A nonlinear dynamic model for unsteady separated flow control and its mechanism analysis

Abstract

In the analysis of the interaction between external periodic excitation and unsteady separated flow in controlling the flow separation, a new nonlinear approximate model has been established. This model is used to describe the typical chaotic and coherent characteristics of a separated flow such as small- or large-scale vortices, the injection, and the dissipation of the kinetic energy based on a simulation of a simplified cross-direction motion of free shear flows. This study presents an appropriate treatment to simulate the external periodic excitation and uses the maximum Lyapunov exponent to evaluate the degree of flow ordering in the different control states. The results of the nonlinear model are compared with experimental and numerical results, showing that the nonlinear model could be used to effectively explain the behaviours of chaotic flows and investigate the rules for controlling separated flows. In addition, as shown in the nonlinear approximate model, the self-synchronization of unsteady flow separation and periodic excitation has been analysed. Initially, the research provided an explanation of the self-synchronization mechanism, which cites that the effects of the separated flow control are independent of the phase difference between the periodic excitation and the unsteady flow. The characteristics of unsteady separated flow control have also been presented in this model, where the corresponding large eddy simulation (LES) was used for separated flows in a curved diffuser. The proper orthogonal decomposition (POD) method was used to analyse the difference between separated vortical structures with or without periodic excitation. The results showed that the model and the simulation had the same mechanism of flow control as for the separated flows. The periodic excitation transforms the original chaotic flow into a relatively ordered flow and decreases the magnitude of the chaotic unstable vortices, rather than completely eliminating the vortices, while flow mixing is reduced, inducing less energy loss.