Flow-pattern identification and nonlinear dynamics of gas-liquid two-phase flow
in complex networks
Zhongke Gao and Ningde Jin
*
School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, People’s Republic of China
Received 22 November 2008; revised manuscript received 11 May 2009; published 4 June 2009
The identification of flow pattern is a basic and important issue in multiphase systems. Because of the
complexity of phase interaction in gas-liquid two-phase flow, it is difficult to discern its flow pattern objec-
tively. In this paper, we make a systematic study on the vertical upward gas-liquid two-phase flow using
complex network. Three unique network construction methods are proposed to build three types of networks,
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 by the community-detection
algorithm based on K-mean clustering, useful and interesting results are found which can be used for identi-
fying five vertical upward gas-liquid two-phase flow patterns. To investigate the dynamic characteristics of
gas-liquid two-phase flow, we construct 50 FDCNs under different flow conditions, and find that the power-law
exponent and the network information entropy, which are sensitive to the flow pattern transition, can both
characterize the nonlinear dynamics of gas-liquid two-phase flow. Furthermore, we construct FSCN and dem-
onstrate how network statistic can be used to reveal the fluid structure of gas-liquid two-phase flow. In this
paper, from a different perspective, we not only introduce complex network theory to the study of gas-liquid
two-phase flow but also indicate that complex network may be a powerful tool for exploring nonlinear time
series in practice.
DOI: 10.1103/PhysRevE.79.066303 PACS numbers: 47.55.Ca, 89.75.Fb, 05.45.Tp, 89.75.Da
I. INTRODUCTION
Gas-liquid two-phase flow very often exists in industrial
applications such as filtration, lubrication, spray processes,
natural gas networks, and nuclear reactor cooling. In the
study of two-phase flow, flow patterns indicate how the
phases are distributed and mixed due to the physical nature
of the system. Two-phase flow patterns depend on the type of
fluid-fluid combination, the flow rates and direction, and the
conduit shape, size, and inclination. Further, heat and mass
transfer rates, momentum loss, rate of back mixing, and pipe
vibration all vary greatly with the flow patterns. Hence, it is
quite important and necessary to discern the flow patterns
and study the nonlinear dynamics in different flow patterns.
The early studies were mostly based on direct observa-
tions. High-speed photography technique, x-ray attenuation
picture, and suchlike are some of the methods in which the
flow patterns are detected from direct observations. Although
these methods are inexpensive and, in most cases, easy to
perform, they are to a great extent subjective. Moreover the
major difficulty in direct observation, even using high-speed
photography, is that the picture is often confusing and diffi-
cult to interpret, especially when dealing with high velocity
flows. Furthermore, in order to increase the objectivity, indi-
rect methods were developed. Such methods mainly deal
with the fluctuating properties of two-phase flow, and the
fluctuations can be observed in the local pressure, the instan-
taneous two-phase mixture ratio, and suchlike. Rouhani and
Sohal 1, and Das and Pattanayak 2 pointed out that there
is a correlation between flow patterns and the fluctuation
characteristics of the two-phase flow properties. Hence, at-
tempts at the characterization of gas-liquid two-phase flow
patterns based on a combination of subjective judgments and
objective methods have been made. Hubbard and Dukler 3
calculated the power spectral density PSD for two-phase
pressure-drop signals. Jones and Zuber 4 and Vince and
Lahey 5 employed transient x-ray attenuation techniques,
and calculated the PSD and the probability density function
for chordal void fraction fluctuations. Zhang et al. 6 calcu-
lated Shannon entropy of two-phase flow systems from the
power spectral density. Daw and co-workers 7–9 inter-
preted experimental pressure-drop measurements from a
complex gas-solid flow system in terms of the methods for
chaotic time-series analysis, and discussed issues concerning
the reconstruction of attractors from experimental chaotic
time-series data using Taken’s method of delays.
In recent years, with the development of modern signal
processing techniques, there has been much progress in the
software measurement techniques. Mi et al. 10 applied a
neural network to two-phase flow pattern identification in a
vertical channel using signals from electrical capacitance
probes. Warsito and Fan 11 utilized a neural network-based
multicriterion optimization image reconstruction technique
for imaging multiphase flow systems from electrical capaci-
tance tomography. Yan et al. 12 identified the two-
component flow regimes using back-propagation networks.
Xiao et al. 13 established the general description method of
chaotic attractor morphological characteristic using refer-
enced sections, and put forward a new gas-liquid two-phase
flow pattern classification method by combining the chaotic
attractor morphological feature parameters of different di-
mensions. Although there has been some achievement in the
study of gas-liquid two-phase flow, in conditions close to a
transition between two patterns, detecting the flow pattern is
crucially difficult. Furthermore, due to the complex nature of
*
Corresponding author; ndjin@tju.edu.cn
PHYSICAL REVIEW E 79, 066303 2009
1539-3755/2009/796/06630314 ©2009 The American Physical Society 066303-1