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Mathematical modelling of Inconel 718 particles in HVOF thermal spraying
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Surface & Coatings Technology 202 (2008) 2715 – 2724 www.elsevier.com/locate/surfcoat
Mathematical modelling of Inconel 718 particles in HVOF thermal spraying S. Kamnis, S. Gu ⁎, N. Zeoli School of Engineering Science, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom Received 21 June 2007; accepted in revised form 1 October 2007 Available online 16 October 2007
Abstract High velocity oxygen fuel (HVOF) thermal spray technology is able to produce very dense coating without over-heating powder particles. The quality of coating is directly related to the particle parameters such as velocity, temperature and state of melting or solidification. In order to obtain this particle data, mathematical models are developed to predict particle dynamic behaviour in a liquid fuelled high velocity oxy-fuel thermal spray gun. The particle transport equations are solved in a Lagrangian manner and coupled with the three-dimensional, chemically reacting, turbulent gas flow. The melting and solidification within particles as a result of heat exchange with the surrounding gas flow is solved numerically. The in-flight particle characteristics of Inconel 718 are studied and the effects of injection parameters on particle behavior are examined. The computational results show that the particles smaller than 10 μm undergo melting and solidification prior to impact while the particle larger than 20 μm never reach liquid state during the process. © 2007 Elsevier B.V. All rights reserved. Keywords: CFD; HVOF; Gas dynamics; Particle modeling
1. Introduction High velocity oxy-fuel (HVOF) thermal spraying offers a versatile technology to produce protective coatings, typically 200 to 500 μm thick, on the surfaces of engineering components. Materials being sprayed include metallic alloys, cermets, and polymers. In the HVOF process, oxygen and fuel are mixed and burnt in a combustion chamber at high flow rates (up to 1000 liter/min) and pressures (up to 12 bar) in order to produce a high-temperature (up to 3000 K), high-speed (up to 2000 m/s) gas jet. Powder particles, normally in the size range 5 to 65 μm, are injected into the gas jet so that they are heated and accelerated toward the substrate to be coated. On arrival at the substrate, particles are ideally in a melted or softened state and, on impact, form lenticular splats, which adhere well to the substrate and to one another. The HVOF gun is scanned cross the substrate to build up the required coating thickness in a number of passes.
⁎ Corresponding author. Tel.: +44 23 8059 8520; fax: +44 23 8059 3230. E-mail addresses: [email protected] (S. Kamnis), [email protected] (S. Gu). 0257-8972/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2007.10.006
In HVOF spraying, the feedstock powder has density three or four orders of magnitude greater than the gas density; its other thermophysical properties are also significantly different from those of gas. A typical approach for modelling this multiphase flow is to treat gas and powder as separate gas and particle phases. The equations that describe the particle motion are solved in a Lagrangian frame and coupled with the Eulerian gas flow. The Euler–Lagrange approach has been used for the modeling of particle-gas interaction in various HVOF thermal spray systems [1–7]. However, most of the particle models are based on the gas fuelled HVOF systems [1–12] while the technology trend is moving towards high throughput liquid fuelled systems which have the advantage of using low cost fuel such as kerosene instead of propylene. The existing simulations on liquid fuelled HVOF guns are very limited. The early model from Yang et al. [13] is 2-dimensional which could not correctly represent the 3-dimensional design of gun and powder injection method. This paper reports the authors' continuation of research on liquid fuelled HVOF system from their latest work [14] which has shown 3-dimensional gas flow patterns of a kerosene burning gun. The purpose of this study is to examine particle motion and heat transfer within the gas flow field by investigating the effect of particle injection parameters.
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Nomenclature CD Cp D dp FD F gx H Hsf kg ks kc Pr Re St r T TL Ts Tk t up ug
drag coefficient particle specific heat capacity (J kg− 1 K− 1) barrel diameter (m) particle diameter (m) drag force per unit particle (N) solid fraction x component of gravitational acceleration (m2 s− 1) convective heat transfer coefficient (W m− 2 K− 1) latent heat (J Kg− 1) gas thermal conductivity (W m− 1 K− 1) particle thermal conductivity (W m− 1 K− 1) partition coefficient Prandtl number (cpμ Κ∞− 1) Reynolds number based on particle diameter Stokes number particle radius temperature (K) liquidius temperature (K) solidus temperature (K) primary element melting temperature (K) time (seconds) particle velocity (m s− 1) gas velocity (m s− 1)
Greek symbols Α thermal diffusivity (m2 s− 1) μg gas viscosity (kg m− 1 s− 1) ρp particle density (kg m− 3) ρg gas density (kg m− 3) ϕ shape factor Ψ(T) correction function Δt time step (s) Δr grid node distance (m) 2. Model development A schematic representation of the HVOF gun is shown in Fig. 1. The mixture of fuel and oxygen stream is injected into the water-cooled combustion chamber, where the gases burn and the combustion products are accelerated down the convergent divergent nozzle and long parallel-sized barrel. Powder particles are injected into the barrel through two holes with a tapping angle in the front of the barrel. The particle laden by gas mixture exits the gun at a high-temperature and velocity toward the substrate to be coated. The three-dimensional simulations are performed in the commercially available finite volume CFD code Fluent 6.3 [15]. The computational geometry includes the gun and external domain as shown in Fig. 2. The grid structure and boundary conditions has been described in [14]. Briefly, a structured grid is used and fine meshes are employed to the sensitive areas such as, the nozzle entrance and exit, the barrel exit and the free-jet centreline where high gradients are ex-
pected and great accuracy is required in order to capture the compressibility effects. Grid sensitivity studies have been carried out by doubling the cell number both axially and radially and the numerical solutions from both meshes are almost identical. The compressible turbulent chemically reacting flow model has been described in [14] and only a brief introduction is given here. For the combustion of kerosene, C12H26 is used to have a representative average value for the individual components. The combustion kinetics is represented by one global reaction scheme which takes dissociations and intermediate reactions into account. n1 C12 H26 þ 18:5n2 O2 →12n3 CO2 þ 13n4 H2 O þ n5 CO þ n6 OH þ n7 O2 þ n8 O þ n9 H2 þ n10 H: These coefficients are dependent on variables such as the combustion chamber pressure, fuel to oxygen ratio, mass flow rate or even the torch geometry. To derive those coefficients, an iterative approach based on a chemical equilibrium model is
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Fig. 1. Schematic representation of the HVOF gun including combustion chamber, convergent divergent nozzle (CDN) section and parallel-sized barrel.
employed to make sure the coefficients representing the correct pressure level and thermal flow field. The eddy dissipation model is used to solve this global reaction. This approach is based on the solution of transport equations for species mass fractions. The reaction rates are assumed to be controlled by the turbulence instead of the calculation of Arrhenius chemical kinetics. The process parameters employed in the computational modelling are 0.003526 kg/s for kerosene and 0.01197 kg/s. The computation of particle dynamics is achieved by coupling
with the Eulerian gas flow. The powder is treated as spherical particles which closely represent the thermally sprayed powder, Inconel 718 which has the composition shown in Table 1 and thermal properties shown in Table 2. The computer model treats the powder feeding as a point injection through the barrel's wall without carrier gas being introduced to the computational domain. Unlike a gas fuelled HVOF system where the carrier gas is injected into the centre of the combustion chamber, the introduction of cross flow carrier gas into a high-speed stream
Fig. 2. Grid and computational domain.
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Table 1 Chemical composition of the Inconel 718 powder (wt.%)
The Reynolds number is defined by
Element
Min
Max
Carbon Manganese Silicon Phosphorus Sulfur Nickel + Cobalt Chromium Cobalt Iron Aluminium Molybdenum Titanium Boron Copper Cb + Ta
– – – – – 50.0 17.0 – Balance 0.35 2.80 0.65 0.001 – 4.75
0.08 0.35 0.35 0.015 0.015 55.0 21.0 1.00 Balance 0.80 3.30 1.15 0.006 0.15 5.50
has given rise to numerical errors and difficulty to control the convergence of the solutions. Considering that the volume fraction of carrier gas is less than 2% of the total flow rate, the carrier gas is expected to have only marginal effect on the flow pattern and the subsequent effect on the behaviour of particles could be marginal. 3. Mathematical models 3.1. Momentum transfer equations The acting force in the particle could involve the drag force, force due to pressure gradients, force due to added mass, Basset history term and external potential forces [16]. In principle, among the factors that affect the movement of particle during the HVOF process, only the drag force plays a dominant role, other factors can be neglected in most cases [16]. The equation of motion for particles can be written as a force balance that equates the droplet inertia with forces acting on the droplet: g z q p qg dup ¼ FD ug up þ ð1Þ qp dt
Re ¼
qg jug up jdp Ag
ð5Þ
As the gas flow is turbulent during HVOF spraying, the influence of the turbulence on the particle behavior needs to be evaluated. The effect of turbulent fluctuation on the particle aerodynamic response could be reflected by the Stokes number (St) which is the ratio of the aerodynamic response time to the time scale associated with larger-scale turbulent eddies. St ¼
qp dp up 18Ap D
The large Stokes number (St &Z.Gt; 1) means a slow response from the particle to the large turbulent eddies. The sprayed powder Inconel 718 with a mean diameter of 20 μm under the present HVOF flow has the Stokes number: St ≈ 300, which implies that the turbulence would not have substantial effect on the particles larger than 20 μm. 3.2. Heat transfer equations The study of heat transfer in thermal spray process [19] demonstrates that the heat transfer due to radiation from the surroundings to particles is negligible compared to the convective heat flux from the gas to the particle, in that case, the particle heating in spherical coordinates is given by: 2 AT A T 2 AT df qp Cp ¼ ks ð6Þ þ þ Hsf qp 2 At Ar r Ar dt Considering an alloy for which the area of solidification in the phase diagram is approximated by straight lines, Eq. (6) can be written as: 2 AT a A T 2 AT ¼ þ ð7Þ At wðT Þ Ar2 r Ar Where the function ψ(T) is defined as [20]: 8 1 > Hsf ðTk TL Þ 1kc < if TS VT VTL 1 þ 2kc wðT Þ Cp ð1 kc ÞðTk T Þ 1kc > : else 1
The drag force per unit particle mass is: 18Ag CD Re FD ¼ qp dp2 24
ð2Þ
Table 2 Thermophysical properties for Inconel 718 [23]
the drag coefficient CD given by Morsi [17]: 24 b3 Re 1 þ b1 Rebd2 þ CD ¼ Re b4 þ Re b1 b2 b3 b4
¼ exp 2:3288 6:4581/ þ 2:4486/2 ¼ 0:0964þ 0:5565/ ¼ exp 4:905 13:8944/ þ 18:4222/2 10:2599/3 ¼ exp 1:4681 þ 12:2584/ 20:7322/2 þ 15:8855/3
the shape factor ϕ is given by Haider [18].
Tk is the melting temperature of the primary element and k is the ratio between solid and liquid concentration.
ð3Þ
ð4Þ
Density (ρp) (kg/m3)
8200
Solidus temperature (TS) [K] Liquidus temperature (TL) [K] Primary element melting point (Tk) [K] Partition coefficient (kc) Specific heat (Cp) [J/kg K] Latent heat (Hsf) [J/kg] Thermal conductivity (k) [W/m K]
1528 1610 1726 0.3 600 227000 T b 1000 K 1000 b T b 1528 1610 b T
21 5.8 + 0.016T 4.95 + 0.013T
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Fig. 3. Particle trajectories at different injection velocities.
This computational model assumes infinite velocity for diffusion (equilibrium condition) in liquid phase and zero in the solid [21]. The boundary conditions associated to Eq. (7) are specified on the surface and in the centre of the particle as:
improve the accuracy of the melting and solidification kinetics. In the same manner, Eq. (8) becomes: hn Dr hn Dr nþ1 þ 1 n TNnþ1 ¼ n Tg ð12Þ TN1 ki ki
AT Ar
Eq. (7) in the centre (r = 0) becomes indeterminate, this means that the relation in Eq. (11) will not be applicable. By applying the theorem of L'Hospital, it is found:
¼ 0; r¼0
AT ks Ar
¼ h T g TR
ð8Þ
r¼R
R represents the radius of the simulated particle, ks is thermal conductivity of particle, Tg is the gas temperature and h is the convective heat transfer coefficient. The heat transfer coefficient is evaluated using the Ranz and Marshall correlation [22]: Nu ¼ 2 þ 0:6Re1=2 Pr1=3
ð9Þ
where Nu is the non-dimensional Nusselt number, defined as: Nu ¼
hdp kg
AT a A2 T ¼3 At wðT Þ Ar2 The discretized form of Eq. (13) is: Dt Dt wn0 þ 3a 2 T0nþ1 3a 2 T1nþ1 D r D r Dt Dt ¼ wn0 3a 2 T0n þ 3a 2 T1n D r D r
ð10Þ
nþ1 nþ1 Dt 1 Dt Dt n T nþ1 a 2 i1 þ 1 Tiþ1 1 T þ 2w þ 2a i i i1 D2 r D2 r i D r n Dt Dt Dt n ¼ a 2 ð1 i1 ÞTi¼1 þ 2wni 2a 2 Tin þ a 2 i1 þ 1 Tiþ1 D r D r D r
a
ð11Þ
N is the number of discretization points along the radius of the droplet and n is the time index. After grid sensitivity analyses to all particle sizes the nodal points were set to 10. For larger particles more discretization points are required to
ð14Þ
At each time step the algebraic system of Eqs. (11), (12) and (14) is solved using the Gauss Seidel iterative method which is implemented as a user defined function in the simulation. The
The discretized form of Eq. (7) is:
i ¼ 1; 2; N N 1
ð13Þ
Fig. 4. Particle velocity profiles at different injection velocities.
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Fig. 5. Particle surface temperature profiles at different injection speeds.
simulation time step is set to 10− 6 s and the convergence condition to 10− 4.
4. Computational results and discussions 4.1. Influence of particle injection velocity The particle injection velocity can be manipulated by carrier gas flow rate. In this calculation, 20 μm diameter Inconel 718 particles are injected from the axial distance of 0.12 m. The injection velocities vary in the range 0–40 m/s. The particle trajectories in Fig. 3 show that the particle is driven by the gas flow and travels along the edge of barrel with zero injection speed; the increase of injection velocity will enable the particle travel cross the gas flow and move towards the centre of the jet at injection speed between 8–10 m/s; the particle travels cross the centre of the gun and spreads outwards at injection speed at 20 m/s; the particle hits the internal surface of the barrel and the trajectory is changed to opposite direction as the result of elastic collision at 40 m/s. Nozzle wear is most frequently encountered
problem for operating HVOF guns and the nozzle needs to be replaced after about 10 h spraying. Examination of the damaged nozzles reveals the particle pathlines along the internal surface of the barrel and cracks in the nozzle by the impact of highspeed particles. The computational results imply that, to spray Inconel 718 powder with a mean diameter of 20 μm, the injection speed needs to be controlled within the range of 8– 10 m/s, in that case, and particularly at 8 m/s, most powder particles will stay in the centre of the gun; powder particles will spread outwards by increase of the injection velocity over 10 m/ s; the particle is most likely to hit the barrel and give rise to nozzle wear when the injection velocity increased above 20 m/s. Zero injection velocity should also be avoided as the particle travels along the edge of barrel, the particle could make mechanical contacts with the barrel or the molten particle could stick on the internal surface of the nozzle and generate the blockage. The advantage of HVOF technology is its ability to accelerate particles to very high speed, therefore, it is desirable to achieve the highest possible velocity of powder particles during the spraying. The velocity profiles in Fig. 4 show that the particles reach high velocity when injection velocity is between 8 to 10 m/s. It is known that the gas flow has the highest velocity in the centre; therefore particles will gain more momentum while traveling in that region. The temperature profiles in Fig. 5 confirm that the particles heated more efficiently for 8–10 m/s injection velocity when the particles travel at the centre of the gas jet. 4.2. Influence of particle injection position The liquid fuelled HVOF gun is designed to inject powders at the front of the barrel instead of feeding the spray powder into the centre of the combustion chamber adopted in gas fuelled HVOF systems such as HV2000 (Praxair, US). The advantage of such design is to suppress the contacts between powders and the gas flame to minimize the undesirable
Fig. 6. Particle velocity profiles from different injection positions.
S. Kamnis et al. / Surface & Coatings Technology 202 (2008) 2715–2724
oxidation for metal powders. The location of injection is also important to generate consistent coating products. The high pressure gas undergoes drastic expansion and compression in the throat of the nozzle as shown in Fig. 6, the substantial pressure fluctuation makes the control of powder feeding very difficult, therefore, it is not practical to inject powders in the throat region. In this calculation, 20 μm Inconel 718 particles are released from 5 axial locations between 0.10 and 0.15 m in the front of the barrel at injection velocity of 8 m/s which is within the range of optimal injection velocities as stated in the previous section. The predicted paths for these particles plotted in Fig. 7 show that all the particles travel at similar trajectory and reach the centre of the jet at the end of the domain. The velocity profiles in Fig. 6 demonstrate that the particles accelerate continuously throughout the domain despite the decline of gas jet near the end of the domain. It is known that the longer distance prolongs the residual time of in-flight particle and the particle accelerates more, therefore, it is sensible to inject powder at the earliest possible point when the gas flow is stabilized. The particle temperature profiles in Fig. 8 show that powder particles are heated rapidly in the barrel and develop steadily from the exit of the gun, the particle temperatures start to decline when the temperature of gas flow drops sharply when cold air penetrates deeply into the gas jet. The computational model has an external domain of 32 cm from the gun exit, which is within the typical range of stand-off distances for the HVOF spray coating. The particle dynamics at the exit of the computational domain (i.e. 32 cm from the gun exit) can be regarded as the impact parameters. The particle impact parameters in Fig. 9a show that the surface temperatures of particles drop below the melting point (1528 K for the Inconel 718 powder). The set of results imply that the particles at the given injection speed will concentrate at the centre of the jet and have similar dynamics from different axial injection distances, while the high impact velocity and temperature will achieve at axial distance closer to the throat of CDN as shown in Fig. 9b. However, too close to the throat of CDN will give rise to practical issue of controlling the pressure fluctuation for the powder feeder, the axial distance of
Fig. 7. Particle trajectories from different injection positions.
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Fig. 8. Particle surface temperatures from different injection positions. (a) Temperature prior to impact. (b) Velocity prior to impact.
0.12 m is adopted in the current design and will be used for the following discussions. 4.3. Influence of particle size Feedstock powder is generally supplied with a range of distribution. This study is to examine the effect of different particle sizes on particle behaviour to provide information on
Fig. 9. Particle impact parameters from different injection positions.
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Fig. 10. Trajectories for different size particles.
the optimum range within the nominal size distribution. In these calculations, different sized Inconel 718 particles ranging from 5 μm to 40 μm were injected at axial distance of 0.12 m with a speed of 8 m/s. The particle trajectories in Fig. 10 show that the small particles are blown away by the gas flow, e.g. 5 μm particle travels along the edge of the barrel and spreads outwards at the external domain as the jet expands outside. The 10 μm particle remains at the outer region of the jet throughout the domain while the large particles e.g. 30 and 40 μm move cross the centre of the gun and spread outwards in the external domain. The particle velocity profiles in Fig. 11 clearly demonstrate that the smaller particles are accelerated more throughout the computational domain. When the particle velocity is higher than the gas velocity, as the gas jet decays outside the gun, the drag force on the particle then changes direction and becomes a resistance to the particle motion. The velocity of the particle is then decreased. The smaller the particle size, the more easily it is decelerated. A larger particle, on the other hand, has greater ability to maintain its velocity during the deceleration stage, because of its larger inertia. The velocity dependence on particle size is more clearly demonstrated in Fig. 12a which is a plot of particle velocity versus particle diameter at the point of impact on the substrate. The temperatures at the impact in relation to the particle size are
Fig. 12. Impact parameters for different size particles.
given in Fig. 12b. The surface temperature plots in Fig. 13 show the particles smaller than 10 μm undergo melting and solidification during the process which will be discussed in details in the following section. 4.4. Melting and solidification within particles The temperature evolution of 10 μm particle in Fig. 14 shows the rapid heating of particle come to a stop when the surface
Fig. 11. Velocity profiles for different size particles. (a) Velocity prior to impact. (b) Temperature prior to impact.
Fig. 13. Temperature profiles for particles at different sizes.
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Fig. 14. Surface temperature profile for 10 μm size particle.
temperature arrives at the solidus temperature (1528 K) at 0.18 ms. The surface temperature increases slowly as the solidus isothermal surface moves towards the centre of the particle. At 0.29 ms the surface temperature reaches the liquidus temperature (1620 K). At this point, the particle is still not in full liquid state, it takes another 0.0001 ms for the liquidus temperature reaches the centre of the particle, which implies that the phase transformation is almost instantaneous once the surface reaches the liquidus temperature for this small 10 μm particle. When the particle is in full liquid state, the surface temperature starts to rise quickly and reaches the maxima. Fig. 8 shows that the gas temperature declines sharply outside the gun and the heat transfer from gas to particle is reversed when the gas temperature drops below the particle temperature. From the maximum value, the surface temperature of particle starts to decrease, drops to liquidus temperature at 0.34 ms and reach the solidus temperature at 0.41 ms. From that point, the particle becomes solid instantaneously and the temperature of particle declines further. Fig. 15 shows the surface temperature of 5 μm particle. In comparison to the profile of 10 μm particle, the 5 μm particle has much shorter melting and solidification periods (0.003 ms of melting for 5 μm particle against 0.11 ms of melting for 10 μm particle); over-heating in liquid state (up to 2000 K in
Fig. 15. Surface temperature profile for 5 μm size particle.
5 μm particle against up to 1700 K for 10 μm particle); and further cooling in solid state (down to 1000 K in 5 μm particle against down to 1400 K for 10 μm particle). 5. Conclusions A 3-dimensional CFD model, using Fluent 6.3 has been developed to investigate the particle dynamic behaviour in a liquid fuelled HVOF spray gun using kerosene. The model employed a Lagrangian particle tracking frame coupled with a steady-state gas flow field to examine particle motion and heat transfer during HVOF spraying. The following conclusions have been obtained. • The computational results show that the particle dynamics vary at different injection velocity. For this Inconel 718 powder, 20 μm particles may hit the internal surface of the barrel and the trajectory may be changed to opposite direction as the result of elastic collision at injection velocity above 20 m/s. An optimal range is found between 8 to 10 m/s where most powder particles could be directly towards the centre of the gun. • Both velocity and temperature profiles of particle dynamics are improved with injection position closer the throat of the nozzle. A suitable location for powder injection is dependent on the powder feeding system to overcome the pressure fluctuation near the throat. • The particle trajectories show that the small particles are greatly affected by the gas flow, the particles smaller than 5 μm have good possibility to make direct contacts with nozzle wall and particles above 20 μm could cross the centre of the gun with a wide spread of coating area. • The history of particle temperature results show that the particles smaller than 5 μm will be overheated while the particles larger than 10 μm may never reach the liquid state during the process. For a typical stand-off distance used in this simulation (0.32 m from the gun's exit), all the particles are in full solid state prior to impact while the particle smaller than 10 μm undergo melting and solidification.
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References [1] G.D. Power, E.B. Smith, T.J. Barber, L.M. Chiapetta, Analysis of a Combustion (HVOF) Spray Deposition Gun, UTRC Report No. 91-8, UTRC, East HARTFORD, CT, 1991. [2] E.B. Smith, G.D. Power, T.J. Barber, L.M. Chiapetta, in: C.C. Berndt (Ed.), Application of Computational Fluid Dynamics to the HVOF Thermal Spray Gun, Thermal Spray: International Advances in Coatings Technology, ASM International, Materials Park, OH, 1992, p. 805. [3] W.L. Oberkampf, M. Talpallikar, J. Therm. Spray Technol. 05 (01) (1996) 53. [4] W.L. Oberkampf, M. Talpallikar, J. Therm. Spray Technol. 05 (01) (1996) 62. [5] B. Hassan, W.L. Oberkampf, R.A. Neiser, T.J. Roemer, in: C.C. Berndt (Ed.), Computational Fluid Dynamic Analysis of a High Velocity OxygenFuel(HVOF) Thermal Spray Torch, Thermal Spray Science and Technology, ASM International, Materials Park, OH, 1995, p. 193. [6] A.R. Lopez, B. Hassen, W.L. Oberkampf, R.A. Neiser, T.J. Roemer, J. Therm. Spray Technol. 07 (03) (1998) 374. [7] S. Gu, C.N. Eastwick, K.A. Simmons, D.G. McCartney, J. Therm. Spray Technol. 10 (03) (2001) 461.
[8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
M. Li, P.D. Christodes, Chem. Eng. Sci. 60 (2005) 3649. S. Kamnis, S. Gu, Chem. Eng. Process. 45 (4) (2006) 246. M. Li, P.D. Christofides, Chem. Eng. Sci. 61 (2006) 6540. M. Li, P.D. Christofides, J. Therm. Spray Technol. 13 (2004) 108. M. Li, P.D. Christofides, Chem. Eng. Sci. 59 (2004) 5647. X. Yang, S. Eidelman, J. Therm. Spray Technol. 5 (1996) 175. S. Kamnis, S. Gu, Chem. Eng. Sci. 61 (16) (2006) 5427. FLUENT User Manual 6.3, Fluent Europe, Sheffield Business Park, Europa Link, Sheffield, S9 1XU, UK, 2006. L. Pawlowski, The Science and Engineering of Thermal Spray Coatings, John Wiley & Sons, England, 1995. S.A. Morsi, A.J. Alexander, J. Fluid Mech. 55 (1972) 193. A. Haider, O. Levenspiel, Powder Technol. 58 (1989) 63. E. Bourdin, P. Fauchais, M.I. Boulos, Int. J. Heat Mass Transfer 26 (1983) 567. V.V. Sobolev, J.M. Guilemany, Int. Mater. Rev. 41 (1) (1996) 13. M.C. Flemings, Solidification Processing, McGraw-Hill, New York, NY, 1974. W.E. Ranz, W.R. Marshall, Chem. Eng. Prog. 48 (1952) 141. G. Pottlachera, H. Hosaeusa, B. Wilthana, E. Kaschnitzb, A. Seiftera, Thermochim. Acta 382 (2002) 255.
Surface & Coatings Technology 202 (2008) 2715 – 2724 www.elsevier.com/locate/surfcoat
Mathematical modelling of Inconel 718 particles in HVOF thermal spraying S. Kamnis, S. Gu ⁎, N. Zeoli School of Engineering Science, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom Received 21 June 2007; accepted in revised form 1 October 2007 Available online 16 October 2007
Abstract High velocity oxygen fuel (HVOF) thermal spray technology is able to produce very dense coating without over-heating powder particles. The quality of coating is directly related to the particle parameters such as velocity, temperature and state of melting or solidification. In order to obtain this particle data, mathematical models are developed to predict particle dynamic behaviour in a liquid fuelled high velocity oxy-fuel thermal spray gun. The particle transport equations are solved in a Lagrangian manner and coupled with the three-dimensional, chemically reacting, turbulent gas flow. The melting and solidification within particles as a result of heat exchange with the surrounding gas flow is solved numerically. The in-flight particle characteristics of Inconel 718 are studied and the effects of injection parameters on particle behavior are examined. The computational results show that the particles smaller than 10 μm undergo melting and solidification prior to impact while the particle larger than 20 μm never reach liquid state during the process. © 2007 Elsevier B.V. All rights reserved. Keywords: CFD; HVOF; Gas dynamics; Particle modeling
1. Introduction High velocity oxy-fuel (HVOF) thermal spraying offers a versatile technology to produce protective coatings, typically 200 to 500 μm thick, on the surfaces of engineering components. Materials being sprayed include metallic alloys, cermets, and polymers. In the HVOF process, oxygen and fuel are mixed and burnt in a combustion chamber at high flow rates (up to 1000 liter/min) and pressures (up to 12 bar) in order to produce a high-temperature (up to 3000 K), high-speed (up to 2000 m/s) gas jet. Powder particles, normally in the size range 5 to 65 μm, are injected into the gas jet so that they are heated and accelerated toward the substrate to be coated. On arrival at the substrate, particles are ideally in a melted or softened state and, on impact, form lenticular splats, which adhere well to the substrate and to one another. The HVOF gun is scanned cross the substrate to build up the required coating thickness in a number of passes.
⁎ Corresponding author. Tel.: +44 23 8059 8520; fax: +44 23 8059 3230. E-mail addresses: [email protected] (S. Kamnis), [email protected] (S. Gu). 0257-8972/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2007.10.006
In HVOF spraying, the feedstock powder has density three or four orders of magnitude greater than the gas density; its other thermophysical properties are also significantly different from those of gas. A typical approach for modelling this multiphase flow is to treat gas and powder as separate gas and particle phases. The equations that describe the particle motion are solved in a Lagrangian frame and coupled with the Eulerian gas flow. The Euler–Lagrange approach has been used for the modeling of particle-gas interaction in various HVOF thermal spray systems [1–7]. However, most of the particle models are based on the gas fuelled HVOF systems [1–12] while the technology trend is moving towards high throughput liquid fuelled systems which have the advantage of using low cost fuel such as kerosene instead of propylene. The existing simulations on liquid fuelled HVOF guns are very limited. The early model from Yang et al. [13] is 2-dimensional which could not correctly represent the 3-dimensional design of gun and powder injection method. This paper reports the authors' continuation of research on liquid fuelled HVOF system from their latest work [14] which has shown 3-dimensional gas flow patterns of a kerosene burning gun. The purpose of this study is to examine particle motion and heat transfer within the gas flow field by investigating the effect of particle injection parameters.
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Nomenclature CD Cp D dp FD F gx H Hsf kg ks kc Pr Re St r T TL Ts Tk t up ug
drag coefficient particle specific heat capacity (J kg− 1 K− 1) barrel diameter (m) particle diameter (m) drag force per unit particle (N) solid fraction x component of gravitational acceleration (m2 s− 1) convective heat transfer coefficient (W m− 2 K− 1) latent heat (J Kg− 1) gas thermal conductivity (W m− 1 K− 1) particle thermal conductivity (W m− 1 K− 1) partition coefficient Prandtl number (cpμ Κ∞− 1) Reynolds number based on particle diameter Stokes number particle radius temperature (K) liquidius temperature (K) solidus temperature (K) primary element melting temperature (K) time (seconds) particle velocity (m s− 1) gas velocity (m s− 1)
Greek symbols Α thermal diffusivity (m2 s− 1) μg gas viscosity (kg m− 1 s− 1) ρp particle density (kg m− 3) ρg gas density (kg m− 3) ϕ shape factor Ψ(T) correction function Δt time step (s) Δr grid node distance (m) 2. Model development A schematic representation of the HVOF gun is shown in Fig. 1. The mixture of fuel and oxygen stream is injected into the water-cooled combustion chamber, where the gases burn and the combustion products are accelerated down the convergent divergent nozzle and long parallel-sized barrel. Powder particles are injected into the barrel through two holes with a tapping angle in the front of the barrel. The particle laden by gas mixture exits the gun at a high-temperature and velocity toward the substrate to be coated. The three-dimensional simulations are performed in the commercially available finite volume CFD code Fluent 6.3 [15]. The computational geometry includes the gun and external domain as shown in Fig. 2. The grid structure and boundary conditions has been described in [14]. Briefly, a structured grid is used and fine meshes are employed to the sensitive areas such as, the nozzle entrance and exit, the barrel exit and the free-jet centreline where high gradients are ex-
pected and great accuracy is required in order to capture the compressibility effects. Grid sensitivity studies have been carried out by doubling the cell number both axially and radially and the numerical solutions from both meshes are almost identical. The compressible turbulent chemically reacting flow model has been described in [14] and only a brief introduction is given here. For the combustion of kerosene, C12H26 is used to have a representative average value for the individual components. The combustion kinetics is represented by one global reaction scheme which takes dissociations and intermediate reactions into account. n1 C12 H26 þ 18:5n2 O2 →12n3 CO2 þ 13n4 H2 O þ n5 CO þ n6 OH þ n7 O2 þ n8 O þ n9 H2 þ n10 H: These coefficients are dependent on variables such as the combustion chamber pressure, fuel to oxygen ratio, mass flow rate or even the torch geometry. To derive those coefficients, an iterative approach based on a chemical equilibrium model is
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Fig. 1. Schematic representation of the HVOF gun including combustion chamber, convergent divergent nozzle (CDN) section and parallel-sized barrel.
employed to make sure the coefficients representing the correct pressure level and thermal flow field. The eddy dissipation model is used to solve this global reaction. This approach is based on the solution of transport equations for species mass fractions. The reaction rates are assumed to be controlled by the turbulence instead of the calculation of Arrhenius chemical kinetics. The process parameters employed in the computational modelling are 0.003526 kg/s for kerosene and 0.01197 kg/s. The computation of particle dynamics is achieved by coupling
with the Eulerian gas flow. The powder is treated as spherical particles which closely represent the thermally sprayed powder, Inconel 718 which has the composition shown in Table 1 and thermal properties shown in Table 2. The computer model treats the powder feeding as a point injection through the barrel's wall without carrier gas being introduced to the computational domain. Unlike a gas fuelled HVOF system where the carrier gas is injected into the centre of the combustion chamber, the introduction of cross flow carrier gas into a high-speed stream
Fig. 2. Grid and computational domain.
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Table 1 Chemical composition of the Inconel 718 powder (wt.%)
The Reynolds number is defined by
Element
Min
Max
Carbon Manganese Silicon Phosphorus Sulfur Nickel + Cobalt Chromium Cobalt Iron Aluminium Molybdenum Titanium Boron Copper Cb + Ta
– – – – – 50.0 17.0 – Balance 0.35 2.80 0.65 0.001 – 4.75
0.08 0.35 0.35 0.015 0.015 55.0 21.0 1.00 Balance 0.80 3.30 1.15 0.006 0.15 5.50
has given rise to numerical errors and difficulty to control the convergence of the solutions. Considering that the volume fraction of carrier gas is less than 2% of the total flow rate, the carrier gas is expected to have only marginal effect on the flow pattern and the subsequent effect on the behaviour of particles could be marginal. 3. Mathematical models 3.1. Momentum transfer equations The acting force in the particle could involve the drag force, force due to pressure gradients, force due to added mass, Basset history term and external potential forces [16]. In principle, among the factors that affect the movement of particle during the HVOF process, only the drag force plays a dominant role, other factors can be neglected in most cases [16]. The equation of motion for particles can be written as a force balance that equates the droplet inertia with forces acting on the droplet: g z q p qg dup ¼ FD ug up þ ð1Þ qp dt
Re ¼
qg jug up jdp Ag
ð5Þ
As the gas flow is turbulent during HVOF spraying, the influence of the turbulence on the particle behavior needs to be evaluated. The effect of turbulent fluctuation on the particle aerodynamic response could be reflected by the Stokes number (St) which is the ratio of the aerodynamic response time to the time scale associated with larger-scale turbulent eddies. St ¼
qp dp up 18Ap D
The large Stokes number (St &Z.Gt; 1) means a slow response from the particle to the large turbulent eddies. The sprayed powder Inconel 718 with a mean diameter of 20 μm under the present HVOF flow has the Stokes number: St ≈ 300, which implies that the turbulence would not have substantial effect on the particles larger than 20 μm. 3.2. Heat transfer equations The study of heat transfer in thermal spray process [19] demonstrates that the heat transfer due to radiation from the surroundings to particles is negligible compared to the convective heat flux from the gas to the particle, in that case, the particle heating in spherical coordinates is given by: 2 AT A T 2 AT df qp Cp ¼ ks ð6Þ þ þ Hsf qp 2 At Ar r Ar dt Considering an alloy for which the area of solidification in the phase diagram is approximated by straight lines, Eq. (6) can be written as: 2 AT a A T 2 AT ¼ þ ð7Þ At wðT Þ Ar2 r Ar Where the function ψ(T) is defined as [20]: 8 1 > Hsf ðTk TL Þ 1kc < if TS VT VTL 1 þ 2kc wðT Þ Cp ð1 kc ÞðTk T Þ 1kc > : else 1
The drag force per unit particle mass is: 18Ag CD Re FD ¼ qp dp2 24
ð2Þ
Table 2 Thermophysical properties for Inconel 718 [23]
the drag coefficient CD given by Morsi [17]: 24 b3 Re 1 þ b1 Rebd2 þ CD ¼ Re b4 þ Re b1 b2 b3 b4
¼ exp 2:3288 6:4581/ þ 2:4486/2 ¼ 0:0964þ 0:5565/ ¼ exp 4:905 13:8944/ þ 18:4222/2 10:2599/3 ¼ exp 1:4681 þ 12:2584/ 20:7322/2 þ 15:8855/3
the shape factor ϕ is given by Haider [18].
Tk is the melting temperature of the primary element and k is the ratio between solid and liquid concentration.
ð3Þ
ð4Þ
Density (ρp) (kg/m3)
8200
Solidus temperature (TS) [K] Liquidus temperature (TL) [K] Primary element melting point (Tk) [K] Partition coefficient (kc) Specific heat (Cp) [J/kg K] Latent heat (Hsf) [J/kg] Thermal conductivity (k) [W/m K]
1528 1610 1726 0.3 600 227000 T b 1000 K 1000 b T b 1528 1610 b T
21 5.8 + 0.016T 4.95 + 0.013T
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Fig. 3. Particle trajectories at different injection velocities.
This computational model assumes infinite velocity for diffusion (equilibrium condition) in liquid phase and zero in the solid [21]. The boundary conditions associated to Eq. (7) are specified on the surface and in the centre of the particle as:
improve the accuracy of the melting and solidification kinetics. In the same manner, Eq. (8) becomes: hn Dr hn Dr nþ1 þ 1 n TNnþ1 ¼ n Tg ð12Þ TN1 ki ki
AT Ar
Eq. (7) in the centre (r = 0) becomes indeterminate, this means that the relation in Eq. (11) will not be applicable. By applying the theorem of L'Hospital, it is found:
¼ 0; r¼0
AT ks Ar
¼ h T g TR
ð8Þ
r¼R
R represents the radius of the simulated particle, ks is thermal conductivity of particle, Tg is the gas temperature and h is the convective heat transfer coefficient. The heat transfer coefficient is evaluated using the Ranz and Marshall correlation [22]: Nu ¼ 2 þ 0:6Re1=2 Pr1=3
ð9Þ
where Nu is the non-dimensional Nusselt number, defined as: Nu ¼
hdp kg
AT a A2 T ¼3 At wðT Þ Ar2 The discretized form of Eq. (13) is: Dt Dt wn0 þ 3a 2 T0nþ1 3a 2 T1nþ1 D r D r Dt Dt ¼ wn0 3a 2 T0n þ 3a 2 T1n D r D r
ð10Þ
nþ1 nþ1 Dt 1 Dt Dt n T nþ1 a 2 i1 þ 1 Tiþ1 1 T þ 2w þ 2a i i i1 D2 r D2 r i D r n Dt Dt Dt n ¼ a 2 ð1 i1 ÞTi¼1 þ 2wni 2a 2 Tin þ a 2 i1 þ 1 Tiþ1 D r D r D r
a
ð11Þ
N is the number of discretization points along the radius of the droplet and n is the time index. After grid sensitivity analyses to all particle sizes the nodal points were set to 10. For larger particles more discretization points are required to
ð14Þ
At each time step the algebraic system of Eqs. (11), (12) and (14) is solved using the Gauss Seidel iterative method which is implemented as a user defined function in the simulation. The
The discretized form of Eq. (7) is:
i ¼ 1; 2; N N 1
ð13Þ
Fig. 4. Particle velocity profiles at different injection velocities.
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Fig. 5. Particle surface temperature profiles at different injection speeds.
simulation time step is set to 10− 6 s and the convergence condition to 10− 4.
4. Computational results and discussions 4.1. Influence of particle injection velocity The particle injection velocity can be manipulated by carrier gas flow rate. In this calculation, 20 μm diameter Inconel 718 particles are injected from the axial distance of 0.12 m. The injection velocities vary in the range 0–40 m/s. The particle trajectories in Fig. 3 show that the particle is driven by the gas flow and travels along the edge of barrel with zero injection speed; the increase of injection velocity will enable the particle travel cross the gas flow and move towards the centre of the jet at injection speed between 8–10 m/s; the particle travels cross the centre of the gun and spreads outwards at injection speed at 20 m/s; the particle hits the internal surface of the barrel and the trajectory is changed to opposite direction as the result of elastic collision at 40 m/s. Nozzle wear is most frequently encountered
problem for operating HVOF guns and the nozzle needs to be replaced after about 10 h spraying. Examination of the damaged nozzles reveals the particle pathlines along the internal surface of the barrel and cracks in the nozzle by the impact of highspeed particles. The computational results imply that, to spray Inconel 718 powder with a mean diameter of 20 μm, the injection speed needs to be controlled within the range of 8– 10 m/s, in that case, and particularly at 8 m/s, most powder particles will stay in the centre of the gun; powder particles will spread outwards by increase of the injection velocity over 10 m/ s; the particle is most likely to hit the barrel and give rise to nozzle wear when the injection velocity increased above 20 m/s. Zero injection velocity should also be avoided as the particle travels along the edge of barrel, the particle could make mechanical contacts with the barrel or the molten particle could stick on the internal surface of the nozzle and generate the blockage. The advantage of HVOF technology is its ability to accelerate particles to very high speed, therefore, it is desirable to achieve the highest possible velocity of powder particles during the spraying. The velocity profiles in Fig. 4 show that the particles reach high velocity when injection velocity is between 8 to 10 m/s. It is known that the gas flow has the highest velocity in the centre; therefore particles will gain more momentum while traveling in that region. The temperature profiles in Fig. 5 confirm that the particles heated more efficiently for 8–10 m/s injection velocity when the particles travel at the centre of the gas jet. 4.2. Influence of particle injection position The liquid fuelled HVOF gun is designed to inject powders at the front of the barrel instead of feeding the spray powder into the centre of the combustion chamber adopted in gas fuelled HVOF systems such as HV2000 (Praxair, US). The advantage of such design is to suppress the contacts between powders and the gas flame to minimize the undesirable
Fig. 6. Particle velocity profiles from different injection positions.
S. Kamnis et al. / Surface & Coatings Technology 202 (2008) 2715–2724
oxidation for metal powders. The location of injection is also important to generate consistent coating products. The high pressure gas undergoes drastic expansion and compression in the throat of the nozzle as shown in Fig. 6, the substantial pressure fluctuation makes the control of powder feeding very difficult, therefore, it is not practical to inject powders in the throat region. In this calculation, 20 μm Inconel 718 particles are released from 5 axial locations between 0.10 and 0.15 m in the front of the barrel at injection velocity of 8 m/s which is within the range of optimal injection velocities as stated in the previous section. The predicted paths for these particles plotted in Fig. 7 show that all the particles travel at similar trajectory and reach the centre of the jet at the end of the domain. The velocity profiles in Fig. 6 demonstrate that the particles accelerate continuously throughout the domain despite the decline of gas jet near the end of the domain. It is known that the longer distance prolongs the residual time of in-flight particle and the particle accelerates more, therefore, it is sensible to inject powder at the earliest possible point when the gas flow is stabilized. The particle temperature profiles in Fig. 8 show that powder particles are heated rapidly in the barrel and develop steadily from the exit of the gun, the particle temperatures start to decline when the temperature of gas flow drops sharply when cold air penetrates deeply into the gas jet. The computational model has an external domain of 32 cm from the gun exit, which is within the typical range of stand-off distances for the HVOF spray coating. The particle dynamics at the exit of the computational domain (i.e. 32 cm from the gun exit) can be regarded as the impact parameters. The particle impact parameters in Fig. 9a show that the surface temperatures of particles drop below the melting point (1528 K for the Inconel 718 powder). The set of results imply that the particles at the given injection speed will concentrate at the centre of the jet and have similar dynamics from different axial injection distances, while the high impact velocity and temperature will achieve at axial distance closer to the throat of CDN as shown in Fig. 9b. However, too close to the throat of CDN will give rise to practical issue of controlling the pressure fluctuation for the powder feeder, the axial distance of
Fig. 7. Particle trajectories from different injection positions.
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Fig. 8. Particle surface temperatures from different injection positions. (a) Temperature prior to impact. (b) Velocity prior to impact.
0.12 m is adopted in the current design and will be used for the following discussions. 4.3. Influence of particle size Feedstock powder is generally supplied with a range of distribution. This study is to examine the effect of different particle sizes on particle behaviour to provide information on
Fig. 9. Particle impact parameters from different injection positions.
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Fig. 10. Trajectories for different size particles.
the optimum range within the nominal size distribution. In these calculations, different sized Inconel 718 particles ranging from 5 μm to 40 μm were injected at axial distance of 0.12 m with a speed of 8 m/s. The particle trajectories in Fig. 10 show that the small particles are blown away by the gas flow, e.g. 5 μm particle travels along the edge of the barrel and spreads outwards at the external domain as the jet expands outside. The 10 μm particle remains at the outer region of the jet throughout the domain while the large particles e.g. 30 and 40 μm move cross the centre of the gun and spread outwards in the external domain. The particle velocity profiles in Fig. 11 clearly demonstrate that the smaller particles are accelerated more throughout the computational domain. When the particle velocity is higher than the gas velocity, as the gas jet decays outside the gun, the drag force on the particle then changes direction and becomes a resistance to the particle motion. The velocity of the particle is then decreased. The smaller the particle size, the more easily it is decelerated. A larger particle, on the other hand, has greater ability to maintain its velocity during the deceleration stage, because of its larger inertia. The velocity dependence on particle size is more clearly demonstrated in Fig. 12a which is a plot of particle velocity versus particle diameter at the point of impact on the substrate. The temperatures at the impact in relation to the particle size are
Fig. 12. Impact parameters for different size particles.
given in Fig. 12b. The surface temperature plots in Fig. 13 show the particles smaller than 10 μm undergo melting and solidification during the process which will be discussed in details in the following section. 4.4. Melting and solidification within particles The temperature evolution of 10 μm particle in Fig. 14 shows the rapid heating of particle come to a stop when the surface
Fig. 11. Velocity profiles for different size particles. (a) Velocity prior to impact. (b) Temperature prior to impact.
Fig. 13. Temperature profiles for particles at different sizes.
S. Kamnis et al. / Surface & Coatings Technology 202 (2008) 2715–2724
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Fig. 14. Surface temperature profile for 10 μm size particle.
temperature arrives at the solidus temperature (1528 K) at 0.18 ms. The surface temperature increases slowly as the solidus isothermal surface moves towards the centre of the particle. At 0.29 ms the surface temperature reaches the liquidus temperature (1620 K). At this point, the particle is still not in full liquid state, it takes another 0.0001 ms for the liquidus temperature reaches the centre of the particle, which implies that the phase transformation is almost instantaneous once the surface reaches the liquidus temperature for this small 10 μm particle. When the particle is in full liquid state, the surface temperature starts to rise quickly and reaches the maxima. Fig. 8 shows that the gas temperature declines sharply outside the gun and the heat transfer from gas to particle is reversed when the gas temperature drops below the particle temperature. From the maximum value, the surface temperature of particle starts to decrease, drops to liquidus temperature at 0.34 ms and reach the solidus temperature at 0.41 ms. From that point, the particle becomes solid instantaneously and the temperature of particle declines further. Fig. 15 shows the surface temperature of 5 μm particle. In comparison to the profile of 10 μm particle, the 5 μm particle has much shorter melting and solidification periods (0.003 ms of melting for 5 μm particle against 0.11 ms of melting for 10 μm particle); over-heating in liquid state (up to 2000 K in
Fig. 15. Surface temperature profile for 5 μm size particle.
5 μm particle against up to 1700 K for 10 μm particle); and further cooling in solid state (down to 1000 K in 5 μm particle against down to 1400 K for 10 μm particle). 5. Conclusions A 3-dimensional CFD model, using Fluent 6.3 has been developed to investigate the particle dynamic behaviour in a liquid fuelled HVOF spray gun using kerosene. The model employed a Lagrangian particle tracking frame coupled with a steady-state gas flow field to examine particle motion and heat transfer during HVOF spraying. The following conclusions have been obtained. • The computational results show that the particle dynamics vary at different injection velocity. For this Inconel 718 powder, 20 μm particles may hit the internal surface of the barrel and the trajectory may be changed to opposite direction as the result of elastic collision at injection velocity above 20 m/s. An optimal range is found between 8 to 10 m/s where most powder particles could be directly towards the centre of the gun. • Both velocity and temperature profiles of particle dynamics are improved with injection position closer the throat of the nozzle. A suitable location for powder injection is dependent on the powder feeding system to overcome the pressure fluctuation near the throat. • The particle trajectories show that the small particles are greatly affected by the gas flow, the particles smaller than 5 μm have good possibility to make direct contacts with nozzle wall and particles above 20 μm could cross the centre of the gun with a wide spread of coating area. • The history of particle temperature results show that the particles smaller than 5 μm will be overheated while the particles larger than 10 μm may never reach the liquid state during the process. For a typical stand-off distance used in this simulation (0.32 m from the gun's exit), all the particles are in full solid state prior to impact while the particle smaller than 10 μm undergo melting and solidification.
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