Recurrence networks from multivariate signals for uncovering dynamic transitions of horizontal oil-water stratified flows

Characterizing the mechanism of drop formation at the interface of horizontal oilwater stratified flows is a fundamental problem eliciting a great deal of attention from different disciplines. We experimentally and theoretically investigate the formation and transition of horizontal oil-water stratified flows. We design a new multi-sector conductance sensor and measure multivariate signals from two different stratified flow patterns. Using the Adaptive Optimal Kernel Time-Frequency Representation (AOK TFR) we first characterize the flow behavior from an energy and frequency point of view. Then, we infer multivariate recurrence networks from the experimental data and investigate the cross-transitivity for each constructed network. We find that the cross-transitivity allows quantitatively uncovering the flow behavior when the stratified flow evolves from a stable state to an unstable one and recovers deeper insights into the mechanism governing the formation of droplets at the interface of stratified flows, a task that existing methods based on AOK TFR fail to work. These findings present a first step towards an improved understanding of the dynamic mechanism leading to the transition of horizontal oil-water stratified flows from a complex-network perspective. Copyright c © EPLA, 2013 Introduction. – Horizontal oil-water two-phase flow is frequently encountered in many industrial processes and the interest in them has greatly increased recently mainly due to the petroleum industry [1,2]. When oil and water flow in a horizontal or slightly inclined pipe, there exist particular flow conditions for which the two immiscible phases are separated from each other by a continuous smooth or wavy interface. For a fixed water flow rate, when the oil flow rate is low, the interface is smooth or may be rippled by very small capillary waves, i.e., stratified (ST) flow pattern occurs. With an increase of the oil flow rate, interfacial waves gradually appear. When the oil flow rate is high, droplets can be formed from the interfacial waves, i.e., an onset of a stratified flow with mixing at the interface (ST&MI) pattern is formed. Note that the horizontal oil-water dispersed flow patterns, including a dispersion of oil in water and water flow pattern and a dispersion of water in oil and oil in water flow pattern, evolve from the ST&MI flow pattern. The investigation on the dynamic transitions from a ST flow pattern to a ST&MI flow pattern can yield deeper insights into the mechanism governing the formation of droplets, which is very crucial for understanding the formation and transition of horizontal oil-water dispersed flow patterns. Therefore, the study of ST flow and ST&MI flow is of paramount importance. Distinct horizontal oil-water flow patterns have been observed [3,4] and the characterization of oil-water flows has attracted much attention from physical and chemical research fields. Numerical simulations [5], wavelet multiresolution technique [2] and theoretical models [6,7] have been employed to study experimental horizontal oil-water twophase flows. But compared to the study of gas-liquid flows, works particularly dedicated to the investigation of horizontal stratified flows are quite limited. In addition, the mechanism of drop formation at the interface of horizontal oil-water stratified flows is still elusive. Therefore, it