Simulation of Separated Flow Past a Bluff Body Using Navier-Stokes Equations

Summary

An analysis is developed for simulating two-dimensional flow past a bluff body, using the incompressible unsteady Navier-Stokes equations in terms of vorticity and stream function. The conservation-law form of the equations is employed, in generalized orthogonal curvilinear coordinates, using the contravariant component of the vorticity. The fully implicit time-marching alternating-direction implicit-block Gaussian elimination (ADI-BGE) method employed is a direct method, with second-order spatial accuracy and, hence, avoids introduction of any artificial viscosity. This unsteady analysis has been carefully applied to simulate flow past a circular cylinder with and without symmetry, requiring the use of either the half or the full cylinder, respectively. For the latter configuration, at early time levels, the evolution of some flow characteristics in the near wake is compared extensively with existing experimental data, in order to partially validate the present analysis. For the half-cylinder configuration, the asymptotic flow structure predicted by the present analysis conforms, to some extent, with the existing numerical and analytical solutions. This analysis has the potential advantage of computing symmetric unstable modes as well as solution bifurcations which may result for flow up to Reynolds number Re = 10⁴ or even Re = 10⁵.