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Analysis of Temperature Distribution and Ablation Gas Concentration Distribution under
Consideration of Nozzle Ablation Caused by Spiral Arc Applied Axial Magnetic Field
โYuki Suzuki, Shoya Nishizawa, Yusuke Yoshifumi Maeda, Toru Iwao (Tokyo City University)
Results
Arc conductance with time.
Bz = 10 mT
3D arc temperature distribution (Bz = 10 mT). Ablation gas concentration distribution (Bz = 10 mT).
EPP-20-081 ใปYuki Suzukiใป Tokyo City University ใป 1 /13 1 /12TA5-S2-015
Current zero
Decrement of arc energy and creating the weak point
[1] Japan Electric Engineersโ Association : http://www.jeea.or.jp/course/contents/05301/
Needs Improving interrupting performance of air circuit breakers and increasing voltage
Target 9.4: Reducing Environmental load
Global warming coefficient of SF6 gas
โ 22800 times CO2
HV, UHV: SF6 gas circuit breaker
Voltage tolerance corves of equipment[1] .
Introduction Improvement of circuit air breaker performance
SF6 gas free circuit breaker
EPP-20-081 ใปYuki Suzukiใป Tokyo City University ใป 2 /13 2 /12TA5-S2-015
Low temperature and electrical conductivity Current interruption
[2] Yokomizu Yasunobu๏ผ โใฌในๅนไปใใซใใๅคง้ปๆตใฎใขใผใฏ้ฎๆญใซ้ขใใๅบ็ค็ ็ฉถโ, Nagoya university doctoral paper (1991๏ผ[3] Toshiyuki Onchi๏ผYasunori Tanaka๏ผKei Kawasaki๏ผYoshihiko Uesugi๏ผโThermofluid Simulation of Arc Plasmas Confined by a Polymer
Hollow Cylinderโ๏ผ IEEJ Trans.PE๏ผVol.131๏ผNo.2๏ผpp.196-204 ๏ผ2011๏ผ
[3]Thermal re-ignition and dielectric re-ignition[2]. Thermodynamic and transport properties of
POM,PTFE vapor and air[3] .
Re-ignitionResearch background
3 /12TA5-S2-015
Axial magnetic fieldResearch background
[4] Satoshi Hirayama, Takayasu Fujino, Motoo Ishikawa, Tadashi Mori, Katsuharu Iwamoto, Hiromichi Kawano, ๏ผ โThree-dimensional Time-dependent Numerical Analysis of SF6 Arc Plasma under Externally Applied
Magnetic Fieldโ, IEEJ Transactions on Power and Energy, Vol.131, No.10, pp.865-871 (2011)
4 /12TA5-S2-015
Ablation gas and axial magnetic fieldResearch model
Bz
(a) w/o axial magnetic field. (b) w/ axial magnetic field.
Arc
Localized ablation gas
blast and contamination
(b) w/ axial magnetic field.
โ Concentrative cooling
of arc
โ Increment of arc voltage
๏ผ
Improvement of arc
interruption performance
5 /12TA5-S2-015
Calculation method
Calculation area.
ใป Electrodes material: Cathode-Cu๏ผAnode-Cu
ใป Gas๏ผ N2 ใป Pressure: 0.1 MPa
ใป Inter electrode distance: 10 mm
ใป Nozzle radius๏ผ 10 mm
ใป Nozzle material: POM
ใป Current๏ผ 1-100-0 A ใป di/dt๏ผ 0.5 A/ฮผs, - 0.5 A/ฮผs
ใปAxial magnetic field : 0, 10, 100 mT
Conditions
Basic assumptions
ใป 3-D rectangular coordinate system
ใป Laminar flow
ใป Local thermal equilibrium
ใป Optically thin
ใปWithout ablation caused by radiation transfer
Governing equation
ใปMass conservation ใป Current continuity equation
ใปMomentum conservation ใป Ohms law
ใป Energy conservation ใปMaxwell Ampere law
ใป Advection diffusion equation
3-D rectangular coordinate system
Current with time at -0.5 A/ยตs of current decrement
ratio and 0.5 A/ยตs of current increment ratio.
Bz
External magnetic
field density
6 /12TA5-S2-015
Ablation gas generation from nozzle
Chemical reaction considering mixed gas of
nitrogen and ablation gas.
Structural diagram of POM.
๐
๐๐ก๐๐ถ +
๐
๐๐ฅ๐๐ข๐ถ +
๐
๐๐ฆ๐๐ฃ๐ถ +
๐
๐๐ง๐๐ค๐ถ =
๐
๐๐ฅ๐ท
๐๐๐ถ
๐๐ฅ+
๐
๐๐ฆ๐ท
๐๐๐ถ
๐๐ฆ+
๐
๐๐ง๐ท
๐๐๐ถ
๐๐ง+ ๐๐
๐
Advection diffusion equation
ฮ๐๐๐ =๐๐
2๐๐pol๐๐
(TโงTmelt)โข Hertz-Knudsenโs equation[3]
๐๐ฃ = ๐0exp๐ฟ๐
๐ ๐๐๐๐๐โ
๐ฟ๐๐ ๐
โข Clausius-Clapeyronโs equation[3]
โข Mass generation[3]
๐๐๐ = ๐polฮ๐๐๐
ฮS
ฮV
ใปP0 [Pa]: Atmospheric pressure
ใปLe [J/kg]: Latent heat of evaporation
ใปR [J/(Kใปmol)]: Gas constant
ใปTboil [K]: Boiling point
ใปPv [Pa]: Saturated vapor pressure
ใปฮabl [1/(m2ใปs)]: Ablation flux
ใปmpol [kg]: Mass of one molecule of polymer material
ใปk [(m2ใปkg)/(s2ใปK)]: Boltzs-mann constant
ใป๐๐๐ kg/(m3ใปs) : Mass generation
Calculation method
7 /12TA5-S2-015
Spiral arcResult and discussion
3D arc temperature distribution.
(a) Without Axial magnetic field (b) Bz = 10 mT (c) Bz = 100 mT
8 /12TA5-S2-015
(a) Without Axial magnetic field (b) Bz = 10 mT (c) Bz = 100 mT
3D arc temperature distribution (t = 240 ฮผs, T = 10000-13000 K).
BzBz
โ Confirmation of the spiral arc caused by axial magnetic field
Result and discussion Ablation gas generation
Ablation gas concentration distribution (X axial center).
(a) Without Axial magnetic field (b) Bz = 10 mT (c) Bz = 100 mT
9 /12TA5-S2-015
Result and discussion Ablation gas generation
3D ablation gas concentration distribution.
(a) Without Axial magnetic field (b) Bz = 10 mT (c) Bz = 100 mT
10 /12TA5-S2-015
Result and discussion Arc length and arc conductance
Arc length with time. Arc conductance with time.
11 /12TA5-S2-015
โ Arc conductance greatly decreased in the case of considering AMF and ablation.
Current zero
Summary
โข The arc was spiraled by applying the axial magnetic field
โข The ablation gas generation rate increased with the magnetic flux density
because the high temperature part of arc is closer to the nozzle caused by
the spiral arc.
ObjectiveAnalysis of Temperature Distribution and Ablation Gas Concentration Distribution
under Consideration of Nozzle Ablation Caused by Spiral Arc
Applied Axial Magnetic Field
โข Three-dimensional temperature distributions of spiral arc caused by axial
magnetic field and ablation gas concentration distributions generated from
nozzle were obtained.
โข The arc conductance decreased the most compared with other conditions in the
case of considering the ablation and axial magnetic field because of the local
cooling of arc and the increment of arc voltage caused by spiral arc
12 /12TA5-S2-015
NOTE
14Supplement
POM:N2 = 10:90
POM:N2 = 20:80
POM:N2 = 90:10
POM:N2 = 80:20
POM:N2 = 70:30
POM:N2 = 60:40
POM:N2 = 50:50
POM:N2 = 40:60
POM:N2 = 30:70POM:N2 = 90:10
POM:N2 = 80:20
POM:N2 = 70:30
POM:N2 = 60:40
POM:N2 = 50:50
POM:N2 = 10:90
POM:N2 = 20:80
POM:N2 = 40:60
POM:N2 = 30:70
POM:N2 = 10:90
POM:N2 = 20:80
POM:N2 = 90:10
POM:N2 = 80:20
POM:N2 = 70:30
POM:N2 = 60:40
POM:N2 = 50:50
POM:N2 = 40:60
POM:N2 = 30:70
POM:N2 = 90:10
POM:N2 = 80:20
POM:N2 = 70:30
POM:N2 = 60:40
POM:N2 = 50:50
POM:N2 = 10:90
POM:N2 = 20:80
POM:N2 = 40:60
POM:N2 = 30:70
Thermodynamic and transport properties
15Supplement
POM:N2 = 20:80
POM:N2 = 60:40
POM:N2 = 50:50
POM:N2 = 40:60
POM:N2 = 30:70
POM:N2 = 10:90
POM:N2 = 90:10
POM:N2 = 80:20
POM:N2 = 70:30
POM:N2 = 10:90
POM:N2 = 20:80
POM:N2 = 90:10
POM:N2 = 80:20
POM:N2 = 70:30
POM:N2 = 60:40
POM:N2 = 50:50
POM:N2 = 40:60
POM:N2 = 30:70
Fig. POM-N2 particle composition 50:50
Thermodynamic and transport properties
16Supplement
Thermodynamic properties of polymer block.
Energy conservation equation
๐
๐๐ฅ(๐๐ฃ๐ฅโ) +
๐
๐๐ฆ(๐๐ฃ๐ฆโ) +
๐
๐๐ง(๐๐ฃ๐งโ)
=๐
๐๐ฅ(๐
๐ถ๐
๐โ
๐๐ฅ) +
๐
๐๐ฆ(๐
๐ถ๐
๐โ
๐๐ฆ) +
๐
๐๐ง(๐
๐ถ๐
๐โ
๐๐ง) + ๐๐ฅ๐ธ๐ฅ + ๐๐ฆ๐ธ๐ฆ + ๐๐ง๐ธ๐ง โ ๐ โ ๐๐
๐ถ(Le + Lm)
[W/m3] = [J/(m3ใปs)]
17Calculation method Governing equation
๐๐
๐๐ก+๐ ๐๐ฃ๐ฅ๐๐ฅ
+๐ ๐๐ฃ๐ฆ
๐๐ฆ+
๐ ๐๐ฃ๐ง๐๐ง
= 0 (1)
๐ ๐๐ฃ๐ฅ๐๐ก
+๐ ๐๐ฃ๐ฅ
2
๐๐ฅ+๐ ๐๐ฃ๐ฆ๐ฃ๐ฅ
๐๐ฆ+๐ ๐๐ฃ๐ง๐ฃ๐ฅ
๐๐ง= โ
๐๐
๐๐ฅ+ ๐๐ฆ ร ๐ต๐ง โ ๐๐ฆ ร ๐ต๐ฆ +
๐
๐๐ฅ
๐๐๐ฃ๐ฅ๐๐ฅ
+๐
๐๐ฆ
๐๐๐ฃ๐ฅ๐๐ฆ
+๐
๐๐ง
๐๐๐ฃ๐ฅ๐๐ง
(2)
๐ ๐๐ฃ๐ฆ
๐๐ก+๐ ๐๐ฃ๐ฅ๐ฃ๐ฆ
๐๐ฅ+๐ ๐๐ฃ๐ฆ
2
๐๐ฆ+๐ ๐๐ฃ๐ง๐ฃ๐ฆ
๐๐ง= โ
๐๐
๐๐ฆ+ ๐๐ง ร ๐ต๐ฅ โ ๐๐ฅ ร ๐ต๐ฅ +
๐
๐๐ฅ
๐๐๐ฃ๐ฆ
๐๐ฅ+
๐
๐๐ฆ
๐๐๐ฃ๐ฆ
๐๐ฆ+
๐
๐๐ง
๐๐๐ฃ๐ฆ
๐๐ง(3)
๐ ๐๐ฃ๐ง๐๐ก
+๐ ๐๐ฃ๐ฅ
2
๐๐ฅ+๐ ๐๐ฃ๐ฆ๐ฃ๐ฅ
๐๐ฆ+๐ ๐๐ฃ๐ง๐ฃ๐ฅ
๐๐ง= โ
๐๐
๐๐ฅ+ ๐๐ฆ ร ๐ต๐ฅ โ ๐๐ฅ ร ๐ต๐ฆ +
๐
๐๐ฅ
๐๐๐ฃ๐ง๐๐ฅ
+๐
๐๐ฆ
๐๐๐ฃ๐ง๐๐ฆ
+๐
๐๐ง
๐๐๐ฃ๐ง๐๐ง
+ ๐0 โ ๐ ๐ (4)
๐ ๐โ
๐๐ก+๐ ๐๐ฃ๐ฅโ
๐๐ฅ+๐ ๐๐ฃ๐ฆโ
๐๐ฆ+๐ ๐๐ฃ๐งโ
๐๐ง=
๐
๐๐ฅ
๐
๐ถ๐
๐โ
๐๐ฅ+
๐
๐๐ฆ
๐
๐ถ๐
๐โ
๐๐ฆ+
๐
๐๐ง
๐
๐ถ๐
๐โ
๐๐ง+ ๐๐ฅ๐ธ๐ฅ + ๐๐ฆ๐ธ๐ฆ + ๐๐ง๐ธ๐ง โ ๐ โ ๐๐
๐(๐ฟ๐ + ๐ฟ๐)(5)
Mass conservation equation
Momentum conservation equation๏ผX, Y, Z direction๏ผ
Energy conservation equation
18Calculation method Governing equation
๐ ๐๐ฅ
๐๐ฅ+
๐ ๐๐ฆ
๐๐ฆ+
๐ ๐๐ง
๐๐ง= 0
(6)
๐๐ฅ = ๐๐ธ๐ฅ๏ผ๐๐ฆ = ๐๐ธ๐ฆ๏ผ๐๐ง = ๐๐ธ๐ง (7)
๐ธ๐ฅ = โ๐๐
๐๐ฅ๏ผ๐ธ๐ฆ = โ
๐๐
๐๐ฆ๏ผ๐ธ๐ง = โ
๐๐
๐๐ง(8)
๐2๐ด๐ฅ
๐๐ฅ2+
๐2๐ด๐ฅ
๐๐ฆ2+
๐2๐ด๐ฅ
๐๐ง2= โยต๐๐ฅ
(9)
๐2๐ด๐ฆ
๐๐ฅ2+
๐2๐ด๐ฆ
๐๐ฅ2+
๐2๐ด๐ง
๐๐ฅ2= โยต๐๐ฆ
(10)
๐2๐ด๐ง
๐๐ฅ2+
๐2๐ด๐ง
๐๐ฆ2+
๐2๐ด๐ง
๐๐ง2= โยต๐๐ง
(11)
๐ต๐ฅ =๐ด๐ง
๐๐ฅโ
๐ด๐ฆ
๐๐ฅ(12)
๐ต๐ฆ =๐ด๐ฅ
๐๐งโ
๐ด๐ง
๐๐ฅ(13)
๐ต๐ง =๐ด๐ฆ
๐๐ฅโ
๐ด๐ฅ
๐๐ฆ(14)
Current continuity equation
Maxwell Ampere's law ๏ผX, Y, X direction๏ผ
๐
๐๐ก๐๐ถ +
๐
๐๐ฅ๐๐ฃ๐ฅ๐ถ +
๐
๐๐ฆ๐๐ฃ๐ฆ๐ถ +
๐
๐๐ง๐๐ฃ๐ง๐ถ =
๐
๐๐ฅ๐ท
๐๐๐ถ
๐๐ฅ+
๐
๐๐ฆ๐ท
๐๐๐ถ
๐๐ฆ+
๐
๐๐ง๐ท
๐๐๐ถ
๐๐ง+ ๐๐
๐ (15) ๐ท =2 2
1๐1
+1๐2
0.5
๐12
๐ฝ12๐1
2๐1
0.25
+๐12
๐ฝ12๐1
2๐1
0.25 (16)
Advection diffusion equationDiffusion coefficient
Current I = 50 A
Bz = 3 mT
Current I = 50 A
Bz = 3 mT
็ดๆต้ปๆตๆใซใใใ็ธฆ็ฃ็ๅฐๅ (Bz = 3 mT)ใๅใผใใขใผใฏๆๅResult
Fig. Temperature distribution with time. Fig. Flow velocity distribution with time.
Fig. Current and electric potential with time.
็ธฆ็ฃ็ใฎๅฐๅ ใซไผดใๅพๆนๅๆต้ใ็บ็ใ๏ผใขใผใฏใในใใคใฉใซๅ 19/21
็ธฆ็ฃ็ๅฐๅ ๆใฎใขใผใฏ้ปๅงๅขๅ ใจ็ฑ็ๅ็นๅผง็บ็ใขใใซModel
Fig. Arc driven model affected by axial magnetic flux density.
Fig. Thermal interruption limit.(a) w/o axial magnetic field. (b) w/ axial magnetic field.
107 ~ 108 A/m2
็ธฆ็ฃ็ๅฐๅ ใซไผดใในใใคใฉใซใขใผใฏใฎๅฝขๆโ้ทใขใผใฏๅโข ้ปๆฅต้ใซใใใๅ่ท้ขใซๅฏพใใฆไบๆณใใใ็ฑ็้ฎๆญ้็ใฎ็ฎๅบใซใใ๏ผ็ฎๆจใฎๆธฉๅบฆใๆ็ขบๅ
ใใฉใบใใธใงใใใใณใณใใญใผใซใใใใจใซใใ๏ผใขใผใฏ้ปๅงใฎๅขๅ ใจๆฅๅณปใชๆธฉๅบฆไฝไธใๅฎ็พ