Unsteady forces acting on a body immersed in viscous fluids. II - Uniformly accelerated flat plate, elliptic cylinder and circular cylinder

The initial stage of flows due to uniformly accelerated flat plate, elliptic and circular cylinders from rest in incompressible viscous fluids are numerically studied by the finite difference method. The time dependence of streamlines and equivorticity lines are shown in flow patterns. The Dufort-Frankel technique is used for solving the vorticity transport equation and the finite Fourier tranform for solving the stream function, which is applied to the analysis of a block tridiagonal matrix equation. The main conclusions are as follows: (1) The Fourier series method is more than ten times faster than the SOR method; (2) numerical experiments here are in very good agreement with real experiments on a flat plate and a circular cylinder; (3) the length of vortex pairs behind a uniformly accelerated elliptic cylinder at the angle of attack 90 deg is obtained as a result of numerical experiments; and (4) the growing process of the secondary vortices behind a circular cylinder is revealed at Re = 731.