Physical Modelling of Aluminum Reﬁning Process Conducted in Batch Reactor with Rotary Impeller

: The reﬁning process is one of the essential stages of aluminum production. Its main aim is to remove hydrogen, that causes porosity and weakens the mechanical and physical properties of casting aluminum. The process is mainly conducted by purging inert gas through the liquid metal, using rotary impellers. The geometry of the impellers and the processing parameters, such as ﬂow rate of gas and rotary impeller speed, inﬂuence the gas dispersion level, and therefore the efﬁciency of the process. Improving the process, and optimization of parameters, can be done by physical modelling. In this paper, the research was carried out with the use of a water model of batch reactor, testing three different rotary impellers. Varied methods were used: visualization, which can help to evaluate the level of dispersion of gas bubbles in liquid metal; determination of residence time distribution (RTD) curves, which was obtained by measuring the conductivity of NaCl tracer in the ﬂuid; and indirect studies, completed by measuring the content of dissolved oxygen in water to simulate hydrogen desorption. The research was carried out for different processing parameters, such as ﬂow rate of reﬁning gas (5–25 L · min − 1 ) and rotary impeller speed (3.33–8.33 s − 1 ). The obtained results were presented graphically and discussed in detail.

built on a 1:1 scale, according to the theory of similarity. If the results obtained from physical modeling can be representative, and could be transferred to real conditions, physical models are built according to strictly defined principles resulting from the theory of similarity. The similarity of physical models of reactors for aluminum refining requires the preservation of similarity criteria, both geometric and dynamic, for water and aluminum. In these models, this is accomplished by means of appropriate criterial numbers. The assumption that the flow in the refining reactor is isothermal and laminar enables the criterial equation to be written in the following form: ϕ(Eu, Sl, Fr, Re) = 0 (1) where Eu-Euler's number, Sl-Strouhal's number, Fr-Froude's number and Re-Reynold's number. NaCl solution, and the location of two sensors, for measuring oxygen desorption from water. The physical model was built on a 1:1 scale, according to the theory of similarity. If the results obtained from physical modeling can be representative, and could be transferred to real conditions, physical models are built according to strictly defined principles resulting from the theory of similarity. The similarity of physical models of reactors for aluminum refining requires the preservation of similarity criteria, both geometric and dynamic, for water and aluminum. In these models, this is accomplished by means of appropriate criterial numbers. The assumption that the flow in the refining reactor is isothermal and laminar enables the criterial equation to be written in the following form: ( , , , ) = 0 where Eu-Euler's number, Sl-Strouhal's number, Fr-Froude's number and Re-Reynold's number. Strouhal's (Sl) criterion can be excluded because the character of the liquid flow is close to laminar. Euler`s (Eu) criterion, which has significance in flows under pressure, can be neglected in cases of flow in open reactors. In the studied system, the flow is steady and the Reynold's number (Re) is in the range of self-modelling. Laminar flows are characterized by small Reynold's numbers, whereas turbulent flows are characterized by high Reynold's numbers, and often transfer from laminar motion to turbulent motion is rapid, and the limiting values of the Re number are then defined as critical. In this range of flows, the values of the Re number are changing insignificantly. Thus, there is no necessity in this area to obtain the equality of criterial numbers. Therefore, the dominating criterion determining the similarity of studied model to real object is Froude's (Fr) criterion. Equation (1) can be then written in the following form: Additionally, the Weber's number, which characterizes the influence of surface tension on the flow of liquid, is the criterion number supporting the achievement of the required similarity of the Strouhal's (Sl) criterion can be excluded because the character of the liquid flow is close to laminar. Euler's (Eu) criterion, which has significance in flows under pressure, can be neglected in cases of flow in open reactors. In the studied system, the flow is steady and the Reynold's number (Re) is in the range of self-modelling. Laminar flows are characterized by small Reynold's numbers, whereas turbulent flows are characterized by high Reynold's numbers, and often transfer from laminar motion to turbulent motion is rapid, and the limiting values of the Re number are then defined as critical. In this range of flows, the values of the Re number are changing insignificantly. Thus, there is no necessity in this area to obtain the equality of criterial numbers. Therefore, the dominating criterion determining the similarity of studied model to real object is Froude's (Fr) criterion. Equation (1) can be then written in the following form: Additionally, the Weber's number, which characterizes the influence of surface tension on the flow of liquid, is the criterion number supporting the achievement of the required similarity of the model to the real object. Table 1 shows the values of calculated criterial numbers (Reynolds, Froude and Weber) for water, at a temperature of 293 K, and aluminum, at a temperature of 973 K.
A well-constructed model gives results that are approximate to those obtained in real conditions, and the criterion numbers are used to preserve the similarity of the model to the real object without physically affecting the process itself-they describe it, but do not direct it. The modelling research was conducted for three different rotary impellers-one of them was a new design, and two were commercial designs (see Figure 2). The research was carried out in the range of processing parameters: rotary impeller from 3.33 to 8.33 s −1 , and flow rate of refining gas from 5 to 25 L·min −1 . However, based on earlier research [1,9,29,36], and their primary results, the number of measurements were decreased to 27, and according to Table 2, the extreme values of flow rate were skipped.  Table 1 shows the values of calculated criterial numbers (Reynolds, Froude and Weber) for water, at a temperature of 293 K, and aluminum, at a temperature of 973 K.
A well-constructed model gives results that are approximate to those obtained in real conditions, and the criterion numbers are used to preserve the similarity of the model to the real object without physically affecting the process itself-they describe it, but do not direct it. The modelling research was conducted for three different rotary impellers-one of them was a new design, and two were commercial designs (see Figure 2). The research was carried out in the range of processing parameters: rotary impeller from 3.33 to 8.33 s −1 , and flow rate of refining gas from 5 to 25 L·min −1 . However, based on earlier research [1,9,29,36], and their primary results, the number of measurements were decreased to 27, and according to Table 2, the extreme values of flow rate were skipped. The research methodology was as follows:  The model tank was filled with water up to 0.7 m, and the processing parameters were changed according to Table 2.


Visualization research was carried out by digital camera, recording the dispersion level for all rotary impellers, whilst changing the processing parameters. The research methodology was as follows: • The model tank was filled with water up to 0.7 m, and the processing parameters were changed according to Table 2.

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Visualization research was carried out by digital camera, recording the dispersion level for all rotary impellers, whilst changing the processing parameters.
• Next, the tank was saturated with oxygen. The saturation level was measured by two oxygen meters CO-401, Elmetron, Zabrze, Poland (location of oxygen meters is shown in Figure 1b). After reaching the saturation level, argon was introduced into the model by rotary impeller, and processing parameters were according to the variants in Table 2. Removal of oxygen from water, as an analog of hydrogen removal from aluminum [1,22,27], was measured every 0.5 min.
The process of aluminum refining in the batch reactor typically lasted 10 min, therefore the process of oxygen removal was carried out for every variant for 10 min. • Finally, for the selected variants, based on visualization results (dispersion level), RTD curves were measured, the NaCl tracer was poured from the top of the tank with water, the measuring device was switched on, and the three conductometers measured the change in conductivity at three different locations of the reactor model. The obtained results were automatically registered by the computer system.

Visualisation Results
The results of the visualization measurements are presented in Figure 3 for impeller A, Figure 4 for impeller B, and Figure 5 for impeller C. These pictures show the level of dispersion for various processing parameters. As mentioned earlier, the results were unsatisfactory under the extreme conditions of 5 and 25 L·min −1 , and 3.33 s −1 . For 5 L·min −1 and 3.33 s −1 , in all cases, the flooding pattern of dispersion (gas rises axially as a bubble column) was observed for all rotary impellers. The flooding pattern, or minimum dispersion, was seen when the flow rate of refining gas was 5 L·min −1 and with the remaining rotary impeller speeds (5.00, 6.66 and 8.33 s −1 ). Thus, this variant was omitted in further studies. Similar patterns were observed for 3.33 s −1 and flow rates of gas from 10 to 25 L·min −1 . Consequently, these variants were also omitted in further studies. For the flow rate of 25 L·min −1 , the uniform dispersion was observed at all rotary impeller speeds, but swirls were also created, and gas bubbles formed chains that caused waves on the surface. This is dangerous, especially under industrial conditions, because the hydrogen could be reintroduced into the liquid metal. Therefore, this case was also rejected.    Table  2, for the commercial design rotary impeller C.            For impeller A, a minimum dispersion level was observed when the rotary impeller speed was 5.00 s −1 and the flow rate of the refining gas was 10, 15 and 20 L·min −1 (variants P1, P4 and P7), as well as for 6.66 s −1 and 10 and 15 L·min −1 (variants P2 and P7). This means that single gas bubbles were rising to the top of the reactor, and the mixing of gas bubbles is near the shaft of the rotary impeller. The best results (uniform dispersion) were obtained with the rotary impeller speed of 8.33 s −1 for almost all refining gas flow rate values (variants P3, P6 and P9).
For impeller B, in all cases, intimate or uniform dispersion were noticed. For variants S1, S4 and S7 the intimate dispersion was seen. The best results were obtained for variants S3 and S6, with a rotary impeller speed of 8.33 s −1 and flow rates of refining gas of 10 and 15 L·min −1 . In case of variant S9, excessive dispersion was seen-chains of gas bubbles were created causing swirls.
For impeller C, variants R1, R4 and R7 produced the worst results (5 s −1 and 10, 15, 20 L·min −1 ) i.e., minimum dispersion was observed. The uniform dispersion could be seen when the rotary impeller speed was 8.33 s −1 and the flow rates of refining gas were 10 and 15 L·min −1 . In these variants (R6 and R9), the single gas bubbles are rising to the top of the reactor, gas bubbles are uniformly mixed with water in the whole model of refining reactor, even beneath the rotary impeller, and the mixing of gas bubbles with water exists. Figure 6 shows the exemplary variants with different cases of dispersion levels: (a) minimum dispersion-single gas bubbles rise to the top of the reactor, dispersion is observed only in the area of gas bubble generation, and lack of dispersion in the whole volume of the tank, (b) excessive dispersion-creation of bubble chains and swirls, (c) uniform dispersion-good mixing of gas bubbles with liquid is observed in the whole volume of the tank. For impeller A, a minimum dispersion level was observed when the rotary impeller speed was 5.00 s −1 and the flow rate of the refining gas was 10, 15 and 20 L·min −1 (variants P1, P4 and P7), as well as for 6.66 s −1 and 10 and 15 L·min −1 (variants P2 and P7). This means that single gas bubbles were rising to the top of the reactor, and the mixing of gas bubbles is near the shaft of the rotary impeller. The best results (uniform dispersion) were obtained with the rotary impeller speed of 8.33 s −1 for almost all refining gas flow rate values (variants P3, P6 and P9).
For impeller B, in all cases, intimate or uniform dispersion were noticed. For variants S1, S4 and S7 the intimate dispersion was seen. The best results were obtained for variants S3 and S6, with a rotary impeller speed of 8.33 s −1 and flow rates of refining gas of 10 and 15 L·min −1 . In case of variant S9, excessive dispersion was seen-chains of gas bubbles were created causing swirls.
For impeller C, variants R1, R4 and R7 produced the worst results (5 s −1 and 10, 15, 20 L·min −1 ) i.e., minimum dispersion was observed. The uniform dispersion could be seen when the rotary impeller speed was 8.33 s −1 and the flow rates of refining gas were 10 and 15 L·min −1 . In these variants (R6 and R9), the single gas bubbles are rising to the top of the reactor, gas bubbles are uniformly mixed with water in the whole model of refining reactor, even beneath the rotary impeller, and the mixing of gas bubbles with water exists. Figure 6 shows the exemplary variants with different cases of dispersion levels: (a) minimum dispersion-single gas bubbles rise to the top of the reactor, dispersion is observed only in the area of gas bubble generation, and lack of dispersion in the whole volume of the tank, (b) excessive dispersion-creation of bubble chains and swirls, (c) uniform dispersion-good mixing of gas bubbles with liquid is observed in the whole volume of the tank. Table 3 summarizes the results of visualization, showing types of dispersion for all studied impellers.

The Research of Oxygen Removal from Water
The research of oxygen removal from water was carried out for all variants presented in Table 2. The level of oxygen concentration was measured in two places (see Figure 1b); however, the results were similar (the placement of sensors was investigated by Chin et al. [37], which indicated that curves for the sensor located in the lower and upper part of the reactor are almost identical). Therefore, the results of the research presented graphically in Figure 7 show the measurements of the top oxygen meter only. In all cases the best results of removing oxygen were obtained for rotary impeller B, they were considerably better than for impeller A and C. The results of impellers A and C were comparable, though rotary impeller C was insignificantly better. In case of flow rate of refining gas 10 L·min −1 , the rotary impeller speed played a significant role in obtaining a better level of oxygen removal. For impeller A and C, at 5.00 s −1 about 10 mg·L −1 oxygen content was obtained, whereas at 8.33 s −1 this level was lower, reaching about 5 mg·L −1 . In case of rotary impeller B, at 5.00 s −1 the oxygen content was 3 mg·L −1 . The same oxygen level was obtained much faster for the rotary impeller speed 8.33 s −1 (about 400 s).
For the flow rate of refining gas 15 L·min −1 at 5.00 s −1 , the oxygen concentration for impeller A was 9 mg·L −1 , and for impeller C 8 mg·L −1 , whereas for impeller B only 2 mg·L −1 . Better results were obtained for rotary impeller speeds 6.6 s −1 and 8.33 s −1 -for impeller A: 6 and 4 mg·L −1 , and for impeller C: 5 and 2.5 mg·L −1 , respectively. For impeller B, the levels of oxygen concentration 2 mg·L −1 were reached after 500 s at 6.66 s −1 and after 400 s at 8.33 s −1 .
For the case of flow rate of refining gas 20 L·min −1 , the results of oxygen concentration for 5.00 s −1 were comparable with those for 15 L·min −1 . This was similar for 6.66 and 8.33 s −1 rotary impeller speeds. However, for rotary impeller B, the time taken to obtain level of oxygen concentration 2 mg·L −1 for rotary impeller speed 8.33 s −1 was quicker, and reached 300 s. C were comparable, though rotary impeller C was insignificantly better. In case of flow rate of refining gas 10 L·min −1 , the rotary impeller speed played a significant role in obtaining a better level of oxygen removal. For impeller A and C, at 5.00 s −1 about 10 mg·L −1 oxygen content was obtained, whereas at 8.33 s −1 this level was lower, reaching about 5 mg·L −1 . In case of rotary impeller B, at 5.00 s −1 the oxygen content was 3 mg·L −1 . The same oxygen level was obtained much faster for the rotary impeller speed 8.33 s −1 (about 400 s).  Because the gas consumption is seen as the important operational cost in cast foundries, it is possible to calculate the efficiency of gas consumption (E), which is defined as total volume of purge gas (Vg) needed to eliminate 90% of the dissolved oxygen, and can be written in the following form [27]: Table 4 shows the results of efficiency of gas consumption for the three studied rotary impellers, and Table 5 presents the total time to eliminate 90% of dissolved oxygen. The best gas consumption was achieved for the new design rotary impeller. For this impeller, the total time needed to eliminate 90% of dissolved oxygen for all variants was smaller than 630 s.

Determination of Residence Time Distribution(RTD) Curves
Theoretical basis of RTD characteristics has the source in the inert function of age distribution, which assumes that in the period between t and ∆t the fraction of substance being in reactor equals the product of I(t)·∆t, I(t). It is a continuous function and after arrangement the relationship can be written in the following form: When assuming the reactor is in equilibrium state, the transport of fluid at the inlet and outlet have advective character and liquid is incompressible, such function can be written in the form: where E(t) can be defined as: where C(t) change of tracer in liquid metal or water as a function of time.
Determination of RTD curves based on measurement of conductivity changes in water with added tracer (aqueous NaCl solution) is in µS·cm −1 . If the obtained results were comparable, the recorded values are calculated to a dimensionless form according to the following Equations (7) and (8) [37]: where C-basic dimensionless tracer concentration, G pom -analog of tracer concentration in time, µS·cm −1 , G max -analog of maximal tracer concentration in modelling liquid, µS·cm −1 , C b -dimensionless concentration of the tracer, c o -base dimensionless concentration of the tracer at the beginning of the process, c ∞ -base dimensionless concentration of the tracer at the end of the process. The determined characteristics make it possible to determine the minimum mixing times of the tracer in the modelling fluid (water). The criterion, which should be fulfilled to determine such values, is the moment when the concentration of the marker for both measuring points reached a plateau in the range of 0.9-1.1, this meant that the tracer was completely mixed into the entire volume of the modelling liquid. The RTD curves were measured for chosen processing parameters, including the best and worst visualization results for: • Impeller A: the worst result (minimum dispersion)-Variant P4 and the best ones P3 and P9. • Impeller B: the worst result (excessive dispersion)-Variant S9 and the best ones S1 and S6.
• Impeller C: the worst result (minimum dispersion)-Variant R7 and the best ones R6 and R9.
RTD curves for all mentioned above variants were presented in Figure 8 in the form of dimensionless concentration as a function of time. Based on these curves, the shortest time for mixing gas bubbles in the whole reactor were calculated and are summarized in Table 6.
The determined characteristics make it possible to determine the minimum mixing times of the tracer in the modelling fluid (water). The criterion, which should be fulfilled to determine such values, is the moment when the concentration of the marker for both measuring points reached a plateau in the range of 0.9-1.1, this meant that the tracer was completely mixed into the entire volume of the modelling liquid. The RTD curves were measured for chosen processing parameters, including the best and worst visualization results for:  Impeller A: the worst result (minimum dispersion)-Variant P4 and the best ones P3 and P9.  Impeller B: the worst result (excessive dispersion)-Variant S9 and the best ones S1 and S6.  Impeller C: the worst result (minimum dispersion)-Variant R7 and the best ones R6 and R9. RTD curves for all mentioned above variants were presented in Figure 8 in the form of dimensionless concentration as a function of time. Based on these curves, the shortest time for mixing gas bubbles in the whole reactor were calculated and are summarized in Table 6.   Estimated time of mixing is the longest for rotary impeller A variant P4 (5.00 s −1 , 15 L·min −1 ), for the last two variants it is shorter (30 s). However, compared with the other two impellers, it was not satisfactory. Results for rotary impeller C were better than that for rotary impeller A, with the shorter time of mixing of 23 s, at rotary impeller speed 8.33 s −1 and flow rate of refining gas at 15 L·min −1 . The best results of mixing time were reached for impeller B, which was 18 s, at a rotary impeller speed of 8.33 s −1 and the flow rate of refining gas at 15 L·min −1 .

Conclusions
On the basis of the conducted research, the following conclusions can be drawn:

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Physical modelling is a helpful method for working out the new design rotary impeller and aids easy identification of the optimal processing parameters.

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The physical model of the refining reactor simulates the conditions prevailing in this reactor during refining process. The rates of gas bubble dispersion significantly influences the efficiency of the hydrogen removal process. Determining the optimal range of gas flow increases the efficiency of the purging process, which in turn reduces its costs.

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The information obtained from the dispersion patterns are dependent on observation and interpretation, and thus improper conclusions can be drawn. • RTD curves, which are quantitative analysis, provide the information about mixing time of tracer with water, and based on such results the identification of processing parameters, such as flow rate of refining gas and rotary impeller speed, is possible. RTD curves do not give a direct and clear answer, but allow for a satisfactory estimation of the technological parameters and the operation of the reactor. • Based on research of oxygen removal from water, as an analog of hydrogen desorption from aluminum, the essential information can be obtained about the process and processing parameters, and also about the time of refining.

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The new design impeller B had the best results in all applied methods, the best variants being 8.33 s −1 and 15 L·min −1 . The next step of the research should now be to test the new design impeller under industrial conditions.
For better understanding of the process, and to complete the obtained results for the new rotary impeller, the numerical modelling could be applied.