1. Introduction
Rectangular channels (RCs) with high heat-transfer efficiency and small size have been widely used in small reactors [
1], compact heat exchangers [
2], and various electronic products [
3]. In particular, the gas–liquid two-phase mixing process in rectangular channels involves chemical engineering [
4], power engineering [
5], etc. Taking the bottom-blow reactor as an example, the mixing state quality of the gas–liquid two phases is closely related to the evolution of the flow patterns. The gas–liquid two-phase flow characteristics are very complicated, due to different gas–liquid mixing modes, different working media, and various intake volumes. Accurate identification of gas–liquid two-phase flow patterns in rectangular channels is not only a basis for obtaining flow parameters, but also directly affects the analysis results of the resistance properties and the heat and mass-transfer properties of the two-phase flow in rectangular channels. In industrial production, some flow patterns not only greatly reduce production efficiency, but even cause serious harm to equipment [
6]. Therefore, the investigation of two-phase flow-pattern identification in rectangular channels is of great significance for understanding the heat-transfer mechanism in rectangular channels and ensuring the safe and efficient operation of relevant industrial production systems.
The many approaches to flow-pattern identification can be divided into direct observation and indirect measurement, according to various applicable principles [
7]. Direct observation usually adopts a direct convection type, such as a high-speed camera or an X-ray machine, for shooting observation and identification [
8,
9]. For instance, using a high-speed camera, Schmid et al. obtained a flow pattern map for the adiabatic two-phase flow of carbon dioxide in a vertical upward and downward direction [
10]. Cely et al. studied and characterized the gas–liquid slug flow in an annular duct using a high-speed video camera, a wire-mesh sensor, and particle image velocimetry [
11]. Skjæraasen et al. studied the measurement of thin liquid films in a gas–liquid pipe flow via X-ray [
12]. Azizi et al. investigated bubble column hydrodynamics using ultrafast X-ray computed tomography and radioactive particle tracking [
13]. The above studies found that fluid motion can be accurately captured by high-speed cameras, as the information obtained is very rich. However, this depends on the fluid being in transparent containers. In addition, an X-ray machine can be used to scan the gas–liquid mixing process, and the measurements are accurate. However, the identification of flow-pattern has higher requirements on an experimental platform.
Compared with this direct method, the indirect measurement method is more widely used, especially in the industrial production process, which does not require direct observation of flow patterns in most cases. The indirect measurement method obtains signals such as capacitance [
14], pressure [
15], temperature [
16], and capacitance [
17] that can be easily measured, and indicate characteristics of different flow patterns by combining signal-processing technology. Then, the flow pattern or mixing state can be classified and recognized according to these characteristics. For instance, Guo et al. proposed a novel method based on temperature fluctuation for identifying the gas–liquid flow pattern [
18]. Oliveira et al. investigated the fluctuations and characteristic frequencies of pressure drop and flow pattern during the flow boiling of isobutane [
19]. Perera et al. measured the flow pattern of oil–water mixtures noninvasively by capacitance tomography [
20]. The indirect measurement method has a large number of potential engineering applications. However, different industrial scenarios require different measurements. Rectangular channels or, more specifically, bottom-blow reactors, are more difficult to identify because of the impact of application scenarios, sizes, and intake volumes.
With the recent development of computer science, machine learning algorithms have been widely applied with good classification ability [
21,
22]. In fact, machine learning can be combined with indirect measurement to identify flow patterns quickly. For instance, Zhang et al. studied the identification of oil–gas two-phase flow patterns based on machine learning and electrical capacitance tomography [
23]. Sestito et al. classified two-phase flow patterns based on frequency-domain features by machine learning-based classifiers [
24]. Amirsoleymani et al. explored two-phase flow-pattern identification in compressed air energy storage systems via dimensional analysis coupled with machine learning [
25]. All of the above studies confirmed the reliability of machine learning for flow-pattern recognition. In particular, some machine learning algorithms provide many advantages for small-size samples or nonlinear patterns and, thus, are among the first choices for flow pattern recognition.
It is worth mentioning that various gas–liquid mixing scenarios can result in various measurements, time series, or signals (see
Table 1). With an appropriate method or model, flow patterns can be accurately identified from these signals. Furthermore, the quantized characteristic parameters can be used as the basis for flow pattern judgment. However, the characteristic parameters of different flow patterns still overlap to some extent, and there is some subjectivity and uncertainty in flow pattern recognition. Feature extraction based on measurements, time series, or signals, combined with machine learning to identify flow patterns quickly and accurately, is urgently needed in engineering research. Liang et al. developed a new joint-probability density function of air density and wind speed [
26]. Meng et al. analyzed the periodicity and frequency of an interfacial wave by power spectral density (PSD) [
27]. Nnabuife et al. attained objective flow-regime identification using spectral features and a support vector machine (SVM) [
28]. However, to date, there is no mature theory to describe flow-pattern recognition on the basis of the conductivity measurements in rectangular channels.
Inspired and motivated by all of the above studies, in this work, the issue we needed to address was how to identify and classify the various flow patterns simply and accurately with characteristic parameters of electrical conductivity measurements of the gas–liquid mixing process in rectangular channels. Accordingly, the aim of this work is to propose a two-phase flow-pattern recognition model or framework combining the time-domain and frequency-domain characteristics and a support vector machine. In fact, a unqualified flow pattern not only greatly reduces production efficiency, but also causes serious harm to equipment. This investigation on gas–liquid two-phase flow-pattern identification is of great significance for understanding the heat-transfer mechanism in rectangular channels and ensuring the safe and efficient operation of relevant industrial production systems. The contribution of this work is two-fold. First, using flow data analysis, this article responds to a number of current growing needs for the in-depth mining of sensor data. It provides a systematic solution for the integrative analysis of conductivity measurements, as the electrical conductivity and the flow images were measured and obtained instantaneously. Thus, the subjective experience of operators can be avoided as much as possible for flow-pattern recognition in rectangular channels. Second, this study used a classification methodology to provide a novel and broad framework for combining a feature vector reflecting time–frequency characteristics with a support vector machine. A large number of models and extensions are potential outcomes within this framework, as several signals—such as conductivity, temperature, and pressure in industrial processes—can be input into the algorithms proposed in this work. Hence, the universality of this work can provide a demonstration for various investigators in related fields, including multiphase flow.
The rest of this paper is organized as follows. In
Section 2, the gas–liquid two-phase mixing experiment in rectangular channels and the data analysis method for conductivity measurements are described. In
Section 3, the main results and discussions of gas–liquid flow-pattern identification in rectangular channels are provided. In
Section 4, concluding remarks are presented.
4. Conclusions
In this work, the gas–liquid mixing process in the rectangular channel was measured, and the flow pattern images and conductivity measurements of the bubble flow, the slug flow, and the mixed flow were obtained. The time-domain and frequency-domain characteristics of the conductivity measurements were analyzed by the probability density function and power spectral density. The feature vector describing the flow pattern in the rectangular channel was constructed by introducing characteristic parameters. The classification and recognition of gas–liquid two-phase flow patterns in the rectangular channel was realized by using a support vector machine, and good results were obtained. The main conclusions can be summarized as follows: (1) The relationship between the gas–liquid flow patterns and electrical conductivity in the rectangular channel was discussed in detail. The bubble flow, the slug flow, and the mixed flow were measured in different conductivity while passing through the conductivity sensor. The evolution of the flow pattern could be qualitatively analyzed by observing the fluctuation of the conductivity measurements. (2) The probability density function and power spectral density were used to process the conductivity measurements of the gas–liquid two-phase mixing process in the rectangular channel for the first time. The five-dimensional feature vector describing the flow pattern was constructed by introducing feature parameters, including , , , , and . (3) Two time-domain feature parameters and three frequency-domain feature parameters were used as the feature vectors of the flow patterns for training and identifying by the support vector machine. The recognition accuracy of the bubble flow was 100%, and the overall recognition accuracy was 93.33%, showing that the recognition accuracy of this model is reliable. (4) The proposed flow-pattern-recognition framework, combining conductivity measurements and the support vector machine, has the advantages of simplicity, accuracy, and universality for rectangular channels. In fact, the generality of the model and the approach would be extended via extracting the other essential features of different flow patterns in rectangular channels by capturing other signals, including pressure, temperature, and resistance.