Abstract

The present work investigated the vortex structure and fluctuation frequency characteristics generated by boundary layer separation of a high-load compressor cascade using modal decomposition methods. The dominant modes and dynamic behaviors of unsteady flow in the cascade were obtained, and the differences of three modal decomposition methods (Proper Orthogonal Decomposition, Dynamic Mode Decomposition and Spectral Proper Orthogonal Decomposition) in feature recognition of cascade flow were discussed. The results show that:(1) The POD method can accurately extract the dominant spatial structure of the flow field, but the modal coefficients are multi-frequency coupled, which makes the dominant modal characteristics of cascade flow unclear. (2) The standard DMD method can obtain the spatial-temporal single frequency mode of cascade flow, as well as their growth rates and frequencies. However, this method is likely to capture the suboptimal mode of large amplitude with large attenuation rate, and fails to obtain the high-frequency coherent structure, which makes it impossible to obtain the dominant feature with limited mode number. (3) The SPOD method, based on spectral characteristics, can obtain spatial and temporal single frequency modes, and there is no modal screening problem. The use of spectral estimation method (SPOD) reduces the sensitivity to numerical noise. This method can obtain the low-rank behavior of cascade flow, which is helpful to understand cascade flow mechanisms. Therefore, SPOD method is more advantageous for the modal analysis of unsteady separated flow in high-load compressor cascade.

Highlights

  • The present work investigated the vortex structure and fluctuation frequency characteristics generated by boundary layer separation of a high⁃load compressor cascade using modal decomposition methods

  • The results show that: ( 1) The POD method can accurately extract the dominant spatial structure of the flow field, but the modal coefficients are multi⁃frequency coupled, which makes the dominant modal characteristics of cascade flow unclear

  • SPOD method is more advanta⁃ geous for the modal analysis of unsteady separated flow in high⁃load compressor cascade

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Summary

Introduction

POD、DMD 和 SPOD 模态分解方法均是通过提 取时间序列的流场快照主要成分,实现非定常流动 分析。 1.1 POD 方法 􀭾A。 为获得相似变换的正交子空间,对秩为 r 的矩阵 X 做奇异值分解:X = UΣVH,且令:A = U􀭾AUH,因此 由于 POD 选取了 6 阶模态,作为对比,DMD 选 取 6 阶模态,即前 9 个模态。 各阶模态的振幅与频 率关系如图 11 所示,前 9 个模态包括一个静态模 态,3 个共轭模态(2 ~ 3,6 ~ 7,8 ~ 9) 和 2 个漂移模态 (4,5) 。 图 13 给出了 DMD 第 2、第 5 和第 6 阶模态实 部云图,虚部与实部仅存在一定的相位差异[16] ,所 以并未给出。 可以看出,流动的主要结构,即吸力面 分离涡和尾缘脱落涡结构均获得,相干结构与 POD 第 1 和第 3 阶模态一致。 DMD 第 6 阶模态并非主 要结构,属于为了获得高频模态需要剔除振幅较大 的伪模态。

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