Particle image velocimetry-based load determination approach for supersonic airfoil by streamline control volume

In this paper, a non-intrusive load determination approach tailored for supersonic airfoils is proposed based on the control volume (CV) method and the velocity field measured by particle image velocimetry (PIV). Compared with the general rectangle-CV (RCV) method, this approach demonstrates significant advantages in supersonic flows, by adopting a novel streamline-CV (SCV) combined with the streamline-based (SLB) pressure reconstruction method. The SLB method improves the reconstruction accuracy of the pressure distribution along the SCV contour, which is beneficial for supersonic lift determination. As the drag is much smaller than the lift for slender models, it is more difficult to achieve high accuracy and robustness in drag determination. This problem can be solved using a novel streamtube-based correction scheme for the mass flow distribution along the SCV contour, to improve the accuracy of the momentum flux integral. The feasibility of the SCV+SLB approach is theoretically analyzed using the velocity field around a supersonic double wedge airfoil with an angle of attack of 6°. Then, based on synthetic velocity fields with a Gaussian distributed error of 1%, the mean coefficients and their standard deviations are determined and evaluated in detail, demonstrating the superior accuracy and robustness of this approach. Finally, a PIV experiment is conducted in a supersonic wind tunnel to verify the practical performance of the method. The SCV+SLB approach performs well, with relative errors of 3.74% and 5.24% in lift and drag determination, whereas the RCV method fails to produce valid results under the same conditions.