sharp edges that are on most thermometers. The crosssection of a proposed encapsulation is shown in figure 5.7. Another possibility is the production of thin film, but well insulated, carbon film thermometers [34].

Figure 5.7. Thermometer encapsulation.

New types . One of the most promising of the novel thermometers would be glass-ceramic

capacitors inserted in a frequency ratio circuit, a proposal suggested by Lawless (1971)

but never put into practice. The most common method of measuring capacitance thermometers

is to use a transformer ratio-arm bridge, though phase sensitive detection and frequency

ratio methods have also been suggested. The capacitors can be used either in a simple

tank circuit (figure 5.8a) or in a more complex frequency ratio circuit.

The latter concept can be illustrated simply in figure 5.8b. A thermally active

capacitor, Ca, and a passive one, C , are connected by an alternating switch into a tank

circuit with an inductor, L. The two frequency signals are fed out to a measuring circuit,

alternate layers in one composite capacitor system. The frequency ratio of the circuit

with the passive element to the one with the active element can be expressed as

f

P

1/2

R = ^ =

a

f 'c"

Since C is temperature dependent, so is the ratio R. Since frequency measurements can be

a made accurately and at relatively low cost, this method has excellent potential. The active

element should be a stront ium-titanate ceramic glass; the passive one a temperature independent material (for example, military specification designation "NPO").

35
(a)

Temperature Dependent --

Glass-Ceramic Capacitor

Tank Circuit To Measuring Circuit or Inductor Frequency Modulation System

(b) Oscillating Switch

Active

C,

Ii V~I Passive

T T

Tank Circuit To Measuring Circuit or Inductor Frequency Modulation System

Figure 5.8. Circuit for capacitance thermometers.

Another material that appears to be valuable for further testing is a carbon- impregnated glass. Though this material has a very high temperature sensitivity, it is also more sensitive to magnetic fields than are regular carbon radio resistors.

These various thermometer types as recommended above exhibit no intrinsic difficulties

which would make them unuseable in power line applications. However, detailed adaptation

and optimization will depend not only the thermometer type and geometrical constraints of

the users (not well established at this time), but also on some of the problems of measuring the electrical signals from remotely located sensors in the presence of high electromagnetic noise. We consider these next.

5.4.2 Signal Processing

There are two effects that can significantly increase the difficulties of accurately

transmitting the temperature signals to the outside instrumentation: the high potential

(to ground) of the thermometer circuit when it is attached to an active conductor, and the

very long spacing, perhaps up to several kilometers, between the transducer and the readout

instrument

.

The high potential problem is not unique to superconducting power lines, though

probably much more instrumentation will be attached to them than to conventional systems,

at least in this development stage. All research groups use some type of wire cage to Isolate the external high-potential cable components and instruments. If the transducer

output is a frequency, transmission of the frequency across this barrier could be accomplished by radio or modulated optical techniques without loss of measurement accuracy. Such

techniques are illustrated in figure 5.9. If the transducer output is a voltage, some sort

of voltage to frequency conversion may be necessary within the cage (i.e., at high potential) before transmission to ground, thus introducing a measurement uncertainty which we

have not evaluated at this time. In either case, some power will be required to run the

transducer (i.e., the thermometer measuring current) and delivering this precisely con- trolled power at the line potential is not a trivial problem, especially if the transducer

is in electrical contact with the high voltage cable at some point a kilometer down the

line. It is further complicated by requiring the instrumentation to function both with

36
37
and without high voltage on the power line. The problem seems additionally difficult if d.c. instrumentation is used, and our present inclination is toward a.c. circuitry operating

at a kilohertz or more.

A long spacing between the transducer and the readout instruments (in the cage, as above

forces consideration of capacitive and, at MHz frequencies, inductive effects of the cable

on the transducer output signal. It is important that the characteristics of the transmission line not "pull" the output frequency of any thermometer-diode combination which generates a frequency in situ. This has been the problem with some of the past attempts in

this direction, though it can be avoided by careful attention to impedance matching. On

the other hand, with d.c. instrumentation, the additional voltage drop as the line carries

additional current to charge up its own self-capacitance (in response to temperature

changes) can be a significant limitation on the frequency response of the measurement

system. In addition, the long leads pick up a correspondingly large amount of 60 Hz noise

on the lines. If large enough, and not adequately filtered out, this noise could saturate

amplifiers, thus losing the signal. It is necessary to obtain realistic estimates of the

noise pickup which may be expected for various practical lead configurations. This again

is frequency dependent. At MHz frequencies, coaxial leads would be required, whereas at d.c, superior noise rejection would be obtained by an "inter-eight weave" type of cable.

We have begun to collect and organize relevant information on these two inter-related

problem areas, but are unprepared to discourse completely on it at this time. Though

discussed here with respect to thermometry, the general concepts apply also to other measurement systems, e.g., pressure transducers. The problems are not new or especially

unique, and we are seeking to assimilate existing information rather than to develop new

techniques.

5.5 Conclusion and Future Plans

For one reason or another, several of the best cryogenic thermometers are not readily

suitable for temperature measurements in transmission lines. These unsuitable thermometers

include gas volume, vapor pressure, platinum resistance and (marginally) germanium resistance

Carbon radio resistors are suitable for diagnostic tests and may be partially suitable for some kinds of practical systems. The most promising thermometers at present appear to be

glass-ceramic capacitors, carbon- impregnated glass, and possibly silicon diodes. The first

type is especially suitable because frequency, rather than voltage, signals can be generated

by a sensor system.

Superconducting transmission lines generally have only moderate magnetic fields, (of

the order of 0.1 T) . Because of this, the errors in thermometry caused by ambient magnetic

fields will be relatively small (for the more suitable thermometers) and those deviations

can probably be corrected for rather easily and accurately. The effects of high gradient

electric fields can be more serious. However it is probable that they can be made negligible with proper design of thermometer encapsulations. The main problems seem to be a)

the adaptation of favorable thermometers to fit specialized instrumentation requirements

in a transmission line and b) the difficulty of removing accurate sensor readings from a noisy electromagnetic environment that is at a high electric potential above ground.

It is our considered judgement that the study of high-potential, long lead signal

processing, must be carried to a reasonable conclusion before embarking on a specific

program of thermometer adaptation and testing as impliclty suggested in 5.5.1, above.

Having identified thermometer types of principle interest, the detailed form and configuration will depend to some extent on the measurement system with which it will be used,

in particular its operating frequency, and its type of output (a voltage amplitude, or a frequency). This system study will be completed within the next reporting period, and

should form a basis for subsequent adaptation and testing of appropriate thermometers,

in conjunction with the needs of the power line programs.

38
5.6 References

1. Belanger, B. C, Paper J-1, Adv. in Cryogenic Engr . Vol. 19 (1974).

2. Belanger, B. C, Cryogenics 15^, 88 (1975).

3. Richards, D. B., Edwards, L. R. and Legvold, S. J., J. Applied Phys. 40, 3836 (1969).

4. Sparks, L. L. and Powell, R. L., J. Research NBS 76A . 263 (1972).

5. Sparks, L. L., Powell, R. L. and Hall, W. J., NBS Monograph 124 (1972).

6. Powell, R. L., Hall, W. J., et al., NBS Monograph 125 (1974).

7. MacDonald, D. K-C . , Thermoelectricity: an introduction to the principles (John Wiley

and Sons, Inc. New York, 1962)

.

8. Schlosser, W. F., Private communication to L. G. Rubin.

9. Berman, R. , Kopp, J., Slack, G. A., Walker, L. T., Phys. Letters 27A, 464 (1968).

10. Berman, R. , Temperature, Vol. 4, part 3, 1537 (1972).

11. Sample, H. H., Neuringer, L. J., Rubin, L. G., Rev. Sci. Instr. 45^, 64 (1974).

12. Sample, H. H., Neuringer, L. J., Rubin, L. G., Low Temp. Physics 13, Vol. 4, 601 (1974).

13. Riddle, J. L., Furukawa, G. T., Plumb, H. H. , NBS Monograph 126 (1973).

14. Neuringer, L. J. and Shapira, Y., Rev. Sci. Instr. 40, 1314 (1959).

15. Neuringer, L. J., Perlman, A. J., Rubin, L. G. and Shapira, Y., Rev. Sci. Instr.

42, 9 (1971).

16. Swartz, J. M. , Swartz, D. L., Rev. Sci. Instr., to be published.

17. Unsworth, J., and Rose-Innes, A. C, Cryogenics 6^, 239 (1966).

18. Logvinenko, S. P. and Brovkin, Y. N., Instr. Exp. Tekhn. 1,, 221 (1968).

19. Barton, L. E., Electronics 35, 38 (1962).

20. Swartz, D. L. and Swartz, J. M. , Cryogenic Tech. 5^, 250 (1969).

21. Arends, J. and Wright, R. C, Cryogenics 9^, 281 (1969).

22. Swartz, J. M. and Gaines, J. R. , Temperature Vol. 4, part 2, 1117 (1972).

23. Schlosser, W. F. and Munnings, R. H., Rev. Sci. Instr. 40, 1359 (1969).

24. Schlosser, W. F. and Munnings, R. H. , Temperature Vol. 4 part 2, 795 (1972).

25. Rubin, L. G., Cryogenics 10, 14 (1970). This includes a review of thermometry

through 1969.

26. Neuringer, L. J., Rubin, L. G., Temperature Vol. 4, part 2, 1085 (1972).

27. Lawless, W. N., Rev. Sci. Instr. 43, 1743 (1972).

28. Swartz, J. M. , Gaines, J. R. and Rubin, L. G., Rev. Sci. Instr. To be published, 1975.

29. Lawless, W. N., Rev. Sci. Instr. 42_, 561 (1971).

30. Lawless, W. N., Radebaugh, R., Soulen, R. J., Rev. Sci. Instr. 42, 567 (1971).

31. Rubin, L. G. and Lawless, W. N., Rev. Sci. Instr. 42, 571 (1971).

32. Cryogenic Data Center, Bibliography on Thermometry (1975)

.

33. Lawless, W. N., Unpublished notes (1971).

34. Collier, R. S., Sparks, L. L. and Strobridge, T. R., unpublished NBS report.

39
6. IMPURITY PROBLEMS IN SUPERCONDUCTING TRANSMISSION LINES

6.1 Introduction

The most promising superconductors for transmission lines require helium refrigeration at or below 10 K. Electrical utilities demand the overall system reliability be

high - at least higher than that of present helium refrigerators.

One of the most frequent causes of helium refrigerator failures or shutdown is plugging by impurities carried by the helium [1,2]. The helium inventory of a transmission

line probably will be many times that of a large helium refrigerator. This report looks

into the potential impurity problem in transmission lines and into ways to minimize it. To gain an "order of magnitude" feel of the possible problem, rough estimates of tolerable

impurity levels are presented. Since the calculations assume that impurities collect in one location, the calculations probably overestimate the severity of the problem. As the

various transmission line designs become finalized the calculations will need refinement.

There are two ways impurities could cause troubles in superconducting transmission

lines. First of all, localized impurity accumulation leading to plugging is a potential

problem in all of the proposed transmission lines. Secondly, if helium is the dielectric

there is the possibility of impurities affecting the voltage breakdown characteristics of

helium. Each of the two topics are considered separately. Then we consider methods of

minimizing the problem.

6.2 Accumulation of Impurities

Plugging problems have always plagued cryogenic refrigerators. At least four different sources of impurities can be present in any refrigeration system:

1. impurities in the original inventory of helium and/or make-up gas,

2. air leakage into the system,

3. oil from the refrigerator compressors, and

4. off-gassing from the walls in the warm sections of the system.

Commercial Grade A helium usually contains 20 to 50 ppm (by volume) of impurities;

these are neon (10 to 15), nitrogen (1 to 10), water (1 to 5) and lesser amounts of hydrogen, oxygen, argon and carbon dioxide [3] . Of all of these impurities neon is the most

troublesome in helium refrigerators because it is in the highest concentration and has a low boiling point (27 K) . Figure 6.1 shows the diameter of a sphere of impurity (assumed to be solid neon) as a function of initial impurity concentration for an 8 km. (5 ml.) long

line with various flow cross-sections. The results are based on the following assumptions:

1. All of the impurity collects at one point.

2. The line contains helium at the density of NBP liquid.

These calculations show that commercially available helium probably requires additional purification if the possibility of plugging is to be minimized. An impurity con- centration of less than 1 ppm would be desirable.

Air leaks are a major source of impurities in helium refrigerators. Two of the most

likely points of leakage are at the suction of the compressor and in low pressure gas

holders. Figure 6.2 shows how fast a sphere of solid air (assumed to be nitrogen) grows as

a function of leak rate. Again it is assumed that all of the impurity collects at one point in the system. Based on figure 6.2, it appears that the average leak rate should be

kept below 0.01 g/day (0.0003 SCF/day) ; this includes the impurities produced by outgassing. This average leak rate should be obtainable by operating the inlet pressure at above atmospheric pressure and by avoiding the use of low pressure gas holders. Calculations indicate that a low pressure gas holder designed to hold the inventory of a large

refrigerator could provide a leak rate in the range of 0.5 to 5 g/day.

Helium contamination by compressor oil is a common problem; in fact, if screw com- pressors are used, oil is injected into the helium. Therefore, oil removal is an important step in any cryogenic refrigerator. Figure 6.3 shows the rate of growth of a sphere

40

A
41
ujo (2NSD)AlldndV\ll P 3d3HdS P d313I^Via

42
LUD *(9£h^'o u SD)nio P 3d3HdS P d313I^Via

43
of oil (taken to be n-heptadecane) as a function of oil concentration in the helium entering the cold section of the refrigerator. For these calculations, a helium flow rate of

300 g/sec is assumed (this corresponds to a 5 Kw refrigerator operating between 8 and 10

K) . The sphere diameter is proportional to the cube root of the flow rate. It can be seen that the oil concentration should be less than 0.1 ppb to prevent the possibility of

plugging.

6.3 Effect of Dispersed Impurities on Voltage Breakdown

If helium is the dielectric, dispersed impurities might lead to a voltage breakdown

problem. Meyerhoff [4] found that the addition of solid air or silicon dioxide did not affect the breakdown strength; however, there was a marked reduction in the breakdown

strength when copper powder was added to the helium containing the Si02. In these tests

the impurities were kept in suspension by using a submerged fan. The size of the particles was given (-325 mesh) but the concentration was not stated. Therefore, it is not clear whether the reduced breakdown strength was due to the presence of a conductor or to the total concentration of particles. However, Meyerhoff [5] feels that the lower breakdown voltage is due to the presence of a conductor instead of the total impurity concentration. Thus it appears that suspended dielectric impurities do not affect the breakdown

strength of helium whereas conductors do reduce the breakdown strength.

When helium is the dielectric there is another process which could lead to voltage

breakdown; this is dielectrophoresis . Dielectrophoresis is the migration of neutral

particles in a nonuniform field [6]. The force on a neutral body is given by

F = 2tt a"^ e V(E^) (6.1)

o where a is the particle radius, e is the permittivity of the free space, E is the electric field and

(}) = K^(K2 - K^)/(K2 + 2K^) (6.2)

where and are the relative permittivities of the helium and particle, respectively.

Since the force depends upon the gradient of the field squared, it is independent of the

sign of the field.

Through 't' the force also depends upon the relative permittivity; since helium has a relative permittivity of approximately unity and solids have a value of 4 or more, the

particles will be drawn towards the high field region. (Also, because > 1, the maximum

value of i> will be one) .

[n transmission lines which use helium as the dielectric the helium flows in the

annular space of a coaxial cable. Thus, if dielectrophoresis takes place, impurities will

migrate toward the center conductor. If there is a rough spot on the conductor wall or some impurity deposited on the wall, the field gradient near that point will be increased;

this, in turn, will cause more impurity to collect at that point. In time this process

could cause a stalagt i te-type formation to grow. Regardless of the relative breakdown

strengths of the helium and impurity, the stalagtite could grow until the distance between

the formation and outer conductor was small enough to possibly cause a breakdown in the

helium.

One way to prevent stalagtite formation (other than eliminating the impurities) is to have a sufficiently strong convective flow to disrupt the dielectrophoresis effects. Tlie relative strength of the dielectrophoresis forces to that of convective forces can be

estimated by comparing the relative velocities. Assuming <t> is one, equation (6.1) for an annular configuration becomes

.

• 3 2

4Tr a L V F= _ (6.3)

r In k

44
where V is the voltage difference between the two conductors, r is the radial position of

the particle and k is the ratio of the inner to outer radius of the coaxial cable; the

minus sign signifies that the particle moves toward the center conductor. Equation 3 is

valid as long as the walls of the conductor are smooth. The force would be greater in the

vicinity of a perturbation of the electric field caused by the presence of impurities.

Assuming lequation 6.3 is valid, the velocity of a particle moving toward the inner conductor

can be found by equating the dielectrophoresis force to the viscous force as given by

Stokes law. The radial velocity at which these forces are equal is

n r In k

where n is the viscosity of helium. (There is also a diffusion force which would oppose

the dielectrophoresis force; this effect is probably small enough to be neglected here).

It is expected that the helium flow will be turbulent which complicates the analysis.

However, there is a small region near the walls where there is a laminar boundary layer.

In this region the axial component of the flow is [7]

(r-kR) ApR

where Ap/L is the pressure drop per unit length. (lEquatlon 6.5 is strictly correct onlv for

pipe flow but it is assumed here to apply to annular flow). Combining equations 6.4 and 6.5

and omitting the minus sign gives

2 2 V 4 e a V

_r_ ^

o C6.6)

"^z 3 S(S+kR)^ In^ k (kR Ap/L)

where S is distance from the wall. Putting in the appropriate values of the variables for

the Linde line [1] gives — = 12800 = 12800 a /S (6.7)

S(24.27S+1)

where a and S are in meters. For this case the laminar boundary layer has a thickness of

roughly two microns and ' the buffer zone plus laminar layer thickness is roughly 10 microns.

Assuming a particle radius of one micron at a distance of two microns from the wall, equation 7 gives a velocity ratio of roughly 0.01. Since the ratio is so small, convective

forces will dominate the motion of the particles, even in the boundary layer. For particles which have a diameter greater than the laminar boundary layer thickness the effect of

dielectrophoresis will be dominated completely by the convective forces of the turbulent

core. Therefore, it appears that dielectrophoresis will not be important as long as there

are no electrical field and fluid flow perturbations. In the regions of surface bumps

and/or low flow rates, the effect of dielectrophoresis would be more pronounced; however,

it is not obvious whether or not it could cause operational problems.

6.4 Methods to Minimize the Impurity Problem

Several options are available which would minimize the impurity problems discussed

above

.

6.4.1 Purification of Helium Supply Gas

Considering first the impurities in commercially available helium, either liquid

filtration _or low temperature adsorption could be used for the initial filling of the

line, and for the make-up gas [8]. Filtering liquid helium from beneath the liquid-vapor

45
interface reduces the total impurity content to around 0.01 ppb

.

If adsorption is used to remove the neon the adsorption bed must be operated at or below 77 K [3]. If the bed is at 35 K or lower, it can be regenerated with Grade A helium.

However, if higher temperatures are used the bed must be regenerated with a portion of the

ultrapure helium; roughly 40 percent of the ultrapure helium is recontaminated by regeneration [8] .

Using adsorption beds currently requires periodic analysis of the effluent to detect

impurity breakthrough. Harrison [9] recently reviewed the commercial instrumentation

available for detecting trace impurities in helium. By using only filtration, this periodic gas analysis would not be mandatory.

6.4.2 Purification of Recirculating Helium

To adequately remove any air which leaks into the refrigeration system requires at least two adsorption beds - one operating at ambient temperature for water and carbon

dioxide removal and one operating at liquid nitrogen temperature for nitrogen, oxygen and

argon removal. The bed effluents should be checked several times a day to determine when

the bed has become saturated. Extreme care will be required to assure that the samples

will not be contaminated by air. However, standard laboratory sampling techniques could

be applied here at least at the prototype stage. Field sampling could be more difficult.

Monitoring the impurity concentration in the adsorption bed would eliminate the

necessity for analysis. Only a qualatative indication of when the impurity concentration

front reaches a given point in the bed would be required. Physical properties of the

adsorbent such as conductance, capacitance or thermal conductivity might be used. However, developmental work will be required to determine which, if any, of the physical

properties is the most attractive.

A possible alternative to adsorption beds is to place filters at various points in

the refrigerator provided that all of the impurities collect in the filters instead of in

critical points in the system.

The practicality of using a filtration system depends upon several factors. If the

impurities form particles that are larger than three microns, commercial filters can be

used. If the particle dimensions are one micron or less, then filtration would be un- practical. Also, the refrigerator must have a configuration which would be suitable for

locating filters in the proper temperature zones. For example, air freezes in the 60 to

65 K range. Thus, it would be desirable to have an expander outlet temperature around 60

K. I'ne outlet gas could then go directly to a filter. In this way the impurities could

be trapped before entering a region such as a heat exchanger where the solids could be

rleposited and cause plugging.

Compressor oil removal from helium requires a demister and adsorption bed (this bed

also could be used for water and carbon dioxide removal). The problem of oil removal is under study at Brookhaven National Laboratory.

6.4. i System Configuration

A system which separates the helium flow in the refrigerator from the flow in the

transmission line looks very attractive for maintenance of purity in the high voltage

sections of the system. This pumped loop system offers at least two advantages over the

single loop system. First of all, if one component fails, the other component may not require shutdov/n if the downtime is short. Ser:ondly, the pumped loop system would essentially eliminate the- addition of impurities into the helium circulating through the transmission line. Since the helium would remain far below ambient temperatures, out-gassing

in the long line would be eliminated. A possible source of impurities would be from the

make-up gas. Because the pumped loop would be isolated from the refrigerator, the make-up

rate in the loop should be minimal.

46
The major disadvantage of the pumped loop configuration is the additional capital

cost for the heat exchanger between the pumped and refrigeration loops and the pump.

However, these costs should be small compared to the total cost of the system; the additional cost would probably be worthwhile in terms of increased overall reliability. Dean

[10] seems to have implied that a pumped loop system would be much less efficient than the

direct refrigeration system; however, two other studies [11, 12] have shown that the two systems have comparable efficiencies over much of the operating range of interest.

6.5 Conclusions and Recommendations

There is a very real possibility that impurities could adversely affect the operation

and reliability of superconducting transmission lines. Simple calculations based on the

accumulation of impurities into a single spherical particle show that to minimize the

impurity problem:

1. the initial impurity level of the helium put into the system

should be less than 1 ppm;

2. the average leak rate of air into the system should be less than 0.01 g/day;

3. the compressor oil concentration in the helium entering cold

sections should be roughly 0.1 ppb or less.

The above numbers are based on conservative assumptions and should be considered as order of magnitude estimates. As the design of the various transmission lines becomes more finalized, the calculations should be repeated for each specific line geometry.

The impurities can be removed by adsorption and/or filtration. A drawback to using

adsorption with present-day technology is that the effluent must be analyzed frequently

and with great precision to determine when the bed is saturated. Although there would be

no sampling problems when analyzing an ambient temperature bed, there could be problems in

sampling the effluent from low temperature beds where air is the impurity and a likely

contaminant of the sample.

It should be pointed out that the major objection to analyzing the effluent is not

the analyses itself, but in obtaining a reliable sample. Analytical equipment exists that can detect impurities in the ppb range [9]. However, obtaining a sample which contains

less than one ppm of contaminants in a field operation will be difficult. Therefore it

is recommended that alternates to sampling and analysis be considered. There are at least

four options which might be better. Some criteria for selecting which, if any, of the

alternates is the best include reliability, reproducibility, sensitivity, simplicity along

with stability during temperature and pressure excursions.

The first alternative is to monitor the concentration of impurities on the solid

adsorbant. A paper study would be required to determine which of the physico-chemical

properties of the solid phase were the most promising as an impuritv detector before any

experimental work was recommended

.

A second alternative would be in situ analysis of the gas flowing through the bed.

There are several physical properties of helium mixtures that might be used as detectors of

increased impurity concentration. However, most of these properties are functions of

temperature and pressure as well as concentration. Also, the sensitivity to concentration

changes might be too low for transmission line applications. Even so, this concept warrants

a theoretical feasibility study; experimental work would follow if a promising detection

method were found.

Filtration of cold gas is the third alternative to sampling the effluent. Therefore,

the feasibility of using filters should be investigated in an experimental program. An

important consideration in filtration is the allowable pressure drop through the filters

which depends upon the flow rate through the filter and the pore size of the filter. Flow

rates can be adjusted by using parallel filters but the pore size depends upon the particle

size distribution of the relevant impurities in helium. Thus the size distribution, at least to determine what fraction of particles are less than one micron, should be determined as a~function of the contaminant, the leak rate to helium flow ratio, i.e. impurity

47
concentration, and the temperature. Commercial filters and gas chromatographs could be

used for this experiment.

Lastly, there is the possibility that a combined adsorption bed and filter system

could be used. In this system a pressure drop change across the filter could be an indication that the adsorption bed was saturated. Probably the major drawback to filtration,

providing the particle sizes were large enough, is the sensitivity of the pressure drop

to temperature or pressure fluctuations; such excursions could mask the true pressure drop

in the filters. Also, with large temperature excursions, some of the impurities might be

"redissolved" in the gas stream and recondensed at some point downstream which could cause

plugging.

To improve the overall reliability of a superconducting transmission line the concept

of the pumped loop system should be considered. This system would prevent impurities

which enter the refrigerator from contaminating the transmission line.

Finally, if helium is to be the dielectric, the possibility of impurities affecting

the breakdown strength of helium should be investigated further. Meyerhoff [5] plans to explore the degradation of breakdown strength by impurities in their coaxial cable design

sometime in the future. At the time of these tests the possibility of effects due to dielectrophoresis should be considered.

48
6.6 References

1. Strobrldge, T. R. , National Bureau of Standards, Boulder, Colorado, private communication, April 1975.

2. Dean, J. W. , Helium refrigeration system reliability for large superconducting systems,

Brookhaven National Laboratory Informal Report BNL 19405 (1974).

3. Purer, A., Stroud, L. and Meyer, T. 0., Simple technique for the ultrapur if ication of

helium. Advances in Cryogenic Engineering, 10^, Plenum Press, New York (1965), p. 398.

4. Meyerhoff, R. W. , Development of a rigid AC superconducting power transmission

line. Advances in Cryogenic Engineering, 19^, Plenum Press, New York (1974), p. 101.

5. Meyerhoff, R. W. , Union Carbide Corporation, Linde Division, Tarrytown, N.Y. , private

communication, April 1975.

6. Pohl, H. A., Nonuniform field effects: dielectrophoresis , electrostatics and its

applications, Ed. by A. D. Moore, John Wiley and Sons, New York (1973), p. 336.

7. Bird, R. B., Stewart, W. E. and Lightfoot, E. N. , Transport phenomena, John Wiley

and Sons, New York (1960), p. 163.

8. Seitz, C. A., Bodine, W. M. and Klingman, C. L. , Apparatus and procedure to reduce

impurities in helium to less than one part per billion, J. of Chrom. Sci. , 9_, (1971) p. 28.

9. Harrison, W. E. , Instrumentation for analysis of helium for trace impurities,

Brookhaven National Laboratory Informal Report BNL 19570 (January 1975).

10. Dean, J. W. , The thermal efficiency of a pumped supercritical refrigeration system.

Cryogenics, 14, (1974), p. 387.

11. Cairns, D. N. H. , Swift, D. A., Edney, K. , and Steel, A. J., Refrigeration and circulation of helium in superconducting power cables. Low Temperature and Electric Power,

Proc. Inst, of Refrig. , London (1969), p. 155.

12. Daney, D. E. , Refrigeration for an 8 K to 14 K superconducting transmission line,

Nat. Bur. Stand. (U.S.) NBSIR 74-375 (October 1974).

49

APPENDIX

NEGATIVE DIFFERENTIAL FLOW-RESISTANCE

IN SUPERCRITICAL HELIUM*

(to be published in Cryogenics )

V. Arp

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

'^A contribution of the National Bureau of Standards and not subject to

copyright.

A-1
Introduction

The development of helium cooling systems for large superconducting

magnets, power lines, etc., leads to consideration of various helium

flow instabilities which can possibly occur in their use. Cooling

system instabilities have been widely documented and analyzed for other

fluids, at higher temperatures of operation [1, 2, and 3] but until

recently there has been comparatively little analysis applied to helium

flow instabilities [4,5], though troublesome helium oscillations con- stitute a well-known lore of cryogenicists . One such instability is the

Ledlnegg Instability, caused by negative differential flow resistance,

which sometimes occurs when two-phase or near-critical fluid flows

through a heated pipe [4,6]. Depending on circuit parameters external

to the heated section, the flow can develop an oscillatory component, or move excursively to a new operating point outside of the region of

negative flow resistance. It is the purpose of this paper to discuss

the conditions under which a negative flow resistance can occur, but not

to discuss the consequent system instabilities which may develop.

A-2
Nomenclature

K

SI units

2 A = flow cross-section m'

c = adiabatic sound velocity m/s

D = effective diameter of flow channel m

(= 4 X Area perimeter)

f = Fanning friction factor —

H = enthalpy J/kg

_ d£_

I _ dimensionless isentropic

s p BP compressibility

L = length of heated channel m

m = mass flow rate kg/s

M = Mach number = u/c —

P = pressure Pa

Q = AL = total heat input W

r = ratio of specific volumes, ^2^^± —

Re = Reynolds number —

u = velocity m/s

3 V = specific volume = 1/p m /kg

w,w' = defined by equations 16 and 17 —

X = distance along channel, in direction of flow m A = heat input /unit channel length W/m

3

p = density = 1/v kg/m

1 aP I p BT I „

CP = — TT— = TT— = Gruneisen parameter — ^ p 8U ' p T Bp ' s ^

A-3
Background

The cause of negative differential flow resistance can be understood

conceptually with the aid of the helium state diagram, figure 1, and the

schematic flow diagram, figure 2. Consider that dense fluid, of enthalpy

Hj^j enters a heated conduit, warming at approximately constant density

until the transposed critical line is crossed, at H , and then at ever

tc

decreasing density (approximately like that of an ideal gas) to the outlet enthalpy H2 given by

H„ = H, + ?

2 1 m

The dense, relatively slow moving fluid at the inlet gives rise to a lower pressure gradient than does the dilute, faster moving vapor near

the outlet (at the same mass flow rate) . An increase in the mass flow

rate causes a decrease in H2 and hence a movement of the point where

H = H^^ towards the conduit exit. As a consequence, a smaller fraction

of the conduit length experiences the relatively high pressure drop

associated with low density flow. In some cases the decreased length

of high velocity flow more than compensates for the higher pressure

gradients in both the low velocity and high velocity sections, resulting in a lower total pressure drop as the flow increases.

The first analysis of this type of unstable flow was made by

Ledinegg [6] in 1937. Since then, a number of other studies have been

made, the most comprehensive of which are by Zuber [1] in 1968, and

Hands [4] in 1974. The major problem with all these studies has been

the lack of a satisfactory description of fluid properties in the

supercritical range and as a result the analyses lack quantitative

accuracy. To quote from Zuber, "It is evident from the preceding

results that the success of any analysis concerned with the mechanism of

flow oscillations and of heat transfer at supercritical pressures will

depend to a great extent upon the ability to describe more accurately

the thermodynamic state of a fluid and the transition phenomena which

take place at supercritical pressures."

A-4
In this paper we start with equations 1-3 which are thermodynamically exact momentum and energy balances for steady one-dimensional,

single-phase fluid flow, in all fluid ranges except right at the critical

point [8]. For flow through a horizontal tube of constant cross-section:

(l-M^)K^ i £ = - (1 + qs^r) I

M^f _ c|^i2

_A_

mc \ = - (1^) f

M^'f + (1-(14<P)M^)

^

(2)

c mc

,T^,2.d ,1 2. ,^,sl 2,,2^, 1 2 A

(1-M ) (- pu ) = (1-Kp) - pu M f + cp - pu —2" (3)

mc

2 where c pK = P (4)

and puA = m. (5)

In numerical work, described later, these equations have been integrated

using a precise helium state equation. However, better insight into the

problem is obtained by first considering approximate forms of the integrated results.

Analytical Framework

The system which we analyze is shov-TL in figure 2. The heated

section of tube lies between the planes 1 and 2. Between planes 2 and 3 is placed a flow restriction across vrhich occurs a pressure drop

^2-3 " ^""^^2

where k is an unspecified coefficient, and the minus sign indicates a pressure decrease, consistent with equation (1) . A pressure restriction downstream of a heated section is known to enhance' the possibility

of density-wave flow instabilities [5 J; an entrance restriction, which

we do not include in the svstem, will tend to inhibit flow instabilities.

A-5
The total pressure drop from 1 to 3 is then found by adding the integrated pressure drop between planes 1 and 2 to AP^_^, or.

-^1-3 = - { f + M(i Pu^)^ + / (f Pu')dx] (7)

where the symbols 1 and 2 in the limits and in the subscript refer to

properties which are evaluated at the planes 1 and 2 of figure 2. It is

important to note that these integrations must be performed simultaneously

with integration of equation (2) for the enthalpy gradient, so that the

two independent parameters P and H in the equation of state p(P,H) are determined at every point from 1 to 2.

We make three basic assumptions: (a) that the fluid velocity

is far below sonic velocity, such that

« 1 (8)

(b) that the heat input per unit length of tube. A, is constant, and

(c) that the enthalpy gradient due to the frictional pressure gradient

can be neglected in equation (2), i.e., that

4^ » I M^fc^ (9) m D

In this approximation the enthalpy increases linearly along the tube,

(10)

AH ^ dH ^ A

L dx m

and the total pressure drop is given by

.2 2 .2 AT> 2 m f /• , , ,^ , k. mA r .9v, , -^1-3 = D — /

A 1 vdx + (1 + 2) -TA

{1 Wp^ •2 m / 0 v. , . 4 _ 2 , , T

° a* 1

where we have neglected the variation in friction factor, f, with

velocity, and used the thermodynamic identity

A-6
^ = (—) (12)

c

In the previous studies, the above integrals, or their equivalents,

have been split up into an incompressible fluid zone plus an ideal

gas zone, sometiines with the addition of a third zone characteristic

of liquid-vapor mixtures. In this study no division into various

zones is made. We assume that the fluid conditions at the inlet (point

1) are specified. Using equation (10), these equations can be revrritten,

-^1-3 =

D -2

i

V dH + (1 + -) - / (g^)p dH

.2 . ^ ^ 1 ^1

J. k m^f 72 1^ 3 + k— +- -- J ^

V dH (13)

iVA H, c 1 where H^ = H^ + .VL/m.

It is important to note that the integrands in eq (13) depend

implicitly on m through their dependence on P(x). However, if the

total pressure drop between 1 and 2 is small compared to the average

pressure, this contribution to the dependence of -^2_-3 °^ TM will be

small compared to that from the factors multiplying the integrals or from the upper limits to the integrals. Point by point within the

heated channel, the relative dependencies of the specific volume v on the two independent parameters P and H is given by the ratio

Bp „ dx o T , 1 1 J H ^ 2_ 1-Kp 2 2 dx

Sv dH D cp ^ ^

dH

^3H^p dx

where we have used (1), (2), (8), (9), (10), and the identity

P 9d

H

A-7
We now make the assumption that this ratio is much less than one, or

- 2 M^f -4r « 1 (lA)

D cp ^2 1

A more stringent requirement is developed later, at least for the case k = 0, so that eq. (14) does not limit the validity of the results.

Using arguments developed later, one can show that (14) will be satisfied

2 for supercritical helium systems provided L/D << (10 to 100) /M , and

also that the last term in eq (13) will be negligible with respect to the

second term. These approximations can be reviewed when the calculation is

completed.

Differentiation of equation 13 thus yields

^ (-AP. „) = (3 /2 V dH - ^ vj am 1-3 I 4^

m 2 D ^2^

kmv^ ,

'

* + -y^ , (15)

A

where (8v/9H) „ is the derivative evaluated at point 2.

P >

It is convenient to define .,

''2 ^2 w E „

= (16)

1 f2 , avg

XT „ J V dH

. "2""l

and

(—) (—

)

—1 r2 ,OV. j„ (^) / (3^)p dH an p,avg

Z L

(17)

A-8
so that equation 16 becomes

mfv

(18)

In physical terms, w and v/ are the ratios of the specific volume (or

volume derivative) at the exit from the heated section to the average

of the same quantity over the length of the heated section. As the

volume expansion ratio v^/v^ increases above 1.0, so will w and w* (when v^ is to the left of the transposed critical line), but at smaller

rates. Only when w reaches 3 or w* reaches 2 can any term in equation

18 become negative. To see which occurs first, we must investigate the

approximate equation of state in the critical region.

A clue to the approximate form of the equation of state in the

near-critical region is contained in figure 4, which shows that the

2 quantity c /cp is approximately constant at the transposed critical

line, and varies only by a factor of about two within the region of

interest for this calculation. This is in noticeable contrast to the

specific heat, C^, for example, which varies by an order of magnitude

in the same region. Thus, as a first, rough, approximation, one can

let c /(p be a constant, and integrate equation 12 to obtain

as the equation of state. This exponential dependence of v on H is seen approximately in the helium data, figure 1. From this figure

one can estimate that this equation of state would be quite inadequate

The Near-Critical Equation of State

V = v^ exp (^2 - ^1^) (19)

c
at expansion ratios

'^2^^l' greater than 3 or 4. However, using this

equation, a short bit of algebra shows that it predicts

w = w* r£ nr r-1 (20)

where r is the expansion ratio, '^2^^1' According to eq. 20, an ex- pansion ratio of 4.9 would be required in order that w* =2, and r must reach 17 before w = 3. These numbers, especially the latter one,

far exceed the realistic range of the model, but they do make the

general point that the condition w' = 2 will be reached more quickly

than the condition w = 3. To explore this further, w(r) was calculated

numerically from figure 1, along the 2.5 atmosphere isobar, starting

at H = 40 J/mole (T = 4.2 K) . The result is shown in figure 5, along

with a similar curve for w* (r) , calculated from the helium data of

reference 7, though starting at 4.0 K. Also shown is the prediction

of equation 20. The important feature is that both w* and w reach a maximum of about 2 to 2.1 and then decrease as exit temperatures continue to rise. The conclusion from both these observations is that

the condition w* > 2 may be attainable in a single-phase expansion but

probably not the condition w > 3. (This latter could probably be

obtained by expansion of a subcooled liquid into the two-phase region.)

At this we have established that the necessary (but not the

sufficient) condition for the existence of negative differential flow

resistance, with or without an exit restriction, is w* > 2, or

Two-Phase Fluid

The calculations to this point have utilized hydrodynamic and

thermodynamic equations derived for single-phase fluid flow. However,

aH>,2 an p,avg

(21)

A-10
to the extent that the flow of a liquid-vapor mixture can be described

in terms of the flow of a homogeneous fluid with a well defined stateequation v(P,H), the results above can as well be applied to two-phase

flow. The previous studies of the Ledinegg instability have all implicitly been based on this assumption. In this respect, the quantity

2 c /cp as used throughout the paper in fact refers to the thermodynamic

derivative defined in equation 12, rather than a measured sound velocity,

which may be anomalously low in a turbulent liquid-vapor medium.

Starting in the subcooled liquid region of figure 1, as the fluid

enthalpy increases, an isobar experiences a sharp increase in slope as the two-phase region is entered, and a second, but smaller, increase in

slope upon entering the vapor phase. Since the isobar is nearly flat

in the subcooled liquid region, equation (21) is easily satisfied by

isobaric expansion from subcooled liquid into the two-phase region,

provided that the pressure is not too close to the critical pressure.

This conclusion is quantitatively consistent with the work of Hands [4].

Numerical Estimate of Necessary Conditions

Values of v, H, and v9H/9v are tabulated for helium as a function of

pressure and temperature in reference [7]. Simple numerical work with this

data leads to figure 5. The inlet pressure and temperature must be within

the shaded region to the left of the liquid-vapor line in order to find any

isobaric expansion process in which eq. 21 is satisfied; when it is satisfi

the final temperature will always be in the two-phase region or very close

to the transposed critical line. The lower portion of that shaded region,

at subcritical pressures, is predictable from the previous work of Hands [4

while the upper limit, at near-critical and supercritical pressures, is

provided by this study. For non-isobaric expansions, the upper limit of

figure 5 should be a little higher, e.g., for expansion from 3.0 to 2.4

atmospheres, w' = 2 can be reached at input temperatures as high as 3.4 K. Considering also our neglect of the friction factor variation with temperature, the upper limit in figure 5 should be regarded as an approximate

limit to input conditions which could lead to negative differential flow

resistance.

A-11
Estimate of Sufficient Conditions for Single-phase Fluid

Assume, with reference to figure A, that it may be possible for v/

to reach a little above 2.0 at the end of the heated section. Because

of the factor (1-2/^?* ) , numerical results are very sensitive to small

changes in v/ , and must be discussed with w* as an adjustable parameter,

On the other hand, for this approximate treatment, let (3/w-l)=l,

suggested by figure 4. Then the sufficient condition for a negative

differential flow resistance, within our approximations, is

or, in more convenient form

2 2

9

. 2Lfc v„ kc v^

2 where c /cp is evaluated at station 2.

In the absence of an exit flow restriction (k = 0) , the enthalpy

gradient required for negative differential flow resistance is

^ = A ^ dT 2f c^ 1 L ih - p dx D (p (l-2w' ) ^ ^

For expansions satisfying equation (21) , starting in the shaded region

of figure 5 and ending near the transposed critical line, one finds that

/ 2 A 2 2 AH will be about 2 x 10 J/kg; then, with c /(p ~ 2 x 10 m /s and

f ~ 0.005, equation (26) becomes

I

< 100 (1 - ^ ) (27)

or L/D < 10 if w* =2.2. Very short channels, with correspondingly high

temperature gradients in them, will be required for the occurrence of

negative differential flow resistance in supercritical helium systems, at

A-12
least in the absence of exit flow restrictions. This is in qualitative

agreement with a prediction of Hands [4], based upon a two-zone description of fluid properties. It should be noted at this point that equation

27 is a much more stringent restriction on L/D than is equation 14.

Physically, equation 26 means that the pressure gradient due to

acceleration of the heated fluid must be relatively large, at least

2/(l-2/w' ) times the frictional pressure gradient. The acceleration

pressure drop can be estimated from eq. 1, within our approximations, as

^ ~ ^avg 2. s c

2 2 -2-3

With cpXH/c < 1, ?s 0.1, and M « 1 (probably < 10 to 10 ) , AP/P will be very small, and the expansion will be quasi-isobaric

.

Exit restrictions, within the context of this paper, could include

orifices, Venturis, valves, or just a section of unheated line where

frictional pressure drop occurs. It is Impossible in this sense to

2 3 give a "typical" value of k, but values as high as 10 to 10 could

be reached with highly constricted orifices.

The exit restriction dominates the requirement when both k » 2 (from the left-hand side of equation 25) and

""2 fL

^1 ^

(from the right-hand side). Under these conditions, negative differential

flow resistance between 1 and 3 should occur when

V

(1 - ^, )AH (^ )„ — > 2 (28)

w 2 2 v^

c 1

The factors on the left-hand side of this equation are inter-related by

the equation of state. Assuming the exponential state equation (19) , one finds that this condition is equivalent to w = w' >2 . 3 . This is not

a reliable numerical result, because of the innaccurate state equation

A-13
used to obtain it, but it does suggest that, with a sizeable exit re- striction in place, a much more stringent condition on the fluid properties is required to reach the sufficient condition, eq. 28, than to

reach the necessary condition, eq. 19. At the same time, the additional requirements of high temperature gradients and short lines, as

for k = 0, do not appear.

Simple numerical work with the helium data [7] shows that

no realistic expansion process can be found in supercritical helium (at

least starting above the X point) which satisfies equation 28. Starting

an isobaric expansion at 2.5 K, the maximum numerical value one can find

for the left-hand side of (28) is about 0.7 at 2 atmospheres pressure;

for non-isobaric expansions the number is a little higher, but not

greatly so. Thus, this theory predicts that, with a large exit restriction in place, negative flow resistance between planes 1 and 3 will

never be found in supercritical helium systems. This is an unexpected

result, in that the existence of the exit flow restriction has the

effect of damping out this type of possible instability, in contrast to

its destabilizing effect on dynamic instabilities [5].

Numerical Integration

To explore the problem without invoking the various approximations

used in this analysis, equations (3) and (4) have been numerically

integrated in conjunction with a precise helium state equation of the

form v(P,H) [8]. The state equation does not correctly describe twophase fluid properties, so that integrations were performed only in the

single phase region, for pressures > 2.5 atm . During the integration,

the friction factor f is calculated from the local value of the Reynolds

number by [10]

-0.32

f = 0.0014 + 0.125 Re

For each integration the inlet pressure and temperature, the mass flow

rate, the channel length and diameter, and heat input must be specified.

A-14
A number of different exit coefficients can be used for each integration,

since they merely add to integrated AP^ ^

.

The numerical integrations are in substantial agreement with the

analysis above. In the absence of a flow restriction, we find that,

for single phase flow,

(1) The maximum value of w' which can be found for supercritical

helium channels is about i-r" '^2.2, starting at temperatures of about 2.5 K

and pressures of 2 to 2.5 atmospheres, though possibly higher values

could be found by expansions ending very near the critical point where

our equation of state is not accurate.

(2) >^egative differential flow resistance can be found with input

conditions of 2.5 K and 2.5 atmospheres, and very high heat inputs to

short tubes, such that w' > 2 at the outlet. This is illustrated by

the lower curves in figure 6. As pointed out by Dr. Hands [11], the

positions of the maxima and minima in these curves are quite sensitive to

small changes in the assumed equation of state of the fluid, and of the

assumed friction factor.

(3) The effect disappears for longer tubes, even though all other

conditions are satisfied. Pnis is illustrated by the upper curves in

figure 6.

(4) With other parameters held constant the effect becomes

marginal when the input temperature is raised to 3.5 K (curve B, figure

7) and is gone at an input temperature of 4.5 K (curve C) ; similarly

the effect becomes marginal at an input pressure of 3.0 atmospheres (curve

D) , and is gone at an input pressure of 4.0 atmospheres (curve E)

.

Curve A in this figure is taken from figure 6.

With a large exit restriction in place, negative flow resistance

between points 1 and 3 of figure 2 is not found under any condition of

the very many that have been tried. This is illustrated in figure 8,

which shows the disappearance of negative flow resistance with increasing

values of k, starting with fluid conditions under which it is a near maximum for helium systems.

A-15
Conclusion

We conclude that negative differential flow resistance, and the

consequent tendency toward a Ledinegg instability, will not occur in

single-phase helium cooling systems except under very restricted con- ditions of low input temperature, near-critical pressure, very high heat

input, short channel lengths, and the absence of a large exit restriction pressure drop.

Acknowledgement

Michael Jones has contributed to many useful discussions of this

topic. Brian Hands has stimulated the work through his publications and

lively correspondence. The work was supported by Brookhaven National

Laboratory and the ERDA.

A-16
References

1. N. Zuber, "An analysis of thermally induced flow oscillations in

the near-critical and super-critical thermodynamic region", NASA

report NAS8-11422 (1966).

2. J. A. Boure, A. E. Bergles, and L. S. Tong, "Review of two-phase

flow Instability", ASME paper 71-HT-42 (1971).

3. J. C. Friedly and V. S. Krishnan, "Prediction of non-linear flow

oscillations in boiling channels", AIChE paper 14 presented at

the ASME-AIChE Heat Transfer Conference, Tulsa, Okla (1971).

4. B. A. Hands, "A re-examination of the Ledinegg instability criterion

and its application to two-phase helium systems", presented at

Symposium on Multi-phase flow systems, Glasgow, Scotland 2-4 April

(1974); also, "Pressure drop instabilities in cryogenic fluids,"

Adv. Cryo. Eng. 20, 355 (1975).

5. M. C. Jones and R. G. Peterson, "A study of flow stability in helium

cooling systems", ASME paper 74-lvA/HT-24 (1974).

6. M. Ledinegg, Die Warme 61, 891 (1938).

7. R. D. McCarty, "Thermophysical properties of helium-4 from 2 to

1500 K with pressures to 1000 atmospheres", NBS Technical Note

631 (1972).

8. V. Arp, "Thermodynamics of single-phase, one-dimensional fluid

flow". Cryogenics 15, 285 (1975).

9. V. Arp, "New forms of state-equations for helium". Cryogenics 14 , 593 (1974).

10. E. C. Koo, ScD thesis, MIT (1932); result quoted in W. H. McAdams

,

Heat Transmission, third edition, p. 155, McGraw Hill, N.Y. (1954).

11. B. A. Hands (private correspondence)

.

A-17
oE uo >.

M-(

U

p.

Co

4-)

(U CO o a.I o S

•H 4-1 y <u 3 +J

0) 4Jo

•HId e c 3 -H

cd

iH cn <u

cu (U

C

•H tH

O

0)0)0 3 cn 4J O O J-i > o a • •H cn (1) (U cn •H !-i o u 3 Pcu CO cn a. cn

cn (U ccJ

0)

a 4-1

H .H cu ^ J3

^< 4J • dJ rH > T3

(U cn td

5-1 3

00

lOLU/ LUD 'A e

A-18
1 2 3

Fl ow

uniform external heat input

_ * i I

jigg high density iiliiSiiijiS

Igl::

1 ov/ ve 1 oc i ty

low density

high velocity

Approximate location of

transposed-critical

pressure and temperature

or liquid-vapor transition

Exit

restri cti on

Figure 2. Schematic diagram of fluid flow through a heated channel,

defining the planes 1, 2, and 3 respectively before and after

the heated section, and after the exit restriction.

A-19
oooCOoCM o•'—>

QiU

U =J <U 6 00

4-1 3 -H S -H

rt

CC

>-l -H tH S ^

CO o

CO o

4->

>^ ,n

13

(U T3

•H>

•HT3T3

CU

>-i CO

:3cr

CO . (U

CO

C

CUU iH

:3CO r-t CO CO (U U

V-l -H CX 4-1 •H e U 3 O

•H

0) (U XI COo

.H

a

CO CO

CU CO > >-i

(1) 4J

CO

(1)

u ^ O 4-t

133O

CO

CO

U-l ^ O +J

>y CU 4J •H IW

CJO

O

H CO

CO

CU>

J-l o

(U

CO

0) • CO U

CO U-l CU CO O

J-l

t)0

•rl

(X4

OO o O

CM

A-20
^3- CNJ

O CO o

•H EC

M-l to

•H ^O >

0) CD

Cu

CO <u

CU cfl bO U

nJ OJ

>-i >

CO ^

II (U

V ^ e

S-i 3

•H

O iH

•H (1) 4-1 CO > a

•I- c

•I- o CO CM •H

CO o

CM c CO

4-1 CO •H

CO

a 4-1 X >-l X 0) o

CO M-l 0) (1) >

4-1 rHo II 14-1 7-t > o O 4-1 •H 12 o CO

M-( •H

•H T3 4J <u U C CJ e

(U ca

C 3 D iH

CO M-l

O>

II CM CO

a

CO •H

Td CO U-l C •H

CO CO

a

u (U CM a- CO 4J CO 0) <u >-i 6 XI •I- cd C u CO

cc! CM CO a :3 o

4-> e

QJ 4-1 4-1 CO CO c • do 0) u3

(30 •H

0) in e • 3 CN

r-l O +J > CO

A-21
TEMPERATURE, Kelvin

Figure 5. Helium phase diagram. All isobaric expansions leading to w' >

(defined by eq. 17) originate within the cross-hatched region on the

left.

A-22

|75X 3925 I
1 \—I / I I I l/L

.001 .01

m, kg/s

figure 6. Calculated pressure drop as a function of nass flow rate, for

several channel lengths. Between the dashed lines eq . (21) is satisfied

(v/ > 2) . Negative differential f lovr resistance disappears at L/D > 50

in this example.

A-23
io3 rr

10

to a.

<1

10'

10

T"—I I I I I I U

A

LA

2.5 cm ^(D= 1.784cm)

20 cm 600 W/m

Inlet Conditions

Pa

J \ I .001 .01

m, kg/s

Figure 7. Calculated pressure drop as a function of mass flow rate for

several fluid conditions at the inlet (plane "1" of figure 1). Curve

A is the L = 0.2 meter curve from figure 6.

A-24
10

10

Q.<

10

10

0

A = 600 W/m _

L = 0.2 m

P = 2.5x10^ Pa _

T = 2.5 K A = 2.5 cm^(D= 1.784cm)

,001 .01 1 m, kg/s

Figure 8. Calculated pressure drop as a function of mass flow rate for

several different exit coefficients k (defined by equation 6) . The

k = 0 curve is the L = 0.2 m curve from figure 6. Between the dashed

lines eq. (21) is satisfied (w' > 2). Negative differential flow

resistance disappears as the exit restriction (k) increases.

A-25
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 75- 823

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

HELIUM RESEARCH IN SUPPORT OF SUPERCONDUCTING POWER

TRANSMISSION

5. Publication Date October 1975

6. Performing Organization Code

275 .05

7. AUTHOR(S) V. D. Arp, D. E. Daney, N. V. Frederick, M. C. Jones,

P. R. Ludtke, W. R. Parrish and R. L. Powell

8. Performing Organ. Report No. NBSIR 75-823

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2750551

11. Contract/Grant No.

ERDA, E(49-18)-2128

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Electrical Energy Systems Division

U.S. Energy Research and Development Administration

Washington, D.C. 20545

13. Type of Report & Period Covered , , Annual

Sept. 1974-Julv 1975

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.) This is the first annual report on a program of helium related research in support

of superconducting power transmission. Program areas reported on are concerned with

the dynamics of helium cooling systems theoretical aspects of oscillatory behavior

and experiments --and helium related measurements. The latter include pressure measure- ment, temperature measurement and the problem of impurity levels in the helium

refrigerant.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Cooling system; cryogenics ; helium-cooled electrical leads;

helium impurities; microwave cavities; negative differential flow resistance; pressure

measurement; system dynamics; thermometers.

18. AVAILABILITY [X Unlimited

I Q_ For Official Distribution. Do Not Release ro NTIS

[3 J Order From Sup. of Doc, U.S. Government Printing Office

Vfashington, D.C. 20402, SD Cat. No. CH

Order From National Technical Information Service (NTIS)

Springfield, Virginia 22^1

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