Flow over a cylinder (steady state vs Transient)

Objective:

• The main objective of this project is to simulate flow over a cylinder using steady and transient mode and Study the the vortex shedding in both the mode
• To calculate Strouhal number for the steady and transient simulations.

Von karman Vortex Shedding:

In fluid dynamics, a Kármán vortex street is a repeating pattern of swirling vortices, caused by a process known as vortex shedding, which is responsible for the unsteady separation of flow of a fluid around blunt bodies

Von karman Vortex can be formed in laminar flow when reynolds number is between 40 and 100. This reynolds number can be controlled by changing the value of dynamic viscosity.

Mesh Model :

For this case Triangular mesh is used in order to capture the effect of vortex shedding accurately and as our objective is to simulate the flow over a cylinder, we are using the inflation layer around the cylinder in order to increase the accuracy of our simulation.

Case 1 : Steady state mode

Mesh size is 0.25mm , steady pressure based solver is used, with air as the working fluid with dynamic viscosity of 0.02 kg/m-s and density of air 1kg/m^3

Monitor point is located at a distance of 10m from the centre of the cylinder to the right as shown in the figure.

Results:

Steady state simualtion was done for 1000 iteration.

Residual plots :

Velocity at the monitor point:

From the abpve two plots we can see that till 150 the values were continously decreasing and after 150 iteration solution is converged.

The sudden rise and all in the velocity plots represents the vortex shedding.

Velocity distrubution:

Vortex shedding can be clearly seen in the above figure, this is for Re:100

Animation

Case 2 :

Transient state mode

Mesh size is 0.25mm , Transient pressure based solver is used, with air as the working fluid with dynamic viscosity of 0.02 kg/m-s and density of air 1kg/m^3.

Residual plots :

Vertex Average of Velocity magnitude at the Monitor point

Here Vortex starts forming around 8000 iterations and and these pattern remains constant after 20000 iteration as shown in figure.

here velocity vs flow time is plotted and we can see that vortex starts to form at around 35 secs and gets converged after 120 secs.

Vortex shedding for transient mode can be seen in above figure.

Animation:

Conclusion:

• The Steady flows take very less no. of iterations to get stable compared to that of Transient flow
• The Transient flow takes a large number of iterations and time to produce a vortex shading compared to that of stable flow.

Strouhal number (St) is a dimensionless number describing oscillating flow mechanisms.

St = fL/U

where,

f: frequency of vortex shedding

L: Characteristics length = 2m

U: Flow Velocity = 1m/s

1. Strouhal Number of Steady flow over a cylinder

It cannot be calculated as the frequency of vortex shading cannot be determined as velocity magnitude and flow-time do not hold any relation.

2. Strouhal Number of Transient flow over a cylinder

f = 11/60 Hz

St = 0.36