8.2 Impulsively translated cylinder

In this section we compute the flow over a cylinder impulsively set into motion with a constant speed $U_\infty$ in the direction perpendicular to its axis. The reason for choosing this test problem is that for this flow a large number of experimental and computational results are available to check our computations. We compute the flow in the reference frame in which the cylinder is stationary and the fluid is streaming past the cylinder from left to right with speed $U_\infty$. The time is nondimensionalized by $U_\infty$ and the radius of the cylinder $a$. The Reynolds number is $Re=2 U_\infty a/\nu$, where $\nu$ is the kinematic viscosity of the fluid. The computational results in this section are presented for the range of Reynolds numbers from 550 to 40,000. All the computations in this section were performed in 64 bit precision on IBM RISC System/6000 and single-node SP-2 computers.

We will establish the accuracy of our computed results by comparing them to experimental, analytical, and recent high-resolution computational results. But first a review of the more recent computations is presented in subsection 8.2.1. Then, we check our results for the streamlines in subsection 8.2.2, our velocity fields in subsection 8.2.3, our vorticity fields in subsection 8.2.4, and our drag forces in subsection 8.2.5. The effect of cut-off circulation parameter (subsection 6.2.5) proves to be very important and is discussed in subsection 8.2.6. The comparison of our results with the theory of unsteady boundary layer separation is given in subsection 8.2.7. The theoretical predictions for the drag force is given in subsection 8.2.8. We compare our results with the results obtained from other numerical methods in subsection 8.2.9.