Numerical Analysis of Current Attachment at Thermionic Cathode for Gas Tungsten Arc at Atmospheric Pressure

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1 Tansactions of JWRI, Vol.38 (2009), No. 1 Numeical Analysis of Cuent Attachment at Themionic Cathode fo Gas Tungsten Ac at Atmospheic Pessue YAMAMOTO Kentao*, TASHIRO Shinichi** and TANAKA Manabu*** Abstact In a gas tungsten ac at atmospheic pessue, electons ae emitted fom a themionic cathode of the tungsten electode, of which the wok function would be educed by geneally adding an emitte mateial such as thoium oxide (ThO 2 ), lanthanum oxide (La 2 O 3 ), and so on. Howeve, thee is still a lack of pactical undestanding of the physical behavio in the electode egion. Fo example, cuent attachment at a themionic cathode is not yet clea. The pesent pape pesents a methodology fo pedicting the cuent attachment at a themionic cathode fo the gas tungsten ac at atmospheic pessue in agon. It is suggested that the cuent attachment at themionic cathode is dependent on wok function, melting point and the Richadson constant of emitte mateials. KEY WORDS: (Numeical simulation), (Gas tungsten ac), (Cathode) 1. Intoduction In gas tungsten ac at atmospheic pessue, electons ae emitted fom a themionic cathode of the tungsten electode, of which the wok function would be educed by geneally adding an emitte mateial such as thoium oxide (ThO 2 ), lanthanum oxide (La 2 O 3 ), and so on 1). Howeve, thee is still a lack of pactical undestanding of the physical behavio in the electode egion. Fo example, cuent attachment at themionic cathode is not yet clea. The emitte mateials such as ThO 2, La 2 O 3, etc would not only affect wok function of the cathode but also cuent attachment at the cathode. The cuent attachment at the cathode affects the plasma state of the ac column due to change in the cathode jet induced by the Loent foce at the cathode egion 1, 2). It is well known that ac flames ae dependent on the kinds of emitte mateials which ae added to the tungsten electode. Weldes, fo example, suggest that a W-ThO 2 electode poduces a had ac flame but a W-La 2 O 3 electode poduces a soft ac one 3). The pesent pape pesents a methodology fo pedicting the cuent attachment at a themionic cathode fo gas tungsten ac at atmospheic pessue in agon. We use a numeical model of a gas tungsten ac whee the ac and its electodes ae teated as a unified system. 2. A unified model The tungsten cathode, ac plasma and anode ae descibed elative to a cylindical coodinate, assuming otational symmety aound the ac axis. The calculation domain is shown in Fig. 1. The flow is assumed to be lamina, and the ac plasma is assumed to be in local themodynamic equilibium (LTE). The diamete of the tungsten cathode is 3.2 mm with a 60 degees conical tip. The anode is assumed to be wate-cooled coppe and its diamete is 50 mm with 10 mm in thickness. The mass continuity equation is 1 ( v ) ( v ) 0 (1) the adial momentum consevation equation is 1 2 ( v ) P ( v v ) j B (2) 1 v v v v (2 ) ( ) 2 2 Received on July 10, 2009 * Gaduate school student ** Assistant Pofesso *** Pofesso Tansactions of JWRI is published by Joining and Welding Reseach Institute, Osaka Univesity, Ibaaki, Osaka , Japan 1

2 Numeical Analysis of Cuent Attachment at Themionic Cathode fo Gas Tungsten Ac at Atmospheic Pessue the axial momentum consevation equation is 1 P ( v ) ( v v ) j B (3) v 1 v v (2 ) ( ) the enegy consevation equation is 1 1 h h ( v h) ( vh) ( ) ( ) c c j E j E R the cuent continuity equation is 1 ( j ) ( j ) 0 (5) and the Ohm's law (6) is p p (4) cuent density, and j i is the ion cuent density. We calculate the electon satuation cuent density at the cathode suface by themionic emission of electons j R fom the Richadson-Dushman equation. The ion cuent density j i is then assumed to be j < j R if j is geate than j R ; whee j = j e + j i is the total cuent density at the cathode suface obtained fom equation. The detailed bounday conditions and numeical method ae given in ou pevious pape 4). Within both electodes, we set v =v =0. The tempeatues at boundaies CD, DE, EF, and FA in Fig. 1 ae taken to be the same oom tempeatue, namely, 300 K. The electic potential is set to eo at the base of the anode, CD, in Fig.1. In ode to avoid the poblem that the equilibium electical conductivity is effectively eo in the plasma close to the electodes owing to the low plasma tempeatue, we employ an LTE-diffusion appoximation 5). The diffeential equations (1) to (7) ae solved iteatively by the SIMPLEC numeical pocedue 6) fo the whole egion of the ac welding pocess. j E ; j E (6) -30 A F and Maxwell's equation is 1 (B ) 0 j. (7) whee t is time, h is enthalpy, P is pessue, v and v ae the adial and axial velocities, j and j ae the adial and axial components of the cuent density, g is the acceleation due to gavity, is the themal conductivity, c p is the specific heat, is the density, is the viscosity, U is the adiation emission coefficient, is the electical conductivity, B is the aimuthal magnetic field, 0 is the pemeability of fee space, E and E ae espectively the adial and axial components of the electic field defined by E =- V/nd E =- V/, whee V is electic potential. Calculations at points on both electode sufaces would need to include the special pocess occuing at the sufaces. Thus, additional enegy flux tems need to be included in equation (4) at each electode suface fo themionic heating and cooling fom the electons, ion heating, and adiation cooling. The additional enegy flux fo the cathode H K and fo the anode H A ae Cathode H K = - T 4 - j e K + j i V i (8) and Anode H A = - T 4 + j e A (9) espectively. Hee is the suface emissivity, is the Stefan-Boltmann constant, K is the wok function of the tungsten cathode, A is the wok function of the anode, V i is the ioniation potential of helium, j e is the electon Axial distance (mm) B Tungsten cathode (1.6 mm) Ac plasma Anode C D Radial distance (mm) Fig. 1 Schematic illustation of simulation domain. 3. Teatment of cuent attachment The in-situ measuements of wok function of a cathode in the agon gas tungsten ac duing opeation at atmospheic pessue wee caied out simultaneously with measuements of suface tempeatue of the cathode 7). This technique was based on the photoelectic effect at the suface of the tungsten cathode with the use of a pulse lase system. The effective wok functions of pue W, W-2% ThO 2 and W-2% La 2 O 3 electodes duing opeation at a cuent of 200 A wee 4.6 ev, 2.8 ev and 3.0 ev fom the in-situ measuements. These esults wee vey close to the wok functions of W, ThO 2 and La 2 O 3 E 2

3 Tansactions of JWRI, Vol.38 (2009), No. 1 as pue mateials obtained fom the liteatue 8). Theefoe, it was concluded that the effective wok function of tungsten electodes adding an emitte mateial, namely, ThO 2 o La 2 O 3, was dominated by the wok function of the emitte mateial even though its addition to the electode was only 2% in weight. Fom ou pevious study 7), we have ou image of cuent attachment at themionic cathode, as follows. (a) Emitte mateial plays a ole of themionic emission of electons due to its lowe wok function independently of its conditions, namely, solid o liquid. (b) Tungsten weakly contibutes to themionic emission of electons due to its highe wok function. (c) Emitte mateial below its melting point is scatteed on the suface of tungsten, as shown in Fig. 2. A sie of an emitte mateial is aound 5 m 1). The emitte mateial pactically coves about 5% of the tungsten suface because 2 wt% of ThO 2 and La 2 O 3 becomes 4 to 6 vol% of ThO 2 and La 2 O 3. (d) Emitte mateial above its melting point coves the whole suface of tungsten. In ode to evaluate the cuent attachment, the space-chage sheath at the cathode suface has to be egulaly calculated with themionic emission of electons 9, 10). Howeve, ou unified model does not take the sheath into account. Theefoe, fo simplification, we assume that the ole of themionic emission of electons by emitte mateial is eplaced with the electical conductivity of ac plasma on the cathode suface, as shown in Fig. 3. If suface tempeatue of the cathode is highe than the melting point of the emitte mateial, the electical conductivity of the ac plasma on the cathode suface is assumed to be a egula value independently of tempeatue because the emitte mateial coves the whole suface of tungsten. If suface tempeatue of the cathode is o the contay lowe than the melting point of the emitte mateial, the electical conductivity of ac plasma in one mesh neighboing on the cathode suface is assumed to be 5% of the egula value because the emitte mateial pactically coves about 5% of the tungsten suface. The flux of ac cuent fom one mesh to anothe mesh is oughly epesented by I = S( E), whee S is the aea between two meshes. We assume to eplace 5%S by 5%. Thee types of tungsten electode, namely, W-2% ThO 2, W-2% La 2 O 3 and W-2% CeO 2 ae calculated in this pape. The numeical values given to a unified model ae tabulated in Table 1. These values ae fom the liteatue 8). In the manufactuing pocess of a tungsten electode, CeO 2 is educed to Ce 2 O 3 afte sinteing in pue hydogen atmosphee 11), and then we also assume that the whole CeO 2 of W-2% CeO 2 electode is changed to Ce 2 O 3 in this pape. Emitte mateial is scatteed on the suface of W Emitte mateial coves the whole suface of W Fig. 2 An image of cuent attachment. T<T m T>T m W electode Below the melting point of emitte mateial Above the melting point of emitte mateial Ac plasma T m : Melting point of emitte mateial : Electical conductivity Fig. 3 Teatment of cuent attachment fo a unified ac electode model. Table. 1 Numeical values given to a unified model. 3

4 Numeical Analysis of Cuent Attachment at Themionic Cathode fo Gas Tungsten Ac at Atmospheic Pessue 4. Results and discussion Figue 4 shows two-dimensional tempeatues and fluid flow velocities of gas tungsten acs fo vaious kinds of electodes at 200 A of ac cuent and 5 mm of ac length. These calculations wee made fo the steady state. The diffeence between calculated ac voltages fo vaious electodes is negligible and the value of the ac voltage is about 11.2 V. This tendency was pointed out by expeiments 1). Howeve, the plasma state of the ac column is locally affected by the electode types. Specifically, the maximum tempeatue of ac plasma close to the cathode tip fo W-2% ThO 2 eaches 19,000 K and it is the highest value in compaison with the othe tempeatues fo W-2% La 2 O 3 and W-2% CeO 2, because the cuent attachment at the cathode tip is consticted by a centalied limitation of liquid aea of ThO 2 due to its highe melting point. This highe tempeatue of the plasma close to the cathode tip at the ac axis would play an impotant ole in the poduction of a had ac flame. In cases of W-2% La 2 O 3 and W-2% CeO 2, the liquid aeas of La 2 O 3 and Ce 2 O 3 ae widely expanded at the cathode tip due to thei lowe melting points and then poduce unifom cuent attachments at the cathode, esulting a soft ac flame. Figue 5 shows tempeatue distibutions at electode sufaces. The maximum tempeatues at the tip ae 3776 K, 3620 K and 3210 K fo W-2% ThO 2, W-2% CeO 2 and W-2% La 2 O 3, espectively. These ae good ageement with expeimental esults epoted by Haida and Fame 12). The tip tempeatue of W-2% La 2 O 3 duing opeation is clealy lowe than that of W-2% CeO 2 although both wok functions of La 2 O 3 and Ce 2 O 3 ae almost the same as shown in Table 1. This eason is deduced fom a diffeence of the Richadson constant between 96.0 A/cm 2 K 2 in La 2 O 3 and 30.0 A/cm 2 K 2 in Ce 2 O 3. Figue 6 shows ac pessue distibutions at the anode suface. The maximum ac pessue fo W-2% CeO 2 eaches 395 Pa and then it is simila to 391 Pa fo W-2% La 2 O 3. Howeve, the maximum ac pessue fo W-2% ThO 2 is clealy lowe than these. Sadek measued ac pessue distibutions at a wate-cooled coppe anode by a semiconducto tansduce, as shown in Fig. 7 1). Since he, unfotunately, employed 45 degee fo the conical tip angle of tungsten electode and 3 mm fo the ac length, we can not compae both esults of expeiment and calculation diectly. Howeve, his expeimental esults show that the maximum ac pessues of W-2% CeO 2 and W-2% La 2 O 3 ae almost the same but that fo W-2% ThO 2 is clealy lowe than these. This tendency is vey simila to the tendency given by calculations as shown in Fig. 6, although the absolute values of ac pessue in both cases ae diffeent due to diffeences of a few conditions as stated above. Figue 8 shows cuent density distibutions at 0 mm of axial distance in Fig. 1. The maximum cuent density fo W-2% ThO 2 is the highest in compaison with those fo W-2% La 2 O 3 and W-2% CeO 2. Howeve, the cuent density fo W-2% ThO 2 dastically deceases towad the adius and then it is lowe than those fo W-2% La 2 O 3 and W-2% CeO 2 at aound 0.5 mm to 2 mm in the adius. This chaacteistic of cuent density distibution fo W-2% ThO 2 locally leads to the highest values in the tip tempeatue of the cathode, in the tempeatue of the ac plasma and in the fluid flow velocity of the cathode jet, but it poduces the lowest value of the ac pessue at the anode suface because an aveage momentum of the cathode jet fo W-2% ThO 2 is smalle than those fo the othe two electodes due to moe unifom cuent density distibutions fo W-2% La 2 O 3 and W-2% CeO 2 than that fo W-2% ThO 2, as shown in Fig. 8. Fom the above esults, it can be concluded that the cuent attachment at themionic cathode fo gas tungsten ac at atmospheic pessue is dependent on wok function, melting point and the Richadson constant of emitte mateials. Fig. 4 Tempeatues and fluid flow velocities of gas tungsten acs fo vaious types of electode. Fig. 5 Tempeatues of electode suface. 4

5 Tansactions of JWRI, Vol.38 (2009), No Conclusions The conclusions of this study ae summaied as follows. Fig. 6 Ac pessues at anode suface. Fig. 7 Expeimental esults of ac pessue at anode suface 1). (1) Study of the cuent attachment at the themionic cathode fo a gas tungsten ac at atmospheic pessue was examined fom numeical calculations of an ac-electode unified model. (2) It is suggested that the cuent attachment at the themionic cathode was dependent on wok function, melting point and the Richadson constant of emitte mateials. (3) The maximum tempeatue of ac plasma close to the cathode tip fo W-2% ThO 2 eached 19,000 K and it was the highest value in compaison with the othe tempeatues fo W-2% La 2 O 3 and W-2% CeO 2, because the cuent attachment at the cathode tip was consticted by a centalied limitation of liquid aea of ThO 2 due to its highe melting point. This highe tempeatue of plasma close to the cathode tip at the ac axis would play an impotant ole in poduction of a had ac flame. (4) In the cases of W-2% La 2 O 3 and W-2% CeO 2, the liquid aeas of La 2 O 3 and Ce 2 O 3 wee widely expanded at the cathode tip due to thei lowe melting points and which then poduce unifom cuent attachments at the cathode, esulting a soft ac flame. (5) The tip tempeatue of W-2% La 2 O 3 duing opeation was clealy lowe than that of W-2% CeO 2 although both wok functions of La 2 O 3 and Ce 2 O 3 wee almost the same. This eason was deduced fom a diffeence of the Richadson constant between 96.0 A/cm 2 K 2 in La 2 O 3 and 30.0 A/cm 2 K 2 in Ce 2 O 3. Refeences 1) Sadek AA, Ushio M and Matsuda M; Metall. Tans. A, 1990; 21 A: p ) Tanaka M et. al.; Plasma Chem. & Plasma Pocess., 2003; 23: p ) Mita T; pivate communication, ) Tanaka M, Ushio M and Lowke JJ; JSME Int. J., Seies B, 2005; 48: p ) Lowke JJ and Tanaka M; J. Phys. D: Appl. Phys., 2006; 39: p ) Patanke SV; Numeical Heat Tansfe and Fluid Flow, Hemisphee Publishing Copoation, ) Tanaka M et. al.; J. Phys. D: Appl. Phys., 2005; 38: p ) Fomenko VS: Emission Popeties of Mateials, Kiev, Naukova Dumka, ) Moow RR and Lowke JJ; J. Phys. D: Appl. Phys., 1993; 26: pp ) Ushio M et. al.; J. Phys. D: Appl. Phys., 1994; 27: p ) Ushio M et.al.; Plasma Chem. & Plasma Pocess., 1991; 11: p ) Haida J and Fame AJD; J. Phys. D: Appl. Phys., 1995; 28: p Fig. 8 Cuent density distibutions at the tip of tungsten electode. 5