A numerical study of separation and stagnation points for steady and unsteady flow over an elliptic cylinder near a moving wall

Abstract

Flow separation around an elliptic cylinder with an aspect ratio of 0.4 near a moving wall is investigated numerically for Re 2 ½5; 150 with G=D 2 ½0:1; 2 (where G denotes the distance between the cylinder bottom and the bottom wall, while D denotes the major-axis length of the cylinder). Four steady flow patterns are identified in (Re; G=D)-space. A new flow pattern where only an anti-clockwise vortex is formed behind the lower part of the cylinder is observed for G=D 0:4 with Re 24. For steady flow, the upper separation point moves upstream as Re increases, while it is less affected by G/D. The lower separation moves first downstream and then upstream as Re increases for G=D 0:4, while for G=D ¼ 0:7, only a large upstream movement is observed. The front stagnation point moves downstream toward the gap as Re decreases (for a given G/D) or as G/D decreases (for a given Re). The rear stagnation point moves first upward and then downward as Re increases for G=D 0:4, while for G=D ¼ 0:7, the opposite behavior is observed. For unsteady flow, the stagnation and separation points oscillate. Here, both the amplitude and the frequency decrease as G/D decreases. The oscillation amplitude for the lower separation point is slightly larger than for the upper separation point due to the stronger vortex shedding behind the cylinder bottom caused by the enhanced velocity through the gap. This mechanism also leads to larger oscillation amplitudes for both the front stagnation point and the lower separation point at larger G/D than for the isolated cylinder.