analysis of temperature distribution and ablation gas
TRANSCRIPT
Analysis of Temperature Distribution and Ablation Gas Concentration Distribution under
Consideration of Nozzle Ablation Caused by Spiral Arc Applied Axial Magnetic Field
âYuki 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 ã»Yuki Suzukiã» Tokyo City University ã» 1 /13 1 /12TA5-S2-015
Current zero
Decrement of arc energy and creating the weak point
[1] Japan Electric Engineersâ 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
â 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 ã»Yuki Suzukiã» Tokyo City University ã» 2 /13 2 /12TA5-S2-015
Low temperature and electrical conductivity Current interruption
[2] Yokomizu YasunobuïŒ âã¬ã¹å¹ä»ãã«ãã倧é»æµã®ã¢ãŒã¯é®æã«é¢ããåºç€ç 究â, Nagoya university doctoral paper (1991ïŒ[3] Toshiyuki OnchiïŒYasunori TanakaïŒKei KawasakiïŒYoshihiko UesugiïŒâThermofluid Simulation of Arc Plasmas Confined by a Polymer
Hollow CylinderâïŒ IEEJ Trans.PEïŒVol.131ïŒNo.2ïŒpp.196-204 ïŒ2011ïŒ
[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, ïŒ âThree-dimensional Time-dependent Numerical Analysis of SF6 Arc Plasma under Externally Applied
Magnetic Fieldâ, 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.
â Concentrative cooling
of arc
â Increment of arc voltage
ïŒ
Improvement of arc
interruption performance
5 /12TA5-S2-015
Calculation method
Calculation area.
ã» Electrodes material: Cathode-CuïŒAnode-Cu
ã» GasïŒ N2 ã» Pressure: 0.1 MPa
ã» Inter electrode distance: 10 mm
ã» Nozzle radiusïŒ 10 mm
ã» Nozzle material: POM
ã» CurrentïŒ 1-100-0 A ã» di/dtïŒ 0.5 A/ÎŒs, - 0.5 A/ÎŒs
ã»Axial magnetic field : 0, 10, 100 mT
Conditions
Basic assumptions
ã» 3-D rectangular coordinate system
ã» Laminar flow
ã» Local thermal equilibrium
ã» Optically thin
ã»Without ablation caused by radiation transfer
Governing equation
ã»Mass conservation ã» Current continuity equation
ã»Momentum conservation ã» Ohms law
ã» Energy conservation ã»Maxwell Ampere law
ã» Advection diffusion equation
3-D rectangular coordinate system
Current with time at -0.5 A/µs of current decrement
ratio and 0.5 A/µs 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.
ð
ðð¡ðð¶ +
ð
ðð¥ðð¢ð¶ +
ð
ððŠðð£ð¶ +
ð
ðð§ðð€ð¶ =
ð
ðð¥ð·
ððð¶
ðð¥+
ð
ððŠð·
ððð¶
ððŠ+
ð
ðð§ð·
ððð¶
ðð§+ ðð
ð
Advection diffusion equation
Îððð =ðð
2ððpolðð
(Tâ§Tmelt)⢠Hertz-Knudsenâs equation[3]
ðð£ = ð0expð¿ð
ð ðððððâ
ð¿ðð ð
⢠Clausius-Clapeyronâs equation[3]
⢠Mass generation[3]
ððð = ðpolÎððð
ÎS
ÎV
ã»P0 [Pa]: Atmospheric pressure
ã»Le [J/kg]: Latent heat of evaporation
ã»R [J/(Kã»mol)]: Gas constant
ã»Tboil [K]: Boiling point
ã»Pv [Pa]: Saturated vapor pressure
ã»Îabl [1/(m2ã»s)]: Ablation flux
ã»mpol [kg]: Mass of one molecule of polymer material
ã»k [(m2ã»kg)/(s2ã»K)]: Boltzs-mann constant
ã»ððð kg/(m3ã»s) : 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 ÎŒs, T = 10000-13000 K).
BzBz
â 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
â Arc conductance greatly decreased in the case of considering AMF and ablation.
Current zero
Summary
⢠The arc was spiraled by applying the axial magnetic field
⢠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
⢠Three-dimensional temperature distributions of spiral arc caused by axial
magnetic field and ablation gas concentration distributions generated from
nozzle were obtained.
⢠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
ð
ðð¥(ðð£ð¥â) +
ð
ððŠ(ðð£ðŠâ) +
ð
ðð§(ðð£ð§â)
=ð
ðð¥(ð
ð¶ð
ðâ
ðð¥) +
ð
ððŠ(ð
ð¶ð
ðâ
ððŠ) +
ð
ðð§(ð
ð¶ð
ðâ
ðð§) + ðð¥ðžð¥ + ððŠðžðŠ + ðð§ðžð§ â ð â ðð
ð¶(Le + Lm)
[W/m3] = [J/(m3ã»s)]
17Calculation method Governing equation
ðð
ðð¡+ð ðð£ð¥ðð¥
+ð ðð£ðŠ
ððŠ+
ð ðð£ð§ðð§
= 0 (1)
ð ðð£ð¥ðð¡
+ð ðð£ð¥
2
ðð¥+ð ðð£ðŠð£ð¥
ððŠ+ð ðð£ð§ð£ð¥
ðð§= â
ðð
ðð¥+ ððŠ à ðµð§ â ððŠ à ðµðŠ +
ð
ðð¥
ððð£ð¥ðð¥
+ð
ððŠ
ððð£ð¥ððŠ
+ð
ðð§
ððð£ð¥ðð§
(2)
ð ðð£ðŠ
ðð¡+ð ðð£ð¥ð£ðŠ
ðð¥+ð ðð£ðŠ
2
ððŠ+ð ðð£ð§ð£ðŠ
ðð§= â
ðð
ððŠ+ ðð§ à ðµð¥ â ðð¥ à ðµð¥ +
ð
ðð¥
ððð£ðŠ
ðð¥+
ð
ððŠ
ððð£ðŠ
ððŠ+
ð
ðð§
ððð£ðŠ
ðð§(3)
ð ðð£ð§ðð¡
+ð ðð£ð¥
2
ðð¥+ð ðð£ðŠð£ð¥
ððŠ+ð ðð£ð§ð£ð¥
ðð§= â
ðð
ðð¥+ ððŠ à ðµð¥ â ðð¥ à ðµðŠ +
ð
ðð¥
ððð£ð§ðð¥
+ð
ððŠ
ððð£ð§ððŠ
+ð
ðð§
ððð£ð§ðð§
+ ð0 â ð ð (4)
ð ðâ
ðð¡+ð ðð£ð¥â
ðð¥+ð ðð£ðŠâ
ððŠ+ð ðð£ð§â
ðð§=
ð
ðð¥
ð
ð¶ð
ðâ
ðð¥+
ð
ððŠ
ð
ð¶ð
ðâ
ððŠ+
ð
ðð§
ð
ð¶ð
ðâ
ðð§+ ðð¥ðžð¥ + ððŠðžðŠ + ðð§ðžð§ â ð â ðð
ð(ð¿ð + ð¿ð)(5)
Mass conservation equation
Momentum conservation equationïŒX, Y, Z directionïŒ
Energy conservation equation
18Calculation method Governing equation
ð ðð¥
ðð¥+
ð ððŠ
ððŠ+
ð ðð§
ðð§= 0
(6)
ðð¥ = ððžð¥ïŒððŠ = ððžðŠïŒðð§ = ððžð§ (7)
ðžð¥ = âðð
ðð¥ïŒðžðŠ = â
ðð
ððŠïŒðžð§ = â
ðð
ðð§(8)
ð2ðŽð¥
ðð¥2+
ð2ðŽð¥
ððŠ2+
ð2ðŽð¥
ðð§2= âµðð¥
(9)
ð2ðŽðŠ
ðð¥2+
ð2ðŽðŠ
ðð¥2+
ð2ðŽð§
ðð¥2= âµððŠ
(10)
ð2ðŽð§
ðð¥2+
ð2ðŽð§
ððŠ2+
ð2ðŽð§
ðð§2= âµðð§
(11)
ðµð¥ =ðŽð§
ðð¥â
ðŽðŠ
ðð¥(12)
ðµðŠ =ðŽð¥
ðð§â
ðŽð§
ðð¥(13)
ðµð§ =ðŽðŠ
ðð¥â
ðŽð¥
ððŠ(14)
Current continuity equation
Maxwell Ampere's law ïŒX, Y, X directionïŒ
ð
ðð¡ðð¶ +
ð
ðð¥ðð£ð¥ð¶ +
ð
ððŠðð£ðŠð¶ +
ð
ðð§ðð£ð§ð¶ =
ð
ðð¥ð·
ððð¶
ðð¥+
ð
ððŠð·
ððð¶
ððŠ+
ð
ðð§ð·
ððð¶
ðð§+ ðð
ð (15) ð· =2 2
1ð1
+1ð2
0.5
ð12
ðœ12ð1
2ð1
0.25
+ð12
ðœ12ð1
2ð1
0.25 (16)
Advection diffusion equationDiffusion coefficient
Current I = 50 A
Bz = 3 mT
Current I = 50 A
Bz = 3 mT
çŽæµé»æµæã«ããã瞊ç£çå°å (Bz = 3 mT)ãåãŒãã¢ãŒã¯æåResult
Fig. Temperature distribution with time. Fig. Flow velocity distribution with time.
Fig. Current and electric potential with time.
瞊ç£çã®å°å ã«äŒŽãåŸæ¹åæµéãçºçãïŒã¢ãŒã¯ãã¹ãã€ã©ã«å 19/21
瞊ç£çå°å æã®ã¢ãŒã¯é»å§å¢å ãšç±çåç¹åŒ§çºçã¢ãã«Model
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
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