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Computational analysis of the effect of nozzle cross-section shape on gas flow and particle acceleration in cold spraying
Surface & Coatings Technology 205 (2011) 2970–2977
Contents lists available at ScienceDirect
Surface & Coatings Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s u r f c o a t
Computational analysis of the effect of nozzle cross-section shape on gas flow and particle acceleration in cold spraying Shuo Yin a,⁎, Xiao-fang Wang a, Wen-ya Li b a b
School of Energy and Power Engineering, Dalian University of Technology, No.2, Linggong Road, Dalian, Liaoning 116024, China Shaanxi Key Laboratory of Friction Welding Technologies, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
a r t i c l e
i n f o
Article history: Received 20 July 2010 Accepted in revised form 1 November 2010 Available online 9 November 2010 Keywords: Cold spraying Numerical simulation Powder release position Nozzle shape Particle acceleration
a b s t r a c t In cold spraying, the spraying of certain complicated surfaces may require nozzles with special cross-sections. In this study, numerical investigation is conducted to study the effect of nozzle cross-section shape on gas flow and particle acceleration in cold spraying. The comprehensive comparison between rectangular nozzles and elliptical nozzles indicates that rectangular nozzles result in slightly lower mean particle impact velocity than elliptical nozzles. However, for rectangular nozzles, more particles may achieve relatively high velocity due to the larger sectional area of their potential core. Furthermore, it can also be found from the numerical results that the mean particle impact velocity increases gradually with the decrease in Width/Length ratio (W/L) of the cross-section because of the diminishing bow shock size. However, when reducing the W/L to 0.2, the mean particle impact velocity begins to decrease steeply, which may be attributed to the rather small area of the potential core for the case of W/L = 0.2. Moreover, the systematic study on the powder release position shows that releasing particles from the nozzle inlet can ensure that particles achieve a high impact velocity and temperature. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Cold spraying (CS) represents a radical difference from conventional thermal spraying methods. The deposition process relies mainly on kinetic energy rather than the combination of thermal and kinetic energies of spraying particles. In this process, spraying particles (typically b50 μm) are accelerated to a high velocity (ranging from 300 to 1200 m/s) by a high speed gas flow, and a coating is formed through the intensive plastic deformation of particles at a temperature well below the melting point [1]. Despite the fact that CS is attracting more and more attention from the world due to its unique advantages, such as the deposition of oxygen-free metallic coatings, there still exist some important concerns to be well revealed. It has been well known that there exists a material-dependent critical velocity, above which particles can adhere to the substrate and form a coating [2,3]. Therefore, the relationship between particle velocity and deposition efficiency has been extensively studied in recent years [4,5]. In addition, there has also been growing interest in gas flow and particle acceleration during the past few years. The existing studies on this field mainly focused on two aspects, including the optimal design of the spraying nozzle and the examination on spraying parameters.
⁎ Corresponding author. Tel./fax.: +86 411 84707905. E-mail address: [email protected] (S. Yin). 0257-8972/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2010.11.002
The optimal design of CS nozzles is always based on the principle of high particle impact velocity at the substrate surface. In 1998, Dykhuizen et al. [6] reported an original work, providing some analytical equations that allow the optimal design for a CS nozzle. Alkhimov et al. [7] also presented a calculating model to optimize the nozzle geometrical dimension and verified their model by experimental data. Later, Li et al. [8,9] optimized the dimension of converging-barrel nozzle (CB) and converging–diverging (CD) nozzle based on their simulation results. Jodoin [10] found the optimal exit Mach number of 1.5–3.0 that can ensure spraying particles to achieve sufficient acceleration. Recently, Pattison et al. [11] reported that medium standoff region (ranging from 60 mm to 120 mm) from the nozzle outlet is the optimal distance for locating the substrate. As for the investigation on spraying parameters, Stoltenhoff et al.'s study [12] showed the effect of inlet stagnation pressure, inlet stagnation temperature, particle diameter and standoff distance on gas flow and particle acceleration using the commercial software FLUENT. Some further experiments conducted by other researchers provided evidence to Stoltenhoff et al.'s numerical results [11,13]. The influence of particle size on particle acceleration was also studied in detail by Jen et al. using numerical method [14]. Meanwhile, they paid special attention to the gas flow structure inside and outside the nozzle, obtaining an insight into the flow field [14]. Moreover, Samareh et al. [15] analyzed the effect of substrate shape on gas flow structure, particle impact velocity and particle footprint distribution at the substrate based on three-dimensional models.
S. Yin et al. / Surface & Coatings Technology 205 (2011) 2970–2977
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Fig. 1. Schematic and dimensions of the geometries used in numerical model.
Besides, some previous studies also focused on other relevant fields. Nickel et al. [16] reported a new CS variant based on the combined application of shock tube facility with a Laval-nozzle and verified this system by both experimental and numerical methods. The most recent study conducted by Han et al. [17] provided a systematical examination on several new powder injector configurations by both computational simulations and experimental tests in order to find a better configuration for promoting the CS coatings. Notwithstanding these meaningful findings, several important problems still need to be further studied. In actual application, some work-pieces with complicated surface may require nozzles with special cross-section shape. In this study, as a first approximation, numerical investigation is conducted on some types of oblate nozzles (rectangular and elliptical) to clarify the effect of cross-section shape on gas flow and particle acceleration, aiming to find a preferable nozzle that can increase the particle impact velocity. On the other hand, it is known that the centerline velocity of a single particle was always employed to characterize the particle impact velocity in previous studies. However, in actual CS process, the particle relative position to the centerline and the particle size distribution significantly affect the particle acceleration and thus the impact velocity. The single particle centerline velocity should not represent the real impact velocity of spraying particles. In this study, owing to the adoption of three-dimensional models, the distribution of particle position and size can be considered. The mean particle impact velocity which is defined as the average velocity of all spraying particles is proposed to clarify the effect of the nozzle crosssection shape on particle impact velocity. Moreover, it has been accepted that powder injector is an important device in CS system, which significantly influences particle impact velocity and temperature. Generally, installing the injector in a preheat chamber before the nozzle inlet is beneficial to the coating formation, but requires relatively high feed pressure for introducing particles. Also, A.I. Kashirin et al. reported that if particles are released
downstream of the nozzle throat, the feed pressure can be lower than the ambient pressure and particles can be easily introduced by the airflow [18], although the impact velocity and temperature could decrease to some extent. In this study, a numerical investigation is also conducted based on performance perspective to find the effect of powder release position on particle impact velocity and temperature.
Table 1 Dimensions of all these geometries at three typical cross-sections used in this simulation. W/L ratio
a, inlet (mm)
b, throat (mm)
c, outlet (mm)
0.2 0.4 0.6 0.8 1.0
2 4 6 8 10
0.4 0.8 1.2 1.6 2.0
0.8 1.6 2.4 3.2 4.0
Fig. 2. Grid at the outlet cross-section for (a) rectangular nozzle and (b) elliptical nozzle (W/L = 1.0).
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2. Numerical methodology 2.1. Geometry The schematic and dimensions of the geometries used in numerical model is shown in Fig. 1. The convergent part has a length of 30 mm and is attached to the throat part as well as the following divergent part with a length of 40 mm. Elliptical nozzles and rectangular nozzles with different Width/Length (W/L) of the crosssection were employed, namely, 0.2, 0.4, 0.6, 0.8 and 1.0. Table 1 summarizes dimensions of all these geometries at three typical crosssections used in this simulation. The long edge of the nozzle crosssection is fixed, and only the short edge changes to keep the same expansion ratio for every case. The long edge for the inlet, throat and outlet cross-section is chosen as 10 mm, 2 mm and 4 mm, respectively. The exit to throat area ratio is chosen as 4 to ensure sufficient acceleration of spraying particles. The flat substrate is located at a distance of 20 mm away from the nozzle exit along the centerline. Generally, particles are released axially from the inlet cross-section to ensure particles can achieve high impact velocity. As for the study on powder release position, nozzles with the W/L ratio of 1.0 are employed and only a single particle is released inside the nozzle along the centerline.
2.2. Computational domain and boundary conditions
Fig. 3. Effect of powder release position on: (a) particle impact velocity and (b) particle impact temperature along the centerline.
Numerical simulations are performed by using FLUENT 6.2 (Fluent Inc., Lebanon, NH) to predict the flow flied of the driving gas and the acceleration of spraying particles in CS. Three-dimensional plane symmetrical models are utilized to reduce the computation time. The computational domain is partitioned into a number of hexahedral cells and the surrounding region of the centerline is refined to ensure the calculation accuracy as a result of generation of the shockwaves in the supersonic flow as indicated in Fig. 2. The total number of grid cells varies between 189 550 and 950 000 depending on the nozzle cross-section shape. A grid dependency test is also performed to
Fig. 4. Contours of (a) gas pressure and (b) velocity at the XY symmetrical plane for nozzles with different W/L.
S. Yin et al. / Surface & Coatings Technology 205 (2011) 2970–2977
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the computational domain is at the same plane that the substrate is located and treated as pressure outlet with the pressure of 0.1 MPa. Standard no-slip condition is used at the nozzle wall and the substrate surface. The heat transfer process between the gas and the wall is not considered, thus a fixed heat flux of zero is enforced at the wall. 2.3. Gas phase and particle phase N2 is chosen as the driving gas in this study. The ideal gas law is used to calculate the density in order to take the compressibility effects into consideration. The governing equations for gas flow include the physical laws of conservation of mass, momentum, and energy. Because the coupled scheme obtains a robust and efficient single phase implementation for steady-state flows, a coupled implicit method is used to solve the flow field and the result of flow field in a steady state is obtained. In order to capture the turbulent flow features accurately, the standard K-ε turbulence model available in FLUENT is utilized for modeling the turbulent flow in the simulation. The choice is made following the work of Li et al. [8,9]. The standard wall function is chosen for the near-wall flow treatment. Copper is used as the spraying particle material. The acceleration of particles is computed using discrete phase modeling (DPM). The model requires that the discrete phase must be present at sufficiently low volume fractions. In this case, all the spray particles are spherical in shape and hence the spherical drag law is used to compute the drag coefficient. Particle–particle interactions and the effect of particles on the gas phase can be neglected. The drag force can be expressed by the following equation: Fd =
18μ Cd Re ρP d2P 24
ð1Þ
where Fd is the drag force, μg is the dynamic viscosity of gas, ρd is the particle density, dp is the particle diameter, Cd is the drag coefficient and Re is the relative Reynolds number, which is defined as:
Re = Fig. 5. Pressure variations along the centerline for nozzles with W/L: (a) elliptical nozzles and (b) rectangular nozzles.
ensure that the solution dependency on the grid size is b2%. The nozzle inlet is treated as pressure inlet with the pressure of 2.5 MPa and temperature of 600 K. The pressure-far-field boundary is applied to the surrounding atmosphere outside the nozzle exit. The outlet of
ρg dp Vg −Vp μg
ð2Þ
where ρg is the gas density, Vp is the particle velocity and Vg is the gas velocity; this equation can be practically applied to a Re b 50000. The drag coefficient Cd can be expressed as: Cd = a1 +
a2 a + 32 Re Re
ð3Þ
where, a1, a2 and a3 are constants that are applied to smooth spherical particles over several ranges of Re given by Morsi and Alexander [14,20]. It is also assumed that heat conduction within a particle is neglected and the particle is therefore treated as isothermal. The heating rate is described by: dTp 6h = T −Tp Cpp ρp dp g dt
ð4Þ
where, Tp is the particle temperature, Tg is the gas temperature, Cpp is the heat capacity of particle and h is the heat transfer coefficient and related to the thermal conductivity of gas (λg) by Nusselt number (Nu) as follows:
Fig. 6. Variation of bow shock thickness with W/L for both elliptical nozzles and rectangular nozzles.
h=
λg Nu dp
ð5Þ
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3. Results and discussion 3.1. Effect of powder release position on particle impact velocity and temperature
Fig. 7. Contours of gas velocity at the nozzle outlet cross-section for nozzles with different W/L.
Nusselt number is given by: 1=3
Nu = 2 + 0:6Pr
Re
1=2
ð6Þ
Prandtl number (Pr) is described as:
Pr =
μg Cpg λg
ð7Þ
where, Cpg is the heat capacity of gas. Models describing the dynamic behavior of in-flight particles during the two-phase flow have been well documented in the FLUENT manual [19].
Fig. 8. Schematic of the velocity distribution in fully developed pipe flow.
Fig. 3 gives the effect of powder release position on particle impact velocity and temperature along the centerline using rectangular nozzle and elliptical nozzle (W/L = 1.0). From Fig 3(a), it is clearly seen that with shifting the release position towards the outlet, the particle impact velocity maintains a continuous high value at the convergent section and decreases gradually at the divergent section. The main reason for this is that driving gas is chiefly accelerated at the throat section and the following divergent section rather than the convergent section. Releasing a particle at the convergent section can ensure the particle to be accelerated completely by the driving gas when passing through the throat section and the divergent section. However, if releasing a particle at the divergent section, the particle is only accelerated at the divergent section. Hence, the particle acceleration time and then impact velocity reduce gradually with shifting the release position from the throat section to the outlet. As for the impact temperature, it decreases with shifting the release position towards the outlet, and the steep decrease presents at the convergent section. This is because the particle chiefly heats up at the convergent section, and shifting the release position towards the outlet can reduce the particle residence time at the convergent section, which leads to the sudden decrease of the particle temperature. From the analysis above, it can be found that releasing particles at the inlet of the nozzle could ensure particles to obtain a relatively high impact velocity and temperature, and thus promoting the deposition efficiency. However, it should be pointed out that some other methods for installing powder injector, such as at the preheat chamber [20] or inside the divergent section [18], also have some advantages as mentioned in the introduction section. Therefore, it is necessary to consider different circumstances and concerns when choosing an installation scheme of powder injector. 3.2. Effect of nozzle cross-section shape on gas flow field Fig. 4 shows contours of the driving gas pressure and velocity for nozzles with different W/L at the XY symmetrical plane. As shown in Fig. 4(a), a well-formed complex wave structure which is composed of oblique shock, expansion wave and bow shock can be clearly observed behind the nozzle exit in each case. The oblique shock near the nozzle outlet is formed due to overexpansion, followed by expansion waves owing to multiple reflections of compression waves at the atmosphere boundary. The reflection can be observed from Fig. 4(a) at the case of W/L = 0.2 and the zone near the atmosphere boundary where gas pressure begins to reverse indicates the occurrence of reflection. In addition, between the nozzle exit and the substrate, there exists a well-formed bow shock in the vicinity of the substrate, which arises from the interaction between the supersonic gas flow and the substrate. The gas pressure and temperature in this bow shock zone is extremely high, which can lead to a sudden deceleration of in-flight particles and off-normal impact on the substrate [15]. These two phenomena can both result in a decrease of deposition efficiency. It also can be found from Fig. 4(a) that some shockwaves are generated surrounding the bow shock zone which also arise from the presence of the substrate. Fig. 4(b) shows contours of the driving gas velocity for nozzles with different W/L at the XY symmetrical plane. From these contours, it is clearly seen that the periodically fluctuant gas velocity is caused by the oblique shock and expansion wave in each case. Inside the bow shock zone, the gas velocity is decelerated to almost zero. The contents reflected from these velocity contours are in harmony with the pressure contours. Moreover, after doing a comparison between nozzles of different W/L, it is found that with decreasing W/L, the amplitude of pressure
S. Yin et al. / Surface & Coatings Technology 205 (2011) 2970–2977
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Fig. 9. Footprint of the particles at the substrate surface for nozzles with different W/L.
fluctuation presents an upward trend and the distance between two adjacent peaks decreases gradually. This variation can be clearly observed in Fig. 5 that shows the gas velocity as a function of position along the centerline in different nozzles. Also, it can be found from Fig. 4 that the size of the bow shock goes down gradually with the W/ L. The variation of bow shock thickness with the W/L ratio as indicated in Fig. 6 gives a more detailed description. With decreasing the W/L, the bow shock thickness decreases gradually. This fact may be attributed to the area of the supersonic potential core. Fig. 7 shows
contours of the gas velocity at the outlet cross-section for nozzles with different W/L. It is clear that the area of the potential core closely relates to the nozzle geometric dimension, reducing with the W/L. Hence, the potential core area that interacts with the substrate also decreases with the W/L, which leads to the decrease of bow shock size. Furthermore, when comparing the elliptical nozzles to the rectangular nozzles as indicated in Fig. 4(a), it can be found that the bow shock size for the elliptical nozzles is slightly smaller than that for rectangular cases, in terms of its thickness. This also can be linked to
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the sectional area of the potential core that interacts with the substrate. Under the same W/L, the sectional area of the potential core is larger for the rectangular case as indicated in Fig. 7, and thus the bow shock is slightly stronger. Form Fig. 7, it can also be seen that the interaction between the nozzle wall and the gas flow results in the decrease of the gas velocity from the centerline towards the nozzle wall due to the viscous effect of the flow. The gas velocity near the wall zone is small with the gas velocity at the center region maintaining a high value. The potential core area is larger than the near-wall low velocity zone. This phenomenon is consistent with the features of the fully developed turbulent pipe flow as indicated in Fig. 8. 3.3. Effect of nozzle cross-section shape on particle acceleration In order to obtain insight in the particle distribution at the substrate surface, Fig. 9 presents the footprint of particles with the diameter of 10 μm at the substrate surface. It can be seen from Fig. 9 that the particle distribution for rectangular nozzles seems equally uniform with that for elliptical nozzles. However, because the sectional area of potential core of rectangular nozzles is larger than that of elliptical nozzles as indicated in Fig. 7, the number of particles inside the potential core zone is bigger for rectangular nozzles. This fact means that under the same W/L, more particles can achieve relative high impact velocity for rectangular nozzles. The distribution of the particle footprint compares well with the gas flow distribution at the outlet section as shown in Fig. 7. Generally, the diameter of CS particles is in the range of 10 μm– 30 μm. In this study, the Rosin-Rammler equation available in FLUENT is employed to distribute the particle diameters, which yields a mean size of 20 μm with a range from 2 μm to 50 μm as shown in Fig. 10. This size distribution is very similar to that in actual CS process. Fig. 11 shows the effect of the nozzle cross-section shape on mean particle impact velocity which is defined as the average velocity of all spraying particles. The standard deviation for each case is also given in Fig. 11. It can be found that with decreasing the W/L, the mean particle velocity rises slightly for both elliptical nozzles and rectangular nozzles. The reason for this phenomenon is that the area of the potential core decreases gradually with the W/L, which results in the decrease of the bow shock strength. Therefore, the negative effect of the bow shock on particle acceleration becomes weak, leading to an upward increment of the mean particle impact velocity. However, it is of great importance to note that when the W/L is decreased to 0.2, the mean particle impact velocity decreases steeply. This is because although the bow shock is the weakest among all cases, which is favorable for particle acceleration, the length and area of the potential core is much smaller and the driving gas cannot accelerate the particles efficiently before they penetrate into the bow shock. Therefore, the mean particle impact velocity is rather low. Furthermore, it also can be found that because rectangular nozzles can yield stronger bow shock compared to elliptical nozzles, the mean particle velocities for the elliptical nozzles are greater than those for the rectangular nozzles in all cases, but the difference is rather slight.
Fig. 10. Size distribution of the spraying particles.
elliptical case is slightly smaller than that for the rectangular case under the same W/L. Hence, the effect of bow shock on particle acceleration is weaker for elliptical nozzles and particles can obtain higher mean particle impact velocity. However, for rectangular cases, more particles may achieve relatively high velocity because their potential core has larger sectional area. Furthermore, it is also found that with decreasing the W/L, the size of the bow shock declines, which results in the gradual increase of the mean particle velocity for both elliptical nozzles and rectangular nozzles. But it is noticed that when the W/L is decreased to 0.2, the mean particle impact velocity begins to decrease steeply, which may be linked to the very small area of the potential core for the W/L = 0.2 case. Moreover, the numerical investigation on powder release position indicates that the nozzle inlet is a better place for releasing particles, which can ensure that particles obtain a relatively high impact velocity and temperature. However, it should be noticed that releasing particles from the nozzle inlet is only from a performance perspective. In practice, the choice of the particle release location may still depend on other factors as well.
Acknowledgments The research was mainly supported by the National Natural Science Foundation of China (No. 50476075). The authors also would
4. Conclusions A numerical study is conducted to investigate the effect of nozzle cross-section shape on gas flow and particle acceleration in CS. Threedimensional models are employed to reveal all features of gas flow and particle acceleration. Based on the calculation results, it is concluded that nozzle cross-section shape can affect the gas flow field, particle acceleration and thus particle impact velocity. In this study, the mean particle impact velocity which takes account of particle distribution is proposed to characterize the particle impact velocity. Comparing nozzles with rectangular cross-section to those with elliptical cross-section, it is found that the bow shock size for the
Fig. 11. Effect of nozzle cross-section shape on mean particle impact velocity.
S. Yin et al. / Surface & Coatings Technology 205 (2011) 2970–2977
like to acknowledge the financial support from the Chinese Ministry of Education's Academic Award for Doctoral Student. References [1] [2] [3] [4] [5] [6] [7] [8]
A. Papyrin, Adv. Mater. Processes 159 (9) (2001) 49. H. Assadi, F. Gartner, T. Stoltenhoff, H. Kreye, Acta Mater. 51 (15) (2003) 4379. M. Grujicic, C.L. Zhao, W.S. DeRosset, D. Helfritch, Mater. Des. 25 (8) (2004) 681. D.L. Gilmore, R.C. Dykhuizen, R.A. Neiser, T.J. Roemer, M.F. Smith, J. Therm. Spray Technol. 8 (4) (1999) 576. C.J. Li, W.Y. Li, H.L. Liao, J. Therm. Spray Technol. 15 (2) (2006) 212. R.C. Dykhuizen, M.F. Smith, J. Therm. Spray Technol. 7 (2) (1998) 205. A.P. Alkhimov, V.F. Kosarev, S.V. Klinkov, J. Therm. Spray Technol. 10 (2) (2001) 375. W.Y. Li, C.J. Li, J. Therm. Spray Technol. 14 (3) (2005) 391.
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[9] W.Y. Li, H. Liao, H.T. Wang, C.J. Li, G. Zhang, C. Coddet, Appl. Surf. Sci. 253 (2) (2006) 708. [10] B. Jodoin, J. Therm. Spray Technol. 11 (4) (2002) 496. [11] J. Pattison, S. Celotto, A. Dhan, W. O'Neill, Surf. Coat. Technol. 202 (8) (2008) 1443. [12] T. Stoltenhoff, H. Kreye, H.J. Richter, J. Therm. Spray Technol. 11 (4) (2002) 542. [13] S.H. Zahiri, W. Yang, M. Jahedi, J. Therm. Spray Technol. 18 (1) (2009) 110. [14] T.C. Jen, L.J. Li, W.Z. Cui, Q.H. Chen, X.M. Zhang, Int. J. Heat Mass Transfer 48 (21– 22) (2005) 4384. [15] B. Samareh, A. Dolatabadi, J. Therm. Spray Technol. 16 (5–6) (2007) 634. [16] R. Nickel, K. Bobzin, E. Lugscheider, D. Parkot, W. Varava, H. Olivier, X. Luo, J. Therm. Spray Technol. 16 (5–6) (2007) 729. [17] T. Han, B.A. Gillispie, Z.B. Zhao, J. Therm. Spray Technol. 18 (3) (2009) 320. [18] A.I. Kashirin, O.F. Klyuev, and T.V. Buzdygar, Apparatus for gas-dynamic coating, U.S. Patent 6 402 050, (2002). [19] FLUENT Inc., Fluent 6.2 User Guide, 1999. [20] T. Schmidt, F. Gaertner, H. Kreye, J. Therm. Spray Technol. 15 (4) (2006) 488.
Contents lists available at ScienceDirect
Surface & Coatings Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s u r f c o a t
Computational analysis of the effect of nozzle cross-section shape on gas flow and particle acceleration in cold spraying Shuo Yin a,⁎, Xiao-fang Wang a, Wen-ya Li b a b
School of Energy and Power Engineering, Dalian University of Technology, No.2, Linggong Road, Dalian, Liaoning 116024, China Shaanxi Key Laboratory of Friction Welding Technologies, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
a r t i c l e
i n f o
Article history: Received 20 July 2010 Accepted in revised form 1 November 2010 Available online 9 November 2010 Keywords: Cold spraying Numerical simulation Powder release position Nozzle shape Particle acceleration
a b s t r a c t In cold spraying, the spraying of certain complicated surfaces may require nozzles with special cross-sections. In this study, numerical investigation is conducted to study the effect of nozzle cross-section shape on gas flow and particle acceleration in cold spraying. The comprehensive comparison between rectangular nozzles and elliptical nozzles indicates that rectangular nozzles result in slightly lower mean particle impact velocity than elliptical nozzles. However, for rectangular nozzles, more particles may achieve relatively high velocity due to the larger sectional area of their potential core. Furthermore, it can also be found from the numerical results that the mean particle impact velocity increases gradually with the decrease in Width/Length ratio (W/L) of the cross-section because of the diminishing bow shock size. However, when reducing the W/L to 0.2, the mean particle impact velocity begins to decrease steeply, which may be attributed to the rather small area of the potential core for the case of W/L = 0.2. Moreover, the systematic study on the powder release position shows that releasing particles from the nozzle inlet can ensure that particles achieve a high impact velocity and temperature. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Cold spraying (CS) represents a radical difference from conventional thermal spraying methods. The deposition process relies mainly on kinetic energy rather than the combination of thermal and kinetic energies of spraying particles. In this process, spraying particles (typically b50 μm) are accelerated to a high velocity (ranging from 300 to 1200 m/s) by a high speed gas flow, and a coating is formed through the intensive plastic deformation of particles at a temperature well below the melting point [1]. Despite the fact that CS is attracting more and more attention from the world due to its unique advantages, such as the deposition of oxygen-free metallic coatings, there still exist some important concerns to be well revealed. It has been well known that there exists a material-dependent critical velocity, above which particles can adhere to the substrate and form a coating [2,3]. Therefore, the relationship between particle velocity and deposition efficiency has been extensively studied in recent years [4,5]. In addition, there has also been growing interest in gas flow and particle acceleration during the past few years. The existing studies on this field mainly focused on two aspects, including the optimal design of the spraying nozzle and the examination on spraying parameters.
⁎ Corresponding author. Tel./fax.: +86 411 84707905. E-mail address: [email protected] (S. Yin). 0257-8972/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2010.11.002
The optimal design of CS nozzles is always based on the principle of high particle impact velocity at the substrate surface. In 1998, Dykhuizen et al. [6] reported an original work, providing some analytical equations that allow the optimal design for a CS nozzle. Alkhimov et al. [7] also presented a calculating model to optimize the nozzle geometrical dimension and verified their model by experimental data. Later, Li et al. [8,9] optimized the dimension of converging-barrel nozzle (CB) and converging–diverging (CD) nozzle based on their simulation results. Jodoin [10] found the optimal exit Mach number of 1.5–3.0 that can ensure spraying particles to achieve sufficient acceleration. Recently, Pattison et al. [11] reported that medium standoff region (ranging from 60 mm to 120 mm) from the nozzle outlet is the optimal distance for locating the substrate. As for the investigation on spraying parameters, Stoltenhoff et al.'s study [12] showed the effect of inlet stagnation pressure, inlet stagnation temperature, particle diameter and standoff distance on gas flow and particle acceleration using the commercial software FLUENT. Some further experiments conducted by other researchers provided evidence to Stoltenhoff et al.'s numerical results [11,13]. The influence of particle size on particle acceleration was also studied in detail by Jen et al. using numerical method [14]. Meanwhile, they paid special attention to the gas flow structure inside and outside the nozzle, obtaining an insight into the flow field [14]. Moreover, Samareh et al. [15] analyzed the effect of substrate shape on gas flow structure, particle impact velocity and particle footprint distribution at the substrate based on three-dimensional models.
S. Yin et al. / Surface & Coatings Technology 205 (2011) 2970–2977
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Fig. 1. Schematic and dimensions of the geometries used in numerical model.
Besides, some previous studies also focused on other relevant fields. Nickel et al. [16] reported a new CS variant based on the combined application of shock tube facility with a Laval-nozzle and verified this system by both experimental and numerical methods. The most recent study conducted by Han et al. [17] provided a systematical examination on several new powder injector configurations by both computational simulations and experimental tests in order to find a better configuration for promoting the CS coatings. Notwithstanding these meaningful findings, several important problems still need to be further studied. In actual application, some work-pieces with complicated surface may require nozzles with special cross-section shape. In this study, as a first approximation, numerical investigation is conducted on some types of oblate nozzles (rectangular and elliptical) to clarify the effect of cross-section shape on gas flow and particle acceleration, aiming to find a preferable nozzle that can increase the particle impact velocity. On the other hand, it is known that the centerline velocity of a single particle was always employed to characterize the particle impact velocity in previous studies. However, in actual CS process, the particle relative position to the centerline and the particle size distribution significantly affect the particle acceleration and thus the impact velocity. The single particle centerline velocity should not represent the real impact velocity of spraying particles. In this study, owing to the adoption of three-dimensional models, the distribution of particle position and size can be considered. The mean particle impact velocity which is defined as the average velocity of all spraying particles is proposed to clarify the effect of the nozzle crosssection shape on particle impact velocity. Moreover, it has been accepted that powder injector is an important device in CS system, which significantly influences particle impact velocity and temperature. Generally, installing the injector in a preheat chamber before the nozzle inlet is beneficial to the coating formation, but requires relatively high feed pressure for introducing particles. Also, A.I. Kashirin et al. reported that if particles are released
downstream of the nozzle throat, the feed pressure can be lower than the ambient pressure and particles can be easily introduced by the airflow [18], although the impact velocity and temperature could decrease to some extent. In this study, a numerical investigation is also conducted based on performance perspective to find the effect of powder release position on particle impact velocity and temperature.
Table 1 Dimensions of all these geometries at three typical cross-sections used in this simulation. W/L ratio
a, inlet (mm)
b, throat (mm)
c, outlet (mm)
0.2 0.4 0.6 0.8 1.0
2 4 6 8 10
0.4 0.8 1.2 1.6 2.0
0.8 1.6 2.4 3.2 4.0
Fig. 2. Grid at the outlet cross-section for (a) rectangular nozzle and (b) elliptical nozzle (W/L = 1.0).
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2. Numerical methodology 2.1. Geometry The schematic and dimensions of the geometries used in numerical model is shown in Fig. 1. The convergent part has a length of 30 mm and is attached to the throat part as well as the following divergent part with a length of 40 mm. Elliptical nozzles and rectangular nozzles with different Width/Length (W/L) of the crosssection were employed, namely, 0.2, 0.4, 0.6, 0.8 and 1.0. Table 1 summarizes dimensions of all these geometries at three typical crosssections used in this simulation. The long edge of the nozzle crosssection is fixed, and only the short edge changes to keep the same expansion ratio for every case. The long edge for the inlet, throat and outlet cross-section is chosen as 10 mm, 2 mm and 4 mm, respectively. The exit to throat area ratio is chosen as 4 to ensure sufficient acceleration of spraying particles. The flat substrate is located at a distance of 20 mm away from the nozzle exit along the centerline. Generally, particles are released axially from the inlet cross-section to ensure particles can achieve high impact velocity. As for the study on powder release position, nozzles with the W/L ratio of 1.0 are employed and only a single particle is released inside the nozzle along the centerline.
2.2. Computational domain and boundary conditions
Fig. 3. Effect of powder release position on: (a) particle impact velocity and (b) particle impact temperature along the centerline.
Numerical simulations are performed by using FLUENT 6.2 (Fluent Inc., Lebanon, NH) to predict the flow flied of the driving gas and the acceleration of spraying particles in CS. Three-dimensional plane symmetrical models are utilized to reduce the computation time. The computational domain is partitioned into a number of hexahedral cells and the surrounding region of the centerline is refined to ensure the calculation accuracy as a result of generation of the shockwaves in the supersonic flow as indicated in Fig. 2. The total number of grid cells varies between 189 550 and 950 000 depending on the nozzle cross-section shape. A grid dependency test is also performed to
Fig. 4. Contours of (a) gas pressure and (b) velocity at the XY symmetrical plane for nozzles with different W/L.
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the computational domain is at the same plane that the substrate is located and treated as pressure outlet with the pressure of 0.1 MPa. Standard no-slip condition is used at the nozzle wall and the substrate surface. The heat transfer process between the gas and the wall is not considered, thus a fixed heat flux of zero is enforced at the wall. 2.3. Gas phase and particle phase N2 is chosen as the driving gas in this study. The ideal gas law is used to calculate the density in order to take the compressibility effects into consideration. The governing equations for gas flow include the physical laws of conservation of mass, momentum, and energy. Because the coupled scheme obtains a robust and efficient single phase implementation for steady-state flows, a coupled implicit method is used to solve the flow field and the result of flow field in a steady state is obtained. In order to capture the turbulent flow features accurately, the standard K-ε turbulence model available in FLUENT is utilized for modeling the turbulent flow in the simulation. The choice is made following the work of Li et al. [8,9]. The standard wall function is chosen for the near-wall flow treatment. Copper is used as the spraying particle material. The acceleration of particles is computed using discrete phase modeling (DPM). The model requires that the discrete phase must be present at sufficiently low volume fractions. In this case, all the spray particles are spherical in shape and hence the spherical drag law is used to compute the drag coefficient. Particle–particle interactions and the effect of particles on the gas phase can be neglected. The drag force can be expressed by the following equation: Fd =
18μ Cd Re ρP d2P 24
ð1Þ
where Fd is the drag force, μg is the dynamic viscosity of gas, ρd is the particle density, dp is the particle diameter, Cd is the drag coefficient and Re is the relative Reynolds number, which is defined as:
Re = Fig. 5. Pressure variations along the centerline for nozzles with W/L: (a) elliptical nozzles and (b) rectangular nozzles.
ensure that the solution dependency on the grid size is b2%. The nozzle inlet is treated as pressure inlet with the pressure of 2.5 MPa and temperature of 600 K. The pressure-far-field boundary is applied to the surrounding atmosphere outside the nozzle exit. The outlet of
ρg dp Vg −Vp μg
ð2Þ
where ρg is the gas density, Vp is the particle velocity and Vg is the gas velocity; this equation can be practically applied to a Re b 50000. The drag coefficient Cd can be expressed as: Cd = a1 +
a2 a + 32 Re Re
ð3Þ
where, a1, a2 and a3 are constants that are applied to smooth spherical particles over several ranges of Re given by Morsi and Alexander [14,20]. It is also assumed that heat conduction within a particle is neglected and the particle is therefore treated as isothermal. The heating rate is described by: dTp 6h = T −Tp Cpp ρp dp g dt
ð4Þ
where, Tp is the particle temperature, Tg is the gas temperature, Cpp is the heat capacity of particle and h is the heat transfer coefficient and related to the thermal conductivity of gas (λg) by Nusselt number (Nu) as follows:
Fig. 6. Variation of bow shock thickness with W/L for both elliptical nozzles and rectangular nozzles.
h=
λg Nu dp
ð5Þ
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3. Results and discussion 3.1. Effect of powder release position on particle impact velocity and temperature
Fig. 7. Contours of gas velocity at the nozzle outlet cross-section for nozzles with different W/L.
Nusselt number is given by: 1=3
Nu = 2 + 0:6Pr
Re
1=2
ð6Þ
Prandtl number (Pr) is described as:
Pr =
μg Cpg λg
ð7Þ
where, Cpg is the heat capacity of gas. Models describing the dynamic behavior of in-flight particles during the two-phase flow have been well documented in the FLUENT manual [19].
Fig. 8. Schematic of the velocity distribution in fully developed pipe flow.
Fig. 3 gives the effect of powder release position on particle impact velocity and temperature along the centerline using rectangular nozzle and elliptical nozzle (W/L = 1.0). From Fig 3(a), it is clearly seen that with shifting the release position towards the outlet, the particle impact velocity maintains a continuous high value at the convergent section and decreases gradually at the divergent section. The main reason for this is that driving gas is chiefly accelerated at the throat section and the following divergent section rather than the convergent section. Releasing a particle at the convergent section can ensure the particle to be accelerated completely by the driving gas when passing through the throat section and the divergent section. However, if releasing a particle at the divergent section, the particle is only accelerated at the divergent section. Hence, the particle acceleration time and then impact velocity reduce gradually with shifting the release position from the throat section to the outlet. As for the impact temperature, it decreases with shifting the release position towards the outlet, and the steep decrease presents at the convergent section. This is because the particle chiefly heats up at the convergent section, and shifting the release position towards the outlet can reduce the particle residence time at the convergent section, which leads to the sudden decrease of the particle temperature. From the analysis above, it can be found that releasing particles at the inlet of the nozzle could ensure particles to obtain a relatively high impact velocity and temperature, and thus promoting the deposition efficiency. However, it should be pointed out that some other methods for installing powder injector, such as at the preheat chamber [20] or inside the divergent section [18], also have some advantages as mentioned in the introduction section. Therefore, it is necessary to consider different circumstances and concerns when choosing an installation scheme of powder injector. 3.2. Effect of nozzle cross-section shape on gas flow field Fig. 4 shows contours of the driving gas pressure and velocity for nozzles with different W/L at the XY symmetrical plane. As shown in Fig. 4(a), a well-formed complex wave structure which is composed of oblique shock, expansion wave and bow shock can be clearly observed behind the nozzle exit in each case. The oblique shock near the nozzle outlet is formed due to overexpansion, followed by expansion waves owing to multiple reflections of compression waves at the atmosphere boundary. The reflection can be observed from Fig. 4(a) at the case of W/L = 0.2 and the zone near the atmosphere boundary where gas pressure begins to reverse indicates the occurrence of reflection. In addition, between the nozzle exit and the substrate, there exists a well-formed bow shock in the vicinity of the substrate, which arises from the interaction between the supersonic gas flow and the substrate. The gas pressure and temperature in this bow shock zone is extremely high, which can lead to a sudden deceleration of in-flight particles and off-normal impact on the substrate [15]. These two phenomena can both result in a decrease of deposition efficiency. It also can be found from Fig. 4(a) that some shockwaves are generated surrounding the bow shock zone which also arise from the presence of the substrate. Fig. 4(b) shows contours of the driving gas velocity for nozzles with different W/L at the XY symmetrical plane. From these contours, it is clearly seen that the periodically fluctuant gas velocity is caused by the oblique shock and expansion wave in each case. Inside the bow shock zone, the gas velocity is decelerated to almost zero. The contents reflected from these velocity contours are in harmony with the pressure contours. Moreover, after doing a comparison between nozzles of different W/L, it is found that with decreasing W/L, the amplitude of pressure
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Fig. 9. Footprint of the particles at the substrate surface for nozzles with different W/L.
fluctuation presents an upward trend and the distance between two adjacent peaks decreases gradually. This variation can be clearly observed in Fig. 5 that shows the gas velocity as a function of position along the centerline in different nozzles. Also, it can be found from Fig. 4 that the size of the bow shock goes down gradually with the W/ L. The variation of bow shock thickness with the W/L ratio as indicated in Fig. 6 gives a more detailed description. With decreasing the W/L, the bow shock thickness decreases gradually. This fact may be attributed to the area of the supersonic potential core. Fig. 7 shows
contours of the gas velocity at the outlet cross-section for nozzles with different W/L. It is clear that the area of the potential core closely relates to the nozzle geometric dimension, reducing with the W/L. Hence, the potential core area that interacts with the substrate also decreases with the W/L, which leads to the decrease of bow shock size. Furthermore, when comparing the elliptical nozzles to the rectangular nozzles as indicated in Fig. 4(a), it can be found that the bow shock size for the elliptical nozzles is slightly smaller than that for rectangular cases, in terms of its thickness. This also can be linked to
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the sectional area of the potential core that interacts with the substrate. Under the same W/L, the sectional area of the potential core is larger for the rectangular case as indicated in Fig. 7, and thus the bow shock is slightly stronger. Form Fig. 7, it can also be seen that the interaction between the nozzle wall and the gas flow results in the decrease of the gas velocity from the centerline towards the nozzle wall due to the viscous effect of the flow. The gas velocity near the wall zone is small with the gas velocity at the center region maintaining a high value. The potential core area is larger than the near-wall low velocity zone. This phenomenon is consistent with the features of the fully developed turbulent pipe flow as indicated in Fig. 8. 3.3. Effect of nozzle cross-section shape on particle acceleration In order to obtain insight in the particle distribution at the substrate surface, Fig. 9 presents the footprint of particles with the diameter of 10 μm at the substrate surface. It can be seen from Fig. 9 that the particle distribution for rectangular nozzles seems equally uniform with that for elliptical nozzles. However, because the sectional area of potential core of rectangular nozzles is larger than that of elliptical nozzles as indicated in Fig. 7, the number of particles inside the potential core zone is bigger for rectangular nozzles. This fact means that under the same W/L, more particles can achieve relative high impact velocity for rectangular nozzles. The distribution of the particle footprint compares well with the gas flow distribution at the outlet section as shown in Fig. 7. Generally, the diameter of CS particles is in the range of 10 μm– 30 μm. In this study, the Rosin-Rammler equation available in FLUENT is employed to distribute the particle diameters, which yields a mean size of 20 μm with a range from 2 μm to 50 μm as shown in Fig. 10. This size distribution is very similar to that in actual CS process. Fig. 11 shows the effect of the nozzle cross-section shape on mean particle impact velocity which is defined as the average velocity of all spraying particles. The standard deviation for each case is also given in Fig. 11. It can be found that with decreasing the W/L, the mean particle velocity rises slightly for both elliptical nozzles and rectangular nozzles. The reason for this phenomenon is that the area of the potential core decreases gradually with the W/L, which results in the decrease of the bow shock strength. Therefore, the negative effect of the bow shock on particle acceleration becomes weak, leading to an upward increment of the mean particle impact velocity. However, it is of great importance to note that when the W/L is decreased to 0.2, the mean particle impact velocity decreases steeply. This is because although the bow shock is the weakest among all cases, which is favorable for particle acceleration, the length and area of the potential core is much smaller and the driving gas cannot accelerate the particles efficiently before they penetrate into the bow shock. Therefore, the mean particle impact velocity is rather low. Furthermore, it also can be found that because rectangular nozzles can yield stronger bow shock compared to elliptical nozzles, the mean particle velocities for the elliptical nozzles are greater than those for the rectangular nozzles in all cases, but the difference is rather slight.
Fig. 10. Size distribution of the spraying particles.
elliptical case is slightly smaller than that for the rectangular case under the same W/L. Hence, the effect of bow shock on particle acceleration is weaker for elliptical nozzles and particles can obtain higher mean particle impact velocity. However, for rectangular cases, more particles may achieve relatively high velocity because their potential core has larger sectional area. Furthermore, it is also found that with decreasing the W/L, the size of the bow shock declines, which results in the gradual increase of the mean particle velocity for both elliptical nozzles and rectangular nozzles. But it is noticed that when the W/L is decreased to 0.2, the mean particle impact velocity begins to decrease steeply, which may be linked to the very small area of the potential core for the W/L = 0.2 case. Moreover, the numerical investigation on powder release position indicates that the nozzle inlet is a better place for releasing particles, which can ensure that particles obtain a relatively high impact velocity and temperature. However, it should be noticed that releasing particles from the nozzle inlet is only from a performance perspective. In practice, the choice of the particle release location may still depend on other factors as well.
Acknowledgments The research was mainly supported by the National Natural Science Foundation of China (No. 50476075). The authors also would
4. Conclusions A numerical study is conducted to investigate the effect of nozzle cross-section shape on gas flow and particle acceleration in CS. Threedimensional models are employed to reveal all features of gas flow and particle acceleration. Based on the calculation results, it is concluded that nozzle cross-section shape can affect the gas flow field, particle acceleration and thus particle impact velocity. In this study, the mean particle impact velocity which takes account of particle distribution is proposed to characterize the particle impact velocity. Comparing nozzles with rectangular cross-section to those with elliptical cross-section, it is found that the bow shock size for the
Fig. 11. Effect of nozzle cross-section shape on mean particle impact velocity.
S. Yin et al. / Surface & Coatings Technology 205 (2011) 2970–2977
like to acknowledge the financial support from the Chinese Ministry of Education's Academic Award for Doctoral Student. References [1] [2] [3] [4] [5] [6] [7] [8]
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