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分数阶微积分理论及其在两相流中的应用研究
The Theory of Fractional Calculus And Its Application in Two Phase Flow
【作者】 李丽;
【导师】 樊春玲;
【作者基本信息】 青岛科技大学 , 控制科学与工程, 2016, 硕士
【摘要】 气液两相流广泛存在于各种科学应用研究领域以及工业生产过程当中。两相流的流型及其动力学特性严重影响着两相流动的传热传质速率、动量损失和压力梯度等参数。通常,采用电导波动信号的特征来判断流型,而电导波动信号的采集会受管道振动等多种因素的干扰影响,因此在研究两相流流型前需要对采集的信号进行滤波处理。采用基于分数阶Fourier变换(Fractional Fourier Transform,FRFT)的分数阶小波变换(Fractional Wavelet Transform,FRWT)理论,对气液两相流信号进行去噪分析。FRWT将传统小波变换的多分辨率分析理论推广到分数阶Fourier域。利用分数阶阶数的灵活性,实现对气液两相流信号更加有效地去噪。流型识别方面,将希尔伯特-黄变换(Hilbert-Huang Transform,HHT)理论与分数阶Hilbert变换(Fractional Hilbert Transform,FHT)方法相融合,利用HHT理论中的EMD分解方法处理信号,得到不同尺度上的IMF分量,对不同流型的的IMF分量做多个阶数上的FHT分析,完成对气液两相流的流型识别。利用分数阶相对熵与符号动力学相结合的方法研究气液两相流不同流型的动力学特性。熵在两相流流行研究方面已经得到广泛的应用,而分数阶熵在流型分析上的几乎未涉及。由于传统的相对熵在反映流型的动力学行为时的效果并不理想,本文通过多个阶数上的符号化相对熵的分布变化规律,研究了流型的分数阶符号化相对熵及其演化机理,为进一步理解流型的动力学特性提供了新思路。
【Abstract】 Gas liquid two phase flow widely exists in all kinds of scientific application research field and industrial production process. The flow patterns and their dynamic characteristics of two phase flow seriously affect the heat and mass transfer rate,momentum loss and pressure gradient of the two phase flow. In general, the flow pattern is determined by the characteristics of the differential pressure fluctuation signal, but the acquisition of pressure fluctuation signal can be influenced by many factors, such as pipe vibration. Therefore, the collected signal is filtered and processed in the study of two phase flow regime.The theory of fractional wavelet transform which based on fractional fourier transform is used to make denoising analysis on the signal of gas-liquid two-phase flow.The multi-resolution analysis theory of traditional wavelet transform is generalized to the fractional fourier domain by FRWT. By using the flexibility of the fractional order, the denoising for the signal of gas liquid two phase flow is realized more effectively.In the aspect of flow pattern recognition, making a fusion of Hilbert-huang transform theory and fractional Hilbert transform method, the IMF component is obtained at different scales by using the EMD decomposition method in HHT theory to process the signal.Then making multi order FHT analysis on the IMF component of different flow patterns, in order to complete flow pattern recognition of gas liquid two phase flow.Dynamic characteristics of different flow regimes of gas liquid two phase flow are studied by the method of combining fractional order relative entropy and symbolic dynamics. Entropy has been widely used in the research of two phase flow, but the fractional order entropy is almost not involved in the flow pattern analysis. The traditional relative entropy is not ideal to reflect the dynamic behavior of flow regime.This paper studies on fractional flow symbolic relative entropy and its evolution mechanism by the change law of symbolic relative entropy of multiple orders, provides a new idea for further understanding of the dynamic characteristics of flow pattern.