Unsteady Forces on a Body Immersed in Viscous Fluids (2nd Report, Uniformly Accelerated Flat Plate, Elliptic and Circular Cylinders)

The early stage of the 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 equi-vorticity lines are shown in the flow patterns. The Dufort -Frankel technique is used for solving the vorticity transport equation and the finite Fourier transform 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 obtained here have very good agreements with real experiments for flat plates and circular cylinders. ( 3) The length of vortex pairs behind an uniformly accelerated elliptic cylinder at the attack angle 90° is obtained as a resultant of numerical experiments. (4) The growing process of the secondary vortexes behind a circular cylinder is revealed at Reynolds number 731.