离心压缩机叶轮旋转失速的相空间重构及分形特征

结合非线性动力学中的相空间重构和分形理论,提出了一种分析离心压缩机叶轮旋转失速动力学特征的方法.采用数值方法对低速离心压缩机(LSCC)叶轮旋转失速状态进行了模拟,得到了失速工况下叶轮出口多个位置的气流压力时间序列.对各压力时间序列进行相空间重构,构造出一低维动力系统,其时间延迟和嵌入维数通过运用C-C方法得出.对重构的动力系统的相图进行了分形特征分析,计算了相应的分形维数.研究表明:叶轮旋转失速后系统的压力信号具有混沌特性,在相图上表现为具有分形结构,揭示了旋转失速后系统的动力学特征.计算分析分形维数后发现,数据采集点位于相同半径处计算得到的分形维数相近,约为3.39;数据采集点的半径增大时,分形维数减小.

Phase space reconstruction and fractal characteristic of rotating stall in impeller of centrifugal compressor

Based on phase space reconstruction and fractal theory in nonlinear dynamics, a method was proposed to analyze the dynamics characteristic of rotating stall in the impeller of centrifugal compressor. The rotating stall of impeller in low speed centrifugal compressor (LSCC) was numerically simulated, and the time series of pressure at rotating stall was obtained at various locations at impeller outlet. The technique of phase space reconstruction was applied to these pressure time series, and a low-dimensional dynamical system, which the dynamic properties were included in, was reconstructed. In order to determine the time delay and the embedding dimension in the reconstructed phase space, C-C method was introduced to deal with the pressure time series. The fractal characteristics of the reconstructed dynamic system phase diagrams were analyzed, and the corresponding fractal dimensions were given. The results show that the pressure signal of the impeller after rotating stall is in chaotic state, and some fractal structures are found in the reconstructed phase space. These fractal structures reveal the intrinsic dynamics of rotating stall flow. When the data collection points in the same radius, they have the similar fractal dimension, nearly 3.39. The fractal dimension decreases with the radius of collection points increasing.