Understanding Cavity Flows Using Proper Orthogonal Decomposition and Signal Processing

Computational Fluid Dynamics (CFD) is increasingly being used to analyse complex flows. However, to perform a comprehensive analysis over a given time period, a large amount of data is provided and therefore a method for reducing the storage requirements is considered. The Proper Orthogonal Decomposition (POD) is a widely used technique that obtains low–dimensional approximate descriptions of high–dimensional processes. To demonstrate the potential for reduction in data storage, and the potential use of POD in CFD, the cavity flow case is used. This case is a challenge for CFD due to its unsteady nature and high frequency content. The POD modes were constructed using flow–field snapshots taken at regular intervals. Spatial POD modes for the cavity case showed that the modes came in pairs with a 90° phase shift. The lower modes represented the large dynamics of the shear layer and the higher modes the small scale turbulent structures. Reconstructions of the flow–fields showed that the very large dynamics could be represented with as few as 11 modes. However, approximately 101 modes (85% of the flow energy) were needed to approximate the frequency spectra below 1 kHz. Therfore a reduction of 70% in disk storage would be achieved over storing the complete set of flow–field snapshots produced by CFD.