NUMERICAL MODELLING OF IMPACT AND SOLIDIFICATION OF A MOLTEN ALLOY DROPLET ON A SUBSTRATE

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1 5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12 th 14 th, 2014, IIT Guwahati, Assam, India NUMERICAL MODELLING OF IMPACT AND SOLIDIFICATION OF A MOLTEN ALLOY DROPLET ON A SUBSTRATE Rajesh Kumar Shukla 1, Sateesh Kumar Yadav 2, Mihir Hemant Shete 3, Arvind Kumar 4* Dept. of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, India, shuklark@iitk.ac.in 2 sateesh@iitk.ac.in 3 mihir@iitk.ac.in 4 arvindkr@iitk.ac.in * Corresponding author Abstract Most of the studies reported for droplet impact and spreading on a substrate in a thermal spray coating process assume that droplet solidifies as a pure substance, i.e., phase change occurs at a fixed temperature. The alloy type behaviour of the droplet impact where it solidifies within liquidus and solidus temperature is not well reported. The role of formation of mushy zone and species composition variation during the coating layer formation while using a multi-constituent alloy material is not known. This work investigates the impact, spreading and solidification characteristics of an alloy droplet impacting on a substrate. Two dimensional axisymetric model has been used to simulate the transient flow and alloy solidification dynamics during the droplet impingement process. Volume of fluid (VOF) surface tracking method coupled with the alloy solidification model within a one-domain continuum formulation is developed to describe the transport phenomena during the droplet impact, spreading and solidification of an alloy droplet on a flat substrate. Using the model the characteristics of alloy solidification in coating formation are highlighted. Keywords: Alloy droplet, Thermal spray coating, Droplet impact and spreading, Solidification. 1. Introduction In coating processes using thermal spraying, powder materials are injected into a high temperature flame where they are melted and propelled towards the surface of a substrate. The individual molten particles impact, spread and solidify to form a coating deposit on the substrate s surface. Prior to the coating development the process involved is impact of the droplet and its flattening and solidification on the substrate. The quality of the coating is directly related to the particle impingement process in which individual particles are flattened and solidified on the substrate forming the individual splats (Kamnis and Gu., 2005; Kumar et al., 2012a). It is essential to have a clear understanding of the physics of droplet impingement on the surface of substrates for better control of the generation of splats and the structure of coating. Experimental investigations provide a link between factors related to droplet impact and final coating morphology and quality. Numerical simulations provide further insights into the mechanism of droplet impingement and coating layer formation. It also provides an idea about tuning the process parameters to suit different coating applications. Computational fluid dynamics (CFD) based volume of fluid (VOF) method is utilized in many cases to track the deformation in the surface of molten droplet during its impact on a substrate. Many studies have been carried out for modelling droplet impact on surfaces. Liu et al. (1993) numerically studied the deformation, interaction and freezing during impact of molten droplets on a substrate in plasma spray processes and reported that the final diameter and total freezing time of the splat depend on the initial droplet velocity, droplet temperature and substrate temperature. Bennett and Poulikakos (1994) and Kang et al. (1994) studied droplet deposition assuming that solidification starts only after complete spreading of droplet in the form of a disk. Theoretical and experimental studies done by Bennett and Poulikakos (1994) showed that the thermal conductivity of the substrate significantly influences the cooling rate of the splat. Rangel et al. (1997) developed a heat transfer model to study the mechanism of substrate remelting and the interactions of relevant parameters during the process of single metal droplet deposition and solidification. Fukumoto et al. (1999) studied the transition behaviour of flattening nickel particles sprayed onto a flat substrate. They showed that splashing is less when there is good wetting between the particle and substrate. Attinger et al. (2001) studied the molten micro droplet impact and solidification on a cold flat substrate that can melt and they reported the melted volume as a function of time for various combinations 522-1

2 NUMERICAL MODELLING OF IMPACT AND SOLIDIFICATION OF A MOLTEN ALLOY DROPLET ON A SUBSTRATE of thermal and fluid dynamics parameters. Shakeri et al. (2002) studied the splashing of molten tins droplets on a rough steel surface. Hong et al. (2005) studied the mmsized molten droplet impacting on a substrate of the same material. It was found that the thermal contact resistance affects not only the droplet spreading but also the substrate remelting volume and remelting front configurations. Kamnis et al. (2005) developed a numerical model to investigate the impingement of tin droplets on a flat stainless steel plate. In this they reported that the solidification of droplets is significantly affected by the thermal contact resistance/substrate surface roughness. Kamnis et al. (2008) studied the sequential tin droplet impingements on a stainless steel substrate using a 3D numerical simulation. Fukumoto et al. (2011) studied the effects of substrate temperature and ambient pressure on flattening and solidification behaviour of free falling droplet. Tabbara et al. (2012) studied the impingement phenomena for molten tin droplets with low to high velocities on a steel substrate and reported that the solidification process may consist of up to three stages: planar solidification, uneven solidification and wave mixing. Kumar et al. (2012a) compared the impingement behaviour of a hollow ZrO 2 droplet and an analogous continuous droplet onto a substrate. Most of the studies reported assume that droplet solidifies as a pure substance, i.e., phase change occurs at a fixed temperature, during its impact and spreading on a substrate. The impingement of an alloy droplet onto a substrate and its spreading behaviour can differ fundamentally from a pure metal droplet. In this connection, the investigation of the impact of an alloy droplet onto a solid substrate is of scientific and applied importance. The current work aims at modelling the impact, spreading and segregation of species of a Pb-Sn alloy droplet on a stainless steel substrate. A sound understanding of the alloy droplet impingement behaviour onto a substrate will improve the knowledge of coating formation by multi-constituents materials in thermal spray coating. 2. Model and Governing Equations A molten Sn-10% Pb alloy droplet with a diameter of at an initial uniform temperature of 519 K is impacting on a stainless steel substrate with a velocity of 4 m/s. Fig.1 shows a schematic of computational domain. From the computational domain shown in Fig. 1, a 2D axisymmetric computational domain is considered. The solidification of the binary eutectic alloy considered in the present study takes place by the formation of a mushy zone. The phase diagram of the binary alloy considered is shown in Fig. 2. The thermophysical property data used in the simulations for the Sn-10% Pb alloy are shown in Table 1 (Bellet et al., 2009). The numerical methodology is based on a previously validated model for a dense droplet impact on a substrate (Kamnis and Gu, 2005). The dense droplet impingement model reported in reference (Kamnis and Gu, 2005) was validated with the experimental measurement of tin droplets (Shakeri and Chandra, 2002). In the droplet impingement model transient fluid flow dynamics during the impact, droplet spreading onto the substrate and solidification heat transfer are considered using the volume of fluid surface tracking method (VOF) coupled with a solidification model within a one-domain continuum approach based on the classical mixture theory (Kamnis and Gu, 2005; Kumar et al., 2012a; Kumar et al., 2012b). However, an alloy solidification model is implemented in the current study as compared to a pure substance solidification model in Kumar et al. (2012a) and Kumar et al. (2012b). The mushy zone, the solidification kinetics and the species transport, as applicable for a binary alloy, are considered in the current model. Shrinkage due to solidification is neglected ( ρs = ρ ). The density for alloy phase is defined as l follows ρ = (1 g ) ρ + g ρ (1) mixture l s l l Due to shrinkage being neglected the volume fraction (g k ) is equivalent to mass fraction (f k ). The solid phase velocity is zero, u s =0. Accordingly, the mixture velocity is given as u r = f u r + f u r = f u r (2) l l s s l l A Volume of Fluid (VOF) method is used to track of the alloy-air interface. The volume of fraction (F) can range from zero to unity. F=0 indicates the cell containing only air, and F=1 indicated the cell containing only alloy. 0<F<1 corresponds to cell containing the alloy-air interface. The volume of fraction function is evaluated using the velocity field and the transport equation. VOF equation: F r = ( uf ) 0 (3) The properties appearing in the transport equation are evaluated by the presence of component phases in each control volume. For example, the density in each control volume is given above. ρ = F ρ + (1 F) ρ (4) alloy air The flow is assumed to be Newtonian and incompressible, the governing equation of continuity is given below. Continuity: 522-2

3 5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12 th 14 th, 2014, IIT Guwahati, Assam, India u r = 0 Momentum conservation: r rr ρ r uur uuur uur ( ρu) + ( ρ uu) = p + µ u + ρ gr + Fvol Su (5) ρl r uur µ lu F = 1 (6) Su = K 0 F < 1 3 fl K = K (7) 0 2 (1 fl ) For computational cells which are undergoing phase change (solidification), the solid-liquid interaction in the momentum conservation (Eq. 6) is considered using Darcy's model of viscous flow through a porous medium using the source term Su (Eq. 7) (Kamnis and Gu, 2005). Permeability is defined by the Carman- Kozeny formula (Eq. 8). Momentum conservation equation (Eq. 6) also accounts for surface tension effects at the free surface, which is considered by a continuum surface force model using the term F vol (Kumar et al., 2012a). Energy conservation: ( 1 ) eff metal air (5) r ( ρceff T ) + ( ρuceff T ) = ( keff T ) + S (8) h k = Fk + F k (9) ( 1 ) c = Fc + F c (10) eff metal air r L ( ρ fl ) ( ρu fl ) F 1 S + = h t (11) = 0 F < 1 where L is latent heat of fusion. The momentum and the energy conservation equations (Eqs. 6 and 9) are coupled. The source term S h (E. 12), for handling the solidification phase change, appearing in the energy conservation (Eq. 9) is active only for the computational cells filled with molten droplet (F = 1). Species transport equation: r + ( ρcl ) + ( ρucl ) = ( D Cl ) + Sc (13) where D = ρ f D k + f D (14) ( s s p l l ) and Sc = ( ρ fscl ) k pcl ( ρ fs ) (15) Species segregation is governed by lever rule model (Eq. 16). The ssolidification path (according to lever rule) is given by: 1 mlc 0 fl = 1 (16) 1 k p T Tm T = Tm + mlc (17) l Only conduction heat transfer will occur in the substrate. For the substrate thermal contact resistance a constant value of m 2 K W -1, corresponding to a stainless steel substrate roughness of 0.06 µm, is used (Kumar et al., 2012). Substrate heat transfer: 3.1 mm ( ρ C T ) = ( k T ) sub sub sub Tin alloy droplet D = T 0 = 519 K U 0 = 4 m/s Substrate (T i = 298 K) 0.2 mm 22.4 mm Symmetry axis Pressure outlet (12) Atmosphere (air) g Wall Figure 1 Schematic diagram of the computational domain The computational domain, shown in Fig. 1, consists of 220,000 structured computational cells with a refined grid at the substrate surface. Both air and droplet phases are simulated and governing equations are considered and solved in both phases. Temperature ( C) (Sn) Liquidus Solidus Linearized lines 246 C (519K) Initial temperature 38.1 % 183 C (Pb) Weight percent (Pb) (Pb) Figure 2 Phase diagram of Sn-Pb binary alloy 2.4 mm 522-3

4 NUMERICAL MODELLING OF IMPACT AND SOLIDIFICATION OF A MOLTEN ALLOY DROPLET ON A SUBSTRATE Table 1 Thermophysical properties Impinging droplet material Sn-10% Pb alloy Substrate material Stainless steel (SS) Gas phase ( the droplet surrounding Air (air) medium) Droplet initial temperature 519 K Substrate initial temperature 298 K Melting point of pure substance 505 K (Tin) Initial concentration (Pb) 10.0 (wt%) Thermal conductivity 55 W (m K) -1 Thermal conductivity (SS) 14.9 W (m K) -1 Thermal conductivity (air) W (m K) -1 Density (liquid alloy) 7000 kg (m) -1 Density (SS) 7900 kg (m) -1 Density (air) kg (m) -1 Droplet surface tension N (m) -1 Viscosity (liquid droplet) kg (m s) -1 Viscosity (air) kg (m s) -1 Specific heat capacity (solid and 260 J (kg K) -1 liquid phase ) Specific heat capacity (SS) 477 J (kg K) -1 Specific heat capacity (air) J (kg K) -1 Latent heat of fusion J (kg) -1 Eutectic Composition 38.1 (wt%) Equilibrium partition coefficient Liquidus slope ( C wt% -1 ) 3. Results and Discussion A diameter Sn-10%Pb droplet is impinging with a velocity of 4 m/s on a stainless steel substrate. The thermophysical properties are given in Table 1. In the following, the characteristics related to impact, flattening and solidification of the alloy droplet are studied and discussed in detail. The initial flattening and impact is mainly dominated by the inertia of the impacting alloy droplet. The flattening and the spreading of the droplet can be seen in Figure 3 which shows the VOF function of the alloy phase. At the periphery the spreading droplet solidifies due to heat transfer with the substrate as shown in the Figure 4. The droplets material at the edge of the splat is found to separate from the spreading droplet. This causes the splat to become discontinuous. Such discontinuous splat can influence the coating quality adversely. Due to solidification occurring between liquidus and solidus there is a formation of mushy zone as seen in Figure 4. This also causes an increase in the solidification time as compared to pure metal droplet. The mushy zone formed is disordered and wavy in shape. The disordered mushy zone offers significant resistance to the droplet material to spread during subsequent flattening process. For better clarity of the mushy zone zoomed images are shown in Figure 5. After the initial impact, most of the potential energy of the alloy droplet gets converted into kinetic energy. At the region of initial impact and then towards the periphery during the subsequent flattening process the droplet velocity becomes significantly high, i.e., around 15 m/s as depicted in Figure 6. Such high velocities combined with disordered mushy zone and rapid freezing at the advancing edge lead to break up of droplet material along the advancing front creating thereby a discontinuous splat. This phenomena is known as freezing induced break up in the solidifying splat which occur at the periphery (Chandra and Fauchais, 2009). Figure 7 shows snapshots of species distribution (mass fraction of Pb). Significant variation in Pb concentration is observed due to macrosegregation caused by the fluid flow in the flattening droplet. The wavy species variation pattern is in tune with the wavy mushy zone as observed in Fig. 4. A clearer look of the species distribution can be seen in Figure 8 where zoomed images are shown. The prediction of species distribution in our model is possible by solving the species transport equation that includes solidification kinetics and macrosegregation of a binary alloy. There is a built up of Pb concentration at the edge of the splat. This built up is caused by transport of solute towards the periphery by the high velocity at the periphery. VOF t =0.02 ms t =0.23 ms t =0.40 ms t =1.00 ms t =1.93 ms Figure 3 Droplet impact and spreading pattern 522-4

5 5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12 th 14 th, 2014, IIT Guwahati, Assam, India Liquid fraction Mass fraction (Pb) t =0.02 ms t =0.23 ms t = 0.02 ms t =0.40 ms t = 0.23 ms t =1.00 ms t =1.93 ms Figure 4 Solidification pattern and formation of mushy zone at various time t = 0.40 ms t = 1.00 ms t = 1.93 ms Figure 7 Snapshots of species distribution (Pb) t=0.40 ms t= 0.40 ms t=1.00 ms Liquid fraction t= 1.00 ms Mass fraction (Pb) Velocity magnitude Figure 5 Zoomed images of mushy zone in rectangular portions marked in Fig. 4 t =0.02 ms t =0.23 ms Figure 6 Spreading velocity at two representative instance Figure 8 Zoomed images of species (Pb) distribution in rectangular portions marked in Fig Conclusion Pure substance solidifies at a constant temperature but in case of alloy it solidifies in a range of temperature with formation of mushy region (solid-liquid region). Comprehensive CFD based model of alloy droplet deposition on a cold substrate is developed. The main conclusions are the following: Alloy droplet spreading and solidification is very different from a pure metal droplet spreading and solidification. The mushy zone formed in case of alloy droplet is disordered and wavy which is very different from the ordered solidification interface formed, as usually reported in the literature, in case of pure metal droplet. The presence disordered and wavy mushy zone causes along with the high spreading velocity near the periphery causes break-up in the flattening droplet which finally produces a discontinuous coating/splat. Significant species variation is found to occur due to macrosegregation caused by fluid flow in the 522-5

6 NUMERICAL MODELLING OF IMPACT AND SOLIDIFICATION OF A MOLTEN ALLOY DROPLET ON A SUBSTRATE flattening droplet. Such inhomogeneous species composition in the splat can influence the mechanical properties of the coating. Nomenclature c Specific heat capacity (m 2 s -2 K -1 ) C Solute concentration (kg kg -1 ) D Solute mass diffusivity(m 2 s -1 ) D o Initial droplet diameter (mm) f l Weight fraction of liquid (kg kg -1 ) f s Weight fraction of solid (kg kg -1 ) F Volume of fluid function Continuum surface tension force source term F vol (N m -3 ) g r Acceleration due to gravity vector (m s -2 ) r k Thermal conductivity (W m -1 K -1 ) k p Equilibrium partition coefficient K permeability of mushy zone (m 2 ) L Latent heat of fusion (J kg -1 ) m L Liquidus slope ( C wt% -1 ) p Pressure (N m -2 ) t Time (s) T Temperature (K) T m Melting point of pure substance (K) u r Continuum velocity vector (m s -1 ) U 0 Initial droplet velocity (m s -1 ) Greek symbols ρ Density (kg m -3 ) µ Dynamic viscosity (kg m -1 s -1 ) Subscript d Droplet subs Substrate air Air alloy Alloy References Attinger, D. and Poulikakos, D. (2001), Melting and Resolidification of a Substrate Caused by Molten Microdroplet Impact, ASME Journal of Heat Transfer, Vol. 123, pp Bellet, M., Combeau, H., Fautrelle, Y., Gobin, D., Rady, M., Arquis, E., Budenkova, O., Dussoubs, B., Duterrail, Y., Kumar, A., Gandin, C.A., Goyeau, B., Mosbah, S. and Zaloznik, M. (2009), Call for Contributions to a Numerical Benchmark Problem for 2D Columnar Solidification of Binary Alloys, International Journal of Thermal Sciences, Vol. 48, pp Bennett, T. and Poulikakos, D. (1994), Heat Transfer Aspects of Splat-Quench Solidification: Modeling and Experiment, Journal of Materials Science, Vol. 29, pp Chandra, S. and Fauchais, P. (2009), Formation of Solid Splats during Thermal Spray Deposition, Journal of Thermal Spray Technology, Vol. 18, pp Fukumoto, M. and Huang, Y. (1999), Flattening Mechanism in Thermal Sprayed Ni Particles Impinging on Flat Substrate Surface, Journal of Thermal Spray Technology, Vol. 8(3), pp Fukumoto, M., Yang, K., Tanaka., K., Usami,. T Yasui, T. and Yamada, M. (2011), Effect of Substrate Temperature and Ambient Pressure on Heat Transfer at Interface Between Molten Droplet and Substrate Surface, Journal of Thermal Spray Technology, vol. 20, no. 1-2, pp Hong, F. J. and Qiu, H.-H. (2005), Modeling of Substrate Remelting, Flow, and Resolidification in Microcasting, Numerical Heat Transfer, Part A, Vol. 48, pp Kang, B., Zhao, Z. and Poulikakos, D. (1994), Solidification of Liquid Metal Droplets Impacting Sequentially on a Solid Surface, ASME Journal of Heat Transfer, Vol. 116, pp Kamnis, S. and Gu, S. (2005), Numerical Modelling of Droplet Impingement, Journal of Physics D: Applied Physics, Vol. 38, pp Kamnis, S., Gu, S., Lu, T.J. and C. Chen. (2008), Numerical Modelling of Sequential Droplet Impingements, Journal of Physics D: Applied Physics, Vol. 41, (7pp). Kumar, A., Gu, S., Tabbara, H. and Kamnis, S. (2012a), Study of Impingement of Hollow ZrO 2 Droplets onto a Substrate, Surface and Coatings Technology, Vol. 220, pp Kumar, A., Gu, S. and Kamnis, S. (2012b), Simulation of Impact of a Hollow Droplet on a Flat Surface, Applied Physics A: Materials Science & Processing, Vol. 109, pp Rangel, R.H. and Bian, X. (1997), Metal-Droplet Deposition Model Including Liquid Deformation and Substrate Remelting, International Journal of Heat and MassTransfer, Vol. 40, pp Shakeri, S. and Chandra, S. (2002), Splashing of Molten Tin Droplets on a Rough Steel Surface, International Journal of Heat and Mass Transfer, Vol. 45, pp Tabbara, H. and Gu, S. (2012), Modelling of Impingement Phenomena for Molten Metallic Droplets with Low to High Velocities, International Journal of Heat and Mass Transfer, Vol. 55, pp