In recent years there is an attempt to control the gas stirring intensity in metal-making ladles with the aid of vibration measurements. Understanding better the induced vibrations in two-phase flows can substantially improve the existing models for gas stirring control. In this work, highly sensitive accelerometers were used for the vibration measurements in a liquid metal alloy; Sn–40 wt pctBi alloy at 200 °C and water at 20 °C. The examination of the liquids was conducted in the ladle mockup integrated into the Liquid Metal Model for Steel Casting facility at Helmholtz-Zentrum Dresden Rossendorf. Single bubbles were generated in the respective liquids by controlled argon injection at low flow rates in the range of 0.01 to 0.15 NL min−1 through a single nozzle installed at the bottom of the ladle. Obtained results demonstrate differences between the induced vibrations in the examined liquids in terms of the magnitude of the root mean square values of vibration amplitude and the shape of the resulting curves with increasing flow rate. Furthermore, continuous wavelet transform reveals variations in the duration and vibrational frequency of the evolved bubble phenomena. The findings suggest that differences in the physical properties of the examined liquids result in variations in the vibrations induced during bubble evolution.
Notes
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Introduction
Gas injection is a common practice in steelmaking for refining processes such as desulphurization, decarburization, degassing and homogenization of the molten steel as well as for inclusions removal.[1] The quality of the final product is directly associated with the homogeneity of the composition and temperature of the molten steel before casting as well as the amount of inclusions left in the liquid steel bath. Commonly, in secondary steelmaking processes, gas injection takes place through one or several plugs located at the bottom of the ladle.[2] Typically, after gas injection in the molten steel, bubbles are formed and rise into the melt inducing turbulences enhancing the stirring of the bath[3‐5] until they reach the steel-slag interface prior to the formation of the open eye.[2] In the other case of gas injection at lower flow rates, finer bubbles are formed in the bath resulting in soft stirring without the formation of the open-eye.[6] Stirring has an important role in clean steel production as it leads to inclusion transportation towards the top surface where they are absorbed by the slag.[7] Bubbles formed during gas injection have an important role in the refining of molten steel and removal of inclusions with their characteristics such as bubble size, shape, and velocity influencing the kinetics of the removal process.[4,8] Understanding the behavior of the bubble flow in the molten metal is important prior to the construction of accurate two-phase models for optimization and control of stirring in metal-making ladles.[9]
Accurate control of gas stirring in ladles can assure quality, productivity, and resource efficiency. In recent years there is an attempt to control the stirring intensity and mixing condition in metal-making ladles with the aid of vibration measurements. Several studies including modeling[1,10‐20‐22]and plant trials[10,20,21,23] have been conducted to examine the feasibility of vibration measurements for gas stirring control in steelmaking processes. The majority of the modeling work as found in literature has been carried out in physical models with water as modeling liquid. The findings of such investigations are considered valuable and reveal the increased potential of the vibration measurements in gas stirring control. Pylvänäinen et al.[10,11] not only succeeded to relate the gas flow rate injection to the intensity of the vibrations but also revealed a significant potential of vibration measurements to detect abnormal stirring and gas leakages based on the signal captured by accelerometers. Yenus et al.[15,16,24] have excessively contributed to the control of the mixing conditions in ladle metallurgy after the implementation of vibration measurements in water models by utilizing accelerometers. Alia et al.[25] provided guidelines for an optimized stirring based on vibrations in physical models using water as modeling fluid. A study by Mucciardi[26] utilizing accelerometers for vibration measurements at a water model was successful in correlating the stirring intensity of the bath with the amplitude of the signal raised to the power of 1.6. In the framework of Ondeco project[19] (EU project) vibration measurements at a water model established a methodology utilizing accelerometers for the examination of vibrations under varying flow rate, pressure on the top surface and bath depth. Results showed that variations in the operational parameters result in relevant variations in the intensity of the produced vibrational levels. The direct relationship between the gas flow rate and the produced vibrational intensity was observed also by Burty et al.[20] by utilizing accelerometers for vibration measurements at a cold model. In addition, the authors proposed a relationship between the vibrational amplitude and the formation of the open eye on the top surface of the bath during ladle treatment. Signal processing of vibration measurements at a water model by Xu et al.[18] showed that such measurements have a great potential in gas stirring control especially when combined with complementary data such as images from the top surface of the bath. This aspect is supported also by results of Dynstir[6] (EU project) proposing an advisory tool consisting of camera based monitoring and vibration measurements for control of stirring in steelmaking processes. The work summarizes the various steps to be followed for establishing a robust methodology for the development of such an advisory system. Vibration measurements are perceived as a high-potential monitoring technique in a variety of steelmaking processes including the AOD converter. Vibration measurements at a water model and plant trials by Odenthal et al.[22] showed a strong correlation between the gas flow rate in the AOD and the recorded vibrational amplitude. In addition, it was shown that the type of injected gas influences the recorded amplitude where injection of nitrogen results in slightly enhanced vibrations. Fabritius et al.[14] after measurements at a physical model and at an industrial environment remarked that the vibrational intensity in an AOD converter is influenced by the characteristics of the penetration of gas jets in the liquid and the wear of the refractory lining.
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Although most of the existing published work regarding the vibrations in two-phase flows is restricted to physical models with water as modeling fluid, the physical properties of water differ significantly from those of molten steel. Therefore, the measurements in water can become inadequate to represent the actual physics of the real processes.[9] Keplinger et al.[27,28] found that bubble dynamics are associated with the physicochemical properties of the liquids where the bubbles evolve. Physical properties of the liquid where the gas is injected influence the characteristics of bubbles such as size, shape, and velocity.[29] Surface tension is dominant in the size of the formed bubbles[30] with the size to increase with increasing value of surface tension.[30,31] Moreover, surface tension is determining factor in the shape of the bubble which in turn affects the bubble dynamics in the liquid.[28,29] Cho et al. concluded that surface tension is the determining factor in bubble dynamics at very early stages of bubble evolution with an effect on their formation, expansion, and elongation.[32]
Events that govern the bubble flow as bubble formation, rise, coalescence, break-up and collapse, differ fundamentally between liquids with different physical properties.[9,33] The interactions between the bubbles and the surrounding liquid are complex and there are inadequacies in two-phase turbulent models. So far, there is little work available in the literature concerning the characterization of the bubble flow in liquid metals with properties close to those of molten steel.[9,27,33,34] Keplinger et al.[27] investigated the bubble flow during argon gas injection in a vessel filled with the eutectic GaInSn alloy. Results by means of high-speed video imaging using X-ray radiography consist of a meritorious database for bubble characteristics as size, number, bubble ejection frequency (bubbles/s) and number of break-up events with increasing gas flow. In addition, experiments with the same alloy by means of X-ray radiography investigated the bubble coalescence as well as bubble characteristics such as shape and velocity with increasing flow rate.[28] Wondrak et al.[9] constructed and implemented a state of the art large-scale test facility for multiphase flows examinations in the binary alloy Sn–40 wt pct Bi at a temperature of 200 °C Liquid Metal Model for Steel Casting (LIMMCAST). Utilization of electrical resistance probes and Ultrasound-Doppler-velocimetry offered strong foundations for measuring the void fraction and terminal velocity of bubbles in liquid metal with properties close to those of molten steel. In the same experimental setup, Rigas et al.[30] utilized for a very first time vibration measurements in liquid SnBi where variations were observed in the vibration signal with increasing flow rate in comparison with measurements in water. Such investigations are expected to contribute to a better interpretation of bubbles’ behavior and are perceived as valuable for the improvement of existing two-phase flow CFD models in relation to steelmaking processes. Such simulations of two-phase flows must be fed with data from well-controlled experiments.[35] In the attempt of establishing solid models for efficient control of gas stirring processes in metal-making supported by vibration measurements, the improved interpretation of the vibrations induced in two-phase flows is essential. Therefore, the vibration analysis of two-phase flows in physical models with liquid metals with properties close to those of molten steel is of high importance. A very first attempt has been carried out in the LIMMCAST setup at HZDR by Rigas et al.[33] revealing the first insights in the oscillatory behavior of the bubble flow in liquid metal. The findings were very encouraging for further investigations on the vibrations in liquids with varying physical properties. Therefore, for a very first time, the current work elaborates in more detail on the influence of the physical properties on the induced vibrations during bubble evolution by examining two different liquids accommodated inside the same ladle –the LIMMCAST setup.
Methodology
This study employs an experimental ladle with an inner diameter of 600 mm and a height of 1000 mm, designed to operate in principle with the binary alloy Sn–40 wt pct Bi. The ladle consists of a slightly concave plate at the bottom, while the wall ladles are equipped with electric heaters and a thermal isolation layer prior to control the temperature of the contained liquid metal during experiments. The concavity of the bottom plate resembles better the bottom of industrial steelmaking ladles. Prior to the experiments, pressurized argon is used to bring the liquid metal inside the experimental ladle from a storage tank besides. The filling process completes as soon as the level of the bath reaches the diameter of the ladle, i.e. 600 mm. Thus, in the experiments, the aspect ratio is unity corresponding to the typical situation in steelmaking processes. The experimental ladle is equipped with a top lid which protects the ladle from the environment and at the same time prevents from liquid metal splashing during operation at high flow rates. The ladle mockup is equivalent to a 1:5.25 model of a 185 tons industrial ladle implemented in the LIMMCAST facility at HZDR as described by Wondrak et al.[9] and Rigas et al.[33] A schematic illustration of the experimental ladle is presented in Figure 1. Investigations were conducted first as the ladle was operated with water at 20 °C. Thereafter, the volume of water was drained with a hydraulic pump and the ladle was cleaned and heated up to accommodate the binary alloy Sn–40 wt pct Bi at a temperature of 200 °C. The physical properties of both liquids, as well as of a common industrial steel grade X5CrNi18-10 are listed in Table I. The Morton number (Mo) is expressed in Eq. [1],
Fig. 1
Sketch of the experimental ladle implemented to accommodate the examined liquids
Table I
Physical Properties of Water, Sn–40 Wt Pct Bi Alloy, X5CrNi18-18 Molten Steel, and Argon Gas
where \(g\) is the gravitational acceleration; \({v}_{L}\) is the kinematic viscosity; \({\rho }_{L}\) is the density of the liquid; \(\sigma \) its surface tension; and and \(\Delta \rho \) the density difference between the two phases.
×
In both of the examined liquids, argon gas was injected in the experimental ladle at varying flow rates from 0.01 to 0.15 NL min−1 controlled by a gas flow controller (MKS, 1179BX52CM1BV) which can supply argon at a maximum flow rate of 0.5 NL min−1 (± 1 pct). This flow range has been selected in the study prior to the formation of single bubbles in the respective liquids in the LIMMCAST setup. The gas was injected into the ladle through a single nozzle of 2 mm diameter installed at the center of the bottom steel plate of the LIMMCAST setup (Figure 2).
Fig. 2
(a) Top-view sketch of the LIMMCAST setup with indicated utilized plug position where the nozzle was installed, and (b) image of the used single nozzle with a diameter of 2 mm used for argon injection
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For the vibration measurements, three mono-axial accelerometers (Wilcoxon 799M) were utilized, mounted at the same height onto the external shell of the top lid of the setup, at three different radial positions (X = 0, X = 180, and X = 270 deg) as presented in Figure 2(a). The utilized accelerometers have a sensitivity of 1000 mV/g (± 5 pct sensitivity tolerance) with a sampling frequency of 25 kHz, calibrated in the frequency range 0.2 to 2500 Hz. A high sensitivity value is important for capturing vibrations from the bubbles in the examined liquids.[33] In such implementations with vibration measurements, the mounting position of the accelerometers affects the recorded vibrational characteristics.[25] Since all three accelerometers ACC A, ACC B, and ACC C were mounted at the same height onto the ladle, all three obtained signals are perceived to contain the same kind and amount of information related to the two-phase flow in the liquids. The signal captured by the accelerometers was transferred to a desktop computer where the raw data was stored in a PostgreSQL database. A detailed description of the measuring system can be found in the previously published study by Rigas et al.[33] where the same vibration measuring equipment was utilized for vibration measurements at LIMMCAST. After data extraction from the database, MatLab® was used for the signal processing and the computation of the RMS values, as well as for the time-frequency analysis.
The vibration signal at each examined flow rate was recorded for five consecutive minutes. At each examined flow rate, data only from the three intermediate minutes of any measurement was used for analysis to assure that the signal refers to the target flow rate only. As in other studies of vibration measurements in physical models,[12,13,19,25,33] RMS is considered as a valuable quantity that describes the energy content of the captured vibrations. In the current study, the RMS values of acceleration were calculated in MatLab® as the square root of the arithmetic mean of the acceleration amplitude at each flow rate, described in detail in a previous work by Rigas et al.[33] For the curve fitting in the produced graphs of RMS with increasing flow rate, the Curve Fitting Tool 3.5.9 as integrated into the MatLab® toolbox was used. Apart from RMS analysis, the signal was treated by means of continuous wavelet analysis (CWT) to examine the time-frequency response of the bubbles in the examined liquids. Although it is commonly accepted that CWT is not computationally efficient, it is proven to offer an exceptional good time and frequency localization which is needed in the current study prior to investigate the vibrations induced by the multiple bubble evolution phenomena during argon injection in the examined liquids. Results from CWT are presented in the produced scalograms as a visual representation of the absolute value of the CWT coefficients of the processed signals plotted as a function of time and frequency. The produced scalograms of the CWT analysis of the acceleration signals were computed as described by MatLab®.[42] For the computation of the scalograms, the CWT was applied with eight voices per octave, and the upper-frequency limit being set at 12,500 Hz as a consequence of the Nyquist theorem.[42] For the overall evaluation of the frequency response of the oscillatory behavior of the bubble flow, the power spectrum of the acceleration was computed in MatLab® too in the range of 0 to 1500 Hz. This particular frequency band was selected after visualization of the signal which exhibited activity up to 1500 Hz.
An Alpha 7 III - full-frame interchangeable lens camera 24.2MP installed at the lid of the LIMMCAST (Figure 3) was used as complementary tool for a better understanding of the origin and interpretation of the vibration signal during argon injection in the liquids. The camera was recording the movement of the bubbles through a glass viewing window of the setup designed for this purpose. Since water is a transparent medium, it was possible to record videos of the overall bubble phenomena in the liquid from the generation at the nozzle to rise and collapse at the top free surface. In the case of non-transparent liquid SnBi, on the other hand, only the point of impingement of the bubbles on the upper free surface could be detected.
Fig. 3
The lid of the LIMMCAST setup indicating the glass viewing windows for recording the top surface of the examined liquids accommodated in the LIMMCAST setup. The three accelerometers ACC A, ACC B, and ACC C are also observed mounted on the periphery of the top lid
×
Results
The generated vibrations of the two-phase flow as a function of the argon flow rate was examined in liquid SnBi and water. Figure 4 shows the calculated values of RMS in both liquids as a function of increasing flow rate up to 0.15 NL min−1. Both in SnBi and water, argon was injected through the same single nozzle placed in the center of the bottom plate at LIMMCAST (Figure 2). As observed in Figure 4, the two liquids exhibit different paths for RMS with increasing flow rate. A linear dependence of the RMS values on the flow rate is observed for SnBi, while a power law dependence is shown for water. As observed in Figure 4, the vibrational amplitude of the RMS varies between the examined liquids with the amplitude in SnBi to achieve higher values than in water.
Fig. 4
Calculated RMS values of acceleration for accelerometers ACC A, ACC B, and ACC C, at varying gas flow rates for argon injection through the single nozzle at the bottom center of the LIMMCAST while operating with (a) liquid SnBi and (b) water
×
After the calculation of the RMS values for all three accelerometers (ACC A, ACC B, and ACC C) in the respective liquids, the study continues to CWT analysis for the examination of the time-frequency response while argon injection. Figure 5 presents the scalograms as produced for SnBi and water at a flow rate of 0.01 NL min−1 after analysis of a 10-second-long signal. The graphs refer to the signal from ACC B, where accelerometers ACC A and ACC C produced similar scalograms.
Fig. 5
Computed scalograms for accelerometer ACC B while argon injection at 0.01 NL min−1 in SnBi (a) and water (b) for 10 s
×
Two distinguished areas are observed in the produced scalograms separated by a white dashed line related to the accuracy of the obtained results of the CWT where the blue area provides an accurate time-frequency representation of the signal. The grey area, on the other hand, is potentially affected by artifacts where the stretched wavelets extend beyond the edges of the observation interval providing a low accuracy of the represented data.
It is interesting to note that variations are observed between the examined liquids regarding the values of the generated frequencies and their amplitude, as well as the number of recorded events in the studied time interval of 10 seconds. The computed scalograms in Figure 5 contain information related to the overall phenomena from bubble formation at the nozzle to rise and collapse at the top free surface of the liquids.
Figure 6 presents the produced scalograms explicitly for the signal captured during bubble generation at the nozzle for both liquids when argon was injected at 0.01 NL min−1. The graphs in Figure 6 are a result of CWT analysis of the same signals processed previously but with higher time resolution to study the vibrational imprint during bubble generation in the two liquids.
Fig. 6
Computed scalograms for accelerometer ACC B while bubble generation in SnBi (a) and water (b) when argon was injected at 0.01 NL min−1. The scalograms were produced by processing the same signal used for the production of scalograms in Fig. 5, but with higher time resolution
×
In the next step, the time-frequency response of the signal while bubble rise and collapse at the top free surface of the examined liquids was evaluated. Results from the CWT analysis regarding these events are presented in Figure 7. The graphs in Figure 7 are a result of CWT analysis of the same signals processed previously (Figure 5) but with higher time resolution to study the vibrational imprint during bubble rise and collapse in the two liquids. In case of liquid SnBi, the generation of a bubble occurs after the former bubble collapses at the top free surface. Whereas during argon injection in water, while some bubbles rise in the volume, some previously generated bubbles reach the top surface where they collapse. Therefore rise of the newly formed bubbles and collapse of the formers occur simultaneously resulting in two different bands as observed in Figure 7(b). The localization of the bubble collapse has been carefully investigated with the aid of a camera installed above the lid where videos during bubbling have been assessed at a msec time-scale. As in the case of bubble generation, the scalograms for bubble rise and collapse differ for the examined liquids concerning the areas of intensified frequencies, their power, and the duration of the examined events.
Fig. 7
Computed scalograms for accelerometer ACC B while bubble rise and collapse at the top free surface in (a) SnBi and (b) water when argon was injected at 0.01 NL min−1. The scalograms were produced by processing the same signal used for the production of scalograms in Fig. 5, but with higher time resolution
×
The vibrations in both liquids were examined during argon injection through the bottom nozzle at varying flow rate. Figure 8 presents the power spectrum of the vibration signal for accelerometer ACC B with an increasing flow rate of up to 0.15 NL min−1 for both liquids.
Fig. 8
Computed power spectrum for accelerometer ACC B for argon injection through the single nozzle at varying flow rate in liquid SnBi (a) and water (b)
×
The liquids exhibit an overall different frequency response as was expected after the examination of the scalograms presented previously in the results. The increase in the power of the spectrum with increasing flow rate is evident in Figure 8 for both liquids. The respective spectrograms are a result of signal analysis of a 20-second-long signal at each flow rate.
As described earlier in the Methodology section, a camera was used to record the behavior of the bubbles in the examined liquids. Images from the bubbles as soon as they reached the top free surface of the liquid SnBi are presented in Figure 9. The captured images show variations concerning the size of the single bubbles with increasing flow rate. Interesting is the case when argon was injected at 0.15 L min−1 where the observation of quasi-single bubbles started to become more frequent.
Fig. 9
Pictures of the bubbles during impingement at the top free surface of the liquid SnBi after argon injection at varying flow rate. The images were captured by an installed camera above the viewing glass window (a) on the lid of the LIMMCAST setup (see Fig. 3)
×
Images from the bubbles during rise in the water bath are presented in Figure 10. The captured images do not reveal variations concerning the size of the single bubbles with increasing flow rate. Variations are mainly observed in the number of rising bubbles with increasing flow rate. Reflections were inevitable on the top surface of the water bath as observed as of 0.05 NL min−1 in Figure 10.
Fig. 10
Pictures of the bubbles during rise in the water bath after argon injection at varying flow rate. The images were captured by a camera installed above the viewing glass window (b) on the lid of the LIMMCAST setup (see Fig. 3)
×
Discussion
In this work, vibration measurements were carried out during argon injection in two different modeling liquids; SnBi and water, accommodated in the LIMMCAST setup. The gas injection was restricted to low flow rates, up to 0.15 L min−1 to fulfill the generation of single bubbles in the respective liquids. A camera installed above the top lid of the setup allowed for bubble monitoring throughout the measurements.
Observations of the Top Surface
For SnBi, due to the opaque nature of the liquid metal, it was not possible to monitor the bubble generation event at the nozzle nor the bubble rise, where only the point of impingement of the bubbles on the upper free surface could be detected. For argon injection in the range 0.01 to 0.05 L min−1, one single bubble was observed to collapse at the top free surface of SnBi every five seconds. Whereas, by further increasing the flow rate above 0.05 L min−1, one single bubble or a pair of two or three bubbles (quasi-single bubbles) were observed to reach the top surface. The observation of quasi-single bubbles became more frequent when argon reached the highest value of 0.15 L min−1. By monitoring the top surface of the liquid SnBi, the size of the bubbles as observed to reach the top surface increased with increasing flow rate (Figure 9). Thus, for the investigated gas injection rates, the flow rate has a more dominant effect on the size of the formed bubbles than on their number. Regarding the experiments at LIMMCAST filled with water, the monitoring of the overall bubble evolution phenomena was possible from bubble generation to rise and collapse at the top free surface. Quasi-single bubbles (two or three) were observed to generate when argon was injected at the lowest flow rate of 0.01 L min−1, while the number started to increase significantly with increasing flow rate. Variations in the flow rate up to 0.15 L min−1 did not result in significant differences in the size of the generated bubbles which seems to remain constant with increasing flow rate.
The behavior of bubbles in a liquid is influenced by the geometry of the injection nozzle as well as by the physical properties of the liquid and the injected gas. In our investigations, vibration measurements were carried out using two different modeling liquids accommodated in the same setup where the same gas was injected at the same flow rate utilizing the same nozzle. Thus, differences in the vibrations are attributed only to the variations in the physical properties of the liquids where they form, rise, and collapse. This offers us a unique opportunity for a direct comparison of the induced vibrations between liquids with different physical properties. Physical properties such as surface tension and density affect the bubble size as well as influence the bubble dynamics in the liquid.[43‐46] The size of the formed bubbles are a function of the surface tension value of the liquid where bubble size decreases with decreasing surface tension.[44,46] Surface tension has a dominant role in bubble formation when leaving the nozzle where it acts as an attachment force and prevents bubble detachment. After bubble generation, the bubble stays attached to the nozzle under the influence of surface tension and expands increasing its volume.[47] The growth stage is followed by the elongation stage with the bubble stretching to an upward direction.[47] The resulting bubble size at the detachment of the bubble is therefore dominated by the balance between the surface tension and the buoyancy forces. In our investigations, observations with the installed camera confirmed the larger size of bubbles in SnBi as these reach the free top surface (see Figures 9 And 10). For liquids with low surface tension, the size of the small formed bubbles has a constant size irrespective of the flow conditions[46] which is as well confirmed in our experiments after monitoring the size of the generated bubbles in water (see Figure 10).
Signal Processing
RMS analysis
As observed in Figure 4, the calculated values of RMS in the two liquids follow a different path with increasing flow rate. The RMS shows a linear dependence on the increasing flow rate in the case of liquid SnBi, while the behavior turns to a power law in the case of water. After the evaluation of the calculated RMS in relation to the observations from the camera, it is shown that the size of the bubbles has a dominant role in the vibrational amplitude. The increasing bubble size with increasing flow rate in liquid SnBi results in a linear increase of the vibrational amplitude. In contrast, in water, the increase of the vibrational amplitude is attributed to the increasing number of the generated bubbles which is not capable itself to maintain the linearity between RMS and flow rate, turning the relationship into a power law. This established observation in this study was previously expressed by the authors in a previous study by Rigas et al.[33] where vibration measurements at LIMMCAST were compared with data from vibration measurements in water as found in the literature. However, in that study, experimental parameters such as the design of the experimental setup and injection conditions varied and therefore there was no possibility for detailed comparison and further elaboration between the vibrations in liquid SnBi and water.
As observed in Figure 4, the amplitude of the calculated RMS values varies between the examined liquids, where in liquid SnBi it appears one magnitude higher than in water. Such differences are attributed exclusively to the variations in the physical properties of the examined liquids. The buoyancy force on a bubble is proportional to the density of the liquid in which the bubble forms and rises. The relatively lower density of water results in decreased buoyancy force on the small rising bubbles reducing the rise velocity and therefore increasing the gas hold up.[48] Another contributing factor in the increased hold up in water is the relatively lower value of surface tension of the liquid.[46] Such a lower value of surface tension is also perceived to contribute to the smaller size of the bubbles.[46] After relating the variation in the number of bubbles in the two liquids with the calculated RMS values of the vibration signal in Figure 4, it is shown that an increased number of produced bubbles does not necessarily result in higher vibrational amplitude. Thus, the vibrational amplitude of the bubbles in a liquid is more prone to the size of the bubbles rather than the size of their hold-up in the liquid. The larger bubbles that are formed in liquid SnBi while remaining attached to the nozzle may be subject to larger deformation due to the higher pressure from the surrounding liquid. Morton number is an important parameter in determining the deformation of bubbles in liquids.[49] Liquids such as SnBi with relatively lower values of Morton number (see Table I) result in higher deformation of the bubbles. Such deformations of the larger forming bubbles in liquid SnBi enhance the amplitude of the vibration signal. After detachment, the higher slip velocity of such large bubbles intensifies the flow around the bubble.[48] The localized pressure gradient at the bottom of the rising bubble increases[44] inducing an upward force to the bottom of the bubble resulting in bubble deformation[50] which in turn is perceived to contribute to the amplitude of the generated vibration signal. The bubble continues its rising path until it reaches the free top surface of the liquid where it collapses releasing its inside pressure. The duration of the bubble collapse is proportional to the size of the bubble as soon as it reaches the surface.[51] A larger bubble size as in the case of liquid SnBi results in more intense and prolonged collapse at the top free surface contributing further to the vibrational amplitude. Consequently, the vibrational amplitude of the bubbles examined in the given flow range, is associated with the bubble-liquid interaction and the bubble size as a function of the physical properties of the liquid. Nevertheless, little differences are observed within the three accelerometers in the amplitude of the RMS values and the slope of the linear dependence with increasing flow rate for the same liquid. As mentioned earlier in this work, all three accelerometers are mounted at the same height around the experimental ladle and therefore their individual signals are perceived to contain the same kind and amount of information. However, the accelerometers are mounted at three different radial positions leading to variations in the apparent intensity of the same collected information. The utilized accelerometers are mono-axial measuring acceleration in a single direction. On the other hand, the rise of the bubbles in the examined liquids may deviate from a straight vertical line leading to variations in the spatial relationship between the bubble and the side wall where the accelerometers are mounted. Such variations may result in distinctions within the signals of the three accelerometers. The influence of the spatial relationship between the bubble and the wall is currently examined and results will be presented in a future publication.
CWT analysis
The scalograms of Figure 5 contain information concerning the overall evolved phenomena from bubble generation to rise and collapse when argon was injected at 0.01 NL min−1. Differences are observed between the liquids throughout the examined time interval, concerning the number of recorded events as well as the regions of the intensified frequencies and their power. The number of recorded events in liquid SnBi within the studied interval of 10 seconds is less than the corresponding number in water. It is evident that the generation frequency of bubbles (let us call this as bubbling frequency to distinguish it from the vibrational frequency induced by bubble generation) in liquid SnBi is much lower than the bubbling frequency in water. This is a consequence of the fact that gas injection in liquids with relatively high surface tension leads to the generation of a lower number of bubbles per unit of time.[52] By comparing the produced scalograms in Figure 5, variations are observed concerning the intensified frequency regions between the examined liquids. Single bubbles in liquid SnBi induce vibrations at a frequency range between 150 and 1100 Hz with most of the power to be distributed over the frequencies 150 to 350 Hz. In the case of water, the frequency response is located within almost same range, while the most power is distributed at higher frequencies, over 900 to 1200 Hz. As observed in the same figure, the vibrations differ also in the magnitude of the power which intensifies for the measurements in liquid SnBi. The enhanced intensity of the relevant phenomena in liquid SnBi as discussed earlier in this work resulted in a larger magnitude of the produced frequencies observed in Figure 5.
Since the induced vibrations in the examined liquids is a result of several consisting evolution events, it is imperative to discuss their time-frequency response individually. With the aid of the recordings of the installed camera, the signal originating from the relevant events was identified and examined for both liquids.
Bubble generation
As presented in Figure 6, the time-frequency response varies between liquid SnBi and water for the generation of a single bubble after argon injection at 0.01 L min−1. The variations concern the intensified frequency region, the magnitude of their power as well as the duration of the bubble generation event. The generation of a single bubble in liquid SnBi produces vibrations at low frequencies within 150 to 350 Hz, while in water the produced vibrations obtain significantly higher values at 900 to 1200 Hz. The density of the liquid as well as the bubble size are determining factors in the oscillating frequency of a bubble and therefore in the induced vibrations, where increased values of density and bubble size result in a lower vibrating frequency.[53] This relates to the variations in the respective frequency ranges for bubble generation in the two liquids. As mentioned previously, the magnitude of the power appears higher for the corresponding frequency response in liquid SnBi due to the intensified bubble generation event. In addition, the CWT analysis shows that the signal produced during the single bubble generation in liquid SnBi is significantly longer than this in water. This is attributed to the role of surface tension in bubble generation as discussed earlier in this work where the bubble generation is prolonged for liquids with higher surface tension. In addition, as observed in Figure 6(a), three distinct frequencies are produced during bubble generation in the liquid SnBi. To this point, we may assume that these frequencies reflect the three individual steps of bubble formation from nucleation to expansion-elongation and detachment. The intensified frequencies are exhibited in chronological order and with a particular duration which consists a good basis for the following interpretations. The first intensified frequency may correspond to the bubble nucleation which occurs as soon as the gas comes in contact with the liquid. The second intensified frequency appears longer and may be perceived as a result of the expansion and elongation of the bubble as more gas is supplied into the bubble increasing its volume. As observed in the scalogram (Figure 6(a)), this characterizing frequency has a longer duration which agrees with the prolonged duration of the expansion stage.[54,55] Following, the third intensified frequency comes during the final step of bubble formation. In this step, the bubble detaches from the nozzle after the sudden cutting of the neck formed during elongation.[54] Such detailed discussion is not feasible for water where the bubble formation happens in shorter times and no distinguished frequencies are clearly observed.
Bubble rise
As the bubble detaches from the nozzle it follows an upward motion due to the density difference between the bubble and the surrounding liquid resulting in a buoyancy force that lifts the bubble upwards. Variations are observed in the frequency of the induced vibrations as bubbled rise in the different liquids. The frequency response in water is characterized by high frequencies at 900 to 1000 Hz while in liquid SnBi the generated vibrational frequencies remain at low levels within 200 to 500 Hz. Monitoring with the camera revealed that the single bubbles that are formed when gas is injected at such a low flow rate do not undergo breakup or coalescence during the rise. This is in agreement with the References 56 and 57 suggesting coalescence and break-up events above certain flow rates. Therefore, the generated vibrational frequencies characterize the rise of the single bubbles oscillating at their natural frequency which is a function of the density of the liquid as well as the size of the bubble.[53] A relatively larger bubble rising in the volume of a liquid with higher density oscillates at a relatively lower frequency and therefore in liquid SnBi the induced vibrations are found at lower levels than those in water.
Bubble collapse
The mechanism of bubble collapse as soon as the bubble reaches the top surface of the molten metal is rather complex as described previously by Han et al.[58] As soon as a bubble collapses at the top surface, the entrapped pressurized air is released to the surroundings along with the emission of a gas jet and the formation of a vortex ring.[59] Surface tension and size of the collapsing bubble have been proven the determining parameters where an increase in these values results in higher traveling speeds for the gas jet and the vortex ring.[59,60] Thus, such variations in the collapse mechanism of bubbles of different sizes between liquids with different surface tension, influence the respective vibrational imprint. Especially bubble size is considered as of major importance in the characteristics of the produced vibrations while bubble collapse. The significantly enlarged size of the bubbles in liquid SnBi leads in larger contact area with the top surface of the liquid resulting in increased interaction and perturbations of the surface. It has been shown that the bubble collapse process in significantly influenced by the size of the bubbles which result in the propagation of waves both in horizontal and downward direction.[61] Thus the amplitude and frequency of such waves are a function of the bubble size reaching the top surface of the liquid. In addition, enhanced bubble size translates into increased volume of entrapped pressurized gas which releases upon collapse resulting in intensified disturbances of the surrounding area. Vibrations that are produced during bubble collapse in liquid SnBi are characterized by a higher frequency in the interval between 700 and 1100 Hz. On the other hand, the corresponding frequency interval for bubbles in water is found at a lower and narrower range between 500 and 600 Hz. The surface tension of the liquid and most important the size of the bubble and the relevant rationality bubble area/surface area contribute to the intensity and complexity of the bubble collapse at the top free surface of liquids influencing the produced vibrations. This is reflected in the obtained scalograms where the duration of the bubble collapse is prolonged for liquid SnBi and the frequencies cover a wider frequency region with enhanced power. To this point, the vibration analysis of the consisting mechanisms such as the formation of the vortex ring and the gas jet is not straight forward as elaborated previously in the vibration analysis of various steps during bubble formation. For bubble collapse, the individual steps occur almost simultaneously along with the generation of surface waves that travel towards the ladle wall. Thus, events are not presented in distinct chronological order which makes their interpretation rather unlikely.
Power spectrum
The vibrations were examined in the two liquids under the influence of the flow rate (Figure 8). At any of the injection rates in the case of liquid SnBi (Figure 8(a)), strong variations are observed in the power of the spectrum over the different intensified frequency regions while the power is distributed mostly over low frequencies of 150 to 400 Hz. This frequency region characterizes the bubble generation at the nozzle and thus bubble generation is the predominant event in the vibrations induced during bubble flow in liquid SnBi for all the examined flow rates. The power enhances with increasing gas flow rate over the spectrum as a result of the individual intensified bubble phenomena in the liquid. However, this pattern deconstructs to some extent for the gas injection at 0.15 NL min−1 where the power slightly decreases over 500 to 700 Hz and the peaks shift to slightly higher frequencies. In contrast, the power over low frequencies of 150 to 350 Hz does not increase significantly from the previous value and the peak remains at the same position. At such a flow rate, the generation of quasi-single bubbles which becomes more often, has an influence on the size of the formed bubbles which appears slightly decreased. Smaller bubbles which are occasionally generated, oscillate at higher frequencies which in turn shifts the vibrational frequencies to higher values. On the other hand, the slight decrease in size results in a corresponding decrease in power.
For water, the power is more evenly distributed over the produced frequency regions for all investigated flow rates as observed in Figure 8(b). Thus, the various aspects of bubble evolution contribute equally to the generated vibration signal at the examined flow rates. Similarly, as in liquid SnBi, the power of the spectrum in water increases with increasing flow rate. Irregularities are observed for argon injection at 0.15 L min−1 where the characterizing peak for bubble generation (900 to 1200 Hz) shifts to a slightly lower frequency. With the aid of the installed camera, it was observed that argon injection at 0.15 L min−1 in water resulted not only in the formation of single bubbles but also in larger bubbles which separate into two smaller ones right after the former leave the nozzle. The formation of a larger bubble at 0.15 L min−1 results in a slight decrease of the vibrational frequency of bubble generation as observed in Figure 8(b) as bubbles of larger size oscillate at lower frequencies.
The current work elaborates on the influencing role of the physical properties of liquids in the produced two-phase flow and further to the induced vibrations captured by accelerometers. The study has shown that size is predominant factor in the recorded vibrational intensity. Size is a crucial parameter of the bubble characteristics in the secondary refining processes where relatively smaller bubbles lead to enhanced efficiency of the interaction between the two phases.[62] Therefore the vibrational imprint of the bubbles should be carefully considered in the monitoring of stirring in secondary refining processes. It is expected that during gas injection in metal making ladles, the generated bubbles will undergo some degree of thermal expansion due to temperature gradients.[63] The large bubbles will continue growing at some growth-rate which has been shown to slow down after a rapid initial expansion.[64] Therefore, variations are expected in the corresponding vibrational intensity following the bubble size-vibrational amplitude dependence.
The current work brings to the fore important aspects in the vibration analysis of bubble evolution events influenced by the physical properties of liquids. This knowledge is perceived as valuable in physical modeling and process optimization and control in metal-making processes. The data presented in this study consist of a good basis for further research in the field and the construction of two-phase models for process optimization and control. The role of physical properties, flow rate, and bubble size is quite complex, while it is imperative to understand their influence on the induced vibrations of two-phase flows. Currently, more research is ongoing for the investigation of the influence of operating parameters such as flow rate, pressure, and type of plug in the vibrations induced from bubble evolution. In addition, vibration measurements are currently performed at an industrial ladle and will be correlated to vibration measurements at the LIMMCAST setup. Results will be presented in future publications.
Conclusions
In this work, to the author’s best knowledge, vibration measurements were examined for the first time for two common used modeling fluids of different physical properties; liquid SnBi and water. The measurements were performed with the exactly same measuring equipment and in the same setup (LIMMCAST) to accommodate the liquids.
The vibrations generated at comparable gas volume flows in liquid SnBi and water can be clearly distinguished from each other followed by variations in the signal amplitude and the frequency distribution. Variations in physical properties of liquids, especially surface tension and density influence the number and size of the produced bubbles affecting the bubble evolution and thus the induced vibrations. For single bubbles, the size is the predominant factor in the vibrational intensity of the evolved phenomena from bubble generation at the nozzle to rise within the liquid and collapse at the free surface. The increasing size of the low number of bubbles in liquid SnBi results in a linear increase of the vibrational amplitude with an increasing flow rate. Such a dependence is not observed in water where the increasing number of small bubbles cannot preserve the linearity, turning the relationship into a power law.
The process of bubble generation, the rise of the bubble and its bursting at the free surface can be well distinguished from each other in the signal. The stronger amplitudes obviously occur during generation/detachment and bursting at the free surface. The bubbling frequency as well as the characteristic frequency regions and the intensity of the evolved phenomena are a function of the size of the bubbles and the physical properties of the liquid. The larger size of bubbles in liquid SnBi along with the higher density of the liquid results in lower induced vibrational frequencies (\(150 {\text{Hz}}\le f\le 350 {\text{Hz}}\)) as they form. On the other hand, higher vibrational frequencies (\(900 {\text{Hz}}\le f\le 1200 {\text{Hz}}\)) were observed for the relatively smaller bubbles that generate in water. For bubble rise, the frequency response in liquid SnBi is located at relatively low frequencies \(200 {\text{Hz}}\le f\le 500 {\text{Hz}}\) while for water elevated frequencies are observed (\(900 {\text{Hz}}\le f\le 1000 {\text{Hz}}\)) owing to the decreased liquid density and bubble size.
Surface tension and size of the collapsing bubble have been proven the determining parameters in the bubble collapse mechanism. Increase in these values results in higher traveling speeds for the gas jet and the vortex ring, inducing vibrations in a larger range with higher upper limit. Identically, bubble collapse result in vibrations of a wide interval (\(700 {\text{Hz}}\le f\le 1100 {\text{Hz}}\)), while in water they are restricted at a lower and narrower region (\(500 {\text{Hz}}\le f\le 600 {\text{Hz}}\)).
Flow rate has an influencing role in the bubble size which in turn affects the induced vibrations during bubble evolution. The triangle physical properties-bubble size-operating parameters is rather complex and needs further investigations for understanding its influence on the vibrations while bubble evolution.
The findings of this study consist of a strong foundation in the interpretation of bubble evolution in liquids by means of vibration measurements. Data from this work may be used for the improvement of the two-phase flow models for optimization and control of metal-making processes.
Conflict of interest
The authors declare that they have no conflict of interest.
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