Modeling of Plasma Spraying of Two Powders

Transcription

1 JTTEE5 10: ASM International Modeling of Plasma Sraying of Two Powders B. Dussoubs, A. Vardelle, G. Mariaux, N.J. Themelis, and P. Fauchais (Submitted 7 July 1999; in revised form 19 October 000) The behavior of metal and ceramic owders co-srayed through a lasma jet was simulated using a commercial fluid dynamics model in which the articles are considered as discrete Langrangian entities. Comutations were carried out for the lasma jet and the injected articles using (a) a steady-state threedimensional (-D) jet and (b) a simlified two-dimensional (-D) model. An analytical method was used to estimate the aroriate injection velocities for the metal and ceramic articles, injected through oosing nozzles erendicular to the lasma flow, so that their mean trajectories would iminge on the same area on the target surface. Comarison of the model rojections with exerimental measurements showed that this method of comutation can be used to redict and control the behavior of articles of widely different roerties. Peer Reviewed Keywords 1. Introduction functionally graded materials, article injection, article modeling, lasma co-sraying The simultaneous sraying of metal and ceramic owders can be used to roduce what is called functionally graded materials (FGM) that exhibit continuous or stewise variations in comosition and/or microstructure. [1] One of the key alications is to reduce the interface effects between coating and substrate, since co-sraying allows a gradual variation of roerties. For examle, this technique has roven useful in avoiding thermal exansion coefficient mismatch in thermal barrier coatings, thus limiting high stress regions and imroving coating lifetime. In lasma co-sraying, it is essential that the slats from the two tyes of articles overla on the substrate. When using a single lasma torch system, two methods of owder injection can be used in the roduction of FGM. The two owders are mixed and fed through a single injection ort; in this case, the higher density articles must be of smaller size than the lighter ones. The two tyes of articles are injected through two searate injectors. In this case, the carrier gas flow, injector-to-substrate distance, and angle between injector and lasma jet axis can be varied searately so as to obtain overlaing of slats on the substrate. In the roduction of FGM by lasma co-sraying, the disersion of articles in the jet flow and the deosition efficiency must be carefully controlled in order to roduce coatings with a consistent comosition. Deviations from the lanned gradient occur when the different owders fed into the lasma do not iminge on the substrate at the same location, leading to inhomogeneities. Therefore, for given lasma oerating conditions, it is imortant to understand the relationshi between article injection ara- meters and the resulting trajectories and temeratures. Mathematical simulation can be of great hel in this matter, as will be discussed in the following sections of this aer. For the uroses of this work, the owder system iron-aluminum oxide was selected because of the range of roerties offered by these two materials.. Mathematical Model Comutations were carried out for the lasma jet and the injected articles using (a) a steady-state three-dimensional (-D) jet and (b) a simlified two-dimensional (-D) model..1 Modeling of -D Plasma Jet The model of the lasma jet issuing in air and iminging normally on a flat substrate is based on the following assumtions: [] steady-state lasma jet flow (i.e., neglecting the effect of the arc movement within the nozzle); turbulent flow excet in the otential core and close to the walls (i.e., front surface of the gun, injectors, and target surface); lasma in local thermodynamic equilibrium and otically thin; B. Dussoubs, LSGM-ENSMN, Parc de Saurut, 5404 Nancy, Cedex, France; A. Vardelle, G. Mariaux, and P. Fauchais, SPCTS, University of Limoges, Limoges, France; and N.J. Themelis, Earth and Environmental Engineering, Columbia University, New York, NY armelle@ensil.unilim.fr. Fig. 1 Calculation domain Journal of Thermal Sray Technology Volume 10(1) March

2 no chemical reaction in the gas hase; multicomonent flow consisting of the lasma-forming gas, owder carrier gas, and ambient gas; and target surface ket at a constant temerature. The governing equations of the gas flow (continuity equation for each comonent of the mixture, Navier-Stokes equations, and energy conservation equation for multicomonent gas system) are solved using the commercial code, ESTET.. [] This code is a -D comutational fluid dynamics ackage simulating transient or steady, comressible, turbulent, and multicomonent reactive flow. Turbulence is modeled by the the k-ε model with the correction of Launder and Sharma, for low Reynolds numbers. [4] The thermodynamic and transort roerties of the gas mixture are calculated using the laws of mixtures and the data of ure gases. [5] Figure 1 shows the comutation domain, the boundary conditions, and the comutational mesh. The rofiles of gas velocity and temerature at the nozzle exit are imosed as [6] r v = v max * 1 R (Eq 1) lasma jet on the torch axis, T m,cu the melting oint of coer, and R the nozzle radius; v max and T max are determined from the lasma-forming gas mass flow rate and the net ower inut to the gun. The conservation equations for the mean values of turbulent flow, turbulent energy, and its rate of dissiation are exressed by Eq. Table 1 shows the transort coefficients and the source terms for all variables involved in these calculations. ( ) = ( ) = div ρv div Γ grad S. Modeling of -D Plasma Jet (Eq ) The -D steady-state model is based on the same assumtions as the -D model. In addition, the jet flow is assumed to have azimuthal symmetry and the governing equations are written in cylindrical-olar coordinates. The effect of the carrier gas flow on the lasma jet cannot be taken into account in the -D model. However, earlier exeriments and mathematical simulations have shown that this effect is negligible for the sray arameters of this study, where the owder is injected externally to the gun and the carrier gas flow rate is less than 10% of the lasma-forming gas flow rate. [7] ( m ) 45. max,cu * 1 T = T T r R + T m,cu (Eq ) where v max and T max are the velocity and temerature of the. Modeling of Particle Dynamics and Heating The acceleration and heating of articles are calculated with a Lagrangian scheme under the following assumtions: [8 10] Table 1 Transort coefficients and source terms for the equations of the flow Γ Σ 1 0 div ( ρv) u µ eff µ µ ρ x div µ = v t f + µ div v ρ eff eff k x x x x v w µ µ ( ) ( ) ( ) ( ) ( ) ( ) ρ div µ y + f + µ div v y y + y y ρ k eff y eff eff eff ρ µ y + fz + div eff µ eff z z z z ρ k + div v H ρκ ( / CP ρ )+ µ t /Prt SH + v grad X ρ D + µ / Sc 0 i i t t k µ + µ t / σk ρ k div v µ t ( div v) + G + ρ( Gk ε) ε µ + µ t / σε ε ρε µ ρ ε ε Cε div v tcε ( div v) + Cε Gk Cε ε k k ( )+ ε ε k C C G 1 l 1 1 with µ t G u v w k + = + ρ x y z 1 µ t ρ G = ρ σ x ρ fi µ ρc k and t = µ ε k i u v + + y x u + w + z x v w + + z y 106 Volume 10(1) March 001 Journal of Thermal Sray Technology

3 sherical articles, no interactions between articles, ossible interactions with the walls resent in the domain, turbulent disersion of articles, lumed caacitance method for article heating, and modification of lasma-article transfer coefficients to account for the variation of gas roerties in the boundary layer and article evaoration. The article size distributions were in the commercially used range and 8 to 1 classes of article sizes were used in the comutation. About 500 article trajectories were calculated for C D drag coefficient C P secific heat, J/kg K d diameter, m F D drag force, kg m/s f body force, kg m/s g gravity vector, m/s h heat-transfer coefficient, W/m K H secific enthaly, J/kg k kinetic turbulent energy, m /s m mass, kg N mass flux, kg/m s OM osition vector, m ressure, Pa Q n, Q ń rate of heat transfer, W r radius, m R radius of the owder injector, m S source term for the equations of conservation T temerature, K V velocity vector, m/s, of comonents u, v, and w in the Cartesian frame (x, y, z ) X mass fraction ε rate of dissiation of turbulent energy, m /s ε R total emissivity w variable H heat of reaction, J/kg G transort coefficient, kg/m s κ thermal conductivity, W/m K µ dynamic viscosity, kg/m s ρ density, kg/m σ Stefan-Boltzmann s constant, W/m K 4 a B eff g max m,cu va Table of Symbols Greek Symbols Subscrits ambient temerature boiling effective gas maximum melting of coer article vaorization each run. The distributions of article velocity and osition at the injector exit were obtained from an earlier calculation of gasarticle interactions inside a art of the iing system and the injector. Since the trajectories of articles in the jet flow are, to a great extent, conditioned by the injection conditions of the owder, the model must reresent the latter in a realistic way. The energy balance on a article of mass m yields m dv P (Eq 4) Integrating Eq 4 twice rovides the osition vector of the article as a function of time. The correlation of Lee et al. [11] was chosen to correct the value of the drag coefficient C D for thermal gradients in the boundary layer around the article. In comuting the disersion of articles due to turbulence, it is necessary to re-create their instantaneous velocities from the mean values of the flow field. This is done by using the Csanady equations. [1 14] As the articles are heated, they are subjected to the following sequence: Heating of solid article 4 4 Q h d T T d T T m C dt P n = π P( P) εrσπ P P a P (Eq 5) P Melting at constant temerature The net amount of heat received by the article from the lasma is converted to latent heat of fusion: Q n P dx = C d v P P v ( vp v ) = Dπ ρ + mpg 4 πd H ρ 6 P P M P ( ) = where X is the molten mass fraction of the article. Heating of liquid article and evaoration ( ) (Eq 6) 4 4 Qn = hπdp( T TP) εrσπdp TP Ta (Eq 7) mc dt P = P + πdpnva H P va In this stage, the article diameter decreases roortionally with the last term of the above equation. The heat-transfer coefficient in the above equations is calculated from the Nusselt number, Nu, using the correction of Lee et al. [11] The value of N va, the mass flux of vaor escaing from the article surface, is determined from the equation roosed by Yoshida. [15] 4. Results and Discussion 4.1 Plasma Sraying Conditions The sraying arameters used as inut data for the model are shown in Table and the characteristics of the feedstock mate- Table Plasma sray arameters Gun nozzle exit 7 mm Plasma-forming gas 45 slm Ar + 15 slm H Gas mass flow rate kg s 1 Arc current 600 A Effective ower 1.5 kw Stand-off distance 100 mm Peer Reviewed Journal of Thermal Sray Technology Volume 10(1) March

4 Fig. Radial article distribution at the exit of the injector: (a) alumina owder and (b) iron owder Table Powder characteristics Material Alumina Iron Melting oint 6 K 1810 K Boiling oint 800 K 0 K Mass density 900 kg m 7800 kg m Secific heat (00 K) 16 J kg 1 K J kg 1 K 1 Thermal conductivity (00 K) 5 W m 1 K 1 5 W m 1 K 1 Particle size µm 45 µm Powder feed rate 15 g min 1 15 g min 1 rials in Table. The lasma jet issued in air at atmosheric ressure. The two owders were injected through 1.8 mm diameter orts located at 4 mm downstream of the nozzle exit and 9 mm off the jet centerline. The simulation of the neumatic transort of owder in the injector showed that the velocity and location of the iron articles at the injector exit deend very little on the article size of the iron articles. The same effect was redicted for the alumina articles, excet for the lightest ones of diameter less than 0 µm. The latter were more subjected to turbulent disersion and collisions with the tube wall; about 5% of these finer articles were close to the wall and exhibited a low velocity, [16] as shown in Fig.. This figure shows the radial distribution of the articles at the injector exit whose radius is 0.9 mm. Position zero corresonds to the injector centerline and osition 0.9 to the injector wall. Three article size grous have been considered for alumina and iron owders: <0 µm, 0 to 50 µm, and >50 µm, the total owder ercentage for each of the three article grous being equal to 100%. The rofiles of article and gas velocity at the injector exit were ractically identical, the velocity of the iron articles being lower than that of alumina articles, as exected. 4. Comarison with Measurements For alumina articles that attained temeratures above 1800 K, the model redictions for the radial distribution of article number density, at 100 mm from the nozzle exit, were found to Fig. Comarison of calculated and measured article jet sreads at a location of 100 mm downstream of the nozzle exit be in good agreement with exerimental measurements, [17,18] as shown in Fig.. This temerature corresonded to the low limit of detection of the exerimental device used to measure article number densities from their thermal radiation. 4. Co-Sraying of Alumina and Iron Powders Using a Single Injector. In this case, the alumina and iron owders were assumed to be mixed in the owder feed line and injected in the lasma jet through a single injector normal to the jet axis (Fig. 1). The carrier gas flow rate of argon was equal to 4 slm. As shown in Fig. 4, this ensured that the distribution of the alumina articles was nearly symmetrical about the jet centerline at the substrate location. However, the alumina and iron sray sots on the substrate did not overla comletely, as the heavier iron articles enetrated deeer the lasma jet due to their higher momentum at the injection oint. 108 Volume 10(1) March 001 Journal of Thermal Sray Technology

5 Fig. 4 Distribution of article number vs vertical distance when alumina and iron owders injected through one injector As noted earlier, when using a single common injector, the only way to rovide for better overlaing of the ceramic and metal article imingement sots on the substrate is by using a finer iron owder. However, this may result in overheating of the metal owder and a corresonding increase in article evaoration or oxidation. Powder Injection Using Two Diametrically Oosed Injectors. In this case, it was assumed that the alumina and iron owders were injected through two injectors normal to the jet centerline and diametrically oosed. Thus, the mixing of owders occurred within the lasma jet. To reduce the number of numerical exeriments, a -D analytical model was used to determine the injection velocity that would rovide for iron and alumina articles of secific sizes to land on the substrate surface at the jet centerline. [7] The controlling kinetic energy balance is obtained by equating the rate of change of momentum of the articles to the drag force F d in their direction of motion, i.e., in the direction y, which is erendicular to the jet flow (direction x): dmv (Eq 8) where m is the mass of a article, v its velocity, and F d the drag force acting on the article. For the Stokes region and a quasisherical article, F (Eq 9) By substituting in the energy balance equation (Eq 8) and integrating from time t = 0 (entry to jet cone) to t, under the assumtion that gas viscosity is constant, the following equation is obtained: vt v ( ) = 0 = π d v µ d = e t ρd F d (Eq 10) This equation shows that the velocity of the injected articles across the jet cone (direction y) decreases exonentially with time of travel. The ower exonent is the dimensionless time of travel; the grouing Fig. 5 Particle injection velocity and carrier gas flow rate as a function of article size for alumina and iron owders under the sray arameters of the study ρd (Eq 11) is a reference time characteristic of the articles/lasma system. The total time of flight of the article in the horizontal direction is determined by the distribution of jet velocity within the cone enveloe and by the above reference time grou. The distance traveled by the articles in the direction y is related to time t by integrating Eq 10: ρ d y = v0 1 e g t ρd (Eq 1) By arbitrarily setting the radial distance y to be traveled by all articles at 10 mm and using Eq 1 and the comuted residence time, the required injection velocity, v 0, can be calculated for each material and average article size, so that all articles land on the same area on the substrate (Fig. 5). The corresonding carrier gas volume flow rate is then calculated as the roduct of this injection velocity and the cross-sectional area of the injector. This simlified calculation resulted in a comuted carrier gas flow rate of.5 slm for the 5 µm iron article, i.e., the average size of article distribution, in comarison to the 4 slm flow rate used for the alumina owder. Figure 6 shows the redicted distribution of article number density at the substrate location. As would be exected, the comutations also showed that the finest articles did not travel as far in the radial direction as the larger ones. This effect was less marked for the heavier iron articles. It is interesting to note that for the lasma co-sraying of zirconia and NiCrAlY, Smith et al. [1] injected the ceramic owder, through an injector 90 to the lasma jet and located below the horizontal torch axis, while the metal owder injector was located above the torch axis and at an angle of 105. Numerical simulation using the same injector configuration for the lasma owder system of this study resulted in good overlaing of both article sray sots on the substrate, when carrier gas flows of 4 slm for alumina and 1.5 slm for iron were used. In this case, the Journal of Thermal Sray Technology Volume 10(1) March

6 5. Conclusions The -D and -D comutational fluid dynamics techniques have been alied to analyze the jet flow and article behavior for the lasma co-sraying of a metal and a ceramic owder. The -D modeling of the steady-state lasma rocess redicts reasonable article history in the jet and distribution of both owders on the substrate. It makes it ossible to take into account the effect of the carrier gas flow rate and the lateral injection of owders. Such a model can hel to determine the article size distribution and the conditions of owder injection so that the article sray jets of the metal and ceramic owders coincide on the same sot on the target surface. Fig. 6 Distribution of article number vs vertical distance when alumina and iron owders are injected through two diametrically oosed injectors Fig. 7 Comarison of -D and -D redictions of the radial distribution of gas temerature stronger interaction between articles and lasma jet hels to diserse the iron articles so that there is no segregation by article size. 4.4 Comarison between -D and -D Comutations There is a reasonable agreement between the -D and -D rofiles, even if the lateral sread of heat is a little faster with the -D model (Fig. 7). References 1. W. Smith, T.J. Jewett, S. Samath, C C. Bern, H. Herman, J. Fincke, and R.N. Wright: Thermal Sray: Practical Solutions for Engineering Problems. C. C. Bern, ed., ASM International, Materials Park, OH, 1996, M. Leylavergne, A. Vardelle, B. Dussoubs, and N. Goubot: J. Thermal Sray Technol., 1998, vol. 7 (4), J.D. Mattei and O. Simonin: Logiciel ESTET, Manuel Théorique de la Version.1, EDF Reort HE 44/9.8B, 199 (in French). 4. B.E. Launder and B.I. Sharma: Lett. Heat Mass Transfer, 1974, vol. 1, M.I. Boulos, P. Fauchais, and E. Pfender: Thermal Plasmas, Fundamental and Alications, Plenum Press, New York, NY, 1995, vol C.H. Chang and J.D. Ramshaw: Plasma Chem. Plasma Processing, 199, vol. 1 (), B. Dussoubs: Ph.D. Thesis, University of Limoges, Limoges, France, 1998, J. Pozorski and J.P. Minier: Lagrangian Modeling of Turbulent Flows, EDF Reort HE 44/94.106, M. Vardelle, A. Vardelle, P. Fauchais, and M.I. Boulos: AIChE J., 198, vol. 9 (), 198, E. Pfender and Y.C. Lee: Plasma Chem. Plasma Processing, 1985, vol. 5 (), Y.C. Lee, Y.P. Chyou, and E. Pfender: Plasma Chem. Plasma Processing, 1985, vol. 5 (4), G.T. Csanady: J. Atm. Sci., 196, vol. 0, A. Paoulis: Probability, Random Variables and Stochastic Processes, McGraw-Hill, New York, NY, S.B. Poe: Progr. Energy Combust. Sci., 1985, vol. 11, T. Yoshida: Ph.D. Thesis, University of Tokyo, Tokyo, M. Vardelle, A. Vardelle, P. Fauchais, B. Dussoubs, T.J. Roemer, R.A. Neiser, and M.F. Smith: Thermal Sray: Meeting the Challenges of the 1st Century, C. Coddet, ed., ASM International, Materials Park, OH, 1998, B. Dussoubs, A. Vardelle, M. Vardelle, P. Fauchais, and N. J. Themelis: Proc. 1th Int. Sym. on Plasma Chemistry, Beijing, Aug. 18-, 1997, C. K. Wu, ed., Beijing University Press, Beijing, 1997, Volume 10(1) March 001 Journal of Thermal Sray Technology