pressure drop in a model of a forced cooled pipe-typr electric cable system with cable snaking

6
IEEE Transactions on Power Apparatus and Systems, Vol. PAS-99,No. 3 May/June 1980 PRESSURE DROP IN A MODEL OF A FORCED COOLED PIPE-TYPE ELECTRIC CABLE SYSTEM WITH CABLE SNAKING Richard Ghetzler and John C. Chato Department of Mechanical and Industrial Engineering University of Illinois at Urbana-Champagn Urbana, Illinois Abstract - An experimental study was conducted of the pressure losses in a scale model of a high pressure oil filled (HPOF) pipe cable system with a wave-like snaking pattern of the cables inside the pipe. In HPOF systems, snaking can be caused by longitudinal thermal expansion of the cables between fixed points of support when the cables are placed under electrical load. Friction factors were determined for a Reynolds number range of 200 to 3800 and longitudinal expansion up to 13.2 percent for cables with and without wire wrap (skid wires). Correlations are given for the friction factors and, consequently, pressure drops along the snaking cables as well as in the downstream region. NOMENCLATURE DH: Hydraulic diameter E: Linear fractional expansion of cables within a fixed length of pipe f: .f fAV: fFD: L: Le: AP: Re: V : P : p: Friction factor = DH AP/2pV2 Friction factor with straight cables Average friction factor Friction factor for fully developed flow Axial length Equivalent length for downstream losses Pressure drop Reynolds number = PVDH/hI Mean axial velocity Density Dynamic Viscosity INTRODUCTION Forced cooling of pipe-type underground electric transmission lines has recently come under considera- tion. Potential benefits are the upgrading of existing self-cooled systems via retrofit and development of new systems of greater capacity. Recent studies have included full scale, model tests, and analytical studies of pressure drop and heat transfer in forced cooled systems [1-8]. In one of the recent fullscale studies [3], thermally induced snaking was directly observed during system dismantl- ing, in conjunction with measurement of significant increases in pressure drop during the tests. We have been involved in experimental scale model and analytical studies of forced cooling for several years [9-17]. The present work was conducted to delin- eate the fluid mechanics of pipe-type cable systems with cable "snaking" present in order to develop appropriate design criteria. F 79 151-2 paper recommended approved by IEEE Insulated Conductors Committee of the IEEE Power Engineering Society for presentation at the IEEE PES Winter Meeting, New York, NY, February 4-9, 1979. Manuscript submitted August 8, 1978; made available for printing January 11, 1979. EXPERIMENTAL METHOD The experimental apparatus utilized the basic fluid mechanic and heat transfer equipment used on the previous and on-going forced convection cooling studies at the University of Illinois at Urbana-Champaign [10,11,14] with modification for the snaking study. Figure 1 diagrams the basic layout of the experi- mental setup. Three, 1.27 cm (.5 in.), O.D. steel tubes simulating the -straight portion of three cables are positioned inside a 4.45 cm (1.75 in.), I.D., 8.4 m long steel tube as shown in Fig. 2. This arrangement pro- vides an entrance length of 469 hydraulic diameters. The snaking test section, shown in Fig. 3, is 0.784 m long and consists of a clear plastic tube enclosing simulated cables made of flexible neoprene tubing. Photographs of the snaking test section with straight cables and for cables with 4.4, 8.8, and 13.2 percent length increases are shown in Figs. 4(a), (b), (c), and (d), respect- ively. The geometries assumed by the cables are the same with and without skid wires and these photographs will be referred to in both cases. The downstream end of the flexible tubes are joined to steel end tubes, 1.07 m (3.5 ft) long. The end tubes are axially movable and extend through the outlet mixing chamber and through holes with internal 0-ring oil seals in an aluminum end plate. The end tubes can be individually moved and locked into place from the outside. Movement of the end tubes inward forces the flexible tubing into wave-like forms and the additional length within the test section simulates the cable thermal expansion. The end plate is rotatable to allow angular displacement which also has been observed in the full scale tests [3]. Skid wires are simulated with 30-gauge (0.053 cm O.D.) Teflon- insulated electric wire, wound in a continuous helix along the length of the rigid and flexible tubes. The spacing was 138 wires per meter (42 per ft) which corresponds to a ratio of pitch to skid wire diameter of 14. Pressure measurements at the inlet and outlet of the test section were made with a differential oil- water manometer for the low range of flow rates and a differential oil-mercury manometer for the high range. Oil temperature was measured with copper-constantan thermocouples and a Fluke Model 2240 A Data Logger. Manometer and room temperature were measured with stan- dard mercury thermometers. Sun No. 4 dielectric oil was used for the tests. Viscosity and density as func- tions of temperature were measured with a modified Ostwald viscometer and a hydrometer calibrated to API standards. Flow rate was measured and controlled with a calibrated rotameter and a venturi. Frictional heat was removed and oil temperature was controlled in the range of 37 to 3900 with bypass flow through the heat exchanger. The friction factor, f, was calculated as a func- tion of the Reynolds number, Re. Total system accuracy in the determination of f was checked by determining the pressure drop in the round pipe with the cables removed. The results were compared with the theoretically known solution of Re * f = 16 for laminar flow. The determination of f was found to be accurate within 5 percent. 0018-9510/80/0500-0919$00.75 1980 IEEE 919

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Page 1: Pressure Drop in a Model of a Forced Cooled Pipe-Typr Electric Cable System with Cable Snaking

IEEE Transactions on Power Apparatus and Systems, Vol. PAS-99,No. 3 May/June 1980

PRESSURE DROP IN A MODEL OF A FORCED COOLED PIPE-TYPE ELECTRIC CABLE SYSTEM WITH CABLE SNAKING

Richard Ghetzler and John C. Chato

Department of Mechanical and Industrial EngineeringUniversity of Illinois at Urbana-Champagn

Urbana, Illinois

Abstract - An experimental study was conducted ofthe pressure losses in a scale model of a high pressureoil filled (HPOF) pipe cable system with a wave-likesnaking pattern of the cables inside the pipe. In HPOFsystems, snaking can be caused by longitudinal thermalexpansion of the cables between fixed points of supportwhen the cables are placed under electrical load.Friction factors were determined for a Reynolds numberrange of 200 to 3800 and longitudinal expansion up to13.2 percent for cables with and without wire wrap

(skid wires).Correlations are given for the friction factors

and, consequently, pressure drops along the snakingcables as well as in the downstream region.

NOMENCLATURE

DH: Hydraulic diameterE: Linear fractional expansion of

cables within a fixed length of pipe

f:

.ffAV:fFD:L:Le:AP:Re:V :P :

p:

Friction factor = DH AP/2pV2

Friction factor with straight cablesAverage friction factorFriction factor for fully developed flowAxial lengthEquivalent length for downstream lossesPressure dropReynolds number = PVDH/hIMean axial velocityDensityDynamic Viscosity

INTRODUCTION

Forced cooling of pipe-type underground electrictransmission lines has recently come under considera-tion. Potential benefits are the upgrading of existingself-cooled systems via retrofit and development of newsystems of greater capacity.

Recent studies have included full scale, modeltests, and analytical studies of pressure drop and heattransfer in forced cooled systems [1-8]. In one ofthe recent fullscale studies [3], thermally inducedsnaking was directly observed during system dismantl-ing, in conjunction with measurement of significantincreases in pressure drop during the tests.

We have been involved in experimental scale modeland analytical studies of forced cooling for severalyears [9-17]. The present work was conducted to delin-eate the fluid mechanics of pipe-type cable systemswith cable "snaking" present in order to developappropriate design criteria.

F 79 151-2 paper recommended approved by

IEEE Insulated Conductors Committee of the IEEE Power

Engineering Society for presentation at the IEEE PESWinter Meeting, New York, NY, February 4-9, 1979.

Manuscript submitted August 8, 1978; made available

for printing January 11, 1979.

EXPERIMENTAL METHOD

The experimental apparatus utilized the basicfluid mechanic and heat transfer equipment used on theprevious and on-going forced convection cooling studiesat the University of Illinois at Urbana-Champaign[10,11,14] with modification for the snaking study.

Figure 1 diagrams the basic layout of the experi-mental setup. Three, 1.27 cm (.5 in.), O.D. steel tubessimulating the -straight portion of three cables arepositioned inside a 4.45 cm (1.75 in.), I.D., 8.4 m longsteel tube as shown in Fig. 2. This arrangement pro-vides an entrance length of 469 hydraulic diameters. Thesnaking test section, shown in Fig. 3, is 0.784 m longand consists of a clear plastic tube enclosing simulatedcables made of flexible neoprene tubing. Photographs ofthe snaking test section with straight cables and forcables with 4.4, 8.8, and 13.2 percent length increasesare shown in Figs. 4(a), (b), (c), and (d), respect-ively. The geometries assumed by the cables are thesame with and without skid wires and these photographswill be referred to in both cases. The downstream endof the flexible tubes are joined to steel end tubes,1.07 m (3.5 ft) long. The end tubes are axially movableand extend through the outlet mixing chamber and throughholes with internal 0-ring oil seals in an aluminum endplate. The end tubes can be individually moved andlocked into place from the outside. Movement of the endtubes inward forces the flexible tubing into wave-likeforms and the additional length within the test sectionsimulates the cable thermal expansion. The end plate isrotatable to allow angular displacement which also hasbeen observed in the full scale tests [3]. Skid wiresare simulated with 30-gauge (0.053 cm O.D.) Teflon-insulated electric wire, wound in a continuous helixalong the length of the rigid and flexible tubes. Thespacing was 138 wires per meter (42 per ft) whichcorresponds to a ratio of pitch to skid wire diameter of14.

Pressure measurements at the inlet and outlet ofthe test section were made with a differential oil-water manometer for the low range of flow rates and adifferential oil-mercury manometer for the high range.Oil temperature was measured with copper-constantanthermocouples and a Fluke Model 2240 A Data Logger.Manometer and room temperature were measured with stan-dard mercury thermometers. Sun No. 4 dielectric oilwas used for the tests. Viscosity and density as func-tions of temperature were measured with a modifiedOstwald viscometer and a hydrometer calibrated to APIstandards.

Flow rate was measured and controlled with acalibrated rotameter and a venturi. Frictional heatwas removed and oil temperature was controlled in therange of 37 to 3900 with bypass flow through the heatexchanger.

The friction factor, f, was calculated as a func-tion of the Reynolds number, Re.

Total system accuracy in the determination of fwas checked by determining the pressure drop in theround pipe with the cables removed. The results werecompared with the theoretically known solution ofRe * f = 16 for laminar flow. The determination of fwas found to be accurate within 5 percent.

0018-9510/80/0500-0919$00.75 1980 IEEE

919

Page 2: Pressure Drop in a Model of a Forced Cooled Pipe-Typr Electric Cable System with Cable Snaking

Fig. 1 Schematic Diagram of Experimental Setup

W4 4.445 cm

1.270 cm

5C

/ 0.476 cm

Fig. 2 Cross-Section of Cable System

AxialMovement

Flexible

Pressu re Ta ps

Tube Plastic Tube

4 0.521 m-

fi

half of a sine-shaped wave with its lowest pointresting on the bottom. The data for this case showsthe friction factor to be slightly less than that forstraight cables for Re < 1000 and about the same for Re> 1000. An explanation of this result can be deducedfrom the geometry shown in Fig. 4(b). The low positionof the three cables in the center portion of the testsection is similar to a cradled configuration whichopens up a large flow channel above the cables and pro-duces a lower friction factor in the laminar region (Re< 500) than the cable configuration of Fig. 2 [15].In the laminar region (Re < 500), the fluid easily flowsaround the downward curving center cable and finds lowresistance in the large channel. In the transition andturbulent regions, Re > 500, the flow around theblocking center cable would produce turbulent eddies andvortices in the flow behind it, resulting in greaterpressure drop. For Re > 1000, the two effects evidentlycompensate for each other resulting in a friction factorequal to that for straight cables.

As indicated in Fig. 5, expansion of 8.8 percentresults in more significant changes in friction factor.The ratio of the friction factor for snaked cables tothose of straight cables (f/fo) increases with Re andreaches a maximum of 1.98 at Re = 3500. Examining thecorresponding photograph, Fig. 4(c), reveals that thecables are wound into intertwined helixes of about 1.5turns along the length of the test section. The flowaround such intertwined cables would produce vortices,eddies, and flow turning. Each of these factors wouldcontribute to earlier transition to turbulence andpressure losses which increase with Re, as shown by thedata.

If the angle of the cables to the axis isincreased and, consequently, the pitch between helixwindings is decreased,the vortices and eddies behindthe cables would increase and the flow turning shouldbe greater. These effects would explain increasedfriction factors for the same basic cable pattern asthe expansion is increased further. In Fig. 4(d), thebasic cable pattern for 13.2 percent expansion is thesame as for 8.4 percent but with closer spacings. Asexpected, the friction fators are higher and a maximumvalue of f/fo = 3.19 is reached at Re = 3520.

Correlations were developed for smooth cablesystems which fit the friction factor data obtainedwithin 15 percent. They are for the fractional expan-sion range investigated: 0 < E < 0.132.

The laminar friction factor was found to bef * Re = 26 for E = 0 (straight cables).

For 0.000 < E < 0.044:

0.610 m

Spacer Positioner

teel Tubes

f = 6.54 - 46.8E

Re(0.765 - 1.02E)

f = 0.83 + 10%ReO.5

++ 15 150 < Re < 2000

2000 < Re < 3800

Fig. 3 Snaking Test Section

DISCUSSION OF RESULTS

Smooth Cables

The friction factor data for cables without skidwires are shown in Fig. 5. For 4.4 percent expansion(Fig. 4(b)), the two lower cables (see cross section inFig. 2) rest on the bottom of the plastic tube for mostof their length and the upper center cable forms one-

For 0.044 < E < 0.132:

2f = 6.54 - 62E + 359E

Re(0-765 - 2.18E + 7.86E2)

150 < Re < 2000

2f = 0.83 - 0.180E + 86E + 10%,

2000 < Re < 3800

920

(1)

(2)

+ 10% (3)

(4)

m .:.t x

MM..

Page 3: Pressure Drop in a Model of a Forced Cooled Pipe-Typr Electric Cable System with Cable Snaking

921

Fig. 4(a) Straight Cables

Fig. 4(c) Snaked Cables with 8.8% Expansion

Rough Cables

Figure 6 shows the results for a cable systemwith skid wires. A comparison of Fig. 6 with Fig. 5reveals that the friction factor for rough straightcables, i.e., with skid wires, is substantially greaterthan for smooth straight cables. At Re = 3522, f =0.0135 for a smooth system, whereas f = 0.0265, abouttwice as great, at Re = 3625 for a rough system. Thevalue of f in the rough system increases less from itsstraight cable value with increasing expansion thanwith smooth cables. A maximum value of f/fo = 1.84was obtained at Re 3500 for 13.2 percent expansioncompared with f/fo = 3.19 obtained with the smoothsystem. For maximum expansion, E = 0.132, the magni-tude of f for the rough system is, at the most, 30 per-cent greater than the smooth system throughout thewhole range of Re. At Re = 3500, f rough is only 13percent greater than f smooth (0.049 compared with0.043). A possible explanation of this phenomenon isthat when both the smooth and rough cable systems arestraight, the skid wires produce a level of turbulencein the rough system which is significantly greater thanthat in the smooth system, causing significantlygreater pressure drop. As the cables expand, resultingin snaking, they themselves cause flow blockage andinduce turbulence of such magnitude that the increment-al effect of the turbulence induced by the skid wireand the resulting incremental pressure drop is small.

Correlations were developed for the rough systemwithin the same fractional expansion range of 0 < E <0.132 as follows:

( 2.15f =33 + 5%, Re <: 16.84 (5)

Re V + 6.7E8

f = 1.96 (1 + 6.7E) + 10%, (6)

ReO.535-

Fig. 4(b) Snaked Cables with 4.4% Expansion

Fig. 4(d) Snaked Cables with 13.2% Expansion

2.1516.84

1 + 6.7E

f = 0.626 (1 + 6.7E) + 10%ReO.385-

< Re < 2000

(7)

2000 < Re < 3800

Rotational and Other Effects

Figure 7 presents the smooth system data for acombination of cable axial expansion and rotation andprovides a comparison with 13.2 percent simple linearexpansion. As shown, the friction factor for the caseof combined 13.2 percent expansion and 10800 rotationis lower than that for simple 13.2 percent expansion.A probable explanation is that the cable rotationaldisplacement combined with the coiling due to linearexpansion results in cable positioning which allowsmore free axial flow. Figure 8 presents rotation datafor a rough system. Here, a rotation of 3600 wasapplied and, as can be seen, the friction factor forcombined rotation and expansion was close to that forsimple expansion.

As can be noted from Fig. 5, the smooth straightcable data diverges less than 10 percent from equationf = 26/Re for Re < 500, indicating laminar flow existsin this region with gradual transition to turbulentflow for Re > 500. The same is true for rough straightcables and Re < 300, but f = 33/Re as indicated in Fig.6. However, for this cable system with skid wires, ifthe cross-sectional flow area and DH are calcu-lated on the basis of cable diameter increased by twoskid wire heights, the laminar friction factor willalso closely match f = 26/Re. From this result, it canbe concluded that in laminar flow, the flow apparentlyskims over the skid wires and the resistance to flow isthe same as for flow with smooth cables but withincreased cable diameters.

Page 4: Pressure Drop in a Model of a Forced Cooled Pipe-Typr Electric Cable System with Cable Snaking

922

100

Q0

X11

10-21g2

Re

Fig. 5 Friction Factors for Snaking Cables withoutSkid Wires (Cable Diameter, 13 mm; PipeDiameter, 45 mm)

v-

cl-

-J

Q-

IC]Ll

i0"

lo-,

ReFig. 6 Friction Factors for Snaking Cables with Skid

Wires (Cable Diameter, 13 mm; Skid WireHeight, 0.53 mm; Pipe Diameter, 45 mm)

Downstream Pressure Losses due to Snaking

Modifications in the velocity profile would beexpected in the flow through a snaked region. Suchmodification should result in increased pressure dropdownstream of a snaked region as the flow re-establishes its fully developed profile--similar to an

entrance region. Since the snaking pattern cannot bepredicted, a conservative estimate would be to assumethat in the worst case, the losses would be the same as

that for an entrance region.Measurements were made of the average friction

factors in an entrance region with and without snaking,and the results are shown in Fig. 9. Shown is theaverage friction factor for the total entrance lengthfor each section with L/DH = 127, 177, and 223. Ascan be seen, no difference was found between the snakedand straight entrance, indicating the flow swirl andturning due to snaking does not contribute signifi-cantly to pressure loss. Fully developed flow existsfor L/DH = 177 since there is no change in fAV be-

100

CY('4

-Ja:

10

ICt

102Re

Fig. 7 Friction Factors for Snaking Cables withoutSkid Wires (13.2% Expansion, 10800 Rotation)

loo

N

a-\lIL01II

Re

Fig. 8 Friction Factors for Snaking Cables with SkidWires (13.2% Expansion, 3600 Rotation)

tween L/DH = 177 and L/DH = 228. Above Re = 2800,in the fully turbulent region, the entrance fAV isthe same as fFD for fully developed flow. A plot ofthe ratio of the average entrance friction factorobtained for L/DH - 127 to the fully developed fric-tion factor, versus Reynolds number, is shown in Fig.10. An equation was developed for fAV/fFD versusRe with a least-square fit through the data points forfAV/fFD > 1.0. The equation is for L/DH - 127:

fAV(entrance) -4fD 1.91 - 3.16 x 10 (Re) (8)

for 350 < Re < 2875 and,

fAV(entrance) 1.0 for Re > 2875

tFD

This can be expressed in terms of an equivalent length,Le*

Symbols Expansion,%A O Symbols Expansion,% Rotation

A 0 0°v 13.2 0°

v v 13.2 10800*^'v

a Y

A~~~~~AA * ~~~VA *~~AA ~~~~YY A

I I . I I..

, , ,,, ,A

102

(9)

Page 5: Pressure Drop in a Model of a Forced Cooled Pipe-Typr Electric Cable System with Cable Snaking

923

Since

f 2 (L+

Le)AP= p V

DH (10)

where theQ P is a function of the .sum of actual lengthand an increment due to the entrance effect. There-fore:

fAV L+Le. 1.91 3.16 . 1o04 x Re

fED L

where L = 127 DH, solving for Le:

Le = (115. - 0.04 Re) DH , Re < 2875 (11)

For example, at Re = 500,

Le = 95 DH.

Therefore, in 300 ft (91.4 m) of 8-inch (20.3 cm) pipecable, (DH= 3.25 in. (8.2 cm)) where L 1100 DH,the increase in pressure drop caused by flow re-establishment downstream of a snaked region is about95/1100 or 8.5 percent.

0.06

0.04

0.02

0 1000 2000 3000 4000 5UuRe = UDH/Wv

Fig. 9 Average Friction Factors for Entrance Regionswith and without Cable Snaking

l I

0~~~~~

U-

4-

1.2

1.0

Re- UDH/v

Fig. 10 fAV'fFD vs. Re for Entrance with L/DH = 127

CONCLUSIONS

Experiments were performed and correlations weredeveloped to determine friction factors as functions ofReynolds number and the amount of snaking for flows inpipe cable systems with and without skid wires. Ourmain concern was to establish a reasonable upper boundcaused by extremely severe cable snaking patterns. Snak-ing due to thermal expansion in a full scale systemcan be of this maximum severity only if the expandedlength creates a concentrated buckling in a shortsection along the cables.

The model configuration used was the open triang-ular one which creates the highest pressure drop forstraight cables. Other configurations can be expectedto have somewhat different friction factors at lowvalues (< 5%) of linear expansion. For example, at4.4% expansion (Fig. 4(b)) the open triangular modelassumed anessentially cradled configuration over mostof its length with a correspondingly reduced frictionfactor (Fig. 5). However, progressive expansions cre-ated strongly snaked patterns which could have resultedfrom any of the initially straight configurations.This, friction factors found for severe snaking crea-ted by expansions of over 8% should be independent ofthe initial, straight configurations. The good corre-lations obtained between previous model and full-scalestudies with straight cables indicate that the dimen-sionless correlations of friction factors with appro-priate Reynolds numbers obtained in model studies canbe used with full scale systems. To apply our results,first the distribution of snaking occurring in a fullscale system has to be established. Then, using themethods described herein, the pressure drop in eachof the snaked portions as well as their downstreamregions can be estimated.

The ratio of the friction factorof a snaked sys-tem to that of a straight system (f/f ), increased withRe. At the maximum Re (3800) and expansion (13.2 per-cent) tested, f/fo is 3.17 for systems without skidwires and 1.80 with skid wires. A combination ofexpansion and rotation (up to 10800) resulted in fric-tion factors which were less than or equal to cases ofsnaking with simple linear expansion.

ACKNOWLEDGEMENT

This work was supported in part by Contract No.EPRI RP 7853-1-B from the Electric Power ResearchInstitute. Oil was furnished by the Sun Oil Company.

REFERENCES

1. Koci, P. F., Glicksman, L. R., and Rohsenow, W.M., "An Analysis of Pumping Systems for theCooling of Underground Transmission Lines," PartIV of IV, MIT Laboratory Report, MIT-EL74006,August 1974.

2. Slutz, R. A., Glicksman, L. R., and Rohsenow, W.M., "Measurement of Fluid Flow Resistance forForced Cooled Underground Transmission Lines,"IEEE Trans. Vol.PAS-94, pp. 1831-1834, September

1975.

3. Williams, J. A., Eich, E. D., and Aibo, T.,"Forced Cooling Tests on 230 kV and 345 kV HPOFCable Systems," IEEE Winter Meeting on PAS,January 1977.

4. Beckenbach, J. W., Glicksman, L. R., and Rohsenow,W. M., "The Prediction of Friction Factors inTurbulent Flow for an Underground Forced CooledPipe-Type Electrical Transmission Cable System,"Part III of IV, MIT Energy Laboratory Report MIT-EL74005, September 1974.

Symbols L/D

o 127A 177 Straight Entrance

a, _.* 228v 127 Snaked Entronce

Ya

* 11 °

A *Y..^,%I

Page 6: Pressure Drop in a Model of a Forced Cooled Pipe-Typr Electric Cable System with Cable Snaking

924

5. Slutz, R. A., et al., "Cooling of UndergroundTransmission Lines: Heat Transfer Measurements,"Part I of IV, MIT Energy Laboratory Report, MIT-EL74003, January 1974.

6. Notaro, J., and Webster, D. J., "Thermal Analysisof Forced Cooled Cables," IEEE Trans. PAS, Vol.90, pp. 1225-1231, May 1971.

7. Kilar, L. A., and Engelhardt, J. S., "UltimatePower Capabilities of HPOF Pipe-Type CableSystems," IEEE Trans. PAS, Vol. 82, pp. 365-379,June 1963.

8. Stoecker, W. F., Williams, J. L., and Zanona, A.,"The Refrigeration of Underground High VoltageElectrical Conductors," Proc., XIIIth Congress ofRefrigeration, 1971, and Progress in Refrigera-tion Science and Technology, 1971.

9. Chato, J. C., and Chern, S. Y., "Effects ofNonuniform Cooling on the Heat Transfer from anInsulated Electric Cable," J. of Heat Transfer,Vol. 97, pp. 424-428, August 1975.

10. Abdulhadi, R. S., "Natural and Forced ConvectiveCooling of Underground Electric Cables," Ph.D.Thesis, Dept. of Mech. and Ind. Engr., Universityof Illinois at Urbana-Champaign, Urbana, IL,1975.

11. Abdulhadi, R. S., and Chato, J. C., "Natural andForced Convection Cooling of Underground ElectricCables," Tech. Report No. ME-TR-609, UILU-ENG 74-4003, 1975, University of Illinois at Urbana-Champaign, Urbana, IL, December 1975.

Richard Ghetzler received his B.S. inMechanical Engineering from Illinois Instituteof Technology and M.S.M.E. from the Univer-sity of California at Berkeley in 1967.

His professional work has included flight testanalysis of the Apollo spacecraft propulsionsystem with NASA and TRW Systems Group,and development of biomedical life supportdevices with Northwestern University. He ispresently completing work toward a Ph.D inMechanical Engineering with a specialty in the

fluid and thermal sciences, at the University Illinois.

John C. Chato is Professor of Mechanical andBioengineering at the University of Illinois atUrbana-Champaign. He received his M.E. de-gree from the University of Cincinnati, M.S.from the University of Illinois and Ph.D. fromM.I.T.

Prior to coming to Illinois in 1964, he was anAssistant Professor of Mechanical Engineeringat M.I.T. His primary research area is heattransfer in such diverse fields as biology,medicine and electrical systems, and he pub-

lished numerous papers in journals such as the IEEE Transactions. Heis a senior member of IEEE, Fellow of ASME, and member ofASHRAE, ASEE and IIR. He was elected to several honor societies;received the Distinguished Engineering Alumnus Award from theUniversity of Cincinnati, the Charles Russ Richards Memorial Awardfrom the ASME, and the Russell B. Scott Outstanding Research PaperAward from the Cyrogenic Engineering Conference Board. He held anNSF Postdoctoral Fellowship in Germany, a Fogarty Senior Interna-tional Fellowship in Switzerland; and visited Hungary under the spon-sorship of the U.S. and Hungarian Academies of Science.He is Associate Editor of the Journal ofBiomechanical Engineering.

Transactions ofASME.

12. Chern, S. Y., and Chato, J. C., "NumericalAnalysis of Convective Cooling of Pipe-TypeElectric Cables," Tech. Report ME-TR-712, UILU-ENG76-4006, 1976.

13. Chern, S. Y., "Numerical Analysis of ConvectiveCooling of Pipe-Type Electrical Cables," Ph.D.Thesis, Dept. of Mech. and Ind. Engr. Universityof Illinois at Urbana-Champaign, Urbana, ILJanuary 1977.

14. Abdulhadi, R. S., and Chato, J. C., "CombinedNatural and Forced Convective Cooling ofUnderground Electric Cables," IEEE Trans., Vol.PAS-96, No. 1, pp. 1-8, January 1977.

15. Chato, J. C., and Abdulhadi, R. S., "Flow and HeatTransfer in Convectively Cooled UndergroundElectric Cable Systems: Part 1-Velocity Distri-butions and Pressure Drop Correlations," J. ofHeat Transfer, Vol. 100, No. 1, pp. 30-35,February 1978.

16. Abdulhadi, R. S., and Chato, J. C., "Flow and HeatTransfer in Convectively Cooled UndergroundElectric Cable Systems: Part 2--TemperatureDistributions and Heat Transfer Correlations,"J. of Heat Transfer, Vol. 100, No. 1, pp. 36-40,February 1978.

17. Chato, J. C., et al., "Free and Forced ConvectiveCooling of Pipe-Type Electric Cables," FinalReport, EPRI EL-147, Project 7821, ERDA E(49-18)-1568, 1977.

Discussion

R. B. Blodgett (The Anaconda Co., Greenwich, CT): The authors' finepresentation would be even better, if they were to clarify theirnonenclature. For example, the U in several figures is not defined. Aspecific conclusion regarding the effect of skid wires would be helpful.They might also refer to a previous study on snaking in pipe cables. (1)Also of interest might be a study of the thernal-mechanical bending pro-blem. (2) The laboratory equipment used in that study was developed toevaluate connectors for aluminum conductor pipe cable. (3)

References

(1) Mcllveen, Edward E., et al; Mechanical Effects of Load Cyclingon Pipe-Type Cable. T-PAS v97n3 May/June 78, 903-913.

(2) Eich, Edward D., Appendix VII in Minutes of 58th Meeting of theIEEE Insulated Conductor Committee, Boston, Mass., April,1976.

(3) Blodgett, Robert B., Supplement to 1972 IEEE UndergroundTransmission Conference 72 CHO 608-0-PWR (Sup), Pittsburgh,May, 1972.

Manuscript received February 28, 1979.

R. Ghetzler and J. C. Chato: The authors appreciate the commentsmade by Dr. Blodgett.The U referred to in the graphs is the average flow velocity calculated

on the basis of the crossectional flow area which excludes only the areaof the cables.For the open triangular configuration tested, the skid wire increases

the friction factor about 25% in laminar flow and 100% in turbulentflow (Re > 3000), when compared with smooth cables. EThe work by Mcllveen et. al., of Reference (1) is of definite related

interest. From the data indicated, the average cable expansion for the205 ft. test length is 1.4°7. It was noted that most of the snaking was

concentrated in the first 40 ft. from the current supply end. This wouldmean that the snaking for this full scale test would be about 7% in thissection, which falls within the range of expansion studied in the presentwork. In fact, the snaking shown in the references photographs appearsmore severe than Figure 4 (b) of the present work (4.4%o expansion) andless severe than Figure 4(c), (8.8% expansion), providing a good matchwith our results.

Manuscript received April 13, 1979.