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The proper orthogonal decomposition (POD) method is employed to analyze the unsteady flow control mechanism because it is a good approach to decouple the spatial and temporal structures of unsteady flow fields. The results showed that the main effect of the periodic excitation is reallocating the energy of each mode, and selectively strengthening or weakening certain modes. Under proper amplitude and frequency of periodic excitation, the energy in higher modes will be transferred to the first mode and the translation of the modal energy is coming from the reconstructing of spatial flow structures and the ordering of modal evolution characteristics. The best control effect will be achieved when the total energy ratio of the first mode is the highest and the excitation frequency reaches the separation vortex frequency at the same time. In order to quantitatively analyze the order degree of the unsteady flow field, the maximum Lyapunov exponent was introduced. The results showed that with the energy in higher modes transferred to the lower modes, the flow field transfers from a disordered pattern to an ordered one.

Application of the Proper Orthogonal Decomposition Method in Analyzing Active Separation Control With Periodic Vibration Wall