analysis of temperature distribution and ablation gas

Analysis of Temperature Distribution and Ablation Gas Concentration Distribution under

Consideration of Nozzle Ablation Caused by Spiral Arc Applied Axial Magnetic Field

◎Yuki 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 ・Yuki Suzuki・ Tokyo City University ・ 1 /13 1 /12TA5-S2-015

Current zero

Decrement of arc energy and creating the weak point

[1] Japan Electric Engineers‘ 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

→ 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 ・Yuki Suzuki・ Tokyo City University ・ 2 /13 2 /12TA5-S2-015

Low temperature and electrical conductivity Current interruption

[2] Yokomizu Yasunobu： ”ガス吹付けによる大電流のアーク遮断に関する基礎研究”, Nagoya university doctoral paper (1991）[3] Toshiyuki Onchi，Yasunori Tanaka，Kei Kawasaki，Yoshihiko Uesugi：”Thermofluid Simulation of Arc Plasmas Confined by a Polymer

Hollow Cylinder”， IEEJ Trans.PE，Vol.131，No.2，pp.196-204 （2011）

[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, ： “Three-dimensional Time-dependent Numerical Analysis of SF6 Arc Plasma under Externally Applied

Magnetic Field”, 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.

✓ Concentrative cooling

of arc

✓ Increment of arc voltage

＋

Improvement of arc

interruption performance

5 /12TA5-S2-015

Calculation method

Calculation area.

・ Electrodes material: Cathode-Cu，Anode-Cu

・ Gas： N2 ・ Pressure: 0.1 MPa

・ Inter electrode distance: 10 mm

・ Nozzle radius： 10 mm

・ Nozzle material: POM

・ Current： 1-100-0 A ・ di/dt： 0.5 A/μs, - 0.5 A/μs

・Axial magnetic field : 0, 10, 100 mT

Conditions

Basic assumptions

・ 3-D rectangular coordinate system

・ Laminar flow

・ Local thermal equilibrium

・ Optically thin

・Without ablation caused by radiation transfer

Governing equation

・Mass conservation ・ Current continuity equation

・Momentum conservation ・ Ohms law

・ Energy conservation ・Maxwell Ampere law

・ 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.

𝜕

𝜕𝑡𝜌𝐶 +

𝜕

𝜕𝑥𝜌𝑢𝐶 +

𝜕

𝜕𝑦𝜌𝑣𝐶 +

𝜕

𝜕𝑧𝜌𝑤𝐶 =

𝜕

𝜕𝑥𝐷

𝜕𝜌𝐶

𝜕𝑥+

𝜕

𝜕𝑦𝐷

𝜕𝜌𝐶

𝜕𝑦+

𝜕

𝜕𝑧𝐷

𝜕𝜌𝐶

𝜕𝑧+ 𝑆𝑝

𝑐

Advection diffusion equation

Γ𝑎𝑏𝑙 =𝑃𝑉

2𝜋𝑚pol𝑘𝑇

(T≧Tmelt)➢ Hertz-Knudsen’s equation[3]

𝑃𝑣 = 𝑃0exp𝐿𝑒

𝑅𝑇𝑏𝑜𝑖𝑙−

𝐿𝑒𝑅𝑇

➢ Clausius-Clapeyron’s equation[3]

➢ Mass generation[3]

𝑆𝑝𝑐 = 𝑚polΓ𝑎𝑏𝑙

ΔS

ΔV

・P0 [Pa]: Atmospheric pressure

・Le [J/kg]: Latent heat of evaporation

・R [J/(K・mol)]: Gas constant

・Tboil [K]: Boiling point

・Pv [Pa]: Saturated vapor pressure

・Γabl [1/(m2・s)]: Ablation flux

・mpol [kg]: Mass of one molecule of polymer material

・k [(m2・kg)/(s2・K)]: Boltzs-mann constant

・𝑆𝑝𝑐 kg/(m3・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 μs, T = 10000-13000 K).

BzBz

✓ 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

✓ 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

𝜕

𝜕𝑥(𝜌𝑣𝑥ℎ) +

𝜕

𝜕𝑦(𝜌𝑣𝑦ℎ) +

𝜕

𝜕𝑧(𝜌𝑣𝑧ℎ)

=𝜕

𝜕𝑥(𝜅

𝐶𝑝

𝜕ℎ

𝜕𝑥) +

𝜕

𝜕𝑦(𝜅

𝐶𝑝

𝜕ℎ

𝜕𝑦) +

𝜕

𝜕𝑧(𝜅

𝐶𝑝

𝜕ℎ

𝜕𝑧) + 𝑗𝑥𝐸𝑥 + 𝑗𝑦𝐸𝑦 + 𝑗𝑧𝐸𝑧 − 𝑈 − 𝑆𝑃

𝐶(Le + Lm)

[W/m3] = [J/(m3・s)]

17Calculation method Governing equation

𝜕𝜌

𝜕𝑡+𝜕 𝜌𝑣𝑥𝜕𝑥

+𝜕 𝜌𝑣𝑦

𝜕𝑦+

𝜕 𝜌𝑣𝑧𝜕𝑧

= 0 (1)

𝜕 𝜌𝑣𝑥𝜕𝑡

+𝜕 𝜌𝑣𝑥

2

𝜕𝑥+𝜕 𝜌𝑣𝑦𝑣𝑥

𝜕𝑦+𝜕 𝜌𝑣𝑧𝑣𝑥

𝜕𝑧= −

𝜕𝑃

𝜕𝑥+ 𝑗𝑦 × 𝐵𝑧 − 𝑗𝑦 × 𝐵𝑦 +

𝜕

𝜕𝑥

𝜕𝜂𝑣𝑥𝜕𝑥

+𝜕

𝜕𝑦

𝜕𝜂𝑣𝑥𝜕𝑦

+𝜕

𝜕𝑧

𝜕𝜂𝑣𝑥𝜕𝑧

(2)

𝜕 𝜌𝑣𝑦

𝜕𝑡+𝜕 𝜌𝑣𝑥𝑣𝑦

𝜕𝑥+𝜕 𝜌𝑣𝑦

2

𝜕𝑦+𝜕 𝜌𝑣𝑧𝑣𝑦

𝜕𝑧= −

𝜕𝑃

𝜕𝑦+ 𝑗𝑧 × 𝐵𝑥 − 𝑗𝑥 × 𝐵𝑥 +

𝜕

𝜕𝑥

𝜕𝜂𝑣𝑦

𝜕𝑥+

𝜕

𝜕𝑦

𝜕𝜂𝑣𝑦

𝜕𝑦+

𝜕

𝜕𝑧

𝜕𝜂𝑣𝑦

𝜕𝑧(3)

𝜕 𝜌𝑣𝑧𝜕𝑡

+𝜕 𝜌𝑣𝑥

2

𝜕𝑥+𝜕 𝜌𝑣𝑦𝑣𝑥

𝜕𝑦+𝜕 𝜌𝑣𝑧𝑣𝑥

𝜕𝑧= −

𝜕𝑃

𝜕𝑥+ 𝑗𝑦 × 𝐵𝑥 − 𝑗𝑥 × 𝐵𝑦 +

𝜕

𝜕𝑥

𝜕𝜂𝑣𝑧𝜕𝑥

+𝜕

𝜕𝑦

𝜕𝜂𝑣𝑧𝜕𝑦

+𝜕

𝜕𝑧

𝜕𝜂𝑣𝑧𝜕𝑧

+ 𝜌0 − 𝜌 𝑔 (4)

𝜕 𝜌ℎ

𝜕𝑡+𝜕 𝜌𝑣𝑥ℎ

𝜕𝑥+𝜕 𝜌𝑣𝑦ℎ

𝜕𝑦+𝜕 𝜌𝑣𝑧ℎ

𝜕𝑧=

𝜕

𝜕𝑥

𝜅

𝐶𝑃

𝜕ℎ

𝜕𝑥+

𝜕

𝜕𝑦

𝜅

𝐶𝑃

𝜕ℎ

𝜕𝑦+

𝜕

𝜕𝑧

𝜅

𝐶𝑃

𝜕ℎ

𝜕𝑧+ 𝑗𝑥𝐸𝑥 + 𝑗𝑦𝐸𝑦 + 𝑗𝑧𝐸𝑧 − 𝑈 − 𝑆𝑝

𝑐(𝐿𝑒 + 𝐿𝑚)(5)

Mass conservation equation

Momentum conservation equation（X, Y, Z direction）

Energy conservation equation

18Calculation method Governing equation

𝜕 𝑗𝑥

𝜕𝑥+

𝜕 𝑗𝑦

𝜕𝑦+

𝜕 𝑗𝑧

𝜕𝑧= 0

(6)

𝑗𝑥 = 𝜎𝐸𝑥，𝑗𝑦 = 𝜎𝐸𝑦，𝑗𝑧 = 𝜎𝐸𝑧 (7)

𝐸𝑥 = −𝜕𝜑

𝜕𝑥，𝐸𝑦 = −

𝜕𝜑

𝜕𝑦，𝐸𝑧 = −

𝜕𝜑

𝜕𝑧(8)

𝜕2𝐴𝑥

𝜕𝑥2+

𝜕2𝐴𝑥

𝜕𝑦2+

𝜕2𝐴𝑥

𝜕𝑧2= −µ𝑗𝑥

(9)

𝜕2𝐴𝑦

𝜕𝑥2+

𝜕2𝐴𝑦

𝜕𝑥2+

𝜕2𝐴𝑧

𝜕𝑥2= −µ𝑗𝑦

(10)

𝜕2𝐴𝑧

𝜕𝑥2+

𝜕2𝐴𝑧

𝜕𝑦2+

𝜕2𝐴𝑧

𝜕𝑧2= −µ𝑗𝑧

(11)

𝐵𝑥 =𝐴𝑧

𝜕𝑥−

𝐴𝑦

𝜕𝑥(12)

𝐵𝑦 =𝐴𝑥

𝜕𝑧−

𝐴𝑧

𝜕𝑥(13)

𝐵𝑧 =𝐴𝑦

𝜕𝑥−

𝐴𝑥

𝜕𝑦(14)

Current continuity equation

Maxwell Ampere's law （X, Y, X direction）

𝜕

𝜕𝑡𝜌𝐶 +

𝜕

𝜕𝑥𝜌𝑣𝑥𝐶 +

𝜕

𝜕𝑦𝜌𝑣𝑦𝐶 +

𝜕

𝜕𝑧𝜌𝑣𝑧𝐶 =

𝜕

𝜕𝑥𝐷

𝜕𝜌𝐶

𝜕𝑥+

𝜕

𝜕𝑦𝐷

𝜕𝜌𝐶

𝜕𝑦+

𝜕

𝜕𝑧𝐷

𝜕𝜌𝐶

𝜕𝑧+ 𝑆𝑝

𝑐 (15) 𝐷 =2 2

1𝑀1

+1𝑀2

0.5

𝜌12

𝛽12𝜂1

2𝑀1

0.25

+𝜌12

𝛽12𝜂1

2𝑀1

0.25 (16)

Advection diffusion equationDiffusion coefficient

Current I = 50 A

Bz = 3 mT

Current I = 50 A

Bz = 3 mT

直流電流時における縦磁界印加 (Bz = 3 mT)が及ぼすアーク挙動Result

Fig. Temperature distribution with time. Fig. Flow velocity distribution with time.

Fig. Current and electric potential with time.

縦磁界の印加に伴い径方向流速が発生し，アークがスパイラル化 19/21

縦磁界印加時のアーク電圧増加と熱的再点弧発生モデル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

縦磁界印加に伴うスパイラルアークの形成⇒長アーク化➢ 電極間における各距離に対して予想される熱的遮断限界の算出により，目標の温度を明確化

プラズマジェットをコントロールすることにより，アーク電圧の増加と急峻な温度低下を実現