Turbulent Natural Convection and Thermal Behaviour of Cylindrical Gas-Insulated Transmission Lines (GIL)

8/11/2019 Turbulent Natural Convection and Thermal Behaviour of Cylindrical Gas-Insulated Transmission Lines (GIL)

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Turbulent Natural Convection and Thermal

Behaviour of Cylindrical Gas-Insulated

Transmission Lines (GIL)

Abdellah Chakir and Hermann

Koch

,41rstmct - This paper presents a numerical study of the natural

convection of gases in a horizontal armulus of gas-umdated

transmission lines (GIL). It consist of thermal analysis of high

voltage power gas insulated transmission lines,

In different case

studies the inner cylinder is heated of a constant heat or kept at a

constant temperature, the outer cylinder is mamtained at constant

temperature.

The

cylinders are

long ancl the flow is assumed to have

axially independent properties. The two dimensional analyses of the

heat transfer and fluid motion are performed for Rayleigh number

ranging from 10S to 100, the radius ratio is at 2,5. Comparisons are

made with experimental test set up and measurements.

Index Terms - Gas-Insulated Transmission Line, natural convection,

thermal behavimrr, numerical study, amnrli, experimental test set-up,

measurement

I. INTRODUCTION

Flows due to the natural convection between two horizontal

isothermal cylinders has been widely studied by many

authors. The study of this type of problem is usually

encountered in many fields specially in solar concentrators,

thermal storage plants, pressurised water reactors and

electrical Gas insulated transmission lines.

Many

experimental and numerical works are carried out for laminar

case or turbulent flow with low Rayleigh number (till 10) and

for isothermal cylinders as boundary conditions. Only a few

papers studied the convection with non isothermal boundary

conditions and for a Rayleigh over than 107. The results of

these experimental and theoretical-numerical studies show the

dependence of the flow patterns on the Rayleigh number, the

Prandtl number and radius ratio. Investigations of the problem

experimental] y and numerically determined the temperature

distribution and the local heat transfer coefficients in air and

in water. The use of two fluid showed the Prandtl number

affect the transition characteristics. In another experimental

study it was shown, that the heat flow is substantially altered

on both cylinders due to the influence of the eccentricity of

the inner cylinder.

Good agreement for the temperatures profiles and the flow

pattern was found and the Graschoff transition number was

determined indirectly. It was shown, that the stream fimction

remain negative, i.e., no secondary counter-rotating cells

generation. The flow regions of convection a three

dimensional spiral flow divided into 5 regions: an inner

boundary layer near the inner cylinder, an outer boundary

layer near the outer cylinder, a vertical plume region above

the inner cylinder, a stagnant region below the inner cylinder,

and a core region surrounded by the four regions.

This study consists of thermal analysis of high voltage power

gas insulated transmission lines (GIL) based on the above

mentioned basic knowledge. Two coaxial cylinders of a

metallic sheath, an inner conductor and outer enclosure are

separated by a dielectric medium, mixture of gas SF6 and Nz.

The GIL is designed to be laid in underground or laid in

Tunnel with a cooling air flow. The cylinders are very larger

than the gap between the inner and outer cylinder, then the

two dimensional is applicable.

The results of the calculations and the experimental

measurements show that for the GIL a ve~ good heat transfer

from the conductor, which is represented by the inner pipe, to

the outer enclosure is given. The temperature drop between

conductor and enclosure is below 10 K. For the practical

application of the GIL this means that for a directly buried

GIL, or a GIL in a tunnel the thermal heat produced by the

current through the conductor is transported fast to the

surrounding of the GIL the soil or the ambient air, and leaves

low maximum temperatures at the conductor.

Compared to a solid insulated cable the maximum

temperatures are much lower at the transition point between

the outer cable or GIL surface and the soil or air around.

Specially in cases of high transmission power ratings of 1500

to 2000 MVA at 420 kV or 550 kV transmission voltage

levels the better heat transmission of the GIL is an important

advantage.

A. Chakir and H. Koch are with Siemens AG, Power Transmission and

Distribu tion, P. (). Box 3220, 91050 Erlangen, Germany

(e-mad: abdelIah,chakw@ev. slemens.de, hermann.koch@ev. siemens.de)

0-7803-7031-7/01/ 10.00 (C) 2001 IEEE

0-7803-7173-9/01/ 10.00 2001 IEEE 162


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o ~~

o 20 40

en 80 IIXJ

120 140 160

180

Alw@ (degreas)

Fig. 2. Nusselt number distribution of the inner cylinder calculated with

different wall function in comparison to e~perimental data presented by

Temperatures for the Angles 60, 70, 60

1

~

0


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Fig. 5b. Measur ing points

TABLE 2 EXPERIMENTAL RESULTS FOR CASE 2 AND 3

E : ~

Ra=2,1 10 Ra=l,7 10

case 2

case 3

Positio inner cylinder outer cylinder

inner cylinder outer cylinder

n of the T(K) T(K) T(K)

T(K)

sensor

o

325.56 (point 309,16 (point 3 ;3.46 (point 335.96 (point

90 1)

2) 1) 2)

180 325.06 (point 311.96 (point

3: 2.86 (point 339.96 (point

3) 4) 3) 4)

325.46 (point 313.36 (point 353.36 (point 341.86 (point

5 6 5)

5

Heat

flux 101.8

110.5

(Wlm2

TABLE 3 COMPARISON OF NUMERICAL AND EXPERIMENTAL

(

&sa

Angle r) experiment Equilibrium

The calculations are made for a constant heat flux

101.8 W/m, 110.5 W/m applied at the inner cylinder obtained

from the experiments and with a temperature constant at outer

cylinder, which is the average value of the three values above

(311 .5K, 339.3 K). The numerical results are presented in

the Tab. 2. The calculation was carried out with radiation be-

tween the two cylinders.

The same numerical results are obtained with the Van Drist

and Spalding model [3]. They arc slightly over the value

obtained with the Equilibrium model. The calculated

temperature clifference between top and the middle is over

than 5,

however the experimental difference is not

significant. One can explain the constant value of temperature

at the inner cylinder in the experiment by the more important

conduction heat phenomena in the wall of inner cylinder than

the convection phenomena at the boundary layer.

This is shown by the Biot number resistance in the wall

(Bi= a

=0.02), i.e., the conduction heat is

JCY,inde, I

Lo

much smaller than the convection heat resistance. The Nusselt

number at the inner and outer cylinder for the three wall

function are presented in fig. 5 for case 2. The inner cylinder

is at a constant heat flux. In the outer cylinder the Nusselt

number increase sharply from the bottom till the horizontal

plan (90 )where remain constant until the region near the top.

For the inner cylinder the temperature decrease slowly from

angle 0 till angle 160 at which an inversion increase the

Nusseh value to the one at OO. The equilibrium model

presents an increased Nusselt-number, while the Spalding and

Van Drist [4] models presents a decrease (fig. 5). This

phenomena of Nusselt-number decrease for Spalding and Van

Drist models appear only for high Ra number (see fig. 1: Ra =

2,5 10). Both wall function Spalding and Van Drist seem not

good for high turbulence. The numerical results obtained with

the equilibrium model presents the best agreements with the

experiment values (Tab 3). So the calculation for the second

experiment are made only with this model and results of

temperatures for inner cylinder are presented in Tab. 4

TABLE 4 COMPARISON OF NUMERICAL AND EXPERIMENTAL

RESULTS (CASE 3)

(Case 3) Ra=l,7 10 inner cylinder

k

ngle ()

o

90

180

7 -

experiment I Equilibrium model

T(K) T(K)

353.3

361.4

352.7

354.6

353.2 I 360.8

OUTER CYUNDER

.

l

Eqlb

60

+

S@ldlm

-c-

Van Dnst

m-

=40-

zsc-

20-

o ~~

o 20 40 60 S6 100

120 140

160

180

Angle (degrees)

Fig. 5 . Nusselt number distribution of the outer cylinder calculated with

different wa ll function for a h igh Rayle igh number (case 2)

Three different studies were made to examine mainly the

effects of a Rayleigh number variation on the convection heat

transfer at the inner and outer cylinder (fig. 6, 7). The

temperature was constant at both cylinders. The radiation

was not considered. The Rayleigh number reach from 2,5e6

to 4,2e9, the other parameter are nearly constant at R+=2,5

and PI=0,7 (case 1,4,5).

0-7803-7031-7/01/ 10.00 (C) 2001 IEEE

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V. CONCLUS1ON

An investigation of turbulent natural convection in a

horizontal concentric annulus wa:s carried out for high

Rayleigh numbers up to Ra=l O1. T he results were presented

in form of temperatures and Nusselt numbers at the inner and

outer cylinder. The numerical results were compared with

experimental data. Three different wall functions were used

to find an accarate model. There were no effects noticeable

for a low tttrlbulent flow. The differences to the achieved

Nusselt results of Goldstein were small. The maximum

temperature deviation was 15Yo.

The equilibrium model shows the best results compared to the

carried out experiment. The temperatures of the middle inner

cylinder were nearly equal. However, high differences

appeared at the top/bottom of the cylinder. This were the

results of the much smaller heat resistance in the wall than the

convective resistance. The calculated temperatures at the

inner cylinder had a uniform trend except the top and bottom,

where they were rising to the highest values at 0 and 180

The Nusselt number as a function of Rayleigh showed the

high dependency. The increasing heat convection for high

Rayleigh numbers occurred especially in the middle part of

the cylinders and in the top of the outer one.

The temperatures in the center of the annulus became

constant for higher turbulence. The temperature gradient at

the wall boundary layers was rising. The trend for high

turbulence is going to small thermal boundary layer at the

inner and outer cylinder with uniform temperatures at the

annulus center.

[1]

[2]

[3]

[4]

[5]

VI. REFERENCES

T.H. Kuebn und R.J. Goldstein, An experimental and theoretical

study of nataral convection in the annulus between horizontal

concentric cyl inders, J Fhrid Mech. 74, 695-719(1976).

T. H. Kuehn, R. J. Goldstein, An experimental study of natural

convection heat transfer in concentric and eccentric horizontal

cylindrical annu li, ASME J. Heat Transfer 100,635-640 (1978).

B. E. Launder, D. B. Spalding, The numerical computation of

torbulent flows, Computer methods in applied mechanics and

engineering Vol. 3,269-289 (1974).

E. R. van Drist, On Turbulent Flow Near a Wall, Journal of the

Aeronautical Sc iences, vol. 23, 1956, p. 1007

Fluid flow, Ansys Theory Reference release 5.4, chap.7, pp 7.1 - pp

7-39 (1996)

VII. BIOGRAPHIES

Institute was f in ished with

Dr.-hrg. Hermann Koch was born in

November 1954 in Hauswarz, Germany.

From 1976-1979 he studied Electrical

Engineering at the Fachhochschtde Riissels-

heim, where he graduated with the d ip loma of

eng ineering (D ipl.-lng.). From 1980-1981 he

studied on a Ftdbright Scholarship at New

Jersey Institute of Techno logy, Newark, New

Jersey, USA. From 1981-1986 he studied

Electrica l Engineering at the Technical Uni-

versity of Darrnstadt, where he graduated with

the diploma of engineering (Dipl.-Ing.). His

continued research work at the High Voltage

his doctoral work about Partial Discharges in

Low Voltage Equipment and the degree of Dr.-hrg. Since 1990 he is

working with Siemens High Voltage Division where he ia head of Gas

Insulated Lines Department. He is committee member of the IEEE Power

Engineering Society in the Gas Insulated Substat ion Committee. In the IEC

he is Secretary of Technical Subcommittee SC I 7C and in CENELEC he is

Secretary of the Technical Commi ttee TC 17.

in research and development

Insulated Substations.

Dr.-lng. Abdellah Chakir was born 1965

in Casablanca, Morocco. He received his

Dipl. Ing. und M. SC. degrees in

mechanical and aeronautical engineering in

1990 from ENSMA (Ecole Nationale

Superieure de

M4canique et

dA&otechnique de Poitiers, France) and

received the Ph. D. degree in Mechanics in

1993 from Poitiers University, France.

From 1993-1996 he was Auxiliar Professor

in mechanical engineering at the

Polytechnic Institute and ISACE of

Guarda, Portugal . S ince 1996 he is working

with Siemens High Voltage Division, Gas-

0-7803-7173-9/01/ 10.00 2001 IEEE 167

Documents

Turbulent Natural Convection and Thermal Behaviour of Cylindrical Gas-Insulated Transmission Lines (GIL)