On the application of variational mechanics in modeling the flow around a cylinder in ground effect

Abstract

For high Reynolds number flow over a cylinder near a flat moving surface, a potential flow model can be used to represent flow over the leading edge. However, the potential flow solution requires knowledge of the circulation around the cylinder. This circulation value can be found with an auxiliary condition using energy methods. Two choices for this variational condition exist at present. Gol'dshtik and Khanin (1978) postulated an ad-hoc variational approach that looks only at the velocity on the cylinder boundary. The other approach is guided by the novel work of Gonzalez and Taha (2022), an extension of Gauss' principle that considers the entire velocity field. The first approach was calculated by Petrov and Maklakov (2022), whereas the second approach has not yet been applied to a cylinder in ground effect. These two models are applied to modeling a cylinder in `ground effect', and the predictions of these two models are compared with a computational fluid dynamics (CFD) simulation by considering the pressure distribution and forces on the cylinder as a function of the cylinders proximity to the wall. For gap-to-radius ratios approximately between 1 and 6, it is demonstrated that gauss' principle provides an acceptable auxiliary condition that gives an accurate potential flow representation of the leading-edge flow. The model is also able to calculate the lift-coefficient given an approximation of the trailing-edge pressure distribution based on experiment.