Analysis of Steady and Unsteady flow over a cylinder.

Steady State Simulation.

      The geometry is created in DesignModeler and meshing is done with tri mesh and inflation layer around the cylinder wall. The total number of elements is 41638, which gives pretty fine mesh. Reynold's number maintained at 100, by giving velocity input 1 m/s, density 1 kg/m3 and viscosity as 0.02 N-s/m2. The solution ran for 1000 iteration and check is done by observing residual, drag and lift coefficient, vertex at downstream, etc. The plot images are shown below.

Residuals:

Drag Coefficient:

Lift Coefficient:

Vertex velocity average at downstream:

Velocity Contour:

Pressure Contour:

The solution can be said to be converged by looking at lift coefficients and vertex velocity at downstream. Both the graphs shows that after 500 iterations, variation is at a constant frequency. Even if residuals are not dropping 1e-3, we can safely say that the solution is converged and the pattern will repeat afterward. The velocity animation is attached with results to get a clear idea about vortex shedding downstream.

Finding strouhal number will not be possible in steady state simulation, because it needs frequency of oscillation. Frequency of oscillation could be found out only by transient simulation. The oscillations are clearly seen in all the graphs above, So it concludes vortex shedding does exist at Reynold's number 100. 

Unsteady-State Simulation. 

All creation is the same as steady-state simulation up to fluent setup. In fluent, for transient analysis solution method used as PISO and transient formulation is done by selecting Bounded second order implicit method. Time step size is varied whenever the solution demands between 0.05 to 0.2. The solution is to run for 16600 iterations and residuals and other parameters are observed. Residuals and lift coefficient is oscillating over the period of time because of vortex shedding downstream. The important plots of images are taken and presented below. The residual value is not a good parameter to judge in the transient analysis whether the solution is converged or not. That's why, other parameters like lift coefficient, vertex velocity downstream is observed to come to the conclusion that solution is converged. 

Residuals:

Lift Coefficient:

Vertex velocity average at downstream:

Velocity Contour:

Pressure Contour:

The strouhal Number is calculated using the lift coefficient graph. The number of peaks for a certain time period is measured and its a value of frequency. 

There are 5 peaks for 50 seconds which will give the frequency 5/50 = 0.1 oscillation/sec. So strouhal number is f*l/V = 0.2, 

where, f = frequency of oscillation.

           l = characteristic dimention(Diameter in our case,D = 2m)

           V = Velocity.(1 m/sec)

Strouhal number for vortex shedding is 0.2