Flow Past Circular Cylinder
The test case described here meets the typical referencial problem for validating cfd software in an unconfined domain (Files for this test case can be download from here).
The simulation run matches the typical referential simulation for obtaining a vortex sheet in the wake of a circular cylinder. The Reynolds number used has been 100, same value used in the following references [32], [30], and [29]:
Qu, L., Norgerg, Ch., Davidson, L., Peng, Sh. and Wang, F. (2013): Quantitive numerical analysis of flow past a circular cylinder at Reynolds number between 50 and 200, Journal of Fluids and Structures, 39, 347-370
Rahman, M., Karim, M. and Alim, A. (2007): Numerical investigation of unsteady flow past a circular cylinder using 2-D Finite Volume Method, Journal of Naval Architecture and Marine Engineering, 4, 27-42
Rajani, B.N., Kandasamy, A. and Majumdar, S. (2009): Numerical simulation of laminar flow past a circular cylinder, Applied Mathematical Modelling 33, 12281247
de Sampaio PAB, Lyra PRM, Morgan K. and Weatherill NP (1993): Petrov-Galerkin solutions of the incompressible Navier-Stokes equations in primitive variables with adaptative remeshing, Computer Methods in Applied Mechanics and Engineering, 106, 143-178.
Behr, M.,Hastreiter,D.,Mittal,S.,Tezduyar,T.E., (1995) : Incompressible flow past a circular cylinder : Dependence of the computed flow field on the location of the lateral boundaries, Computer Methods in Applied Mechanics and Engineering 123, 309316
The domain used for this simulation can be seen in the following figure:
The length of the domain in the x direction has to be large enough so that any effect caused by the cylinder vanishes when the right limit of the domain is reached.
In this case, the exit has been set at a distance of 32 times the diameter length from the centre of the cylinder. Behr et al studied the influence of the location
of the lateral boundaries on 2D computation of unsteady incompressible flow past a circular cylinder. They concluded that the distance between the cylinder
and the lateral boundaries have a significant effect on the Strouhal number and other flow quantities. They found that the minimum distance at which this
in uence vanishes for Reynolds equal to 100 is 32 times the diameter of the cylinder. For this reason, in this simulation, the distance between the upper
and bottom boundary of the domain has been set to 64 times the diameter of the cylinder, in order to rule out any influence of the boundary conditions in
the solution obtained.
The strategy followed for the generation of the mesh has been using a finner grid in the vicinity of the circular cylinder, (see next gure), and in the wake of the
cylinder, whereas a coarser mesh has been used in the rest of the domain. The number of nodes used has been 77011, and the number of TRIA elements used
has been 153318.
The project for can be found here.
The results shows that the flow past a circular cylinder is a periodic flow for a low Reynolds number (100). When the stationary regime is reached, a vortex of shear stress is established in the wake of the cylinder. The variation of the vertical velocity (u2) in a point located at the wake of the cilinder in the middle point of exit vertical plane (x=64.0, y=32.0) is shown in the following figure.
It can be seen the periodic behaviour of the velocity. The Strouhal number obtained for the simulation was 0.165, which matches the value obtained by Rahman (0.165) and it deviates 0:01% from the value obtained by Qu et al (0.164). The value obtained for the Strouhal number provides confidence in the code developed.
Additionally, the simulation was run for Re=200, obtaining a Strouhal number of St = 0.1954, which deviates -0.18% from the value obtained by Qu et al (0.1958). A comparison of the results obtained with the references is done in next table.
Several snapshots of the flow field have been taken and inserted in here
