A Numerical Test Bench for Supersonic Oxygen Nozzles and Its Application to the BOF Process

Tathagata Bhattacharya1, Ling Zhan2, Bernard Chukwulebe1

1ArcelorMittal Global R&D – East Chicago 3001 E Columbus Drive, East Chicago, IN, USA 46312

Phone: (219) 399 6453 Email:  tathagata.bhattacharya@arcelormittal.com

2Department of Mechanical Engineering, Carnegie Mellon University

5000 Forbes Avenue, Pittsburgh, PA, USA 15213 Phone: (412) 230-7622

Email: lzhan@andrew.cmu.edu

Keywords: CFD, Supersonic Oxygen Nozzle, BOF, Top Blowing Process, Post-combustion ports

INTRODUCTION The ever-increasing demand for more productivity and better refining in BOF steelmaking is the main driver for improved supersonic lance designs so that a higher rate of oxygen can be blown into the converter. In this work, various computational fluid dynamic (CFD) models are developed to investigate the behavior of supersonic nozzles. These models, which also include the characteristics to design a minimum-length supersonic nozzle, could be used to characterize and optimize supersonic nozzle designs and examine the effect of nozzle geometries on jet behavior. Finally, an aerodynamic model for the BOF top blowing process is developed to examine the effects of the main ports and the post-combustion ports on the erosion and buildup behavior of the furnace inner profile.

NUMERICAL ANALYSIS SETUP AND VALIDATION

Fluid flow simulations of supersonic oxygen nozzles are performed in the commercial computational fluid dynamics software ANSYS Fluent, which is based on control volume method. Supersonic oxygen nozzles jet flow is assumed to be two dimensional, axisymmetric, compressible and steady state. The shear-stress transport (SST) k-ω turbulence model, which is widely used in aerodynamic applications, is used in the simulation. Compressibility effect is taken into account.

Nozzle geometry and boundary conditions are specified to meet the experimental study [e.g., 1], in which the characteristics of supersonic oxygen jet at three outlet temperatures -- 285K, 772K, and 1002K are studied. A conventional convergent divergent nozzle with throat diameter 0.933 inch and exit diameter 1.087 inches is used for this simulation. As shown in Figure 1, the mesh used for this CFD simulation is an unstructured quadrilateral dominant mesh, which consists of around 60000 elements (99.7% quadrilaterals

and 0.3% triangles). The exit diameter of the nozzle is defined as de. A large quadrilateral zone is added ahead the nozzle inlet as reservoir. After testing different outflow sizes, the outflow is chosen to be 70 de downstream from the nozzle exit and 15 de normal to nozzle centerline in order to eliminate the effects of the wall on jet flow. Mesh density is very high near nozzle and jet region. On the nozzle wall, inflation layers are created in order to accurately capture the large velocity gradient. The following boundary conditions are defined. Pressure inlet boundary condition, with pressure of 5.026 atm and temperature of 285 K, is used at inlet. At outlet, boundary condition is set as pressure outlet with pressure of 1 atm and temperature of 285 K, 772K, and 1002K. Axis is set as symmetry boundary condition.

Figure 1. Mesh and boundary conditions

Mesh adaption (solution-adaptive mesh refinement) is performed to efficiently reduce the numerical error and obtain mesh independent solution [e.g., 2]. Since there is a pressure discontinuity across shock, scaled pressure gradient is used as mesh adaption criterion in order to more accurately capture the shock wave. After several mesh adaptions, element number increased from around 60000 to around 100000. Figure 2 shows the original mesh and the mesh after adaptions. ANSYS FLUENT is run with steady state pressure based coupled solver (PBCS). Coupled scheme is applied for Pressure-Velocity Coupling. Pseudo transient is set up to improve the stability and convergence behavior of PBCS. To achieve the best accuracy, the double precision solver is applied and the second-order scheme is used to discretize the governing equations.

Figure 2．(a) Original mesh near nozzle, (b) mesh after adaptions

Three simulations with increasing outlet temperatures are studied. Figure 3 (a) illustrates the velocity distribution at nozzle downstream. At high outlet temperature the high velocity portion of jet increase. Axial velocity distribution from CFD simulation matches with experimental data very well at 285K. At higher temperature, CFD simulation under-predicts the axial velocity. Figure 3 (b) shows the temperature distribution at nozzle downstream. After having some oscillations due to shock waves near the nozzle exit, the temperature continues increasing to the exit temperature. The temperature distributions on jet axis have a very good agreement between simulation and experimental results at all the three outlet temperatures. Because this simulation model is used to compare the effects of different nozzle designs on jet flow characteristics, the inconsistence of the axial velocity distribution between simulation and experimental results is acceptable.

Figure 3. Comparison of simulation and experimental data at the nozzle downstream The numerical results are also validated with the isentropic theory for the convergent divergent nozzle [e.g., 3]. The isentropic theory assumes the flow to be uniform across cross section, inviscid, steady, no friction and heat loss with wall. As shown in equation (1), the Mach number is proved to be exclusively governed by the nozzle cross-section area ratio A/A* and   ratio of specific heatsγ, in which A* stands for cross-section area at nozzle throat andγequals to 1.4 for oxygen.

𝐴𝐴∗

!

=1𝑀!

2𝛾 + 1

1 +𝛾 − 12

𝑀!(!!!) (!!!)

                                                                                                                                     (1)

The nozzle in Figure 4 (a) is tested and a set of boundary conditions as shown in Figure 4 (b), which comes from the operating conditions of this nozzle, is specified. Figure 5 shows the axial Mach inside a conventional convergent divergent nozzle, where x/de is set as the center of the throat part. Simulation results fits well with the results from isentropic theory.

         

Figure 4. (a) A conventional convergent divergent nozzle in BOF lance, (b) boundary conditions

 

 Figure 5 Axial Mach inside a conventional convergent divergent nozzle

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  BOF LANCE NOZZLE DESIGN

A supersonic jet flow can only be produced by a convergent divergent nozzle. A supersonic core is defined as the jet flow region with Mach number larger than one. In BOF, an oxygen jet with longer supersonic core will increase the height of penetration, and consequently improve the mixing intensity. Downstream, shock waves (diamond pattern) reduce the supersonic core length. Hence, in this study, a good supersonic lance nozzle for basic oxygen steelmaking process is assumed to have long supersonic core and few shock waves. In order to optimize the design of a conventional convergent-divergent nozzle (Figure 4), a parametric study of nozzle convergent, throat and divergent section variations is performed. In the following simulation for different nozzle designs, boundary conditions are kept the same. For a supersonic convergent divergent nozzle, the convergent part functions to accelerate the flow to be sonic. Nozzles with convergent length of 0.5 inch, 1 inch, 2 inch, 3 inch and 4 inch are tested with the CFD simulation model established previously. All other conditions are kept the same. Figure 6 shows convergent length has little effect on supersonic core length.

 Figure 6. (a) Different convergent length, (b) axial Mach at jet flow of nozzles with different convergent length

  Throat part is designed to make the flow uniform and parallel before flow entering the divergent part. Throat length x with values of 0 inch, 0.5 inch, and 1 inch are tested. All other conditions are kept the same. Figure 7 shows throat length has little effect on the supersonic core length.

 

 Figure 7. (a) Different throat length, (b) axial Mach at jet flow of nozzles with different throat length

Divergent part, which further accelerates the sonic flow from throat to be supersonic, is the most important part of a convergent divergent nozzle. Using the method of characteristics to design a minimum length nozzle [e.g., 4], divergent wall is designed to cancel all the expansion waves, and hence reduce the shock waves and increase the supersonic core length of the jet flow. In this method, the flow is assumed to be 2-D steady, supersonic, inviscid, and irrotational. It’s also assumed that flow is uniform and parallel at nozzle throat and exit.

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2.984   12.984   22.984   32.984   42.984   52.984   62.984  

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 Figure 8. Inputs for the method of characteristics

 Following the method of characteristics, different flow conditions at nozzle throat and nozzle ambient will lead to different divergent nozzle profile. In this study, throat and ambient conditions are calculated from CFD simulation of a conventional convergent divergent nozzle as shown in Figure 8 and Figure 1. With the calculated throat and ambient condition as inputs for the method of characteristics, a new divergent part (red zone) is designed. CFD simulations with the same boundary conditions are set up to compare the jet flow characteristics of these two designs. As shown in Figure 9, divergent part of nozzle designed by the method of characteristics significantly increases the supersonic core length by 8%, and its axial Mach number is less oscillating than conventional nozzle design, which means it has less shock waves. Mass flow rates calculated from simulation are the same for these two designs.

 Figure 9. Mach number of a conventional convergent divergent nozzle and a nozzle redesigned by the method of characteristics

AN AERODYNAMIC MODEL FOR BOF TOP BLOWING PROCESS

During the BOF top blowing process, supersonic oxygen jets imping onto the slag-melt interface and form a depression on the liquid surface. The depression can be identified as three modes: dimpling, splashing and penetrating [e.g., 5]. The depression not only drives the bath mixing, but also changes the furnace inner profile and the lance outer profile. In this study an aerodynamic fluid flow model is developed to examine the effects of the main ports and the post-combustion ports on the erosion and buildup behavior during the top blowing process. The geometry for the whole BOF is shown as Figure 10. In order to reduce the computational cost, the bath top surface is assumed to be a fixed wall with high temperature, and only one phase fluid flow model need to be set up. The main ports consist of 4 convergent-divergent supersonic nozzles, while post combustion ports consist of 12 cylinder-shape sonic nozzles. Due to geometrical

symmetry, a 45°slice of the whole BOF is taken to be meshed and computed.

 

Figure 10. Geometry of a Basic Oxygen Furnace containing a lance with four main ports and twelve post combustion ports The mesh and boundaries are shown in Figure 11 (a). Pressure inlet boundary condition is defined at lance inlet, and pressure outlet is used at converter top opening. All wall boundaries are set as zero heat flux. This unstructured mesh consists of around 7 million elements. High-density mesh is defined near the nozzle region. Inflation layers along nozzle wall and slag top surface are generated to capture high gradient velocity.

   

Figure 11. (a) Mesh and boundary conditions, (b) Mach contour of post combustion, (c) mergence of post combustion jets The aerodynamic fluid flow in the top blowing process is considered as three dimensional, compressible, supersonic and steady state

flow. Though the prediction results of k-ε turbulence model is deviated by the anisotropic turbulence feature of the multiple jets, this model is used in this simulation for its reasonable computational cost [e.g., 6]. The simulation uses realizable k-ε turbulence model with standard wall function. Density Based Solver (DBCS) is set up to solve the governing equations. Convective flux type is chosen as Advection Upstream Splitting Method (AUSM). The governing equations were discretized using the first-order scheme in order to reduce the computational cost. In Figure 11 (b), the post combustion simulation result is observed to be a highly under-expanded jet with a ratio of exit pressure P1 and ambient pressure PC of 4.72. This high ratio causes two Mach disks, and leads to the fast decay of the supersonic core. Attracted by the main ports jets, post combustion jets deflected from nozzle axis to lance wall. As shown in Figure 11 (c), post combustion jets merge together after certain distance, and form a high-speed annular oxygen flow, which can protect the lance from splashing slag.

               Figure 12. (a) Mach contour of main ports combustion, (b) main port jet deflection from nozzle axis

  Figure12 (a) shows the main port has a nozzle exit pressure of 0.96 atm and a ambient pressure of 0.99 atm, which means main ports is slightly over expanded. As long as the nozzle exit pressure is not lower than 40% of the ambient pressure, over expansion will merely reduce nozzle efficiency and will not cause flow separation and damage the nozzle [e.g., 7]. Besides, phenomenon of multiple jets coherence is also observed. Figure 12 (b) shows the deflection of main port jet from nozzle axis. When x/de is large than 15, due to the effect from the bath top surface jet deflection rate from nozzle axis becomes smaller. Lance jet flow will effect the erossion and build up of the furnace. Figure 14 shows the possible skulling build up area with low tenperature and wall shear stress is near the mouth of the furnace. Besides, the possible erosion area with hight wall shear stress and temperature is observed at the bottom of the furnace.

CONCLUSIONS Conclusions

• Designs from experience can not significantly improve jet flow. • Convergent and throat part of linear nozzle have little effect on the supersonic core length. • Using the method of characteristics to design the divergent part can significantly improve supersonic core length.

• Post combustion jets are attracted by main port jet flow (jet coalescence) and merge together after certain distance.

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• Main port nozzle jet flows also attract each other (jet coherency). Future Work

• Different lance design parameters may be tested. • Add thermal radiation to enhance current model. • Using VOF multiphase model to study the effects of jet on bath.

 Figure 13. Simulation results of the top blowing process (a) pressure, (b) temperature, (c) density, (e) Mach, (d) streamline

 

 Figure 14. (a) Wall temperature, (b) wall shear stress, (c) velocity vector field above bath top surface

ACKNOWLEDGEMENTS

The authors would like to thank Hoyong Hwang (ArcelorMittal), Jason Ankarlo (ArcelorMittal).

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