Computational Investigation of the Splashing Phenomenon Induced

Article pubs.acs.org/IECR

Computational Investigation of the Splashing Phenomenon Induced by the Impingement of Multiple Supersonic Jets onto a Molten Slag− Metal Bath Mingming Li,†,‡ Qiang Li,*,†,‡ Shibo Kuang,§ and Zongshu Zou†,‡ †

School of Metallurgy, Northeastern University, Heping District, Shenyang, 110819, China Key Laboratory of Ecological Utilization of Multi-metallic Mineral of Education Ministry, Northeastern University, Heping District, Shenyang, 110819, China § Department of Chemical Engineering, Monash University, Clayton, Victoria 3800, Australia ‡

ABSTRACT: This paper presents a study of the splashing phenomenon caused by the impingement of supersonic jets onto the slag−metal molten bath under real oxygen steelmaking conditions using numerical simulations. The validity of the mathematical model has been verified through different applications. The time-sequenced occurrence process and generation mechanism of splashing are revealed, and the splashing rate is determined with respect to lance height and operation pressure by combining the multifluid volume of fluid model with the blowing number theory. The results show that the generation of splashing is a result of the collective effects of the direct ejection of individual droplets and the tearing of “splash sheets” or “large tears”. It is also found that the splashing process is unstable and normally irregular during the blowing, and the splashing is enhanced in terms of the tearing of splash sheets or large tears with declining lance height or increasing operation pressure.

1. INTRODUCTION The impingement of high-speed jet(s) onto a deformable liquid surface is commonly encountered in many industrial engineering applications. A typical example is the basic oxygen furnace (BOF) steelmaking process, which is the dominant method used to produce crude steel in the modern steel industry. In BOF operations, multiple supersonic oxygen jets generally strike the molten slag−metal bath and create a cavity. During this cratering process, the so-called “spitting” or “splashing”1 occurs, in which the metal phase is torn from the molten bath bulk around the surface of the formed cavity. Splashing can play a critical role in forming major phenomena in a process unit and thus controls the performance of the reactor. It essentially gives rise to the emulsification of gas−slag−metal phases in a BOF, which guarantees that the key reactions proceed at high rates in the reactor. More specifically, the emulsification promotes the reactions to remove the carbon in the metal melt to achieve a high refining efficiency of BOF.2−4 The removal of carbon in turn significantly affects the amount of splashing, the behaviors of the subsequent droplets, and the associated mass and heat transfer in the processes of dephosphorization, slag generation, scrap melting, etc.5−7 Therefore, it is necessary to study the splashing phenomenon to achieve high BOF performance. One important aspect of splashing is its generation mechanism. This topic has attracted continuous interest, but © 2016 American Chemical Society

the reported results cannot be compared with each other, as briefly reviewed below. Deo and Boom8 reported that the generation of splashing stems from the impingement of the jet and the shearing action of the gas flow from the impact region when the jet strikes on the metal surface and the gas is deflected upward. Standish and He9 suggested that the splashing phenomenon is generated in the “dropping” and “swarming” regions, which are dependent on the gas flow rate, using their two-dimensional (2-D) laboratory water model system. They also showed that the generation rates in the two regions are both a function of the blowing rate and have their own characteristics. On the other hand, the generation of splashing was reported to originate from the surface waves formed inside the cavity and the propagation of the surface waves.6,10−15 In particular, Peaslee and Robertson10 found that the surface waves formed metal fingers near the edge of the cavity, and these fingers were unstable and ultimately torn from the surface. A similar generation mechanism was also observed by Alam et al.14 who studied the impingement of a shrouded supersonic jet onto a water surface by a two-dimensional volume of fluid (VOF) model. The above discussion suggests Received: Revised: Accepted: Published: 3630

September 7, 2015 December 30, 2015 March 14, 2016 March 14, 2016 DOI: 10.1021/acs.iecr.5b03301 Ind. Eng. Chem. Res. 2016, 55, 3630−3640

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Industrial & Engineering Chemistry Research

fluids. If the qth fluid’s (gas, slag, metal) volume fraction in a computational fluid dynamics (CFD) cell is denoted as αq, then the following three conditions are possible: (1) αq = 0: The cell is empty (of the qth fluid). (2) αq = 1: The cell is full (of the qth fluid). (3) 0 < αq < 1: The cell contains the interface between the qth fluid and one or more other fluids. Overall, the sum of the volume fractions for all the phases involved in each cell is equal to 1. The tracking of the interface between gas and melts was performed by the solution of a continuity equation for the volume fraction of the phase. For the qth phase, the conservative equation can be expressed as follows:

that the generation mechanism of splashing has not been clearly understood, and further efforts are thus needed for this topic, particularly using quantitative methods. Another important aspect of splashing is to quantitatively depict this phenomenon under different conditions. In this direction, in the past years different investigators5,9,12,14,16−22 have experimentally and/or theoretically investigated the quantity and size distribution of the splashing metal droplets and their trajectories and residence time in the slag for BOF applications. Recently, Sabah and Brooks15,23,24 studied the effect of wave behavior inside the cavity on splashing and the effect of positioning of sampling on estimation of splashing generation rate by a novel approach in an air−water system corresponding to BOFs. They also comprehensively reviewed the previous findings about the amount of splashing generated in the emulsion zone and identified observable discrepancies. Nonetheless, to date, the studies on the splashing process during the impingement of supersonic jets onto a multilayer liquid bath are very few, particularly at a high ambient temperature, because of the limits of measurement technology at this stage of development and the high costs in experimentation. However, such a phenomenon is widely encountered in steelmaking or other similar processes. This paper presents a numerical study on the impingement of supersonic jets onto the slag−metal bath of a 150 ton commercial BOF at a steelmaking temperature by a multifluid VOF model, with special reference to the splashing phenomenon. From such a study, the generation mechanism of the splashing phenomenon was visualized and expounded. Furthermore, by combining the VOF model with “blowing number” theory, the generation rate of splashing was quantified with respect to lance height and operation pressure.

∂(ρq αq)

where ρq and αq are the density (kg·m ) and volume fraction of phase q, respectively, and the oxygen gas is treated as an idea gas and thus conforms to the relation p = ρRT. In the VOF model, all the fluids, regardless their differences in properties, were modeled by the same set of momentum as given in eq 2. The resulting velocity field is shared among the phases. Accordingly, the fields for all variables and properties are shared by the phases involved and represented volumefraction-averaged values. ∂ (ρ u) + ∇(ρ uu) = −∇p + ∇·[μeff (∇u + ∇uT )] + ρg + fσ ∂t (2)

where u is the velocity vector (m·s−1), p the pressure (Pa), g the gravity vector (m·s−2), ρ the density (kg·m−3),and μeff (= μ + μt) the effective viscosity (Pa·s). ρ = αgasρgas + αslagρslag + αsteelρsteel

slag

oxygen

density, ρ (kg/m3) viscosity, μ [kg/(m·s)] surface tension, σ (N/m) heat capacity, cp [J/(kg·K)] thermal conductivity, λ [W/(m·K)] temperature, T (K)

7000 0.005 1.6 670 40 1873

3500 0.1 0.4 1200 1.7 1873

ideal gas 1.19 × 10−5 − 919.31 0.0246 −

(3)

μ = αgasμgas + αslagμslag + αsteelμsteel

(4) −3

fσ in eq 2 is the surface tension (N·m ) and is calculated using the continuum surface force (CSF) model developed by Brackbill et al.32 In the model, the surface tension effect is treated as body forces: fσ =

∫V σκ∇α dV = σκp(∇αp)Vp

(5)

where VP is the volume of cell P and κP is the curvature calculated by ⎡ ⎛ ∇ α ⎞⎤ ⎟ κp = −(∇·n)̂ = −⎢∇·⎜ ⎥ ⎣ ⎝ |∇α| ⎠⎦ p

(6)

where n̂ is the unit vector normal to the surface. Similarly, the energy equation is also shared among the phases: ∂(ρE) + ∇·[u(ρE + p)] = ∇·(λeff ∇T ) + S h ∂t

Table 1. Physical Properties of the Fluids steel

(1) −3

2. MODEL DESCRIPTION The present mathematical model has been recently established to study the BOF steelmaking process.25−30 It is threedimensional and involves multiphases in a steelmaking BOF, i.e., molten slag, metal, and oxygen gas. Corresponding to the BOF practice, the time-dependent impingement of multiple supersonic oxygen jets onto a bath with immiscible molten slag and metal was modeled under nonisothermal conditions. The gas phase was regarded as a Newtonian fluid and compressible, while the molten steel and slag were treated as incompressible, having constant viscosities and surface tensions. The physical properties of the phases considered are listed in Table 1. At present, the chemical reactions were neglected. The model is outlined below for completeness. 2.1. Governing Equations. The tracking of the sharp gas− slag−melt interface was accomplished using the VOF approach originated from the work of Hirt and Nichols.31 In this method, a variable, namely, the volume fraction α of phase, is introduced to describe the free boundary configurations of immiscible

property

+ ∇(αqρq u) = 0

∂t

(7)

where the energy E is treated as a mass-averaged variable. This treatment is also applied to the temperature T (K). n

E=

∑q = 1 (αqρq Eq) n

∑q = 1 (αqρq )

(8)

where Eq is based on the specific heat of qth phase and the shared temperature by all the each phases involved. 3631

DOI: 10.1021/acs.iecr.5b03301 Ind. Eng. Chem. Res. 2016, 55, 3630−3640

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Industrial & Engineering Chemistry Research In eq 8, the source term Sh incorporates the contributions from the radiation as well as any other volumetric heat sources. λeff (= λ + λt) is the effective thermal conductivity (W·m−1·K−1) and shared by all the phases, the same as other properties: λ = αgasλgas + αslagλslag + αsteelλsteel

(9)

2.2. Turbulence Model. The flow in the BOFs experiences the complicated interactions among compressible gas, liquid metal, and slag and also involves highly dynamic supersonic jets. It is therefore a turbulent flow. In the present mathematical model, the standard k−ε model33 with compressibility correction is used as the turbulence model. It is arguable that other turbulence models such as the k−ω model and Reynolds stress model should be used although they are theoretically better than the k−ε model. In particular, our preliminary tests suggested that the k−ω model and Reynolds stress model caused numerical instability for the complicated flow system considered. Also, it should be pointed out that a series of model validations in our previous studies26−30 indicate that the standard k−ε model is acceptable in the modeling of BOF, which gives the emphasis to numerical solutions ultimately for industrial applications. In fact, this model has been widely used in the previous studies of BOF (see, e.g., refs 14 and 34−42). In the present turbulence model, the transportation equations for the turbulence kinetic energy (k) and the turbulence dissipation rate (ε) are thus expressed as

Figure 1. Computational domain and mesh representations of the converter considered.

Table 2. Geometrical and Operational Conditions parameter nozzle throat diameter, d* (mm) Nozzle outlet diameter, de (mm) number of nozzles, N (−) nozzle-to-nozzle angle, θ (deg) Mach number, Ma (−) designed pressure, P0 (Pa × 101 325) converter back-pressure, Pb (Pa × 101 325) inlet oxygen temperature, T (K)

μ ⎞ ∂k ⎤ ∂(ρkui) ∂(ρk) ∂ ⎡⎢⎛ + = ⎜μ + t ⎟ · ⎥ + G k + G b ∂t ∂xi ∂xj ⎢⎣⎝ σk ⎠ ∂xj ⎥⎦ − ρε − YM

(10)

(11)

where μt is the turbulent viscosity and is given by μt = Cμρ

k2 ε

parameter

value 1873

6 17.5

converter temperature, Tb (K) converter capacity, (ton) bath diameter, D (m) melt height, Hm (m)

2.25 11.56

slag height, Hs (m) lance height, H (m)

0.17 1.2−1.8

1

operating pressure, P (Pa × 101 325) oxygen flow rate, Q (N m3 h−1)

0.8P0, P0, 1.2P0 24210, 30283, 36871

43.4

308

150 5.685 1.545

with the structured nonuniform grids. Note that CFD grids are important to obtain meaningful numerical results, and they are mainly determined by mesh type, size, and arrangement. In this study, the computational domain was divided by hexahedral cells for gaining numerical stability and efficiency. Moreover, the grids between the lance tip and the free surface are finer than the remainder of the converter because the flow varies more significantly there. On this base, some preliminary tests were conducted to select fine enough grids so that the numerical solution is converged and becomes grid-independent. For this purpose, the number of grids was varied from 0.5 to 1.2 million to select the appropriate grids for results analysis. A moderate grid number was thus confirmed referring to the key flow characteristics and process parameters such as cavity depth, as detailed elsewhere.28,29 In all the simulations, a pressure boundary condition was used at the outlet where the gauge pressure was set to zero while the local atmospheric pressure was set to 101 325 Pa. The same boundary condition was applied to the inlets located at the nozzle exits. However, the values of the gauge pressure there were calculated according to the isentropic theory44 of gas flow:

μ ⎞ ∂ε ⎤ ∂(ρεui) ∂(ρε) ∂ ⎡⎢⎛ + = ⎜μ + t ⎟ · ⎥ ∂xj ⎢⎣⎝ ∂t ∂xi σε ⎠ ∂xj ⎥⎦ ε ε2 + C1ε (G k + C3εG b) − C2ερ k k

value 30

(12)

The items in eqs 11 and 12 are as follows: Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients (kg·m−1·s−3). Gb is the generation of turbulence kinetic energy due to buoyancy (kg·m−1·s−3). YM represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate (kg·m−1· s−3); YM = 0 for the incompressible fluid and YM = 2ρεMt2 for the compressible fluid. Mt (= k1/2/a) is the turbulent Mach number, where a (= γRT)1/2 is the sonic velocity (m·s−1). C1ε, C2ε, C3ε, σk, σε, and Cμ are constants, and their values are 1.44, 1.92, 0.8, 1.0, 1.3, and 0.9, respectively.33,43

3. SIMULATION CONDITIONS AND SOLUTION ALGORITHMS Figure 1 illustrates the computational domain considered, corresponding to a 150 ton commercial steelmaking BOF operated with an oxygen lance of six convergent−divergent nozzles. The dimension details are listed in Table 2. Here, only one-half of the converter was considered to alleviate the computational loading. The computational domain was meshed

Pe ⎛ κ − 1 2⎞⎟−κ / κ − 1 Ma = ⎜1 + ⎝ ⎠ P 2

(13)

Te ⎛ κ − 1 2⎞⎟−1 Ma = ⎜1 + ⎝ ⎠ T 2

(14)

where κ is the isentropic index and equal is to 1.4 for the diatomic gas, and Te (K) is the temperature at the Laval nozzle exit. A standard wall function33 was used to model the velocity near the wall, combined with a no-slip wall condition at the 3632


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splashing phenomenon occurs. Figure 2a−d shows the surface shapes of the whole molten bath when the jets are introduced

wall. The pressure−velocity decoupling was achieved using the PISO algorithms.45 To improve the convergence and the stability of the simulations considered, the PRESTO scheme43 was employed to interpolate the pressure values at the cell faces from the surrounding cell nodes in the solution of the momentum equations. Additionally, the compressive interfacecapturing scheme for arbitrary meshes (CICSAM)46 was used to track the free surface deformation. CICSAM is applicable for the high ratio of viscosities between phases, as considered in this work, and can produce an interface almost as sharp as that of the geometric reconstruction scheme. The second-order upwind scheme was taken for the discretization of convection terms of the momentum, turbulence, and energy conservation equations. The time step was initially set to 10−5 s and then switched to the adaptive scheme based on the limitation of a global Courant number of 1. The convergence criteria were set to 1 × 10−6 for the absolute residual of energy, while 1 × 10−3 was used for those of other dependent variables. The model was built in the framework of a software package ANSYS-Fluent. The calculations were carried out on a modern Linux cluster with a maximum of 24 parallel processors. The physical time of 1 s typically lasted for the wall time of around 48 h. Because of the long time required for the calculations, the real BOF process of approximate 12 s was calculated for each case.

Figure 2. Molten bath surface shapes at the incipient blowing stages of (a) 0.5 s, (b) 1.5 s, (c) 2.25 s, and (d) 3.0 s for the lance height of 1.2 m and the operating pressure of P0. The curved lines show the streamlines of the gas flow.

4. RESULTS 4.1. Model Applicability. It is necessary to verify the validity of the mathematical model before applying it to numerical experiments. This has been done by comparing the numerical results against the experimental results and theoretical calculations through different applications,25−30 from simple to complex. The data used in the comparisons include (1) the centerline velocity of each individual jet, as measured by Cheslak et al.;47 (2) the Mach number and mass flow rate of the jet at the nozzle exit, as given by the isentropic theory;44 (3) the velocity at the lance geometrical axis and the offset distance of an individual jet center to its nozzle geometrical axis, as reported in the previous experimental work;48 (4) the profile and dimensions of cavity measured by the present authors;28 (5) the penetration depth determined by the theoretical calculation of Koria and Lange;49 and (6) the flow rate of kinetic energy through the horizontal crosssectional area from the empirical model developed experimentally by Nakanishi et al.50 The first two groups of data considered single jet flows, while multiple jets were considerd for the third group; the interaction between jet(s) and the onelayer/two-layer bath was considered for the last three groups. Overall, reasonably good agreements between the calculated results and the measured ones or theoretical predictions have been achieved for all the parameters listed above. These results have been detailed in our previous studies25−30 and thus are not included here. All the results obtained thus far from the comparisons suggest that the present model can successfully be used to reproduce the key phenomena associated with the jet(s) and the impingement of jet(s) onto one-/two-layer liquid bath, at least qualitatively. 4.2. Generation Mechanism of Splashing. 4.2.1. Oscillation of the Whole Molten Bath. The in-furnace phenomena are complicated and usually interrelated with each other in flow systems such as a steelmaking BOF. It is therefore necessary to first investigate the macroscopic behavior of the whole molten bath to ultimately obtain a full picture about how the associated

at the lance height of 1.2 m and the operating pressure of P0. The result reveals that the surface shape apparently varies with the evolution of time at the initial stage of the blowing operation. Here, the first three seconds of the blowing time is considered to clearly show the variation. Overall, the surface is relatively smooth and quiet, and the jets just penetrate into the molten slag with slag splashing at the blowing time of 0.5 s (Figure 2a). As the blowing operation proceeds, the molten slag is completely pushed from the impact zone, the jets penetrate into the metal bath, and the whole surface becomes irregular. Also, the cavity and the whole molten bath oscillate with time and are shown to be unstable (Figure 2b−d). To characterize the flow behavior inside the molten bath, Figure 3 presents the temporal variation of the velocity at the monitoring point, which is 0.26D from the center of the molten bath and 0.55 m from the initial metal level. As seen from this

Figure 3. Velocity variations at the monitoring point during the simulated blowing process for the lance height of 1.2 m and the operating pressure of P0. 3633


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Industrial & Engineering Chemistry Research figure, the velocity is very different during the simulation time considered, indicating that the flow field of the molten bath is unstable. It is of interest to note that the velocity variation is more evident during the first half of the time period simulated because at this moment the flow just starts to develop toward achieving a macroscopically steady state. This result should be viewed from two aspects. On one hand, the velocity variation represents the stochastic characteristics of the turbulent flow. On the other hand, the different interactions between jets and slag and between jets and metal somewhat account for the variation of velocity with time. It should be noted that the variation trends shown here may not always be observed during the subsequent blowing process or when the lance position is changed. A similar result was also reported by Zhou et al.51 for an air−water system. These time-dependent variations of molten bath surface shapes and velocity field inside the molten bath as given in Figures 2 and 3 confirm the unstable characteristics of the whole bath during the blowing operation, at least at the initial stage. Lee et al.6 reported that such instability is derived from the instability and/or oscillation of the formed cavity. Furthermore, there is strong evidence6,10,11,13,14,27−29 that the surface waves formed inside the cavity propagate across the entire bath surface and contribute the oscillations of the cavity and the whole bath when the gas jet(s) strike(s) on the liquid bath surface. The oscillations of the cavity and liquid(s) bath are in turn responsible for the generation of splashing.6,14,15,28 4.2.2. Generation Process of Splashing. Figure 4 shows the predicted generation process of splashing over the blowing time

molten metal surface in the impact region, which drives the flows on the surfaces of the melts as well as that of the molten bath bulk. The velocity difference on the two sides of the interface between the gas and metal induces the instability of the gas−metal interface. As such, the developed instability results in the growth and motion of the surface waves and finally the onset of splashing. All these numerical results confirm that the generation of splashing is a result of the oscillation of the cavity and even the whole molten bath when the ambient temperature is high. This is in line with the understandings postulated from qualitative observations at room temperature.13−15 The velocities, especially their radial components, are linked with the shearing effect on the interface between the gas and molten bath and hence affect the splashing to a large extent. Figure 5 shows the representative spatial distribution of velocities in the furnace and the radial velocity profiles at different height levels. It can be seen from this figure that the maximum velocity inside the molten bath is present around the impinging region of jets because of the strong shearing resulting from the deflecting gas flow. The maximum value of the velocities decreases from 0.3 to 0.06 m·s−1 when the height level varies from 1.2 to 0.4 m, and it eventually becomes very small if not zero near the bottom region of the furnace. Expectedly, the radial velocity profile initially shows large peaks and tends to be uniform as the height level decreases (Figure 5b). 4.2.3. Generation Mode of Splashing. The results in section 4.2.2 suggest that the growth and propagation of surface waves inside the cavity are a necessary prerequisite for a splashing phenomenon to occur. Sabah and Brooks15 observed that socalled “splash sheets” form at the rim of the cavity based on their water model experiments. Such sheets rise to a certain height until becoming unstable, and then fingers form and ultimately break into droplets. Figure 6 shows representative images of the splash sheet and the splashing, obtained by the present model. It should be pointed out that the phenomena from the present model are encouragingly similar to experimental observations of Sabah et al.15,23 via a high-speed imaging method considering that the conditions involved are not the same and the present model is not perfect; for example, it requires a considerably refined mesh to reproduce all the small-scale droplets normally with diameter in a range of 0.04− 70 mm.16 Notably, the calculated results show two generation mechanisms of metal splashing, that is, the direct ejection of individual droplets out of metal body at the rim of cavity and crushing and tearing of splash sheets or “large tears” formed at the rim of cavity into several small droplets by deflecting gas flow, as shown in Figure 6b. Also, these results can directly be reflected from Figure 4, where the small droplets and larger sheets as well as their tearing are indicated. These two mechanisms stem from the ripples formed in the cavity surface. According to the experimental observation of Standish and He,9 the small ripples result in the direct ejection of individual droplets, and the bigger ones result in the generation of splash sheets or large tears. This understanding can well be reflected from Figures 4 and 6, which reveal that the two types of ripples may be produced simultaneously as a result of cavity oscillation during the impinging process. 4.3. Generation Rate of Splashing. To experimentally and numerically obtain all scales of the droplets and corresponding rate of splashing caused by the interaction between liquid bath and jet(s) is extremely difficult if not

Figure 4. Splashing generation process during the blowing period for the lance height of 1.2 m and the operating pressure of P0: (a) macroscopic surface structures inside the cavity and (b) microscopic perspectives related to surface waves.

for a given lance height and operating pressure. This figure also includes the information about the surface structures inside the cavity in relation to the splashing process. As seen from Figure 4, when the jets strike on the molten metal surface, a surface deformation occurs and a cavity with surface waves inside it is developed. The surface waves are then spread out, leading to the oscillation of the cavity in both the horizontal and vertical directions, as well as to the uneven slag−metal interface. Accordingly, the splashing originating from the wave motion occurs and follows the periodic motion pattern of the wave. According to the Kelvin−Helmholtz theory,11 as the jets impinge on the molten metal surface, the gas flow is deflected upward. The deflecting gas flow exerts a shearing force on the 3634


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Figure 5. Snapshots showing (a) velocity contour map and (b) radial velocity profiles at different height levels on the plane x = 0 for the lance height of 1.2 m and the operating pressure of P0.

Figure 7. Variation of blowing number (NB) over the blowing time for the lance height of 1.2 m and the operating pressure of P0.

interface between the jets and molten bath according to the work of Alam et al.,14 as highlighted by the white coarse line. It can be seen from Figure 7 that the value of the blowing number fluctuates with the evolution of time because of the abovediscussed unstable features of the molten bath and cavity. Notably, the oscillation of the cavity affects the generation mode, amount, and distribution of splashing. Here, a mean value of the blowing number is 10.0. The blowing number was in the range of 6−8.5 as reported by Holappa and Kostamo53 for a 55 ton steelmaking BOF when the lance height varied from 0.9 to 1.25 m, and it was in the range of 1−13 as reported by Standish et al.9 for a water model of a BOF. Subagyo et al.12 developed a correlation between the splashing rate per unit volume of blown gas and the blowing number according to the experimental data at high temperature and those of He and Standish9,18 at room temperature:

Figure 6. Snapshots showing (a) formation of splash sheets and (b) generation of splashing, calculated by the present simulations for the lance height of 1.2 m and the operation pressure of P0. The blowing time is 0.5 s for panel a and 1.5 s for panel b.

impossible. Subagyo et al.12 proposed a “blowing number (NB)” to assess the splashing rate based on the Kelvin−Helmholtz theory following the previous works:6,11,52

NB =

ρg ug 2 2 σgρ1

RB (NB)3.2 = FG [2.6 × 106 + 2.0 × 10−4(NB)12 ]0.2

(15)

where NB is the dimensionless parameter; ρg and ρl are the gas and liquid density, respectively (kg·m−3); σ is the liquid surface tension (N·m−1); g is the gravitational acceleration (m·s−2); and ug is the critical gas velocity (m·s−1). When eq 15 is combined with numerical results, the spatial distribution of the blowing number is hence determined and used to identify the onset of splashing, which occurs when NB > 1, as shown in Figure 7. In this figure, the gas velocity ug is defined as the velocities on the

(16) 3 −1

where FG is the volumetric flow of blown gas (N·m ·s ) and RB is the splashing rate (kg·s−1). This correlation was confirmed by Sabah and Brooks23 when the dimensionless lance height H/ de ≤ 50. Figure 8 shows the variation of the splashing rate with blowing time for the lance height of 1.2 m and operating pressure of P0. Note that the results shown in this figure (also in Figures 10 and 13) were calculated according to eq 16. 3635


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Figure 9 shows the representative splashing patterns at different lance heights for the blowing time of 1.5 s and the operating pressure of P0. The results reveal that the splashing phenomenon becomes fairly more evident when the lance height is lowered. To be quantitative, Figure 10 plots the blowing number and the splashing rate per unit volume of blown gas against the lance height. In this figure, the variance is also given to show how the data is spread out related to the nature of the fluctuations as discussed in section 4.2.2. As seen from Figure 10, as the lance height descends from 1.8 to 1.2 m, the blowing number significantly increases, e.g., from 4.4 to 10 under the considered conditions. Accordingly, the splashing rate per unit volume of blown gas increases from 6.1 to 34.4 kg· N·m−3. These results are consistent with the soft and hard blowing in practice and may be explained as follows. When the lance height is high, a shallow depression with relatively weak oscillation and small ripples inside the surface is formed, as reported elsewhere.28 In this case, more splashing may be generated by the direct ejection of individual droplets around the edge of the cavity. A further decline of lance height increases the intensity of the jet momentum input at the initial liquid level. A deeper depression with more intense oscillation and bigger ripples formed inside the surface is developed. Consequently, more splashing may be generated by so-called splash sheets or large tears. The depression is the dimpling mode when the lance height is 1.8 m and transits into the splashing mode as the lance height gradually lowers to 1.5 m, according to our previous results.28 Therefore, the change of the cavity mode leads to different splashing rate, which is consistent with the cavity mode classification by Molloy.54 Similar to the analysis in section 4.2, the radial velocity profiles are also examined at different lance heights, and the results are given in Figure 11. It can be seen from this figure that the maximum radial velocity decreases and the position corresponding to the maximum gradually moves toward the

Figure 8. Splashing rate variation over the blowing time for the lance height of 1.2 m and operating pressure of P0.

Generally, the variations of the blowing number and the splashing rate show a similar trend. The splashing rate here has a mean value of 34.4 kg·N·m−3 for per unit volume of blown gas. That is, the total splashing rate is 289.4 kg·s−1, obtained by substituting the gas volume flow rate into eq 16.

5. DISCUSSION 5.1. Effect of Lance Height on Splashing. Lance height can have significant impact on the splashing phenomenon in the molten bath. It is a prime operating parameter and often varies to control slag formation and decarburization in the BOF steelmaking process. For example, there are two well-known operations in the BOF practice, namely, “soft blowing” and “hard blowing”, which correspond to high and low lance positions, respectively. Through the combination of numerical simulation and blowing number theory, the effect of lance height on splashing is visualized and quantified for the first time.

Figure 9. Snapshots showing the splashing patterns at the lance heights of (a) 1.2 m, (b) 1.5 m, and (c) 1.8 m for the blowing time of 1.5 s and the operating pressure of P0. 3636


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Figure 10. (a) Blowing number and (b) splashing rate per unit volume of blown gas as a function of lance height for the operating pressure of P0.

side wall as the lance height varies from 1.2 to 1.8 m. This result should be due to the decrease of the shearing force exerted on the gas−metal interface as the lance rises. 5.2. Effect of Operating Pressure on Splashing. Operating pressure is a key parameter that dominates the hydrodynamic behaviors of jets and their impingement onto the molten bath surface and thus the splashing process. Figure 12 shows the representative splashing patterns in the molten bath at different operation pressures. It is observed that with the increase of operating pressure, the splashing phenomenon becomes less evident, similar to the trend as a result of the decreased lance height. Accordingly, the blowing number and the splashing generation rate per unit volume blown gas increase, as shown in Figure 13, although the cavities here are all in the splashing model according to the previous study.28 This result implies that the splashing rate can be somewhat different even in the same cavity mode. The increased operating pressure leads to the greater intensity of the jet momentum and hence the bigger ripples formed at the cavity surface. As such,

Figure 11. Radial velocity profiles of different lance heights at the vertical distance of 1.0 m from the furnace bottom and the operating pressure of P0.

Figure 12. Snapshots showing the splashing patterns at the blowing time of 1.5 s under the operating pressures of (a) 0.8P0, (b) P0, and (c) 1.2P0 for the lance height of 1.2 m. 3637


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Figure 13. (a) Blowing number and (b) splashing rate per unit volume of blown gas as a function of operating pressure for the lance height of 1.2 m.

special reference to a real BOF steelmaking process. The major findings from the present study can be summarized as follows: (1) The splashing phenomenon under harsh oxygen steelmaking conditions referring to extremely high temperature (1600 °C) and velocity (supersonic) is successfully predicted. The temporal occurrence process of splashing is shown and found to follow the periodic motion pattern of waves but not for the generation modes and amount of splashing. Two splashing mechanisms, including the direct ejection of individual droplets at the rim of cavity and the tearing of splash sheets or large tears into several different-sized smaller droplets by the deflecting gas flow, are identified. These two mechanisms simultaneously occur, rather than depending of the gas flow rate as reported by Standish and He,9 and contribute to the splashing phenomenon in BOF practice. (2) Through the combination of the multifluid VOF model and blowing number theory, the splashing phenomenon is quantified under different conditions. The results show that both the blowing number and the splashing rate fluctuate during the blowing process because of the oscillating nature of the process, but such fluctuations normally are irregular. The typical blowing number and splashing rate are in the range of 4.4−10 and 6.1−34.4 kg·N·m−3, respectively, for the current varying lance height (1.8 to 1.2 m), and in the range of 7.2− 12.8 and 24.0−42.2 kg·N·m−3 for the current varying operating pressure (0.8P0 to 1.2P0). (3) Both the blowing number and the splashing rate monotonically decrease with the lifting lance height or decreasing operating pressure under the current conditions considered, but the splashing shows to be more evidently affected by the variation of lance height than that of operating pressure. The decline of lance height or the increase of operating pressure can both lead to more splashings being generated by splash sheets or large tears, which finally enables the increase of the splashing rate.

more splashing may be produced by means of splash sheets or large tears as the operating pressure increases. Figure 14 shows the radial velocity profiles at different operating pressures. As seen from this figure, the maximum

Figure 14. Radial velocity profiles of different operating pressures at the vertical distance of 1.1 m from the furnace bottom and the lance height of 1.2 m.

velocity decreases sharply when the operating pressure varies from P0 to 0.8P0, which indicates that the shearing forces exerted on the cavity surface rapidly decrease. Finally, it should be pointed out that in the top-blown BOF practice, the crucial factor affecting the splashing phenomenon is the transfer of the jets’ momentum rather than the changes in physical properties of melts.28,55 Therefore, the effects of physical properties of melts are not considered in the present study. Furthermore, the results from this work indicate that the quantitative relation between cavity oscillation and splashing rate may be useful for developing new ways to describe the splashing. How to achieve this development is open for further study and will be considered in the next stage of our present project.

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6. CONCLUSIONS Splashing can play a critical role in forming major phenomena in a process unit and thus control the performance of the unit. This paper presents a numerical study of the splashing phenomenon induced by the intense interaction between multiple supersonic oxygen jets and the bath with immiscible melts by the recently developed multifluid VOF model, with

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*Tel.: +86 24 8368 7724. E-mail: [email protected]. P.O. Box 312, Northeastern University, 3-11 Wenhua Road, Heping District, Shenyang, Liaoning, P.R. China, 110819. Notes

The authors declare no competing financial interest. 3638


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ACKNOWLEDGMENTS The authors are grateful for the financial support by the National Natural Science Foundation of China (Grant 51104037) and the Fundamental Research Funds of the Central Universities of China (Grants N120402010, N140204008).

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Computational Investigation of the Splashing Phenomenon Induced

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