151
Two-dimensional Physical and CFD Modelling of Large Gas Bubble Behaviour in Bath Smelting Furnaces Yuhua Pan1 and David Langberg 2
1CSIRO
Process Science and Engineering Box 312, Clayton South, VIC 3169, Australia E-mail:
[email protected] 2Formerly CSIRO Process Science and Engineering Received: 9 March 2010, Accepted: 23 July 2010 Abstract The behaviour of lar ge gas bubbles in a liquid bath and the mechanisms of splash generation due to gas bubble rupture in high-intensity bath smelting furnaces were investigated by means of physical and mathematical (CFD) modelling techniques. In the physical modelling work, a two-dimensional Perspex model of the pilot plant furnace at CSIRO Process Science and Engineering was established in the laboratory . An aqueous glycerol solution was used to simulate liquid slag. Air was injected via a submerged lance into the liquid bath and the bubble behaviour and the resultant splashing phenomena were observed and recorded with a high-speed video camera. In the mathematical modelling work, a two-dimensional CFD model was developed to simulate the free surface flows due to motion and deformation of lar ge gas bubbles in the liquid bath and rupture of the bubbles at the bath free surface. It was concluded from these modelling investigations that the splashes generated in high-intensity bath smelting furnaces are mainly caused by the rupture of fast rising large gas bubbles. The acceleration of the bubbles into the preceding bubbles and the rupture of the coalescent bubbles at the bath surface contribute significantly to splash generation.
1. INTRODUCTION Bath smelting reactors such as the Sirosmelt, Ausmelt and Isasmelt furnaces are examples of modern, high-intensity pyrometallur gical reactors characterised by high-productivity and good feedstock flexibility. Submerged injection of gases at high flowrates produces rapid mixing in the bath ensuring fast chemical reactions and bath homogenisation. However , the strong dynamic interactions between the injected gas and the liquid bath lead to intensive splashing. This can be a problem if the splashes become so heavy that they form accretions on the furnace wall and roof and in the gas offtake duct. This can cause unscheduled shutdowns which adversely affect productivity. In addition, the splashes can cause safety problems. Therefore, in order to find ef fective means to control the splash intensity in Sirosmelt and other bath smelting furnaces, the present work was carried out to investigate the behaviour of lar ge gas bubbles in slag baths and the mechanisms of splash generation in such furnaces by using both physical and mathematical (CFD) modelling techniques. Splashing phenomena due to submerged injection of gas into a liquid bath has been extensively studied. Past investigations of such phenomena have been well reviewed by Liow [1], Cullinan [2] and Guerra [3]. Among the past studies, the splashes caused by gas bubble rupture received broad attention and were investigated more extensively . However, as pointed out by Liow et al. [4], the majority of the previous work was made only on small bubbles (less than 10 mm in diameter or equivalent). In Sirosmelt furnaces, for example, the size of the bubbles formed in the liquid bath can be expected to be very lar ge (above 50 mm in diameter). This situation requires new interpretations of the mechanisms of splash generation in such furnaces. Therefore, since mid1980s, extensive physical modelling studies on the splash generation in Sirosmelt furnaces were Volume 2 · Number 3 · 2010
152
Two-dimensional Physical and CFD Modelling of Large Gas Bubble Behaviour in Bath Smelting Furnaces carried out at The University of Melbourne and at CSIRO Process Science and Engineering (formerly CSIRO Minerals) [4-7]. Besides the physical modelling investigations, a number of mathematical modelling studies on the fluid flow phenomena in Sirosmelt furnaces were also carried out by means of CFD simulation techniques [8-10]. In addition, high-temperature experiments were conducted on a pilot-scale Sirosmelt furnace in the laboratory of CSIRO Process Science and Engineering. In these experiments, natural gas and air were injected via a swirled lance into a 300 kg slag bath heated to a temperature around 1300 °C. Two types of slags (fayalite slag and calcium ferrite slag) were tested and the slag splashes were sampled from the top of the furnace by using a plate sampler . Based on the measured sample weight and the plate area, the splash intensity in terms of splash flux (kg/m 2⋅s) was calculated. In this work, influences of a number of factors such as lance injection gas flowrate, lance submer gence depth, lance design, sampling position and furnace temperature on the splash intensity were investigated. The results of this high-temperature sampling and measurement of splash intensity were reported elsewhere [1 1]. Nevertheless, the underlying mechanisms of such influences still remain unanswered but the observations from the top of the furnace pointed to the behaviour and rupture of large gas bubbles at the slag bath free surface. However, the published research results reveal that the behaviour of lar ge gas bubbles at the liquid bath free surface and the mechanisms of resultant splash generation in bath smelting furnaces are yet to be fully understood and more relevant experimental data are necessary to verify the CFD model simulations. Therefore, the major objective of this work is to apply both physical and CFD modelling techniques to investigate the lar ge gas bubble behaviour and the mechanisms of splash generation in bath smelting furnaces. 2. PHYSICAL MODELLING In order to investigate two-phase flows and resultant splashing phenomena occurring in Sirosmelttype bath smelting furnaces by using physical modelling techniques, we first established a fullscale three-dimensional (3D) cylindrical Perspex model of the 300 kg pilot Sirosmelt furnace mentioned earlier and measured the splash flux by sampling the splashes with a plate sampler . Water and 91.5% (wt./wt.) aqueous glycerol solution (aqueous glycerol for short) were respectively used as the modelling media in the physical model to simulate liquid slag in the pilot Sirosmelt furnace. The selection of the model size identical to that of the furnace was to simulate the splashing phenomena inside the furnace and to directly compare the splash intensities between the model and the furnace. The results of this physical modelling and measurement of the splash intensity were also reported in Ref. [1 1]. Figure 1 and 2 schematically illustrate, respectively , the prototype 300 kg pilot Sirosmelt furnace and its full-scale 3D physical model. The physical model was built based on the modified Froude number similarity, which is defined as below: Frm′ = Frp′
u g2 ρg u g2 ρg or = gL ρl m gL ρl p
(1)
where, Fr ’ is modified Froude number; u is gas velocity at the exit of the injection lance; ρ is density; g is gravitational acceleration; L is characteristic length; and subscripts g, l, m, p stand for gas, liquid, model and prototype furnace, respectively . Table 1 gives the dimensions of the model and the modelling parameters determined by using eqn. (1). Table 2 lists the material properties used in the present physical and CFD modelling work. On the 3D physical model shown in Figure 2, we mainly conducted the following two sets of experiments: • •
Splash measurement by using a plate sampler; and, Splash visualization and recording by using a video camera.
Journal of Computational Multiphase Flows
Yuhua Pan and David Langberg
153
Figure 1. Schematic diagram of the CSIRO 300 kg pilot Sirosmelt furnace
Figure 2. Schematic diagram of a fullscale three-dimensional cylindrical physical model of the CSIRO 300 kg pilot Sirosmelt furnace
Table 1. Parameters for a full-scale 3D physical model of 300 kg pilot Sirosmelt furnace based on modified Froude number similarity criterion Parameter
Prototype furnace
Modified Froude number (Fr ’) Fluid media Temperature (˚C) Bath diameter (m) Bath height (m) Lance diameter (m) Lance submergence depth (m) Lance flowrate (m 3/h)
0.304 0.872 Slag Gas 1300 1300 0.3 0.3 0.03 0.15 300 520
Physical model 0.304 0.872 Aq. glycerol Air 20 20 0.3 0.3 0.03 0.15 80 140
Table 2. Material properties used in the physical and CFD models Material Aqueous glycerol at 20 °C [14] Water at 20 °C [15] Air at 20 °C [16] Liquid fayalite slag at 1300 °C [17]
Volume 2 · Number 3 · 2010
Density (kg/m3)
Dynamic viscosity (Pa⋅⋅s)
1240 998 1.205 3650
0.35 0.001 1.82 × 10-5 0.25
154
Two-dimensional Physical and CFD Modelling of Large Gas Bubble Behaviour in Bath Smelting Furnaces In the first set of experiments, as already mentioned above, the splash intensity was measured by sampling the splashes with a plate sampler. In the second set of experiments, an ordinary video camera was used to observe fluid flow and splashing phenomena inside the model during air injection. The observations were made through the side and the top of the model. However, during the experiments it was found that, when air was injected into the aqueous glycerol bath, the transparency of the model became very poor . This was because emulsification of the liquid bath occurred due to gas injection and the emulsion was opaque. Consequently , it was very hard to clearly observe the splashing phenomena from the sidewall of the 3D model. Therefore, on the 3D model, only observations from the top of the model, where an opening is available for monitoring the bath free surface and the space above the bath, were made by using the video camera. For the above-mentioned reasons, two-dimensional (2D) physical models were specially set up in the same laboratory to observe, from the wide sidewall of the model, the interactions between the air bubbles and the liquid bath, as schematically illustrated in Figures 3 and 4. On the 2D model shown in Figure 3, experiments were carried out to observe the air bubble motion and rupture as they cross the liquid bath surface, by using a high-speed video camera. The lance injection air flowrate was scaled down from that for the 3D model (Figure 2) according to liquid bath volume difference. The flowrate was calculated to be ranging from 18 m 3/h to 30 m3/h. In the experiments, however , air was injected into an aqueous glycerol or water bath held in the model at different flowrates with an extended flowrate range from 2 to 60 m 3/h. The height of the liquid bath was 30 cm and the lance immersion depth was 15 cm measured from the quiescent bath free surface (cf., Figure 3).
Figure 3. Schematic diagram of a twodimensional physical model set-up of the CSIRO pilot Sirosmelt furnace
Figure 4. Schematic diagram of twodimensional physical model set-up for liquid film thickness measurement
Another set of the experiments was performed on the physical model set-up shown by Figure 4 to measure the liquid film thickness above a solid object approaching the liquid surface for validation of the CFD model developed in the present work. In this model set-up, as compared with Figure 3, the injection lance was replaced with a hanging solid cylindrical object. This object was immersed into the liquid bath and then lifted out of the bath at dif ferent velocities, simulating flotation of a “rigid bubble” in the liquid bath. In each experiment the object was lifted manually at dif ferent velocities out of the liquid bath by using a thread mounted onto the object. The experiments were performed on both an aqueous glycerol bath and a water bath. As the object rose across the bath surface, a liquid film remaining on the leading cylindrical surface of the object was recorded by using a high-speed video camera. The thickness of this liquid film was measured from the recorded video images and then, as a means of model validation, compared with the CFD model predictions.
Journal of Computational Multiphase Flows
Yuhua Pan and David Langberg
155
3. COMPUTATIONAL FLUID DYNAMICS MODELLING 3.1 Assumptions In the present modelling work, one major assumption was that, since we only focused on gas bubbles with fairly large sizes (diameter ≥ 80 mm), the effect of liquid surface tension force would be very small compared to fluid inertia and gravity and thus neglected. Another assumption was that the injection lance and bubble growth at its tip were neglected. Thus, it was assumed that a gas bubble with a certain initial size can suddenly appear in the liquid bath. In addition, as implied by the physical model shown in Figure 3, the developed CFD model is two-dimensional, which means that the gas bubble generated by the physical model and thus simulated by the CFD model is cylindrical in shape. Therefore, we refer the diameter of the cylindrical bubble to as the size of the bubble. 3.2 Governing Equations The free surface flow phenomena due to motion of lar ge gas bubbles in a liquid bath in the abovementioned physical model were mathematically simulated by using a commercial CFD modelling package PHOENICS-3.5 [12] and a transient two-dimensional numerical model was developed. In this modelling work, an approach called the Scalar -Equation-Method (SEM) in-built with PHOENICS-3.5 was applied to simulate the flow phenomena of interest. In this mathematical approach, a set of governing partial differential equations are solved, which, in a generalised vector notation form, reads ∂ ( ρφ ) + ∇ ⋅ ( ρφ u ) = ∇ ⋅ ( µl + µt ) ∇φ + Sφ ∂t
(2)
where, φ is a general variable standing for unity (continuity equation), velocity components (momentum equations), turbulence kinetic ener gy and dissipation rate of the turbulence kinetic energy (standard k-ε turbulence equations); ρ is density; u is velocity vector; t is time; µl is laminar (dynamic) viscosity; µt is turbulent viscosity; and S φ is source term associated with φ. In SEM simulation of free surface flows, the following equation is derived from eqn (2), by setting φ equal to a dimensionless scalar variable α and neglecting the diffusion and source terms, for tracking the location of the gas-liquid interface (i.e., free surface): ∂α + ∇ ⋅ (α u ) = 0 ∂t
(3)
where α, having a numerical range between 0 and 1, is used as a fluid marker . By convention, α = 0 refers to the lighter fluid (gas); α = 1 to the heavier fluid (liquid); and 0
