Steady Vs Unsteady flow over a cylinder
Objective:Simulation of flow over a 2D cylinder by Steady and Unsteady Approach and illustration of Karman Vortex effect.
Introduction of Karman Vortex Effect:
Vortex formation behind a circular cylinder.
A vortex is in the process of formation near the top of the cylinder surface. Below and to the right of the
first vortex is another vortex which was formed and shed a short period before. Thus, the flow process in
the wake of a cylinder or tube involves the formation and shedding of vortices alternately from one side
and then the other. This phenomenon is of major importance in engineering design because the
alternate formation and shedding of vortices also creates alternating forces, which occur more frequently
as the velocity of the flow increases.
When the frequency is in the audible range, a sound can be heard and the body appears to sing.
Resonance may occur if the vortex shedding frequency is near the structural-vibration frequency of the
body. A dimensionless number, the Strouhal number Sr, is commonly used as a measure of the
predominant shedding frequency fs.
`Sr=(f*L)/U`
f--Shedding Frequency
L--Characterstic Length (equal to the diameter D in case of a circular cylinder or tube in cross flow).
U--Free stream Velocity.
According to the Newton's second law, time rate change of the linear momentum is equal to the sum of
all external forces acting on a system. Therefore, an integration of the linear momentum inside a
control voulme surrounding the circular cylinder can provide information of the aerodynamic forces (lift
and drag) acting on the cylinder.
When vortices shed from the cylinder, uneven pressure distribution develops between the upper and
lower surfaces of the cylinder, generating an oscillatory aerodynamic loading (lift) on the cylinder.
A simple balance of the momentum flow in and out of the control volume surrounding the object
suggests that there is net force acting on the object. This net force along the flow direction is called the
drag.
Importance of Karman Vortex street:
The Karman street can lead to unwanted noise or even cause failure of structures when the vortex
shedding frequency coincides with the natural frequency of structure. This type of vortex-induced
oscillations can occur in a variety of situations such as chimneys, bridges, heat exchanger tubes,
overhead power cables and marine structures. Therefore understanding the physics of the Karman
vortex street is crucial to avoid disasters in these situations.
Part-1
a).Simulation of Steady and Unsteady case for Reynolds number equal -100 and Strouhal Number calculation:
1.Steady State simulation for flow over a cylinder:
Approach for simulation is simple
First start from Geometry,Then Meshing it and then setting up case ,for Getting Solution.
a.Geometry:
We have 2D cylinder of diameter 2 metre and dimension of domain is 20 x 60 metre.
b.Meshing:
Mesh grid size is 0.25 m.
For capturing better results near cylinder ,we have added inflation layers near cylinder walls.
c).Setup:
Laminar model was used as Reynolds number was in laminar range, i.e.100.
A monitor point was created 8 m away at the right side from centre of cylinder for analyzing velocity at that point.
Reference Values was set to:
Area-2 `m^2`;
Length-2 m;
Depth-1m;
Density-1 `(kg)/m^3`;
Velocity-1 m/s;
Dynamic Viscocity- 0.02 kg/m-s;
Vertex average ,Drag and Lift coefficient report was created in the form of plot and text file.
d).Solutions:
1.Residual Plot:
2.Vertex average plot of Velocity(@Monitor point)
3.Coefficient of Lift Plot
4.Coefficient of Drag Plot:
5.Velocity simulation Result(showing Vortex shedding Effect)
## As we can see from Vertex Average Plot of Velocity,around 400 iterations ,the plot is following pattern and it has reached a steady state.From there we can conclude ,the solution has converged.
##As in steady state approach solution is not dependent on time step,so we cannot find the frequency of vortex shedding for any particular period of time,as a result it is not possible to evaluate Strouhal Number .
1.Unsteady State simulation for flow over a cylinder:
Approach for simulation is simple
First start from Geometry,Then Meshing it and then setting up case ,for Getting Solution.
##Geometry,Mesh size will remain same as above,only change will be in setup.
Transient approach will be followed :
Time step size=0.5sec
Max. Iteration /time step=5
Solution Results:
1.Residual Plot:
2.Vertex average Plot for Velocity(@ Monitor Point)
3.Coefficient of Lift Plot:
4.Coefficient of Drag plot
5.Velocity Simulation Result showing Vortex Shedding:
6.Strouhal Number for Re=100:
For Reynold number equal 100 ,Strouhal number comes out to be 0.0159.
Part 2-
1. Calculation of Drag coefficient and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000. (Run with steady solver)
| Reynold Number | Average Coefficient of Drag | Average Coefficient of Lift |
| 10 | 3.324 | 0.00092 |
| 100 | 1.336 | 0.0164 |
| 1000 | 1.06 | -0.011 |
| 10000 | 0.95 | -0.038 |
| 100000 | ~0.8 | 0.0219 |
Collage of Drag coeffient with different Reynold numbers:
Part -2:
2. Effect of Reynolds number on the coefficient of drag
Trend of variation of Drag Coefficients with Reynold number :
From the graph ,it can be seen that:
With the increase in Reynold number,drag coefficient value decreases.With Reynolds number usually velocity also increases,so it can be said that with the increase of velocity drag coefficient decreases.
##Description of Material Used:
Material used was user defined material:
Density-1 `(kg)/m^3`
For Re=10,100,1000,10000
Dynamic Viscocity- 0.02 `(kg)/(m-s)`
For Re=100000
Dynamic Viscocity- 0.002 `(kg)/(m-s)`
Conclusion:
1.When Re number was 10 then only ,we didnt get Karman Vortex Street.
Otherwise for all Re number we captured Vortex shedding.
2.For capturing Vortex shedding accurately near cylinder walls,adding Inflation layer was very important .
3.For achieving results near experimental results,Y plus value or first layer thickness is utmost important.
4.Drag coefficient decreases with increase in Reynolds number.