with the 3D solver OpenFOAM - A comparison of different - PowerPoint PPT Presentation

IIW Annual Assembly 2011 SG212: the physics of welding Electric welding arc modeling with the 3D solver OpenFOAM - A comparison of different electromagnetic models - Isabelle Choquet,¹ Alireza J. Shirvan,¹ and Håkan Nilsson² ¹University West, Dep. of Engineering Science, Trollhättan, Sweden ²Chalmers University of Technology, Dep. of Applied Mechanics, Gothenburg, Sweden IIW Doc.212-1189 -11

• Cont ntext / / Motiv tivation: better understand the heat source • So Software Open enFOAM-1.6 .6.x .x - open source CFD software - C++ library of object-oriented classes for implementing solvers for continuum mechanics IIW Doc.212-1189 -11

IIW intermediate meeting, Trollhättan, Doc. XII-2017-11 ” Numerical simulation of Ar- x%CO₂ shielding gas and its effect on an electric welding arc ” Influence of BC on anode an cathode Influence of gas composition Here focus on a comparison of different electromagnetic models IIW Doc.212-1189 -11

Model: thermal fluid part Main assumptions (plasma core): • one-fluid model • local thermal equilibrium • mechanically incompressible and thermally expansible • steady flow • laminar flow(assuming laminar shielding gas inlet) IIW Doc.212-1189 -11

Model: thermal fluid part Main assumptions (plasma core): • one-fluid model • local thermal equilibrium • mechanically incompressible and thermally expansible • steady flow • laminar flow(assuming laminar shielding gas inlet) IIW Doc.212-1189 -11

Model: thermal fluid part Main assumptions (plasma core): • one-fluid model • local thermal equilibrium • mechanically incompressible and thermally expansible • steady flow • laminar flow(assuming laminar shielding gas inlet) IIW Doc.212-1189 -11

Model: thermal fluid part Main assumptions (plasma core): • one-fluid model • local thermal equilibrium ρ T • mechanically incompressible, and thermally ( ) expansible • steady flow • laminar flow(assuming laminar shielding gas inlet) IIW Doc.212-1189 -11

Model: thermal fluid part Argon plasma density as function of temperature. IIW Doc.212-1189 -11

Model: thermal fluid part Main assumptions: • one-fluid model • local thermal equilibrium  ( T ) • mechanically incompressible, and thermally expansible • plasma optically thin • steady • laminar flow(assuming laminar shielding gas inlet) IIW Doc.212-1189 -11

Model: thermal fluid part Main assumptions: • one-fluid model • local thermal equilibrium  ( T ) • mechanically incompressible, and thermally expansible • plasma optically thin • steady laminar flow • laminar flow(assuming laminar shielding gas inlet) IIW Doc.212-1189 -11

Model: electromagnetic part • 3D model with • 2D axi-symmetric models:  Electric potential formulation  Magnetic field formulation IIW Doc.212-1189 -11

Model: electromagnetic part     • 3D model with V , A E , J , B • 2D axi-symmetric models:  Electric potential formulation  Magnetic field formulation IIW Doc.212-1189 -11

Model: electromagnetic part     • 3D model with V , A E , J , B • 2D axi-symmetric models:    Electric potential formulation V E , J B θ  Magnetic field formulation IIW Doc.212-1189 -11

Model: electromagnetic part     • 3D model with V , A E , J , B • 2D axi-symmetric models:    Electric potential formulation V E , J B θ    Magnetic field formulation B E , J θ IIW Doc.212-1189 -11

Model: electromagnetic part     • 3D model with V , A E , J , B • 2D axi-symmetric models:    Electric potential formulation V E , J B θ    Magnetic field formulation B E , J θ M.A. Ramírez , G. Trapaga and J. McKelliget (2003). A comparison between two different numerical formulations of welding arc simulation. Modelling Simul. Mater. Sci. Eng , 11 , pp. 675-695. IIW Doc.212-1189 -11

Test case: Tungsten Inert Gas welding Applied current: I=200A Ar shielding Shielding gas  gas inlet inlet u 2 . 36 m / s Picture of a TIG torch Sketch of the cross section of a TIG torch IIW Doc.212-1189 -11

 r μ      B ( A ) 0 B J ( l ) l dl θ θ θ axial r 0 Magnetic field magnitude calculated with the electric potential formulation (left) and the 3D approach (right).

 r μ      B ( A ) 0 B J ( l ) l dl θ θ θ axial r 0 Why ? Magnetic field magnitude calculated with the electric potential formulation (left) and the 3D approach (right).

Maxwell’s equations   B    Gauss’ law for magnetism: 0         ε μ μ  Ampère’s law: E B J 0 0 t 0        Faraday’s law: B E t       Gauss’ law: ε 1 E q 0 tot       + charge conservation 0 q tot J t            J J J J J J + generalized Ohm’ s law drift ind Hall diff ther IIW Doc.212-1189 -11 •

Assumptions (plasma core)    8 m  10  L local electro-neutrality Debye c  quasi-steady electromagnetic phenomena   IIW Doc.212-1189 -11

Maxwell’s equations   B    Gauss’ law for magnetism: 0         ε μ μ  Ampère’s law: E B J 0 0 0 t        Faraday’s law: B E t       Gauss’ law: ε 1 E q 0 tot 0       + charge conservation q tot J 0 t 0            J J J J J J + generalized Ohm’ s law drift ind Hall diff ther 0 0 IIW Doc.212-1189 -11 •

Assumptions (plasma core)    8 m  10  L local electro-neutrality Debye c     μ L , t E J  quasi-steady electromagnetic c c 0 t phenomena   IIW Doc.212-1189 -11

Maxwell’s equations   B    Gauss’ law for magnetism: 0         ε μ μ E B J  Ampère’s law: 0 0 t 0 0        Faraday’s law: B E t 0       Gauss’ law: ε 1 E q 0 tot 0       + charge conservation q tot J 0 t 0            J J J J J J + generalized Ohm’ s law drift ind Hall diff ther 0 0 IIW Doc.212-1189 -11 •

Assumptions (plasma core)    8 m  10  L local electro-neutrality Debye c     μ L , t E J  quasi-steady electromagnetic c c 0 t phenomena       σ          σ / 1 J J B J E Lar Lar coll Hall drift n e   IIW Doc.212-1189 -11

Maxwell’s equations   B    Gauss’ law for magnetism: 0         ε μ μ E B J  Ampère’s law: 0 0 t 0 0        Faraday’s law: B E t 0  ε      Gauss’ law: 1 E q 0 tot 0       + charge conservation q tot J 0 t 0            J J J J J J + generalized Ohm’ s law drift ind Hall diff ther 0 0 0 IIW Doc.212-1189 -11 •

Assumptions (plasma core)    8 m  10  L local electro-neutrality Debye c     μ L , t E J  quasi-steady electromagnetic c c 0 t phenomena       σ          σ / 1 J J B J E Lar Lar coll Hall drift n e      Re   σ   1 J u B J m ind drift  IIW Doc.212-1189 -11

Maxwell´s equations   B    Gauss’ law for magnetism: 0         ε μ μ E B J  Ampère’s law: 0 0 t 0 0        Faraday’s law: B E t 0  ε      Gauss’ law: 1 E q 0 tot 0       + charge conservation q tot J 0 t 0            J J J J J J + generalized Ohm’ s law drift ind Hall diff ther 0 0 0 0 IIW Doc.212-1189 -11 •

Maxwell´s equations   B    Gauss’ law for magnetism: 0         ε μ μ E B J  Ampère’s law: 0 0 t 0 0        Faraday’s law: B E t 0  ε      Gauss’ law: 1 E q 0 tot 0       + charge conservation q tot J 0 t 0            J J J J J J + generalized Ohm’ s law drift ind Hall diff ther 0 0 0 0 IIW Doc.212-1189 -11 •