Steady Vs Unsteady flow over a cylinder

Aim:

Part 1:

Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100

Part 2:

100000. a) 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)
100001. b) 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 %]

Explanation on Vortex Shedding:

Vortex shedding happens when a fluid (generally low viscosity such as air, water) passes over a bluff body at specific fluid velocity and shape of the body over which fluid is flowing. It causes oscillating high-low pressure variation in the flow past the body, and so, the body starts moving in the direction of low-pressure region. The frequency and velocity of moving body if matches with the resonating frequency, vortex shedding may damage the body.

There are examples of structures such as chimneys, bridges etc. damaged due to vortex shedding.

The frequency at which shedding takes place, is called as shedding frequency.

 `Strouhal number =(shedding frequency ×characteristic length)/(flow velocity)`

                                                                    PART 1

Case Setup:

For both, Steady and Transient simulations, mesh size is kept same.

Mesh Description:

Triangular Mesh,

Number of Nodes: 20532 and Number of elements: 40172

The inlet velocity was 1m/s for all cases and Kinematic viscosity used as 0.05 kg-m/s, So that Reynold’s number is 100.

                                                                        Steady simulation

                                                                                     TRANSIENT

Shedding frequency is 1 cycle in 7.5 seconds, i.e 0.133 Hz

 Strouhal number =(0.133 ×2)/1

Strouhal number =0.26`            

PART II

For Re = 10

Changing velocity values, v = 0.1 m/s

Cl ()

-------------------------------- -------------------

cylinder_wall 0.0001214242

Cd ()

-------------------------------- -------------------

cylinder_wall 0.017319841

For Re = 100

Velocity = 1 m/s

Cd ()

-------------------------------- -------------------

cylinder_wall 0.692283

Cl ()

-------------------------------- -------------------

cylinder_wall -0.032736148

For Re = 1000

Velocity v = 10 m/s

Cd ()

-------------------------------- -------------------

cylinder_wall 40.055892

For Re = 10000

Air velocity = 100 m/s

Conclusion:

Value of Cd is dependent on Re value, in this case, velocity value. And the value increases as velocity is increased.

Similar relation for Coefficient of lift Cl, as velocity is increasing, the amplitude of oscillation is increasing.