Leading edge vortex formation and wake trajectory: Synthesizing measurements, analysis, and machine learning

Abstract: The strength and trajectory of a leading edge vortex (LEV) formed by a pitching-heaving hydrofoil (chord $c$) is studied. The LEV is identified using the $Q$-criterion method, which is calculated from the 2D velocity field obtained from PIV measurements. The relative angle of attack at mid-stroke, ${\alpha_{T/4}} $, proves to be an effective method of combining heave amplitude ($h_0/c$), pitch amplitude ($\theta_0$), and reduced frequency ($f^*$) into a single variable that predicts the maximum value of $Q$ over a wide range of operating conditions. Once the LEV separates from the foil, it travels downstream and rapidly weakens and diffuses. The downstream trajectory of the LEV has two characteristic shapes. At low values of ${\alpha_{T/4}}$, it travels straight downstream after separating from the foil, while at higher values of ${\alpha_{T/4}} $, an accompanying Trailing Edge Vortex (TEV) forms and the induced velocity generates a cross-stream component to the vortex trajectories. This behavior is accurately predicted using a potential flow model for the LEV and TEV. Supervised machine learning algorithms, namely Support Vector Regression and Gaussian Process Regression, are used to create regression models that predicts the vortex strength, shape and trajectory during growth and after separation. The regression model successfully captures the features of two vortex regimes observed at different values of ${\alpha_{T/4}} $. However, the predicted LEV trajectories are somewhat smoother than observed in the experiments. The strengths of the vortex is often under-predicted. Both of these shortcomings may be attributed to the relatively small size of the training data set.