ఫ్లూయిడ్ మెకానిక్స్: ఓపెన్ యాక్సెస్

Vortex ring formation is a limited growth process. Upon reaching a non-dimensional formation number, the vortex ring pinches off and secondary vortices form in the trailing jet. However, since a larger vortex ring is associated with higher propulsive efficiency, it is desired to delay vortex ring pinch-off. In this study, a numerical model based on vortex sheet method was used to study vortex ring formation from a piston-cylinder apparatus, with the focus on the vortex ring pinch-off at formation number F. Studies on the various piston velocity programs showed that piston acceleration is able to delay the vortex ring pinch-off and the formation of secondary vortices. The delay is more significant when the vortex ring pinch-off occurs while the piston is accelerating. Acceleration of piston before a constant velocity period would still delay the vortex ring pinch-off, but to a much smaller extent.

A NACA 4412 airfoil tested in wind tunnel at flow conditions close to maximum lift is used for testing the accuracy of various turbulence models. What makes this test case unique is the appearance of a stable separation vortex on the upper surface of the airfoil, near the trailing edge. The linear k-ω turbulence model, a non-linear Explicit Algebraic Stress Model and a modified version of the algebraic Baldwin-Lomax model are tested using the same grid and input file. It is found that the tested turbulence models capture the physics of unsteady separated flow. However, the size and shape of the predicted separation vortex are different for each tested turbulence model. Also, good agreement between computational and experimental surface pressures is observed. The results support the view that such a simple configuration is appropriate to be used as benchmark for validating turbulence and LES models.