Hydraulic experiment on macro-instability in the lead smelting side-blown furnace

Macro-instability phenomenon in side-blown furnace was first reported in this paper, and the occurrence conditions, influencing factors and rules, eliminating measures were studied and analyzed by hydraulic experiment. The results show that the occurrence of macro-instability in side-blown furnace needs to meet certain conditions, which is mainly related to the liquid level above the jet nozzle, the number and arrangement of jet nozzles. However, the frequency macro-instability is irrelevant the nozzle height, liquid level, air flow and the nozzle diameter, the number and arrangement of jet nozzles, and the frequency of this model is 1.2Hz.The macro-instability phenomenon in side-blown furnace can be avoided or eliminated by adoption certain measures which can be used as the reference for side-blown furnace design and operation.


Introduction
High-speed and high-pressure gas flow is injected into high-temperature molten bath through the jet nozzle, which is widely used in metallurgical industry [1][2][3] .Metallurgical furnace can be classified into bottom-blown furnace, side-blown furnace, top-blown furnace, and combined-blown furnace according to the installation location of jet nozzle.Side-blown furnace is extensively applied in the smelting of nonferrous metals such as lead and copper [4] .Side-blown gas flow is injected into sideblown furnace through the lance, strongly stirring the molten bath and enhancing the heat transfer, mass transfer and chemical reaction process in side-blown furnace.
Fluid macro-instability is a large scale low frequency transient quasi-periodic phenomenon existing in stirred vessel [5] .Wizard et al. [6 ] reported macro-instability phenomenon in stirred vessel for the first time.Bruha et al. [7] found that macro-instability in stirred vessel was caused by the alternation of single-cycle flow and double-cycle flow in the system driven by the impeller during its rotation.Liu [8] studied the influence of double rigid-flexible impeller on the frequency of macro-instability with wavelet analysis and flow field visualization method.There are many studies on macro-instability in stirred vessel [9][10][11] , while the macro-instability in side-blown furnace have not been reported before.The present research mainly focuses on the penetration depth [4] , the formation and distribution of bubbles [12][13][14] , behaviors of jet flow [15][16][17] and emulsification phenomena [18] .The side-blown furnace actually is also a typical stirred system, the molten bath in the side-blown furnace is strongly stirred by the high-speed gas jet flow.Macro-instability will affect the mass and energy transfer behavior in sideblown furnace, corrosion of refractory, and scouring effect on the furnace wall.Therefore, it is necessary to study the macro-instability in side-blown furnace.

Similarity criterion
The experimental setup in the current paper is similar to a side-blown furnace provided by some company.Similarity criterion must be established to ensure that the model flow and prototype flow are similar.The similarity criterion in this study includes geometric similarity and dynamic similarity.
Geometric similarity was the first condition that must be followed in a similarity criterion.This feature indicates that a model and prototype must have the same geometric shape; their corresponding size must have the same ratio, and their corresponding angles must be similar.The value of geometric similarity is computed using equation ( 1), modified Froude number was selected in dynamic similarity, as shown in equation (2).The modified Froude number of the model and prototype must be the same, as described in equation (3).
where,  is the number of geometric similarity; m L is the length of the model, m; and p L is the length of the prototype, m. where, g v is the velocity of gas, m/s; g is the acceleration of gravity, m/s 2 ; 0 d is the diameter of a jet nozzle, m; g  is the density of gas kg/m 3

Experimental parameters
The geometric similarity number of 1:2 was established based on various factors, including dimensions of the prototype, the size of the laboratory, and the economic cost.Table 1 illustrates the specific structural parameters of both the model and the prototype.

Experimental device
The experimental facilities in the experiment included a furnace model, an air supply system, a valve station, a digital image processing system.Figure 1 show the schematic diagram .
The working process for this experiment is as follows: (1) Dry and clean air was provided by an air supply system, which included air compressor, air storage tank, air dryer and QPS air filter.
(2) A valve station, which included Flow regulating valve, flowmeter, pressure gauge, gas pipelines and ball valves can realize functions of air flow regulation and display, pressure display.
(3) The air was jetted into a furnace model through a jet nozzle.
(4) Experimental phenomena were recorded by a high-speed camera and digital images were processed by the computer using graphics processing software.

Macro-instability phenomenon
During the normal injection process, the melt pool will experience irregular fluctuation and turbulence-like splashing, as shown in figure 2.

Figure 2. Normal injection process without macro-instability phenomenon.
The fascinating macro-instability phenomenon in the side-blown furnace was serendipitously observed during a hydraulic experiment.The molten pool in the furnace model presented a periodic fluctuation and swaying phenomenon, which was referred to as macro-instability phenomenon due to its large-scale oscillation at a fixed frequency.Figure 3 illustrates the liquid level fluctuation in a half cycle after the occurrence of macro-instability phenomenon.The side-blown air jet flow was ejected from the nozzle, and after a certain penetration depth, it began to float up due to buoyancy and regularly oscillate at a fixed frequency.As depicted, regular fluctuations and swaying phenomenon occur in the melting pool of the side-blown furnace, which can be directly observed behind the sideblown jet nozzle.If serious macroscopic instability occurs in the side-blown furnace, it will lead to increased corrosion of the refractory and scouring effect on the furnace wall.This will result in a shorter service life for the furnace and a higher frequency of maintenance.Therefore, it is necessary to study the factors and rules of macro-instability in the side-blown furnace.

Effects of liquid level and jet nozzle height
This paper conducted an experiment to investigate the effect of nozzle height and liquid level on the macro-instability phenomenon in the side-blown furnace.We maintained a steady liquid level of 460mm in the molten pool at 460mm and air flow rate of 10m 3 /h, while adjusting the nozzle height.Macro-instability phenomenon occurred in the side-blown furnace, at nozzle height of 125mm and 250mm, but not at a nozzle height of 375mm.We also kept air flow rate at 10m 3 /h and maintained a constant the liquid level above the nozzle of 210mm, and observed that the macro-instability phenomenon occurred at nozzle heights of 125mm, 250mm and 460mm in the side-blown furnace, with the same frequency of 1.2Hz.Table 3 shows the experimental data, which indicates that the liquid level above the nozzle has a significant impact on the occurrence of macro-instability.In addition the nozzle height plays a key role in the occurrence of macro-instability.Experimental data in table 4 clearly demonstrates that the occurrence of macro-instability in the side-blown furnace is significantly affected by the liquid level above the nozzle that should be maintained within a specific range.(1) Experiments indicate that when the nozzle height was 250mm and air flow is 10m 3 /h, the occurrence of macro-instability in the side-blown furnace was observed within the range of 395mm-555mm liquid level, but would not occur when the liquid level was outside the range.(2)Additionally, once the macro-instability occurred, the frequency of the model was 1.2Hz, independent of nozzle height or liquid level.

Effects of air flow and nozzle diameter
The effects of air flow and nozzle diameter on side-blown furnace were studied in this experiment, and table 5 summarizes the experimental data.The "time needed" refers to the duration of time between the initial static state and the occurrence of macro-instability inside the furnace after the injection of side-blown air flow through the nozzle.This parameter can serve as a useful measure to evaluate the difficulty of the occurrence of macro-instability and the difficulty of maintaining stability of the sideblown furnace.Table 5 shows that the fluctuation range of liquid level increased with the increase of air flow and the time needed for the occurrence of macro-instability decreased correspondingly.When the diameter of the nozzle decreased, the fluctuation range of liquid level decreased and the time needed for the occurrence of macro-instability also decreased.The frequency of macro-instability had no relation with the air flow rate and the nozzle diameter, and the frequency of this model was 1.2Hz.

Effects of the number and arrangement of jet nozzles
The effects of the number and arrangement of jet nozzles were analyzed when liquid level was 460mm and air flow of single nozzle was 5m 3 /h, the experimental data was represented in table 6.Table 6 reveals that the number and arrangement of nozzles have a significant impact on the occurrence of macro-instability in the side-blown furnace.Specifically, the macro-instability phenomenon occurred in Case① and case④, while it did not in case②、case ③、case ⑤ and case ⑥.Interestingly, the frequency of macro-instability in the side-blown furnace, regardless of the number and arrangement of jet nozzles, was the same for all cases, with a value of 1.2Hz, indicating the need for further investigation.

Effects of the type of macro-instability phenomenon
Under different conditions, the side-blown furnace would occur different types of macro-instability phenomenon which were shown in Figures 4-6.The macro-instability frequency is related to the type of macro-instability phenomenon, type A "left and right shaking " is 0.93 Hz, type B "central tearing" is 1.47 Hz and type C "front and rear shaking" is 1.63 Hz。

Discussions
The side-blown air jet flow was ejected from the jet nozzle, the high-pressure and high-speed air flow formed a gas column, and then penetrated a certain distance into the molten pool.After a certain penetration depth, the airflow started to float up due to buoyancy force and regularly swing with a fixed frequency.The process of "penetration-floatation-swing" was repeated, during which the kinetic energy of airflow was transformed into the kinetic energy of the molten pool in the side-blown furnace continuously.The molten pool in the furnace started to fluctuate and sway because of the floating and swinging airflow, so the molten pool had gravity potential energy and kinetic energy, and the gravity potential energy and kinetic energy were transformable.When the airflow and bubbles escaped from the molten pool, some airflow would blow the surface of the molten pool like wind.The side-blown furnace was a closed vessel with furnace wall made of refractory material, the gas-liquid two flow in the furnace would be limited by the geometrical size and affected by the wall effect.Under the combined action of various factors, the macro-instability phenomenon with fixed frequency occurred in the molten pool above the jet nozzle in the side-blown furnace, while the molten pool below the jet nozzle kept a "macro-static" state, as shown in figure 2.
The continuous injection of side-blown airflow was the main power source of the stirring of the molten pool in the side-blown furnace, and the occurrence of macro-instability was mainly related to the liquid level above the jet nozzle.If the liquid level above the jet nozzle was too high, it was difficult for the molten pool to oscillate regularly and there was no macro-instability phenomenon in the side-blown furnace because of the great inertia force.If the liquid level above the jet nozzle was too low, and the swing frequency of the side-blown air flow was very fast and its amplitude was very small, there was no macro instability because the molten pool was very shallow.Therefore, macroinstability in the side-blown furnaces occurred only within a certain range of liquid level.The number and arrangement of jet nozzles would also affect the occurrence of macro-instability.Under singlenozzle injection and face-to-face double-nozzle injection conditions, it was easy to occur macroinstability in the side-blown furnace.While when arrangement of the jet nozzles was double-nozzle injection with an angle of 45° or three-nozzle injection or four-nozzle injection, the macro-instability phenomenon would not occur in the side-blown furnace, because the regular swinging phenomenon of air jet flow can be broken by multi-airflow.
The macro-instability in the side-blown furnace have not been reported before, this paper provided a preliminary analysis of the macro-instability in the side-blown furnace.In the next step, we will do more theoretical research based on the theory of wave formation and wall effect, hydraulic model experiment and numerical simulation.

Conclusions
(1) The macro-instability in the side-blown furnace is a frequently occurring and complex phenomenon that requires specific conditions.Its occurrence is mainly affected by the liquid level above the jet nozzle, several factors including the nozzle height, liquid level, number and arrangement of jet nozzles can affect the occurrence of macro-instability.However, once the macro-instability occurs, the frequency remains constant and independent of the nozzle height, liquid level, air flow and the nozzle diameter.
(2) The frequency of the macro-instability in the side-blown furnace is related to the furnace specifications and macroscopic instability types.In the circular side-blown furnace model, the frequency of the macro-instability phenomenon is 1.2Hz.While in the rectangular side-blown furnace, the frequency of the type A "left and right shaking " macro-instability phenomenon is 0.93 Hz, the type B "central tearing" is 1.47 Hz and type C "front and rear shaking" is 1.63 Hz。 (3) The time needed for the occurrence of macro-instability varies depending on the air flow and diameter of the jet nozzle.An increase in air flow or decrease in jet nozzle diameter reduces the time needed for the occurrence of macro-instability, which means the macro-instability was easier to occur.(4) Optimizing the number and arrangement of the nozzles, along with increasing the liquid level and reducing the jet nozzle height, can help avoid or eliminate the macro-instability phenomenon in the side-blown furnace, providing guidance for furnace design and operation.

Figure 3 .
Figure 3. Macro-instability phenomenon in a half cycle.

Figure 4 . 7 Figure 5 .Figure 6 .
Figure 4. Type A "left and right shaking" macro-instability phenomenon in a half cycle , and l  is the density of liquid, kg/m 3 .

Table 1 .
Structural parameters of model and prototype.

Table 2 .
Parameters of prototype and the model.

Table 3 .
Experimental data in different nozzle height.

Table 4 .
Experimental data in different liquid level.

Table 5 .
Experimental data in different air flow and nozzle diameter.

Table 6 .
Experimental data in different number and arrangement of jet nozzles.