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Numerical analysis of the effect of the gas temperature on splat formation during thermal spray process
Applied Surface Science 257 (2010) 1643–1648
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Numerical analysis of the effect of the gas temperature on splat formation during thermal spray process A. Abdellah El-Hadj a,∗ , M. Zirari b , N. Bacha c a b c
Laboratory LMP2M, University of Medea, Medea 26000, Algeria Laboratory LPTRR, University of Medea, Medea 26000, Algeria Laboratory LTSM, University of Blida, 09000, Algeria
a r t i c l e
i n f o
Article history: Received 29 June 2010 Received in revised form 29 August 2010 Accepted 30 August 2010 Available online 27 September 2010 Keywords: Coating Impact Splat VOF Gas temperature Solidification
a b s t r a c t Thermal spray coatings are affected by various parameters. In this study, the finite element method with volume of fluid (VOF) procedure is used to investigate the deposition process which is very important for the quality of sprayed coatings. The specific heat method (SHM) is used for the solidification phenomenon. A comparison of the present model with experimental and numerical model available in the literature is done. A series of numerical calculations is carried out to investigate the effect of the surrounding gas temperature on the splat formation. The variation of the surrounding gas temperature has a significant effect on splat morphology and can affect the adhesion of the splat on the substrate. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Thermal spraying is a surface treatment method, used generally for protecting surfaces against wear, corrosion and thermal barrier, providing by means of thick coatings (approximately 20 m to several mm). Coating materials available for thermal spraying include metals, alloys, ceramics, plastics and composites. The material is fed in powder or wire form, projected at high speed and heated to a molten state or semi-molten on a solid substrate in the form of micrometer-size particles. Coating quality is usually assessed by measuring its porosity, oxide content, macro- and microhardness, bond strength and surface roughness. Generally, the coating quality increases with increasing particle velocities [1,2]. Optimization and control of the complex phenomenon in thermal spray processes has been reported in several works [3–6]. At impact, the liquid material is spread on the surface which then solidifies with a quenching speed of around 106 –108 K/s. The flattering process continues until the kinetic energy of the particle hitting the surface is completely converted into viscous energy and surface tension. The properties of thermal sprayed coatings are essentially linked to the structure of a single splat and the quality of contact between the pilled-up splats. These properties of adhesion and cohesion and thermo-physical properties are related to
∗ Corresponding author. Fax: +213 25586501. E-mail address: lmp2m [email protected] (A.A. El-Hadj). 0169-4332/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2010.08.115
the morphology of the individual splats and to the contact quality between these splats and the substrate. The formation of the splat depends on the parameters related of the suspended particle (its size, its velocity, its temperature, its melting state at impact and its thermo-physical properties) and on the parameters related to the substrate (its properties, its surface state, its preheated temperature and the presence of oxides). Understanding of melting and solidification of the substrate is essential for appropriate bond coat selection as well as avoidance of substrate damage [7–9]. Experimental works have been devoted for studying an individual splat for a better understanding of the different mechanisms which govern its faltering and solidification [10–12]. It is found that the preheated temperature of the substrate has an important role in determining the morphology of the splat. There is a critical preheated temperature of the substrate named the transition temperature, above which the splat has a regular disc form and bellow which it has a shredded form [8]. Other researchers have studied numerically the splat formation phenomenon [13–18]. These numerical models which use the volume of fraction method (VOF) take into account the hydrodynamic aspects of the splat formation and the heat transfer between the splat and the substrate. Xu et al. [19] experimentally investigated the corona splashing due to the impact of a liquid drop on a smooth dry substrate. It is suggested that splashing results from the compressibility of the gas and it can be inhibited by decreasing the surrounding gas pressure. The threshold of the gas pressure depends on the impact velocity, molecular weight of the gas, and
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A.A. El-Hadj et al. / Applied Surface Science 257 (2010) 1643–1648
Fig. 1. Example of contourlines temperature of plasma spray jet (Ar-H2 ) issuing into air [3].
the liquid viscosity. It can be deduced from this result that the temperature of the surrounding gas can influence the splat formation and morphology. In thermal spray process, the surrounding gas can reach a high temperature in vicinity of the substrate (Fig. 1). However, this parameter has not been studied in these previous researches. Therefore, the aim of this work is to investigate the splat formation under different surrounding gas temperatures around the particle. The Galerkin finite element method is used to solve the set of governing equations using Ansys/Flotran code. The VOF method is used to track the free surface deformation. In this study, some pertinent parameters that influence the quality and the morphology of the deposit (the spread factor, the impact pressure and the temperature histories in the affected zone of the substrate) are considered.
2. Mathematical formulation Numerical simulations are used for modeling the impact of the droplet. A set of the governing equations for the continuity, the momentum and the energy are adopted. The procedure is based on the use of the Galerkin finite element method [20] to solve system of equations and the VOF method to track the interface displacement [18]. The thermo-physical properties of the materials are given in Table 1 [18]. The physical domain with boundary conditions is illustrated in Fig. 2. The fluid flow is assumed to be incompressible. The dynamic and energy equations are coupled only by material properties which are temperature dependent. They are solved alternatively for every timestep until the final time is reached.
Fig. 2. Physical domain of a 3.92 mm droplet impacting a substrate.
2.1. Dynamic model In the VOF method, the cell containing a fluid is governed by the following equations [18]: · (˛ · V ) = 0 ∇
(1)
∂(˛ · V ) p + ˛v∇ 2 V + ˛ F )V = −˛ ∇ + (˛V · ∇ b ∂t
(2)
where V is the velocity vector, is the density, p is the pressure, ˛ is called fraction of fluid volume, v is the kinematic viscosity and t the time. Fb is the body force applied to the fluid. The surface tension is an important parameter that contributes in the deformation of the droplet. It is considered as a volume force applied to the free surface of the liquid. The electrostatic forces between the molecules of the surrounding gas are very small compared to those of the liquid due to their molecular distances. The resultant of the forces is directed toward the inside of the particle. This force characterizes the liquid surface tension ( in N/m). The liquid evolves spontaneously to minimize its surface tension (its free surface energy). According to the VOF methodology, the fraction of fluid volume ˛ is used for the all domain where its value indicates the presence or the absence of the fluid. We attribute the value of 1 for a point occupied by the metal and 0 in the other domain part. The mean
Table 1 Thermo-physical properties of aluminum and steel H13 [20]. Properties 3
Density [kg/m ] Temperature of melting [◦ C] Melting heat [J/kg] Kinematic viscosity [m2 /s] as a function of temperature (◦ C) Thermal conductivity of liquid [W/(m K)] Specific heat of liquid [J/(kg K)] Superficial tension [N/m] Thermal conductivity of solid [W/(m K)] as a function of temperature (◦ C)
Specific heat of solid [J/(kg K)] as a function of temperature (◦ C)
Aluminum alloy 380
Steel H13
2570 570 389 T 78 2000 70 1000 1.07 T 100 200 300 400 T 300 300 479
7800 – – –
v 4.5E−7 4.E−7
K 144.5 147.5 152.5 148.0 C 980 1050 1150
– – – T 27 204 427 649 T 20 500 600
K 17.6 23.4 25.1 26.8 C 460 550 590
A.A. El-Hadj et al. / Applied Surface Science 257 (2010) 1643–1648
1645
value in the element k presents the function of the fluid volume occupied by the metal [18]:
˛=
⎧ ⎪ ⎨1 ⎪ ⎩
inside the fluid
0<˛<1
contain a free surface
0
empty cell
(3)
The element with a value of ˛ between 0 and 1 is containing the free surface or the interface. To find ˛(x,t) for all points of the domain x ∈ ˝ (˝ is the physical domain 1 in Fig. 2), it is necessary to solve the transport equation [21]: ∂˛ d˛ + V · ∇˛ = dt ∂t
with ˛(x, 0) = ˛0 (x)
(4)
Due to a low density, the inertia of the gas is usually negligible. The sole effect of the gas is the pressure acting on the interface. Hence the region of gas need not be modeled, and the interface is simply modeled as a boundary with constant pressure. The arbitrary Lagrangian–Eulerian method is used to track the interface location of the droplet. The fluid flow boundary condition at the droplet–substrate interface is no slip and no-penetration. 2.2. Heat transfer model The SH method is used in order to take into account for the phase changing in metal particle. This formulation uses the equivalent specific heat which takes in account the latent heat in the energy equation as [22]: ∂T dfs ∂T ∂(h) eq ∂T = cp − Lf = cp dT ∂t ∂t ∂t ∂t
(5)
where h is the enthalpy, T is the temperature, cp is the metal specific eq heat, cp is the equivalent specific heat, Lf is the latent heat of fusion and fs is the solid fraction. The following is the definition of the equivalent heat capacity used to simulate the latent heat effect:
eq cp
=
⎧ cp ⎪ ⎪ ⎨ ⎪ ⎪ ⎩
cp − Lf
df s
dT
T ≤ Tm − ıT (solid) Tm − ıT ≤ T ≤ Tm
(6)
Fig. 3. Simulation of sequential impact of an aluminum droplet of 3.92 mm in diameter on smooth steel substrate at 200 ◦ C with 3 m/s of impact velocity.
T ≥ Tm (liquid)
cp
where Tm is the melting temperature, and ıT is the phase change transition temperature. This leads to a modified heat transfer equation, where the phase change is treated as nonlinearity in the physical properties:
∂t
+ ∇ · (cp T · V ) = ∇ · (K ∇ T ) + Q eq
(7)
where K is the metal thermal conductivity and Q is the source term. The equation governing of transient heat transfer in the substrate is given by: ∂T = ∇ · (Kb ∇ T ) b cb ∂t
(8)
where cb is the substrate specific heat, b is the substrate density and Kb is the substrate conductivity. The transient heat transfer equations are solved for droplet and substrate. The interface between substrate and droplet is assumed to respect the continuity condition (same flux). The effect of contact resistance at the substrate–droplet interface is not considered here. The surface of the droplet and of the substrate in contact with the gas is taken to be at the gas temperature. All other boundaries are assumed to be insulated.
The spread factor ( ξ)
eq ∂T
cp
4
3
2 Present work Experiment [13] Simulation [13]
1
0 0,0
1,0x10 -3
2,0x10 -3
3,0x10 -3
Time (s) Fig. 4. The spread factor of an aluminum droplet (3.92 mm of diameter) with the 3 m/s of impact velocity on a smooth surface.
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Fig. 5. Simulated temperature distribution inside an aluminum droplet (3.92 mm of diameter) for gas temperature at 300 ◦ C.
3. Results and discussion The numerical model used to simulate droplet impact solves the coupling equations using a finite element technique. An aluminum alloy 380 particle of 3.92 mm in diameter with the impact velocity of 3 m/s projecting onto flat H13 tool steel substrate at initial temperature of 200 ◦ C is used. The initial particle temperature is taken above the melting temperature as 630 ◦ C. This model has been validated earlier [23]. The computer generated images of sequential impact of the particle are shown in Fig. 3. The shape of the flattering behavior is similar to those of the experimental results [13]. Fig. 4 shows the evolution of the spread factor ( = DP /DP0 ) which is calculated by normalizing the diameter DP measured from images by the initial diameter DP0 of the present model compared to the measured and predicted ones of Xue et al. [13]. The discrepancy between the two numerical models is due to the different methods used. In order to obtain a better quantitative
comparison between the different models, the predicted values of the spread factor () is considered. Fig. 5 displays the temperature distribution of the particle for different times following impact for the gas temperature at 300 ◦ C. When the particle splats on the substrate, it takes a lamellar form by lateral spreading of the liquid under the effect of the particle pressure. The kinetic energy of the particle is transformed to the viscous deformation and to the surface energy at the splatting end. As shown in the figure, the splatting of the droplet is divided in three steps, initial impact, particle spreading and cooling and solidification. A series of numerical calculations shows that the temperature of the surrounding gas (Tgas ) can affect significantly the spreading and the morphology of the splat. This effect is obvious when Tgas is above the melting temperature of the droplet. Fig. 6 illustrates the distribution of the temperature for the droplet for different times following the impact as in Fig. 5 with almost identical conditions.
Fig. 6. Simulated temperature distribution inside an aluminum droplet (3.92 mm of diameter) for gas temperature at 700 ◦ C.
A.A. El-Hadj et al. / Applied Surface Science 257 (2010) 1643–1648
1647
Fig. 7. Simulated temperature distribution inside an aluminum droplet (3.92 mm of diameter) for gas temperature at 800 ◦ C.
The sole difference is the surrounding gas temperature, which is 700 ◦ C for this case. From this figure, it can be observed that the dynamics of splat is not similar to the previous case (Tgas = 300 ◦ C). After the end of the spreading process, the splat is not cooled and it maintains its liquid phase. Therefore, shrinkage of the splat occurs under the effect of surface tension before the splat is cooled and solidified. This phenomenon is also shown in Fig. 7, which presents the temperature distribution in the case of Tgas = 800 ◦ C. Consequently, the shrinkage of the splat is proportional to the surrounding gas temperature as it is above the melting temperature of the particle. The effect of the surrounding gas on droplet dynamic is due to the change in metal viscosity. At high temperature, the viscosity decreases which leads relatively to a weak viscous force.
Additionally, the effect of the surrounding gas temperature is shown in Fig. 8, which displays histories of the spread factor for different Tgas . This factor is measured as the contact region of the splat with the substrate. Fig. 9 presents the calculated pressure distributions at the contact surface of the droplet with the substrate at t = 0.3, 0.7 and 2 ms for gas temperature at 300 ◦ C and 800 ◦ C. Initially (t = 0.3 ms) there is a high pressure region under the splat. For Tgas = 300 ◦ C, the contact pressure remains constant (∼16 kPa) and decreases rapidly to zero. For Tgas = 800 ◦ C, the contact pressure increases from the center of the splat (∼27 kPa) to its frontier (∼45 kPa), and finally it decreases rapidly to zero. This increase in the value of pressure for a high gas temperature case can therefore lead to the improvement of adhesion of the splat to the substrate.
5
t=0.3ms t=0.7ms
4
4x10
t=2ms 4
3
Pressure (Pa)
The spread factor ( ξ)
4
2
3x10
4
2x10
4
1
0 0,000
0,002
0,004
1x10
Tgas=300°C
Tgas=400°C
Tgas=500°C
Tgas=600°C
Tgas=700°C
Tgas=800°C
0
0,010
0,000
0,006
0,008
0,012
Time (s) Fig. 8. The spread factor for an aluminum droplet impact for different gas temperature.
0,001
0,002
0,003
0,004
Radial position (m) Fig. 9. Contact pressure distribution at the interface during impact of an aluminum droplet for two surrounding gas temperatures 300 ◦ C (—) and 800 ◦ C (- - - - -).
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A.A. El-Hadj et al. / Applied Surface Science 257 (2010) 1643–1648
References
600 67.9 μm in the substrate
At the substrate surface 550
135.7 μm in the substrate
407 μm in the substrate
1.3 μm in the substrate 500
Temperature (°C)
450 400 350 300 250 200 150 0,000
0,002
0,004
0,006
0,008
0,010
Time (s) Fig. 10. Simulation of temperature histories at five locations in the substrate for gas temperature at 300 ◦ C (—) and 800 ◦ C (- - - - -).
Fig. 10 shows the temperature histories of the steel substrate under the splat center during the impact of the aluminum alloy droplet for five positions in the substrate at two different surrounding gas temperatures (300 ◦ C and 800 ◦ C). There is a small discard due to the high thermal resistance of the substrate metal. 4. Conclusion A review of the main studies of the deposit of the droplet on the substrate is briefly presented. The finite element method is used to solve a set of equations governing the impact of aluminum particle on a flat surface. The VOF method is used to track the free surface deformation. The present model is used to investigate the impact of partially molten aluminum alloy 380 particle on a H13 tool steel substrate. The model is in good agreement with the experiment and previous numerical data. In thermal spray process, a high gas temperature can exist in the vicinity of the substrate. According to the performed numerical simulations, the present model has shown that the surrounding gas temperature has a significant effect on the shape of the splatting. When this temperature is above the melting temperature of the particle, a delay of the solidification of splat is observed allowing the shrinkage of the splat. However, a high gas temperature can lead to a good adhesion of the splat with the substrate due to relative improvement of the contact pressure compared to low gas temperature case.
[1] J.R. Davis, et al. (Eds.), Handbook of Thermal Spray Technology, first ed., ASM international, Materials Park, OH, 2004. [2] P. Fauchais, A. Vardelle, B. Dussous, Quovadis thermal spraying? J. Therm. Spray Technol. 10 (1) (2005) 44. [3] A. Abdellah El-hadj, N. AitMessaoudène, Comparison between two turbulence models and analysis of the effect of the substrate movement on the flow field of a plasma jet, Plasma Chem. Plasma Process. 25 (6) (2005) 699. [4] N. Ait-Messaoudene, A. Abdellah El-hadj, Effect of substrate and of thermophoresis and acceleration and heating of particles during HVOF Spraying, Surf. Coat. Technol. 106 (2–3) (1998) 140. [5] L. Williamson, J.R. Fincke, C.H. Chang, A computational examination of the sources of statistical variance in particle parameters during thermal plasma spraying, Plasma Chem. Plasma Process. 20 (3) (2000) 115. [6] M. Pasandideh-Fard, S. Chandra, Mostaghimi, A three-dimensional model of droplet impact and solidification, Int. J. Heat Mass Transfer 45 (11) (2002) 2229. [7] Y. Mebdoua, Etude numérique des Phénomènes thermiques contrôlant la solidification d’une lamelle en projection thermique: application à la formation du dépôt, Ph.D. thesis, University of Limoges, France, 2008. [8] M. Fukomoto, M. Shiiba, H. Haji, T. Yasui, Three-dimensional transition map of flattering behaviour in the thermal spray process, Pure Appl. Chem. 77 (2) (2005) 429. [9] L. Li, X.Y. Wang, G. Wei, A. Vaidya, H. Zhang, S. Sampath, Substrate melting during thermal spray splat quenching, Thin Solid Films 468 (2004) 113. [10] J. Cedelle, M. Vardelle, P. Fauchais, Influence of stainless steel substrate preheating on surface topography and on millimeter and micrometer sized splat formation, Surf. Coat. Technol. 201 (2006) 1373. [11] M. Mellali, P. Fauchais, A. Grimaud, Influence of substrate roughness and temperature on the adhession/cohesion of alumina coatings, Surf. Coat. Technol. 81 (1996) 275. [12] S. Amada, K. Imagawa, S. Aoki, Splat profile of impinging droplets on rough substrates: influence of surface roughness, Surf. Coat. Technol. 154 (2002) 27. [13] M. Xue, Y. Heichal, S. Chandra, J. Mostaghimi, Modeling the impact of a molten droplet on a solid surface using variable interfacial thermal contact resistance, J. Mater. Sci. 42 (2007) 9. [14] J.C. Fang, L. Wang, W.J. Xu, Z.Y. Zhao, Numerical simulation of splat formation dynamics in plasma spray forming, Trans. Nonferrous Met. Soc. China 17 (2007) 41. [15] M. Pasandideh-Fard, R. Bhola, S. Chandra, J. Mostaghimi, Deposition of tin droplets on a steel plate: simulations and experiments, Int. J. Heat Mass Transfer 41 (1998) 2929. [16] R. Ghafouri-Azar, S. Shakeri, S. Chandra, J. Mostaghimi, Interactions between molten metal droplets impinging on a solid surface, Int. J. Heat Mass Transfer 46 (2003) 1395. [17] S. Brossard, P.R. Munroe, A.T.T. Tran, M.M. Hyland, Study of the effects of surface chemistry on splat formation for plasma sprayed NiCr onto stainless steel substrates, Surf. Coat. Technol. 25 (2010) 1599. [18] M. Xue, An extended numerical model for predicting the microstructure of thermal spray coatings, Ph.D. thesis, Totonto University, Canada, 2007. [19] L. Xu, W.W. Zhang, S.R. Nagel, Drop splashing on a dry smooth surface, Phys. Rev. Lett. 94 (2005) 18. [20] O.C. Zienkiewicz, The Finite Element Method, McGraw-Hill Company, London, 1997. [21] Manual of Ansys Ver. 11, Ansys Inc., USA. [22] M. Hamide, Modélisation numérique du soudage à l’arc des aciers, Ph.D. thesis, ENS des Mines de Paris, France, 2008. [23] M. Zirari, A. Abdellah El-hadj, N. Bacha, Numerical analysis of partially molten splat during thermal spray process using the finite element method, Appl. Surf. Sci. 256 (11) (2010) 3581.
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Numerical analysis of the effect of the gas temperature on splat formation during thermal spray process A. Abdellah El-Hadj a,∗ , M. Zirari b , N. Bacha c a b c
Laboratory LMP2M, University of Medea, Medea 26000, Algeria Laboratory LPTRR, University of Medea, Medea 26000, Algeria Laboratory LTSM, University of Blida, 09000, Algeria
a r t i c l e
i n f o
Article history: Received 29 June 2010 Received in revised form 29 August 2010 Accepted 30 August 2010 Available online 27 September 2010 Keywords: Coating Impact Splat VOF Gas temperature Solidification
a b s t r a c t Thermal spray coatings are affected by various parameters. In this study, the finite element method with volume of fluid (VOF) procedure is used to investigate the deposition process which is very important for the quality of sprayed coatings. The specific heat method (SHM) is used for the solidification phenomenon. A comparison of the present model with experimental and numerical model available in the literature is done. A series of numerical calculations is carried out to investigate the effect of the surrounding gas temperature on the splat formation. The variation of the surrounding gas temperature has a significant effect on splat morphology and can affect the adhesion of the splat on the substrate. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Thermal spraying is a surface treatment method, used generally for protecting surfaces against wear, corrosion and thermal barrier, providing by means of thick coatings (approximately 20 m to several mm). Coating materials available for thermal spraying include metals, alloys, ceramics, plastics and composites. The material is fed in powder or wire form, projected at high speed and heated to a molten state or semi-molten on a solid substrate in the form of micrometer-size particles. Coating quality is usually assessed by measuring its porosity, oxide content, macro- and microhardness, bond strength and surface roughness. Generally, the coating quality increases with increasing particle velocities [1,2]. Optimization and control of the complex phenomenon in thermal spray processes has been reported in several works [3–6]. At impact, the liquid material is spread on the surface which then solidifies with a quenching speed of around 106 –108 K/s. The flattering process continues until the kinetic energy of the particle hitting the surface is completely converted into viscous energy and surface tension. The properties of thermal sprayed coatings are essentially linked to the structure of a single splat and the quality of contact between the pilled-up splats. These properties of adhesion and cohesion and thermo-physical properties are related to
∗ Corresponding author. Fax: +213 25586501. E-mail address: lmp2m [email protected] (A.A. El-Hadj). 0169-4332/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2010.08.115
the morphology of the individual splats and to the contact quality between these splats and the substrate. The formation of the splat depends on the parameters related of the suspended particle (its size, its velocity, its temperature, its melting state at impact and its thermo-physical properties) and on the parameters related to the substrate (its properties, its surface state, its preheated temperature and the presence of oxides). Understanding of melting and solidification of the substrate is essential for appropriate bond coat selection as well as avoidance of substrate damage [7–9]. Experimental works have been devoted for studying an individual splat for a better understanding of the different mechanisms which govern its faltering and solidification [10–12]. It is found that the preheated temperature of the substrate has an important role in determining the morphology of the splat. There is a critical preheated temperature of the substrate named the transition temperature, above which the splat has a regular disc form and bellow which it has a shredded form [8]. Other researchers have studied numerically the splat formation phenomenon [13–18]. These numerical models which use the volume of fraction method (VOF) take into account the hydrodynamic aspects of the splat formation and the heat transfer between the splat and the substrate. Xu et al. [19] experimentally investigated the corona splashing due to the impact of a liquid drop on a smooth dry substrate. It is suggested that splashing results from the compressibility of the gas and it can be inhibited by decreasing the surrounding gas pressure. The threshold of the gas pressure depends on the impact velocity, molecular weight of the gas, and
1644
A.A. El-Hadj et al. / Applied Surface Science 257 (2010) 1643–1648
Fig. 1. Example of contourlines temperature of plasma spray jet (Ar-H2 ) issuing into air [3].
the liquid viscosity. It can be deduced from this result that the temperature of the surrounding gas can influence the splat formation and morphology. In thermal spray process, the surrounding gas can reach a high temperature in vicinity of the substrate (Fig. 1). However, this parameter has not been studied in these previous researches. Therefore, the aim of this work is to investigate the splat formation under different surrounding gas temperatures around the particle. The Galerkin finite element method is used to solve the set of governing equations using Ansys/Flotran code. The VOF method is used to track the free surface deformation. In this study, some pertinent parameters that influence the quality and the morphology of the deposit (the spread factor, the impact pressure and the temperature histories in the affected zone of the substrate) are considered.
2. Mathematical formulation Numerical simulations are used for modeling the impact of the droplet. A set of the governing equations for the continuity, the momentum and the energy are adopted. The procedure is based on the use of the Galerkin finite element method [20] to solve system of equations and the VOF method to track the interface displacement [18]. The thermo-physical properties of the materials are given in Table 1 [18]. The physical domain with boundary conditions is illustrated in Fig. 2. The fluid flow is assumed to be incompressible. The dynamic and energy equations are coupled only by material properties which are temperature dependent. They are solved alternatively for every timestep until the final time is reached.
Fig. 2. Physical domain of a 3.92 mm droplet impacting a substrate.
2.1. Dynamic model In the VOF method, the cell containing a fluid is governed by the following equations [18]: · (˛ · V ) = 0 ∇
(1)
∂(˛ · V ) p + ˛v∇ 2 V + ˛ F )V = −˛ ∇ + (˛V · ∇ b ∂t
(2)
where V is the velocity vector, is the density, p is the pressure, ˛ is called fraction of fluid volume, v is the kinematic viscosity and t the time. Fb is the body force applied to the fluid. The surface tension is an important parameter that contributes in the deformation of the droplet. It is considered as a volume force applied to the free surface of the liquid. The electrostatic forces between the molecules of the surrounding gas are very small compared to those of the liquid due to their molecular distances. The resultant of the forces is directed toward the inside of the particle. This force characterizes the liquid surface tension ( in N/m). The liquid evolves spontaneously to minimize its surface tension (its free surface energy). According to the VOF methodology, the fraction of fluid volume ˛ is used for the all domain where its value indicates the presence or the absence of the fluid. We attribute the value of 1 for a point occupied by the metal and 0 in the other domain part. The mean
Table 1 Thermo-physical properties of aluminum and steel H13 [20]. Properties 3
Density [kg/m ] Temperature of melting [◦ C] Melting heat [J/kg] Kinematic viscosity [m2 /s] as a function of temperature (◦ C) Thermal conductivity of liquid [W/(m K)] Specific heat of liquid [J/(kg K)] Superficial tension [N/m] Thermal conductivity of solid [W/(m K)] as a function of temperature (◦ C)
Specific heat of solid [J/(kg K)] as a function of temperature (◦ C)
Aluminum alloy 380
Steel H13
2570 570 389 T 78 2000 70 1000 1.07 T 100 200 300 400 T 300 300 479
7800 – – –
v 4.5E−7 4.E−7
K 144.5 147.5 152.5 148.0 C 980 1050 1150
– – – T 27 204 427 649 T 20 500 600
K 17.6 23.4 25.1 26.8 C 460 550 590
A.A. El-Hadj et al. / Applied Surface Science 257 (2010) 1643–1648
1645
value in the element k presents the function of the fluid volume occupied by the metal [18]:
˛=
⎧ ⎪ ⎨1 ⎪ ⎩
inside the fluid
0<˛<1
contain a free surface
0
empty cell
(3)
The element with a value of ˛ between 0 and 1 is containing the free surface or the interface. To find ˛(x,t) for all points of the domain x ∈ ˝ (˝ is the physical domain 1 in Fig. 2), it is necessary to solve the transport equation [21]: ∂˛ d˛ + V · ∇˛ = dt ∂t
with ˛(x, 0) = ˛0 (x)
(4)
Due to a low density, the inertia of the gas is usually negligible. The sole effect of the gas is the pressure acting on the interface. Hence the region of gas need not be modeled, and the interface is simply modeled as a boundary with constant pressure. The arbitrary Lagrangian–Eulerian method is used to track the interface location of the droplet. The fluid flow boundary condition at the droplet–substrate interface is no slip and no-penetration. 2.2. Heat transfer model The SH method is used in order to take into account for the phase changing in metal particle. This formulation uses the equivalent specific heat which takes in account the latent heat in the energy equation as [22]: ∂T dfs ∂T ∂(h) eq ∂T = cp − Lf = cp dT ∂t ∂t ∂t ∂t
(5)
where h is the enthalpy, T is the temperature, cp is the metal specific eq heat, cp is the equivalent specific heat, Lf is the latent heat of fusion and fs is the solid fraction. The following is the definition of the equivalent heat capacity used to simulate the latent heat effect:
eq cp
=
⎧ cp ⎪ ⎪ ⎨ ⎪ ⎪ ⎩
cp − Lf
df s
dT
T ≤ Tm − ıT (solid) Tm − ıT ≤ T ≤ Tm
(6)
Fig. 3. Simulation of sequential impact of an aluminum droplet of 3.92 mm in diameter on smooth steel substrate at 200 ◦ C with 3 m/s of impact velocity.
T ≥ Tm (liquid)
cp
where Tm is the melting temperature, and ıT is the phase change transition temperature. This leads to a modified heat transfer equation, where the phase change is treated as nonlinearity in the physical properties:
∂t
+ ∇ · (cp T · V ) = ∇ · (K ∇ T ) + Q eq
(7)
where K is the metal thermal conductivity and Q is the source term. The equation governing of transient heat transfer in the substrate is given by: ∂T = ∇ · (Kb ∇ T ) b cb ∂t
(8)
where cb is the substrate specific heat, b is the substrate density and Kb is the substrate conductivity. The transient heat transfer equations are solved for droplet and substrate. The interface between substrate and droplet is assumed to respect the continuity condition (same flux). The effect of contact resistance at the substrate–droplet interface is not considered here. The surface of the droplet and of the substrate in contact with the gas is taken to be at the gas temperature. All other boundaries are assumed to be insulated.
The spread factor ( ξ)
eq ∂T
cp
4
3
2 Present work Experiment [13] Simulation [13]
1
0 0,0
1,0x10 -3
2,0x10 -3
3,0x10 -3
Time (s) Fig. 4. The spread factor of an aluminum droplet (3.92 mm of diameter) with the 3 m/s of impact velocity on a smooth surface.
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Fig. 5. Simulated temperature distribution inside an aluminum droplet (3.92 mm of diameter) for gas temperature at 300 ◦ C.
3. Results and discussion The numerical model used to simulate droplet impact solves the coupling equations using a finite element technique. An aluminum alloy 380 particle of 3.92 mm in diameter with the impact velocity of 3 m/s projecting onto flat H13 tool steel substrate at initial temperature of 200 ◦ C is used. The initial particle temperature is taken above the melting temperature as 630 ◦ C. This model has been validated earlier [23]. The computer generated images of sequential impact of the particle are shown in Fig. 3. The shape of the flattering behavior is similar to those of the experimental results [13]. Fig. 4 shows the evolution of the spread factor ( = DP /DP0 ) which is calculated by normalizing the diameter DP measured from images by the initial diameter DP0 of the present model compared to the measured and predicted ones of Xue et al. [13]. The discrepancy between the two numerical models is due to the different methods used. In order to obtain a better quantitative
comparison between the different models, the predicted values of the spread factor () is considered. Fig. 5 displays the temperature distribution of the particle for different times following impact for the gas temperature at 300 ◦ C. When the particle splats on the substrate, it takes a lamellar form by lateral spreading of the liquid under the effect of the particle pressure. The kinetic energy of the particle is transformed to the viscous deformation and to the surface energy at the splatting end. As shown in the figure, the splatting of the droplet is divided in three steps, initial impact, particle spreading and cooling and solidification. A series of numerical calculations shows that the temperature of the surrounding gas (Tgas ) can affect significantly the spreading and the morphology of the splat. This effect is obvious when Tgas is above the melting temperature of the droplet. Fig. 6 illustrates the distribution of the temperature for the droplet for different times following the impact as in Fig. 5 with almost identical conditions.
Fig. 6. Simulated temperature distribution inside an aluminum droplet (3.92 mm of diameter) for gas temperature at 700 ◦ C.
A.A. El-Hadj et al. / Applied Surface Science 257 (2010) 1643–1648
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Fig. 7. Simulated temperature distribution inside an aluminum droplet (3.92 mm of diameter) for gas temperature at 800 ◦ C.
The sole difference is the surrounding gas temperature, which is 700 ◦ C for this case. From this figure, it can be observed that the dynamics of splat is not similar to the previous case (Tgas = 300 ◦ C). After the end of the spreading process, the splat is not cooled and it maintains its liquid phase. Therefore, shrinkage of the splat occurs under the effect of surface tension before the splat is cooled and solidified. This phenomenon is also shown in Fig. 7, which presents the temperature distribution in the case of Tgas = 800 ◦ C. Consequently, the shrinkage of the splat is proportional to the surrounding gas temperature as it is above the melting temperature of the particle. The effect of the surrounding gas on droplet dynamic is due to the change in metal viscosity. At high temperature, the viscosity decreases which leads relatively to a weak viscous force.
Additionally, the effect of the surrounding gas temperature is shown in Fig. 8, which displays histories of the spread factor for different Tgas . This factor is measured as the contact region of the splat with the substrate. Fig. 9 presents the calculated pressure distributions at the contact surface of the droplet with the substrate at t = 0.3, 0.7 and 2 ms for gas temperature at 300 ◦ C and 800 ◦ C. Initially (t = 0.3 ms) there is a high pressure region under the splat. For Tgas = 300 ◦ C, the contact pressure remains constant (∼16 kPa) and decreases rapidly to zero. For Tgas = 800 ◦ C, the contact pressure increases from the center of the splat (∼27 kPa) to its frontier (∼45 kPa), and finally it decreases rapidly to zero. This increase in the value of pressure for a high gas temperature case can therefore lead to the improvement of adhesion of the splat to the substrate.
5
t=0.3ms t=0.7ms
4
4x10
t=2ms 4
3
Pressure (Pa)
The spread factor ( ξ)
4
2
3x10
4
2x10
4
1
0 0,000
0,002
0,004
1x10
Tgas=300°C
Tgas=400°C
Tgas=500°C
Tgas=600°C
Tgas=700°C
Tgas=800°C
0
0,010
0,000
0,006
0,008
0,012
Time (s) Fig. 8. The spread factor for an aluminum droplet impact for different gas temperature.
0,001
0,002
0,003
0,004
Radial position (m) Fig. 9. Contact pressure distribution at the interface during impact of an aluminum droplet for two surrounding gas temperatures 300 ◦ C (—) and 800 ◦ C (- - - - -).
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References
600 67.9 μm in the substrate
At the substrate surface 550
135.7 μm in the substrate
407 μm in the substrate
1.3 μm in the substrate 500
Temperature (°C)
450 400 350 300 250 200 150 0,000
0,002
0,004
0,006
0,008
0,010
Time (s) Fig. 10. Simulation of temperature histories at five locations in the substrate for gas temperature at 300 ◦ C (—) and 800 ◦ C (- - - - -).
Fig. 10 shows the temperature histories of the steel substrate under the splat center during the impact of the aluminum alloy droplet for five positions in the substrate at two different surrounding gas temperatures (300 ◦ C and 800 ◦ C). There is a small discard due to the high thermal resistance of the substrate metal. 4. Conclusion A review of the main studies of the deposit of the droplet on the substrate is briefly presented. The finite element method is used to solve a set of equations governing the impact of aluminum particle on a flat surface. The VOF method is used to track the free surface deformation. The present model is used to investigate the impact of partially molten aluminum alloy 380 particle on a H13 tool steel substrate. The model is in good agreement with the experiment and previous numerical data. In thermal spray process, a high gas temperature can exist in the vicinity of the substrate. According to the performed numerical simulations, the present model has shown that the surrounding gas temperature has a significant effect on the shape of the splatting. When this temperature is above the melting temperature of the particle, a delay of the solidification of splat is observed allowing the shrinkage of the splat. However, a high gas temperature can lead to a good adhesion of the splat with the substrate due to relative improvement of the contact pressure compared to low gas temperature case.
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