Nonlinear Analysis of Gas-Water/Oil-Water Two-Phase Flow in Complex Networks (SpringerBriefs in Applied Sciences and Technology)

Understanding the dynamics of multi-phase flows has been a challenge in the fields of nonlinear dynamics and fluid mechanics. This chapter reviews our work on two-phase flow dynamics in combination with complex network theory. We systematically carried out gas-water/oil-water two-phase flow experiments for measuring the time series of flow signals which is studied in terms of the mapping from time series to complex networks. Three network mapping methods were proposed for the analysis and identification of flow patterns, i.e. Flow Pattern Complex Network (FPCN), Fluid Dynamic Complex Network (FDCN) and Fluid Structure Complex Network (FSCN). Through detecting the community structure of FPCN based on K-means clustering, distinct flow patterns can be successfully distinguished and identified. A number of FDCN’s under different flow conditions were constructed in order to reveal the dynamical characteristics of two-phase flows. The FDCNs exhibit universal power-law degree distributions. The power-law exponent and the network information entropy are sensitive to the transition among different flow patterns, which can be used to characterize nonlinear dynamics of the two-phase flow. FSCNs were constructed in the phase space through a general approach that we introduced. The statistical properties of FSCN can provide quantitative insight into the fluid structure of two-phase flow. These interesting and significant findings suggest that complex networks can be a potentially powerful tool for uncovering the nonlinear dynamics of two-phase flows. Acknowledgments 5 Contents 6 Nomenclature 8 Abstract 11 1 Introduction 12 References 14 2 Definition of Flow Patterns 18 2.1...Vertical Upward Gas-Water Flow Patterns 18 2.2...Horizontal Gas-Water Flow Patterns 19 2.3...Inclined Oil-Water Flow Patterns 21 2.4...Vertical Upward Oil-in-Water Flow Patterns 21 References 22 3 The Experimental Flow Loop Facility and Data Acquisition 23 3.1...Vertical Gas-Water Two-Phase Flow Experiment 23 3.2...Horizontal Gas-Water Two-Phase Flow Experiment 25 3.3...Inclined Oil-Water Two-Phase Flow Experiment 25 3.4...Vertical Upward Oil-Water Two-Phase Flow Experiment 32 References 33 4 Community Detection in Flow Pattern Complex Network 34 4.1...Community Detection in Gas-Water Flow Pattern Complex Network 34 4.1.1 Flow Pattern Complex Network 34 4.1.2 Flow Pattern Identification in Flow Pattern Complex Network 37 4.2...Community Detection in Oil-Water Flow Pattern Complex Network 40 References 42 5 Nonlinear Dynamics in Fluid Dynamic Complex Network 44 5.1...Gas-Water Fluid Dynamic Complex Network 44 5.1.1 Construction of Fluid Dynamic Complex Network 44 5.1.2 Network Degree Distribution and Its Physical Implications 46 5.1.3 Network Information Entropy 50 5.1.4 Nonlinear Dynamics of Gas-Water Two-Phase Flow in FDCN 51 5.2...Oil-Water Fluid Dynamic Complex Network 52 References 55 6 Gas-Water Fluid Structure Complex Network 56 6.1...Phase-Space Complex Network from Time Series 56 6.2...Fluid Structure of Gas-Water Flow in Fluid Structure Complex Network 69 References 70 7 Oil-Water Fluid Structure Complex Network 72 References 79 8 Directed Weighted Complex Network for Characterizing Gas-Liquid Slug Flow 81 8.1...Methodology 81 8.2...Characterizing Chaotic Dynamic Behavior in Slug Flow 85 References 91 9 Markov Transition Probability-Based Network for Characterizing Horizontal Gas-Liquid Two-Phase Flow 92 9.1...Methodology 92 9.2...Dynamical Characterization of Horizontal Gas-Liquid Flow Patterns 96 References 99 10 Recurrence Network for Characterizing Bubbly Oil-in-Water Flows 101 10.1...Recurrence Network Analysis of Time Series from Dynamic System 101 10.2...Dynamic Characterization of Flow Patterns 105 References 108 11 Conclusions 109 Front Matter....Pages i-xiii Introduction....Pages 1-6 Definition of Flow Patterns....Pages 7-11 The Experimental Flow Loop Facility and Data Acquisition....Pages 13-23 Community Detection in Flow Pattern Complex Network....Pages 25-34 Nonlinear Dynamics in Fluid Dynamic Complex Network....Pages 35-46 Gas-Water Fluid Structure Complex Network....Pages 47-62 Oil-Water Fluid Structure Complex Network....Pages 63-71 Directed Weighted Complex Network for Characterizing Gas-Liquid Slug Flow....Pages 73-83 Markov Transition Probability-Based Network for Characterizing Horizontal Gas-Liquid Two-Phase Flow....Pages 85-93 Recurrence Network for Characterizing Bubbly Oil-in-Water Flows....Pages 95-102 Conclusions....Pages 103-103