Complexity Analysis Of Gas-Liquid Two-Phase Flow Structure

The two-phase/multi-phase flow is widely encountered in nature and in industrial applications such as beer transportation, well drilling and nuclear reactor cooling, etc. The two-phase/multi-phase flow exhibits the characters of diversity, unsteady and complexity owing to the local relative movements between gas and liquid phase, and the phase interfacial interaction. Therefore, the two-phase/multi-phase flow is the most challenging subject in all thermodynamic subjects. So far there has been no satisfactory understanding of the underlying dynamics leading to the formation and governing the evolution of the two-phase/multi-phase flow structures. As a growing number of two phase flow pro blems unresolved in actual engineering applications, a new theoretically method is strongly required to detect and describe the different flow structures and their nonlinear dynamics including their complexity from the perspective of new theories and modern information processing tools. Entropy, which provide us with a new viewpoint and an effective tool for understanding a complex system like the two-phase flow from the law of systematic motion, not only may be a powerful tool for revealing the evolvement rules of the complex behaviors of the flow systems, but also can be used for exploring the complexity of the inner structure of nonlinear systems. In this thesis, we focus our research on the horizontal gas- liquid two phase flow. Based on the global and local conductance signals measured from horizontal multi-electrode array sensor and mini-conductance probes, we propose and construct different entropy measures, i.e. multiband spectral entropy, multiscale spectral entropy and two statistical complexity models for two-phase flow. Furthermore, through investigating the different gas-liquid two-phase entropy measures and statistical complexity, we make a systematic study on the complexity of two-phase flow. The effectivenesses of the entropy measures proposed a nd statistical complexity models for two-phase flow are to be demonstrated and their applicabilities are articulated. The creative points of this thesis are as follows:(1) We use a new method called ―the 0-1 test‖, without constructing the phase space, to detect the presence of chaos in the signals measured from experimental gas-water two-phase bubble flow, plug flow and slug flows, respectively. The results show that there exist chaos in the three flow regimes under study and a strong randomness is also reserved in the bubble flow. These results will provide the theoretical basis for complexity analysis of two-phase flow.(2) We propose an entropy measure, i.e., multiband spectral entropy, for structural complexity analysis of two-phase flow. Take some typical nonlinear systems, e.g. Logistic map, white noise, 1/f noise and Sine signals, for example, tests the effectiveness of multiband spectral entropy for analysis structural complexity of a system and the result is fine. Through detecting the structural complexity of gas-water two-phase wavy flow, plug flow and slug flow by multiband spectral entropy, we find the frequency structure and power spectrum of the two-phase flow vary with the change of the frequency factor,and the multiband spectral entropy can better reveal the structural complexity of two-phase flow. Moreover, the average value of multiband spectral entropy in the frequency range from 0 to 8.3Hz presents good identification of gas- liquid two-phase flow pattern, which can be taken as a new rule of flow pattern identification.(3) We propose a new entropy measure based coarse graining method and FFT, i.e., multiscale spectral entropy, to track the complexity variation of the two-phase flow with the changing scale factor in frequency domain. Firstly, the reliability and validity of multiscale spectral entropy are tested by Logistic map, white noise, Henon map and composite Sine signal respetively. Based on above study, multiscale spectral entropy is used to investigate the multiscale complexity of bubble flow, plug flow and slug flow respectively in frequency domain. Compared with the wave energy entropy and IMF energy entropy based on EMD decomposition, multiscale spectral entropy value can reflects the differences between various flow patterns, especially for the plug flow and slug flow which can not be separated by wave energy entropy and IMF energy entropy. The multiscale spectral entropy provides a new approach for uncovering the complexity of different flow patterns in two-phase flow.(4) We put forward two statistical complexity models for two-phase flow through combining the new statistical complexity measures proposed in the thesis with the permutation entropy and Tsallis entropy repectively. Take the Logistic map as example, we first demonstrate the effectiveness and tatistic analysis capability of the two statistical complexity models proposed, and the results from two statistical complexity models are consistent and show higher sensitivity to the changes of non- linear dynamics characteristics of Logistic map with different value of parameter?which ranges from 3.5 to 4 Then the two statistical complexity models are applied to calculate the statistical complexity of bubble flow, plug flow and slug flow respectively. The results show that the interphase forces on the propagation including wall shear stress, virtual mass force and drag force affect the nonequilibrium of two-phase flow, which lead to lower statistical complexity of bubble flow and the highest statistical complexity value of slug flow, although bubble flow presents higher permutation entropy and Tsallis entropy than those of plug flow and slug flow. The results agree with the fact that slug flows have strong shocks and destructive in the actual industrial production, which also verify the reliability of statistical complexity models for two-phase flow. In addition, we find the statistical complexity model based on Tsallis entropy has higher statistical analysis capacity than that of the statistical complexity model based on permutation entropy and is more suitable for practical application. Our results suggest that the statistical complexity model based on Tsallis entropy can potentially be a powerful tool for quantitative measuring the complexity of the two phase flow.