Abstract:
The plane problem of the initial stage of motion of a circular cylinder under the free surface of an ideal, incompressible, heavy fluid is considered. It is assumed that the cylinder moves from the rest state in the vertical direction with constant acceleration. A feature of this problem is that under certain conditions, liquid particles separate from the surface of the body, and an attached cavity is formed behind the body. This phenomenon occurs when the cylinder moves at a high acceleration rate or when the accelerated motion of the body is accompanied by artificial cavitation. Assuming additionally that the separation points are immobile, the possibility of representing the problem solution in terms of an asymptotic power series with respect to small time intervals is considered. The desired expansion with the first two terms of the asymptotics exists only at a certain Froude number and pressure in the cavity. These values are chosen such that the Kutta-Zhukovskii condition is exactly fulfilled at the separation points.
Keywords:circular cylinder, separation acceleration, attached cavity, fixed separation points, small times, power asymptotics, Froude number, cavity pressure.
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