Research Paper
Journal of Chemical Engineering of Japan, Vol. 50, No. 4, pp. 254–261, 2017
Numerical Simulations of Particle-Laden Turbulent Flows to Characterize the Two Different Types of Paint Spray; Bell-Cup Atomizer and Powder Spray Gun Tatsuya Soma1, Shun Amemiya1, Tomoyuki Katayama1, Yasuhiro Saito1, Yohsuke Matsushita1, Hideyuki Aoki 1, Takao Inamura2, Masatoshi Daikoku3 and Junichi Fukuno4 Department of Chemical Engineering, Graduate School of Engineering, Tohoku University, 6-6-07 Aoba, Aramaki, Aoba-ku, Sendai-shi, Miyagi 980-8579, Japan 2 Department of Intelligent Machines and System Engineering, Faculty of Science and Technology, Hirosaki University, 3 Bunkyo-cho, Hirosaki-shi, Aomori 036-8561, Japan 3 Department of Mechanical Engineering, Faculty of Engineering, Hachinohe Institute of Technology, 88-1 Ohbiraki, Myo, Hachinohe-shi, Aomori 031-8501, Japan 4 Research and Development Division, Honda Engineering Co., Ltd., 6-1 Hagadai, Haga-Machi, Haga-Gun, Tochigi 321-3395, Japan 1
Keywords: Bell-cup Atomizer, Powder Spray Gun, Euler–Lagrange Approach, Numerical Simulation The motions of particles injected from two different sprayers were investigated. The present investigation deals with automotive paint sprayers, a high-speed rotary bell-cup atomizer and a powder spray gun. The liquid droplets and powder coatings in each paint system were modeled as undeformable spherical particles, and the two-phase flow was numerically computed with the Euler–Lagrange approach. The Reynolds averaged Navier–Stokes equation was solved with the standard k–ε model. As a result, despite the difference in spray system, the spread of spray near the nozzle, so called ghost, was observed in both sprayers. When electric voltage was applied, the bell-cup atomizer had relatively strong tendencies of the motion behavior of paint particles compared with powder spray gun: (a) large particles in ghost propagated radially outward and missed the target, and (b) the transfer efficiency was sensible to Sauter mean diameter. On the other hand, when zero electric voltage was applied, an opposite trend was observed. Thus, in the case of the industrial spray process using bell-cup atomizers with high voltage, the control technique of the particle diameter might be of great significance in order to improve transfer efficiency.
Received on August 19, 2016; accepted on October 25, 2016 DOI: 10.1252/jcej.16we251 Correspondence concerning this article should be addressed to T. Soma (E-mail address:
[email protected]).
lecting and reusing non-adherent particles, they have never become mainstream in auto painting due to being inferior to the bell-cup atomizer in external appearance quality of coated film. In both sprayers, an attempt has been carried out to optimize the paint system in order to improve the transfer efficiency, but the behaviors of the paint particles under various conditions are not completely understood. There have been many numerical studies of the paint spray to investigate the droplet motions during the last two decades. Domnick et al. (2005, 2006) performed simulation of the bell-cup atomizer, and the obtained fluid velocity and the film thickness agreed well with the experimental value. Yasumura et al. (2011a, 2011b) pointed out that the dominating factor in the decrease of transfer efficiency is droplets traveling with the air flow around the target. Toljic et al. (2011, 2012) indicated that the transfer efficiency is a weak function of the average particle size. Ye and co-authors presented the simulation of the powder spray gun using the renormalization group k-ε turbulence model, and the obtained fluid velocity and the film thickness agreed well with the experimental value (Ye et al., 2002; Ye and Domnick, 2003). However, these studies remained within a single variety of sprayer, and there are few numerical studies of a comparison among various kinds of sprayers because quan-
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Introduction High-speed rotary bell-cup atomizers, which are widely used in automotive painting, spray liquid paint by centrifugal force. The trajectories of the droplets are controlled by the shaping air which blows from the rear of the bell cup and the electric voltage which charges droplets. The bell-cup atomizers generate fine droplets and form a uniform film on the target surface. The atomizers have high productivity, but they have the disadvantage in that portions of paint could not adhere to the target, and the non-adherent particles cause paint loss and pollution. On the other hand, powder spray guns are known as a powder coating technology. The solid paint particles entrained in the gas stream spread along deflector. At that time, the particles take charge due to free ions produced by corona discharge around an electrode which bulges from the front surface of the deflector. Although the guns have the advantage in that a transfer efficiency of nearly 100% can be achieved due to ease of col-
Copyright © 2017 Journal The Society of Chemical of Chemical Engineering Engineers, of Japan
titative comparison under the same conditions is difficult due to the difference of the spray mechanism. In the present paper, to identify the characteristics of the bell-cup atomizer by comparing with a powder spray gun, the spray flow was numerically computed with the Euler– Lagrange approach. We mainly investigated the sensitivity of the Sauter mean diameter and applied voltage on the motion of particles and the transfer efficiency.
1. Methods Schematic diagram of the computational domain is shown in Figures 1 and 2. The bell-cup atomizer or powder spray gun was used as a sprayer. The bell-cup atomizer consists of a bell cup and a shaping air ring which is located posterior to the bell cup, and blows air. The powder spray gun consists of a tube, a deflector, and a corona electrode. The target was a flat circular disc, and its face was at a distance of 250 mm from the end of the atomizer. The geometry was divided using a three-dimensional unstructured grid, and the numbers of the grids for the bell cup and powder spray gun were 698,592 and 585,116, respectively. The surfaces of the atomizer and target were treated as fixed walls, and the wall function (Spalding, 1961) was applied with the turbulence model in order to estimate the shear stress on the wall boundary. The outflow boundary condition proposed by Matsushita (Matsushita, 2011; Matsushita et al., 2014) was used at the rear of the target. For other boundaries, the slip wall boundary condition was applied.
The electric potential at the surfaces of the electricallygrounded target was set to zero. The applied voltage, φ0, was given at the surface of the bell cup or corona electrode. The Neumann boundary condition was imposed on the others, slip wall, inflow and outflow boundaries. The fluid flow is governed by the Reynolds-averaged Navier–Stokes equations in steady state. ∂ui =0 ∂xi
(1)
∂ ∂ 1 ∂p + (ui u j ) = − (−τ ij + 2νSij )+ Sp,i ∂x j ρ ∂xi ∂x j
(2)
Here, ¯ S p,i was the source term from the dispersed phase and calculated using the Particle-Source-In-Cell model (Crowe et al., 1977) and the Reynolds stress τij was evaluated using the standard k-ε model (Launder and Spalding, 1974). τ ij = −2ν t Sij +
ν t = Cμ
2
2 δk 3 ij
(3)
k ε
(4)
Here, Cμ is the empirical constant of the turbulence model. The kinetic energy of turbulence, k, and turbulent energy dissipation rate, ε, were calculated from followings.
∂ ∂ (ku j ) = −τ ij Sij − ε + ∂x j ∂x j
νt ∂k ν + σ ∂x k j
∂ ∂ ε (εu j ) = (−Cε1τ ij Sij − Cε 2ε)+ k ∂x j ∂x j
Fig. 1 Analytical object: (a) geometry of bell-cup atomizer, (b) overall view
(5)
ν t ∂ε ν + σ ∂x ε j
(6)
The parameters for these equations are summarized in Table 1. The governing equations were discretized via the finite volume method on the three-dimensional unstructured grids. The convective–diffusive terms were discretized using the power-law scheme (Patankar, 1980). The Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm (Patankar and Spalding, 1972) was applied for pressure-velocity coupling. As the matrix solver, the algebraic multigrid solver (AMGS library, 2016) was used for the pressure correction equation, and the Bi-Conjugate Gradient Stabilized Method with polynomial preconditioning (Bi-CGSTAB) (van der Vorst, 1992) was for transport equations of momentum, kinetic energy of turbulence and dissipation rate. The electric field, generated by applied voltage, is governed by the Poisson’s equation for electrostatic potential. div (gradφ) = −
ρe ε0
(7)
Table 1 Parameters for governing equations Fig. 2 Analytical object: (a) geometry of powder spray gun, (b) overall view Vol. 50 No. 4 2017
Cμ
Cε1
Cε2
σk
σε
0.09
1.44
1.92
1.0
1.3
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ρe =
k
N p, kQ p, k ΔV
(8)
Here, φ is the electrical potential, ρe is the total space charge density, ε0 is the permittivity of void, Np is the number of particles in the parcel, Qp is the charge of the parcel and ΔV is the volume of the cell. The equation was discretized with the second-order central difference scheme, and was solved by using the AMGS (AMGS library, 2016). The electric field intensity was calculated as the gradient of the electrical potential. A dispersed phase was solved by tracking a large number of particles using the discrete phase model. The equation of motion is written as Eq. (9). dx p, i = up, i dt
dup, i 3μf CD Rep = (uf, i − up, i )+ qp Ei dt 4 ρpdp2
(9) (10)
Here, Rep is the particle Reynolds number based on the particle diameter and relative velocity to the gas. The ambient gas velocity, uf, i, is separated into the mean component and the fluctuating component derived from the turbulent kinetic energy, and the fluctuating velocity component was randomly obtained from the normal distribution based on the following standard deviation σ in consideration of isotropic turbulence. σ =
2k 3
(11)
The drag coefficient, CD, was calculated from the literature (Clift and Gauvin, 1970). CD =
24 0.42 (1+ 0.15 × Rep0.687 )+ Rep 1+ 4.25 ×104 Rep−1.16
(12)
The second term on the right side of Eq. (10) is the electrostatic effect. The specific charge, qp, was 2.96 µC/g for the bell cup (Bell and Hochberg, 1981) and 1.00 µC/g for the powder spray gun (Ye et al., 2002). Time discretization was achieved by the second-order Runge-Kutta method. No particle collisions and coalescence were considered due to the dilute spray. Table 2 lists the numerical conditions on each atomizer. Different numerical conditions were given to the two sprayers. The quantitative comparison between sprayers could not be necessarily effective due to the differences of conditions, however useful knowledge could be obtained from the comparison of two sprayers in terms of the sensitivity to the operating conditions in the range of real applications. In the bell-cup atomizer, the shaping air flow rate was 400 NL/min, the paint flow rate was 150 g/min, and the bell-cup rotational speed was 35,000 rpm. The paint was assumed to be water-based paint, and its density was 1,000 kg/m3. In the powder spray gun, the air flow rate was 100 NL/min, and the paint flow rate was 100 g/min. The density of the powdered paint was 1,500 kg/m3. The particle size distribution was de256
Table 2 Numerical conditions Bell-cup atomizer Applied voltage Sauter mean diameter Air flow rate Paint flow rate Density of paint Bell rotating speed
[kV] [µm] [NL/min] [g/min] [kg/m3] [rpm]
Powder spray gun
−90–0 20, 40, or 60 400 150 1000 35,000
100 100 1500 —
termined by fitting the experimental data (Kazama, 2003) to the Rosin-Rammler distribution function. β d fV p = D 32 1 Γ 1 − β
dp β D 32
β −1
1 dp ×exp − D Γ 1 − 1 32 β
β
(13)
The best fit parameter was β=3. A total of 80,000 particles were calculated on each condition. In the case of the bellcup atomizer, the particles were initially located at the rim of the bell, and the initial velocities were 10–35% of the bellcup rotational speed (128 m/s). Meanwhile, in the powder spray gun, the particles were located at the inflow boundary plane, and the initial velocity was the same as the gaseous one. The case studies were performed with a varying Sauter mean diameter or applied voltage. Note that no effects of applied voltage upon the particle diameter nor the amount of charge were considered here because of very little quantitative data, but we stressed that the two sprayers were evaluated of the same conditions in this regard.
2. Results and Discussion 2.1 Sensibility of total transfer efficiency The calculated transfer efficiency is shown in Figure 3. The transfer efficiency is defined as the ratio between the amount of paint deposited on the target and the supply of paint. For the bell-cup atomizer, the transfer efficiency increased with the intensity of the applied voltage and remained practically constant over about −60 kV. In the case of the powder spray gun, negative applied voltage increased the transfer efficiency drastically, but the magnitude of applied voltage had an insignificant effect on the transfer efficiency. In the absence of an electric field, the transfer efficiency decreased with the increase of Sauter mean diameter for both sprayers. Under the influence of an applied voltage, the bell-cup atomizer denoted the same tendency. However, although the amount of charge increased with the particle diameter, the Sauter mean diameter had no practical impact on the transfer efficiency in the case of the powder spray Journal of Chemical Engineering of Japan
Fig. 4 The flow fields around the bell-cup atomizer on the y-z planes at φ0 =0 kV, (top) spray mass density distributions, (bottom) axial velocity distributions
Fig. 5 The flow fields around the powder spray gun on the y-z planes at φ0 =0 kV, (top) spray mass density distributions, (bottom) axial velocity distributions Fig. 3 Comparison of the total transfer efficiencies
gun. These tendencies can be understood by considering the interaction between the charged paint particles, flow field and electric field as shown in the next subsection. 2.2 The flow and electric field In this subsection, in order to correlate the results described in Subsection 2.1 to the flow and electric phenomena around sprayers, the flow and electric fields generated by the bell-cup atomizer or powder spray gun were compared. Figure 4 shows the distributions of the spray mass density and axial velocity around the bell-cup atomizer (φ0 =0 kV). The particles were ejected from the bell-cup atomizer parallel to the target by rotation, and then were curved in the vertical direction by shaping air flow blown from rear of the bell cup. This spread of spray near the nozzle was called ghost. The small droplets were rapidly entrained in the shaping air flow around the center-axis, and the large droplets moved radially due to the rotational inertia. Though the increase of Sauter mean diameter of droplets caused the paint to spread radially, the spray mass density around the target was not decreased with the spread of spray compared to the powder spray gun as described below. This is because the pressure dropped around the center axis due to the swirl flow induced by bell rotation, and the ghost was drawn toward the inside of the spray by the pressure difference. In the case of the powder spray gun, the particles were injected toward the target and spread by colliding with the deflector as shown in Figure 5. As in the case with the bell-cup atomizer, the relatively large particles spread radially due to the inertia, and the paint particles were widely spread with Vol. 50 No. 4 2017
Sauter mean diameter. As shown in Figures 4 and 5, regardless of the spray system, the relatively large Sauter mean diameter resulted in the expanse of the spray, thereby decreasing the transfer efficiency in the case of φ0 =0 kV. The fluid behavior around the powder spray gun differed from that of the bell-cup atomizer in that the spray mass density around the target decreased with an increase of Sauter mean diameter. This is why the Sauter mean diameter of particles caused a significant decrease in the transfer efficiency compared to the bell-cup atomizer. Examples of the flow field on the x-y planes are shown in Figures 6 and 7. In the case of the bell cup, although the velocity magnitude was almost axial symmetry, spray mass density slightly had a distribution in a circumferential direction due to the fluctuation components of turbulence. In the case of the powder spray gun, velocity slightly had a distribution in a circumferential direction. The flow might be stabilized in the presence of the swirl by bell rotation. In any case, the flow fields are roughly considered axisymmetric turbulence, so that the flows could be discussed from cross-section views like Figures 4 and 5. We have also carried out some simulations assuming that a high voltage was applied to the bell-cup atomizer or emitting electrode needles composing the powder spray gun. Distributions of the spray mass density and axial velocity around the bell-cup atomizer at φ0 =−60 kV are shown in Figure 8. Although the expanse of the spray was suppressed to some extent by the electric force acting on the charged particles from the electric field, the changes of the spray mass density distributions with respect to Sauter mean diameter were similar to the case of zero electric field. Since the electric force increased the particle velocity, hence the reduction of the sojourn time of the particles, the spray mass densities were dramatically small compared to the 257
Fig. 10 The flow fields around the powder spray gun on the y-z planes at φ0 =−60 kV, (top) spray mass density distributions, (bottom) axial velocity distributions Fig. 6 The flow field on the x-y planes at z=200 mm in the case of the bell-cup atomizer (φ0 =0 kV, D32 =40 µm)
Fig. 11 The electrical phenomena around the powder spray gun on the y-z planes at φ0 =−60 kV, (top) space charge, (bottom) electrostatic potential
Fig. 7 The flow field on the x-y planes at z=200 mm in the case of the powder spray gun (φ0 =0 kV, D32 =40 µm)
Fig. 8 The flow fields around the bell-cup atomizer on the y-z planes at φ0 =−60 kV, (top) spray mass density distributions, (bottom) axial velocity distributions
Fig. 9 The electrical phenomena around the bell-cup atomizer on the y-z planes at φ0 =−60 kV, (top) space charge, (bottom) electrostatic potential
case without voltage. Figure 9 shows the distributions of the space charge and the electrostatic potential at φ0 =−60 kV. The space charge distributions were the same as the spray mass density because the charges of the particles were given 258
based on the mass. The electrostatic potential near the bell cup decreased with an increase of Sauter mean diameter due to the decline of the space charge. Thus, the average electrostatic force acting on the certain size particles decreased with the increase of Sauter mean diameter due to the low electric field intensity. In the case of the powder spray gun, as in the case with the bell-cup atomizer, the applied voltage decreased the spray mass density and spread of spray as shown in Figure 10. Figure 11 shows the distributions of the space charge and electrostatic potential. With an increase in Sauter mean diameter, the electrostatic potential and the electric field intensity around the powder spray gun decreased due to dilute spray. Although the two different spray systems had a lot in common, they differed in the dependence of transfer efficiency on the particle diameter as shown in Figure 3. This is because the particles sprayed from the bell-cup atomizer moved in the radial direction relatively easily due to the relatively large radial momentum as previously explained. Figures 12 and 13 show the effect of applied voltage on the flow and electric field with the bell-cup atomizer at D32 =40 µm. The charged particles tended to be pulled toward the target easily by electric force with high voltage, and the spray angle decreased with the increase of applied voltage. Thus, some particles, especially relatively large particles, moved radially before they were drawn toward the center axis by the pressure difference, and the spread of the spray increased. The increase of applied voltage resulted in the improvement of transfer efficiency seen in Figure 3. Meanwhile, the voltage levels had negligible effects on spray mass density and gas velocity in the case of the powder spray gun as shown in Figures 14 and 15, since the electrostatic potential was approximately constant relative to the applied Journal of Chemical Engineering of Japan
Fig. 12 Comparison of flow field of each applied voltage in the case of the bell-cup atomizer at D32 =40 µm, (top) spray mass density distributions, (bottom) axial velocity distributions
Fig. 13 Comparison of electrostatic potential of each applied voltage in the case of the bell-cup atomizer at D32 =40 µm, (top) space charge, (bottom) electrostatic potential
Fig. 14 Comparison of flow field of each applied voltage in the case of the powder spray gun at D32 =40 µm, (top) spray mass density distributions, (bottom) axial velocity distributions
Fig. 15 Comparison of electrostatic potential of each applied voltage in the case of the powder spray gun at D32 =40 µm, (top) space charge, (bottom) electrostatic potential
voltage due to a small electrode size. The spread of spray by electric voltage was observed as with the bell-cup atomizer, but the spreading of the spray was small compared to the target length. 2.3 Transfer efficiency on each particle In Subsections 2.1 and 2.2, the effects of the Sauter mean diameter of the particles and applied voltage on transfer efficiency were estimated under each electric field. Note that the above discussion is based on the average particle size Vol. 50 No. 4 2017
Fig. 16 Transfer efficiencies of each diameter with bell-cup atomizer
and have no mention of the behaviors of each particle. In this subsection, the transfer efficiencies of each particle size are presented. Figure 16 shows the particle size distributions computed and the transfer efficiencies of each diameter for the case of the bell-cup atomizer. The smaller particles easily adhered to the target when the applied voltage was φ0 =0 kV regardless of the Sauter mean diameter, but the transfer efficiency was about 60% at best. The applied voltage increased the transfer efficiency wholly, but the transfer efficiency of the relatively large particle decreased. This is because there was a separate effect because of the rotation of the air flow and the electric force, and the large particles tended to extend outward as pointed out in Subsection 2.2. A similar effect has been noted in the literature (Domnick et al., 2005, 2006). Thus, the non-adhesion particles increased. The relatively small particles were entrained to the shaping air flow and came close to the target, but some particles were entrained by airflow along the target and would not adhere to the target. Despite of their small charges, the relatively small particles were affected by electric force easily due to the low particle mass. Moreover, the well-adherent particles were about 20 µm regardless of the Sauter mean diameter. 259
cles increased as a value of the Sauter mean diameter. Therefore, it has been felt that this tendency was common regardless of the spray system. In this regard, a decrease of the transfer efficiencies of large particles as shown in the case of the bell-cup atomizer was not observed, which causes the low sensitivity of total transfer efficiency under the influence of an applied voltage to particle diameter compared to the bell-cup atomizer.
Conclusions
Fig. 17 Transfer efficiencies of each diameter with powder spray gun
Meanwhile, although the total transfer efficiency decreased with the Sauter mean diameter, the range in diameter of well-adherent particles increased with Sauter mean diameter. Figure 17 shows the particle size distributions and the transfer efficiencies of each diameter for the case of the powder spray gun. Without applied voltage, the transfer efficiencies increased with the decrease of the particle diameter as in the case with the bell-cup atomizer, and the transfer efficiency was 80% at best. Although the total transfer efficiencies of the spray gun were lower than those of the bell-cup atomizer except the case of D32 =20 µm as shown in Figure 3, the maximum values of the local transfer efficiencies were higher. This suggests that the size of each particle has a profound effect on transfer efficiency compared to the case of the bell cup when no voltage was applied. This is because no shaping air flows were blown to the periphery of the spray unlike the bell-cup atomizer, and the particles which moved in the radial direction were hardly drawn to the central part. Furthermore, the applied voltage increased the transfer efficiency. When the voltage was applied, in common with the bell-cup atomizer, the well-adherent particles were about 20 µm, and the range of the diameter of well-adherent parti260
In this paper, to obtain insight into the spray characteristics, the motions of particles injected from two different sprayers (i.e. bell-cup atomizer and powder spray gun) were investigated. As a result, in these analytical conditions, two different spray systems show similarities: · The relatively small droplets were easily adhered to the target with no applied voltage. · Applying voltage to the spray systems was effective for improving transfer efficiency. · With applied voltage, the correlation between the size and the transfer efficiency of individual particles was complicated and could vary according to conditions. Moreover, compared to the powder spray gun, the bell-cup atomizer has the following characteristics: · The swirl flow was generated due to the bell-cup rotation. · The relatively large particles were less subject to get to the target because of the inertia and swirl. · When zero voltage was applied, the transfer efficiency was relatively high because of the shaping air flow. · The transfer efficiency was more sensible to Sauter mean diameter when the electric voltage was applied. Therefore, the control technique of the particle diameter is critically important in order to improve the transfer efficiency, especially for the bell-cup atomizer. Acknowledgement This work was supported by Grant-in-Aid for JSPS Fellows (No. 16J02921).
Nomenclature CD = Cμ, Cε1, Cε2 D32 = E = d = k = Np = p = Qp = q = Re = Sij = ¯ S p,i = t = u = ΔV =
drag coefficient = constants in k–ε model Sauter mean diameter electrostatic field diameter kinetic energy number of particles in the parcel pressure charge of the parcel specific charge of particle Reynolds number strain rate source term for particles elapsed time velocity volume of the cell
[—] [—] [m] [V] [m] [m2/s2] [Pa·s] [C] [C/kg] [—] [1/s] [s] [m/s] [m3]
Journal of Chemical Engineering of Japan
x
= coordinate
β Γ δij ε ε0 ν ρ ρe σ σk, σε τ φ φ0
= = = = = = = = = = = = =
distribution constant gamma function delta function eddy dissipation rate permittivity kinetic viscosity density space charge density standard deviation Schmidt number Reynolds stress tensor electric voltage applied electric voltage
[m]
[m2/s3] [F/m] [m2/s] [kg/m3] [C/m3] [—] [—] [m2/s2] [kV] [kV]
‹Subscripts› f = fluid i, j = direction p = particle t = turbulence
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