Numerical study on viscous flow past two circular circular cylinders

In the present work. two mathematical models have been developed in order tostudy the flow past one or two circular cylinders in a uniform flow for40 ~ Re ~ 5 xl 03• The stream function vorticity formulation is used ill both models tosolve the time-dependent, two-dimensional, incompressible Navier-Stokes equationsby the [mite difference method FDM. The solution algorithms employ a hybriddifference formulation for the convective terms of the flow equations. The first modelis based on log-polar coordinate system transformation to solve the flow around asingle circular cylinder. This model is checked by a series of tests. The obtained resultsshowed good agreement with those of previous experimental and numerical works.The second model is based on PDE’s elliptic transformation to simulate the flowaround one and two circular cylinders. Transformation from the physical tocomputational space is introduced to overcome geometric difficulties. Thistransformation is accomplished by specifying a generalized coordinate system whichmaps the non rectangular grid system in the physical space into a rectangular uniformgrid in the computational space. A series of validation tests were performed to checkthe accuracy of the PDE’s transformation model. The obtained results for the flowabout a single circular cylinder showed very good agreement with those obtained usingthe log-polar model.Numerical investigations are carried out to clarify the behavior of the flow pasttwo circular cylinders for Re = 1 x 102, 1 x 103 and 5 x 103• The flow about the twocylinders was investigated for two different arrangements: (i) the two cylinders intandem arrangement, at longitudinal spacing Lld ranging from 1.1 to 5 and (ii) the twocylinders face the flow side-by-side at transverse spacing Hid ranging from 1.25 to 3.5.In the tandem arrangement evolution with time for streamlines and equi-vorticitylines about the two cylinders are calculated and presented for different values of Lld.Three different flow regimes have been observed. At Lld=l.l, the free shear layersseparated from the upstream cylinder do not reattach to the downstream cylinder. At1.5 ~ Lld ~ 3. 0 or 3.5 depending on Re, the free shear layers separated from the