Study on Nonlinear Correlation in Modal Coefficients of the Bionic Airfoil

Abstract

Applying bionic airfoils is essential in enlightening the design of rotating machinery and flow control. Dynamic mode decomposition was used to reveal the low dimensional flow structure of Riblets, Seagull, and Teal bionic airfoils at low Reynolds numbers 1 × 105 and is compared with NACA4412 airfoils. The attack angle of the two-dimensional airfoil is 19°, and the SST k-ω turbulence model and ANSYS fluent were used to obtain the transient flow field data. The sparse identification of nonlinear dynamics reveals the nonlinear correlation between modal coefficients and establishes manifold dynamics. The results show that the bionic airfoil and NACA4412 airfoil have the same type of nonlinear correlation, and the dimension and form of the minimum reduced-order model are consistent. The modal coefficients always appear in the manifold equation in pairs with a phase difference of 90°. The dimension of the manifold equation is two-dimensional, and the absolute value of the coefficient corresponds to the fundamental frequency of airfoil vortex shedding. The reconstructed flow field based on the manifold equation is highly consistent with the numerical simulation flow field, which reveals the accuracy of the manifold equation. The relevant conclusions of this study emphasize the unity of the nonlinear correlation of bionic airfoils.