Direct measurement of the Sears function in turbulent flow

Abstract

The applicability of the strip assumption in the estimation of the unsteady lift response of a two-dimensional wing in turbulent flow is investigated. The ratio between the lift spectrum calculated from the two-wavenumber analysis and the lift spectrum calculated from the strip assumption is used to evaluate the accuracy of the strip assumption. It is shown that the accuracy of the strip assumption is controlled by the ratio of the turbulence integral scale to the chord and the aspect ratio. With an increase of these two parameters, the ratio for evaluating the accuracy of the strip assumption increases, the one-wavenumber transfer function obtained from the strip assumption approaches the Sears function gradually. When these two parameters take suitable values, the strip assumption could be applicable to the calculation of the unsteady lift on a wing in turbulent flow. Here, the term aspect ratio refers to the ratio of the specified span (an finite spanwise length of the two-dimensional wing) to the chord, the unsteady lift is calculated over this specified spanwise length. The theoretical analysis is verified by means of force measurement experiments conducted in a wind tunnel. In the experiment, a square passive grid is installed downstream of the entrance of the test section to generate approximately homogeneous and isotropic turbulence. Three rectangular wings with different aspect ratios ($\unicode[STIX]{x1D703}=3$, 5 and 7) are used. These wing models have an NACA 0015 profile cross-section and a fixed chord length $c=0.16~\text{m}$. The testing results show that, at a fixed ratio of turbulence integral scale to chord, the deviation between the experimental one-wavenumber transfer function obtained from the strip assumption and the Sears function is reduced with increasing aspect ratio, as expected by the theoretical predictions. However, due to the effect of thickness, the experimental values at high frequencies cannot be captured by the Sears function which is derived based on the flat plate assumption. In practical applications, the effect of thickness on the transfer function should be considered.