Steady Vs Unsteady flow over a cylinder

AIM:

To simulate the flow over a cylinder and explain the phenomenon of Karman vortex street and

PART-I

1. To simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.

PART-II

1. Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000. (Run with steady solver)
2. Discuss the effect of Reynolds number on the coefficient of drag. [ Results should be validated with any standard literature and error should be within 5 %].

Karman vortex street:

It 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.

A vortex street will form only at a certain range of flow velocities, specified by a range of Reynolds numbers (Re), typically above a limiting Re value of about 90.

The Reynolds number for a flow is a measure of the ratio of inertial to viscous forces in the flow of a fluid around a body or in a channel, and may be defined as a nondimensional parameter of the global speed of the whole fluid flow:

where:

U = the free stream flow speed
L = a characteristic length parameter of the body or channel

= the free stream kinematic viscosity parameter of the fluid

Strouhal number:

Strouhal number is a dimensionless number describing oscillating flow mechanisms.

where

f = the frequency of vortex shedding

L = the characteristic length

U = the flow velocity.

Procedure:

1. Geometry:

Initially create the geometry by using space claim with the total length of 60m, width of 20m and cylinder diameter of 2m as shown below.

2. Mesh:

The generated mesh and its details are mentioned below.

Setup & Solution:

The Solver details are mentioned below.

The Residual plot, Vertex Average of Velocity Magnitude, coefficient of drag, lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000:

STEADY STATE :

For Re = 10:

Residual Plot:

Vertex Average of Velocity Magnitude:

Drag Coefficient:

Coefficient of Lift:

Velocity contour:

For Re = 100:

Residual Plot:

Vertex average of velocity magnitude:

Drag Coefficient:

Coefficient of Lift:

Velocity contour:

For Re = 1000:

Residual Plot:

Vertex average of Velocity magnitude:

Drag coefficient:

Coefficient of Lift:

Velocity contour:

For Re = 10000:

Residual plot:

Vertex average of Velocity magnitude:

Drag coefficient:

Coefficient of Lift:

Velocity contour:

For Re = 100000:

Residual plot:

Vertex average of Velocity magnitude:

Drag Coefficient:

Coefficient of Lift:

Velocity contour:

The Residual plot, Vertex Average of Velocity Magnitude, coefficient of drag, lift over a cylinder by setting the Reynolds number to 100:

TRANSIENT STATE :

For Re = 100:

Residual Plot:

Coefficientof Lift:

Drag Coefficient:

Vertex average of velocity magnitude:

Velocity contour:

Strouhal Number for Re= 100:

Steady State:

Transient state:

Material Used:

The material used is air which is created as user defined.

Density is 1kglm3 and Viscosity is 0.02kg/m-s.

Conclusion:

1.The simulation of steady and transient cases and the Strouhal number is plotted for both Steady and Transient conditions for Re=100.

2. The changes of Coefficient of Drag and Lift by increasing the Reynolds number is observed.

3. The statement that "A vortex street will form only at a certain range of flow velocities, specified by a range of Reynolds numbers (Re), typically above a limiting Re value of about 90", is correct, which we can observe the Vortex at different Reynolds number.

4. The vortex shedding around the cylinder and along the length is observed by Velocity Contour.