Relationship between vibration and process parameters
Vibration RMS versus gas flow rate
In the nominal case, corresponding to the physical similarity with the industrial ladle (\(H_3\), presence of oil, two nozzles operating), the evolution of the vibration level of the eight sensors with respect to the gas flow rate is illustrated in Fig. 4.
As reported in the studies [10, 12, 13, 19, 20], the vibrations amplitude increases with the gas flow rate. The relationship between the vibration level and the gas flow rate is nonlinear, rather logarithmic. It is interesting to note that this shape is similar to the ones obtained in Ref. , although different geometries and materials are used in the physical model.
In Fig. 4, it can be clearly seen that the vibrations RMS values of the four accelerometers close to the nozzles, i.e., sensors 3, 4, 7, and 8 are significantly higher than the sensors which are diametrically opposed to them (1, 2, 5, and 6), respectively. In addition, they also increase faster with the gas flow rate than the opposite sensors. This indicates that the radial position of the sensors plays a major role in the measured vibration intensity.
The comparison between the top and bottom sensors which are close to the nozzles (3 vs 7 and 4 vs 8) shows that the vibrations amplitude in the top tends to be slightly stronger than the ones in the bottom.
In the other cases (\(H_1\) and \(H_2\), without oil, one nozzle operating), the results are similar; they are not reproduced here. Only the vibrations amplitude is different.
Vibration RMS versus water height
In the case where Q is fixed, and no oil layer is employed; the evolution of the vibration RMS values with respect to the water height is given in Fig. 5 for the bottom and top sensors.
It can first be seen that the vibrations of the bottom sensors tend to increase with higher water heights. This conclusion confirms the results obtained by Nadif et al. , where different experimental configurations with the same order of magnitude as those in the present work have been conducted. Regarding the top sensors, it is more difficult to distinguish any trend. It should be noted, however, that in the particular case \(H_1\), i.e., when the sensors are located above the free surface, the vibrations are much higher than those in the cases \(H_2\) and \(H_3\). Once the sensors are at the same level (\(H_2\)) or below the free surface (\(H_3\)), the vibrations drop. Since the height difference between \(H_2\) and \(H_3\) is quite small, the vibrations amplitude seems to be hardly affected by a small water height change.
By comparing the case \(H_1\) between top and bottom sensors in Fig. 5, it can be further noticed that the signals measured by the top accelerometers are 30–90% higher than those measured by the bottom ones, even if they are relatively far from the gas plumes (e.g., diametrically opposed). This has been observed for all gas flow rates and nozzle configurations employing \(H_1\), including the case where the oil layer is added.
It is still an open question why the sensors located above the free surface have these higher vibrations levels. Unlike the bottom sensors, they are not facing the fluid and are subjected only to free vibrations of the structure. One possible reason could be that they are less dampened than the bottom sensors, leading to stronger vibrations amplitude.
These cases suggest that the vibrations amplitude strongly depends on the vertical position of the sensors relatively to the water height. In order to only capture stirring-related vibrations, it is recommended to place the sensors in the height of the bath rather than above the free surface level, i.e., along the gas plumes, between the ladle bottom, and the open eyes.
Vibration RMS versus presence of oil layer
Figure 6 illustrates the vibrations intensity with and without oil layer, in the nominal configuration.
It can be observed that the top sensors are slightly more sensitive to the slag height than the bottom sensors, although this is not significant. More generally, as it has also been seen in the other configurations, the vibrations tend to slightly increase in the presence of the oil layer. Since this increase is not significant when the oil height is increased from 0 to 3 cm, small fluctuations of oil heights would be even more difficult to capture in the vibrations measurements. Even if, in industrial practice, the slag is much thicker and heavier than the parameters used in this experiment, thanks to the physical similarity, the same conclusion might be applicable for industrial vibrations measurements.
Detection of nozzle clogging using several sensors
Sensors close to nozzles
Since the previous results have shown that the strongest vibration intensity is obtained with the sensors close to the two gas plumes, only these four sensors are considered here: 3 and 7 (SW-top and SW-bottom) and 4 and 8 (NW-top and NW-bottom). Figure 7 shows the difference between the three operating conditions: both nozzles SW and NW, nozzle SW only, and nozzle NW only.
Interestingly, one can notice that the vibrations of the sensors SW (respectively, NW) in the case where only nozzle SW (respectively, NW) operates are very similar to their level when both nozzles operate simultaneously. In other words, the vibrations close to one nozzle (e.g., SW) seem to be relatively independent from the operating condition of the other nozzle (e.g., NW). This is an important result, since it makes it easier to distinguish the operating conditions of the two nozzles, by using (at least) one sensor close to each nozzle, or, in other words, close to each gas plume.
Furthermore, the vibrations amplitude of sensors 4 and 8 (NW-top and NW-bottom), when the nozzle NW operates, is close to the one of the sensors 3 and 7 (SW-top and SW-bottom) when the nozzle SW operates, at equivalent flow rates.
The differences of RMS amplitudes between the three operating configurations are computed in Table 4. It can be seen that the nozzle clogging results in a significant drop of the RMS value (\(-\,36\) to \(-\,59\%\)) of the sensors located close to the clogged nozzle, in comparison with its value where both nozzles work normally. Except for low flow rates, the vibrations of the sensors close to the operating nozzle are not affected very much by the clogging of the second nozzle and the absence of its corresponding gas plume (less than 10% change, for gas flows superior to 15 L/min). With low flow rates, the clogging of one nozzle results in a perceptible drop in the vibration intensity of the sensors close to the operating nozzle.
If only one sensor was used to detect the clogging of a nozzle among several ones, it would have been difficult to identify the reason for a vibration drop: decreasing stirring intensity of the one nozzle (e.g., gas leakage) or the clogging of the other. Using several sensors can be, in this regard, more advantageous.
Note about other sensors
Finally, another interesting result, which is related to the four sensors diametrically opposed to the gas plumes and visible in Fig. 8, shows that the vibration levels of all of them can significantly decrease (up to 30%) when only one nozzle is operating, in comparison with the case with two working nozzles. Although their vibration level always remains lower than those of the four sensors close to the gas plumes, this result can be useful in practice: using a third sensor located far from the gas plumes can give an additional hint on the operating conditions of the nozzles.