Evolution of High-Viscosity Gas–Liquid Flows as Viewed Through a Detrended Fluctuation Characterization
2.1. Test Apparatus
3. Results and Discussion
3.1. Pressure Response
3.2. Spectral Evolution of the Flow
3.3. Detrended Fluctuation Analysis (DFA)
- : The fluctuations are anti-correlated.
- : The fluctuations are uncorrelated and represent noise; i.e., white noise.
- : The fluctuations have positive autocorrelation.
- : The fluctuations represent noise; i.e., pink noise.
- : The fluctuations are non-stationary.
- : The fluctuations represent noise; i.e., Brownian noise.
- The pressure drop exhibits a space-wise evolution. It may be caused by local variations of the phase volume fractions, which take place as the mixture evolves downstream along the pipe. For example, consider the flow produced with (0.005 kg/s, 1.3 kg/s) (upper most squares of columns 1, 4 and 7 of the table). The pressures appear to be autocorrelated except at the downstream section.In other words, the pressure measured at P1 corresponds to the pressures measured at P2 and P3, the three being in-phase because (positive autocorrelation). On the downstream section, however, the pressure measured at P4 does not correspond to any of the measurements at P1, P2 or P3. Hence, three possibilities arise: a) the coherence may be lost to the strong effects induced by the ejection of irregular liquid lumps at the outlet, b) secondary flows at the U-turn may have a disruptive effect on the properties of the pressure waves, and c) a combination of the two. The reason for these possibilities is that the U-turn and the outlet are the only two points in the flow system where the two following effects can take place: secondary flows due to the centripetal acceleration undergone by the flow inside the U-turn section, and the sudden depressurization caused by the ejection of the liquid slugs into the separator tank.
- Apparently, very few flows exhibit white noise characteristics or non-stationary fluctuations. The former are more related with higher liquid and gas flow rates, while the latter are more related with low and high liquid .The non-stationary cases represented by are interesting, because they indicate that the mean values of the pressures are varying with time (or equivalently with position). Even though these variations might be slight, the method is still capable of identifying them. This opens up the prospect of designing techniques for industrial applications. Obvious examples would be the development of methods to detect small leakages in pipelines, or to detect slow corrosion processes.
- It is worth noticing that pink noise processes are mostly observed at the outlet section of the pipe. In general, the values of this section appear to show a relative increase with respect to the values of the inlet section. This suggests that the scaling exponent increases in the direction of the flow.Since pink noise refers to scalability, the reproduction of self-similar patterns and small scale traits of the signal would suggest the existence of an energy distribution process (analogous to the energy cascade in turbulence). However, it is noted that only the cases corresponding to the inlet flow rates (0.005 kg/s, 4.9 kg/s) and (0.01 kg/s, 6.1 kg/s) maintain this behavior. On the other hand, only the flow combination (0.005 kg/s, 6.1 kg/s) seems to correspond to this process in the U-turn. Overall, from the physical point of view, these characteristics would be mostly related with the ejection effects produced at the outlet of the pipe.
- Interestingly, not a single combination of inlet gas–liquid flow rates produced fully random processes in this kind of flow system. The question still remains whether such Brownian noise patterns would eventually emerge in a longer pipeline, or not. The same question could be asked regarding the flow rates.Anti-correlated flows for which seem to dominate in the U-turn section of the pipe. This is particularly true with high flow regimes, that is, those produced with elevated inlet mass flow rates. Similar anti-correlations are also observed at the inlet and outlet section of the pipe with high flow rates. These cases indicate that the phases of the pressure waves shift by approximately radians, as they progress from one pressure port to the next one.
Conflicts of Interest
|i, k, n||dummy indices|
|N||number of data points|
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|Interfacial Tension |
|Glycerine||1.1||1.2 × 10||6.3 × 10|
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Hernández, J.; Galaviz, D.F.; Torres, L.; Palacio-Pérez, A.; Rodríguez-Valdés, A.; Guzmán, J.E.V. Evolution of High-Viscosity Gas–Liquid Flows as Viewed Through a Detrended Fluctuation Characterization. Processes 2019, 7, 822. https://doi.org/10.3390/pr7110822
Hernández J, Galaviz DF, Torres L, Palacio-Pérez A, Rodríguez-Valdés A, Guzmán JEV. Evolution of High-Viscosity Gas–Liquid Flows as Viewed Through a Detrended Fluctuation Characterization. Processes. 2019; 7(11):822. https://doi.org/10.3390/pr7110822Chicago/Turabian Style
Hernández, J., D. F. Galaviz, L. Torres, A. Palacio-Pérez, A. Rodríguez-Valdés, and J. E. V. Guzmán. 2019. "Evolution of High-Viscosity Gas–Liquid Flows as Viewed Through a Detrended Fluctuation Characterization" Processes 7, no. 11: 822. https://doi.org/10.3390/pr7110822