The Importance of Viscous and Interfacial Forces in the Hydrodynamics of the TopSubmergedLance Furnace
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Abstract
The purpose of this work is to focus on the hydrodynamics of a TopSubmergedLance (TSL) smelting furnace, understanding how liquid properties and operational parameters act on key factors of a TSL process, such as splashing, mixing, mass transfer area, and bubble development. A deep knowledge of all those aspects is needed since they all influence the smelting reaction rates; hence the efficiency of the reactor. The characterization and scaling of the TSL gas injection are commonly based on the modified Froude number, the ratio of dynamic and gravitational forces. Detailed literature research reveals a potential weakness of this approach, since it does not consider the effects of viscosity and surface tension. To investigate this question an extensive parametric study was performed applying computational fluid dynamics to cold and nonreactive flows, which provided a broad overview of the physics of the flow. The analysis was performed on fluid dynamic properties (liquid density, liquid viscosity, surface tension) and operational variables (gas volume flow, lance immersion depth). The coupled Level Set—Volume of Fluid model, available in the commercial solver ANSYS Fluent^{®}, was used to resolve the gas–liquid interface in the multiphase flow. The results of the work underscore the significance of the viscous and interfacial forces for gas injection in smelting slags, confirming the incompleteness of applying only the Froude number to describe such flows.
Introduction
The TopSubmergedLance (TSL) technology today plays an active and significant role in the pyrometallurgical industry. Developed in the early 1970s to improve the tin smelting process, this technique rapidly reached commercialization, extending the field of application to other metals such as copper, lead, nickel, and zinc.[1] Eighteen percent of worldwide copper production employs TSL furnaces, as reported by Kapusta,[2] and recent investigations on metal recycling employ it to achieve sustainability in process metallurgy.[3] According to Reuter,[4] 64 commercial Ausmelt furnaces are being used to process Cu, Sn, Zn, Pb and Ni. Nevertheless, the young age of this process means that is still requires indepth scientific research to improve its resource efficiency and reliability.
The main feature of these furnaces is the direct injection of process gas (air or O_{2}enriched air) through the topsubmerged lance into the liquid slag bath at a temperature range of 1100 °C to 1400 °C: this creates a strong turbulent agitation in the bath, with the aim of increasing the gas–liquid interface and the mass transfer, and hence the overall reaction rates. The bubble rise and consequent breakup and splashing generate a recirculating structure in the liquid phase, which leads to a higher mass transfer in the liquid bath. The formation of stagnant zones is also prevented and, by that means, the localized solidification of slag. It therefore follows that knowledge of the hydrodynamic behavior of these furnaces is of crucial importance for a global comprehension of the entire process. It has to be noted that due to the high temperatures and the aggressive nature of the slags, insitu measurements and optical inspections are still very challenging, meaning that many aspects of the underlying physics are currently not fully understood, and are handled with empirical approaches. The usage of Computational Fluid Dynamics (CFD) can help overcome these difficulties and answer many questions. However, the high complexity of this multiphase flow and the respective models (high temperature, reactive, and intrinsically transient) still restricts the applicability of this technique to smalltopilotscale reactors or to simplified test cases.
The same conclusion was reached by Krishnapisharody and Irons,[11] who reviewed the usage of the modified Froude number in ladle metallurgy in favor of a proposed model based on plume parameters. Critical remarks were directed at various aspects of the modified Froude number, such as the characteristic length used, or the importance of the initial momentum of the injected gas in comparison with buoyancy forces.
It should be noted that all of those works concern ladle metallurgy operations, where gas is injected at moderate regimes, in most cases from the bottom of the reactor and in hot liquid steel, which has different physical properties than those of the smelting slags. Despite that, these models have been applied in the literature for the hydrodynamic modeling of TSL smelting processes. Huda et al.[12] performed a CFD study of an Eulerian twofluids model based on the work by Morsi et al. (see above) investigating the effect of swirling jetting on the nature of the flow, and proposed a semiempirical equation to estimate the gas penetration depth as a function of the modified Froude number. Pan and Langberg[13] examined the behavior of large bubbles in bath smelting furnaces with 2D physical and numerical modeling, focusing on the mechanism of liquid splashing above the bath. The gas injection was scaled from a prototype Sirosmelt furnace under the condition of dynamic similarity of equal modified Froude number; they offered a qualitative overview of the splash generation, finding the liquid viscosity, the bubble size, and its detachment frequency as control parameters. A similar approach was used by Zhao et al.[14,15] for the experimental study of an air–water system: the authors analyzed the mixing process in the liquid phase using a saline solution as a tracer, and estimated the interface area of the main bubble formed at the lance.
Liovic et al.[16,17] implemented a MultiFluid Volume of Fluid (MFVOF) to resolve metallurgical flows, overcoming the difficulties of modeling multiphase systems with high density ratios: the shifted grid approach was used to compute density and the surface tension force was implemented with a fully kernelbased Continuum Surface Force (CSF) method. The model was tested on a scaled model of the Ausmelt furnace, but unfortunately no detailed information is given about the scaling procedure used. Their simulations were performed on air–water and air–glycerol systems to qualitatively understand the effect of viscosity on the multiphase flow field. A recent work was published by Wang et al.,[18] who investigated the usage of the appropriate turbulence model, using a Volume of Fluid approach. The results were compared with experimental data obtained from a setup with air injection in paraffin oil, using a vessel of 0.135 × 0.135 × 0.195 m. They found that the Renormalization Group \(k\epsilon \) model (RNG) and the Reynolds Stress Model (RSM) are able to predict timeaveraged velocity fields. However, the Large Eddy Simulation (LES) model showed a better behavior in predicting fluctuating velocities and the Reynolds stress terms. Nevertheless, the usage of a LESVOF approach could still be prohibitive to bigger labscale or even pilotscale simulations, since a LES approach requires a considerably higher grid resolution than a RANS approach,[19] with consequent reduction of the time step to ensure that flow Courant number is less than 1. Some modeling activities have been carried out on pilotfurnace scales: Solnordal et al.[20] developed a mathematical model to calculate the heat transfer coefficient at the lance wall of a Sirosmelt prototype plant, as well as the thermal conductivity of the slag layer present over it. Huda et al.[21,22] provided a detailed analysis of the zinc slag fuming process in a TSL furnace, modeling the reactive slag bath as well as the coal combustion at the gas injector with an Eulerian multifluid approach.
The present study examines the importance of viscous and interfacial forces on the multiphase flow due to TSL gas injection. It is shown that the usage of only a modified Froude number is not sufficient when applied to injection into nonferrous slag systems. To that end, an extensive parametric study has been done on the effect of physical properties (liquid density, viscosity, and surface tension) and operational parameters (vertical lance position, gas volume flow). The inclusion of these parameters is of considerable importance because, in addition to providing information about the hydrodynamic characterization, it can suggest some practical conclusions about how the control parameters affect important phenomena of the process, such as the mass transfer surface and the mixing of the liquid.
The Hydrodynamics of the TSL Injection in Smelting Furnaces
In this section, different aspects of the TSL process are discussed and the importance of hydrodynamics is highlighted.
SlagGas Interface Area
In TSL technology the interface between the slag and gas is a key element, since the smelting reactions take place there, unlike with a flash smelter, where the ores are oxidized in the socalled reaction shaft before reaching the settling region.[23]
There have been attempts to experimentally monitor this area in labscaled models,[14,15] despite obvious limitations. Zhao et al. monitored the flow with a highspeed camera and used image postprocessing to calculate the contact area of the bubble at the lance in the instant of maximum penetration depth. The 2D view provides only a side projection of the interface; furthermore visibility is limited in the presence of an intense bubbling flow. The application of CFD coupled with multiphase interfacetracking methods such as Volume of Fluid (VOF), Level Set (LS), or FrontTracking (FT) provides additional information and gives a deeper insight into the flow. In these methods, the spatial structure of all interfaces is known; hence the surface area can be readily computed, as well as its transient development.
Mixing Process in the Slag Phase
The downward gas injection into the slag bath generates a recirculating structure in the liquid flow, increasing heat and mass transfer.[24] As a consequence, the mixing process ensures high reaction rates and favors the transport of the matte from the reactive zone to the bath, where a gravitydriven settling process takes place. An unsuccessful stirring of the slag could cause the formation of solid agglomerates in regions where the recirculation is limited, which can lead to severe accidents such as explosions if they contain unburned fuel (coal, oil). Hence, an understanding of the mixing and recirculation is of importance for the process resource efficiency and selectivity, as well as for the process safety.
Slag Splashing
What makes a TSL furnace unique is the possibility to perform prompt manipulations of the mass transfer surface, which leads the smelting process. Besides the bubbles in the bath, the splashing of slag droplets represents a source of interface area. Its intensity and spread are critical design parameters. Properly designed, the splashing is beneficial to the productivity of the process and the lifetime of the furnace. However, if too intense splashing occurs, the spatters of slag constantly reach the refractory wall of the reactor, eroding it due to mechanical impact, thermal stress, and chemical degradation.[25] In the case of weak splashing, the gasliquid interface and the mixing process inside the slag bath are reduced with direct consequences on the efficiency of the furnace. The optimal design should guarantee a range of splashed slag droplets comparable with the radius of the vessel, in order to prevent refractory deterioration and ensure mixing. The slag droplets also encounter the lance placed at the center of the chamber, on which they solidify, cooled by the inflowing process gas. The solid layer preserves the lance from the aggressive environment and from a direct contact with the slag. If the lance was not coated, the continuous alternation of gas and liquid slag could lead to disruptive phenomena such as thermal striping, a form of thermal fatigue damage. Well known in the design of nuclear reactors cooled with liquid metals (LMFR), it is caused by a random temperature fluctuation and a consequent thermal stress fluctuation because of the high thermal conductivities of the liquid, together with flow instabilities or the presence of a gas phase (as in the TSL reactor).[26]
Bubble Dynamics
The dynamics of the gas bubbles is of central relevance for the description of the TSL injection. Indeed it defines all the other aspects that have been discussed. The rise of the bubble towards the free surface induces a liquid displacement, which gives a poloidal direction to the streamlines inside the bath. This recirculating flow is what governs the slag mixing process.
Furthermore, the splashing phenomenon originates from the breakup of the bubbles once they reach the free surface, further increasing the interface area.
This can described in terms of bubble size and bubble detachment frequency, which are also closely connected.[13,15]
Rotational Sloshing Wave
It has been observed that gas injection into a liquid bath excites nonaxisymmetric modes. In the presence of a cylindrical vessel, the waves generated from this instability begin to swirl around the central axis, generating the socalled rotational sloshing phenomenon.[27,28] When a heavy liquid, such as the slagmatte system, is agitated with a similar swirling motion, this can cause serious issues regarding the refractory nature of the wall and its mechanical structure.
Similarity Considerations
The presence of a gap in this topic is evident and challenging, because of the number of variables and hydrodynamic phenomena to examine.
Modeling Approach, Verification and Validation, and Data Analysis
The subject of this hydrodynamic study is gas injection through the lance into the bath. Other aspects of the process, such as the solid feed stream and the matteslag interface, are not taken into account at the moment. In this section, the computational methods used in the CFD investigations are presented and explained in detail.
The CLSVOF Method
The modeling approaches used to describe a twophase flow (gas, liquid) can be classified into two main categories: “multifluid” and “onefluid” formulations.
In the multifluid model, also known as the Euler–Euler model, the phases interpenetrate in the domain and one set of Navier–Stokes equations is solved for each phase: to assure momentum and energy conservation, closure terms are needed for the interfacial friction and the heat transfer, since the interface is not resolved.
The Coupled Level Set—Volume of Fluid (CLSVOF) model merges the two approaches to capitalize on their strengths, by solving the VOF advection algorithm and additionally computing the LS equation. Because of the direct advection of the volume fraction in the VOF algorithm, the mass conservation is preserved, which is a main issue of the LS approach. On the other hand, the implementation of the surface tension force is a potential weakness of the VOF model, especially when applied to high density and surface tension ratios,[34,35] as for modeling smelting slags and mattes. According to the continuum surface force (CSF) model proposed by Brackbill et al.,[36] the surface tension is included as a volumetric source term in the momentum equation, and the discontinuity of the volume fraction does not allow the direct calculation of the normal vector and the curvature of the interface. The imbalance of forces at the interface leads to pressure fluctuations and consequently to the formation of the socalled “spurious currents”, which are unphysical phenomena and can even cause the breakup of the interface.[37]
The CLSVOF model is available in the commercial software ANSYS Fluent^{®}, used for the research activity presented in this article.
Model Verification and Validation
The model is first verified and validated to show its reliability for the subsequent parametric study in the TSL furnace geometry.
Verification assessment
The verification of a model should demonstrate the correct implementation of the theoretical concepts. Therefore, reference cases for this step should be analytical solutions, or benchmark numerical solutions to ODEs or PDEs. Unfortunately, it is almost impossible to have analytical solutions of interfacial flows with complex topological transitions.
Configurations of the Test Case
Test Case  \(\rho _{\text {A}}\)  \(\rho _{\text {B}}\)  \(\mu _{\text {A}}\)  \(\mu _{\text {B}}\)  g  \(\sigma \)  Re  Eo  \(\rho _{\text {A}}/\rho _{\text {B}}\)  \(\mu _{\text {A}}/\mu _{\text {B}}\) 

1  1000  100  10  1  0.98  24.5  35  10  10  10 
2  1000  1  10  0.1  0.98  1.96  35  125  1000  100 
As the first step of this assessment, an analysis of grid convergence was performed on three different cells sizes h (1 / 100, 1 / 200, 1 / 400 mm). A deviation of 7.5 pct was observed for the bubble rise velocity between Grid 1 and Grid 3, and 1.6 pct for the bubble’ s center of mass. Consequently, the finer grid was used for the following evaluations (Figure 2).
Validation assessment
A validation study should prove the capability of a model to represent a real physical phenomenon and determine its reliability as an engineering tool. The numerical results must be compared to experimental data, directly obtained from the system under investigation or from a simplified test rig.
The experimental campaign carried out by Morsi et al.[5] carried out at CSIRO is taken as a reference to validate the CLSVOF model for the simulation of a TopSubmergedLance gas injection into a liquid bath. As reported in the first chapter, a onesixteenthscale air–water model (Figure 6) was used to investigate the effect of the swirl gas injection on the multiphase flow. The air (\({\dot{Q}} = 2.67\times 10^{3}\)\({\text{m}}^{3}/{\text{s}}\)) flows through the lance into the water bath, encountering a helical element with a swirling angle of 57.5 deg. The velocity field was measured with a 2D Laser Doppler Anemometer (LDA) on 9 \(\mu \)m seeding particles, the results are available on a vertical plane passing through the center line of the cylindrical vessel, in the form of timeaveraged profiles and contour plots.
Grid Convergence Analysis
Name  Number of Cells  h (mm)  Pressure Drop (Pa) 

Grid 1  12,057  2.5  1273 
Grid 2  30,639  1.75  1103 
Grid 3  74,736  1  1068 
Grid 4  155,720  0.75  1060 
Parametric Study
Varied Parameters in the Simulation Study
Reference  Viscosity (kg/ms)  Density (kg/m^{3})  Surface Tension (N/m)  Gas Flow (l/s)  Lance Position (m) 

Water  0.001  1000  0.074  1.250  0.025 
  0.01  2000  0.194  1.875  0.050 
  0.1  3000  0.314  2.500  0.075 
\(\downarrow \)  1  4000  0.434  3.125  0.100 
Slag  —  —  —  3.750  0.125 

2D axisymmetric approach

CLSVOF method

\(k\epsilon \)Realizable RANS model

SIMPLE scheme for \(pu\) coupling

SecondOrder Upwind: momentum, velocity

FirstOrder Upwind: turbulence, Level Set function

Grid size: 0.001 m (independence proved)

Time size: 1 × 10^{−5} s (Courant number < 0.5)
Gas–liquid contact area
The timedependent contact area between the gas and liquid is directly extracted from the CFD simulation, monitoring the isosurface computed at \(\alpha \) = 0.5. A timeaveraged value, on a time range of 20 seconds, is then calculated. The first 4 seconds are skipped for averaging, to avoid initialization effects.
Liquid splashing
Global mixing time
Bubble size at detachment
Results
The next paragraphs present the results of the parametric study. For each independent variable, the effects on the observed phenomena previously described are quantified and presented in percentages relative to the baseline configuration. To help the reader, the base configuration is reported with a white dot in the plots.
Operational Parameters
The vertical shift of the lance and the amount of gas injected into the bath are the principal control parameters of a TSL furnace. Therefore, it is extremely valuable to have a deeper understanding of their action on phenomena such as mixing or mass transfer at the gasliquid interface. They have a direct influence on the hydrodynamics of the flow; hence they must be taken into account when a scaling approach is applied to these reactors.
Lance immersion depth
Gas flow
Fluid Properties
The parametric analysis of the fluid properties \(\rho \), \(\mu \) and \(\sigma \), ranging from water to slag values, is intended to understand the importance of gravitational, viscous, and interfacial forces in the hydrodynamics of the TSL gas injection.
Liquid viscosity
Concerning the Global Mixing Time, a curious behavior is encountered: an increase in mixing time by around 400 pct is observed when the dynamic viscosity is increased from 0.001 to 0.1 Pa/s, and then it steeply drops all the way back to a value of about − 30 pct for a viscosity of 1 Pa/s. Since the tracer is transported exclusively via convection, the explanation must lie on the recirculation structures of the liquid bath, which are induced by the rise of the bubbles around the lance. Figure 22 depicts the timeaveraged cells of recirculation for the four cases, with the visualization of streamlines for the liquid phase. It is evident that, in the fourth configuration, the eye of the recirculating structure has an elongated shape and is positioned lower, compared with the first three viscosities, probably because of the high gas entrainment. The dead zone in the lower corner of the domain is also much smaller. Hence there is a better distribution of the tracer throughout the domain for the highest viscosity, whereas for the lower viscosities the global mixing time is governed by the slow process of the tracer being transported into the lower corner of the domain. This change in the recirculating flow is also confirmed by a change in the shape and motion of the main bubble, as observed in the plots of bubble surface and sphericity. The trend of decreasing surface and increasing sphericity is interrupted at \(\mu _4\).
Liquid density
Surface tension
Summary and Conclusions
The Coupled Level Set—Volume of Fluid model was applied to investigate the hydrodynamics of gas injection with a TopSubmergedLance in a liquid bath. A parametric study on liquid properties and operational parameters was carried out to assess the response of the multiphase system and to show the importance of the viscous and interfacial forces involved; hence to gain knowledge for its hydrodynamic characterization. Various phenomena of the multiphase flow were monitored, such as the gasliquid interphase, liquid splashing, the mixing process in the bath, and the detachment of the bubbles. All these aspects of the flow must be considered to entirely describe the hydrodynamics of a TSL smelter since they all strongly influence the mass and heat transfer in the process, and by that the reaction rates. The results presented in Sections IV–A–1 through IV–A–3 show a strong effect of the liquid viscosity and the surface tension on the nature of the flow. As a consequence, the usage of the Froude number as a unique dimensionless group can not be sufficient to characterize the multiphase flow and scale down a TSL smelting furnace, since viscous and interfacial forces are not taken into account. It was furthermore observed that an increase in viscosity and surface tension does not produce a consistent response when different phenomena are studied: i.e., if the splashing of the liquid is reduced by higher \(\mu \) and \(\sigma \), on the other hand the interphase area escalates with \(\mu \) and diminishes with \(\sigma \). This indicates that a scaling approach applied to scale down phenomenon A may not be appropriate to scale down phenomenon B, even taking into account viscous and interfacial forces. More effort should be made in the development of a thorough dimensional analysis of the TSL hydrodynamics, together with the exploration of new fluids which are easy to handle in labs and whose properties are closer to the smelting slags.
Notes
Acknowledgments
The authors would like to thank the Center for Information Services and High Performance Computing (ZIH) at TU Dresden for the allocation of the computing time. The German Federal Ministry of Education and Research (BMBF) has funded this research within the framework of the Center for Innovation Competence Virtuhcon (Project Number 03Z22FN11). The author is responsible for the content of the publication.
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