Steady Vs Unsteady flow over a cylinder

 

Aim

• Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100. 
• 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)
• Discuss the effect of Reynolds number on the coefficient of drag.[Results should be validated with any standard literature & error must be within 5%.

 

Solution:

Construction of the cylinder :

 

 

                                                                 2 m cylinder 

 

 

 

                                                  Creation of Wind Tunnel 

 

                                                                                    Meshing

 

We have used the following in the meshing of the cylinder as shown :

Inflation layer meshing : 

We need to have a sufficiently fine mesh to adequately capture regions where the flow will experience rapid change in key variables such as pressure, velocity or temperature. To do this, we need to use inflation layer meshing to accurately capture the boundary layer region for any wall-bounded turbulent flows.

 

Mesh Sizing :

We  easily apply a face sizing to any given face, or groups of faces, to control the mesh size on those particular faces.  This is one of the more common ways that you can control the mesh and ensure that you are getting a consistent, high-quality mesh sizing in your desired regions. We can also set the local growth rate, which will affect how fast the mesh will grow away from the face.

 

Part 1 :

Now we will produce a fine mesh with an element size of 0.5 m as shown below :

 

 

Now in order to calculate the vortex shedding for the different reynolds number we ll have to calculate the velocity for that particular reynolds number :

Now we know that the reynolds number is given by :

 

Re = Density * velocity * length / viscosity

Therefore the velocity for Re = 100 is given by :

Velocity = 1.41 × 10^-5 *100/1.2 * 2 

            = 0.0754 m/s 

 

Now we will be defining strouhal number as below : 

The Strouhal Number is a dimensionless value useful for analyzing oscillating unsteady fluid flow dynamics problems.

The Strouhal Number can be expressed as   

St = ω l / v       

where

St = Strouhal Number

ω = oscillation frequency

l = characteristic length

v = flow velocity

The Strouhal Number can be important when analyzing unsteady, oscillating flow problems. The Strouhal Number represents a measure of the ratio of the inertial forces due to the unsteadiness of the flow or local acceleration to the inertial forces due to changes in velocity from one point to an other in the flow field.

 

Now we will be doing analysis of the cylinder as shown and calculate the strouhal number :

Case1 : Steady State Condition 

 

 

 

 

Now frequency = 1/ Time period 

Since we are doing a steady state analysis which is independent of time period we cannot calculate the time period ,the frequency and hence the strouhal number cannot be calculated for steady state condition.

Case2 : Transient state 

 

 

Now we know that the frequency = no of cycles / time change 

                     Therefore frequency = 2 /1100 -900

                                                   = 2/200

                                                  = .01 hz

 

Now we know St = ω l / v       

Therefore St = 0.01*2/0.06

                   =  0.333 

Therefore strohal number for transient state is 0.33

 

 

 

Part -2 :

 

Now we will be calculating  the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10, 100, 1000, 10000 & 100000.

 

1.Reynolds Number = 10 

Now we know that :

Re = Density * velocity * length / viscosity

Therefore the velocity at inlet will be given by :

Velocity = 1.41 × 10^-5 *10/1.2 * 2 

            = .00005 m/s

 

Coefficient of Drag :

 

 

Coefficient of Lift : 

 

 

Convergence : 

 

Coefficient of Lift :

2.8354567e-09

Coefficient of drag : 

7.0997502e-07

 

2.Reynolds Number = 100

Now we know the velocity for Re =100 is  0.0754 m/s .

Coefficient of drag :

 

0.0076731182

Coefficient of Lift :

 

 

Convergence :

 

Coefficient of drag : 0.0076731182

Coefficient of Lift :   0.0015169003

3.Reynolds Number = 1000

Now the velocity will be given by :

 

Velocity = 1.41 × 10^-5 *1000/1.2 * 2 

            = 0.0058 m/s 

Coefficient of drag :

 

Coefficient of Lift :

 

Convergence :

 

Coefficient of Lift : -8.6979697e-07

Coefficient of Drag : 4.6596986e-05

 

4.Reynolds Number = 10000

Velocity = 1.41 × 10^-5 *10000/1.2 * 2 

            = 0.0585 m/s 

 

Coefficient of Drag : 

Coefficient of Lift :

 

Convergence : 

 

 

Coefficient of Lift :    0.00068644252

Coefficient of Drag : 0.0046045126

 

5.Reynolds Number = 100000

Velocity = 1.41 × 10^-5 *10000/1.2 * 2 

            = 0.585 m/s 

 

Coefficient of Drag

 

 

Coefficient of Lift 

 

 

 

Convergence :

 

 

Coefficient of Lift :   0.21898922

Coefficient of Drag : 0.43486551

 

Conclusion

Effect of Reynolds number on Coefficient of drag and Lift :

As the reynolds number increases the coefficient of lift and drag also increases .