A two-state Markov chain model for slug flow in horizontal ducts
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Intermittent flows are common flow patterns in gas?liquid horizontal flow and attract attention and great research effort due to its importance for industrial and engineering applications. The slug flow is typically modelled based on a unit cell varying from an elongated air bubble with a liquid film in segregated flow pattern and an aerated liquid plug, the slug region, with remarkable stochastic characteristics of its alternating regions. In this paper, a two-state Markov chain model is proposed to represent the stochastic dynamics of developed slug flow in horizontal pipes. Each state represents either the liquid slug or the elongated bubble regions and the transition probabilities dictate the change of the given discrete time measurement to stay at a given state or change. This simple but insightful description of the phenomenon allows an analytical treatment of the statistics of Markov chain stochastic process. Measurement stations with two double wire resistive sensors are used to obtain the void fraction time series and a corresponding two-state representation. Each state is classified by a threshold defined by an unsupervised and non-parametric pattern recognition approach. The state transition matrix is then estimated for each corresponding experimental point. Thus random samples can be synthetically regenerated with the same statistical features of the corresponding measurements. It is shown that the Markov chain model can successfully represent second-order statistics of the measurement, such as the autocorrelation and power spectral density, given an appropriate choice of the chain order. Moreover, a cross correlation-based time delay estimation is proposed for the two-sensor measurement station and additional information is obtained from the slug flow. Subsequently, statistics of some slug flow features are estimated using the proposed approach and their interpretation as random variables derived from the void fraction stochastic process is discussed.