Influence of Ambient and Oxygen Temperatures on Fluid Flow Characteristics Considering Swirl-type Supersonic Oxygen Jets

Abstract

In vanadium extraction converter steelmaking, the swirl-type oxygen lance has been applied to improve the dynamic condition of the molten bath reaction to achieve a higher oxidation rate of vanadium and better vanadium slag quality, because the swirl-type jet can generate not only axial and radial forces but also tangential ones. Recently, the swirl-type supersonic jet with preheated oxygen was proposed to further enhance the agitation ability of the oxygen jet on the molten bath. In this study, the effects of the ambient temperature and oxygen temperature on the swirl-type supersonic jet behavior were analyzed to achieve better formulation and optimization of the process parameters. The flow characteristics of swirl-type oxygen jets were simulated by computational fluid dynamics software at 300 K, and 1700 K ambient and 300 K, 450 K and 600 K oxygen temperature, and partial results were validated against data from a preheating jet experiment. An analysis of the results shows that the centerline jet velocity was increased by preheated oxygen, and at higher ambient temperature, a longer core length was formed and the velocity fluctuation was aggravated. The influence of the preheating temperature on the core length was more evident at lower ambient temperature. From a dynamic perspective, the molecular motion was improved and with respect to energy, the internal energy of the oxygen jets could be preserved at higher ambient temperature.

1. Introduction

In modern basic oxygen furnace (BOF) steelmaking, supersonic oxygen jets are widely used for their ability to control the molten bath stirring, metallurgical reaction kinetics, and foaming slag formation by exchanging the balance of momentum, mass and heat between the molten slag and steel.^1,2,3,4) The top-blown oxygen jet exerts a significant influence on the high reactor efficiency and stable process operation in BOF, with its abilities of sufficient oxygen supplementation and powerful impingement impact. Particularly in vanadium extraction converter steelmaking, an optional oxidation process of vanadium and carbon to improve the comprehensive utilization of complex ore, the impact and stirring effect of the top-blown oxygen jet is essential just because the temperature of molten bath is low and carbon-oxygen reaction is restrained by the thermodynamic condition of the vanadium extraction reaction.^5,6) Therefore, the swirl-type oxygen lance was applied in the vanadium extraction converter to improve the dynamic condition of the molten bath reaction to achieve a higher oxidation rate of vanadium and better vanadium slag quality.⁷⁾

Figure 1 shows a conventional top-blown oxygen lance and the swirl-type oxygen lance with four holes from Li.⁸⁾ In contrast to the conventional top-blown oxygen lance, the swirl-type oxygen lance can generate airflow at not only the axial and radial directions but also tangentially, which would help to improve the molten bath fluidity. The jet characteristics formed from the swirl structure lance were also considered to be affected by the preheating temperature of supersonic oxygen jet.⁹⁾ As for the heat balance, although a certain amount of heat was released from the oxidation reaction, the heat loss of the molten bath resulted from full interaction area between the swirl-type oxygen jets at a relatively lower temperature, and the slag slowed the substance transfer between the slag and molten steel. To compensate for the side effect of the heat loss, oxygen jet preheating technology was developed through a heat exchanger assembled before the jets are injected from the lance.

Fig. 1.

Jets generated by different oxygen lances. (Online version in color.)

The fluid flow characteristics and impingement efforts of the conventional top-blown oxygen jet and the swirl-type oxygen jet have been widely investigated and analyzed by numerical simulations as well as experiments:^{8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24)} Li⁸⁾ constructed the dynamic characteristics of supersonic swirling jets with numerical simulations and analyzed the effects of the nozzle twist angle on the swirling flow intensity and dynamic parameter distributions of the jets. In his early research¹⁰⁾ the coalescence characteristics of supersonic jets were numerically studied, and the influences of the ambient temperature, nozzle number, and nozzle inclination angle were simulated. Maia^11,12) studied jet penetration at different inner furnace pressure and oxygen temperature, and applied a cold water model¹³⁾ to simulate the effects of a twisted and non-twisted nozzle on the jet-bath interaction and bath mixing time. Amini¹⁴⁾ and Singh¹⁵⁾ numerically studied the heat transfer of impinging jets injected from a twisted nozzle and found the jet-to-plate distance, Reynolds number, and twisted ratio were significant for the jet heat transfer. Bhattacharya¹⁶⁾ established several computational fluid dynamics (CFD) models of supersonic oxygen nozzles, based on the method of characteristics (MOC) and multi-objective genetic algorithm (MOGA), to characterize and optimize oxygen nozzles applied in the BOF steelmaking industry. Todorovic¹⁷⁾ summarized the slop-detection system in Tenova Goodfellow’s i BOF, this protective system could help to clarify the slop situation by the vibration of an oxygen lance, and a furnace with the system applied suggested higher productivity and lower operation costs. Li¹⁸⁾ compared four different fluid dynamic algorithms at first when cold supersonic conventional oxygen jets were injected into ambient at room temperature by means of numerical simulations and experimental validations, and then the best-matched algorithm was applied to simulate the jet characteristics at higher ambient temperature. Feng¹⁹⁾ improved a series of oxygen lance nozzle parameters via actual and theoretical methods to reduce excessive oxygen consumption and relevant equipment spoilage. Tang²⁰⁾ focused on the orifice space of an oxygen lance; their influences on the impact area were simulated by Fluent and found negative. Yang²¹⁾ added a shrouding oxygen jet to the main jet, and simulated the effects of different shrouding oxygen temperature on the jet velocity and temperature distribution.

Compared with the studies on jet characteristics, studies on preheating technology applied in supersonic oxygen jets in steelmaking have not advanced to the same extent. In Zhao’s study,⁹⁾ oxygen jet injections of three different temperatures were simulated. The higher temperature jet was found to be faster, with more dynamic pressure at both the outlet and endpoint. But the velocity and dynamic pressure of the jet decreased more unsteadily at a higher temperature, because of the density difference between the jet and ambient gas. Besides, preheating supersonic jet technology was proposed by preheating the oxygen to enhance the agitation ability of the supersonic oxygen jet, and this demonstrated significant advantages.^22,23) With the high temperature, high pressure, and low density of the shrouding gas, the turbulence intensity of the jet maintains a low level over a longer distance.²⁴⁾ However, the fluid flow characteristics of a swirl-type supersonic jet with preheated oxygen have not been reported. Therefore, it is necessary to understand the effects of both the ambient and jet gas temperature on the fluid flow characteristics of a swirl-type supersonic oxygen jet for the process parameter formulation and optimization.

In this study, the fluid flow characteristics of supersonic oxygen jets injected from four swirl-type lances with four different ambient and oxygen temperatures were studied by means of numerical simulations. Experiments of preheating supersonic jets were carried out to validate numerical simulation results. The dynamic characteristics and temperature distribution of oxygen jets in the radial direction were obtained, and the relationships among the jet velocity, momentum, dynamic pressure, and oxygen temperature were also clarified. Further studies on the impingement of jets on the molten bath, as well as the influences of swirl-type oxygen jets on vanadium oxidation, could be performed in accordance with appropriate oxygen jet reheating temperatures.

2. Numerical Model

2.1. Equations Applications

Several assumptions were proposed to meet the demands of accuracy and fewer computational errors of the simulation:

(i) The gas is considered as a Newtonian and compressive fluid. The molecular viscosity of the gas is considered as a function of the temperature.

(ii) The flow is three-dimension, steady, and non-isothermal in the fluid domain and isentropic in the Laval nozzle.

(iii) The gas was considered as a perfect gas that obeys the ideal gas law, and the specific heat was fixed as constant.

The present study involved equations including governing equations, molecular viscosity equations, and turbulence equations. For the governing equations, the mass, momentum and energy transport (Eqs. (1), (2), (3)) were constructed in accordance with the assumptions above and the Navier-Stokes equations:   

$$\frac{\partial (\rho u_i)}{\partial x_i}=0$$(1)

where ρ is the gas density (kg/m³) and u_i is the velocity component in the ith direction (m/s).   

$$\frac{\partial (\rho u_i{u}_j)}{\partial x_j}=-\frac{\partial p}{\partial x_i}+\frac{\partial ({\tau }_{ij}-\rho \overline{u_i{u}_j})}{\partial x_j}$$(2)

where p is the system pressure (Pa), ρu_iu_j are the Reynolds stresses, which arise from the nonlinear term in the un-averaged equations. And τ_ij is the viscous stress resulting from the molecular viscosity (Pa), as defined in Eq. (4).   

$$\begin{array}{l}{\displaystyle \frac{\partial \left[u_i\left(\rho C_{p}T+p\right)\right]}{\partial x_i}}=-{\displaystyle \frac{\partial }{\partial x_i}}\left(\lambda {\displaystyle \frac{\partial T}{\partial x_i}}+{\displaystyle \frac{C_p{\mu }_{\text{t}}}{{Pr}_{\text{t}}}}{\displaystyle \frac{\partial T}{\partial x_i}}\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+{\displaystyle \frac{\partial }{\partial x_i}}\left({\tau }_{ij}{u}_j-u_j\rho \overline{u_i{u}_j}\right)\end{array}$$(3)

where C_p is the specific heat capacity, J/(kg∙K); λ is the thermal conductivity, W/(m∙K); and P_rt is the turbulence Prandtl number, which illustrates the correlation between the temperature boundary layer and flow boundary layer. The Prandtl number is determined by the fluid’s physical parameters, i.e., the dynamic viscosity coefficient, thermal conductivity, and specific heat at constant pressure, as follows: Prt = (Cp∙μ_t)/λ_t. In this study, P_rt is set as 0.85.   

$${\tau }_{ij}=\mu \left(\frac{\partial u_j}{\partial x_i}+\frac{\partial u_i}{\partial x_j}-\frac{2\partial u_k}{3\partial x_k}{\delta }_{ij}\right)$$(4)

For the molecular viscosity equations, in Eq. (4), the Kronecker delta δ, is introduced. The value of δ is 0 when i ≠ j and is 1 when i = j. u and μ are the velocity component (m/s) and molecular viscosity (Pa∙s), respectively. The parameter subscripts represent the vector direction. The values of the parameters μ were defined in accordance with Sutherland’s viscosity in Eq. (5):   

$$\frac{\mu }{{\mu }_{\text{ref}}}={\left(\frac{T}{T_{\text{ref}}}\right)}^{\frac{3}{2}}\cdot \frac{T_{\text{ref}}+B}{T+B}$$(5)

When air was selected, the reference temperature T_ref, reference μ_ref, and constant B were respectively set as 273 K, 17.16×10⁻⁶ Pa∙s and 110 K. For the turbulence equations, four two-equation turbulence models were provided by Fluent, and Wilcox’s k-ω model was shown to be more accurate than the others when oxygen was injected at high ambient temperature or from supersonic swirl-type lance.^8,18,25) The equations of the model are as follows:   

$$\frac{\partial (\rho k{u}_j)}{\partial x_j}=\frac{\partial }{\partial x_j}\left[\left(\mu +\frac{{\mu }_t}{{\sigma }_k}\right)\cdot \frac{\partial k}{\partial x_j}\right]+G_k-Y_k+S_k$$(6)

  

$$\frac{\partial (\rho \omega u_j)}{\partial x_j}=\frac{\partial }{\partial x_j}\left[\left(\mu +\frac{{\mu }_t}{{\sigma }_{\omega }}\right)\cdot \frac{\partial \omega }{\partial x_j}\right]-\frac{\alpha {\omega }^2}{k}{G}_k-Y_{\omega }+S_{\omega }$$(7)

  

$${\mu }_t=\frac{\rho k}{\omega }$$(8)

The parameters k and ω are defined by the first and second equation. These two parameters were connected by the turbulence viscosity μ_t, as expressed in Eq. (9). The parameter G_k is the generation of turbulence kinetic energy, and G_ω is the generation of the specific dissipation rate. Y_k and Y_ω are the dissipations of k and ω respectively. S_k and S_ω are the user-defined source terms. The term $-\rho \overline{u_i{u}_j}$ in the expression of G is also defined as the Reynolds stress term and given in Eq. (9) according to the Boussinesq equation:²⁶⁾   

$$-\rho \overline{u_i{u}_j}={\mu }_{\text{t}}\left(\frac{\partial u_j}{\partial x_i}+\frac{\partial u_i}{\partial x_j}\right)-\frac{2}{3}\left(\rho k+{\mu }_{\text{t}}\frac{\partial u_k}{\partial x_k}\right){\delta }_{ij}$$(9)

where μ_t is the turbulence viscosity, Pa∙s; and k is the turbulence kinetic energy, m²/s².

2.2. Computational Domain and Simulation Conditions

A full-sized oxygen lance equipped with four Laval nozzles was applied to establish a mesh model, to include the influences among all the gas flows and to achieve simulation results closer to real gas flows. Four Laval nozzles in the same structure were applied. The detailed information of nozzle geometry parameters and how the swirl-type jets were formed from the nozzles is shown in Fig. 2. The inclination angle formed by the axes of the Laval nozzle and the oxygen lance was 10°. The Mach number was designed as 2 for each nozzle. After the entrance of the Laval nozzle was rotated by an angle θ clockwise around point C (center point of oxygen lance) while the nozzle exit was fixed, the intersection of the lance and Laval nozzle axes disappeared. From the top view of the nozzle-twisted lance, no single line goes through A (center point of Laval nozzle’s exit), B (center point of Laval nozzle’s entrance) and C. The characteristics of the jet from the nozzle were then remarkably changed considering an initial swirl jet caused by the deflection angle. However, in the regular oxygen lance, the axis intersection exists, and the three points A, B and C from the top view were on a single line. The angle θ in the present study was set at 10°.

Fig. 2.

Geometry structure of nozzle-twisted lance. (Online version in color.)

The geometry of the computational domain with the structure of four Laval nozzles and boundary categories are shown in the left part of Fig. 3, and a mesh with approximately 700000 grids of the computational domain established by ICEM CFD is shown in the right side. During the simulation process, the pressure of each inlet was maintained constant at 600000 Pa, the pressure of the ambient gas was set as atmospheric pressure, and the oxygen jet preheating temperature and ambient gas temperature was adjustable. The simulation schemes are listed in Table 1. The boundary settings and calculation process were accomplished by the CFD software package Fluent 16.2.

Fig. 3.

Geometry and mesh of computational domain. (Online version in color.)

Table 1. Simulation schemes.

Lance categories	Ambient temperature (K)	Preheat temperature (K)
Nozzle-twisted lance	300	300450600
	1700	300450600
Regular lance	300	300450600
	1700	300

2.3. Experimental Verification System

An oxygen jet with ambient gas at room temperature was formed, and its characteristics were obtained by the system introduced in Fig. 4. The system mainly consisted of three parts, including an air supply part (A), the control part (B) and collection part (C). The preheating temperature was achieved by an electric heat exchanger. Sensors were installed at the distances of 200, 300, and 400 millimeters from the lance exit. The jets velocities were recorded by a computer. Data from the experimental devices were used for the validation and correction of the calculation results.

Fig. 4.

Experimental system of the oxygen lance. (Online version in color.)

3. Results and Discussions

3.1. Simulation Results on Single Jet and Validation

Numerical and experimental studies of a single jet were carried out first to ensure the credibility of the subsequent multiple-nozzle lance numerical experiments. A jet injected from a regular oxygen lance at different preheating temperatures was studied. The velocity distribution of the jet centerline along the distance from the nozzle exit and the experimental results are shown in Fig. 5.

Fig. 5.

Velocity distribution of regular jet centerline at different preheating temperatures. (Online version in color.)

It could be concluded that the numerical results agree well with experimental ones. Moreover, with the increase in the preheating temperature, the oxygen jet velocity increased synchronously. The increasing velocity was caused by the exchange between the sum of the enthalpy and the kinetic energy of the gas in the Laval nozzle. The correlation between these two parameters is expressed in Eq. (10):   

$$H_0=H+\frac{{\upsilon }^2}{2}$$(10)

where H₀ represents the isentropic stagnation enthalpy of the gas at the nozzle inlet, J; H represents the enthalpy of the gas after it is injected into the computational domain, J; and υ represents the velocity of the gas, m/s. The enthalpy of the gas is expressed under the third assumption in Section 2.1 with constant specific heat.   

$$H=c_{p}T=\frac{\kappa }{\kappa -1}RT$$(11)

where T represents the gas temperature of the gas, K, and the gas temperature in different states is suggested by the subscript which is the same for H. κ represents the adiabatic coefficient and is the same as applied in the denominator part transformation of the local sound speed in Eq. (12). For air, oxygen, nitrogen and other diatomic molecule, κ is usually set at 1.4.²⁷⁾ As a result, the correlation between the temperature and velocity of the gas was established:   

$$Ma=\frac{v}{a}=\frac{v}{\sqrt{\kappa RT}}$$(12)

  

$$v=\sqrt{2\times \frac{\kappa \text{R}(T_0-T)}{\kappa -1}}$$(13)

where T₀ is the gas temperature in the nozzle entrance. Ma represents the dimensionless Mach number. v represents the gas velocity, m/s. The simulation results could be validated by the above equation, indicating that the kinetic energy was increased by the internal energy of the gas. Appropriate preheating applied to the oxygen jet could yield a better effect on the dynamic interaction between the jet and the ambient gas.

3.2. Influences of Ambient Temperature on a Single Jet

The first picture of Fig. 6 shows the centerline velocity distribution of a regular single jet at 300 K preheating temperature and a single swirl-type oxygen jet at different preheating temperatures. In this study, the centerline velocity is the jet velocity on the central axis of the jet nozzle. Each swirl-type jet with different preheating temperatures is represented by the preheating temperature value with unit K, and the regular jet is indicated by the symbol R. The jet characteristics were concluded according to repeated calculations. The axial velocity, showing velocity component along jet forward direction, together with dynamic pressure distribution of jet, was drawn as supplement. From the centerline velocity distribution of a single jet, another significant phenomenon is that the velocity fluctuation is aggravated with the increase in the preheat temperature. Additionally, the fluctuations of the axial velocity and the dynamic pressure are severer. The fluctuation was caused by the molecular movement resulted from the significant difference in energy between the jet and ambient gas. The severe change in axial velocity did not result in a rapid decrease in its magnitude, compared with the dynamic pressure. This means at the early stage, the jet’s energy is mainly consumed in the interaction between jets and ambient gas. When the interaction tends to be stable, the fluctuation of the jet axial velocity was suppressed while the dynamic pressure was not, which suggests the jet’s energy consumption in the stable decrease period is mainly caused by the temperature difference between jet and ambient rather than the velocity difference.

Fig. 6.

Kinetic parameter distribution of single jet simulation. (Online version in color.)

A centerline velocity difference between the swirl-type lance with 300 K preheating temperature and regular lance could be found at 300 K ambient temperature but was not evident at 1700 K ambient temperature. When the ambient temperature at 300 K, the velocity of swirl-type oxygen jets increase early than the regular ones, but the velocity features vanished when the ambient temperature at 1700 K. Besides, when the ambient temperature was increased to 1700 K, the fluctuation became more severe given the more substantial energy difference between the jet and the surroundings. Nevertheless, the fluctuation of the regular jet and swirl-type jet at 300 K preheating temperature was not noticeable compared with other jets at 300 K ambient temperature. According to the data comparison, during the distance range from 320 mm to 1325 mm, 170 velocity data points were picked up, the fluctuation section of the jet, defined as the proportion of data points with velocity at least less than their next point by 2 m/s among all points, from the regular lance and the swirl-type lance with 300 K preheating temperature took up the same percentage as 13.5%, while the fluctuation section of the jet from the swirl-type lance with 450 K and 600 K preheating temperature took up 23.5% and 28.8%. It could be seen that the energy difference between oxygen jets and ambient gas results in the velocity fluctuation, and the fluctuation degree and temperature are not in a linear relationship. Besides, the attenuation of momentum as the jet moves forward was weakened. The most apparant attenuation appeared in the distribution of dynamic pressure, for the decrease of dynamic pressure occurred earlier than those of velocity parameters at a distance of less than 250 millimeters. And the magnitude did not reduce monotonously until the jet reached an axial distance of 1000 millimeters from the lance nozzle exit. Compared with jets centerline velocity and dynamic pressure distribution at higher ambient temperature, the decrease in gas density and the sharp fluctuation did not transfer too much energy owing to the molecular motion of the ambient gas increased with higher temperature, which could help maintain the gas kinetic energy to improve the dynamic condition at a further distance. Therefore, the slow decrease in velocity occurred. However, the impact area of the jet reaches a limitation as a result of insufficient kinetic transfer at the early stage.

The Mach number of each jet scheme could be obtained according to the jet velocity distribution. The Mach number of the jet at 300 K preheating temperature was found to meet the designed magnitude. However, the Mach number of the higher preheating temperature jet was more significant than the designed value. In the BOF steelmaking industry, the core length is used to describe the gas kinetic ability. The total length of a gas jet with a Mach number more massive than 1.0 are regarded as core length. The trends of the core length at different ambient temperature are shown in Fig. 7. Longer core lengths were formed at higher ambient temperature, and the influence of preheat temperature on the core length was more evident at lower ambient temperature.

Fig. 7.

Core length of the single jet. (Online version in color.)

3.3. Influence of Temperature on Multiple Nozzle Jets

3.3.1. Jet Characteristics of the Centerline

Jets from an entire oxygen lance with four nozzles were simulated and analyzed. The jets characteristics were concluded according to repeated calculations. The dynamic characteristics of the swirl-type and regular jet were studied at first (Fig. 8). The maximum jet velocity with 300 K and 600 K preheating temperature did not change obviously at different ambient temperatures. However, the jet at 450 K and higher ambient temperature presented a higher velocity than that at lower ambient temperature. Thus, a balance between the jet momentum and energy at higher ambient temperature was suggested. The more acute fluctuation of the jets at high ambient temperature still appeared, but not as acute as with the single jet. This is because when four jets were injected into the computational domain, energy transfer between the jets and ambient gas proceed. The gas in the central region obtains kinetic energy more effectively and energy loss of it was restrained due to the closed area formed by four jets (red circle in Fig. 10). Thus another velocity attenuation buffer area is formed in the central region of the jets. The kinetic energy consumption of some oxygen jets close to this central region was postponed. As a consequence, the effects of kinetic energy transfer of all jets abated, and the fluctuation range shrank.

Fig. 8.

Dynamic parameters of multiple-nozzle jets. (Online version in color.)

Fig. 10.

Velocity distribution at 1.5 m from lance exit. (Online version in color.)

The trend of the core length along the centerline of each jet is shown in Fig. 9 based on the Mach number calculated according to the velocity distribution. The maximum Mach number of multiple nozzle jets was less than that of a single jet, which suggested that the compressibility of multiple jets was reduced, owing to by the increased compression resistance strengthened by the multiple jets. The core length of multiple jets was shorter than that of a single jet under the same conditions, although the trend of the variation in core length was the same as in a single jet.

Fig. 9.

Core length of multiple-nozzle jets. (Online version in color.)

3.3.2. Velocity Distribution

The cross-section at 1.5 meters from the Laval exit was chosen to analyze the interactions between the jet and the surroundings, in which the Mach number of the jet reduced to approximately 1.0, fluctuation of kinetic parameters disappeared basically then the radial molecular motion of jet cloud be analyzed accurately. Thus, this section was applied to represent the jet cavity formed on molten steel in the steelmaking industry. The velocity magnitude (Fig. 10) was obtained to evaluate the cavity depth. From the figure the velocity at the center part of each jet and central region in four jets increased with the increase of preheating temperature, which proved the promoting effect on the velocity of the preheating temperature and the preservation effect of the ambient temperature on jets kinetic inferred in section A. In addition, the velocity of the central region increased with the change from the swirl-type jet to the regular jet, as a result of the higher tangential velocity in the swirl-type jet. The impact area (Table 2) of the jets was applied to evaluate the cavity width. The cavity width increased with the preheating temperature at higher ambient temperature. Moreover, the impact areas of the swirl-type jets were smaller than those of the regular jets, because the kinetic energy was consumed more in the movement of the swirl-type jets. It could be concluded that a positive correlation existed between the cavity and preheating temperature.

Table 2. Impact area at 1.5 m from the lance exit.

Impact area (m2)	Regular	300 K	450 K	600 K
300 K	0.652	0.645	0.652	0.651
1700 K	0.679	0.674	0.698	0.711

The radial data was obtained to study influences of both preheating and ambient temperature on swirl-type jets characteristics, based on the swirl effects. And Figs. 11 and 12 show the velocity and dynamic pressure of swirl-type oxygen jets along radial direction at different distances from the lance exit. The diameter of the jets increased as they advanced, but it was not significantly influenced by preheat temperature. The dynamic pressure of the jets at higher ambient temperature was more than 250000 Pa when the jets were injected into the domain at the early stage, but decayed rapidly and reached a magnitude close to that at the lower ambient temperature. Further improvements in the jet characteristics could involve the preservation of the dynamic pressure in this region of rapid decreasing.

Fig. 11.

Velocity distribution along the radial direction. (Online version in color.)

Fig. 12.

Dynamic pressure distribution along the radial direction. (Online version in color.)

3.3.3. Temperature Distribution

Figure 13 shows the centerline temperature distribution of multiple nozzle jets. All the jet temperatures reduced at first and then increased gradually. In the cooling phase, temperature difference increased at higher preheating temperature. The temperature fluctuation appeared at the following heating section was closely related to the above acute velocity change at the same distance. It should be noted that the temperature of both the regular jet and swirl-type jet at 300 K ambient temperature eventually closely approached 300 K. The temperature difference at 2500 mm suggests part of internal energy was compensated to retard kinetic energy consumption as the jets advanced. Moreover, the jet temperature would reach its peak after 1250 mm far away from the nozzle exit, the peak suggest the influence of the ambient gas exceeded that of the oxygen jets themselves on the jet temperature distribution. Three black arrows were signed to locate the distance from the nozzle exit to jet’s temperature peak. It could be concluded the higher the preheating temperature, the earlier the dominate influence on the jet inner energy change from the jet own temperature to the ambient gas occurs.

Fig. 13.

Temperature distribution of multiple-nozzle jets, (a) 300 K ambient temperature, (b) 1700 K ambient temperature. (Online version in color.)

In addition, the temperature recovery of the swirl-type jet at 300 K preheating temperature was faster than that of the regular jet, but the regular jet absorbed more energy over the same distance than the swirl-type jet at the higher temperature. This suggested that compared with the tangential direction, the energy transfer in the axial direction was faster. The temperature contour of each jet injection scheme at 1.5 meters from the lance exit is shown in Fig. 14. The temperature in the central region of the jets increased at 300 K ambient temperature, but the temperature in the central region of four jets at 1700 K ambient temperature was lower than 1700 K, and increased monotonically with the increase in the preheating temperature. The temperature distribution of the jet along the radial direction is shown in Fig. 15. It could be concluded that the heat loss of the ambient was reduced by the preheating process. Note that at higher ambient temperature, the temperature of the central part of four jets decreased gradually, and the variation degree was negatively correlated with the preheating temperature. For the higher preheating temperature, the central region area temperature more close to the 1700 K ambient temperature, the temperature decrease was lower. However, changes in velocity of central region area are on the contrary, as shown in Fig. 16. The higher preheating temperature, the faster increase occurred in velocity. To put it into a nutshell, the preheating temperature of the jets could make the velocity and temperature of central region area vary in two different directions and reach a balance point, with the least reduction in inner energy and the most enhancements in kinetic energy. Thus the best influence of the jets central region on the molten steel could be obtained.

Fig. 14.

Temperature distribution at 1.5 m from lance exit. (Online version in color.)

Fig. 15.

Temperature distribution along the radial direction. (Online version in color.)

Fig. 16.

Velocity and temperature change of central region area with different oxygen temperature at 1700 K ambient temperature. (Online version in color.)

3.3.4. Vector and Vorticity Distribution

The details of the velocity change could be expressed by the velocity vector. The vector distribution of each jet injection scheme is illustrated in Fig. 17. The area with gathered vector points represents jets there contain more kinetic energy. The gathered effect was not evident at lower ambient temperature, and the number of vector points increased with the increase in the preheating temperature at 1700 K ambient temperature. In addition, compared with that of the regular jet, the distribution of vector points in the swirl-type jet at any temperature was only centrosymmetric; the points of each jet deviated counterclockwise. This is caused by the swirl characteristic of the jet. To study the correlation between the temperature and the deviation of molecular motion, the curl parameter of the vector, called the vorticity was applied. The vorticity is expressed by the following equation in Cartesian coordinates:   

$$\overrightarrow{\mathrm{\Omega }}=\left(\frac{\partial u_z}{\partial y}-\frac{\partial u_y}{\partial z}\right)\overrightarrow{i}+\left(\frac{\partial u_x}{\partial z}-\frac{\partial u_z}{\partial x}\right)\overrightarrow{j}+\left(\frac{\partial u_y}{\partial x}-\frac{\partial u_x}{\partial y}\right)\overrightarrow{k}$$(14)

where υ represents the flow velocity vector, m/s. In continuum mechanics, the vorticity was applied as a pseudovector field to describe the tendency of a continuum to rotate.²⁸⁾ In the present study, the vorticity distribution was applied to confirm whether the deviation of molecular motion was caused by the rotation of the jets and the degree of the rotation. The result of each jet injection scheme is illustrated in Fig. 18. Two concentric circles with a small circle occurred on each jet, and the small circle was formed by the lowest-vorticity-magnitude region, resulting from molecular motion with high straight-line speed. The middle-size concentric circle was made up of the highest vorticity magnitude, which was caused by the continuous energy transfer between the outside jet and the ambient gas. The remaining energy of the middle part was thus preserved temporarily and diffused gradually into the surroundings. A particular part of the internal energy was transferred into the continuum angular speed of the jet, according to the trend of the vorticity magnitude with the preheating temperature.

Fig. 17.

Vector distribution at 1.5 m far from lance exit.

Fig. 18.

Vorticity distribution at 1.5 m far from lance exit. (Online version in color.)

Figure 19 shows the vorticity component distribution in the axial direction, which is defined as the Z-Vorticity in this study. The Z-vorticity of the continuum along the jet centerline was greater than zero, and the parts lower than zero indicate that those continuum rotated against jet centerline. The vorticity magnitude was twice the mean angular velocity of the particles in accordance with the right-hand rule. As a result, vectors along the jet direction were entrained away, and those against the jet direction were delayed at the instantaneous cross-section, and the gathered vectors phenomenon formed. The degree of molecular movement in the jet could be indicated by the increasing absolute value and range of Z-vorticity with the increase in the preheating temperature. It could be concluded further that the jet molecular radial motion strengthened by the increase in the initial energy of the jet.

Fig. 19.

Z-vorticity distribution at 1.5 m far from lance exit. (Online version in color.)

4. Conclusions

Swirl-type jet characteristics from a nozzle-twisted oxygen lance at different preheating and ambient temperatures were numerically calculated and analyzed in this study. Conclusions with respect to the kinetic and internal energy aspects in the axial and radial directions of the jets were drawn as follows:

Three different preheating temperatures of swirl-type jet injected into a gas at two different ambient temperatures were numerically simulated. Validation of a regular oxygen jet at the same preheating temperature was carried out.

The centerline velocity distribution of a regular single jet at 300 K preheating temperature and a swirl-type single jet at different preheating temperatures were studied. The centerline velocity difference between the swirl-type lance and regular lance at 300 K preheating temperature could be found at an ambient of 300 K, but it was not evident at 1700 K, where the advanced change in velocity in the swirl-type jet vanished. A longer core length was formed at higher ambient temperature, and the influence of the preheating temperature on the core length was more evident at the lower ambient temperature suggested by the slope of core length segment.

The maximum jet velocity at 300 K and 600 K preheating temperature did not change obviously at different ambient temperatures. However, the jet at 450 K temperature and higher ambient temperature shows a larger velocity than that at lower ambient temperature. The dynamic pressure of jets at higher ambient temperature was more than 250000 Pa when jets were injected into the domain at the early stage, but it decayed rapidly and reached a magnitude close to that at lower ambient temperature.

The temperature recovery of the swirl-type jet at 300 K preheating temperature was faster than that of the regular jet, but the regular jet absorbed more energy over the same distance than the swirl-type jet at a higher temperature. The Z-vorticity of the continuum moved along the jet centerline was more significant than zero, and the part lower than zero indicated that those rotated the against jet centerline.

For better vanadium extraction effects, the temperature of the molten bath was expected to be kept lower to improve the oxidation of vanadium and resist carburization. Nevertheless, the dynamic condition of the bath deteriorated if the bath was overcooled. The heat balance between vanadium extraction and the bath dynamic condition could be obtained from further studies concerning impingement of swirl-type supersonic jets on the bath.

Acknowledgments

Financial supports from the National Natural Science Foundation of China (No. 51804345), Natural Science Foundation of Hunan province in China (No. 2017JJ3386) are gratefully acknowledged.

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