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molten metal interaction
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Original Research Paper
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A numerical simulation study of the path-resolved breakup behaviors of molten metal in high-pressure gas atomization: With emphasis on the role of shock waves in the gas/molten metal interaction
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Rashed Kaiser a, Chengguo Li a, Sangsun Yang b,⇑, Donggeun Lee a,⇑
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a b
School of Mechanical Engineering, Pusan National University, Busan 46241, South Korea Powder and Ceramics Division, KIMS, Changwon 51508, South Korea
a r t i c l e
i n f o
Article history: Received 21 October 2017 Accepted 6 December 2017 Available online xxxx Keywords: High-pressure gas atomization Metal powder Shock waves Path-resolved secondary breakup Gas-to-metal interaction
a b s t r a c t Although high-pressure gas atomization has been widely used for the large-scale production of fine metal powders, high operating costs remain one of its biggest issues. The key to efficiency lies in how to strengthen the gas/molten metal interaction. Despite this, most of the extensive previous studies have focused on evaluating various nozzles by flow visualization and the size measurement of the resulting powder. It is known that strong shock waves are inevitably produced by a pressure mismatch through the nozzle, however the effect of those shock waves on gas flow and breakup behavior is still unclear. The purpose of this numerical simulation study was to determine whether any efficient paths for maximizing the gas-melt interaction exist, and to elucidate possible effects of the shock waves. Two types of supersonic nozzles were employed for the simulations: an annular slit nozzle, versus an isentropic plug nozzle working in shock-free mode. Single particle analysis was performed by injecting a single coarse droplet at different locations near the nozzle exit and then monitoring the local gas velocity and breakup characteristics along its path. The same path-resolved analysis was repeated for continuous droplet injection under various gas-to-melt ratios. The results indicate that more efficient paths exist for the maximal use of gas kinetic energy, and that shock waves are detrimental to producing smaller sized powders. Ó 2017 Published by Elsevier B.V. on behalf of The Society of Powder Technology Japan. All rights reserved.
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1. Introduction
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Powder metallurgy involves the fabrication of metal powders using various techniques, and today includes a wide range of procedures and applications. Presently, the high-pressure gas atomization (HPGA) approach is attracting attention, since it allows for the efficient and consistent production of fine spherical particles (1–250 µm) at industrial scales [1]. The products that can be obtained using this method include powders of pure metals, such as Fe, Cu, Sn, Ti, and Ni, and their alloys [1]. The HPGA method uses gas, which imparts kinetic energy directly to the molten metal, leading to rapid disintegration and solidification of the melt into a fine metallic powder with high purity [2]. However, in spite of the versatility of the method and the high purity of the resulting powders, it is still considered a costly process, because of its inefficient use of energy. HPGA involves high temperatures and pressures and consumes large amounts of gases
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⇑ Corresponding authors. E-mail addresses: [email protected] (S. Yang), [email protected] (D. Lee).
[1,3]. In fact, the energy efficiency of the HPGA method is very low, approximately 2–4% [4]. A number of experimental [1,3,5] and simulation studies [6,7] have focused on changing the design of the nozzle to further reduce particle size. In addition, there have been experimental [9,10] and simulation based [11,12] parametric evaluations involving varying gas pressures, temperatures, and gas to metal ratios (GMR), with the same goal. However, it is still unclear how to make the HPGA process more efficient without adversely affecting the size and properties of the resulting powder. The atomization of a molten metal is a complex process that involves aerodynamic (high-speed gas) and hydrodynamic (liquid droplet formation) mutual responses between the gas and the metal melt. When the molten metal is introduced to a melt-feeding tube (as seen in Fig. 1), breakup starts near the nozzle exit with the formation of wavy melt surfaces, which disintegrate into small droplets due to the intensive transfer of kinetic energy from the gas to the melt. This energy transfer is normally characterized by the Weber number (We) [13], defined as the ratio of kinetic energy of the gas to the surface tension of the melt:
https://doi.org/10.1016/j.apt.2017.12.003 0921-8831/Ó 2017 Published by Elsevier B.V. on behalf of The Society of Powder Technology Japan. All rights reserved.
Please cite this article in press as: R. Kaiser et al., A numerical simulation study of the path-resolved breakup behaviors of molten metal in high-pressure gas atomization: With emphasis on the role of shock waves in the gas/molten metal interaction, Advanced Powder Technology (2017), https://doi.org/ 10.1016/j.apt.2017.12.003
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Fig. 1. Geometries of the computational domains used: (a) ASN and (b) IPN. 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124
We = qg(Urel)2rp/r where qg refers to gas density, Urel is the relative velocity, rp is the radius of droplet that will undergo further breakup, and r is the surface tension of the molten metal [7]. Since a higher We is required to produce a metal powder with a smaller particle size, the supersonic gas flow must be kept in contact with the liquid melt as much as possible. Given the importance of this factor, it is notable that there is no report that offers detailed guidance for how to maximize the gas-to-melt interaction, despite the large number of numerical simulations. At the very least, it would certainly be helpful to know the most efficient approach to ensure maximal use of the gas, and what happens to the melt droplets in the gas flow. From the perspective of the interaction, shock waves that are inevitably produced by a pressure mismatch through the nozzles and can abruptly dissipate the kinetic energy of the gas should be minimized. On the other hand, shock waves may make a positive contribution to the breakup, because the shocks can subject the coarser droplets to a sudden change in the velocity of the gas, and the instantaneous increase in velocity relative to the gas can presumably promote the We. Only a limited number of studies have been conducted to identify the effects of shock waves on the atomization process [14,15]. And, most of those studies have focused on visualizing the apparent difference in patterns of water sprayed by subsonic and supersonic air blast atomizers [14] or the spray penetration of diesel fuel [15]. Understanding the role of the shock waves in the gas-melt interaction, and the resulting melt breakup behaviors, might be essential to exploiting the shock waves to increase the degree of atomization and further reduce the particle size. The present study was motivated by these considerations. Its aim was to determine the existence of any efficient paths for maximizing the gas-melt interaction, as well as elucidating the possible roles of shock waves. Two types of spray nozzles were considered: a typical converging-diverging nozzle known as an annular slit nozzle (ASN) [16,17], versus an external expansion nozzle called an isentropic plug nozzle (IPN) [7,18–24]. A single particle analysis was performed by injecting a single coarse droplet at different locations near the nozzle exit and then monitoring the local gas velocity and breakup characteristics along its path. Then, this path-resolved analysis was repeated for continuous injection with various gas-to-melt ratio conditions.
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2. Computational fluid and particle dynamics simulations
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2.1. Supersonic gas flow simulations
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Two different computational domains, schematically shown in Fig. 1, were created for computational fluid dynamics (CFD) simu-
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lations based on the two types of supersonic nozzles. The domain includes a nozzle and melt feeding tube assembly, a far-field radial boundary, and a downstream exit. The far-field boundary in the radial direction was set in the same position as the typical radius of the HPGA system, while the downstream exit was positioned far enough downstream of the melt feeding tube (MFT), 12.5 diameters, based on our previous work [11]. Structured grids with 20,429 and 27,000 cells were generated for the ASN and IPN, respectively. Local grid refinement was also applied in the area of interest, i.e., near the nozzle and MFT, where large pressure and velocity gradients were expected. Fig. 1(a) shows that the ASN, which has been widely used [16,17] in conventional HPGA processes, is a convergingdiverging slit nozzle with a throat created by a concentric nozzle wall and the curved outer surface of the MFT; note that the nozzle wall is shaped so sharply that the MFT tip seems to be extended into the chamber (compare the positions of the ‘Nozzle exit’ and ‘MFT tip’ in Fig. 1(a); and refer to the design of the MFT tip in Ref. [17]). The IPN shown in Fig. 1(b) was designed to enable nearisentropic expansion with minimal shock formation and thereby to improve the transfer of kinetic energy from gas to melt [7,18– 24]. Note that this nozzle, consisting of a tapered nozzle wall and a gently shaped MFT, is supposed to allow near optimal expansion of gas from the throat as it is being guided along the MFT surface [25]. Nitrogen, the atomizing gas, was assumed to be an inert, compressible ideal gas. Molten steel at 2000 K was selected to be the liquid (melt) phase to be broken up, and its physical properties are summarized in Table 1. The inlet boundary of the gas was subjected to a constant injection pressure of 11 atm and a temperature of 300 K, while the pressure at the exit of the domain was set to 1 atm. The CFD simulations for the gas were performed using the commercial code Ansys Fluent 16 under the assumptions of unsteady, axisymmetric, two-dimensional supersonic gas flow. Due to the high velocity of the gas, the gas flow is essentially tur-
Table 1 Material properties of molten steel. Properties
Value
Reference
H. latent heat [J/kg] C liquid [J/kg K] Density [kg/m3] Viscosity [kg/m s] Thermal conductivity [W/mK] Surface tension [N/m] Boiling point [K] Vaporization point [K]
250,000 825 7700 0.0056 16.3 1.2 3003 2273
[7] [7] [7] [7] [7] [7] [8] [8]
Please cite this article in press as: R. Kaiser et al., A numerical simulation study of the path-resolved breakup behaviors of molten metal in high-pressure gas atomization: With emphasis on the role of shock waves in the gas/molten metal interaction, Advanced Powder Technology (2017), https://doi.org/ 10.1016/j.apt.2017.12.003
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bulent and treated by the Reynolds-stress model [16]. To improve accuracy and to avoid the divergence problem, a sufficiently small time step of 10 ls was used for the gas-phase simulations.
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2.2. Melt breakup modelling and droplet dynamics simulations
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The HPGA process of the metal melt has often been modelled as two successive atomization steps: the primary and the secondary breakup [26]. The melt, upon first contact with the supersonic gas jet, deforms and begins to form millimeter-sized coarse droplets soon after detachment from the melt surface: this is known as the primary breakup. These coarse droplets, if further exposed to the supersonic jet stream, undergo a secondary breakup into fine metal droplets [26]. Because the final droplet size is determined mainly by the secondary breakup, within 10% deviation [3,27], only the secondary breakup was taken into account in this study, to reduce the calculation load. The secondary breakup in the HPGA process has often been characterized by two distinct regimes: bag breakup vs stripping breakup, depending on the kinetic energy transfer from gas to droplet [28]. These two types of breakup have recently been modelled by the Taylor analogy breakup (TAB) model and Kelvin-Helmholtz (KH) instability model [16]. According to Liu et al. [28] and Zeoli and Gu [16], the sizes of the fine droplets produced during the secondary breakup were successfully predicted using the KH model. Thus, only the KH model was considered in this study. The secondary breakup model was implemented for the two nozzle designs, as follows. The gas-phase momentum conservation equations were two-way coupled with the discrete phase model in Ansys Fluent, and the resulting mass loading effect was involved in the droplet dynamics simulations. After the gas flow reached a stead state, coarse (parent) droplets with a diameter of 1 mm were continually released from the melt at the corner of the MFT tip, at a mass flow rate of 0.29 kg/s (corresponding to a GMR of 1.1), and the resulting fine (child) droplets were monitored by recording their position, size, and velocity relative to the gas, with a time step of 1 ls. The mean diameter of the child droplets was repeatedly measured at the exit at a specific time interval, i.e., every 1 ms, until the diameter became time-invariant. The final size distribution of the child droplets was obtained as a result. In the present study, a single particle analysis was developed to identify the most efficient way to minimize the size of the child droplets. Since the gas stream undergoes large velocity gradients in the vertical (radial) direction from the nozzle axis (i.e., the y direction in Fig. 1), a parent droplet would experience significantly different gas-velocity paths depending on its initial release position, presumably resulting in path-dependent breakup behaviors. To clarify this effect, three spherical parent droplets with an equal diameter of 1 mm were released individually at three different radial positions but at an equal distance (8 mm) from the MFT tip; and then their positions and velocities relative to the gas were monitored along the paths. 8 mm was chosen so that they would undergo vigorous secondary breakup, based on Mates and Settles’ visualization experiments [3]. As the first case, a parent droplet was released at the farthest radial position, and the trajectory that it showed was called ‘‘zone 1”; the droplet is called the zone-1 droplet thereafter. Likewise, the zone-3 droplet represents another parent droplet released at the nearest position to the nozzle axis. The zone-2 droplet indicates the case of being released between zone 1 and 3. During the secondary breakup, a parent droplet shortly disintegrates into and/or peels off tiny child droplets, reducing its size to some degree. This in turn reduces the Weber number that the parent droplet experiences. The radius of the parent droplet was assumed to be invariant unless the mass removal reached 3% of its initial mass [11]. Because a large number of child droplets, coex-
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isting with their parent droplet, could take different paths and move with different speeds than one another, to simplify the single particle analysis the main focus here was the behavior of the parent droplet.
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3. Results and discussion
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3.1. Gas flow dynamics
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The performance of the two nozzles was evaluated through simulations involving only the gas flow. The upper portion of Fig. 2 shows the velocity contour of the gas with a schematic drawing of its interesting features, while the lower graph depicts the variations in pressure along the main stream of the gas. The xaxis of the graph was drawn on the same scale as the nozzle geometry so that the local gas velocity could be studied in conjunction with the corresponding pressure. For the same purpose, important parts in the design of the nozzles are marked with vertical lines in the figure; refer to the nozzle throat, exit, and MFT tip of the ASN (in Fig. 2(a)) in comparison with nozzle throat and MFT tip of the IPN (in Fig. 2(b)). The main stream of the gas marked with an oval is also enlarged and shown at the top of the figure. As the high-pressure gas jet passes through the throat of the ASN, the gas is supersonically accelerated in the diverging part up to the exit (refer to ‘1’ in Fig. 2(a)) while the gas pressure falls rapidly below the chamber pressure of 1 atm. Accordingly, the gas jet, right after the exit (‘1’), first appears to be overexpanded, and then decelerated, due to the action of oblique shock (marked with ‘A’), which raises the pressure above 1 atm (refer to the pressure profile in Fig. 2(a)). Due to the excessive pressure recovery, the gas is again expanded near the MFT tip. As illustrated in the magnified snapshot of the gas main stream, this expanding gas jet (‘3’) encounters a series of Prandtl-Meyer expansion waves (‘B’) and their reflected compression waves (‘C’); and is guided toward the symmetric axis along its sonic line (‘F’), creating a subsonic recirculation region (‘D’). This seemingly pulsating gas jet is enveloped by an external turbulent layer (‘G’) with lower velocity. The repeated expansioncompression pattern results in a pressure oscillation around 1 atm and continues until the pressure matches the chamber pressure (1 atm), as shown in the graph of Fig. 2(a). Meanwhile, the upper portion of Fig. 2(b) illustrates the three distinct flow characteristics in the IPN: (1) the velocity and pressure fluctuations become so weakened that the pressure very quickly matches the chamber pressure, (2) roughly suggesting the absence of strong oblique shocks, and (3) the supersonic jet (named ‘6’) passing through the IPN throat forms almost flattened sonic boundaries (‘7’), presumably as a result of the near isentropic expansion of the gas. With the help of the gradually-expanding divergent part of the nozzle, the gas can go through a more gentle velocity change without creating strong shocks. One may notice that the maximum speed of the gas in the ASN appears to be a little higher than in the IPN. However, it is still unclear if the shock waves in the ASN are beneficial to the gas atomization, because the shocks can alter the particle trajectories, as well as the path-dependent breakup efficiency. This will be discussed in detail in the next section.
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3.2. Single-particle analysis
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Fig. 3 displays the successive positions of an individual parent droplet belonging to each zone. Here, the zone-1, zone-2 and zone-3 parent droplets are highlighted with red, blue and black circles, respectively. In the ASN, as shown in Fig. 3(a), the zone-1 droplet appears to take a detour around the first oblique shock and
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Fig. 2. Characteristics of gas flow before introducing the melt, and contour plots of the velocity magnitude of the gas of the (a) ASN and (b) IPN.
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moves away from the main stream toward the outer subsonic region. On the other hand, the zone-3 droplet directly penetrates into the shock and undergoes a series of alternating gas velocity and pressure oscillations because of the shock. The zone-2 droplet shows a trajectory in between the zone-1 and zone-3 droplet paths. Clearly, the zone-2 droplet undergoes similar strong gas velocity oscillations in the beginning, and then moves out of the main stream about 50 mm downstream of the MFT tip of the ASN. Fig. 3(b) shows that the parent droplet in the IPN exhibits quite similar behavior in the red and black cases (i.e., zone-1 and zone-3, respectively), however the blue (zone-2) droplet, as it encounters the weaker shock, compared to the ASN, does not necessarily deflect from the high-velocity region, but rather keeps going through the main stream of the gas. Compared to the two zone-2 droplets in Fig. 3(a) and (b), the zone-2 path in the IPN is likely more efficient than the one in the ASN. A more quantitative analysis was attempted to compare the effects of the designs of the two nozzles on particle breakup. Fig. 4(a1) and (a2) show the profiles of velocity and Weber number that each parent droplet will experience as a function of
Fig. 3. Comparison of gas flow characteristics and trajectories for a parent droplet, depending on its launching zones in the (a) ASN and (b) IPN.
axial distance from the ASN tip. Fig. 4(a3) shows where child droplets belonging to each parent are in the calculation domain and what size they are. In Fig. 4(a1), the gas velocity along the zone1 path slowly decreases with large fluctuations up to an axial distance of 70 mm, and then oscillates around 200 m/s further downstream in response to weakened alternating shocks. Along the zone-2 path, the gas velocity rapidly decreases with a certain level of fluctuation owing to the opposing shock-induced pressure. The zone-3 path shows that the gas velocity remains above 480 m/ s up to the axial distance of 100 mm, suggesting that the path provides a way to obtain maximal use of the shocks. These findings are consistent with the expectation based on Fig. 3(a). In contrast, the velocities of the parent droplets are almost invariant regardless of their paths; not being affected by the shocks, possibly due to their large inertia, they can keep going on with a fairly constant speed. As shown in Fig. 4(a2), the Weber number was calculated from the velocity difference between the gas and droplets along each zone. The Weber number of the zone-1 droplet quickly decreases below 50, at 35 mm from the MFT tip. Meanwhile, the zone-3 droplet maintains a high level Weber number for the longest distance, up to 65 mm from the tip. The Weber number of the zone-2 droplet, though it starts from the highest value of 400, falls rapidly below 50, at 50 mm from the MFT tip. Such a sharp decrease can be understood by the rapid decrease in gas velocity along the zone-2 path shown in Fig. 4(a1). Beyond 70 mm of the axial distance, the Weber numbers for both zone-2 and -3 droplets become smaller than 10, which implies that the droplet breakup will stop [11]. Unlike the process of tracking parent droplets along their paths, tracking child droplets is not easy, even in this single particle analysis, because of the complexities involved. (1) Different numbers of child droplets are occasionally born from a single parent droplet while it is moving, but with different sizes, depending on the local position of their parent droplet. (2) A small difference in the birth position of the child droplets can cause a large difference in their path and further breakup behavior. (3) Some of the child droplets
Please cite this article in press as: R. Kaiser et al., A numerical simulation study of the path-resolved breakup behaviors of molten metal in high-pressure gas atomization: With emphasis on the role of shock waves in the gas/molten metal interaction, Advanced Powder Technology (2017), https://doi.org/ 10.1016/j.apt.2017.12.003
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Fig. 4. Velocity and Weber number distributions of the parent droplets and the diameters of the child droplets for the three zones in the (a) ASN and (b) IPN.
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can take high-speed paths and disappear from the calculation domain, while the rest of them are still observed. In consideration of these complexities, a snapshot was taken in an attempt to visualize the sizes and positions of the child droplets remaining in the domain, instead of tracking them. As an example, Fig. 4(a3) was obtained from a snapshot taken 2 ms after releasing a single parent drop at each zone. Note that the parent droplet is
not shown for simplicity. In Fig. 4(a3), only four child droplets have been produced from the zone-1 parent droplet, and they stay upstream (axial distance < 30 mm). At the same point in time, both zone-2 and zone-3 parent droplets produced many more child droplets, which move faster downstream. Note that these child droplets reached 180 mm downstream of the MFT tip. It is interesting to note that some of them (particularly the smaller
Please cite this article in press as: R. Kaiser et al., A numerical simulation study of the path-resolved breakup behaviors of molten metal in high-pressure gas atomization: With emphasis on the role of shock waves in the gas/molten metal interaction, Advanced Powder Technology (2017), https://doi.org/ 10.1016/j.apt.2017.12.003
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ones) were found to have escaped from the domain. Moreover, most of the zone-2 and zone-3 child droplets are smaller than the zone-1 child droplets. This observation suggests that the zone-2 and zone-3 paths are more beneficial than the zone-1 path for producing powders with smaller sizes and larger populations, which sounds consistent with the aforementioned expectation from Fig. 4(a1–a2). Because the IPN produces fewer shock waves, the supersonic jet stream through the nozzle shows almost non-oscillatory velocity profiles along the paths as seen in Fig. 4(b1). In comparison with Fig. 4(a1), the most noticeable difference appears in the zone-2 path; the gas flow velocity remains high up to the 80-mm axial distance, unlike in the ASN. As a result, the zone-2 parent droplet in the IPN is able to experience a high We above 100, up to 65 mm in axial distance, as shown in Fig. 4(b2). This might explain why there are no zone-2 child droplets larger than 50 lm present in Fig. 4(b3). These connected results indicate that the (shock-free) IPN is superior to the ASN, at least in one (zone-2) of the major paths.
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3.3. Continuous particle analysis
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Injecting the parent droplets on a continuous basis in the secondary breakup phase might produce somewhat different results than those of the single droplet injection, because it involves a much larger number of new-born particles and thus more vigorous gas-particle two-way interactions [29]. Hence, this section is devoted to checking whether the path-dependent breakup features described in Section 3.2 are still valid in the more-realistic case, i.e., continuous droplet injection. Identical parent droplets (of 1 mm diameter) were injected at the same radial positions as in the single particle analysis, however, continually, under control of the GMR at 1.1. Fig. 5(a) and (b) shows the contour plots of the Mach numbers of the gas flow fields through the ASN and IPN, respectively. It should be recalled that the figures represent the gas flow at the steady state in both nozzle systems upon continuous droplet injection. In comparison with Figs. 2 and 3, there is a notable difference in the gas flow: the supersonic region, which was as long as 160 mm, is greatly shortened by the continuous droplet injection in both nozzles. Note that the greenish (supersonic) stripes in Fig. 5 (a) turn blue (subsonic) within 50 mm in axial distance, whereas
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the greenish area in the IPN extends up to 5–6 diameters of the MFT (90 mm) (see Fig. 5(b)). The reduced supersonic zone indicates rapid gas deceleration resulting from the transfer of kinetic energy from the gas to the (parent and child) droplets. As a result, the gas seems to expand outward (radially) to avoid a group of existing droplets, which looks like a typical under-expanded supersonic jet plume from a rocket. This is clearly related to the well-known mass loading effect [3,11]. The radial expansion is more noticeable in the ASN (see Fig. 5(a)). In contrast, the gas which is expanding less in the IPN likely experiences relatively low flow resistance, implying that smaller droplets exist ahead. Fig. 6(a) and (b) shows the snapshots of sprayed droplets taken 20 ms from the beginning of droplet injection in the ASN and IPN, respectively. In Fig. 6 (a), blue (<100 lm) droplets from the ASN apparently diverge significantly in the radial direction, accompanied by two greenish streaks (larger than 100 lm) of particles. In the IPN (see Fig. 6(b)), however, the droplets are clearly less diverged and the greenish droplets change their color gradually and eventually becomes blue (sub-hundred micrometer) at the exit boundary. This observation again sounds consistent with the expectation from Fig. 5. Let us further discuss the breakup behavior from the pathdependent view. Unlike the single-particle analysis, where the mass loading effect is negligible, under continuous injection the near-axis gas flow is now subsonic (Compare Figs. 3 and 5), deactivating the zone-3 paths (near the axis) in both nozzles to some extent. Instead, the zone-1 paths appear to be upgraded with the help of the radial expansion of the gas. It is naturally presumed that the zone-2 paths positioned between the zone-1 and -3 paths are likely to be much less affected by the existence of droplets, and still remain favorable for droplet breakup in both nozzles. It is interesting to note the Schlieren image taken by Mates et al. [3], where a number of un-atomized coarse droplets were similarly seen in the jet core. A quantitative assessment of the breakup performance of each path was attempted by injecting droplets in one of the three locations and repeating the breakup calculation. Fig. 7(a) shows the cumulative size distributions of the child droplets coming from each path in the ASN. As predicted above, the zone-1 path turns out to be efficient for droplet breakup in the case of continuous zone-1 injection, producing droplets as small as 50 lm in mass
Fig. 5. Contour plots of Mach number in the gas flow of (a) ASN and (b) IPN with continuous particle injection.
Please cite this article in press as: R. Kaiser et al., A numerical simulation study of the path-resolved breakup behaviors of molten metal in high-pressure gas atomization: With emphasis on the role of shock waves in the gas/molten metal interaction, Advanced Powder Technology (2017), https://doi.org/ 10.1016/j.apt.2017.12.003
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Fig. 6. Snapshots of particle generation during high-pressure gas atomization using (a) ASN and (b) IPN.
Fig. 7. Cumulative mass size distributions of particles originated from three different zones and generated with the combined mode, in (a) ASN and (b) IPN.
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median diameter (d50). The zone-2 path still remains the best choice, and is capable of producing the smallest (d50 = 46 lm) droplets with the narrowest size distribution. The zone-3 path, unlike
the results for the single-particle analysis, is significantly downgraded, so that the resulting droplets are significantly larger, with d50 = 100 lm. When the droplets are differentiated according to their origins (zones), the zone-3 droplets, particularly the large ones, are confirmed to move toward the axis where the gas flow is subsonic, as represented by the greenish droplets in Fig. 6(a). For comparison, a cumulative size distribution of droplets was obtained for the combined injection at the three locations, and added in Fig. 7(a). The size distribution gets closer to the curves of the zone-1 or zone-2 paths, away from the curve of the zone-3 path. One may wonder why the zone-1 and -2 paths dominate the breakup behaviors under the combined injection. It is worth noting that the zone-3 large droplets pass through the exit boundary much slower than the others, which results in a sampling bias towards fast-moving droplets (just like the concept of cup-mixing sampling [30]). Those size measurements were repeated for the IPN and the results are shown in Fig. 7(b). Overall, similar trends were observed in those size distributions; the zone-1 and -2 paths are superior to the zone-3 path and their results are almost identical to the combined-mode size distribution. It should be noted, however, that the IPN produces smaller droplets than the ASN; for example, d50 = 45 lm and d84 = 70 lm in the IPN vs d50 = 52 lm and d84 = 90 lm in the ASN. From the perspective of size reduction, it is concluded that the shock waves produced in the ASN are not beneficial, at least under the present conditions. In order to test both nozzles under harsher conditions, Anderson and Terpstra [5]’s HPGA conditions were additionally taken into account. Their nozzle, consisting of 22 convergent-divergent discrete jets, was operated at higher pressures of 27.6 and 55.2 atm, and tested for HPGA using molten stainless steel and argon gas; refer to Table 1 in Ref. [5] for further details of the experiments. Under two different GMR conditions (0.36 and 1.29; corresponding to the low and high pressure, respectively), both designs of the ASN and IPN (after matching the GMR values) were simulated. The simulation results at the two gas pressures are shown and compared with the experimental data in Fig. 8(a) and (b), respectively. Under both pressure conditions, the IPN again turns out to be more efficient than the ASN, producing smaller droplets with a narrower size distribution (see the inset table). Both figures also confirm that the size distributions obtained from the experiments are in better agreement with those from the ASN. This might
Please cite this article in press as: R. Kaiser et al., A numerical simulation study of the path-resolved breakup behaviors of molten metal in high-pressure gas atomization: With emphasis on the role of shock waves in the gas/molten metal interaction, Advanced Powder Technology (2017), https://doi.org/ 10.1016/j.apt.2017.12.003
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Fig. 8. Comparison of simulated cumulative mass size distributions with experiment [5] at (a) 27.6 atm (b) 55.2 atm gas pressure.
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be attributed to the fact that the discrete jet holes in the experiment are more similar to the ASN design, rather than the IPN.
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4. Conclusions
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In this study, numerical simulations of the HPGA process were performed with two types of nozzles, with the aim of highlighting the effects of shockwaves on gas flow and particle breakup. Single particle analysis was performed by injecting a single coarse droplet at different locations near the nozzle exit, in an attempt to monitor the gas velocity and breakup characteristics that the coarse droplet undergoes along its path. As a result, it was found that favorable flow paths for reducing the resulting droplet size clearly exist; the efficiency of the paths is affected by the shock waves to some degree. The path-resolved analyses were repeated for continuous injection under various gas-to-melt ratio conditions. The results indicated again that the most favorable path was still valid under realistic conditions and apparently dominates other paths, although the other less favorable paths were likely affected by the mass loading effect. Shock waves turn out to be unfavorable for reducing the powder size, at least under the conditions in this study.
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Acknowledgements
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This work was supported by the National Research Foundation (NRF) of Korea (No. 2016R1A2B2014141), which is funded by the
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Ministry of Education, Science and Technology (MEST), Korea, and by the ‘‘Development of the Preparation Technology of 0.1– 10 µm Sized Metal Powders and Fine-Components for Micro Electronics” project of the Ministry of Knowledge Economy (MKE), Korea, and the Korea Research Council for Industrial Science and Technology (ISTK).
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Contents lists available at ScienceDirect
Advanced Powder Technology journal homepage: www.elsevier.com/locate/apt
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Original Research Paper
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A numerical simulation study of the path-resolved breakup behaviors of molten metal in high-pressure gas atomization: With emphasis on the role of shock waves in the gas/molten metal interaction
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Rashed Kaiser a, Chengguo Li a, Sangsun Yang b,⇑, Donggeun Lee a,⇑
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a b
School of Mechanical Engineering, Pusan National University, Busan 46241, South Korea Powder and Ceramics Division, KIMS, Changwon 51508, South Korea
a r t i c l e
i n f o
Article history: Received 21 October 2017 Accepted 6 December 2017 Available online xxxx Keywords: High-pressure gas atomization Metal powder Shock waves Path-resolved secondary breakup Gas-to-metal interaction
a b s t r a c t Although high-pressure gas atomization has been widely used for the large-scale production of fine metal powders, high operating costs remain one of its biggest issues. The key to efficiency lies in how to strengthen the gas/molten metal interaction. Despite this, most of the extensive previous studies have focused on evaluating various nozzles by flow visualization and the size measurement of the resulting powder. It is known that strong shock waves are inevitably produced by a pressure mismatch through the nozzle, however the effect of those shock waves on gas flow and breakup behavior is still unclear. The purpose of this numerical simulation study was to determine whether any efficient paths for maximizing the gas-melt interaction exist, and to elucidate possible effects of the shock waves. Two types of supersonic nozzles were employed for the simulations: an annular slit nozzle, versus an isentropic plug nozzle working in shock-free mode. Single particle analysis was performed by injecting a single coarse droplet at different locations near the nozzle exit and then monitoring the local gas velocity and breakup characteristics along its path. The same path-resolved analysis was repeated for continuous droplet injection under various gas-to-melt ratios. The results indicate that more efficient paths exist for the maximal use of gas kinetic energy, and that shock waves are detrimental to producing smaller sized powders. Ó 2017 Published by Elsevier B.V. on behalf of The Society of Powder Technology Japan. All rights reserved.
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1. Introduction
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Powder metallurgy involves the fabrication of metal powders using various techniques, and today includes a wide range of procedures and applications. Presently, the high-pressure gas atomization (HPGA) approach is attracting attention, since it allows for the efficient and consistent production of fine spherical particles (1–250 µm) at industrial scales [1]. The products that can be obtained using this method include powders of pure metals, such as Fe, Cu, Sn, Ti, and Ni, and their alloys [1]. The HPGA method uses gas, which imparts kinetic energy directly to the molten metal, leading to rapid disintegration and solidification of the melt into a fine metallic powder with high purity [2]. However, in spite of the versatility of the method and the high purity of the resulting powders, it is still considered a costly process, because of its inefficient use of energy. HPGA involves high temperatures and pressures and consumes large amounts of gases
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⇑ Corresponding authors. E-mail addresses: [email protected] (S. Yang), [email protected] (D. Lee).
[1,3]. In fact, the energy efficiency of the HPGA method is very low, approximately 2–4% [4]. A number of experimental [1,3,5] and simulation studies [6,7] have focused on changing the design of the nozzle to further reduce particle size. In addition, there have been experimental [9,10] and simulation based [11,12] parametric evaluations involving varying gas pressures, temperatures, and gas to metal ratios (GMR), with the same goal. However, it is still unclear how to make the HPGA process more efficient without adversely affecting the size and properties of the resulting powder. The atomization of a molten metal is a complex process that involves aerodynamic (high-speed gas) and hydrodynamic (liquid droplet formation) mutual responses between the gas and the metal melt. When the molten metal is introduced to a melt-feeding tube (as seen in Fig. 1), breakup starts near the nozzle exit with the formation of wavy melt surfaces, which disintegrate into small droplets due to the intensive transfer of kinetic energy from the gas to the melt. This energy transfer is normally characterized by the Weber number (We) [13], defined as the ratio of kinetic energy of the gas to the surface tension of the melt:
https://doi.org/10.1016/j.apt.2017.12.003 0921-8831/Ó 2017 Published by Elsevier B.V. on behalf of The Society of Powder Technology Japan. All rights reserved.
Please cite this article in press as: R. Kaiser et al., A numerical simulation study of the path-resolved breakup behaviors of molten metal in high-pressure gas atomization: With emphasis on the role of shock waves in the gas/molten metal interaction, Advanced Powder Technology (2017), https://doi.org/ 10.1016/j.apt.2017.12.003
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Fig. 1. Geometries of the computational domains used: (a) ASN and (b) IPN. 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124
We = qg(Urel)2rp/r where qg refers to gas density, Urel is the relative velocity, rp is the radius of droplet that will undergo further breakup, and r is the surface tension of the molten metal [7]. Since a higher We is required to produce a metal powder with a smaller particle size, the supersonic gas flow must be kept in contact with the liquid melt as much as possible. Given the importance of this factor, it is notable that there is no report that offers detailed guidance for how to maximize the gas-to-melt interaction, despite the large number of numerical simulations. At the very least, it would certainly be helpful to know the most efficient approach to ensure maximal use of the gas, and what happens to the melt droplets in the gas flow. From the perspective of the interaction, shock waves that are inevitably produced by a pressure mismatch through the nozzles and can abruptly dissipate the kinetic energy of the gas should be minimized. On the other hand, shock waves may make a positive contribution to the breakup, because the shocks can subject the coarser droplets to a sudden change in the velocity of the gas, and the instantaneous increase in velocity relative to the gas can presumably promote the We. Only a limited number of studies have been conducted to identify the effects of shock waves on the atomization process [14,15]. And, most of those studies have focused on visualizing the apparent difference in patterns of water sprayed by subsonic and supersonic air blast atomizers [14] or the spray penetration of diesel fuel [15]. Understanding the role of the shock waves in the gas-melt interaction, and the resulting melt breakup behaviors, might be essential to exploiting the shock waves to increase the degree of atomization and further reduce the particle size. The present study was motivated by these considerations. Its aim was to determine the existence of any efficient paths for maximizing the gas-melt interaction, as well as elucidating the possible roles of shock waves. Two types of spray nozzles were considered: a typical converging-diverging nozzle known as an annular slit nozzle (ASN) [16,17], versus an external expansion nozzle called an isentropic plug nozzle (IPN) [7,18–24]. A single particle analysis was performed by injecting a single coarse droplet at different locations near the nozzle exit and then monitoring the local gas velocity and breakup characteristics along its path. Then, this path-resolved analysis was repeated for continuous injection with various gas-to-melt ratio conditions.
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2. Computational fluid and particle dynamics simulations
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2.1. Supersonic gas flow simulations
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Two different computational domains, schematically shown in Fig. 1, were created for computational fluid dynamics (CFD) simu-
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lations based on the two types of supersonic nozzles. The domain includes a nozzle and melt feeding tube assembly, a far-field radial boundary, and a downstream exit. The far-field boundary in the radial direction was set in the same position as the typical radius of the HPGA system, while the downstream exit was positioned far enough downstream of the melt feeding tube (MFT), 12.5 diameters, based on our previous work [11]. Structured grids with 20,429 and 27,000 cells were generated for the ASN and IPN, respectively. Local grid refinement was also applied in the area of interest, i.e., near the nozzle and MFT, where large pressure and velocity gradients were expected. Fig. 1(a) shows that the ASN, which has been widely used [16,17] in conventional HPGA processes, is a convergingdiverging slit nozzle with a throat created by a concentric nozzle wall and the curved outer surface of the MFT; note that the nozzle wall is shaped so sharply that the MFT tip seems to be extended into the chamber (compare the positions of the ‘Nozzle exit’ and ‘MFT tip’ in Fig. 1(a); and refer to the design of the MFT tip in Ref. [17]). The IPN shown in Fig. 1(b) was designed to enable nearisentropic expansion with minimal shock formation and thereby to improve the transfer of kinetic energy from gas to melt [7,18– 24]. Note that this nozzle, consisting of a tapered nozzle wall and a gently shaped MFT, is supposed to allow near optimal expansion of gas from the throat as it is being guided along the MFT surface [25]. Nitrogen, the atomizing gas, was assumed to be an inert, compressible ideal gas. Molten steel at 2000 K was selected to be the liquid (melt) phase to be broken up, and its physical properties are summarized in Table 1. The inlet boundary of the gas was subjected to a constant injection pressure of 11 atm and a temperature of 300 K, while the pressure at the exit of the domain was set to 1 atm. The CFD simulations for the gas were performed using the commercial code Ansys Fluent 16 under the assumptions of unsteady, axisymmetric, two-dimensional supersonic gas flow. Due to the high velocity of the gas, the gas flow is essentially tur-
Table 1 Material properties of molten steel. Properties
Value
Reference
H. latent heat [J/kg] C liquid [J/kg K] Density [kg/m3] Viscosity [kg/m s] Thermal conductivity [W/mK] Surface tension [N/m] Boiling point [K] Vaporization point [K]
250,000 825 7700 0.0056 16.3 1.2 3003 2273
[7] [7] [7] [7] [7] [7] [8] [8]
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bulent and treated by the Reynolds-stress model [16]. To improve accuracy and to avoid the divergence problem, a sufficiently small time step of 10 ls was used for the gas-phase simulations.
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2.2. Melt breakup modelling and droplet dynamics simulations
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The HPGA process of the metal melt has often been modelled as two successive atomization steps: the primary and the secondary breakup [26]. The melt, upon first contact with the supersonic gas jet, deforms and begins to form millimeter-sized coarse droplets soon after detachment from the melt surface: this is known as the primary breakup. These coarse droplets, if further exposed to the supersonic jet stream, undergo a secondary breakup into fine metal droplets [26]. Because the final droplet size is determined mainly by the secondary breakup, within 10% deviation [3,27], only the secondary breakup was taken into account in this study, to reduce the calculation load. The secondary breakup in the HPGA process has often been characterized by two distinct regimes: bag breakup vs stripping breakup, depending on the kinetic energy transfer from gas to droplet [28]. These two types of breakup have recently been modelled by the Taylor analogy breakup (TAB) model and Kelvin-Helmholtz (KH) instability model [16]. According to Liu et al. [28] and Zeoli and Gu [16], the sizes of the fine droplets produced during the secondary breakup were successfully predicted using the KH model. Thus, only the KH model was considered in this study. The secondary breakup model was implemented for the two nozzle designs, as follows. The gas-phase momentum conservation equations were two-way coupled with the discrete phase model in Ansys Fluent, and the resulting mass loading effect was involved in the droplet dynamics simulations. After the gas flow reached a stead state, coarse (parent) droplets with a diameter of 1 mm were continually released from the melt at the corner of the MFT tip, at a mass flow rate of 0.29 kg/s (corresponding to a GMR of 1.1), and the resulting fine (child) droplets were monitored by recording their position, size, and velocity relative to the gas, with a time step of 1 ls. The mean diameter of the child droplets was repeatedly measured at the exit at a specific time interval, i.e., every 1 ms, until the diameter became time-invariant. The final size distribution of the child droplets was obtained as a result. In the present study, a single particle analysis was developed to identify the most efficient way to minimize the size of the child droplets. Since the gas stream undergoes large velocity gradients in the vertical (radial) direction from the nozzle axis (i.e., the y direction in Fig. 1), a parent droplet would experience significantly different gas-velocity paths depending on its initial release position, presumably resulting in path-dependent breakup behaviors. To clarify this effect, three spherical parent droplets with an equal diameter of 1 mm were released individually at three different radial positions but at an equal distance (8 mm) from the MFT tip; and then their positions and velocities relative to the gas were monitored along the paths. 8 mm was chosen so that they would undergo vigorous secondary breakup, based on Mates and Settles’ visualization experiments [3]. As the first case, a parent droplet was released at the farthest radial position, and the trajectory that it showed was called ‘‘zone 1”; the droplet is called the zone-1 droplet thereafter. Likewise, the zone-3 droplet represents another parent droplet released at the nearest position to the nozzle axis. The zone-2 droplet indicates the case of being released between zone 1 and 3. During the secondary breakup, a parent droplet shortly disintegrates into and/or peels off tiny child droplets, reducing its size to some degree. This in turn reduces the Weber number that the parent droplet experiences. The radius of the parent droplet was assumed to be invariant unless the mass removal reached 3% of its initial mass [11]. Because a large number of child droplets, coex-
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isting with their parent droplet, could take different paths and move with different speeds than one another, to simplify the single particle analysis the main focus here was the behavior of the parent droplet.
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3. Results and discussion
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3.1. Gas flow dynamics
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The performance of the two nozzles was evaluated through simulations involving only the gas flow. The upper portion of Fig. 2 shows the velocity contour of the gas with a schematic drawing of its interesting features, while the lower graph depicts the variations in pressure along the main stream of the gas. The xaxis of the graph was drawn on the same scale as the nozzle geometry so that the local gas velocity could be studied in conjunction with the corresponding pressure. For the same purpose, important parts in the design of the nozzles are marked with vertical lines in the figure; refer to the nozzle throat, exit, and MFT tip of the ASN (in Fig. 2(a)) in comparison with nozzle throat and MFT tip of the IPN (in Fig. 2(b)). The main stream of the gas marked with an oval is also enlarged and shown at the top of the figure. As the high-pressure gas jet passes through the throat of the ASN, the gas is supersonically accelerated in the diverging part up to the exit (refer to ‘1’ in Fig. 2(a)) while the gas pressure falls rapidly below the chamber pressure of 1 atm. Accordingly, the gas jet, right after the exit (‘1’), first appears to be overexpanded, and then decelerated, due to the action of oblique shock (marked with ‘A’), which raises the pressure above 1 atm (refer to the pressure profile in Fig. 2(a)). Due to the excessive pressure recovery, the gas is again expanded near the MFT tip. As illustrated in the magnified snapshot of the gas main stream, this expanding gas jet (‘3’) encounters a series of Prandtl-Meyer expansion waves (‘B’) and their reflected compression waves (‘C’); and is guided toward the symmetric axis along its sonic line (‘F’), creating a subsonic recirculation region (‘D’). This seemingly pulsating gas jet is enveloped by an external turbulent layer (‘G’) with lower velocity. The repeated expansioncompression pattern results in a pressure oscillation around 1 atm and continues until the pressure matches the chamber pressure (1 atm), as shown in the graph of Fig. 2(a). Meanwhile, the upper portion of Fig. 2(b) illustrates the three distinct flow characteristics in the IPN: (1) the velocity and pressure fluctuations become so weakened that the pressure very quickly matches the chamber pressure, (2) roughly suggesting the absence of strong oblique shocks, and (3) the supersonic jet (named ‘6’) passing through the IPN throat forms almost flattened sonic boundaries (‘7’), presumably as a result of the near isentropic expansion of the gas. With the help of the gradually-expanding divergent part of the nozzle, the gas can go through a more gentle velocity change without creating strong shocks. One may notice that the maximum speed of the gas in the ASN appears to be a little higher than in the IPN. However, it is still unclear if the shock waves in the ASN are beneficial to the gas atomization, because the shocks can alter the particle trajectories, as well as the path-dependent breakup efficiency. This will be discussed in detail in the next section.
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3.2. Single-particle analysis
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Fig. 3 displays the successive positions of an individual parent droplet belonging to each zone. Here, the zone-1, zone-2 and zone-3 parent droplets are highlighted with red, blue and black circles, respectively. In the ASN, as shown in Fig. 3(a), the zone-1 droplet appears to take a detour around the first oblique shock and
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Fig. 2. Characteristics of gas flow before introducing the melt, and contour plots of the velocity magnitude of the gas of the (a) ASN and (b) IPN.
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moves away from the main stream toward the outer subsonic region. On the other hand, the zone-3 droplet directly penetrates into the shock and undergoes a series of alternating gas velocity and pressure oscillations because of the shock. The zone-2 droplet shows a trajectory in between the zone-1 and zone-3 droplet paths. Clearly, the zone-2 droplet undergoes similar strong gas velocity oscillations in the beginning, and then moves out of the main stream about 50 mm downstream of the MFT tip of the ASN. Fig. 3(b) shows that the parent droplet in the IPN exhibits quite similar behavior in the red and black cases (i.e., zone-1 and zone-3, respectively), however the blue (zone-2) droplet, as it encounters the weaker shock, compared to the ASN, does not necessarily deflect from the high-velocity region, but rather keeps going through the main stream of the gas. Compared to the two zone-2 droplets in Fig. 3(a) and (b), the zone-2 path in the IPN is likely more efficient than the one in the ASN. A more quantitative analysis was attempted to compare the effects of the designs of the two nozzles on particle breakup. Fig. 4(a1) and (a2) show the profiles of velocity and Weber number that each parent droplet will experience as a function of
Fig. 3. Comparison of gas flow characteristics and trajectories for a parent droplet, depending on its launching zones in the (a) ASN and (b) IPN.
axial distance from the ASN tip. Fig. 4(a3) shows where child droplets belonging to each parent are in the calculation domain and what size they are. In Fig. 4(a1), the gas velocity along the zone1 path slowly decreases with large fluctuations up to an axial distance of 70 mm, and then oscillates around 200 m/s further downstream in response to weakened alternating shocks. Along the zone-2 path, the gas velocity rapidly decreases with a certain level of fluctuation owing to the opposing shock-induced pressure. The zone-3 path shows that the gas velocity remains above 480 m/ s up to the axial distance of 100 mm, suggesting that the path provides a way to obtain maximal use of the shocks. These findings are consistent with the expectation based on Fig. 3(a). In contrast, the velocities of the parent droplets are almost invariant regardless of their paths; not being affected by the shocks, possibly due to their large inertia, they can keep going on with a fairly constant speed. As shown in Fig. 4(a2), the Weber number was calculated from the velocity difference between the gas and droplets along each zone. The Weber number of the zone-1 droplet quickly decreases below 50, at 35 mm from the MFT tip. Meanwhile, the zone-3 droplet maintains a high level Weber number for the longest distance, up to 65 mm from the tip. The Weber number of the zone-2 droplet, though it starts from the highest value of 400, falls rapidly below 50, at 50 mm from the MFT tip. Such a sharp decrease can be understood by the rapid decrease in gas velocity along the zone-2 path shown in Fig. 4(a1). Beyond 70 mm of the axial distance, the Weber numbers for both zone-2 and -3 droplets become smaller than 10, which implies that the droplet breakup will stop [11]. Unlike the process of tracking parent droplets along their paths, tracking child droplets is not easy, even in this single particle analysis, because of the complexities involved. (1) Different numbers of child droplets are occasionally born from a single parent droplet while it is moving, but with different sizes, depending on the local position of their parent droplet. (2) A small difference in the birth position of the child droplets can cause a large difference in their path and further breakup behavior. (3) Some of the child droplets
Please cite this article in press as: R. Kaiser et al., A numerical simulation study of the path-resolved breakup behaviors of molten metal in high-pressure gas atomization: With emphasis on the role of shock waves in the gas/molten metal interaction, Advanced Powder Technology (2017), https://doi.org/ 10.1016/j.apt.2017.12.003
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Fig. 4. Velocity and Weber number distributions of the parent droplets and the diameters of the child droplets for the three zones in the (a) ASN and (b) IPN.
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can take high-speed paths and disappear from the calculation domain, while the rest of them are still observed. In consideration of these complexities, a snapshot was taken in an attempt to visualize the sizes and positions of the child droplets remaining in the domain, instead of tracking them. As an example, Fig. 4(a3) was obtained from a snapshot taken 2 ms after releasing a single parent drop at each zone. Note that the parent droplet is
not shown for simplicity. In Fig. 4(a3), only four child droplets have been produced from the zone-1 parent droplet, and they stay upstream (axial distance < 30 mm). At the same point in time, both zone-2 and zone-3 parent droplets produced many more child droplets, which move faster downstream. Note that these child droplets reached 180 mm downstream of the MFT tip. It is interesting to note that some of them (particularly the smaller
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ones) were found to have escaped from the domain. Moreover, most of the zone-2 and zone-3 child droplets are smaller than the zone-1 child droplets. This observation suggests that the zone-2 and zone-3 paths are more beneficial than the zone-1 path for producing powders with smaller sizes and larger populations, which sounds consistent with the aforementioned expectation from Fig. 4(a1–a2). Because the IPN produces fewer shock waves, the supersonic jet stream through the nozzle shows almost non-oscillatory velocity profiles along the paths as seen in Fig. 4(b1). In comparison with Fig. 4(a1), the most noticeable difference appears in the zone-2 path; the gas flow velocity remains high up to the 80-mm axial distance, unlike in the ASN. As a result, the zone-2 parent droplet in the IPN is able to experience a high We above 100, up to 65 mm in axial distance, as shown in Fig. 4(b2). This might explain why there are no zone-2 child droplets larger than 50 lm present in Fig. 4(b3). These connected results indicate that the (shock-free) IPN is superior to the ASN, at least in one (zone-2) of the major paths.
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3.3. Continuous particle analysis
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Injecting the parent droplets on a continuous basis in the secondary breakup phase might produce somewhat different results than those of the single droplet injection, because it involves a much larger number of new-born particles and thus more vigorous gas-particle two-way interactions [29]. Hence, this section is devoted to checking whether the path-dependent breakup features described in Section 3.2 are still valid in the more-realistic case, i.e., continuous droplet injection. Identical parent droplets (of 1 mm diameter) were injected at the same radial positions as in the single particle analysis, however, continually, under control of the GMR at 1.1. Fig. 5(a) and (b) shows the contour plots of the Mach numbers of the gas flow fields through the ASN and IPN, respectively. It should be recalled that the figures represent the gas flow at the steady state in both nozzle systems upon continuous droplet injection. In comparison with Figs. 2 and 3, there is a notable difference in the gas flow: the supersonic region, which was as long as 160 mm, is greatly shortened by the continuous droplet injection in both nozzles. Note that the greenish (supersonic) stripes in Fig. 5 (a) turn blue (subsonic) within 50 mm in axial distance, whereas
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the greenish area in the IPN extends up to 5–6 diameters of the MFT (90 mm) (see Fig. 5(b)). The reduced supersonic zone indicates rapid gas deceleration resulting from the transfer of kinetic energy from the gas to the (parent and child) droplets. As a result, the gas seems to expand outward (radially) to avoid a group of existing droplets, which looks like a typical under-expanded supersonic jet plume from a rocket. This is clearly related to the well-known mass loading effect [3,11]. The radial expansion is more noticeable in the ASN (see Fig. 5(a)). In contrast, the gas which is expanding less in the IPN likely experiences relatively low flow resistance, implying that smaller droplets exist ahead. Fig. 6(a) and (b) shows the snapshots of sprayed droplets taken 20 ms from the beginning of droplet injection in the ASN and IPN, respectively. In Fig. 6 (a), blue (<100 lm) droplets from the ASN apparently diverge significantly in the radial direction, accompanied by two greenish streaks (larger than 100 lm) of particles. In the IPN (see Fig. 6(b)), however, the droplets are clearly less diverged and the greenish droplets change their color gradually and eventually becomes blue (sub-hundred micrometer) at the exit boundary. This observation again sounds consistent with the expectation from Fig. 5. Let us further discuss the breakup behavior from the pathdependent view. Unlike the single-particle analysis, where the mass loading effect is negligible, under continuous injection the near-axis gas flow is now subsonic (Compare Figs. 3 and 5), deactivating the zone-3 paths (near the axis) in both nozzles to some extent. Instead, the zone-1 paths appear to be upgraded with the help of the radial expansion of the gas. It is naturally presumed that the zone-2 paths positioned between the zone-1 and -3 paths are likely to be much less affected by the existence of droplets, and still remain favorable for droplet breakup in both nozzles. It is interesting to note the Schlieren image taken by Mates et al. [3], where a number of un-atomized coarse droplets were similarly seen in the jet core. A quantitative assessment of the breakup performance of each path was attempted by injecting droplets in one of the three locations and repeating the breakup calculation. Fig. 7(a) shows the cumulative size distributions of the child droplets coming from each path in the ASN. As predicted above, the zone-1 path turns out to be efficient for droplet breakup in the case of continuous zone-1 injection, producing droplets as small as 50 lm in mass
Fig. 5. Contour plots of Mach number in the gas flow of (a) ASN and (b) IPN with continuous particle injection.
Please cite this article in press as: R. Kaiser et al., A numerical simulation study of the path-resolved breakup behaviors of molten metal in high-pressure gas atomization: With emphasis on the role of shock waves in the gas/molten metal interaction, Advanced Powder Technology (2017), https://doi.org/ 10.1016/j.apt.2017.12.003
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Fig. 6. Snapshots of particle generation during high-pressure gas atomization using (a) ASN and (b) IPN.
Fig. 7. Cumulative mass size distributions of particles originated from three different zones and generated with the combined mode, in (a) ASN and (b) IPN.
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median diameter (d50). The zone-2 path still remains the best choice, and is capable of producing the smallest (d50 = 46 lm) droplets with the narrowest size distribution. The zone-3 path, unlike
the results for the single-particle analysis, is significantly downgraded, so that the resulting droplets are significantly larger, with d50 = 100 lm. When the droplets are differentiated according to their origins (zones), the zone-3 droplets, particularly the large ones, are confirmed to move toward the axis where the gas flow is subsonic, as represented by the greenish droplets in Fig. 6(a). For comparison, a cumulative size distribution of droplets was obtained for the combined injection at the three locations, and added in Fig. 7(a). The size distribution gets closer to the curves of the zone-1 or zone-2 paths, away from the curve of the zone-3 path. One may wonder why the zone-1 and -2 paths dominate the breakup behaviors under the combined injection. It is worth noting that the zone-3 large droplets pass through the exit boundary much slower than the others, which results in a sampling bias towards fast-moving droplets (just like the concept of cup-mixing sampling [30]). Those size measurements were repeated for the IPN and the results are shown in Fig. 7(b). Overall, similar trends were observed in those size distributions; the zone-1 and -2 paths are superior to the zone-3 path and their results are almost identical to the combined-mode size distribution. It should be noted, however, that the IPN produces smaller droplets than the ASN; for example, d50 = 45 lm and d84 = 70 lm in the IPN vs d50 = 52 lm and d84 = 90 lm in the ASN. From the perspective of size reduction, it is concluded that the shock waves produced in the ASN are not beneficial, at least under the present conditions. In order to test both nozzles under harsher conditions, Anderson and Terpstra [5]’s HPGA conditions were additionally taken into account. Their nozzle, consisting of 22 convergent-divergent discrete jets, was operated at higher pressures of 27.6 and 55.2 atm, and tested for HPGA using molten stainless steel and argon gas; refer to Table 1 in Ref. [5] for further details of the experiments. Under two different GMR conditions (0.36 and 1.29; corresponding to the low and high pressure, respectively), both designs of the ASN and IPN (after matching the GMR values) were simulated. The simulation results at the two gas pressures are shown and compared with the experimental data in Fig. 8(a) and (b), respectively. Under both pressure conditions, the IPN again turns out to be more efficient than the ASN, producing smaller droplets with a narrower size distribution (see the inset table). Both figures also confirm that the size distributions obtained from the experiments are in better agreement with those from the ASN. This might
Please cite this article in press as: R. Kaiser et al., A numerical simulation study of the path-resolved breakup behaviors of molten metal in high-pressure gas atomization: With emphasis on the role of shock waves in the gas/molten metal interaction, Advanced Powder Technology (2017), https://doi.org/ 10.1016/j.apt.2017.12.003
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Fig. 8. Comparison of simulated cumulative mass size distributions with experiment [5] at (a) 27.6 atm (b) 55.2 atm gas pressure.
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be attributed to the fact that the discrete jet holes in the experiment are more similar to the ASN design, rather than the IPN.
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4. Conclusions
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In this study, numerical simulations of the HPGA process were performed with two types of nozzles, with the aim of highlighting the effects of shockwaves on gas flow and particle breakup. Single particle analysis was performed by injecting a single coarse droplet at different locations near the nozzle exit, in an attempt to monitor the gas velocity and breakup characteristics that the coarse droplet undergoes along its path. As a result, it was found that favorable flow paths for reducing the resulting droplet size clearly exist; the efficiency of the paths is affected by the shock waves to some degree. The path-resolved analyses were repeated for continuous injection under various gas-to-melt ratio conditions. The results indicated again that the most favorable path was still valid under realistic conditions and apparently dominates other paths, although the other less favorable paths were likely affected by the mass loading effect. Shock waves turn out to be unfavorable for reducing the powder size, at least under the conditions in this study.
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Acknowledgements
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This work was supported by the National Research Foundation (NRF) of Korea (No. 2016R1A2B2014141), which is funded by the
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Ministry of Education, Science and Technology (MEST), Korea, and by the ‘‘Development of the Preparation Technology of 0.1– 10 µm Sized Metal Powders and Fine-Components for Micro Electronics” project of the Ministry of Knowledge Economy (MKE), Korea, and the Korea Research Council for Industrial Science and Technology (ISTK).
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