INFLUENCE OF PHYSICAL PROPERTIES OF SLAG AND OPERATIONAL PARAMETERS ON SLAG SPLASHING PROCESS IN
AN OXYGEN CONVERTOR
Paula Maria Gomes Cunha Leão1Eliana Ferreira Rodrigues1Carlos Antonio da Silva1Itavahn Alves da Silva1Varadarajan Seshadri2
1Universidade Federal de Ouro Preto, Minas Gerais, Brazil 2 Universidade Federal de Minas Gerais , Minas Gerais, Brazil
Keywords: basic oxygen Furnace; slag splashing, mathematical modeling Abstract
A mathematical model using Fluent 14.0 was implemented in order to describe the flow of Nitrogen and slag under transient and isothermal conditions in the slag splashing process for the improvement of refractory life. The influence of parameters affecting this process and the consequent effects on refractory linings has been investigated applying the model. For a given blow pattern, the influence of parameters such as temperature, density, viscosity and interfacial tension of the fluids involved have been discussed. The results are compared with projection data available in the literature.
Introduction
The wear causes of refractory lining of an oxygen converter result from a combination of thermal, chemical and mechanical phenomena occurring inside the reactor. The thermal effects are linked to temperature fluctuations and thermal shock, while the degradation of the linings can be caused by chemical interactions between the refractory, slag and the gases in the converter.
Those of mechanical origin are associated with erosion due to scrap charging, liquid movement between refractory surface and the metal, oxygen blowing and effect of gas movement at high temperatures in the vicinity of the refractory lining. Through wear profile monitoring technique of the refractory lining by laser beam, it is possible to obtain a map of the lining wear profile in each region of the converter.. The regions where the liquid steel flows out of the convertor after each blow and zone of impact due to scrap charging are the most susceptible to degradation.
With this knowledge, one can establish a suitable repair strategy for the worn out regions to extend the campaign life of the linings of the reactor. Maintenance and repair techniques of refractory lining include coating with slag. This is done through slag splashing or gunning refractory material towards the damaged lining. The slag splashing process is characterized by projecting chemically reconditioned molten slag in the convertor through nitrogen blowing through a lance ,on the hot surface of the convertor lining(1,2) Many factors affect this projection of slag such as converter dimensions, nitrogen blowing rate, height, tilt and shape of nitrogen lance, temperature, composition and volume of slag. The duration of this practice is 1 to 4 minutes and it is possible to maintain the lining for 10,000 converter runs or more. The influence of parameters such as trajectory and size distribution of droplets on the slag splashing process has been evaluated(3). There is an optimum height of lance and optimal nitrogen flow so that the projection rate of slag droplets and the thickness of the slag layer on the refractory lining can be optimized (4).As the critical gas flow for ejection of the droplets is independent of lance height, the main contributing factor for increased generation of slag droplets is likely to be,
Advances in Molten Slags, Fluxes, and Salts: Proceedings of The 10th International Conference on Molten Slags, Fluxes and Salts (MOLTEN16) Edited by: Ramana G. Reddy, Pinakin Chaubal, P. Chris Pistorius, and Uday Pal TMS (The Minerals, Metals & Materials Society), 2016
change in the surface area of the cavity formed in the impact zone of gas and slag ( 5). The generation of drops (Figure 1) by splashing is possible in different ways like generation of individual or discrete drops or swarm of drops characterized by production of several drops of various sizes (6). The increase in the gas blowing velocity or reduction of height of the lance for gas blowing may cause reduction in the amount of ejected drops of slag (7,8). This can be attributed to the increased depth of the cavity generated by the gas jet due to increased dynamic pressure of the gaseous jet. These can also cause oscillation and vorticity of the slag. This work on CFD simulation of slag splashing has the objective of evaluating the influence of physical parameters such as slag density and viscosity of slag on projection in the inside walls of the converter.
Figure 1 - Characteristics of liquid phase interaction with a vertical gas jet (8) Methodology
The motion of slag and gas has been described with the aid of Navier-Stokes equations, the 𝜅 − 𝜖 turbulence model along with the volume fraction formulation -VOF (for tracking the position of the interface between nitrogen and slag). Where there is presence of more than one fluid phase, the VOF formulation is used to express the interactions between the gas and slag. For the incompressible and Newtonian fluid flow the equation of Momentum Conservation can be given as:
𝜌 (𝜕𝑢⃗⃗ 𝜕𝑡+ 𝑢⃗ ∙ ∇𝑢⃗ ) = −∇𝑝 + 𝜇𝑒𝑓𝑓∇2𝑢⃗ + 𝜌𝑔 + 𝐹 (1) where: ρ = fluid density, 𝑢⃗ = velocity vector, t = time, g = gravity, p = pressure, 𝜇𝑒𝑓𝑓= effective viscosity of the fluid and F are the other forces. There is a balance between the inertial (𝐹𝑖), interfacial (𝐹𝛾), and gravitational forces (𝐹𝑔) when the droplet breakaway occurs [1,15],
Fi= 𝐹𝛾 +Fg (2)
The droplet diameter (𝑑) derived from the balance of forces of (2) is given by:
𝑑 =3𝑈8𝑔2(1 − (1 −128 𝛾𝑔3𝜌𝑈4)) (3) where 𝑈 is the magnitude of the jet velocity at the impact point and 𝛾 is the surface tension.The computation involves the 𝜅 − 𝜖 model with the following equations for conservation of turbulent kinetic energy and rate of dissipation of turbulent kinetic energy, respectively:
𝝆𝝏𝑲𝝏𝒕+ 𝝆𝒗𝒋𝝏𝒙𝝏𝑲
𝒋=𝝏𝒙𝝏
𝒋(𝝈𝝁𝒕
𝑲
𝝏𝑲
𝝏𝒙𝒋) + 𝝁𝒕𝝏𝒗𝝏𝒙𝒋
𝒊(𝝏𝒗𝝏𝒙𝒊
𝒋+𝝏𝒗𝝏𝒙𝒋
𝒊) − 𝝆𝜺 (4)
𝝆𝝏𝝐
𝝏𝒕+ 𝝆𝒗𝒋𝝏𝜺
𝝏𝒙𝒋= 𝝏
𝝏𝒙𝒋(𝝁𝒕
𝝈𝜺
𝝏𝜺
𝝏𝒙𝒋) + 𝑪𝟏𝝁𝒕𝜺
𝑲
𝝏𝒗𝒋
𝝏𝒙𝒊(𝝏𝒗𝒊
𝝏𝒙𝒋+𝝏𝒗𝒊
𝝏𝒙𝒊) − 𝑪𝟐𝜺
𝑲𝝆𝜺 (5)
Where: K = kinetic energy of turbulence, ε = the rate of dissipation of kinetic energy of turbulence; 𝒗𝒋 = velocity component; 𝝁𝒕 = turbulent viscosity; 𝒙𝒋 = coordinate distance;
𝑪𝟏 and 𝑪2 = model constants. The effective viscosity is the sum of molecular (𝝁𝒐) and turbulent (𝝁𝒕) viscosities :
𝝁𝒆𝒇𝒇=𝝁𝟎+ 𝝁𝒕 𝑎𝑛𝑑 𝜇𝑡=𝜌𝐶𝜇𝐾2
𝜀 (6)
Where: K = kinetic energy of turbulence, ε = the rate of dissipation kinetic energy of turbulence; 𝑪𝛍= constant; ρ = fluid density. The location of the liquid slag /nitrogen interface is determined by the volume fraction VOF formulation, and the continuity equation for a couple of phases is represented by:
𝜕
𝜕𝑡(𝑟𝛼𝜌𝛼) + ∇ • (rαραUα) = 0 (7) where: r = the fraction by volume; ρ = density; 𝑈 = velocity ; 𝛼 = a given phase, gas or slag.
Also the sum of volume fractions is unitary, ie:
∑ 𝒓𝜶 𝜶= 1 (8)
In order to reduce the computational effort, one ¼ of a three-dimensional isothermal converter was considered. The Navier-Stokes equations, turbulence model equations and VOF model equations were numerically solved using by means of Ansys software – FLUENT. The segregated algorithm (pressure based) was used with the implicit scheme linearization. In order to obtain a solution more accurate the Second-order Upwind scheme was employed in the discretization of the governing equations. PRESTO algorithm was used for the interpolation of the pressure values on the faces of the cells using the equation of motion and PISO algorithm to obtain pressure-velocity coupling. A tetrahedral mesh composed of 627 535 cells was used for this purpose. The maximum processing time for all the simulations was 2 seconds with a timestep of 1x10-5seconds. For this analysis the nitrogen jet speed was taken as 520 m·s−1 which is injected downwards through a one hole nozzle with a diameter of 0.064 m. A lance height of 1m above the slag bath and a molten slag depth of 1 m were assumed. Slag kinematic viscosities were varied as 16, 23, 40, 200 e 400x10-6 m2.s-1 in the computations. The surface tension value amounted to 1.54 N·m−1 . Slag densities of 2500 and 3490 kg·m−3 were considered.
Non slipping conditions were assumed at slag walls interfaces. Boundary conditions for k and ε at the inlet nozzle is calculated from [11]: 𝑘 = 0.01𝑈𝑔𝑎𝑠2 and = 2 𝑘1.5⁄𝐷𝑛 , where Ugas and Dn
are the inlet nominal velocity and the nozzle diameter respectively.
Results and discussion
The results as given by Figures 2 and 3 show erratic behavior in respect of droplets trajectories as suggested by an uneven deposition on the walls. This is probably associated with transient and unstable behavior at the impact zone of the gas jet on the slag. This type of behavior was also observed by other researchers (9,10,11). Figure 2 shows the effect of the density of the slag on the projection. Greater the density of the slag lower is the projection rate. Lower viscosity of the
slag leads to increasing depth of penetration of the gas jet and higher projection (9). However, more fluid slag tends to run down the wall of the converter, resulting in a fine coating layer on the surface of the refractory. The quality of projection (height, number of projected drops and thickness of the coating layer) is strongly affected by the viscosity of the slag. High viscosity values lead to lower projection rate, which would also require higher temperatures and flow rates of nitrogen. So good efficiency of repair requires optimization of composition and temperature of the slag and other parameters affecting the process of slag splashing. From an operational point of view, the covering of the upper side walls of the converter (regions of the trunnions and the upper cone) can be improved by increasing the nitrogen blowing rate and the reduction of the slag density. For the operating conditions investigated, the results obtained show that the slag is unevenly projected (Figure 3) and increasing the viscosity of the slag decreases the projection rate. This behavior is expected , as can be seen in Figure 4. Studies on slag splashing with a physical model have been made(9). Their results show the influence of the blowing pattern (slag lance height, blow rate from the bottom, the top blowing rate), lance nozzle geometry, the degree of filling of the reactor by residual slag, and the physical properties of the slag on slag projection rate.
Figure 2 ¬ - Projection against the wall using a slag of viscosity of 0.058 Nsm-2 and density of a) 3490kg.m3 b) 2500 kg. m3 (left) and using a slag of viscosity of 1 N.sm-2 and density of c) 3490kg.m-3 and d) 2500 kg.m-3 (Right) ; lance to slag distance of 1m, gas velocity of 520m/s;
according to results of CFD simulation.
Figure 3: Fraction of slag covering the wall of the converter in time of 2 seconds in the case of kinematic viscosities of (a) 23x10-6 m2.s-1;(b) 40x10-6 m2.s-1 ; (left) (c) 200x10-6 m2.s-1 and d) 400x10-6 m2.s-1 (Right) ; lance to slag distance of 1m, gas velocity of 520m/s; according to CFD simulation
Fig. 4 - Effect of kinematic viscosity on slag projection rate, for lance height of 140mm, 170mm and 200mm (9)
From the analysis of the experimental results , using physical modeling, (9) the following equation was obtained for the rate of projection of slag A (g / m2s) as a function of lance height h (in mm) and the kinematic viscosity of the slag𝜈 (10-6m2 / s) :
A = - 0.6 - 0.286𝜈 + 1.42h - 0.00371h2 +0.000572𝜈2 -0.000953𝜈ℎ (R2 = 0,82) (7) For a given viscosity of the slag, there is a optimum lance height when the slag projection rate is maximum. Table 1 shows the specific flow rate of slag as a function of the distance to the slag layer and the slag viscosity as per CFD simulation in this work. The flow is greater in the lower region of the converter (slag line) compared with the area of the sleeve and the upper region.
This result is consistent with the results of other researchers (9). According to the present work on CFD simulation of slag splashing, the slag line region receives 66.8% of the projected mass, the sleeve receives 29.2% and the upper cone about 3%. It can be noted also that the increase of the viscosity of the slag decreases the projection rate of the slag line region.
Table 1: Slag mass flow in transverse planes of the converter values kg.m-2.s-1; initial lance to slag distance of 1m; gas velocity of 520 m/s; according to CFD simulation
Distance from slag layer
Slag viscosity 1m 2m
0.1 N.s.m-2 0.0621 kgm-2s-1 0.0008 kgm-2s
1 N.s.m-2 0.0552 kgm-2s-1 0.0008 kgm-2s
The area of the inner surface of the investigated converter is 126,6m2. According to this work, (Figure 5 (a)), the rate of deposition for a slag with viscosity of 23x10-6m2 /s is close to 1.30 m2/s. Thus the time required to coat the refractory lining of the reactor would be 93s (1.55 min.).
To this duration of this process one should also add a fraction of ¼ to ½ as an incubation period (9). The coating time of the converter could be considered greater than 2min. This is consistent with operational practice (1), which ranges from 2 to 4 minutes. The model presented in this work enables also to evaluate the quantitative effects of increasing kinematic viscosities on decreasing the area of the coating, as shown in Figure 5 (b) However others have suggested that decreasing the viscosity of the slag, while facilitating the projection to higher levels inside the reactor,results in the thinning of the coating layer, which is detrimental to the repair of the refractory .
(a) (b)
Figure 5 – (a) Variation of the covering area of the walls of the converter by slag ( for kinematic viscosity of slag equal to 23x10-6 m2/s; initial lance to slag distance of 1m; gas velocity of 520m/s) with time computed from CFD modeling (b) Effect of the viscosity of slag on the coated area fraction; initial lance to slag distance of 1m; fractional area initially covered by slag ~ 0.198; gas velocity of 520m/s .
This behavior has also been observed by other researchers. Accordingly there is need to adjust the viscosity of the slag by adding fluxes or other raw materials(9,10). From physical modeling results it was concluded that only 46.8% of the amount of slag is effectively used for coating the refractory (9). Taking this as a reference, and a 340 ton steel converter with 40 tons of refining slag, about 18.7 tons of this slag would be used for the repair. However, it is also reported that the amount of slag actually used for the purpose is around 14 tons (1). To simplify, assuming that the thickness of the coating is uniform and the area of the refractory lining of the converter 126.6m2, the amount of adhered slag would be about 147.70kg / m2. However the results of this mathematical modeling showed the heterogeneous nature of the projection of slag drops and, consequently, the non-spatial uniformity of the coating. The quality of droplets ejection (number, size) depends on the instability of the cavity formed by the impact the gas jet with the slag (3,9,13). Results for simulation of temperature profile inside the furnace refractory as well as the internal atmosphere as given by CFX are shown in Figure 6. Refractory thermophysical data for this simulation are given on Table 2; a heat flow of 12,000 W/m2 has assumed in the simulations
Table 2: Refractory thermophysical data for thermal profile simulation Property Refractory 1 Refractory 2 Refractory 3 Refractrory 4 Steel casing Lance
k [w.m-1.K-1] 5.2 18.84 12.21 5.2 41.87 5.2
ρ [kg.m-3] 3100 2820 2950 2950 7800 2950
c [J.kg-1.K-1] 1.046 1.046 1.129 1.129 0.487 1.129
Slag coating is given as a combination of droplets ejection and their adhesion to the refractory.
The latter is influenced by the temperature. A wide temperature distribution is apparent and the same is expected from physical properties. It is possible to observe the formation of cavities resulting from the projection of slag, confirming similar conclusions from other authors like Mills et al. (1). The simulated results obtained in the present work are fairly consistent with those provided by other authors, and this also includes data obtained from experimental results. Hence the described procedure is a reliable and efficient tool which can help to obtain better results in the steel industry . Additionally the simulated results can help to clarify the refractory material behavior and provide an insight into the refractory damage process. The likelihood of efficient droplet projection is influenced by dimensionless numbers such as Weber (We) and the moment (Mn). Higher values of these lead to higher rate of projection (1) :
𝑊𝑒 = 𝜌𝑔𝑎𝑠𝑈𝑔𝑎𝑠2
√𝜎 𝑔 𝜌𝑠𝑙𝑎𝑔 M𝑛 =𝜌𝑔𝑎𝑠𝐴𝑜𝑟𝑖𝑓𝑈𝑔𝑎𝑠2
𝜌𝑠𝑙𝑎𝑔 𝑔 ℎ𝑐𝑎𝑣3 (8) Where 𝜌𝑠𝑙𝑎𝑔 , 𝜌𝑔𝑎𝑠, 𝐴𝑜𝑟𝑖𝑓 , 𝑈𝑔𝑎𝑠 , 𝜎 , 𝑔, ℎ𝑐𝑎𝑣 are the specific mass of slag and gas; area of the gas injection orifices; velocity of the gas jet, interfacial tension, acceleration due gravity and depth of the cavity generated by the jet of nitrogen, respectively. The above dimensionless numbers enable to quantify the (negative) effects of increasing viscosity and density of slag. These negative effects can be counterbalanced by adopting a standard nitrogen blowing pattern with optimum height and geometry of the nozzle and gas flow (1,5,9) . With this, one can provide additional moment forces, improving the formation of small dense slag droplets, favoring the coating of the upper regions of the converter. However, as shown by this simulation the quality and uniformity of the coating can be an issue. The thermal profile of the converter is transient and heterogeneous as shown in Figure 6. Slag coating is given as a combination of droplets ejection and their adhesion to the refractory and the latter is influenced by the temperature. The dimensionless numbers (We, Mn) given above have a decisive influence on the generation and projection of drops of slag. That is to say the physical properties of slag (viscosity, surface tension and density), and the rate of solidification of the slag coating are affected by temperature.
Therefore, it is important to further investigate the effects of the thermal profile in the converter on the characteristics of instability of the impact area of the jet of nitrogen and the area covered by slag. This has been planned as a future work. With this the effect of temperature profile in the converter on the projection height and the adhesion rate of drops of slag can be investigated. The impact region of the nitrogen jet has low temperature ( blue and green regions in Figure 6) as nitrogen is blown at normal ambient temperature the gas gets heated up later.
Figure 6. CFD Simulation results
of temperature distribution inside the converter slag during the projection operation (to reduce the computational effort, ¼ of a three-dimensional isothermal converter was considered for simulation)
Conclusions
The efficiency of the slag splashing process requires optimization of blow pattern variables suchas gas flow rate and lance to slag distance as well as slag properties dictated by its composition. However this simulation weighs the importance of physical properties like viscosity, density. The projection rate increases with decreasing viscosity of the slag and with decreasing density.These observations are in agreement with the findings in the actual slag splashing process adopted in the industry. The CFD simulation results would be of help in optimizing the variables mentioned above in the industrlal slag splashing process for repair of refractories. Models such as the one developed in this work are useful to industry since actual data regarding physical properties and operational parameters are mostly unknown. This model stresses the importance of these properties for better efficiency of the slag splashing process.
Acknowledgements
The Scientific program of UFOP, Gorceix Foundation, Fapemig, Capes and CNPQ of Brasil.
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