Application of QuickField Software to Heat Transfer Problems i j k By Dr. Evgeni Volpov

Basic Formulations for GIS HT model Boundary Conditions 1. T(S) = T 0 Const Temperature T(S) = T 0 + k.S Linear Temp. T(S) = T 0 + k.S Linear Temp. 2. F n = -q s Flux F n (+) - F n (-) = -q s F n (+) - F n (-) = -q s 3. F n = a(T - T 0 ) Convection a - film coefficient T 0 – temperature of contacting medium F n = b.K sb (T 4 - T 0 4 ) Radiation 4. F n = b.K sb (T 4 - T 0 4 ) Radiation K sb - Stephan-Boltzmann constant; b - emissivity coefficient Classical Heat Transfer Equations

Boundary conditions & domain characterization Volume element Surface element Point-Source element

Joule losses distribution at central conductor 1000 A 1920 W/m W/m 3 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 kV Thermo-static field mapping in GIS compartment

SF6 GIS HT Model Parameters 1. SF6 Thermal Conductivity g = W/m.K 2. Air Thermal Conductivity a = W/m.K 3. Epoxy Thermal Conductivity e  ( ) W/m.K 4. Aluminum Thermal Conductivity al  ( ) 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  ( ) 10 3 < Gr.Pr < 10 6 (for SF6 GIS) 6.2. External Air space: a c  (2-10) W/K.m 2 ; T 0  (20-25  C) 7. Radiation Parameters: equivalent emissivity coefficient : b e  ( )

GIS Geometric Model examples Symmetry Axis Air layer (a) L L (b) Hot-spot

 - r  - r r - Z r - Z Geometric Models & results presentation

Thermal Field mapping for BB model 1.2 m T 0 (ambient) = 20  C 28.8 C28.8 C29.8  C 64  C60.1  C 64  C54.0  C 28.1  C29.7  C Conductivity only 23.0  C23.8  C 64  C63.0  C 1.2 m1.2 m Hot-spot Flange 1000 A Conductivity + convection Conductivity + convection+ radiation

29.1  C31.0  C 64  C54.1  C 23.1  C23.9  C 64  C62.6  C 26.8  C29.5  C 64  C43.0  C 2.3 m Conductivity + convection Conductivity + convection+ radiation Conductivity only Flange T 0 (ambient) = 20  C 1000 A Thermal Field mapping for BB model 2.3 m Hot-spot

T max  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 Temperature drop along the enclosure

L [m] Max temperature on the enclosure Enclosure length T max  C 50 kW/m kW/m 3 Specific Joule loss in the damaged contact R = 100  I = 1000 A V = 1000 cm 3 Enclosure temperature with no damaged contact T 0 (ambient) = 20  C Enclosure overheating as a function of the BB length Conductivity + convection Conductivity + convection+ radiation

T  C 3   sec 2.3 m Q 2 = 2 kW/m 3 Q 1 = 100 kW/m 3 HT Transients for BB model g  k = 0.10 Conductivity + convection Steady State distribution Initial distribution 1000 A 0 A T 0 (ambient) = 20  C