Modeling of a 3D plasma thermal spraying and the effect of the particle injection angle

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1 Revue des Energies Renouvelables CISM 08 Oum El Bouaghi (008) 05-6 Modeling of a 3D plasma hermal spraying and he effec of he paricle injecion angle D. Khelfi *, A. Abdellah El-Hadj and N. Aï-Messaoudène 3 Cenre de Recherche Nucléaire de Birine, COMENA, Algérie Laboraoire LMPM, Universié de Médéa, Algérie 3 Laboraoire des Applicaions Energéiques de l Hydrogène, Universié de Blida, Algérie Résumé - Une comparaison a éé faie enre deu modèles de urbulence - e RNG d un je de plasma d argon/hydrogène déchargé dans l air. Le je de plasma d argon déchargé dans l air es simulé par les modèles - e RNG pour une configuraion 3D. Le comporemen des paricules a éé modélisé à l aide des rajecoires de paricules solides. Les calculs son effecués avec le code CFD Fluen. Tou d abord, on a fai une validaion pour la projecion des paricules de Ni e de ZrO. Cee parie de l éude monre que les paramères des paricules son mieu prédis avec le modèle RNG. Enfin, nous avons consaé que l angle d injecion des paricules a un effe imporan sur le chauffage e l accéléraion des paricules. Absrac - A comparison is made beween wo urbulence models for an argon/hydrogen plasma discharged ino air amosphere. Three dimensional plasma je flow is prediced wih he sandard - model and he RNG model of urbulence. Paricles behaviour has been modelled by using sochasic paricles rajecories. Compuaions are performed wih he Fluen CFD code. Firs, a validaion is made for spray parameers of Ni and ZrO paricles. This par of he sudy shows ha he paricle parameers are beer prediced wih he RNG model. Finally, we have found ha he paricle injecion angle has an imporan effec on paricle heaing and acceleraion. Keywords: Plasma spraying RNG - Injecion angle.. INTRODUCTION Thermal plasmas have found eensive indusrials applicaions in he area of maerials processing, such as plasma spraying, cuing, welding, ulra-fine paricle synhesis, ec. []. Plasma spraying consiss of injecing solid paricles ino a high emperaure, high velociy gas je, in which he je acs as a ranspor medium for heaing and acceleraing he spraying paricles. Acceleraion and heaing of paricles are crucial in hermal spraying o boh process efficiency and coaing qualiy. For a given process, he paricles need o achieve a specific range of hermal and ineic energy. In many cases, he parameers ha affec he heaing and moion of paricles are inerrelaed and ineracion effecs are comple. In order o beer undersand he hermal spray process, grea effors have been performed in he las years in he area of heoreical modeling. Research effors have been devoed o plasma je characerisics and he behavior of injeced paricles in he plasma je. Ye, he physics of plasma hermal spraying remains lile conrolled. One of he major difficulies is he presence of urbulence which complicaes he modeling of hermal plasma, prevening a full undersanding of he plasma-paricle ineracion phenomena. The complemen brough by simulaion o * Khelfi_djillali@homail.com _ lmpm_cum@yahoo.fr _ naimessaoudene@yahoo.com 05

2 06 D. Khelfi e al. eperimenal measuremens is essenial because measuremens are ofen difficul o realize considering he range of emperaures concerned. Mos of he simulaions have been conduced in a D compuaional domain. Twodimensional models suppose an aial symmery [-5]. D modeling can significanly simplify he numerical effors. However, i canno simulae any hree-dimensional (3D) process occurring in hermal plasma sysems. Bu 3D modeling of hermal plasma sysems is sill a challenging problem, as demonsraed by some recen publicaions [6-0]. Mos of hem were performed using commercial CFD sofware. Since he 980s, boh he mehodology in compuaional fluid dynamics (CFD) and compuing capaciies have grealy improved. As a resul, CFD has been applied o plasma spray research since early 990 s and offers a grea poenial for process opimizaion. Several researchers have used a CFD code o simulae plasma spraying processes. For eample, D.T. Gawne e al. [7] sudy he effecs of radial injecion of a waer je ino swirl and no swirl plasma jes. The auhors use he Sar-CD CFD code o solve he problem. K. Ramachadran e al. [8], sudy he effecs of radial injecion of waer je ino swirl and non-swirl plasma jes. The auhors use he Phoenics CFD code. Y.Y. Zhao e al. [] developed a numerical model o calculae spaial disribuions of plasma gas emperaure, enhalpy, velociy and fracions of dissociaed and ionized species in a vacuum plasma spraying. The auhors use he Fluen CFD code. Ahmed e al. [] sudied he behavior of ceramic paricles in Ar-H plasma je using a 3D model coupled wih he commercial compuaional code Fluen. The urbulence model is eclusively used in plasma spraying modeling. The sandard model falls wihin he simples wo-equaion urbulence models. A popular alernaive model is he RNG (ReNormalized Group) urbulence model. The RNG urbulence model [3] was derived using a rigorous saisical echnique (renormalized group heory). In addiion o high Reynolds number effecs, he RNG model also aes ino accoun low Reynolds number effecs and i can even predic some laminar behavior. The RNG model improves predicions for high sreamline curvaure and srain rae, ransiional flows, and wall hea and mass ransfer. In his sudy, we begin performing a comparison beween wo models of urbulence, he model and RNG model for an Argon plasma je flow discharged ino air environmen. Ne, we invesigae he comparison beween he wo models of urbulence for modeling he paricle behavior during Ar/H plasma hermal spraying. Finally, we sudy he effecs of injecion direcion or injecion angle on paricle behavior during plasma hermal spraying.. MATHEMATICAL MODEL The plasma orch, he injecion por, and he subsrae are schemaically shown in figure.. Plasma je The gaseous species are supposed o behave as ideal gases a amospheric pressure. The sysem is in seady sae, wih ime-averaged urbulen flucuaions aen ino accoun. The plasma componens are in local hermodynamic equilibrium. In addiion,

3 CISM 008: Modeling of a 3D plasma hermal spraying and he effec of he paricle 07 he plasma is modeled as a urbulen free je composed of a high emperaure miure of Ar-H issuing ino ambien air. The ranspor properies for gases (plasma (Ar and H ) and air) are calculaed from daa repored in Boulous e al. [4]. The ranspor properies are calculaed based on he Chapman-Ensog heory. Miure ranspor properies are calculaed wih he Wile s formula [4]. Because of heir anicipaed small effec on sprayed paricles and he epense of including hem in a fully ellipic hree-dimensional simulaion, chemical reacions wihin he plasma are no modeled here. I is esimaed ha he reacions would conribue o less han 0 percen of he paricle heaing. I is noed ha a higher level of uncerainy is associaed wih values of ranspor properies [4]. The effec of neglecing chemical reacions for plasma je simulaion has been adoped in a number of recen wors [7, 8, ]. The equaions o be solved for he gases are conservaion of mass, momenum, enhalpy, species (Ar, H and air), and urbulence ineic energy as well as is dissipaion as presened in [9]. Two models of urbulence are used in he sudy, he model and he RNG model [3]. A general-purpose CFD code, Fluen, is used in his sudy. Fluen uses FVM (Finie Volume Mehod) [5] for predicing he fluid dynamics of he plasma je and he ambien air. The ranspor equaions are se in inegral form:..d V..V.d A..d A S.d V φ φ = Γ φ φ () V A A V Unseady Convecion Diffusion Generaion Where φ is a variable ha is used o describe a general ransporable quaniy, and S φ is he source erm [6]. Table, gives a subse of he variables ha are solved. Field variables (sored a cell ceners) mus be inerpolaed o he faces of he conrol volumes in he FVM according o: ( φ) ( φ). V F. φf.vf.af = ΓF ( φ),f.af Sφ. V () Faces Table : Corresponding φ for ranspor equaions Equaion Coninuiy Momenum (, y, z) Energy Turbulen Kineic energy Turbulen dissipaion rae Species ranspor Variable for φ Velociy (u, v, w) Enhalpy (h) K Mass fracion of species ( Y i ) The ranspor equaion for φ is presened in a simple form: a P. φp anb. φnb = bb. The soluion converges, if he residue R = R P is cells small enough for all equaions, where RP = ap. φp anb. φnb bb. The sandard Fluen inerface canno be programmed o anicipae every user s needs. The use of UDFs (User Defined Funcion), however, enables he user o

4 D. Khelfi e al. 08 cusomize he code o fi paricular modeling needs. UDFs can be used for a variey of applicaions [6]. Thermophysical properies and inle velociy and emperaure are se by UDF funcions. For he wo urbulence models ( model and RNG model), he urbulen ineic energy equaion is: ( ) ( ) ( ) Φ = z z y y z w y v u (3) The dissipaion rae equaion is: ( ) ( ) ( ) C C z z y y z w y v u Φ = (4) Where φ, he viscous dissipaion erm, in ensor noaion is given by: i i i u u u = Φ (5) Defaul values for various consans in he sandard model are given in Table [4]. Table : Sandard model coefficiens C C C In he RNG model [3] a consan C is used. The value is specified wih a separae command han he one used o specify he C in he sandard model. The same is rue of he consan C. As shown in he above able, he diffusion mulipliers have differen values han he defaul model, and hese parameers also have heir own commands for he RNG model. Quaniies in equaions (3) e (4) no specified in Table are covered by Table 3. Table 3: RNG model coefficiens C C β η In he RNG model, he consan C in dissipaion equaion is replaced by a funcion of one he invarians: 3.4 C βη η η η = (6) The invarian η is given by: j i j i S. S = η (7) Where j i S is he symmeric deformaion ensor equal o ( ) j,i j, u i u.

5 CISM 008: Modeling of a 3D plasma hermal spraying and he effec of he paricle 09 The soluion of he urbulence equaions is used o calculae he effecive viscosiy: e = C (8). Compuaional domain and boundary condiions The boundary condiions are based on he physical configuraion described in Fig.. Fig. : Illusraion of he compuaional domain The compuaional grid is polar cylindrical, wih dimensions of 50 mm, 80 mm and π radians in he radial, aial, and azimuhal direcions. The mesh is more refined near he ais in he radial direcion as well as near he je ei in he aial direcion. I is uniform in he angular direcion. An analysis of differen mesh dimensions reveals ha 60 nodes in X direcion, 50 in r direcion, and 34 in θ direcion are sufficien. The velociy and emperaure a he nozzle ei are prescribed and given by [8]: n ν = 0, w = 0 and r u = u m (9) R m r T ( Tm Ta ) = T a (0) R Where u m and T m are he maimum velociy and emperaure a he plasma je cenerline and R he inner radius of he nozzle. T a is he nozzle wall emperaure which is aen as 300 K. The eponens values in he equaions above are m = 4.5 and n = u ' ' [8]. The urbulence inensiy I =, u being RMS of he flucuaing componen) is u specified along wih he lengh scale ( l ) se o he orch ei diameer (hence a he 3/ 4 3/ 3 C orch ei = u', = ). l The effec of DC arc flucuaions, which are originally driven by random arc iniiaion and eincion beween he cahode and he anode, is no a rue urbulence phenomenon. However, because of he lac of undersanding of he deailed arc physics, his flucuaion is accouned for by specifying a high level of urbulence a he je ei, wih I = 0 percen [9]. The wo equaions urbulence models will no predic correc

6 0 D. Khelfi e al. near-wall behavior if inegraed all he way down o he wall. A special near-wall reamen is required. We use he sandard wall funcions for he velociy and emperaure fields..3 Paricles-plasma ineracions Lagrangian equaions of moion and hea balance are used o simulae he paricle behavior in he plasma je. Dilue sprays assumpion is considered here, where cooling and redirecion of plasma gases by he paricles is negleced. Thus, one way coupling is used for he discree phase [6]. The velociy of a paricle can be calculaed according o he force balance on he paricle [6]: ( ν νp ) Fh d vp = FD () d where ν P and ν are he paricle and gas velociies respecively, and F D is he drag force per uni paricle mass, which is given by: 8 CD Re FD = ().d 4 P P where P is he paricle densiy, d P is he paricle diameer, C D is he drag.d P. νp ν coefficien and Re is he relaive Reynolds number defined as: Re =. The drag coefficien C D is a funcion of he relaive Reynolds number: a a C 3 D = a (3) Re Re where a, a and a 3 are consans given by Morsi and Aleander [6]. Small paricles suspended in a gas ha has a emperaure gradien eperience a force in he direcion opposie o ha of he gradien. This phenomenon is nown as hermophoresis. Fluen can opionally include a hermophoresis force on paricles in he addiional force erm inended for his purpose. The epression of he hermophoresis force suggesed by Tablo [6] is given by: C S, Fh ( K' C n ) 6π.d. P.CS. T = (4) ( 3Cm n )( K' C n ) mpt C m, C are model consans [6]. n is he Knudsen number. K ' = p, where g p is he paricle hermal conduciviy and g he gas hermal conduciviy. In he presen wor, a paricle sochasic rajecory model is used. The paricles are assumed o be defleced by eddies when hey cross hem. The ime of paricle ineracion wih he randomly sampled field (eddies) is assumed o be he minimum of he eddy lifeime and ransi ime required for he paricle o cross he eddy. The eddy lifeime and paricle ransi ime are given as: l e e = (5) ν'

7 CISM 008: Modeling of a 3D plasma hermal spraying and he effec of he paricle l e γ = (6) ν' νp where he eddy size is: 3/ 4 3/ C l e = (7) Assuming ha he paricle is heaed by convecive and radiaion hea ransfer only, he emperaure is uniform hroughou he paricle and here are no phase ransformaions in he paricle. The paricle emperaure can be calculaed from [6]: dt ( ) ( 4 4 m P P CP = η.a T TP P.A. θ R T P ) (8) d where m P is he mass of he paricle, C P is he specific hea of he paricle, T P is he paricle emperaure, A is he surface area of he paricle, η is he convecive hea coefficien, θ R is he radiaion emperaure, P is he paricle emisiviy, is he Sefan Bolzman consan ( W/m K 4 ) and T is he local gas emperaure. The hea ransfer coefficien is evaluaed using he Ranz-Marshall correlaion [6]: ( / / 3 P Re.Pr ) η = (9) dp Some facors are no included in he discree phase model. Ai-Messaoudene e al. [0] presens a full paricles model used in hermal spraying. 3. RESULTS AND DISCUSSION 3. Paricles behavior Resuls of previous model of paricles (also using ) and measuremens [9] are compared wih he presen compuaions. The sysem used is Meco-9MB plasma spray orch. Operaing condiions are: a orch curren and volage of 500 A and 70 V respecively. The gas composiion is 40 slm of Ar and slm of H. The nozzle ei diameer is 7.5 mm. The paricles o be injeced have an iniial emperaure of 300 K. Fig. -a shows he paricle velociy for hree heoreical models and he eperimenal daa. For he sae of comparison, a group of 56 7 m diameer of zirconium paricles is used. The iniial ransverse inward velociy for zirconium paricles is aen 4.5 m/s. For he velociy, resuls show ha he RNG model is in beer agreemen wih eperimenal measuremens han he model. In addiion, Fig. -b shows a comparison of paricles hermal hisory. The RNG model sill gives beer resuls. For eample, a 05 mm from he nozzle ei, he RNG model yields a velociy which is 3 % lower han eperimenal daa. A he same posiion, he model gives a resul 45 % lower han eperimenal daa. For he emperaure a he same posiion, he differences compared o eperimenal daa are 9 % and 99 % for he RNG and he model respecively. The same comparison for a group of nicel paricles of m diameer is presened in figure 3. The iniial ransverse inward velociy for nicel paricles is aen 9.8 m/s. In his figure, we can sill see he advanage of he RNG model compared o he model. For eample, a 85 mm from he nozzle ei, he RNG model gives a

8 D. Khelfi e al. lower velociy compared wih eperimenal daa by approimaely 70 %. A he same posiion, he model underesimaes he velociy by 30 %. For he emperaure a he same posiion, he differences compared wih eperimenal daa are % and 36 % for he RNG model and he model respecively. ( a ) ( b ) Fig. : ZrO Paricle (a) velociy and (b) emperaure along he aial disance in an Ar H Plasma je ( a ) ( b ) Fig. 3: Nicel Paricle (a) velociy and (b) emperaure along he aial disance in an Ar H plasma je 3. Effec of paricle Injecion angle The las plasma sysem is used in his case. Here he injecor angle wih respec o he je cenerline is changed. A single paricle of ZrO is numerically injeced ino he plasma je. Three paricle sizes (30 m, 50 m and 70 m) are used. In his par of he sudy, he effec of paricle injecion direcion is invesigaed. We use hree ypes of injecion angles, verical posiion, 45 upsream inclined injecion and 45 downsream

9 CISM 008: Modeling of a 3D plasma hermal spraying and he effec of he paricle 3 inclined injecion. The paricle injecion velociy is 4.5 m/s in magniude for all cases. Fig. 4 illusraes hese hree injecion possibiliies. Fig. 4: Differen paricles injecion configuraions Fig. 5 shows he velociy evoluion along he je ais. From his figure, we can see ha upsream inclined injecion increases he paricle velociy as i moves upsream. I should be noed ha a he injecion posiion, upsream injecion confers a lower iniial aial velociy since paricles are injeced couner flow. By conras, downsream injecion leads a lower paricle velociy. a b c Fig. 5: Paricle velociy along aial posiion for hree injecor direcions

10 4 D. Khelfi e al. The emperaure hisories are illusraed in Fig. 6. In his case also, upsream injecion gives higher values of emperaure han he ohers. This is due o he fac ha when paricles are injeced oward he nozzle ei region, encouner a higher energy and momenum regions of he plasma je. This leads o a higher acceleraion and heaing of he paricles. This seems an ineresing resul for real process applicaions and should be invesigaed eperimenally. a b c Fig. 6: Paricle emperaure along aial posiion for hree injecion direcions 4. CONCLUSION The main conribuion of his sudy is he comparison of wo urbulence models, and RNG for he simulaion a hree dimensional plasma hermal spraying je configuraions. In a firs sep, a comparison is made for he gases flow alone. The compuaions show ha he RNG model is in beer agreemen wih eperimenal daa. Secondly, he moion and heaing of paricles in he je during plasma spraying is simulaed for nicel and ZrO powders. In his case again, he RNG model yields more realisic resuls compared o he model. Therefore, alhough here is a lile supplemen in compuaion ime wih he RNG model, i should be preferred in plasma hermal spraying simulaion sudies.

11 CISM 008: Modeling of a 3D plasma hermal spraying and he effec of he paricle 5 Finally, he effec of he injecion angle of he paricles is invesigaed. For he same paricle injecion velociy magniude, i is found upsream inclined injecion leads o higher levels of heaing and acceleraion of he paricles. This suggess a very simple process configuraion change for enhancing coaing qualiy. I should be ineresing o confirm his resul eperimenally. a E, a W, a P, b : Consans of finie volumes mhod a, a, a 3 : Consans NOMENCLATURE Re : Reynolds number S φ : Source erm C D : Coefficien of drag T : Temperaure C p : Specific hea T m : Maimum emperaure a he C, C, C, C 3, β, e Consans of RNG and model D : Coefficien of diffusion d : Diameer of he orch d p : Diameer of paricle : F d : Drag force F h : Thermal force η : Invarian h : Enhalpie I : Inensiy of urbulence K :Turbulen ineic energy K ' : Raion of conduciviies l : Scale lengh l e : Dimension of he swirl R : Inner radius of he nozzle REFERENCES plasma je cenreline u m : Maimum velociy a he plasma je cenerline V : Velociy u, ν, w : Consans of velociy Y i : Species : Turbulen dissipaion rae Γ : Coefficien of diffusion : Densiy : Sefan-Bolzman consan φ : Variable ha is used o describe a general ransporable quaniy Φ: Viscous dissipaion erm e :Life ime for he paricle RR : Residue [] W. Smih and R.D. Fas, Welding Journal, Vol. 43, 994. [] N. Eladdah, J. Mcellige and J. Szeely, Meallurgical Transacions B5B, Vol. 59, 984. [3]Y.C. Lee and E. Pfender, Plasma Chem., Plasma Process., Vol. 7, N, p., 987. [4] P.C. Huang, T. Heberlein and E. Pfender, Surface and Coaings Technology, Vol. 73, p. 4, 995. [5] J. Par, J. Heberlein e al., Plasma Chem., Plasma Process, Vol. 8, p. 3, 008. [6] Xi. Chen and H. Li, Surface and Coaings Technology, Vol. 7, p. 4, 003. [7] D.T. Gawne, T. Zhang and B. Liu, Surface and Coaings Technology, Vol. 53, p. 47, 00. [8] K. Ramachadran, N. Kiuawa and H. Nishiyama, Thin Solid Films, Vol. 435, p. 98, 003.

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