'Reference

NBS

Fubli V, ^

cations

NBSIR 79-1618

AlllDM SSlSfiE

HELIUM RESEARCH IN SUPPORT OF

SUPERCONDUCTING POWER TRANSMISSION

ANNUAL REPORT

(October 1977-September 1978)

Prepared by

THERMOPHYSICAL PROPERTIES DIVISION

NATIONAL BUREAU OF STANDARDS

BOULDER, COLORADO 80303

-Qe

100

.U56

79-1618

1979

Prepared for

BROOKHAVEN NATIONAL LABORATORY

POWER TRANSMISSION PROJECT

UPTON, NEW YORK 11973

NBSIR 79-1618

1 » I

Bureaa JAN 3 1

HELIUM RESEARCH IN SUPPORT OF

SUPERCONDUCTING POWER TRANSMISSION

Annual Report for the Period

October 1, 1977 - September 30, 1978

Prepared by

Thermophysical Properties Division

Center for Mechanical Engineering and Process Technology

National Bureau of Standards

Boulder, Colorado 80303

D.E. Daney, Editor

Contract No. 433475-S

Prepared for

Brookhaven National Laboratory

Power Transmission Project

Upton, New York 11973

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Luther H. Hodges, Jr., Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

1980

CONTENTS

Page

1.0 THERMAL CYCLE TESTS OF MODEL CABLE 1

1.1 Introduction 1

1.2 Experimental Apparatus 1 1.2.1 Instrumentation 5 1.2.2 Test Procedure 8

1.3 Cable Clamp Assembly Procedure 9

1.4 Results and Discussion 13

1.4.1 Cable One 13

1.4.2 Cable Two 15

1.4.3 General Discussion 18

2.0 CABLE COOL-DOWN EXPERIMENTS 23

3.0 COOL-DOWN COMPUTATIONS 26

Cool-down of Superconducting Power Transmission Lines with

Single Phase Helium (paper presented at the 71st Annual Meeting of AICHE, Miami Beach, Florida, Nov. 12-16, 1978) 1

1 i i
During FY 78, the NBS Thermophysical Properties Division program of

supporting research for Superconducting Power Transmission Line (SPTL)

development focused on three tasks:

1) Numerical computation of SPTL cool down by both single stream and

counter flow methods

2) Experimental modeling of counterflow SPTL cool down

3) Thermal cycling of lengths of lead-sheathed model cable destined for

testing in the BNL 5th Ave. facility.

The preparation of computer codes and numerical computation of SPTL cool

down were completed and the results are given in Section 3. These

calculations confirm our original intuitive judgment that cool-down times for

the counterflow arrangement can be long - twenty days or more. Greater than anticipated computer run times and costs required a reduction of effort on experimental modeling of counterflow cool down.

Consequently, completion of this task will be delayed until FY 79.

Two sections of cable underwent extensive thermal cycling, and the

results of these tests are given in Section 1. The complex structure of the

cable leads to unusual (although reproducible) load vs time curves. Funding limitations required postponement until FY 79 of the

experimental evaluation of heat flow sensors as a means of non-intrusive

vacuum indication for SPTL vacuum envelopes. This task together with

experimental modeling of cool down will form the heart of our program in

FY 79 .

Key words: Cable cool-down; cool-down helium; liquid helium; superconducting

power transmission, thermal cycling, thermal stress.

iv
1.0

THERMAL CYCLE TESTS OF MODEL CABLE

(C. F. Sindt and P. R. Ludtke)

1.1 Introduction

The goal of these tests was to investigate the thermo-elastic behavior

of a 3.5 meter section of BNL model cable while the cable is subjected to

repeated thermal cycles between ambient temperature and operating

temperature. In practice, the ends of the SPTL cable will be fixed (i.e.,

the length of the cable held constant) so that a significant thermally

induced axial stress will develop in the cable as it is cooled.

The cable is built up from a number of helically wrapped layers (bronze

core, superconductor, dielectric), one of the outer layers being a lead

sheath which provides a hermetic seal (see figure 1.1). The cool-down

tensile load produces an elastic deformation in the helically wound elements

which act as coil springs. If friction between these elements is neglected,

then this spring load is small compared to the load on the lead sheath,

which is stressed beyond its elastic limit during cool-down. Likewise, the

lead sheath will be compressed beyond the elastic limit during warm-up.

Although repeated thermal cycling of an operating SPTL is not expected, it is

nevertheless necessary to provide for this contingency. Thus the cable must

remain functional throughout a number of thermal cycles.

In these tests, two different 3.5 m lengths of cable were subjected to a number of thermal cycles while maintaining the cable length constant. The

primary test objective was to observe if physical damage to the cable would

occur as a result of thermal cycling. Additional objectives were: to

determine the cable tensile and compressive loads during thermal cycling; to

test the ability of the end clamps to withstand thermal and assembly cycles;

and to determine if the cable or end clamps developed leaks at operating

temperature and pressure.

1.2 Experimental Apparatus

The test fixture, figures 1.2 and 1.3, must meet several requirements in

these constant length thermal cycling tests: 1) it requires a mechanism for

maintaining the cable length constant with varying load; 2) it requires a dewar and cryogenic fluid system for cooling the cable to LN 2 temperature

(77 K); and 3) it requires a gripper and seal arrangement to transmit load

from the cable to the test fixture while maintaining a hermetic seal with the

lead sheath.

The test fixture, which accommodates a cable segment, has a rectangular

steel framework built up from two 100 mm square tubes 5.4 m long that are bridged at each end by 75 x 127 mm H beams, 0.5 meters long. A screw mechanism at each end may be manually adjusted so as to maintain the cable
Figure 1.1 Cable cross section, cut back view

2
3

Figure

1.2

Cable

test

apparatus
4

Figure

1.3

Photo,

cable

test

apparatus
length constant in the face of variable loads- The cable is enclosed in a polyurethane foam insulated spool piece (74 mm ID) and the end clamps are enclosed in the vacuum insulated housings at each end. The cable, spool

piece and end housings are all supported at either end by rails with linear

ball bearings, figure 1.4.

The cable assembly is isolated from forces in the support structure by means of internal and external bellows in the end housings, as well as by means of 0-ring slip joints at the end housings, figure 1.5.

1.2.1 Instrumentation

The length of the cable is monitored with 30 power microscopes which

are aligned with view ports 86 mm from each end of the spool piece. These

microscopes are supported from the concrete floor by heavy duty tripods, so their position is independent of the load on the cable and test fixture. The

cable length reference points are scribe marks on invar rods which are attached to the end fixtures. The cable length was held constant to within + 0.12 mm using this system of microscopes and adjusting screws. Cable temperatures were determined with type T thermocouples

referenced to a boiling liquid nitrogen bath. For the first cable segment

tested temperatures were measured at three positions: at the axial midpoint

on the lead sheath, at the load cell end of the bronze core, and 15 mm into

the wrapped dielectric.

For the second cable segment tested, a single thermocouple was mounted in the wrapped dielectric at the load cell end. The uncertainty in

the measured temperatures is estimated to be less than 1 K.

The cable was cooled from one end rather than uniformly along its

length, so the purpose of these temperature measurements was to determine

when the entire cable segment had cooled to the desired temperature. The

measurements were not intended to represent the temperature of the cable

composite since the sensor could not be placed in the body of the cable

without destroying the integrity of the lead sheath.

The axial tensile or compressive load on the cable was determined with a load cell (9000 N (2000 lb) capacity). A purely axial load at the cell is

assured by the guide mechanism for the cable extension tube shown in figure

1.4. The calibration accuracy of the load cell is .25 percent of full scale

(2000 pounds). The precision of the load cell was checked with class S weights; the measurement uncertainty was 0.1 percent.

The axial load on the cable due to external forces differs from the

force on the load cell and is given by the expression

F

c Fd + ^ ± Ff ( 1 )

5
Figure

1.4

Load

cell

end,

test

apparatus
O)O

7

Figure

1.5

End

assembly

schematic
where is the force on the cable, is the force measured by the load

cell, Fp is the pressure force due to the differential pressure across the

end fixtures, and Ff is the friction force on the cable and cable

extensions. The friction force from the supports and 0-ring seal is

estimated to be less than ^ 45 N (+ 10 lbs) —small compared to the other

forces. The pressure force, Fp, is due to the differential pressure across

the inner bellows assembly. A tensile force of 151 N (34 lbs.) results.

In considering the effect of internal pressurization of the cable, we note that the behavior of a composite cable can be much less predictable and

reproducible than the behavior of a noncomposite cable. Referring to figure

1.5, the axial force on the composite cable due to internal pressurization

is approximately

^cp = P - (A3-A^) d-a)C] (2)

where P is the differential internal pressure, Ag is the inside area of the

lead sheath, A^ is the inside area of the bronze core, a is the void

fraction of the composite inside the lead sheath, and C is the degree of

coupling between the inner composite and the lead sheath and clamp assembly.

For complete coupling (C=l) and zero porosity equation 2 gives the pressurization force on the cable as that for a heavy wall tube with inside area . For zero coupling, the force is that for a thin walled tube with inside area

Ag . For an internal cable differential pressure of 1.5 MPa, F^p may vary

from 2470 N (555 lbs.) to 340 N (77 lbs.), depending on the voids in the inner

composite and the degree of coupling between the lead sheath and the inner

composite.

Another important consideration is the effect internal pressurization

has on the spring constant of the various metal helices in the cable. The

bronze core and other metal helices may exert axial forces as a result of

temperature change, and these forces may change as the result of internal

pressurization. This is because the various helices behave as springs in the

absence of friction, but could tend to behave as rigid tubes if there is

friction between them. Such friction could decrease if the lead sheath were pushed radially away by pressure, or increase if the sheath contracted more

than the rest of the cable during cooldown.

1.2.2 Test Procedure

Two cable samples were tested, each by a different procedure. Cable

one was cooled and then pressurized, whereas cable two was cooled with the

cable interior pressurized. The latter procedure simulates the expected

operating conditions more closely.

8
Cable one was first leak checked by pressurizing the cable interior

with helium gas to 1.5 MPa and measuring the rate of pressure decay in the

valved-off system over a 15 minute period. The sensitivity of the pressure

measurement was 3.4 kPa. All pressurization and depressurization cycles were

made in 345 kPa increments, so that the cable could be maintained at a fixed

length by means of the adjusting screws. After the leak check, the pressure was bled down to ambient pressure

and the cable was cooled to liquid nitrogen temperature by flowing LN 2 through the bronze core and around the outside of the cable. The LN 2 flow

rate was adjusted so as to achieve cool-down in about 90 minutes. The cable

was then again leak checked by 'meas ur ement of the pressure decay using helium

gas prechilled to about 80 K. Following the leak check, the cable interior

was bled down to ambient pressure (again in 345 kPa increments to allow for

cable adjustment) and the cable was warmed by flowing 350 K nitrogen gas

through and around it. The cable warmed to 200 K in about 3 hours. The

remainder of the warm-up was achieved unattended in the following 12 hours

using a low flow rate of ambient temperature nitrogen gas.

The procedure for cable two was the same, except it was cooled down

with the interior pressurized to 1.5 MPa. Cable one was cycled 20 times and

then removed for inspection. Cable two was cycled 5 times, removed for

inspection, then reassembled and cycled an additional 15 times.

Both cables were preloaded with 590 N (134 lbs) tension (440 N, 100

lbs, load cell and 150 N, 34 lbs, bellows force) before the first thermal

cycle. The cable length was then referenced by fixing the microscope cross hairs on the scribe marks of the invar rods, and this length was maintained

throughout the test series.

1.3 Cable Clamp Assembly Procedure

Because the cable clamp assembly procedure may be of interest in its own right, we have included it here in some detail. The lead seal and terminal

clamp assembly for attaching the end of the cable to the test fixture was provided by BNL . An enclosure cap was added to the clamp assembly, as shown

in figure 1.6, to facilitate pressurization of the inner line and to provide

the structural link between the cable and the test fixture.

The clamp assembly was installed as instructed by BNL. Two layers of

nylon filament tape were wrapped over the mylar-bronze wrap of the cable for

the 76 mm length covered by the flexible end of the outer clamp assembly.

After positioning the outer sleeve assembly, an aluminum ring was slipped

over the flexible end while a regular hose clamp compressed the flexible

fingers. The sleeve assembly O.D. was 60.3 mm (2.375") and the ring I.D. was 59.8 mm (2.356") x 19 mm wide. In addition to the ring, a regular hose clamp

9
10

Figure

1.6

Lead

seal/terminal

clamp

assembly
was also used midway on the flexible end. It was Impossible to use the clamp

provided by BNL because there was insufficient room in the test fixture spool

piece for the clamp.

After securing the outer sleeve assembly, specially prepared tools with

well-rounded corners were used to form the lead into a cone shape against the

outer sleeve. Extreme care was necessary when forcing the inner cone inside

the lead sheath; it was very easy to score the lead with the sharp leading

edge of the inner cone. The inner cone was drawn into position with the

bolts used to connect it to the outersleeve. The bolts were evenly tightened

to keep the cone and sleeve flange faces parallel. The inner cone bolts were retlghtened 3 to 5 times after relaxation periods of 3 hours to allow the

lead to flow between the cone-shaped enclosure.

Next, the stainless steel strands were pulled tight across the back of

the inner cone and bent sharply around the outer corner in the inboard

direction. The ends were clamped flat against the outside of the inner cone piece with metal clamps. The end cap was then bolted securely to the back of

the inner cone clamping the stainless steel strands, while maintaining

uniform spacing between the end cap and inner cone.

A solid copper wire of 1.6mm diameter was tapped in between the end cap

and the stainless steel strands in order to keep the 90° corner of the

stainless steel strands tight against the inner cone corner. The metal clamp

around the ends of the strands was then replaced with two layers of nylon

filament tape, thus securing the ends of the stainless steel strands to the

O.D. of the inner cone, as shown in figure 1.7.

A split clamp 1.3 cm thick, was then bolted together around the inner

bronze core. One side of the split clamp fit flat against the end plate and

the opposite side was machined to fit just inboard of the rivets securing the

inner bronze core (2 helices). The split clamp was used to complete the

structural link between the bronze inner core and the clamp assembly, thus

incorporating the bronze core as a structural member when the cable incurs

tensile stress, i.e., the clamp transmits only tension forces from the bronze

core to the end cap.

An enclosure cap was then bolted to the outer sleeve flange with

aluminum bolts. Aluminum bolts rather than stainless steel were used to

eliminate a differential contraction seal problem. Indium wire of 1.5 mm diameter was used to seal the cap to the outer flange. A special step design

with close tolerances was used to trap the indium. The spacing between the

flanges was maintained uniform while tightening the bolts. The flange bolts were retightened several times after 3 hour periods to allow indium flow and

subsequent relaxation of the bolt stress.

A 25 mm O.D. stainless tube was then bolted to the end of the enclosure

cap using the same type of indium seal. This support tube completed the

11
Figure 1.7 Photo, lead seal/terminal clamp

12
enclosure of the inner line and served as the structural member between the

cable ends and the test apparatus.

Disassembly of the clamp was quite straightforward, except care was required in removing the inner cone and outer sleeve from the cable.

Removing the inner cone was accomplished by using 3 pieces of thread stock

with nuts and washers between the inner and outer cone pieces. The nuts were adjusted to slowly force the cones apart. Hammering at the inner cone or prying between the two would damage the stepped seal surfaces. Once the lead

sheath is separated from the inner cone, the cone slides off freely.

Removing the outer sleeve from the cable also requires care. It is

possible to exert sufficient fojrce on the outer sleeve to cause yielding of

the entire lead sheath inboard from the clamp. In order to remove the outer

sleeve with minimal force, the lead must be carefully worked away from the

outer cone with a rounded tool. Separating the lead from the outer sleeve

significantly reduces the force required to swage the lead back to a cylindrical shape while removing the outer sleeve.

The lead seal clamp assembly worked very well during the two

twenty-cycle test periods; each clamp was Installed and removed three times.

The assembly functioned well as a cable terminator, with no damage to the

cable ends. There was no significant leakage during the entire test period.

1.4 Results and Discussion

1.4.1 Cable One

Figure 1.8 presents load cell vs. time for four typical thermal

cycles of the 20 cycles to which cable one was subjected. The test data is

constrained to definite time intervals, i.e., actual cool-down time may have

varied slightly (+ 10 minutes) from the 1-1/2 hours indicated. Following the

first thermal cycle, the preload on the cable changed from the initial 440 N (99 lbs) tension (load cell reading) to 1330 N (299 lbs) compression and

remained near this value for the remaining 19 tests. This shift in the

initial cable (load cell) load occurred with both cables and is attributed to

the yielding of the lead sheath which occurs during the first thermal cycle.

As the cable is cooled the load passes through a maximum and then decreases

slightly as the cable comes to equilibrium at 76 K. This behavior may be due

to creeping of the spirally wound core with respect to the lead sheath.

As the cable is pressurized, the load cell force is reduced by

approximately 4000 N (900 lbs) compared to the maximum of 2469 N (555 lbs)

that we calculate for the pressure x area term. For a solid cable the two

forces must be equal. In this case, however, it is likely that pressurizing

the lead sheath releases the grip of the sheath on the inner composite

sufficiently that the composite relaxes even though its length is held

13
14

Figure

1.8

Cable

1,

thermal

cycle

test

results
constant. A recovery of 800 N (180 lbs) in the tension load occurs as the

cable core is depressurized. This is within the range of 343 N (77 lbs) to 2466 N (554 lbs) which may be attributed to the pressure x area term, but

differs appreciably from the average change of 1600 N (360 lbs) which occurred

when the cable was pressurized for leak checks at ambient temperature. The

hysteresis in these ambient temperature pressure cycles was small. The load

decreased by 1646 N (370 lbs) with pressurization and increased by 1557 N (350 lbs) with depressurization.

The maximum and initial load cell force for each cycle is given in

figure 1.9. As both figure 1.8 and figure 1.9 indicate, the behavior of the

cable was consistent from cycle to cycle.

After test number 20, the cable was removed from the test fixture.

The enclosure cap and split end cap were removed from the clamp assembly,

revealing the end of the cable inside the stainless steel strands. We found

that the dielectric and outer dielectric screen had unraveled slightly as shown in figure 1.7. This was probably due to relative movement between the

cable layers near the severed end of the cable.

After removing the cable from the center spool piece, we found that

the lead sheath had extruded radially outward between the bronze wrapping, as shown in figure 1.10. This radial bulge or spiral annulisra occurred at the end

opposite that where liquid nitrogen coolant was introduced. In spite of the

spiral annulism the lead sheath remained intact, and there was no leakage in

this area. After inspecting and photographing the annulism, the cable was sent

to BNL for inspection and evaluation.

1.4.2 Cable Two

In view of the problem with cable one, the test procedure was reviewed and it was decided that cable two should be cooled down under pressure since this is the manner in which the cable will be cooled down in

practice. It was also decided to thermal cycle the cable 5 times and then remove it for inspection before completing the full 20 cycle test.

Upon inspection after 5 thermal cycles we found that the lead sheath

of cable two had expanded outward slightly at the "windows", where the lead

sheath was covered with only mylar. Otherwise the cable looked exactly as when it was installed in the test fixture. We saw this same "window" expansion with cable one. After consulting with BNL, we reinstalled the cable in the test

fixture and continued testing it for another 15 cycles. Again, we found no perceptible damage other than the slight expansion at the "windows", which

was noted after the first five cycles, and a waviness in the surface which

became noticeable when looking down along the cable.

15
Maximum

Load

Cell

Force

During

Cooldown

cc: LU

CQ

^3

O

o

—

J

o

o

o

N0ISN31 N0ISS3ddN03

sqL ‘33aOJ 1133 QVOl

16

Figure

1.9

Cable

1,

starting

and

maximum

forces
17

Figure

1.10

Photo,

cable

1

lead

sheath,

annulism
The outside diameter of the cable was measured at random locations

along its length, at 90° angles, in order to determine the magnitude of the

surface irregularities. From 18 different measured diameters in the two

planes, the maximum difference was 1.55 mm (.061 Inches). Cable two showed

no evidence of the dielectric and outer dielectric screen unraveling or fraying as shown in figure 1.7.

Load cell vs. time measurements for four of the first five cycles is

shown in figure 1.11, and data for five of the last fifteen cycles is shown

in figure 1.12. The initial and maximum load cell forces for cable two are shown in figure 1.13. As with cable one, the data is quite repeatable.

During a typical test on cable two, pressurization of the inner line

(ambient temperature) resulted in a decrease in load cell force of 2220 - 2670 N (500 - 600 lbs) as shown in figures 1.11 and 1.12. During cool-down

the load cell force went from approximately 1100 N (250 lbs) compression to

7120 N (1600 lbs) or 7560 N (1700 lbs) tension.

Cable two was then warmed in the same manner as cable one (no

internal pressure). The resulting load cell force the next morning, with no internal pressure, averaged 670 N (150 lbs) compression for the first five

cycles and approximately 1330 N (300 lbs) for the later 15 cycles, as shown

in figures 1.11 and 1.12.

We installed both cables with a tensile force of 440 N (100 lbs) (no

internal pressure) but after the first cool-down cycle, this changed to 1110

N (250 lbs) compression on cable one as shown in figure 1.9 and a load cell

force of 2670 - 3110 N (600 - 700 lbs) compression on cable two as shown in

figure 1.13; the load cell forces given in figure 1.13 are considerably

higher than those in figure 1.9 because the cable is internally pressurized.

1.4.3 General Discussion

There was no measurable leakage across the lead sheath during any of

the 40 tests. For six of these tests the leak rate was monitored with a wet

test flowmeter and for the remainder of the tests the pressure decay method

was used

.

The cause of the annulism in the lead sheath of cable one is not

clear. It could be the result of buckling due to the compressive forces that occur on warm-up. If some yielding due to pressure forces had already

occurred at that "window" site then it would be more susceptible to buckling.

Whether or not the change in the operating procedure prevented cable two from

developing an annulism is problematical, since the mechanism of failure for

cable one is unclear. It could be fortuitous that cable one buckled and

cable two did not. On the other hand, it is possible that cooling the cable

under pressure prevented the annulism by either: a) maintaining tight

contact between the lead sheath and the outer mylar-bronze wrapping, thus

18
un

0/ x>

i-j

Cr t/» c at — c

j2 r- o

= o c < u.—

\

N0ISN31 NOISSaadWOO

•SQL ‘30y03 3133 QV03

19

Figure

1.11

Cable

2,

thermal

cycle

test

results,

first

series
• i- o.

to Q. o

<D <u <t3

J=> ^ I— O

<T3 E O C O cc

N0ISN31 NOISSnydWOD

•sqt ‘3DdOJ 113D QVOI

20

Figure

1.12

Cable

2,

Thermal

cycle

test

results,

second

series
Maximum

Load

Cell

Force

During

Cooldown

LiJ GO

O

Q

O

o

o

CNJ CM

CM

I

N0ISN31 N0ISS3ddW03

sqi ‘3Dd03 3333 aV03

21

Figure

1.13

Cable

2,

starting

and

maximum

forces
preventing relative movement and random enlargement of the window, or b)

allowing freer movement of the core with respect to the sheath, and thus

reducing the compressive load that the core exerts on the sheath during

warm-up . The thermo-elastic behavior of the cable is quite complex as evidenced by figures 1.8, 1.11 and 1.12. In particular, note the change in

load cell force as the cable is pressure cycled between 0.1 and 1.5 MPa,

summarized in table I.

Table I. Effect of Cable Pressure on Load Cell Reading

Change in load cell force, N (lbs)

Cable 1 Cable 2 Warm

Pressurize to 1.5 MPa - 1650 (~ 370) - 2220 to 2670 (- 500 to -600)

Depressurize to 0.1 MPa + 1560 ( + 350)

Cold

Pressurize to 1.5 MPa - 4000 (- 900)

Depressurize to 0.1 MPa + 800 ( + 180) + 440 (+ 100)

Without a detailed stress analysis of the complex cable structure, we can do

little more than speculate on the cause for such differences in the change in

the load cell force. It would seem clear, however, that the thermal-pressure

history, and how this history affects the coupling between the lead sheath and

the inner composite has a large effect on the force transmitted from the cable

to the fixtures

.

22
2.0 CABLE COOL-DOWN EXPERIMENTS

(D . E . Dane y

)

The time required to cool down a superconducting power transmission line

is critical to the success of these lines since excessive cool-down or warmup times would result in unacceptable long interruptions of service when

repairs are required. For example, Jones (section 3.0) has calculated a cool-down time of 20 days for a 15 km line cooled by a two stream counterflow

method.

The aim of the cool-down experiments is to model the cool down of

counterflow cooled SPTL's such as the ones currently under consideration at

BNL and LASL. The two principle goals are to complement the numerical cool

down calculations (section 3.0) by providing an empirical test of their

validity, and to provide an empirical base for a general theory of

counterflow cool down.

The details of the experimental approach are given in our last annual

report [1]. To briefly summarize this approach, we are modeling the

transmission line with special dual-passage heat exchange tubing which has a controlled thermal resistance (1 mm thick x 9 mm wide stainless steel web)

between the two flow channels. This webbing simulates the thermal

resistance, which is due primarily to the dielectric, of the prototype cable.

Analysis of the cool-down problem indicates the model and cable should have

the same value of NTU (number of heat exchanger transfer units) for similar

cool-down behavior.

During the past year the work on the cool-down experiment has proceeded

at a rather low level so that the cool-down calculations and cable thermal

cycling tests could be completed. In FY 79 the cool-down experiments will

receive top priority.

The dual-passage heat exchanger tubing, which will be used to model

counterflow cooling of the transmission line, has been wound into a 14-inch

diameter coil as shown in figure 2.1. After el ec t r o pol i sh ing and plating,

the coil will be instrumented and placed in the experimental chamber.

Radiation heat leak from the model presents a special problem because

the temperature of the model varies both temporally and spatially during the

cool down.

Conceptually, radiation heat leak could be reduced to a very low level

by use of multiple radiation shields along the length of the cable, with each

shield held at the same temperature and cooled at the same rate as the

section of tubing it surrounds. This approach was judged to be impractical,

however, for our spirally-wound model. Instead, we will use a single

23
Figure 2.1 Dual passage heat exchange tubing, wound and ready for plating

24
radiation shield enclosing the entire model. This shield will be held at some spatial average temperature of the model and will be cooled down with

the model

.

The heat leak can be reduced to about 10 percent of the heat removal

rate by 1) reducing the length of the model from 36 m to 18 m, 2) goldplating the model to reduce its emissivity, 3) wrapping the model with

approximately 10 layers of aluminized mylar (too many layers will give too

great an uncertainty in the heat capacity) and 4) starting the cool down near

200 K rather than 300 K. The shortened length of the test section requires a reduced thermal

impedance per unit length between the two streams in order to achieve the same value of NTU • Thus, we plan to electro-deposit a 0.002 inch-thick layer

of copper beneath the gold layer.

[1] M. C. Jones, Editor, Helium Research In Support of Superconducting Power

Transmission, HCP/T6010-01

25
3.0 COOL-DOWN COMPUTATIONS

The work on numerical calculation of transmission line cool-down is

essentially complete and is summarized in the attached paper by M. C. Jones.

This paper will be presented at the 71st Annual Meeting of AICHE, Miami

Beach, Florida, November 12-16, 1978.

26
Cool-down of Superconducting Power Transmission Lines with Single Phase Helium JonesM. C. **

Thermophysical Properties Division

National Bureau of Standards

Boulder, Colorado 80303

ABSTRACT

Numerical solutions of the- one-dimensional conservation equations of

fluid flow are given for the problem of the cool-down of superconducting

power transmission cables.. By including the continuity and momentum con- servation equations, both time dependent and spatially dependent mass flow

may be treated. The equations are applied to specific designs in which one stream of helium fills the bore of a cable while a second fills the space

between the outside of the cable and an enclosing pipe. Both co-current

flow and counter flow are treated with a variety of boundary conditions.

Temperature profiles as a function of time, and total cooldown times are given.

Work supported by ERDA, Division of Electric Energy Systems and by the Brookhaven National Laboratory, Power Transmission Project.

** Present address: Colorado School of Mines, Chemical and PetroleumRefining Engineering Department, Golden, CO 80401

1
Introduction

The successful development and design of Superconducting Power transmission Lines (SPTL's) depends among other things on a thorough knowledge

of the fluid mechanics, heat transfer characteri sties and thermodynamics

of the helium coolant. One problem of particular importance is the initial

cool-down of the line from ambient to operating temperature, which is the

subject of this paper. This is one of several time-dependent problems,

others being the response to a thermal disturbance in an operating line,

or the response following a disturbance in the refrigeration system. All

are governed by essentially the same set of partial differential equations

which are described here.

It is important to develop modeling methods for these problems because

the cost of carrying out even small scale laboratory tests in quite considerable. Suitable modeling methods enable the scale-up to full scale apparatus

to be made. At the present time, no suitable laboratory results are available

for even this, so it is important to make some purely predictive calculations.

A few years ago there were several SPTL development programs active around

the world and various cable configurations were suggested. In this paper we

consider two such configurations as being representative and reasonably up-todate. The first is that developed by the Brookhaven National Laboratory (BNL)

for an ac, three phase SPTL, the second by the Los Alamos Scientific Laboratory

(LASL) for dc. Here we consider two specific designs worked out by these laboratorys for economic evaluations of specific applications. In the case of BNL, we

give calculations for a design proposed for a 70 km run of a 345 kV, 4800 MVA

SPTL. This is for a power transmission corridor under construction by the Long

Island Lighting Company (LILCO) in New York connecting a nuclear power plant

2
on Long Island to a substation near the city. For precise identification,

this is referred to as LILCO case III (see reference 1.) For LASL, we performed calculations for a design proposed for an application in Pennsylvania.

Evaluations were carried out by the Philadelphia Electric Co. (PECO) for a

hypothetical 10,000 MVA transmission corridor between a power station on the

Susquehanna River to Philadelphia - a distance of 106 km. We performed calculations on a design submitted by LASL and identified as PECO case C. [2.]

As currently envisaged, SPTL cables are composites of many different

materials. In both the LILCO-IIIB and PECO-C designs, hollow core coaxial

cables are located inside a stainless steel pipe. In normal operation,

coolant flow is through the center of the cables returning, after expansion

in a "far-end" turbine expander, in the space between the pipe and the outside

of the cables. Moving radially outward, a single coaxial cable consists-at

the minimum-of a flexible support helix; conductor tapes or wires plus aluminum

or copper stabilizer; dielectric layers; the outer stabilizer and superconductor;

a gas-tight shield and/or armor. For a more complete description see references

[1,2.] The situation is represented in figure 1. for a 3 phase ac design.

The dc case may be thought of as a single such cable inside a pipe.

For the purposes of calculating the cool-down process we have simplified

the construction even further, without loss of accuracy and in table 1 we list

the compositions assumed in the calculations. Stabilizer and superconductor

composite have been lumped to-gether as copper. In the LILCO design, the outer

gas seal is a lead sheath, whereas for PECO it is again copper. In table 2,

we list the salient dimensions.

In this paper we have calculated the cool-down process for these designs

by simultaneous numerical solution of the exact one-dimensional conservation

3
Helium

"Return

4

Figure

1.

Cut-away

view

of

superconducting

power

transmission

li
Table 1. Cable compositions used in calculation (kg/m)

BNL, LILCO-IIIB. LASL, PECO-C

Plastic insulation

Copper + Superconductor

A1 umi num Stainless steel

Lead

25.9

} 29.5

f 26.6

36.2

4.8

6.5

- 118.2 11.3

Outer Pipe (Stainless 12.6 2.7

steel

)

Total mass/m 130.8 14.0

Table 2. cable details (mm.)

BNL, LILCO-III B LASL, PECO-C

Inner pipe diameter

Outside diameter of cable

Inner diameter of insulation

Outer diameter of insulation

Inside diameter of outer pipe

50.8

135.0

60.2

116.6

348.0

34.0

96.8

39.2

84.3

no

Distance between refrigeration station, km; 15 6

Assumed steady heat leak from 0.450 0.20

ambient temperature W/m

Assumed ideal refrigeration 0.80 0.18

available, MW.

5
equations for the helium streams with appropriate boundary conditions. It did

not appear feasible at this time to compute simultaneously the time-dependent

radial diffusion of heat through the cable composite, and therefore the cable

temperatures at any time and axial position are computed as cross sectional

means, i.e., we use a one-dimensional description for these. As will be seen,

the results for cooldown-time are probably not sensitive to this assumption.

Previous work on this problem has been of limited extent. For a single

coolant stream with constant mass flow, a good value for the cooldown time can

be evaluated if the temperature profiles are step-like by an energy balance

across the step as proposed by Burke. [3.] If material properties were independent of temperature (decidedly not the case here) the problem is the inverse of

packed bed regeneration, and a closed form solution exists. [4.] But again the

mass flow rate is assumed uniform and constant. Baron et. al. [5.] presented a

numerical method for a single coolant stream for a rigid metal pipe type SPTL.

Mass flow rate was not constrained to becci.stant, but momentum and continuity

equations were not solved and therefore the mass flow rate had to be arbitrarily

specified. These authors did, however, correctly account for variable helium

and pipe properties. Hoffer [6.] has improved on these calculations by determining flow from overall pressure drop, but still assumes uniformity of mass

flow. None of the above methods dealt with cooling by two counter-flowing

streams which was one of our objectives here.

6
Analytical Model

The essence of the model is illustrated in Figure 2 where it is

seen that the outer pipe, the cable and the two helium streams are each

represented by uniform temperature regions for an element of length, dx.

Considering any one of the helium streams we may write down the familiar

one-dimensional forms of the mass, energy and momentum conservation equations

with pressure P, mean enthalpy H, and mean velocity V as dependent variables

l£ + V3£ ^ Q (1

9t 3x 3x ^

P_9 I \ +P dt \ 2 J

9x

iE.

3t + A ( 2 .)

^ M. = _ i iE. _ P _ M

3t 3x ' p 3x ~ 2a " 3x (3.)

Here, the density p is regarded as a known function of P and H, the potential

energy $ is a known function of x, accounting for changes in elevation, and A

is the heat transfer to the fluid stream per unit length. The friction factor

f could be calculated from the local fluid Reynolds no., or, as we have done

here, set equal to a constant for typical conditions, p and a are wetted

perimeter and cross sectional area of the appropriate helium channel.

There are advantages to retaining P and H as the thermodynamic

variables rather than P and T as pointed out by Arp. [7.] In this way we

avoid thermodynamic derivatives like specific heat and thermal expansivity

which are non-analytic at the critical point and sharply peaked at the transposed

critical temperature. The density derivatives in equation (1) can be

written in terms of P and H derivatives using the thermodynamic identities

7
RADIANT

HEAT

LEAKAGE,

4-J o

8

Figure

2.

Model

for

computations
^

\ M

3H)p ^2

H

l+({)2

= £ /£l

t 1 9p

where 4) - I'^l ~ the Gruneisen parameter - and c

s . V" / s acoustic velocity. If we then take linear combinations of (1.) (2.) and (3.)

( 5 .)

( 6 .)

where c is the

we can arrive at a set in which only one time derivative - , :;-r or — - dt d L d

t

occurs in each equation, this form being preferable for numerical solution. The

resulting set - equation (3.) being unchanged as equation (9.) - is

If.

9t

V9P pc 9V

9x 9x

A + pv t ivi P

a 2a (7

9t 9x

2

c 9V

¥x

1 + 4) P

A p V^f IVi p

a 2a

(8

^ _ 1 9P

_ _ f

_ 9i

9t p 9x ~ 9x ~ 2a 9x

(9.

There is one such set of three equations for each fluid stream and the independent

variables and coefficients can be subscripted 1 and 2 for the inner and outer

streams respectively. They are coupled to appropriate energy equations for

the cable and outer pipe through the heat transfer terms Ay and A^.

9
For the cable composite the appropriate one-dimensional energy conservation

equation is of the form

^^cable ^^cable\ „ cable „ cable ^ 3t 3x jh ~h

where p^. , , k^. and a^. are the density, specific heat, thermal conductivity

t h and cross sectional area of the i— cable component. It is easy to show that

the heat conduction term on the right hand side is quite negligible in all cases

considered. A similar equation can be written for the outer pipe

(pCa) 3T _ 9 ft P^P^ ^ 9x

(ka) pipe 9x Q

- pipe

( 11 .)

where again for practical purposes the first term on the right hand side can

be neglected. Q is the radiant heat leakage per unit length to the outer

pipe from the ambient temperature vacuum pipe (not shown in figures 1 and ?.)

through a multilayer insulation which is assumed to cover the outer pipe.

4 4 In the computations it is given a simple

("^ambient

" "^pipe^ dependence.

In the equations (7.) and (8.) written respectively for stream 1 and

stream 2 the heat transfer terms may be written

. ^ cable (12.)

. _ . cable + , pipe (13.)

^2 ^2 ‘^2

In the absence of numerical evaluations of the radial diffusion of heat to

determine and we are forced to adopt a fairly crude model.

10
Since the thermal conductance through the cable is typically an order of

magnitude smaller than the fluid film conductance, the latter is assumed

to be infinite and we assume these terms are proportional to the difference

between the mean cable temperature and the appropriate fluid stream temperature. Thus

cabl e

1 ^1^1 ^"^cable (14.)

cabl e (T uT - T

' cable 2' (15.)

where "

r

/ <7 * *'2 “

r 11 ^

2 r

and r.| , and are the inner and outer radii of the plastic insulation, r

the mean radius and k the thermal conductivity of the insulation evaluated

at In other words, we compute the conductances h-j , and h^ as steady

state values. In fact, for the transient cooling of a slab, following a step

change in temperature a linear heat transfer relationship for the average

slab temperature is approached after about 2 time constants, this being given

2 by 6 /a where a is the thermal dffusivity and 6 the slab hal f- thi ckness . For

3 the cases considered here, this time constant is of the order of 10 seconds at

2 room temperature and 10 seconds at operating temperature, so the approximation

should be good whenever the active cooling period greatly exceed this. The

sensitivity of the results to this approximation is discussed further below.

Finally for the term in (11) and (13) we use an average heat

transfer coefficient, h^, for turbulent flow with Reynolds number based on a

11
mean hydraulic diameter

A pipe L Ao = Poh~ V

- 2 ^33 pipe (T - T, (17.)

In addition to the above set of equations, boundary conditions must be

specified appropriate to the particular mode of cooldown being used. We have

investigated the following modes. Co-current flow through cable cores and

the space between cables and outer pipe; counterflow with return stream

expanded down to lower pressure at fixed isentropic efficiency (far-end

expander); counterflow with return stream refrigerated to specified thermodynamic state (far-end refri gerator ) . For all cases, since the heat conduction

terms of (10) and (11) have been neglected, no boundary conditions were needcci for

either or T . . For the set of equations (7.), (8.) and (9.) applied

to each stream, we need three boundary conditions, but note that they may be

at different ends of the cable (x = o and x = L) and, further, we may have

two conditions on one dependent variable, one on a second and none on a third.

The alternatives are displayed in table 3. In some cases, such as H, at x = o,

an explicit time dependence is given, while in other cases such as and at

X = L, one dependent variable is expressed as a function of others.

For initial conditions the entire system was assumed to be at ambient

temperature with a steady state velocity and pressure profile specified.

M aterial Properties

2 In equations (7.)-(9.) the coefficients p, c , ({> and, through A, T are

to be regarded as known functions of the dependent variables P and H. For

12
XJc

OJ

I S-fO > ^ ^ o

sOJ XS- c

O) fO -M CL

c: X

13 <D OO

t-o

o

c;fO -M

COco

u

c

fO

COco

o

CNJ in =

II C\J C\J n= oCVJ r- > >

OJ r- Q. O.

OJ «-

OJ •—

Q. Q.

II C

03 4->

I/) Co

u

CO

c:oO CLo

s- c

a; OJ

sS- 13

13 CO a CO

OJ o S- o CL

II CO X co

a

oIIX

+->c

fO

+-> COco

o

co

o

c

ro

+-> O

U

ii OJ m

OJ

Q_

13
fast computer evaluation it was found advantageous to express these as

polynomials. These were fitted to the more exact data derived from the

equation of state of McCarty in the range 0,3 - 2.0 MPa and 4 to 300K.

For p the average error was -^.b% or less at higher temperatures with a

2 maximum of 1.7% near the transposed critical state. For c the average

error was +^2% for P < 1.2 MPa and 3% for 1.2 < P < 2.0 MPa. The average

error in if) was -3% or less for P > 0.5 MPa and +6% for P < 0.5 MPa. Finally,

temperature error averaged +0.05K for P > 0.4 MPa, and j^O.lK for 0.3 < P < 0,4

with a maximum error of 0.2K occuring near transposed critical states. The

2 functions c (P,H) and cf)(P,H) are shown plotted in figure 3.

In equations (10.) and (11.) it is assumed first that the specific

heats C^. of the cable components are available as functions of temperature

^^cable "^pipe^' expressions were again fitted to selected data from

the literature [9, 10, 11, 12] for fast computer evaluation and these are

illustrated in figure 4 for polycarbonate , copper, lead and stainless steel.

These fits are generally better than +^5%,

Perhaps the most important property is the thermal conductivity of the

plastic insulation needed in equation (16.) This is not a simple property

to measure experimentally because in fact the insulation consists of many

layers of thin tape wound under tension and, in operation, impregnated with

helium. Our calculations were based on measurements [1.] of the thermal conductivity of four layers of 75 ym polycarbonate in the presence of helium

gas at about 0.5 MPa pressure. Polycarbonate is a candidate insulation with

high density polyethylene and polysul phone . Pressure was shown to increase

the effective thermal conductivity of the layers but appeared to have

reached a limit for polycarbonate at about this pressure. Thermal conductivities

14
y3i3wvyvd N3Si3Nna9

^(s/m) ‘AiI3013A ONHOS

15

Figure

3.

The

functions

c‘^(P,H)

and

(|)(P,H)
HEAT

CAPACITY,

J/kg

Figure 4. Heat capacities of cable components; the functions C^. (T)

16
were measured at 4.2, 20, 100, and 300K. Unfortunately, a sharp increase

takes place between 100 and 300K and therefore, although we could fit a

ploynomial to these data quite accurately, the actual form of the temperature dependence between these two temperatures is unknown, and the fitted

curve shown in figure 5 must be regarded as rather approximate.

N umerical Method .

Integration of the set of eight partial differential equations was

accomplished using the computer program PDECOL developed by Madsen and

Sincovec. [13] This program is based on the method of lines and uses finite

element collocation for the discretization of the spatial variable. Using

piecewise polynomials for the trial function space, the procedure reduces

the system to a set of first order ordinary differential equations with

time as the independent variable. The program then uses established procedures for stiff systems to perform the time integration. PDECOL has

been tested by its authors and found to be up to an order of magnitude

faster than a similar finite difference technique for the same accuracy.

Since PDECOL was designed for non-linear partial differential equations

it was relatively straightforward to introduce a properti es subrouti ne to calculate

the properties discussed above for every new value of the solution vector

and supply the solution dependent coefficients in the differential equations.

This adds significantly to the run time, but was still less than 10% in our

computati ons

.

Results of Computation s.

There are essentially two schemes which may be used to cool a SPTL down.

In the first, cold helium gas from a refrigerator enters the cable cores and

the outside space between cables and enclosing pipe in co-current flow.

17
o

>|.uj/M ‘ AiiAiionaNOo ivwy3Hi

o

o

18

Figure

5.

Thermal

conductivity

of

helium

impregnated

polycarbonate

layers
The cooldown time of the refrigerator is likely to be a few hours compared to

days for the transmission line, so for most of the cooldown period the refrigerator, in this mode of cool-down, receives return helium gas or fresh make-up

gas at ambient temperature and supplies gas at tlie coldest temperature operating

much as a liquiefier. In the second scheme, the refrigerator supplies only

the cable cores and at the far end the helium is either re-refrigerated or

expanded to produce more refrigerati on prior to being returned in counter-flow

in the outside space. Because o-f the great length, the cable behaves as a

highly effective counterflow heat exchanger, despite the poor conductivity

of the insulation, so in this case cooldown takes much longer for a given mass

flow. On the other hand, no storage or return piping is needed. A further

advantage of this second scheme is that temperature stress is much reduced both

axially and radially.

We have calculated cooldown of the cable designs described for both the

co-current flow and counterflow alternatives and we find that the cooldown

time is limited in two different ways. In co-current flow, cool-down proceeds

very rapidly and is only limited by the capacity of the refrigerator to supply

the cable with helium. Therefore, in these calculations a constant total mass

flow rate was maintained from start to finish. In counterflow cooling, because

of the inherently greater duration of the process, it was found that much

higher mass flow could profitably be used, and that the rate of cool-down

was limited by the permissable pressure drop. These calculations were therefore done with a constant pressure drop, and so the mass flow necessarily

ncreased during the course of cooldown.

As an example of co-current cooling, we give results from a computation

for the LASL/PECO cable design (6 km length) in figures 6 and 7. In this

19
example, most of the mass flow was in the outer space. After an initial

transient, during which inlet temperature was lowered to 10 K with a time

constant of 2.8 hours, the total mass flow at inlet was held at 25 g/s.

The mass flow profiles of figure 6 show a non-uniformity as the cable

free space is filled with dense fluid from the left. Figure 7 shows the

correspond! ng cable temperatures, complete cooldown occuring in 75 hours.

After the initial transient, the ideal refri gerati on was steady at 0.15 x

10^ W which is a shade less than what is expected to be available during

cooldown for this case. Available refrigeration is based on steady state

loads and the need for a standby machine. Both machines would be available

during cooldown.

A similar calculation was performed for the BNL/LILCO design. Mass flow

rate was 129 g/s with a near uniform pressure of 1.52 MPa, and the time constant for the initial lowering of the temperature 28 hours. The ideal refrigeration power, 0.75 x 10^ W, is again just inside the 0.8 x 10^ W expected to

be available. Because of time limitations, this calculation was terminated

after cooldown was about 1/2 complete. However, at this point the cold front

was moving at a constant velocity of 33.2 meters per hour and so the total

cooldown time can be confidently estimated to be 472 hours. (19.7 days)

For both of the above calculations, boundary conditions were of type (ii).

It was found that a solution could only be obtained if mass flow and pressure

were fixed at opposite ends. Further, if mass flow in the outer space were

fixed at inlet, the mass flow in the core had to be fixed at outlet, otherwise,

to conserve mass, the solution sometimes called for a warm gas inflow from the

far end. This was true for small mass flow rates in the cores which, when

fixed at the cold inlet were insufficient to fill the core at the rate dictated

by heat transfer to the outer stream.

20
3.0x10 o

21

Finure

6.

’'lass

flow

orofiles

for

cooldown

of

the

L^SL/PECO

desicn

usino

cocurrent

flow

of

the

helium

streams.

These

orofiles

are

for

flow

in

the

soace

outside

the

cable.

Flow

in

the

core

was

an

addition 1

g/s

held

constant

at

outlet.
22

Figure

7.

Temuerature

profiles

for

the

cable

and

the

outside

helium

stream.
To illustrate couterflow cooling, we show results for the BNL/LILCO design

in figures 8 and 9. In the case shown, two refrigerator stations were assumed

to supply helium at 10 K to the core and outer space, respectively, at the near

and far ends of 15 km length of cable. Boundary conditions were of type (iii).

Using a pressure of 1 . 5 MPa at the first refri gerator, pressure drop in the

cores was held at 1.0 MPa, while at the far-end the emerging mass flow was assumed to pass to the second refrigerator station, re-entering the cable again

in the outer space. Specification of the pressure of the return stream at the

first refrigerator station completes the boundary conditions. Runs were made

with both 1.5 MPa and 0.5 MPa for this pressure with only marginal differences

in the resulting cooldown time. The cooldown time was 20.5 days. The ideal

refrigeration powers for the two refrigerators were of course variable and are

plotted in figure 9 as a function of time as is also the mass flow (in this case

it was essentially uniform in the spatial dimension).

The importance of this calculation for the BNL/LILCO design is that it is

probably the fastest possible cooldown using the counterflow mode. In fact it

is not planned to position a refrigerator at the far-end, but only an expander.

Here we run into the difficulty that in order to obtain a high mass flow for rapid

cooldown, pressure drop in the cable cores is at the expense of available expansion

As an example, we ran a calculation for BNL/LILCO where the helium from the

refrigerator entered the cable cores at 1.5 MPa with 0.8 MPa pressure drop. With

5.0 MPa specified for the helium return pressure at the refrigerator this left

an expander pressure ratio of only 1.09. Thus the expander, with an assumed

isentropic efficiency of 75%, contributed very little refrigeration and the cooldown time was 58 days. We do not feel that much improvement in the cooldown time

can be obtained by this method.

23
o

Q

UJ

h-J h—

(

_J<c

ccCD

3yniVH3dW3i

24

Figure

8.

Temoerature

orofiles

for

cooldown

of

the

BML/LILCO

design

with

counterflow

of

the

heliun

streams.

It

is

assumed

that

refrigerators

are

positioned

at

both

ends

of

the

cable

suoplying,

resoecti

vely

,

the

cores

and

outside

space

with

helium

at

10

K.
TIME

S/6>| ‘M01J SSVW

CO

o

o

o

OOro

OoC\J

o

o

UDO

o CO CD C\J o

f t o O O

MW

‘ N01iva39iaj3d 1V3QI

o

25

Fiaure

9.

Plots

of

ideal

refrinerator

power

and

nass

flow

of

helium

at

inlet

to

the

cores

vs.

time,

for

the

BNL/LILCO

case

with

counter-flow

of

the

helium

streams.
The corresponding case for counterflow cooling of the LASL/PECO design using

a similar far-end expansion resulted in a cooldown time of 7,0 days when the pressure drop in the cold core was held constant at 0,5 MPa. This is, however, not

the fastest possible case as the core pressure drop is still relatively small.

However, we have not determined the optimum distribution of pressure drop between

cable core and expander.

A final point concerns all of the calculations: in order to obtain stable

flow it was found necessary to lower the inlet helium enthalpy continuously

with time until the desired inlet temperature was reached and to take a small

pressure drop across an upstream restriction. Failure to do this led to flow

reversals and pressure pulsations in the solution with excessive computational

time. Thus, the constant inlet pressure actually refers to pressure upstream

of the restriction. In view of the fact that in experiments such pulsations

are common we believe this to be physical and not an artifact of the calculation.

9 In all calculations we have taken AP .

. , . /pV = 15, and the inlet enthalpy restriction ^ 4 5 reduced linearly to its constant value in either 10 or 10 seconds.

Discussion of the Results .

The first part of this discussion is concerned with the validity of the

cooldown results predicted by the model and the integration procedure used.

First of all, the number of collocation points and the desired local relative

error to be maintained during the integrations were arrived at by preliminary

single stream calculations on a simple pipe with constant properties and constant

coolant mass flow. This problem has an exact solution [4]. For long pipes,

Shutt arrived at a simple asymptotic expression for cooldown time.

For 202 and 102 collocation points our calculations of cooldown time were

within 0.3% and 1.3% respectively when the local relative error was held at

0.1%. All calculations reported above were performed with 102 colocation

26
points and relative error 0.1%. Therefore we believe our numerical errors

on cooldown time to also be of the order of 1%. In any counterflow calculation, on the other hand, the error should be smaller because

cooldown is more gradual and solutions are less sharply varying in the x

di recti on

.

Of the approximations made in the model we believe only the pseudo-steadystate heat transfer resistance across the cable insulation to be weak, and then

only for co-current calculations which involve the most rapid cooldown. For a

single stream and pipe with constant properties, Shutt has shown that when the

width of the active cooldown zone is small compared to the pipe length the cooldown

time is independent of the heat transfer coefficient. This is certainly the case

for the co-current runs reported here as seen in figure 7, for example. To verify

this we ran the calculations from which this figure is taken with the thermal resistance arbitrarily doubled. No significant change in cooldown time resulted. Therefore we believe that our computed cooldown times are reliable. Furthermore, through

considerable experience in running these cooldown problems and other transient helium

flow and heat transfer problems at this laboratory, we feel that the combination

of the differential equation set as formulated here and the computational package

PDECOL has considerable potential as a modeling tool. It has shown itself to be both

flexible and robust, capable of handling flow reversals and pressure wave propagation in addition to the slower density wave propagation characteristic of cooldown.

We now consider the practical results of these calculations. Certainly cocurrent flow is the fastest cooldown mode. Were it not for the fact that in this

mode one is limited by available refrigeration, even faster cooldown could be

achieved. (For example, calculations were made on LASL/PECO with, first, a fixed

pressure drop of 1.2 MPa until the flow rate reached 200 g/s. Thereafter the flow

rate was held constant at this value. The resulting cooldown time was T7 hours.

27
But required ideal refri gerati on capacity was 1.2 MW -- at least a factor of six ,

higher than would be available.)

For counterflow cooling, the 7 days (a conservative estimate) computed for t

LASL/PECO using a far-end expander is certainly an acceptable time and this would i

be an attractive cooldown mode, being essentially the same operating mode as for I

steady state operation. On the other hand, we have only been able to broadly

bracket cooldown time for BNL/LILCO. The one certainty is that it will be hard

to beat the 20.5 day cooldown time computed using a far-end refrigerator. Some

investment will have to be made to achieve this time; either the cost of a mobile

refri geration unit for such temporary duty, or the use, say, of liquid nitrogen

in a heat exchanger at the far-end, or, as shown above we could fall back on the

co-current mode, which gave 19.7 days cooldown time but which requires a separate

warm gas return line. Yet another possibility, which may avoid further investment,

however, is to evacuate the outer space, supply helium to two cable cores using

the third as a warm gas return. In this way the thermal coupling between streams

should be greatly reduced allowing cooldown to proceed up the first two cables and

down the third as with a single stream or the co-current flow examples discussed

above. Since in this mode pressure drop will not be a limitation there is no

reason why the full capacity of available refrigeration should not be used and

a cooldown time of about 20 days should be attainable.

Concl usions

1. The formulation of the transient flow equations with P, H and V as dependent

variables, together with the numerical partial differential equation package

PDECOL of Madsen and Sincovec provides a powerful, accurate, and flexible

tool for transient sinnle phase variable property flow calculations, particularly

with coupled streams.

28
2. Cooldown for specific SPTL Designs was investigated with a reasonably detailed

description of the cable construction from the standpoint of thermal capacity.

Realistic estimates of cooldown times were made for a variety of different

operating modes.

Acknowledgments

Helpful discussions with Neil Madsen of the Lawrence Livermore Laboratory on

the use of PDECOL allowed the author to do things that it was not ori ginal ly desinned

for. His guidance and patience was' greatly appreciated.

Vincent Arp of the National Bureau of Standards showed his customary helpful

interest and contributed the polynomial fits for helium properties.

29
References

.

1. Power Transmission Project-Progress through Fiscal Year 1976.

Report PTP#69, BNL 22202. Brookhaven National Laboratory December 27, 1976.

2. Details are given in internal reports of the Los Alamos Scientific

Laboratory (1976) and are available on request from F. J. Edeskuty.

3. Burke, J. C., Byrnes, R. , Post, A. R., and Russia, F. E. Advances in

Cryogenic Engineering, vol . 4 (Plenum Press, New York, 1960) p 378.

4. Carslaw, H. S. and Jaeger, J. C. Conduction of Heat in Solids, Second

Edition. (Oxford University Press, 1959)

5. Baron, A. M., Eroshenko, V. M. , Yaskin, L. A. Cryogenics (1977)

6. Hoffer, J. K. private communication, see reference 2.

7. Arp, V. D. Cryogenics 1_5 , 285 (1975)

8. McCarty, R. D., J. Phys. Chem. Ref. Data 923 (1973)

9. Schramm, R. E., Clark, A. F., and Reed, R. P. NBS Monograph 132.

(U.S. Dept, of Commerce, National Bureau of Standards, 1973)

10. Miller, A. P. and Brockhouse, B. N. Can. J. Phys. 704 (1971 )

11. Collings, E. W., Jelinek, F. J., Ho, J. C. and Mathur, M. P. Advances in

Cryogenic Engineering vol 22 (Plenum Press, New York, 1977) p 159.

12. Corruccini, R. J. and Gniewek, J. J. NBS Monograph 21 (U.S. Dept, of

Commerce, National Bureau of Standards, 1960)

13. Madsen, N. K. , and Sincovec, R. F. in Numerical Methods for Differential

Systems, L. Lapidus and W. E. Schiesser, editors, (Academic Press, Inc

New York, 1976.

)

14. Shutt, R. P. Internal report of the Brookhaven National Laboratory,

(1976) available on request.

30
NBS-114A (REV. 9-78)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 79-16182.Gov*t. Accession No.

4. TITLE AND SUBTITLE

HELIUM RESEARCH IN SUPPORT OF SUPERCONDUCTING POWER

TRANSMISSION

3. Accession No.

5. Publication Date October 1979

7, AUTHOR(S)

David E. Daney

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

national BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

11. Contract/Grant No. 433475-S

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (-Sfreer, City, state, ziP)

Brookhaven National Laboratory

Upton, New York 11973

13. Type of Report & Period Covered Interim/FY 78

15. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Softvoare Summary, is attached.

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.) During FY 78, the NBS Thermophysical Properties Division program of supporting research

for Superconducting Power Transmission Line (SPTL) development focused on three tasks:

1) Numerical computation of SPTL cool down by both single stream and counter flow

methods

.

2) Experimental modeling of counterflow SPTL cool down.

3) Thermal cycling of lengths of lead-sheathed model cable destined for testing in

the BNL 5th Ave. facility.

The preparation of computer codes and numerical computation of SPTL cool down were

completed and the results are given in Section 3. These calculations confirm our original intuitive judgment that cool-down times for the counter flow arrangement can be

long—twenty days or more. Greater than anticipated computer run times and costs required a reduction of effort

on experimental modeling of counterflow cool down. Consequently, completion of this

task will be delayed until FY 79.

Two sections of cable underwent extensive thermal cycling, and the results of these

tests are given in Section 1. The complex structure of the cable leads to unusual

(although reproducible) load vs time curves. Funding limitations required postponement until FY 79 of the experimental evaluation

offbeat —w f^^Dw, law. senso^rs^as sensors as a, means .^pf pf ngn-intrpsqve non- intrusive ^ajuum vc i^dical^ign^for^JJT|,^vac^m en- yelopes^ This task tggether^with experimental modeling

heart of our program in itv 79.

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)

Cable cool-down; cool-down helium; liquid helium; superconducting power transmission,

thermal cycling, thermal stress.

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