Three-dimensional aerodynamic lift on a rectangular cylinder in turbulent flow at an angle of attack

Abstract

The aim of the present work is to derive the closed-form solution for the three-dimensional aerodynamic admittance (3D AAF) of the lift on a 5:1 rectangular cylinder in turbulent flow at an angle of attack (AoA), which can be used to study the unsteady effects of AoA. The separated one- and two-wavenumber aerodynamic admittances are introduced to assess the contributions of u and w components of turbulence to the lift force at an AoA. These admittances are divided into two parts: the two-dimensional aerodynamic admittance (2D AAF) for fully coherent gusts and the gust-related spanwise correction factors. The closed-form expressions for the one- and two-wavenumber spanwise correction factors of the 3D AAF are derived provided that the floating parameters in the coherence models of the lift force and turbulence are determined experimentally. Although the proposed 3D AAF model is a semi-analytical solution, it still provides explicit insight into the unsteady effects of u and w components of turbulence and the distortion of the free-stream turbulence. Based on theoretical and experimental investigations, it is shown that the unsteady effects of AoA on the coherence and spectra of the lift become more prominent with the increase of AoA, and reach their maximum as the AoA reaches 10°. This phenomenon can be attributed to the contribution of the u component, which plays a dominant role in determining the aerodynamic behaviour of the lift as the AoA approaches 10°. Notably, the spanwise correction factors of the 3D AAF will amplify the results based on the strip theory at low frequencies as the AoA is within 7°, and vice versa. In addition, it should be noted that the proposed approach allows us to quantitatively study the unsteady behaviour of the lift force on bluff bodies with complicated cross-sectional shapes, such as a streamlined bridge deck.