Steady Vs Unsteady flow over a cylinder

Aim:

1. To simulate fluid flow over a circular cylinder and visualize the formation of Von Karman vortices for both steady and unsteady flow for a Reynolds number of 100.
2. To obtain plots of coefficient of lift and drag and observe the effect of the Reynolds number on them by simulating for different Reynolds number

Theory:

When a fluid moves past a blunt solid object vortex shedding occurs downstream. Von Karman vortex is a repeating pattern of swirling vortices.

Strouhal number is a dimensionless quantity that describes the oscillating flow phenomenon. It is described as the product of the frequency of vortex shedding and the characteristic length divided by the flow velocity.

Case setup:

Part-1

Both the steady and transient cases use the same mesh.

Mesh :

All triangles

No of nodes : 31641

The inlet velocity is fixed at 1 m/s and the kinematic viscousity is 0.02 m^2/s this gives a Reynolds number of 100.

Steady State simulation:

The plot of the vertex average of the velocity-magnitude at a location 8m from the cylinder centeris given here.

The residuals are given here , they appear to converge.

The contour plot is shown here . The vortex formation is clearly shown.

Unsteady state simulation:

The plot of vertex average velocity indicated that the fluid oscillates between 250s and 300s 6 times , therefore factoring in the value of the characteristic length as 2.4 and U=1 , the strouhal number is gievn as 2.4

The movie of the vortex formation-

Part-II

The plots of the coefficient of lift and drag are plotted using a force report. For reynolds number 100,1000,10000,100000.

Reynolds number-10

Reynolds number -100

Reynolds number -1000

Reynolds number -10000

Reynolds number -100000

Conclusion -

The value of Cd depends on the velocity on the inflow and it increases as the reynolds number increases. The Cl variation (oscillation) increases as the reynolds number increases