It is important to understand the physical interaction between top-blown oxygen jet and liquid bath in basic oxygen steelmaking furnaces (BOF). In this study, cold model experiments were carried out to investigate the cavity depth, diameter and the instability at the gas-liquid interface. Images of the cavities were captured by a high-speed video camera to study cavity performances. A modified judging equation of the gas-liquid interface instability was developed by the critical jet flow and the critical jet height at a determined jet diameter. The critical parameters were in good agreement with experimental measurements

Guo, L. X.

Pang, H. X.

Xu, D.

Zheng, B.

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335METALURGIJA 61 (2022) 2, 335-337D. XU, B. ZHENG, L. X. GUO, H. X. PANGA MATHEMATICAL MODEL OF CRITICAL JET HEIGHTS CAUSING DROPLETS SPLASHING IN BOF STEELMAKINGReceived – Primljeno: 2021-08-23Accepted – Prihvaćeno: 2021-11-10Original Scientific Paper – Izvorni znanstveni radD. Xu, B. Zheng Email: 695260997@qq.com Technology Innovation Cen-ter for High Quality Cold Heading Steel of Hebei Province, Hebei Univer-sity of Engineering, Handan, China L. X. Guo, H. X. Pang Email: wangxi950715@sina.com Technology Innovation Center for Wear Resistant Steel Plate of High plasticity and High Toughness of Hebei Province, Hebei Puyang Iron and Steel Corp.Ltd, Handan, ChinaIt is important to understand the physical interaction between top-blown oxygen jet and liquid bath in basic oxy-gen steelmaking furnaces (BOF). In this study, cold model experiments were carried out to investigate the cavity depth, diameter and the instability at the gas-liquid interface. Images of the cavities were captured by a high-speed video camera to study cavity performances. A modified judging equation of the gas-liquid interface instability was developed by the critical jet flow and the critical jet height at a determined jet diameter. The critical parameters were in good agreement with experimental measurements.Keywords: steelmaking, BOF, mathematical model, gas-liquid interface, critical lance heightINTRODUCTIONIn liquid surface impinged behaviors, droplet splash-ing is a fascinating phenomenon attracting wide studies [1-4]. The ejection of the liquid phase by splashing is an important issue in the oxygen steelmaking process. The droplets splatter accompanying the unstable penetrating cavity generates the metal/slag/gas emulsion and causes splashing of metal/slag from the vessel in the BOF [3]. Therefore, the determination of the critical penetration pa-rameters is of great significance for improving the BOF performance. In fact, it should be noted that only a few attempted to establish a model for predicting the critical states. He and Standish [2,5] proposed the “nominal We-ber number”, NNWe, as similarity criterion for droplet gen-eration rate through top gas blowing. Deo et al. [6] further developed the Weber number into a correlation for pre-dicting metal droplet generation in oxygen steelmaking. Moreover, Deo et al. reported that the onset of droplet generation in BOF steelmaking occurs at a value of NNWe equals ten. However, the effect of the Froude number (Fr) on the splashing process is ignored during the determina-tion of the dimensionless criterion number. This may lead to some deviation in the actual blowing process.The aim of present work is to evaluate the relation-ship between cavity shape and operating parameters. Critical jet heights causing droplets splashing were studied for different penetrating conditions, which were further expressed by a modified formula. ISSN 0543-5846METABK 61(2) 335-337 (2022)UDC / UDK 669.18: 669.184: 51-62.001.57: 66.069.82 = 111EXPERIMENTAL METHODSThe water model experiment is carried out using the experimental device shown in Figure 1. In order to elimi-nate the refraction effect and accurately observe the cav-ity shape, a cylindrical vessel with an inner diameter (D) of 400 mm and a height of 500 mm was set inside the square vessel which has a side length of 500 mm. The depth of the water bath (h) was maintained at 50 mm, 70 mm and 100 mm respectively. Five different single-hole nozzles were employed. The internal diameter (de) and the corresponding number were listed in Figure 2.Figure 1 Schematic of experimental setupFigure 2 Nozzles and cavity shape336  METALURGIJA 61 (2022) 2, 335-337D. XU et al.: A MATHEMATICAL MODEL OF CRITICAL JET HEIGHTS CAUSING DROPLETS SPLASHING IN BOF...Experiments were carried out at the temperature of 20 C° and the environment pressure of 101,3 kPa. A rotameter with a range of 2,5 m3/h for air was used to regulate the flow. To record the pressure of the gas, a pressure gauge was connected just before the jet. Com-pressed air was used for water model experiments and a surge tank with an effective volume of 0,3 m3 was used to establish a stable pressure of the system.The nozzles were positioned at different heights above the surface of the liquid ranging between 30 - 130 mm. The jet height (H) vertically from the nozzle to the liquid level of the container was adjusted by a lifting platform with an accuracy of 1 mm. The gas jet momen-tum would create droplets and the violent swing of the cavity at higher gas flow rates. Thus, the characteristic behaviors were observed in the stable and unstable states of gas-liquid interface by a high-speed video camera (EOS 1D X Mark II) In order to record the cav-ity size, a graduated wire was fixed horizontally at the gas–liquid interface. The cavity size obtained by repro-ducing six times the same experiment. An example of the observed cavity shape was illustrated in Figure 2.RESULTS AND DISCUSSIONCavity size affected by penetrating parametersObviously, the cavity size was determined by the penetrating parameters. Various sets of penetrating pa-rameters can be found to generate in equable cavity size. a correlation Thus, giving between the cavity size and all penetrating parameters is significant to guide jet controls in industrial applications. Figure 3 presents the penetration depth versus the jet height at different gas flow rate with different nozzles. It was found that the cavity depth nearly linearly increases by raising the jet flow rate with a same jet height. The above phenome-non can be explained from the perspective of energy balance, i.e., greater flow rate provides more jet energy, thus pushing more heavy liquid away to create a deeper cavity. Comparisons of Figure 3(a) - (d) seem to suggest that smaller nozzle diameter creates deeper cavity under the same operating parameters. It can also be seen that an increasing jet height decreases the penetration depth at a given gas flow rate.Besides, the cavity diameter versus the jet height at different gas flow rate with different nozzle diameter was shown in Figure 4. Similar as the cavity depth, the diam-eter of cavity also exhibits linear growth by raising the jet flow rate with a same jet height. However, the influence of jet height on the cavity diameter is little under the same nozzle diameter and jet flow rate. Identical conclu-sions were obtained in studies of Cheslak [7].Modified instability criterion modelCritical cavities size were obtained under different jet height H and different jet diameters. It was clarified that the critical jet depth of the cavity is about 15 mm under various penetrating parameters. The behavior is in agreement with previous findings of Chatterjee and Bradshaw[8]. They determined the critical cavity depth to create droplets are 1,54 cm.Banks and Cheslak served as the pioneers have launched comprehensive researches on the cavity size. The model suggested by Banks is accurate for the pre-diction of the cavity depth under critical conditions. Combined equation (2) and n0 = 15 mm in critical state, equation (1) can now be expressed as equation (3).  (1)  (2)  (3)Figure 3  Experimental results of the penetration depths as a function of the flow rate at different jet heights337D. XU et al.: A MATHEMATICAL MODEL OF CRITICAL JET HEIGHTS CAUSING DROPLETS SPLASHING IN BOF...METALURGIJA 61 (2022) 2, 335-337For value of constant K = 7,9, an equation for deter-mining the critical jet heights of different nozzles was given.  (4)All of the penetration depths under different jet di-ameters were plotted against the corresponding jet flow rates. The generalized correlation of equation (4) was also plotted in the same Figure 5. The modified equa-tion (4) compares with the present experimental results. Calculation result of equation (4) shows well consistent with the present experimental results. Therefore, the equation presents a valuable relationship between Q Figure  5 Comparison of equation 2(K = 7,9) with experimental resultsand H, which not only provides jet control for industrial applications, but also reveals the mapping relationship between the jet height and instability in science. It is noteworthy that the results are all about the in-teraction of single gas jet with the liquid bath. In indus-try, the oxygen lance is with a multi-nozzle structure. Therefore, it is necessary to further verify the cavity depth prediction model of porous oxygen lance. CONCLUSIONSThe size created by the impinging jet was character-ized under different penetrating conditions, including dif-ferent nozzle diameters, bath depths, gas flow rates and jet heights. Critical jet heights causing cavity stability transition judged by the phenomenon of droplet splatter were studied for various penetrating conditions. An opti-mized equation for determining the critical jet heights of different nozzles was proposed. The experimental results showed good agreement with the equation. The investi-gation of the characteristic size of the cavity and the in-stability behavior in this paper can provide useful criteria for the jet controls in actual industry applications.REFERENCES[1] Q. L. He, N. Stand ish, A model study of droplet generation in the BOF steelmaking, Isij International 30 (2007) 4, 305-309.[2] Q. Li, M. Li, S. Kuang, Z. Zou, Numerical simulation of the interaction between supersonic oxygen jets and molten slag–metal bath in steelmaking BOF process, Metallurgi-cal and Materials Transactions B 46 (2015) 3, 1494-1509.[3] M. J. Luomala, T. M. J. Fabritius, E. O. Virtanen, T. P. Sii-vola, Physical model study of selective slag splashing in the BOF, Isij International 42 (2002) 3, 1219-1224.[4] K. Myrillas, A. Gosset, Technique for delaying splashing in jet wiping process, Chemical Engineering & Processing Process Intensification 50 (2011) 5-6, 466-470.[5] N. Standish, Q. L. He, Drop generation due to an impin-ging jet and the effect of bottom blowing in the steelma-king vessel, Isij International 29 (2007) 6, 455-461.[6] B. Deo, A. Overbosch, B. Snoeijer, D. Das, Control of slag formation, foaming, slopping, and chaos in BOF, Transac-tions of the Indian Institute of Metals 66 (2013) 5-6, 543-554.[7] F. R. Cheslak, J. A. Nicholls, M. Sichel, Cavities formed on liquid surfaces by impinging gaseous jets, Journal of Fluid Mechanics 36 (1966) 1, 55-63.[8] A. Chatterjee, A. V. Bradshaw, The influence of gas phase resistance on mass transfer to a liquid metal, Metallurgical Transactions 4 (1973) 5, 1359-1364.Note:  Hong Xuan Pang is the responsible translator and the correspond-ing author, Handan, Hebei, China.Figure 4  Experimental results of the cavity diameter as a function of the flow rate at different jet height

A mathematical model of critical jet heights causing droplets splashing in BOF steelmaking

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