Wake induced vibration is a common phenomenon in the field of aeroelasticity which can cause forced vibrations of the structure. This phenomenon can endanger the integrity and the fatigue life of the excited structure. In this paper, wake induced vibration is studied by an approximate model with upstream cylinder and downstream blade. The cylinder in freestream produces Karman vortex street with a specific frequency. When the cylinder wake encounters the downstream blade, continuous pulse excitation is applied to the blade. Two-dimension numerical simulation based on Fluent illustrates the shedding vortex and transient process of blade from static to vibration at its natural frequency, and the detail information of transient flow field is obtained. Based on the unsteady transient results, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are applied for the decomposition and the reconstruction of the pressure field near the vibrating blade. The modal frequency and the evolution process are extracted to capture the main flow structure of wake induced vibration. The comparison of two modal analysis methods shows that POD reconstruction has a smaller maximum residual than DMD, and DMD has more advantages in single frequency mode extraction and corresponding evolution analysis.
XIE Hairun,WU Yadong,OUYANG Hua,WANG Anzheng
. Modal Analysis of Wake Induced Vibration Transient Process
Based on POD and DMD[J]. Journal of Shanghai Jiaotong University, 2020
, 54(2)
: 176
-185
.
DOI: 10.16183/j.cnki.jsjtu.2020.02.009
［1］BRIKA D, LANEVILLE A. The flow interaction between a stationary cylinder and a downstream flexible cylinder［J］. Journal of Fluids and Structures, 1999, 13(5): 579-606.
［2］ASSI G R S. Wake-induced vibration of tandem and staggered cylinders with two degrees of freedom［J］. Journal of Fluids and Structures. 2014, 50: 340-357.
［3］刘丹青. 振荡流中串列双圆柱涡激振动数值模拟［D］. 天津: 天津大学, 2016.
LIU Danqing. Numerical investigation of vortex-induced vibration of two circular cylinders in tandem arrangements in oscillatory flow［D］. Tianjin: Tianjin University, 2016.
［4］LUMLEY J. The structure of inhomogeneous turbulence［C］//Atmospheric Turbulence & Wave Propagation. Moscow: Nauka, 1967: 166-178.
［5］MUNDAY P M, TAIRA K. Separation control on NACA 0012 airfoil using momentum and wall-normal vorticity injection［C］//32nd AIAA Applied Aerodynamics Conference. Atlanta: AIAA, 2014-2685.
［6］MURRAY N, SLLSTRM E, UKEILEY L. Properties of subsonic open cavity flow fields［J］. Physics of Fluids, 2009, 21(9): 178-479.
［7］FENG L H, WANG J J, PAN C. Proper orthogonal decomposition analysis of vortex dynamics of a circular cylinder under synthetic jet control［J］. Physics of Fluids, 2011, 23(1): 014106.
［8］SHI L L, LIU Y Z, WAN J J. Influence of wall proximity on characteristics of wake behind a square cylinder: PIV measurements and POD analysis［J］. Experimental Thermal and Fluid Science, 2010, 34(1): 28-36.
［9］ROWLEY C W. Model reduction for fluids, using balanced proper orthogonal decomposition［J］. International Journal of Bifurcation and Chaos, 2005, 15(3): 997-1013.
［10］SIEBER M, PASCHEREIT C O, OBERLEITHNER K. Spectral proper orthogonal decomposition［J］. Journal of Fluid Mechanics, 2016, 792(7): 798-828.
［11］SCHMID P J. Dynamic mode decomposition of numerical and experimental data［J］. Journal of Fluid Mechanics, 2010, 656(10): 5-28.
［12］ROWLEY C W, MEZI I, BAGHERI S, et al. Spectral analysis of nonlinear flows［J］. Journal of Fluid Mechanics, 2009, 641: 115-127.
［13］丁杰, 胡晨星, 刘鹏寅, 等.无叶扩压器中非定常流动的DMD模态分析［J］.动力工程学报, 2017, 37(6): 447-453.
DING Jie, HU Chenxing, LIU Pengyin, et al. Dynamic mode decomposition of the unsteady flow in a vaneless diffuser［J］. Journal of Chinese Society of Power Engineering, 2017, 37(6): 447-453.
［14］PAN C, XUE D, WANG J. On the accuracy of dynamic mode decomposition in estimating instability of wave packet［J］. Experiments in Fluids, 2015, 56(8): 1-15.
［15］NOACK B R, STANKIEWICZ W, MORZYSKI M, et al. Recursive dynamic mode decomposition of transient and post-transient wake flows［J］. Journal of Fluid Mechanics, 2016, 809: 843-872.
［16］寇家庆, 张伟伟, 高传强. 基于POD和DMD方法的跨声速抖振模态分析［J］. 航空学报, 2016, 37(9): 2679-2689.
KOU Jiaqing, ZHANG Weiwei, GAO Chuanqiang. Modal analysis of transonic buffet based on POD and DMD method［J］. Acta Aeronautica et Astronautica Sinica, 2016, 37(9): 2679-2689.
［17］陈静涛. 圆柱绕流的二维数值模拟和尾迹分析［J］. 计算机辅助工程, 2013, 22(6): 1-6.
CHEN Jingtao. 2D numerical simulation and wake analysis on flow around circular cylinder［J］. Compu-ter Aided Engineering, 2013, 22(6): 1-6.
［18］TU J H, ROWLEY C W, LUCHTENBURG D M, et al. On dynamic mode decomposition: Theory and applications［J］. Journal of Computational Dynamics, 2014, 1(2): 391-421.
［19］詹昊, 李万平, 方秦汉, 等. 不同雷诺数下圆柱绕流仿真计算［J］. 武汉理工大学学报, 2008, 30(12): 129-132.
ZHAN Hao, LI Wanping, FANG Qinhan, et al. Numerical simulation of the flow around a circular cylinder at varies Reynolds number［J］. Journal of Wuhan University of Technology, 2008, 30(12): 129-132.
