Correlation methods in cutting arcs

Transcription

1 ournal of Pysics: Confrnc Sris Corrlation mtods in cutting arcs To cit tis articl: Prvosto and H Klly 11. Pys.: Conf. Sr Viw t articl onlin for updats and nancmnts. Rlatd contnt - On t us of t Prandtl mixing lngt modl in t cutting torc modling B Mancinlli, F O Minotti and H Klly - Prdiction of lctrical caractristics of anon-transfrrd arc-plasma torc using principls ofdynamic similarity A M Paingankar, A K Das, V S Sirodkar t al. - Numrical modling of t gas brakdown dvlopmnt in t spac carg layr insid t nozzl of a transfrrd arc torc B Mancinlli, Prvosto and F O Minotti Tis contnt was downloadd from P addrss on 5/4/18 at 1:43

2 FUDOS 1: X Mting on Rcnt Advancs in t Pysics of Fluids and tir Applications OP Publising ournal of Pysics: Confrnc Sris 96 (11) 15 doi:1.188/ /96/1/15 Corrlation mtods in cutting arcs. Prvosto 1 and H. Klly 1,,* 1 Grupo d Dscargas léctricas, Dpartamnto ng. lctromcánica, Univrsidad Tcnológica Nacional, Rgional Vnado Turto, aprida 651, Vnado Turto (6), Santa F, Argntina nstituto d Física dl Plasma (CONCT), Dpartamnto d Física, Facultad d Cincias xactas y Naturals (UBA) Ciudad Univrsitaria Pab., (148) Bunos Airs, Argntina * Mmbr of t CONCT -mail: prvosto@waycom.com.ar Abstract T prsnt work applis similarity tory to t plasma manating from transfrrd arc, gas-vortx stabilizd plasma cutting torcs, to analyz t xisting corrlation btwn t arc tmpratur and t pysical paramtrs of suc torcs. t as bn found tat t ntalpy numbr significantly influnc t tmpratur of t lctric arc. T obtaind corrlation sows an avrag dviation of 3 % from t tmpratur data points. Suc corrlation can b usd, for instanc, to prdict cangs in t pak valu of t arc tmpratur at t nozzl xit of a gomtrically similar cutting torc du to cangs in its opration paramtrs. 1. ntroduction Plasma cutting is a procss of mtal cutting at atmospric prssur by an arc plasma jt, wr a transfrrd arc is gnratd btwn a catod and a work-pic (t mtal to b cut) acting as t anod. Small nozzl bor, xtrmly ig ntalpy and opration at rlativly low arc currnt ( 1 ) ar a fw of t primary faturs of ts torcs [1]. T pysics involvd in suc arcs is vry complicatd. T convrsion of lctric nrgy into at witin small volums causs ig tmpraturs and stp gints []. Dissociation, ionization, larg at transfr rats (including losss by transparnt iation), fluid turbulnc and lctromagntic pnomna ar all involvd. n addition, wid variations of pysical proprtis, suc as dnsity, trmal conductivity, lctric conductivity and viscosity av to b takn into account. Ts factors mak oplss to gt an analytical solution for suc arcs. Rcntly, commrcial computational fluid dynamic softwar as bcom widly availabl and tn numrical plasma modlling as racd a stat advancd noug to b of practical us in t study of t cutting arc procsss. Howvr, as suc programs wr not initially dvlopd for t dscription of trmal plasma procss, ty nd to b complmntd wit lctromagntic and plasma proprtis packags [3]. Ts packags ar not asy to obtain. Also t commrcial softwar rsults somwat xpnsiv. On t otr and, xprimntal data on cutting arcs ar ard to obtain du to t ars ambint conditions. Most of t availabl xprimntal data ar rlatd to spctroscopic [1] and prob masurmnts [4-6] in t xtrnal plasma rgion, giving dirct information of only part of t variabls involvd, mainly t tmpratur. Publisd undr licnc by OP Publising td 1

3 FUDOS 1: X Mting on Rcnt Advancs in t Pysics of Fluids and tir Applications OP Publising ournal of Pysics: Confrnc Sris 96 (11) 15 doi:1.188/ /96/1/15 n tis scnario, t knowldg of a propr corrlation mtod to mak advantagous us of t xprimnts aly prformd on cutting arcs bcoms important from t nginring point of viw. T prsnt work applis similarity tory [7,8] to t plasma manating from transfrrd arc, gas vortx stabilizd plasma cutting torcs, to analyz t xisting corrlation btwn t plasma tmpratur (a quantity of primary importanc in suc dvics) and t pysical paramtrs of suc torcs.. Arc dimnsionlss numbrs.1. Matmatical modl Sinc a numbr of complx, intracting, nonlinar procsss ar simultanously occurring in cutting arcs (lctromagntic, gas dynamic as wll as trmal ffcts), t consrvation quations wr usd as t starting point for dtrmining dimnsionlss numbrs. T most frquntly usd cutting arc modls assum t local trmodynamics quilibrium (T) approximation [3], so t plasma is caractrizd by a singl tmpratur T. T fluid part of t trmal plasma modl dscribing suc an arc can b xprssd as follows. Total mass consrvation ( u ) =. (1) Momntum consrvation ( u u τ ) + p B =. () nrgy consrvation u + q p u + Q& = (3) ( ), wr rprsnts t total mass dnsity, u t fluid vlocity, p t prssur, τ t strss tnsor, t currnt dnsity, B t magntic fild, t ntalpy, q t total at flux, t lctric fild and Q & t powr lost by transparnt iation. Two mor quations ar rquird to dscrib t lctromagntic part of t plasma modl. T first is t currnt continuity quation =, (4) wr = σ, (5) wil t scond is on of Maxwll s quations B = ~ µ, (6) wr σ is t lctric conductivity and ~µ t fr spac magntic prmability. T total at flux in quation (3) dscribs t at transportd by conduction and t ntalpy transport by mass diffusion, and is dfind as [3] q κ T +, (7) wr κ is t ffctiv trmal conductivity and is t lctron mass diffusion tat can b approximatd by m, (8) wr is t lmntary lctric carg and m is t lctron mass. quation (8) nglcts t carg transportd by ions. n quation (7) = 5kB T ( m) rprsnts t spcific lctron ntalpy (k B is t Boltzmann s constant). T ffctiv viscosity is µ = µ l + µ t, (9) and t ffctiv trmal conductivity is µ t C p κ = κ +, (1) P r

4 FUDOS 1: X Mting on Rcnt Advancs in t Pysics of Fluids and tir Applications OP Publising ournal of Pysics: Confrnc Sris 96 (11) 15 doi:1.188/ /96/1/15 wr C p, µ l and κ ar t constant-prssur plasma spcific at, viscosity and trmal conductivity, rspctivly. T turbulnt viscosity µ t and t Prandtl numbr P r rquir xtra rlationsips (wic ar commonly rfrrd to as t turbulnc modl) to calculat t turbulnt nancd viscosity and trmal conductivity. Rlationsips xprssing t dpndnc of gas composition, trmodynamic proprtis, transport cofficints and iation powr losss on tmpratur and prssur; must b also addd in ordr to mak t st closd. To mak t problm dfinit it is ncssary also to spcify boundary conditions for all of suc variabls... Dimnsionlss numbrs n wat follows, t st of quations ar xprssd in dimnsionlss form by making us of rfrnc valus (dnotd by t subscript zro ) for t abov plasma quantitis, and wit as a scal lngt: ( u ) =, (11) τ p B ( u u ) τ + p B =, (1) u u u u q p u Q& ( u ) + q p u + Q& =, (13) =, (14) σ =, (15) µ B =. (16) B T suprscript (*) indicat dimnsionlss numbrs, obtaind by dividing dimnsional variabls by t appropriat scal valus (, u u u and so on). T quation (1) givs tr dimnsionlss numbrs, p τ B N,,. N m R u u u T first and t scond ar t wll-known ulr and Rynolds numbrs. T tird numbr sows t rlativ wigt btwn t lctromagntic and inrtial forcs. T quation (13) givs four dimnsionlss numbrs, u p u q Q, wf, q,. Ts numbrs rflct t convrsion of lctric nrgy into otr forms. T ntalpy numbr taks into account nrgy wic is usd for ating t plasma flow, tims ( ) 1 N is basd on nrgy usd for acclration, and q and involv nrgy losss by conduction and mass diffusion; and nrgy losss by lctromagntic iation, rspctivly. T Om s and Ampr laws giv t numbrs, σ µ, B. B Ts numbrs rflct t rlation btwn slf and xtrnal magntic filds (if any), and t procss of cargd particl transfr in an lctric fild. n addition to ts numbrs, from t boundary conditions various paramtric numbrs can b obtaind. T boundary condition for t arc currnt () = ds, (17) 3 S wf

5 FUDOS 1: X Mting on Rcnt Advancs in t Pysics of Fluids and tir Applications OP Publising ournal of Pysics: Confrnc Sris 96 (11) 15 doi:1.188/ /96/1/15 (S rprsnts t ara of t arc cross sction) in dimnsionlss form bcoms = ds, (18) and nc givs t currnt numbr Also, t numbrs S. d Prl d, ip p account for t nozzl gomtry (diamtr (d)) and t influnc of t inlt gas prssur (P rl ) on t arc quantitis. T st of dimnsionlss quations (11-16) givs nin indpndnt dimnsionlss numbrs in agrmnt wit t Buckingam π-torm, sinc t numbr of quantitis is tirtn and t numbr of dimnsions four. Bsids, t arc boundary conditions introduc two nw paramtric numbrs. Most of ts numbrs contain pysical proprtis, suc as dnsity and lctric conductivity, wic vary widly bcaus of t larg tmpratur rang, and crtain rfrnc valus av trfor to b takn. n tis work, t scal valus of t plasma pysical proprtis wr dtrmind for a man tmpratur T wic corrsponds to an lctron concntration of 1 % in t plasma at t ambint prssur [8]. Ts plasma scals (listd in Tabl 1), wr takn from t calculatd valus in [9]. Tabl 1. Scal valus of t plasma pysical proprtis. Pysical variabls Oxygn Nitrogn Air Tmpratur (T ) (µ 1 3 K) lctrical conductivity.3 µ µ µ 1 3 (s ) (W -1 m -1 ) ntalpy ( ).86 µ µ µ 1 7 ( kg -1 ) Dnsity ( ) (kg m -3 ).1 µ µ µ 1-3. Data on cutting arcs T xprimntal data on cutting arcs tmpratur corrspond to t xtrnal plasma rgion (opn rgions wr t prssur as rlativly small variations around t atmospric valu). Pak valus of t arc tmpratur clos to t nozzl xit for currnts in t wid rang 1 A, and for tr diffrnt working gass (air, nitrogn and oxygn); wr takn from t litratur. 4. Gnralizd arc tmpratur corrlation Not all of t obtaind dimnsionlss numbrs ar of qual importanc. nsid t torc t prssur forcs ar almost balancd by inrtial forcs (i.., otr procsss as viscosity and lctromagntic acclration ar considrably lss rlvant) and so only t ulr numbr bcoms important in t momntum quation. On t otr and, sinc t lctrical powr dlivrd in t arc is almost usd for ating t plasma flow (i.., t convrsion of lctric nrgy into kintic nrgy, wil t nrgy losss by trmal conduction, mass diffusion and iation ar lss important); only t ntalpy numbr bcoms rlvant in t nrgy quation. Also from t lctromagntic quations only t lctric fild numbr is important. Hnc, t tr rlvant dimnsionlss numbrs ar 4

6 FUDOS 1: X Mting on Rcnt Advancs in t Pysics of Fluids and tir Applications OP Publising ournal of Pysics: Confrnc Sris 96 (11) 15 doi:1.188/ /96/1/15 p u σ N,,. u Ts numbrs can b combind wit t paramtric numbrs to liminat t unknowns. T following modifid form of t ntalpy numbr can b usd as a gnralizd argumnt to construct t gnralizd plasma tmpratur corrlation for t considrd typ of arc ( ) ( ) ( ) ( ) = σ d. ( 1) N d ip P rl (19) T gnralizd function of t pak valu of t arc tmpratur at t nozzl xit may b takn to b t simpl ratio ) T T xit T, () and nc t gnralizd arc tmpratur corrlation may b xprssd as T (1) (,,,,, ) = f ( ). = f (1) N d ip Figur 1. Corrlatd arc tmpratur for cutting torcs ranging from 1 to A. T gnralizd function of t arc tmpratur for most of t tmpratur data rportd in t litratur is sown in Fig. 1. Tis figur sows tat t gnralizd function T can b accuratly dscribd by t rlationsip (in S units: p rl in Pa; d in m; in A; T in K) ) ( xp{.44 ( 1/ 1/ 3 Txit = T + Prl σ d )} ).. () T valus of t arc tmpratur prdictd using suc corrlation sow a dviation not largr tan 1 % wit rspct to t xprimntal data (wit an avrag dviation of 3 %); in spit of t fact tat suc data includ diffrnt torcs ranging from 1 to A. Not tat () sows tat t cntr-lin valu of t arc tmpratur strongly dpnds on bot, arc currnt and nozzl diamtr; but sligtly on t typ of gas and its inlt prssur. T 1/ factor σ is a numbr qual to º 9.4 µ 1 9 for oxygn, 1.7 µ 1 1 for nitrogn, and 1.1 µ 1 1 kg 1/ s - m -1/ W, for air. 5. Conclusions T tory of dynamic similarity as bn usd to construct a gnralizd arc tmpratur corrlation of a vortx-stabilizd cutting plasma torc. T ntalpy numbr obtaind from t nrgy quation as bn found to significantly influnc t tmpratur of t lctric arc. T obtaind corrlation sows an avrag dviation of 3 % from t tmpratur data points. Suc corrlation can b usd, for instanc, to prdict cangs in t pak valu of t arc tmpratur at t nozzl xit of a gomtrically similar cutting torc du to cangs in its 5

7 FUDOS 1: X Mting on Rcnt Advancs in t Pysics of Fluids and tir Applications OP Publising ournal of Pysics: Confrnc Sris 96 (11) 15 doi:1.188/ /96/1/15 opration paramtrs (lctric currnt, nozzl diamtr, working gas spci or/and t inlt gas prssur); at last witin t givn paramtrs rang. T rlation sows tat t cntr-lin valu of t arc tmpratur strongly dpnds on bot, arc currnt and nozzl diamtr; but sligtly on t typ of gas and its inlt prssur. ACKNOWDGMNTS Tis work was supportd by grants from t Univrsidad d Bunos Airs (PD X18), CONCT (PP 5378) and Univrsidad Tcnológica Nacional (PD Z 1). RFRNCS [1] Nmcinsky V A and Svranc W S 6. Pys. D: Appl. Pys. 39, R43 [] Prvosto, Klly H and Mancinlli B 9. Appl. Pys. 15, 1339 [3] Glizs A, Gonzálz and Frton P 5. Pys. D: Appl. Pys. 38, R153 [4] Prvosto, Klly H and Mancinlli B 8 Trans. Plasma Sci. 36, 63 [5] Prvosto, Klly H and Minotti F O 8 Trans. Plasma Sci. 36, 71 [6] Prvosto, Klly H and Mancinlli B 9 Trans. Plasma Sci. 37, 19 [7] Yas ko O 1969 Brit.. Appl. Pys. (. Pys. D), 733 [8] Paingankar A M, Das A K, Sirodkar V S, Srkumar K P and Vnkatramani N 1999 Plasma Sourcs Sci. Tcnol. 8, 1 [9] Boulos M, Faucais P, Pfndr 1994 Trmal Plasmas, Fundamntals and Applications Vol. 1 (Plnum Prss) [1] Colombo V, Conctti A, Gdini, Dallavall S and Vancini M 8 Trans. Plasma Sci. 36, 389 [11] Frton P, Gonzalz, Glizs A, Camy Pyrt F, Caillibott G and Dlznn M. Pys. D: Appl. Pys. 35, 115 [1] Girard, Tult P, Razafinimanana M, Glizs, Camy-Pyrt, Baillot and Ricard F 6. Pys. D: Appl. Pys. 39, 1543 [13] Sakuragi S 1995 ng. Sci. Rports, Kyusu Univrsity 16, 383 [14] Pardo Sanjurjo C, Gonzálz-Aguilar, Rodríguz Yunta A and Caldrón M A G Pys. D: Appl. Pys. 3, 181 [15] Ptrs, Hbrlin and indsay 7. Pys. D: Appl. Pys. 4, 396 6