Phase space reconstruction and fractal characteristic of rotating stall in impeller of centrifugal compressor
-
摘要: 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.Abstract: 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.
-
Key words:
- centrifugal compressor /
- impeller /
- rotating stall /
- phase space reconstruction /
- fractal
-
[1] 楚武利,姜桐.离心压气机无叶扩压器旋转失速实验研究[J].航空动力学报,1990,5(2):163-165. CHU Wuli,JIANG Tong.An experimental investigation of rotating stall in a centrifugal compressor with vaneless diffuser[J]. Journal of Aerospace Power,1990,5(2):163-165.(in Chinese) [2] 戴冀,陈静宜.低压离心叶轮小流量失速特性的实验观察[J].航空动力学报,1997,12(2):159-162. DAI Ji,CHEN Jingyi.An experimental observation on stall oscillation at low flowrate in a centrifugal impeller[J].Journal of Aerospace Power,1997,12(2):159-162.(in Chinese) [3] 郭强,竺晓程,杜朝辉,等.低速离心压缩机旋转失速的试验研究[J].实验流体力学,2007,21(3):38-43. GUO Qiang,ZHU Xiaocheng,DU Chaohui,et al.Rotating stall experimental study of a low-speed centrifugal compressor[J].Journal of Experiments in Fluid Mechanics,2007,21(3):38-43.(in Chinese) [4] Stein A,Niazi S,Sankar L N.Computational analysis of stall and separation control in centrifugal compressor[J].Journal of Propulsion and Power,2000,16(1):65-71. [5] 耿少娟,戴冀,张宏武,等.低速离心压气机的全工况数值模拟和校核[J].工程热物理学报,2005,26(增刊):81-84. GENG Shaojuan,DAI Ji,ZHANG Hongwu,et al.The numerical simulation and verification of low-speed centrifugal compressor in whole flow-rate range[J].Journal of Engineering Thermophysics,2005,26(suppl.):81-84.(in Chinese) [6] 张家忠,李凯伦,陈丽莺.翼型失速的非线性动力学特性及其控制[J].航空学报,2011,32(12):2163-2173. ZHANG Jiazhong,LI Kailun,CHEN Liying.Nonlinear dynamics of static stall of airfoil and its control[J].Acta Aeronautica et Astronautica Sinica,2011,32(12):2163-2173.(in Chinese) [7] LIU Yan,LI Kailun,WANG Hang,et al.Numerical bifurcation analysis of static stall of airfoil and dynamic stall under unsteady perturbation[J].Communications in Nonlinear Science and Numerical Simulation,2012,17(8):3427-3434. [8] Packard N H,Crutchfield J P,Farmer J D,et al.Geometry from a time series[J].Physical Review Letters,1980,45(9):712-716. [9] 刘洪,李必强.混沌时间序列的预测[J].系统辩证学学报,1996,4(1):57-60. LIU Hong,LI Biqiang.Forecasting chaotic time series[J].Journal of Systemic Dialectics,1996,4(1):57-60.(in Chinese) [10] Farmer M E.Chaotic phenomena from motion in image sequences[R].Orlando FL:the 2007 International Joint Conference on Neural Networks (IJCNN),2007. [11] 高坤华,李天亮.基于混沌吸引子的压气机失速分析[J].空军工程大学学报:自然科学版,2007,8(1):4-6. GAO Kunhua,LI Tianliang.Compressor stall analysis based on chaotic attractor[J].Journal of Air Force Engineering University:Natural Science Edition,2007,8(1):4-6.(in Chinese) [12] GU Yongxia,ZHOU Zhongning,LI Yimin.Characteristic of fan stalling based on correlated dimensions[J].Transactions of Nanjing University of Aeronautics and Astronautics,2011,28(4):362-366. [13] Hathaway M D,Chriss R M,Strazisar A J,et al.Laser anemometer measurements of the three-dimensional rotor flow field in the NASA low-speed centrifugal compressor[R].NASA Paper 95-3527,1995. [14] Takens F.Detecting strange attractors in turbulence[J].Dynamical System and Turbulence,1981,898:366-381. [15] 张家忠.非线性动力系统的运动稳定性、分岔理论及其应用[M].西安:西安交通大学出版社,2010. [16] Grassgerber P,Prociccia I.Measuring the strangeness of strange attractors[J].Physica D:Nonlinear Phenomena,1983,9(1/2):189-208. [17] Kugiumtzis D.State space reconstruction parameters in the analysis of chaotic time series:the role of the time widow length[J].Physica D:Nonlinear Phenomena,1996,95(1):13-28. [18] Kim H S,Eykholt R,Salas J D,et al.Nonlinear dynamics,delay time and embedding windows[J].Physica D:Nonlinear Phenomena,1999,127(1/2):48-60. [19] 刘秉正,彭建华.非线性动力学[M].北京:高等教育出版社,2005.
点击查看大图
计量
- 文章访问数: 1331
- HTML浏览量: 0
- PDF量: 789
- 被引次数: 0