Direct numerical simulation of melt–gas hydrodynamic interactions during the early stage of atomisation of liquid intermetallic

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 419–427

journal homepage: www.elsevier.com/locate/jmatprotec

Direct numerical simulation of melt–gas hydrodynamic interactions during the early stage of atomisation of liquid intermetallic Mingming Tong ∗ , David J. Browne School of Electrical, Electronic & Mechanical Engineering, Engineering and Materials Science Centre, University College Dublin, Belfield, Dublin 4, Ireland

a r t i c l e

i n f o

a b s t r a c t

Article history:

The dynamic interactions between Raney Ni–Al intermetallic melt and argon gas at the start

Received 25 June 2007

of atomisation, near the nozzle of close-coupled gas atomiser, for the first time, are numer-

Received in revised form

ically investigated using a front-tracking formulation. Some key geometric parameters of

21 September 2007

a real device are used in the model in order to simulate the real atomiser. In the model

Accepted 11 October 2007

predictions of gas/melt movement, the gas jets cause melt stream pinch off and force the melt stream to wet the melt nozzle tip. Meanwhile, the melt flow has a strong influence on the evolution of gas recirculation via significant feedback. The simulated evolution of the

Keywords:

melt stream topology up to disconnection is positively supported by related experimental

Front-tracking model

results. The mechanism of the stagnation point formation proves to be very different from

Raney nickel

that predicted in conventional gas-only case studies. The peak pressure along the vertical

Intermetallic

centre line significantly varies once the melt stream becomes disconnected. The pressure

Gas recirculation

gradient within the melt stream in the vertical direction contributes to the aspiration pres-

Powder production

sure, which is over-ambient with the specific parameters of this paper. This is the first time

Powder metallurgy

that direct numerical simulation has been used to investigate the melt–gas two-fluid flow

Gas atomisation

in a real gas atomiser. Besides delivering a deep insight into the physical process involved, this new model has the potential to supply industrially applicable predictions. © 2007 Elsevier B.V. All rights reserved.

1.

Introduction

Gas atomisation is a very efficient processing route to powders in the powder metallurgy field. Compared with conventional manufacturing techniques, it can produce fine, clean, and spherical powders. By treating the Ni–50 wt.%Al powders with solvent, like concentrated sodium hydroxide, some aluminum atoms are removed and the Raney Ni–Al powders are obtained (Raney, 1927). Because of high porosity, the Raney powders are very good candidate catalysts for use in hydrogenation industry and can be sintered to produce Ni–Al fuel cell electrodes

∗

Corresponding author. Tel.: +353 1 7161978; fax: +353 1 2830534. E-mail address: [email protected] (M. Tong). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.10.012

with the purpose of replacing expensive noble metals. Gas atomisation is also one of the key stages in the spray forming process. Atomisation affects the properties of spray formed product via its influence on the metal melt droplets and particles. The hydrodynamic and thermal interactions between melt stream, atomising gas jets and the chamber ambient gas, especially those near the nozzle of atomiser, are deserving of study since knowledge of such interactions permits prediction of the evolving flow and temperature field of the melt stream in the atomisation zone. Modelling and numerical simulation of gas atomisation has attracted the attention of many

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researchers because of its powerful potential to reveal the physical process, e.g. the melt–gas interface instability during atomisation, and to predict the atomisation result, e.g. the thermal history of droplets, and hence to help to find the optimum processing parameters (Fritsching, 2004). Referring to the modelling of gas atomisation, the atomisation process can be roughly subdivided into three subprocesses. They are (i) the melt flow in the tundish and gas flow within the gas nozzles, (ii) melt stream disintegration caused by atomising gas jets which occurs in the atomisation zone near the melt orifice, and (iii) the droplet/particle spray in the chamber. Compared with the modelling of other subprocesses, treating the modelling of melt–gas dynamic interactions near the atomiser nozzle remains very challenging. The melt stream disintegration process includes strong melt–gas interactions, both hydrodynamic and thermal, which are very unsteady, complicated and coupled. Focused on the effects of gas flow on melt stream disintegration, many researchers have worked to simulate the gas flow in a gas-only case, in which the atomised liquid is not present. Fritsching and Bauckhage (1992) simulated the gas flow field near the nozzle of a free fall atomiser. Anderson et al. (Mi et al., 1996) examined the effects of parametric variation of gas atomising pressure on gas flow field. Ting and Anderson (2004) investigated the gas dynamics of the open-wake and closed-wake conditions of a close-coupled atomiser. Espina et al. (1998) simulated the effect of jet pressure ratio on the gas-only atomisation flow. Although, such gas-only studies can provide very helpful hints to investigate the mechanism of melt stream disintegration, it is far away from the status of the real gas atomisation process because of the strong feedback of the melt stream flow, which is caused by the high melt density (normally several thousand kg/m3 ) and temperature (may be well over 1000 ◦ C), significantly affecting the gas flow and makes the melt–gas interactions not negligible. The conventional modelling methods of melt–gas interactions can be reduced to two categories. One is the analytical method to investigate the initialisation and growth of surface waves at the melt–gas interface by using linear stability analysis, such as the Taylor case (Rayleigh, 1878) and the Kelvin–Helmholtz (K–H) instability case (Bradley, 1973a,b). Markus et al. (2002) have analytically investigated the growth of surface waves on the gas–liquid boundary in a free fall atomiser by using such linear stability analysis. Although this analysis is of significant theoretical value, many assumptions and simplifications included in this method make it difficult to fit real experimental data. For example, in these analyses, the gas flow field close to the nozzles is extremely simplified and regarded as constant. The gas viscosity and gravity force are normally neglected. The second approach to simulating melt–gas interactions, with the purpose of industrial application, is an empirical one. In such an approach, the droplet size distribution is directly predicted according to variation of experimental parameters, like the material properties and operational settings. A famous droplet-size correlation is Lubanska’s model (Lubanska, 1970). Although empirical models have often been successfully applied in industrial applications research, they cannot deliver a deep insight into the melt–gas dynamic interactions because they are not capable of analysis of the detailed physical process.

Nowadays, due to the rapid development of computer hardware, direct numerical simulation is becoming more and more applicable in the field of multi-fluid flow research. By modelling the K–H instability, accompanied by a variety of different interface tracing models, direct numerical simulation has been used by many researchers to investigate the melt–gas hydrodynamic interactions. The group of Zaleski (Scardovelli and Zaleski, 1999; Thomas et al., 2004; Li et al., 2007) has used the volume of fluid (VOF) model (Hirt and Nichols, 1981) to investigate melt ligament and droplet formation from a liquid sheet during the non-linear development of K–H instability. The group of Tryggvason (Tryggvason and Unverdi, 1999; Tauber and Tryggvason, 2000; Tauber et al., 2002) has used a front-tracking formulation to carry out simulation of the K–H instability, investigating the linear and non-linear evolution of surface waves in both 2D and 3D. In the above-mentioned research work, although different interface tracing models are used, the same simulation case study is used: liquid–gas parallel flow with periodic boundary condition. This case study totally excludes the complexity of gas flow near the nozzle of a close-coupled atomiser. In a real gas atomiser, the gas nozzles are not parallel to the melt nozzle but are inclined at an angle (typically 22.5◦ in a close-coupled atomiser). This gas nozzle arrangement, accompanied by feedback from the melt stream flow, makes the gas flow near the nozzle of atomiser very complex, turbulent and dynamic, especially at the start of the atomisation process when the gas first hits the melt stream. It is clear that such a gas flow field is essentially different from that of the aforementioned periodic liquid–gas parallel flow case and significantly affects the melt–gas interaction process. The dynamic interactions between melt and gas in a real atomiser is very unsteady. Especially at the start of gas atomisation process, the status of the melt–gas flow significantly varies with time. The melt–gas dynamic interactions at the start of gas atomisation are of great research importance, because they are the origin of the whole atomisation process and, industrially, they will determine whether melt orifice choking occurs, which is very harmful to smooth process operation. In this paper, by using a front-tracking formulation, direct numerical simulation is carried out to investigate the melt–gas interactions near the nozzle of a close-coupled atomiser during the initial stage of gas atomisation of an intermetallic melt, within a simulation domain, of which some key geometric parameters are set to try to imitate a real atomiser design. In this work, all the fluids are assumed to be incompressible, viscous and Newtonian. The simulation is in 2D. The gas compressibility and 3D effects will be investigated in future research. Although modelling heat transfer is possible in the current model, the results of thermal interactions between melt and gas are not analysed here but they are included in Tong and Browne (2007) in detail. This paper concentrates on the hydrodynamic interactions between melt and gas during the initial stage of gas atomisation process.

2.

Models and numerical formulation

Because complex interface geometry and significant and frequent interface topology changes are inherent to the nature

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of the melt–gas interactions during gas atomisation near the atomiser nozzle, a “one-fluid” model (Tong and Browne, 2007, in press; Unverdi and Tryggvason, 1992; Tryggvason et al., 2001) is used by the authors. All the fluids are regarded as the same fluid with spatially variable material properties and hence are governed by a single set of governing equations. Thus, a separate boundary condition at the inter-fluid interface is not necessary, although these interfaces are resolved in the model. The momentum conservation equation and continuity equation are as follows (Unverdi and Tryggvason, 1992; Tryggvason et al., 2001): ∂(u) + ∇ · (uu) = −∇p + f + ∇ · (∇u + ∇ T u) + FSF , ∂t

(1)

∇ · u = 0.

(2)

These equations are valid in the whole simulation domain with multi-fluids. Here  is the density,  the dynamic viscosity, u the velocity, p the pressure, f the body force and FSF is the surface tension per unit volume. In the energy equation of this multi-fluid flow system, heat convection, heat conduction and heat radiation are all considered as: ∂(cT) 4 4 + ∇ · (cTu) = ∇ · (k∇T) − aε(Tms − Tw ), ∂t

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1992; Shin et al., 2005) as:

 −→ FSF (x ) = −∇I(x )∇ ·

∇I(x )

  ∇I(x )

 ,

∇ 2 I(x ) = ∇ · ∇I(x ),

∇I(x ) =



− → ˆ D(x − x(l) )n(l) l,

(4)

(5)

(6)

l

−→ where FSF (x ) is the surface tension force per unit volume on the Eulerian grid at position x , which is localised so that it is zero outside the interface region,  the surface tension coefficient, ˆ − → n(l) the unit normal vector to the interface at position x(l) and l is the length of interface segment l. The indicator function I(x ) at position x is defined as a characteristic function used to distinguish different fluids, and it varies smoothly across the interface between 1 and 0 (Tong and Browne, in press; Unverdi − → and Tryggvason, 1992; Brackbill et al., 1992). D(x − x(l) ) is the discretization of ı function with the scheme of Peskin (1977). The density, dynamic viscosity, specific heat and thermal conductivity of all the fluids are mapped, respectively, onto the Eulerian grid as:

(3)

where T is the temperature, c the specific heat, k the thermal conductivity, a the length of the melt–gas interface per control volume (in 2D), ε the global emissivity of the melt–gas interface,  the Stephen–Boltzmann constant, Tms the temperature of the melt–gas interface, and Tw is the temperature of the chamber wall which is assumed to remain at room temperature. The momentum conservation equation (1), continuity equation (2) and energy equation (3) constitute the governing equations of this multi-fluid flow problem. In the model, a marker and cell (MAC) grid (Harlow and Welch, 1965) is employed to discretize the governing equations and a projection method (Unverdi and Tryggvason, 1992; Tryggvason et al., 2001) is used to solve them. In this front-tracking formulation, the interface between different fluids is explicitly tracked by a series of computational markers composing a Lagrangian grid (Tong and Browne, 2007, in press; Browne and Hunt, 2003, 2004; Banaszek and Browne, 2005), while the governing equations are solved on an Eulerian grid (i.e. the MAC grid as aforementioned). In essence, it is an Eulerian–Lagrangian formulation. In this model, the algorithm of the marker connection and marker reallocation is like that of Tryggvason et al. (Unverdi and Tryggvason, 1992; Tryggvason et al., 2001). The interface is advected by the movement of markers, of which the velocity is obtained from the velocity field on the Eulerian grid. Because the governing equations are solved on an Eulerian grid, the variables which are dependent on the Lagrangian grid, e.g. the surface tension force at the gas–melt interface, have to be mapped from the Lagrangian grid onto the Eulerian grid. The surface tension force is mapped onto the Eulerian by using a continuum surface force (CSF) model (Brackbill et al.,

(x ) = 1 I1 (x ) + 2 I2 (x ) + 3 (1 − I1 (x ) − I2 (x )),

(7)

(x ) = 1 I1 (x ) + 2 (1 − I1 (x )),

(8)

c(x ) =

c1 1 I1 (x ) + c2 2 I2 (x ) + c3 3 (1 − I1 (x ) − I2 (x )) , 1 I1 (x ) + 2 I2 (x ) + 3 (1 − I1 (x ) − I2 (x ))

k(x ) =

k1 k2 , I1 (x )(k2 − k1 ) + k1

(9)

(10)

where I1 (x ) and I2 (x ) are the indicator functions characterizing the gas–melt interface and atomising gas–ambient gas interface, respectively. Except for the indicator functions, the suffix 1 denotes melt, the suffix 2 denotes atomising argon gas and the suffix 3 denotes ambient argon gas. In this paper, the dynamic viscosity, specific heat and thermal conductivity of atomising argon gas are assumed to equal those of the ambient argon gas. An interface merging and breakup algorithm is necessary when dealing with the interface topology changes. In this paper, the topology change model of Tryggvason et al. (Tryggvason et al., 2001; Homma et al., 2006; Esmaeeli and Tryggvason, 2004) is employed. Each interface consists of sub-elements, each of which connects two consecutive computational markers. Topology changes takes place when the centroid of two such sub-elements, which either belong to different interfaces, or different parts of the same interface, come closer than a predefined distance threshold s. In this paper, s is set to be half the Eulerian grid spacing. Such a topology change involves both a fluid breakup and a fluid merger; for example, if a ligament of liquid breaks in two, there is also a corresponding merger of gas. This front-tracking model has been verified in a previous publication of the authors (Tong and Browne, 2007, in press),

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by its application to simulation of the K–H instability in a traveling wave case study. In Tong and Browne (2007, in press), some more details of the model and numerical formulation can be found.

3.

Modelling results and discussion

The target physical process is the melt–gas dynamic interaction near the nozzle of a close-coupled atomiser at the start of atomisation of molten Raney Ni–50 wt.%Al with argon. The simulation domain is the rectangle shown in Fig. 1a. A descending melt stream (in black) flows into the domain through the melt nozzle orifice which is located at the top edge of the domain. Two converging atomising argon jets (in grey) just emerge from surrounding nozzles and are symmetrically ejected into the domain. Other parts of this domain are full of ambient argon gas. In this paper, atomising argon gas and ambient argon gas are regarded as two different gases with the same material properties except for density. Gravity force is in the vertical direction. This simulation domain is used in an attempt to imitate a rectangular zone near the nozzle of a real close-coupled atomiser as highlighted by the dotted rectangle in Fig. 1b. The size of the melt nozzle orifice and gas nozzle orifice and the gas nozzle incline angle are determined according to a real atomiser design from CERAM, UK, a research partner of the authors. The detailed data is not included in this paper for the sake of confidentiality. Because the gas nozzles used in the CERAM atomiser are cylindrical, the maximum exit velocity that can be achieved is Mach 1.0, irrespective of the gas pressure at which the die is operated. For this reason, both atomising gas and ambient gas are assumed to be incompressible in this research, in order to simplify the model. The computation grid is composed of 501 × 502 nodes with an equal grid spacing of 0.1 mm.

3.1.

Initial and boundary conditions

The Ni–50 wt.%Al intermetallic is melted and heated up to 1813 K to reach a superheat of 200 K, prior to atomisation. The melt inlet velocity is determined by the melt flow rate and melt nozzle diameter as 3.16 m/s. The gas inlet velocity is determined by the gas flow rate and gas nozzle geometry as 127.8 m/s. The material properties of Raney Ni–Al, such as the dynamic viscosity and surface tension coefficient, are from experimental results provided by research partners of

the authors, mainly University of Ulm (Germany), DLR Institute (Germany) and NPL Management Ltd. (UK). The plenum pressure of atomising argon gas is 3 MPa. Because the gas is assumed to be incompressible, in this paper, the density of atomising argon gas is set at the plenum pressure, and remains constant throughout the argon gas flow in the simulation domain. Since the chamber is open to atmosphere, at the beginning of computation, the ambient gas pressure is atmospheric. Apart from density, all the material properties of both atomising argon gas and ambient argon gas, e.g. the dynamic viscosity, are set to remain at the value for argon at atmospheric pressure and room temperature. Referring to Fig. 1a, apart from the melt and gas nozzle orifices, the top edge of the simulation domain is a rigid wall, where a free-slip boundary condition is used. A part of the top edge near the melt nozzle orifice is set to be at 1813 K to imitate the hot melt nozzle tip. The side and bottom edges of the domain are open boundaries, through which fluids can flow. In this paper, the modelling is focused on the melt–gas dynamic interactions near the atomiser nozzle. This means that the melt flow in the tundish and through the melt nozzle and the atomising gas flow through the gas nozzles are not considered. Neither is the droplet spray process included.

3.2. Topology evolution of the melt stream and gas flow The predicted movement of the Raney Ni–Al melt and argon jets is consecutively displayed in Fig. 2. The black fluid is melt stream and the grey fluid is atomising argon gas. It can be seen that, from Fig. 2b, the high-speed argon jets are initially isolated from each other by the melt stream and hence have to flow along it. As the argon jets gradually impact the melt stream, shown in Fig. 2c, a concavity of the melt stream gradually occurs. When this melt stream concavity gradually becomes obvious, there is a significant gas recirculation within it, which is shown in Fig. 2d and e. At the same time, the melt stream significantly becomes thinner and thinner. This melt stream pinch eventually causes a melt stream disconnection as shown in Fig. 2f. After this, atomising gas pushes the upper part of the broken melt stream which is connected to the melt nozzle orifice, causing it to move upwards and stretches it in the radial direction, to wet the nozzle (Fig. 2g–i). Then the edge of the melt stream becomes elongated in the vertical direction, forming melt arms in 2D (Fig. 2j and k). The nozzle wetting

Fig. 1 – Schematics of the simulation domain.

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Fig. 2 – Consecutive movement of the Raney Ni–Al melt (black) and argon jets (grey), at various times (a, 0 ms; b, 0.145 ms; c, 0.289 ms; d, 0.434 ms; e, 0.578 ms; f, 0.651 ms; g, 0.723 ms; h, 0.867 ms; i, 1.01 ms; j, 1.16 ms; k, 1.30 ms; l, a local magnification of figure d).

by atomised fluid has been reported by many experimental researchers. A phenomenon worthy of notice is shown in Fig. 2l, which is a local magnification of Fig. 2d. Accompanied by the melt stream pinch, the significant gas recirculation forces a part of the melt stream to move upwards and stretch it in the radial direction to form melt rim as highlighted by the dotted circle, although the overall movement of the melt stream is still downwards. In the experimental results of Anderson et al. (2006), a very similar melt rim formation process is clearly recorded by high-speed video. The numerical predictions of the model are thus positively supported by experimental results. Atomising gas jets are conventionally believed to be dominant during gas atomisation. Current simulation results, predicting the successive movement of melt and gas jets

clearly show, however, that there is significant feedback from melt flow to gas flow, and that the manner in which the gas flow further affects the melt flow is influenced by this feedback. This means there are significant hydrodynamic interactions between melt and gas. The reason is that the momentum of the melt stream is comparable with that of the atomising gas jets since the density of Raney Ni–Al is about 60 times that of high-pressure atomising argon gas, although the velocity of atomising argon gas jets is about 40 times that of melt stream. As shown in Fig. 2b–e, the concave shape of the melt stream caused by the impact of atomising gas jets strongly feeds back to the gas jets by causing gas recirculation. Because of the initial existence of the continuous melt stream, atomising gas jets can only apply a shear force on the melt in the vertical direction and hence the downward-flow of argon jets is dominant (Fig. 2b–d). Once the melt stream becomes so

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Fig. 3 – Pressure (MPa) contour at 0.578 ms.

thin (Fig. 2e) that disconnection occurs (Fig. 2f), significant gas recirculation entraps a large amount of gas (both atomising and ambient), to directly apply normal force to the end of the upper part of the broken melt stream pushing it upwards as shown in Fig. 2f–k. This is the reason why we predict that the melt nozzle tip is not significantly wetted until the melt stream disconnection occurs, although this occurs within 1 ms of the start of the process.

3.3.

Analysis of pressure and velocity field

The pressure that the melt stream experiences is a topic of interest. Fig. 3 shows the pressure contours at 0.578 ms. The pressure is only sampled at locations downstream from the melt orifice within a distance of 0.015 m. The sample region includes mostly part of the melt stream, with some gas. Indeed, as illustrated in Fig. 4, which covers the same subdomain, the symmetry centre line of Fig. 3 is completely liquid intermetallic. Pressure is in units of MPa. It is found that the pressure field is very non-uniform both in the radial direction and in the vertical direction. In the radial direction, the pressure at the centre of the melt stream is high and produces pressure gradient towards both sides. It is clear that this radial pressure profile is caused by the converging impact of atomising gas jets on the melt stream. In the vertical direction, the pressure takes two local maximum values at points A and B. The position of these two points is clearly shown in Fig. 4, which shows the pressure and velocity profiles along the centre line of the simulation domain at 0.578 ms in the downstream vertical direction. The high pressure at point A is

Fig. 4 – Pressure and velocity profile along the centre line of the domain in the downstream direction at 0.578 ms (points D and E are stagnation points).

Fig. 5 – Velocity field of the melt at 0.578 ms.

caused by the counter flow of the downward moving melt just emerging from the melt orifice and the upward moving melt forced by the gas recirculation. The high pressure at point B is caused by the nearly normal impact of the atomising gas jets on the extended melt stream. The pressure at point B is actually the highest pressure along the whole melt stream. This high pressure significantly forces the part of melt stream at the downstream side of point B to move and eventually causes the melt stream disconnection (see Fig. 2f). Note that the high pressure at point A results in a pressure gradient from point A towards point C (in Fig. 3), of which there is an overambient aspiration pressure of 1.16 × 105 Pa, at the centre of melt orifice. The velocity profile along the centre line of the simulation domain in the downstream direction, as shown in Fig. 4, is also of interest. It is found that, in the velocity profile, there are two stagnation points, where the velocity is zero. These two stagnation points are marked as points D and E in Fig. 4. Generally, according to the research results by using gas-only case study (e.g. Ting and Anderson, 2004), the stagnation point is found in the gas near gas recirculation. However, in the modelling results shown in Fig. 4, stagnation point D does not exist in the gas but exists in the melt stream. Fig. 5 shows part of the melt stream flow field which includes points D and E. At the upstream side of point D, forced by the top pressure in the furnace and the hydrostatic pressure of the melt in the crucible, the melt stream just emerging from the melt orifice flows downwards. On the contrary, at the downstream side of point D, the melt stream, forced by the significant gas recirculation, moves upwards. At point D, the upward moving melt stream meets with the downward moving melt stream and hence the velocity at this position is zero. The melt stream at point D has

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Fig. 7 – Velocity field of gas at 0.651 ms. Fig. 6 – Pressure and velocity profile along the centre line of the domain in the downstream direction at 0.651 ms.

no other choice but to move radially and form the melt rim, which is mentioned in Section 3.2. The analysis of the stagnation point D supplies useful information in two ways. Firstly, the mechanism of stagnation point formation in the melt–gas interaction case, which essentially corresponds to the real gas atomisation process, is significantly different from that in a gas-only case. It shows that the melt–gas interaction is too significant to be neglected when investigating gas atomisation. Secondly, information on the top pressure in the furnace is of predicted value. It is clear that the position of the stagnation point D tends to move towards the melt orifice if a reduced top pressure and hence a reduced melt inlet velocity is used in the gas atomiser operation. In order to prevent choking of the melt orifice and to ensure continuous gas atomisation operation, a reasonably high top pressure in the furnace is desirable. The mechanism of the formation of stagnation point E is similar to that predicted in a gas-only case. The upstream movement of recirculation gas and the downstream movement of gas jets make the melt stream move in the upstream and downstream directions, respectively around point E and hence the velocity is zero there. As the system evolves to 0.651 ms, the melt stream disconnects (Fig. 2f). At a first glance, the melt stream disconnection seems nothing special but the result of the gradual pinch. But according to the model prediction, this disconnection has significant effects on the physical process of interest. Fig. 6 illustrates the pressure and velocity profile along the centre line of part of the domain. By comparing the pressure profile in Fig. 6 and that in Fig. 4, it can be seen that, as the melt stream disconnection occurs (from 0.578 ms to 0.651 ms), the peak pressure significantly moves towards melt orifice from point B (4.78 × 105 Pa) in Fig. 4 to point F (1.03 × 106 Pa) in Fig. 6. At 0.578 ms (Figs. 2e and 5), since the melt stream is still continuous although it is very thin, the atomising gas jets can merely force a shear stress on the melt in the vertical direction. Once the melt stream is disconnected (Figs. 2f and 7), the upward moving recirculating gas directly forces a normal force at the end of the broken melt stream (point F) in the vertical direction. In addition to the shear effects of the recirculating gas, this very high peak pressure forces the broken melt stream, which is connected to the melt orifice, to move upwards to wet the melt nozzle (Fig. 2g–k). At 0.651 ms, the aspiration pressure

is still over-ambient and its value 2.29 × 105 Pa is higher than that at 0.578 ms. At 0.651 ms, there are still two stagnation points (points G and H in Fig. 6). Compared with the location of stagnation points of the system before melt stream disconnection (at 0.578 ms shown in Fig. 4), the most obvious difference is that the stagnation point (H) is located in gas. The mechanism of the formation of stagnation point H is the same as that in the gas-only case. By comparing the velocity profile in Fig. 4 and that in Fig. 6, it is obvious that the velocity of the melt stream is much lower than that of the gas by about 2 orders of magnitude even though the system has evolved such that melt stream disconnection occurs. At the start of gas atomisation, the flow fields close to the melt orifice, with and without considering the melt stream flow, are significantly different. For example, in the gas-only case study of Ting and Anderson (2004), a gas recirculation zone is found to be located adjacent to the melt orifice. However, according to the modelling results of this paper, the zone adjacent to melt orifice is found to be full of melt and there is no melt recirculation within there (Figs. 2e and f and 5), either before or after the melt stream disconnection. When the melt stream extends significantly in the radial direction to wet the melt nozzle tip (Fig. 2j and k), the gas recirculation is isolated from the orifice by a layer of melt and that gas recirculation is very unsteady due to the significant effects of the surrounding melt. The last conclusion that be drawn is that both the melt and gas flows are very unsteady. Generally, the flow field of a gas-only case study, e.g. Ting and Anderson, 2004, is believed to be a steady state solution of governing equations. That means all the parameters do not vary with time. When the melt–gas interactions are considered, our model predicts that the melt–gas system is very unsteady. As shown by Fig. 2a–k, the atomising gas jets affects the melt flow and the melt flow strongly feeds back to the gas flow, and then the modified gas further affects melt with that feedback. These melt–gas interactions make the flow of melt and gas very unsteady. When the system evolves for a long time (e.g. far beyond 1.30 ms), the flow remains very unsteady. The movement and breakup of the melt arms (similar to those shown in Fig. 2k) still significantly affect the gas flow—the melt approaches the gas nozzles caused by the melt nozzle tip wetting in such a close-coupled atomiser.

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Summary and conclusions

As an advance on the melt–gas parallel flow case or the gasonly case, a new front-tracking model of melt–gas interactions is used to simulate the start of the atomisation process of liquid intermetallic by gas. Initial parameters and boundary condition are chosen to imitate the situation in a real closecoupled gas atomiser. A one-fluid model is used to solve the governing equations of the melt–gas viscous, incompressible two-fluid flow by taking account of surface tension. The melt–gas interface is explicitly tracked by using the fronttracking formulation. The successive movement of both melt and gas is shown. The pressure field and velocity field are investigated by analysing the pressure contour and the downstream profile of pressure and velocity along the centre line of the domain. The detailed velocity vector plot is used to help understand the profile of velocity and pressure. The melt–gas hydrodynamic interactions significantly affect the topological evolution of the melt stream and the gas flow. The impact of atomising gas jets and shear of the gas recirculation cause the pinch and disconnection of melt stream. The simulated melt rim formation is positively supported by related experimental results. The melt nozzle tip wetting by melt is well simulated. As a strong feedback of the melt to gas, an obvious gas recirculation is found. As a proof of the feedback effects of the melt on the gas, the effects of gas on the melt stream is found to be very different before and after the melt stream disconnection, e.g. the peak pressure location. The pressure field is very non-uniform both in radial and vertical direction. The pressure gradient in the vertical direction causes an over-ambient aspiration pressure at the melt orifice with the specific parameters used in this paper. The velocity field is also very non-uniform. Because of the existence of the melt, the mechanism of the stagnation point formation is different from that in the gas-only case. To summarise, the modelling results of this work show that the hydrodynamic interactions between the melt and gas are so significant that they cannot be neglected when investigating gas atomisation.

Acknowledgements This work is financially supported by European Commission (contract number NMP-CT-2004-500635) Sixth Framework Programme as the project “Intermetallic Materials Processing in Relation to Earth and Space Solidification”, which is co-funded and coordinated by the European Space Agency.

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