Numerical Modeling of Powder Flow during Coaxial Laser Direct Metal Deposition Comparison between Ti-6Al-4V Alloy and Stainless Steel 316L

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1 Numerical Modeling of Powder Flow during Coaxial Laser Direct Metal Deosition Comarison between Ti-6Al-4V Alloy and Stainless Steel 316L S. Morville 1, M. Carin *1, D. Carron 1, P. Le Masson 1, M. Gharbi, P. Peyre and R. Fabbro 1 LIMATB, Université de Bretagne-Sud/UEB, PIMM / UMR 8006 CNRS, Arts et Métiers Paris Tech *Corresonding author: Centre de recherche C. Huygens, rue de Saint Maudé, BP 9116 Lorient, FRANCE, muriel.carin@univ-ubs.fr Abstract: This aer resents a 3D numerical model to redict the whole rocess of coaxial owder flow, including the article stream flow in and below the nozzle and also the laserarticle interaction rocess. The Particle Tracing Module of Comsol Multihysics is used to solve the couled momentum transfer equations between the article and gas hase while incororating article temerature evolution. A turbulence k-ε model is emloyed to describe the behavior of the gas flow. The trajectory of the discrete hase article is calculated by integrating the force balance on each article while taking into account gravity and drag forces. Heating of owder articles accounts for laser intensity, convection and radiation losses. The owder concentration and article heating rocess are analyzed for two materials: Ti-6Al- 4V alloy and 316L stainless steel. The influence of laser ower distribution is analyzed. The numerical results are comared with exerimental data. Keywords: direct metal deosition, coaxial nozzle, owder flow, laser, heat transfer and fluid flow 1. Introduction Direct Metal Laser Deosition (DMLD) has received significant attention due to its diversified otential. In this rocess, a thin layer is obtained through melting metallic owder coaxially delivered on the substrate. The layerby-layer deosition of the material makes it ossible to roduce 3D metal objects of comlex shaes. However, the quality and efficiency of DMLD largely deend on the owder stream structure below the nozzle. The develoment of numerical models has roven useful for imroving the rocess. In the ast decade, many analytical and numerical models have been develoed by researchers, revealing the rocess deendences on related arameters. Pinkerton [1] roosed an analytical model of the owder stream and article heating using the geometry of the nozzle. No account was taken of the article drag and loss of momentum. More realistic models have been develoed taking into account the interaction between gas flow and article stream. These models use generally a turbulent two-hase flow model solved with the software FLUENT. This has been done by Lin [] and Zhu [3] for a two-dimensional axial symmetry model and Zekovic [4] who roosed a 3D model. However, beam attenuation and owder heating were not considered in these works. Ibarra-Medina [5] has roosed a single fullycouled model of laser cladding rocess. This model simultaneously calculates the owder motion by gas drag and collisions with nozzle and substrate walls, thermal interactions between the owder stream and laser beam, article catchment and ricocheting, melt ool formation and melt ool flows, heat transfer from owder to melt ool and mass addition. The volume of fluid method is alied to determine the free surface of the clad. In this work, the commercial code CFD-ACE+ is used. Tabernero [6] has recently roosed a 3D model of owder stream. This model estimates the attenuation suffered by the laser beam due to the interaction with the owder flow during the laser cladding rocess. This model is calibrated and validated exerimentally for two different materials. However, the reorted literature does not include much work on the imrovement of surface finish. In this aer, a numerical model is develoed to redict metal owder flow in coaxial nozzle for DMLD. This model is used to better understand the influence of the oerating arameters on the surface finish. The Particle Tracing Module of Comsol Multihysics is chosen to solve the couled momentum transfer equations between the article and gas hase while incororating article temerature Excert from the Proceedings of the 01 COMSOL Conference in Milan

2 evolution. The owder concentration and article heating rocess are analyzed for two materials: Ti-6Al-4V alloy and 316L stainless steel. The influence of the distribution of the laser beam is studied. The choice of D axial symmetry or 3D geometry is discussed. The numerical results are comared with exerimental data.. Governing equations A schematic of the DMLD rocess is shown in Fig. 1. The metal owder is injected through a coaxial nozzle into a melt ool obtained by a moving laser beam. With laser scanning, the melt solidifies raidly and a track is formed. The whole art is obtained by the layer-by-layer deosition of the material. A continuous wave disk Yb:YAG laser is used as a heat source. Nozzle Scanning direction the articles will bring when hitting the melt ool. The resent model simulates the gas flow and heat transfer henomena occurring in the owder stream. The comutational domain comrises the inner geometry of the nozzle annular channels and the sace between the nozzle exit and the substrate. The first ste starts by calculating the gas flow. As the owder articles volume fraction is less than 10%, a dilute gas-article stream is assumed. This assumtion allows the alication of one-way couled discrete hase modelling. During the second ste, the motion of the articles is determined. Finally, the heating of owder articles is treated using a lumed caacitance aroach. z Otics rotection gas (0.01 L.min -1 ) Powder + conveying gas ( L.min -1 ) Powder stream + inert gas Laser Shielding gas (1 L.min -1 ) r Figure 1. Schematic of DMLD rocess. The gas flow at the nozzle exit is roduced by the combination of argon streams from the central, middle and outer channels. The central and outer gas streams ensure the otics rotection and oxidation rotection resectively. In the middle inlet, argon is used as a driving gas, in order to convey the owder to the melt ool (Fig. ). The shae of the nozzle is chosen in order to roduce a converging annular stream of owder articles which are focused towards the substrate. Indeed, travelling along the nozzle, articles collide with the nozzle walls. These collisions determine the concentration distribution and disersion of articles. After exiting the nozzle, the owder articles are drawn downward by the action of gravity and drag force from the different gas flows. The time and the satial characteristics of the interaction between the owder and the laser beam are critical for the rocess. Indeed this interaction determines how much additional thermal energy Figure. D axial-symmetry geometry for owder flow model.1 Gas flow The steady turbulent gas flow in the owder stream is described by the standard k-ε model. In such model, the governing equations for laminar flows are modified using the time-averaging method known as Reynolds averaging. All the equations can be found in [-4]. The values of the emirical constants describing the turbulent model are taken from the default values roosed by COMSOL Multihyscis. The equations are exressed with a comressible formulation (Mach number < 0.3), as recommended by Kovalev et al [7]. Excert from the Proceedings of the 01 COMSOL Conference in Milan

3 . Powder stream Immersed in the surrounding gas, each article is treated by the Lagrangian aroach. Discrete hase model is used to solve each article s dynamic behavior. Particles are driven by the forces of gas flow drag and gravity. This force balance equates the article inertia with the forces acting on the article, and can be written as: du,i 18 µ CD Re k g i ( ρ ρ g ) = u g,i ξ u,i + dt ρ d ρ where ρ, d, u,i are the density, diameter, and velocity in the i-direction of each article, resectively. ρ g, µ and u g,i reresent the density, the dynamic viscosity and the velocity in the i direction of the gas, resectively. Re is the Reynolds number, g i is the i-comonent of gravity force. C D is the drag coefficient and is detailed in [8]. A shae factor of 0.8 is assumed to account for non-sherical articles, which is classical when the articles are obtained by gas atomization. The additional term ξ k 3 gives a random motion of the article which reresents turbulent effects. The arameterξ is a normally distributed random number with zero mean and unit standard deviation and k is the turbulent kinetic energy. No collision between each two articles is considered due to the very low owder feed rate. The articles are injected randomly at each time ste. To describe the size distribution of articles comrised between 45 and 75 µm, a Normal low is considered for both materials (stainless steel 316L and Ti-6Al-4V alloy). During their flight, the articles will travel through the laser irradiation zone where they are heated u. The heating of owder articles is modeled using the lumed caacitance aroach, as the Biot number is less than 0.1. To consider the rocess of hase change for a article, the energy equation is roosed as follows: m c T dt 4 4 ( T T ) 4π r ε σ ( T T ) 4π r * ( ) Il r h dt = η π where m is the article mass, c * is the equivalent secific heat caacity which includes the latent heat, T and r are the temerature and the radius of a article, resectively. I l denotes the laser intensity, η the article absortivity of laser ower, ε the emissivity of article, σ the Stefan-Boltzmann constant, and T the temerature of the surrounding gas. h is the convective heat transfer coefficient, which is determined from Nusselt number correlations [8]. This coefficient deends on the gas and article velocities. The material roerties are taken from [9] and [10] for 316L and Ti-6Al-4V alloys resectively. The gas roerties for argon come from [11]. Two laser distributions are studied: an uniform and a Gaussian distributions. The uniform distribution is given by: Plaser Il = π rlaser where P laser reresents the laser ower (30 W) and r laser is the radius of the laser beam (0.65 mm). The Gaussian distribution is as follows: I N P laser r ex N π rlaser r l = laser with N = 5. The values of N and r laser have been obtained using a laser beam analyzer. Concerning the boundary conditions of the turbulent roblem, velocity is set for the three inlets based on the exerimental gas flow rates (Fig. ). Wall function is chosen for the interior walls of the nozzle and the substrate surface. An oen boundary is set for the lateral boundary between the substrate and the nozzle exit. A condition of symmetry is alied for the other boundaries. Concerning the roblem of article flow, an inlet condition is chosen for the middle channel entry. A owder feed rate of 1 g.min -1 for both materials is used. An outlet condition with a freeze wall condition is set for the substrate surface and a disaear wall condition for the lateral outlet. A bounce wall condition is chosen for all the walls of the nozzle. The calculations are erformed using Particle Tracing Module and CFD Module. The comutation time for the 3D model is around 3 hours (4 x 3.33 GHz, 96 Go RAM) using linear tetrahedral finite elements of 0.5 mm for the boundaries and 1 mm inside the domain. Excert from the Proceedings of the 01 COMSOL Conference in Milan

4 3. Results and discussion V article V gas Figure 3 deicts the simulated owder stream structure formed by multi-article trajectories for 316L and Ti-6Al-4V alloys. At the nozzle exit, the articles have a convergent trajectory for both materials. The article streams merge into a main stream to form a waist, at a distance of 6.6 mm below the nozzle ti for the 316L steel and 9.9 mm for the Ti-6Al-4V alloy. After traveling further distance, the main stream diverges. The difference between focus lane locations is due to a higher article mass for 316L steel. The heavier articles are less influenced by the axial gas flow and reach the nozzle axis at a higher osition than the Ti-6Al-4V articles. Note that the gas velocities and article size are identical for both materials. Moreover, in order to obtain the same owder feed rate, the number of injected articles for 316L steel is reduced. It is worth to mention that the surface finish in direct metal deosition is imroved when the substrate surface is located at the focus lane of the owder stream [1, 13]. Nozzle exit Focus lane Figure 3. Particle stream structure obtained with Ti- 6Al-4V (left) and 316L (right) alloys. Figure 4 illustrates the velocity of the gas and owder article calculated for Ti-6Al-4V. The substrate is a disk of 30 mm diameter and located at 4 mm from the nozzle exit. Due to the symmetry of the roblem, only a quarter of the nozzle and substrate is modeled. It can be observed that the maximum gas velocity is reached at the exit of the channel containing the carrier gas and is 1. m.s -1 whereas the maximum velocity of article is 1.1 m.s -1. The gas velocity dros down raidly before it reaches the substrate. Figure 4. Velocity field and streamlines obtained for Ti-6Al-4V alloy. Figure 5 comares the measured and modeled owder distributions at the substrate 4 mm below the nozzle exit. The owder distribution was measured by dislacing a late with a hole in a radial direction. The mass of the owder articles having crossed the hole is measured in order to determine the article concentration rofile. Powder concentration (kg.m -.s -1 ) Powder V article Exeriment (Ti-6Al-4V) D axial symmetry model (Ti-6Al-4V) 3D model (Ti-6Al-4V) D axial symmetry model (316L) 3D model (316L) V gas Axial distance (mm) Figure 5. Measured and calculated article concentration rofiles at the substrate surface The figure 5 comares also the numerical results obtained with the 3D model and a D axial symmetry model. The exerimental results show clearly a Gaussian concentration distribution, which is less visible in the calculated results, esecially for the Ti-6Al-4V alloy. This effect is due to the location of the substrate which is above the focus lane, as reviously reorted by Pinkerton [1]. It can be seen that the eak concentration values are greater with the D axial symmetry model than with the 3D model. Excert from the Proceedings of the 01 COMSOL Conference in Milan

5 This is due to the D assumtion which forces the articles to cross the axis. The concentration eak is then overestimated. Figure 6 comares the calculated owder temeratures at the substrate surface obtained with both materials (Ti-6Al-4V and 316L) and two laser distributions (uniform and Gaussian). Temerature (K) T melting (Ti-6Al-4V) Laser T melting (316L) Uniform distribution (Ti-6Al-4V) Gaussian distribution (Ti-6Al-4V) Uniform distribution (316L) Gaussian distribution (316L) Axial distance (mm) Figure 6. Calculated owder temeratures at the substrate surface for Ti-6Al-4V and 316L alloys using uniform or Gaussian laser distribution For both materials, it is observed, as exected, a sharer temerature distribution with the Gaussian distribution. The eak temeratures are also higher for the Gaussian distribution and are above the melting oint excet for the stainless steel using a uniform temerature. It is worth to mention that the surface finish in direct metal deosition is better when the articles reaching the melt ool are melted. Moreover, it can be noticed that the owder temerature of 316L steel is lower that the temerature of Ti-6Al-4V alloy near the axis but becomes higher far from the axis. The lower heating near the axis can be exlained by the high thermal inertia of steel. However, the greater heating far from the axis is due to a longer interaction time between 316L article and laser beam. As observed in Figure 3, some articles of 316L steel have a divergent trajectory at 4 mm from the nozzle exit. These articles interact with the laser beam during a longer time, inducing an excessive heating. This exlains why some articles have a temerature higher than ambient temerature in the region away from the laser beam radius. 4. Conclusions A numerical model that describes the dynamic and thermal behavior of the coaxial owder flow for direct metal deosition rocesses has been resented. The model accounts for henomena of owder motion by gas drag and collisions with nozzle and substrate walls and thermal interactions between the owder stream and laser beam. This model is used to redict the location of the owder focus lane, which corresonds to the osition where the substrate needs to be laced for an otimal deosition quality. Two materials are comared: a stainless steel 316L and a Ti-6Al-4V alloy. It has been shown that the focus oint of the owder stream is located at a distance closer to the nozzle exit with the stainless steel. The heating of steel articles is lower at the center of the stream due to their inertia, but higher at the outers, because the interaction time with laser is greater. Two energy distributions of the laser beam have been analyzed. With a Gaussian distribution, the melting temerature is easily reached, comared to a uniform distribution, which leads to a more uniform temerature distribution. A good agreement between the numerical and exerimental concentration rofiles confirms that the model is caable of redicting the owder flow behaviour during the coaxial owder feeding of the direct metal deosition rocess. The future develoment will take into account the collisions between articles and the laser beam attenuation due to owder stream. The couling of this model with a melt ool model will also be considered in order to account for heat transfer from owder to melt ool and mass addition. 5. References 1. A.J. Pinkerton, An analytical model of beam attenuation and owder heating during coaxial laser direct metal deosition, J. Phys. D: Al. Phys., 40, (007). J. Lin, Numerical simulation of the focused owder streams in coaxial laser cladding, J. Mater. Process. Tech., 105, 17-3 (000) 3. G. Zhu, D. Li, A. Zhang, Y. Tang, Numerical simulation of metallic owder flow in a coaxial nozzle in laser direct metal deosition, Ot. Laser Technol., 43 (011), Excert from the Proceedings of the 01 COMSOL Conference in Milan

6 4. S. Zekovic, R. Dwivedi, R. Kovacevic, Numerical simulation and exerimental investigation of gas-owder flow from radially symmetrical nozzles in laser-based direct metal deosition, Int. J. Mach. Tool. Manu., 47, (007) 5. J. Ibarra-Medina, M. Vogel, A.J. Pinkerton, A CFD model of laser cladding: from deosition head to melt ool dynamics, Proc. ICALEO 011, Orlando, FL, USA, October 3-7 (011) 6. I. Tabernero, A. Lamikiz, S. Martinez, E. Ukar, L.N. Loez de Lacalle, Modelling of energy attenuation due to owder flow-laser beam interaction during laser cladding rocess, J. Mater. Process. Tech., 1, (01) 7. O.B. Kovalev, A.V. Zaitsev, D. Novichenko, I. Smurov, Theoretical and exerimental investigation of gas flows, owder transort and heating in coaxial laser Direct Metal Deositionn (DMD) rocess, J. Therm. Sray Techn., 0(3), (011) 8. S.Y. Wen, Y.C. Shin, J.Y. Murthy, P.E. Sojka, Modeling of coaxial owder flow for the laser direct deosition rocess, Int. J. Heat Mass Tran., 5, (009) 9. S. Morville, M. Carin, P. Peyre, M. Gharbi, D. Carron, P. Le Masson, R. Fabbro, D longitudinal modeling of heat transfer and fluid flow during multilayered DLMD rocess, J. Laser Al., 4 doi: / (01) 10. B. Wilthan, H. Reschab, R. Tanzer, W. Schützenhöfer, G. Pottlacher Thermohysical roerties of a Chromium-Nickel-Molybdenum steel in the solid and liquid hases, Int. J. Thermohys., 9, (008) 11. htt://encycloedia.airliquide.com/ encycloedia.as 1. G. Pi, A. Zhang, G. Zhu, D. Li, B. Lu, Research on the forming rocess of threedimensional metal arts fabricated by laser direct metal forming, Int. J. Adv. Manuf. Technol., 57, (011) 13. G. Zhu, D. Li, A. Zhang, G. Pi, Y. Tang, The influence of laser and owder defocusing characteristics on the surface quality in laser direct deosition, Otics & Laser Technology, 44, (01) 6. Acknowledgements This work is suorted by the French National Research Agency (ANR), under ASPECT roject No. ANR-09-BLAN Excert from the Proceedings of the 01 COMSOL Conference in Milan