Application of QuickField SoftwareApplication of QuickField Software

to Heat Transfer Problemsto Heat Transfer Problems

i

jk

By Dr. Evgeni Volpov

Basic Formulations for GIS HT model Basic Formulations for GIS HT model

Boundary Boundary ConditionsConditions

11. . T(S) = TT(S) = T0 0 Const Const TemperatureTemperature

T(S) = TT(S) = T00 + k.S Linear Temp. + k.S Linear Temp.

22. . FFnn = -q = -qs s FluxFlux

FFnn(+) - F(+) - Fnn(-) = -q(-) = -qss 3. 3. FFnn = a(T - T = a(T - T00) ) ConvectionConvection

a - film coefficient T0 – temperature of contacting medium

4. FFnn = b.K = b.Ksbsb(T(T44 - T - T0044) Radiation) Radiation

Ksb - Stephan-Boltzmann constant;

b - emissivity coefficient

Classical Heat Transfer Classical Heat Transfer EquationsEquations

Boundary conditions & domain characterization

Volume element

Surface element

Point-Source element

Joule losses distribution at central conductor1000 A

1920 W/m3

500 W/m3

Electric Field distribution in GIS compartment

100 kV AC

enclosure

2.3 MV/m

epoxy spacer

53 C

31 C

HV conductor current 1000 A

P SF6 = 0.6 MPa

Air

Spacer deformation under SF6 pressure

epoxy spacer

enclosure

Coupling Problems solution for SF6 GIS 170 kVCoupling Problems solution for SF6 GIS 170 kV

Thermo-static field mapping in GIS compartment

SF6 GIS HT Model Parameters1. SF6 Thermal Conductivity g = 0.0136 W/m.K

2. Air Thermal Conductivity a = 0.026 W/m.K

3. Epoxy Thermal Conductivity e (0.3-0.6) W/m.K

4. Aluminum Thermal Conductivity al (140-220)

W/m.K

5. Copper Thermal Conductivity cu = 380 W/m.K

6. Convection Parameters:6.1. Internal SF6 space:

k = 0.133(Gr.Pr)0.28 (1.2 - 6.0)

103 < Gr.Pr < 106 (for SF6 GIS)

6.2. External Air space:

ac (2-10) W/K.m2 ; T0 (20-25C)

7. Radiation Parameters:

equivalent emissivity coefficient: be (0.01 - 0.6)

GIS Geometric Model examples

2 0 0 0

R 0R 1R 2

Symmetry Axis

Air layer

R0R1R2

L > 5 0 0 0

(a)L

L

(b)

Hot-spot

- - rr rr - Z - ZGeometric Models & results presentation

Geometric Models & results presentation

Thermal Field mapping for BB model 1.2 m T0 (ambient) =

20C

28.8 C29.8 C

64 C 60.1 C

64 C 54.0 C

28.1 C29.7 C

TemperatureT (K)

337.0

332.6

328.2

323.8

319.4

315.0

310.6

306.2

301.8

297.4

293.0

Conductivity only23.0 C23.8 C

64 C 63.0 C

1.2 m

Hot-spot Flange

1000 A

1000 A

1000 A

Conductivity + convection

Conductivity + convection+ radiation

TemperatureT (K)

337.0

332.6

328.2

323.8

319.4

315.0

310.6

306.2

301.8

297.4

293.0

29.1 C31.0 C

64 C 54.1 C

23.1 C23.9 C

64 C 62.6 C

26.8 C29.5 C

64 C 43.0 C

2.3 m

Conductivity + convection

Conductivity + convection+ radiation

Conductivity only

Flange

T0 (ambient) = 20C

1000 A

1000 A

1000 A

Thermal Field mapping for BB model 2.3 m

Hot-spot

0

1

2

3

4

5

6

60 70 80 90 100 110 120

Tmax C

T C

BB length 2 m

BB length 1 m

Including radiation

Enclosure overheating as a function of Hot-spot temperature

Hot-spot temperature

Tem

pera

ture

dro

p al

ong

the

encl

osur

e

10

20

30

40

50

60

0.5 1.0 2.0 3.0 4.0 5.0

L [m]

Max t

em

pera

ture

on t

he

en

closu

re

Enclosure length

Tmax C

50 kW/m3

100 kW/m3

Specific Joule loss in the damaged contact

R = 100 I = 1000 AV = 1000 cm3

Enclosure temperature with no damaged contact

T0 (ambient) = 20C

Enclosure overheating as a function of the BB length

Conductivity + convectionConductivity + convection+

radiation

TemperatureT (K)

96.40

88.76

81.12

73.48

65.84

58.20

50.56

42.92

35.28

27.64

20.00

T CT C

3 2.6 10 5 sec

2.3 m

Q2 = 2 kW/m3Q1 = 100 kW/m3

HT Transients for BB model

g k = 0.10

Conductivity + convection

Steady State distribution

Initial distribution

1000 A

0 A

T0 (ambient) = 20C