Steady Vs Unsteady flow over a cylinder

Objective:

Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street.

Theory:

Karman vortex street: It is a repeated pattern of swirl, caused due to vortex shedding.

Vortex shedding is an oscillating flow that takes place when a fluid such as air or water flows past a bluff body at certain velocities, depending on the size and shape of the body.

The vortices create low-pressure zones on the downwind side of the object on alternate sides.

As the fluid flows to fill the low-pressure zone, it produces a vibration at a specific calculable frequency.

This vibration is only a major concern if it happens to coincide with the natural frequency of the structure.

To calculate vortex shedding we need to calculate the Strouhal number

The Strouhal number formula:`St = (f L)/U`

where f is the frequency of vortex shedding, L is the characteristic length and U is the flow velocity.

Geometry:

Cylinder diameter - 2 m.

fluid properties:

Kinematic viscosity – 0.05 kg/m-s

Density – 1 kg/m3

monitor point: 4 times diameter away from centre of the circle.

Mesh:

element size - 0.25 m

edge sizing - 50

Transient solver:

drag force on the cylinder

monitor point velocity:

lift force on the cylinder:

velocity contour:

Pressure contour:

Residuals:

Freq = 1/3.2 per second

Strouhal number = 0.3125

steady-state solver

Re = 10

Re = 100

Re = 1000

Re = 10000

re = 100000

Reynold's number (Re)	Drag force(Fd)	Lift force(Fl)
10	0.0114	max 7.01e-4 min -6.1e-4
100	0.788	max 0.41465 min -0.273
1000	76.2	max 48.7 min -49.44
10000	7100	max 7000 min -5000
100000	800000	max 750000 min -750000

Conclusion:

• Thus simulation has run successfully and Karman vortex street is formed
• For Reynolds number of 100 for the given cylinder strouhal number of 0.3125.
• Increase in Reynolds number, increases drag force and lift force.

Reference: