Vortex street simulation for a cylindrical body

Introduction:

Through the simulation of laminar flow over a cylinder, the phenomenon of ‘von Karman vortex street’.  It is a physical process where a repeating pattern of swirling vortices are caused due to vortex shedding. It responsible for the unsteady separation of flow of a fluid around blunt bodies. In this report, the flow over a cylinder is simulated in ANSYS fluent to visualize the ‘von Karman vortex street’ in a steady and transient environment to determine the Strouhal number.

Case Description:

The simulation case is modelled in SpaceClaim to represent the fluid flow over the cylinder as shown in the figure 1. A 2D rectangular surface is created and a circular area is removed so that it will be considered as an obstacle and not interfere with the fluid computations. A circle with a 2m diameter is placed at a distance of 20m from the inlet with a downstream length of 40m. The width of the inlet and outlet is 20m. 

The volume is meshed appropriately with an initial element size of 2 m and it is continuously refined to capture the physics more accurately. The final mesh with an element size of 0.2m is displayed in the figure 2.

Steady simulation:

The simulation is performed with a laminar model with a Reynolds number of 100. The Reynolds number is defined through density and viscosity and it is calculated using the formula

Where,

Re - Reynolds number (-)

U - Velocity (m/s)

d - Diameter of cylinder (m)

ρ - Density (kg/m3)

μ - Dynamic viscosity (kg m/s)

The Reynolds number of 100 is defined in fluent with a density of 1 and a dynamic viscosity of 0.02. The velocity of 1 m/s is defined with a velocity boundary condition at the inlet. The pressure boundary condition at the outlet with a gauge pressure of 0 Pa implies that the outlet is open to the atmosphere. The circular edge is defined with a no-slip boundary condition, signifying the obstacle in the flow. The top and bottom edges are assigned the symmetry boundary condition allowing us to implement the free stream flow condition in confined geometry.

A monitor point was defined at a distance of 8m downstream of the cylinder. The velocity at this monitor point was measured at each iteration and plotted to determine the frequency of the vortex shedding. The simulation is run for 600 iterations and the convergence is achieved when the average value of velocity has reached a periodic oscillation as it can be observed from figure 3. In this case, it happens at 220^th iteration.

A velocity contour is created to visualise the variation of velocity as the simulation proceeds forward. The vortex street can be seen clearly once the simulation reaches a steady state. The figure 4 displays the snapshot of the vortex street produced at the end of the simulation.

Strouhal Number:

The strouhal number is a dimensionless number describing oscillating flow mechanisms. It is calculated by the following formula,

Where,

St – Strouhal number (-)

f – Frequency of vortex shedding (1/s)

U – Flow velocity (m/s)

The frequency of vortex shedding cannot be calculated in a steady simulation since there is no time parameter associated. Hence a transient simulation is performed for the same case.

Transient simulation:

For the simulation to achieve convergence in the transient analysis, the mesh size was decreased to 0.2 m and the Reynolds number was increased to 166. Now, the case is simulated in a transient environment and the average velocity at the monitor point was observed for convergence. The frequency of vortex shedding is determined from the convergence plot of velocity in figure 2.

The frequency of vortex shedding = 0.25 s^-1

St = 0.25 * 2/1.5

    = 0.33 (-)

Conclusion:

The above simulation was executed successfully in ANSYS Fluent and the Strouhal number was determined to be 0.33. As an extension, the experiment can be repeated for different shapes to compare the effects on the Strouhal number.