Study of flow over a cylinder using Ansys Fluent

I>PART 1

I. Introduction

This project is on analyzing the flow over a cylinder to study the effects of shedding of vortex in Steady as well as transient state.Vortex shedding is a phenomenon which occurs when fluid air or water passes through a cylinder or a bluff body wall.The vortex shedding depends on parameters like velocity of the fluid,type of the fluid and shape and size of the object.

The vortex shedding occurs above a particular value of Reynolds Number>For the current simulation we have taken the reynolds Number to be 100.

Here we will be performing 2D simulations for modifying Reynolds Number by creating a customized fluid. Also, vortex shedding would be studied and observed by adding monitor points which act as a sensor to capture flow parameters like pressure, velocity,lift coefficient or drift coefficient etc at that point of concern.

The computational domain is created using SpaceClaim utility in Ansys to carry out this project like the dimensions given in the figure below.

The cylinder is of 2m diameter. For inlet velocity Boundary conditions are used and for the outlet , pressure based boundary conditions are used along with the symmetry boundary conditions on top and bottom side of the flow domain.

Vortex Shedding:

In fluid dynamics, a vortex is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved.It has low pressure in the centre/core. Vortex shedding is an oscillating flow that takes place when a fluid such as an air or water flows past over a bluff body depending on size and shape of the body.

II. Objective

To simulate Flow over a cylibder using steady and transient mode of fluid flow past a cylinder by Ansys fluent and to study the convergence criteria of the study and at last to determine or evaluate the Strouhal Number.

III. Geometry creation and Meshing

Geometry created in SpaceClaim(Ansys Fluent).

Meshing:

Method chosen: triangular

Elements : 40373

Element size : 0.25m

Edge sizing of cylinder: 56 no. of divisions

Inflation layer is applied across the boundary of the open cylinder: Option-First layer thickness

Maximum Layers-2

Growth rate - 1.2

IV. Case Setup to run the simulation of flow in Steady and Transient state

1. pressure based solver is used
2. Velocity Formulation- Absolute is used for this simulation
3. Time: Steady & Transient(both cases were run)to observe the variations in vortex shedding and the steady state was performed again at various Reynolds Number.
4. Viscous model - Laminar is chosen for the viscous flow as there is no scope of turbulence or eddies formation
5. Inlet velocity - 1m/s is applied across the inlet(Boundary Condition)
6. Outlet - Gauge Pressure: 0 pascal:1 atm
7. Hybrid Initialization was done before running the simulation
8. Density- 1kg/`m^3`(constant) and Viscosity- 0.02 kg/m-s(constant) is taken that of water(automatic)
9. Boundary conditions are applied as in the geometry mentioned above.

The reason to put custom material values is to make Reynolds No. 100

`Re = (rho*v*D)/mu= (1*1*2)/0.02 = 100`

Initial conditions Contour plot with grid lines

Velocity

Pressure

V. Steady State

Residual plot:

Simulation was run for 1800 iterations. We can observe that the residuals converges at (400-450)iterations after the values stop fluctuating.

X-velocity and Y-velocity residuals get steady for approx 1e-3 value.

Velocity plot:

The average monitor point velocity plummets till 150 iterations . We can observe that the velocity plot also repeating in periodic fashion after 400-450 iterations showing vortex shedding formation.We have reached steady state and converged near 600 iterations which can be seen from the plot.

Vortex shedding formation in steady state-Velocity:Velocity contour plot

Here a smooth vortex shedding has been obtained for Re. 100.

Von Karman street effect is also observed.

Animation:

Pressure zone:

Transient state:

Here we ran it for 1000 no. of time steps with 0.1 s of time step size.

Residual plot:

We can see the residuals of the solution go up and down a lot finally maintaining a stable solution.We can notice the convergence , and converges at 19000 iterations.

In transient flow, residuals plot of continuity,x-velocity and y-velocity produce very high frequency and hence doesn\'t get steady or stabilize.

Velocity plot:Vertex average of velocity magnitude at the monitor point.

Plot as a function of no. of iterations

The vortex starts forming at 9000 iterations and then raises again and get stabilized at approx 20000 iterations.

A plot as a function of Flow time

We can observe the vortex shedding beginning to take place at around 50 seconds of flow time as the solution reaches convergence with the progress of simulation.

Vortex shedding formation in transient state:Velocity contour plot

Von Karman street effect is also observed.

Animation:

VII. Strouhal Number

The Strouhal Number(Sr) is a dimensionless number describing oscillating flow mechanisms. Experimental results show that it depends on the Reynolds Number and can be made into a graph.

It is given by `Sr = (f*D)/v`

where f = frequency

D = diameter

`v`= velocity

in steady state Since we cannot capture oscillations of velocity wrt time and the state isn't time dependent, it is actually impossible to capture the frequency requires to calculate Sr.

We can see the oscillations are periodic and follows a stable cycle from 50s flow time to 100s flow time and has acycle of 7.5 with velocity 1m/s and diameter 2m.

Hence we have `f = 7.5/50=0.15`

Therefore `Sr = 0.30`

II>PART 2

I)Re = 50, viscosity of the fluid = 0.04 m^2/s

Residual plot:

As we can see from the plot `C_d` remains 0 throughout at every iterations. So there is no drift force existing near the walls of the cylinder.

Plot of drift coeff vs iteration

The velocity at the point chosen(of concern) at 8m from the centre of the cylinder, where the vertex average of velocity or the monitor point velocity decreases uptill 200 iterations and then converges or relaxes at nearly 0.1 m/s after that. We can see that at later stage there is no fluctuations in the velocity,so we can assume that there is no evolution of vortex or there is no vortex shedding taking place at Re = 50.

Plot of lift coefficient vs iteration

We can see from the plot that since there is no evolution of vortex at Reynolds Number of 50, so lift coeffecient remains uniform throughout and stable at a value nearly equal to 0.

There is no evolution of vortex which can be proved from the below contour plot of velocity field round the cylinder.There is no vortex shedding past the flow and hence there is no von-Karman vortex street evolving.

Velocity contour plot

Animation:

II) Re = 100, is already performed and the results are discuseed in part I

III)Re =150, viscosity of the fluid = 0.01333 m^2/s

Residual plot:

We can see from the plot the solution converges from 200th iterations

As we can see from the plot `C_d` remains 0 throughout at every iterations.So there is no drift forces existing near the walls of the cylinder.

Plot of drift coeff vs iteration

Plot of lift coefficient vs iteration

We can see from the plot there is a periodic oscillation in the value of lift coefficient and the periodicity starts at 150th iteration with a deviation range of 20-25(approx) and then starts to increases and after 300-350th iteration the range of amplitude starts to stabilize with a range of 70-80.So, there is lot of fluctuations in the value of the lift coefficient with the increase in iterations and the behaviour of fluctuation is a periodic oscillation.These fluctuations are because of the shedding of vortices which happens at this reynolds No. of 150 and is seen from 100th iteration

We can see from the below plot of the velocity at the point chosen(of concern) at 8 m from the centre of the cylinder where the monitor point velocity decreases uptill 125th iteration and then increases and decreases i.e it starts to fluctuate from 150th iteration and then it starts to stabilize from 250 iteration. The result we are seeing is a periodic oscillation which is due toi the evolution of vortex past the flow at this Reynolds No.

The evolution of vortex or the von-Karman street can be validated from the below contour plot.

Velocity contour plot

Animation:

IV)Re = 200, viscosity of the fluid = 0.01 m^2/s

Residual plot:

We can see the solution converges at a earlier stage than the case with reynolds Number of 150 i.e here at (150-175)th iteration

As we can see from the plot `C_d` remains 0 throughout so there is no drift force existing past the cylinder.

Plot of drift coefficient vs iteration

Plot of lift coefficient vs iteration

We can see from the plot compared to previous Reynolds No. of 150, here in this case vortex starts to evolve faster. We can see the fluctuation in between (50-100)th iteration and then the value of lift coefficient starts to periodically oscillate with a deviation range of 100 from (100-125)th iteration.

Here we see the same trend in the plot of monitor point velocity vs iteration to that in the case of Reynolds No. 150

Velocity contour plot

Animation:

V)Re = 250, viscosity of the fluid = 0.008 m^2/s

Residual plot:

We can see from the plot that thje solution converges or stabilizes at 150 th iteration.

Plot of drift coefficient vs iteration

Here also we can see that `C_d` remains 0 all throughout and there is no existence of drift force around the walls of the cylinder.

Plot of lift coefficient vs iteration

Here in this case the vortex starts to evolve in between (50-100)th iteration and the value of lift coefficient starts to fluctuate right before 50th iteration and from 150th iteration the periodic oscillation starts with a stable periodicity with a deviation of 140 in the value of lift coefficient.So the the value of lift coefficient oscillates over a larger range than the previous two cases.

Plot of monitor point velocity vs iteration

Velocity contour plot:

Evolution of vortex at this Reynols Number can be evaluated from this figure.

Animation:

VI)Re = 300, viscosity of the fluid = 0.0066 m^2/s

Residual plot:

We can see from the plot, the solution converges in between (100-150)th iteration.

Plot of drift coefficient vs iteration:

Here we can see that `C_d` remains 0 all throughout and there is no existence of drift force around the walls of the cylinder.

Plot of Lift Coefficient vs iteration

We observe the same trend to that of with Reynolds Number 250 and 200.

Plot of monitor point velocity vs iteration

Velocity contour plot:

Animation:

VII)Conclusion

We observe vortex shedding at Reynolds Number 100 and higher but not at Reynolds Number of 50.There is no variation or effect of Reynolds Number on Drift coefficient as the Drift forces is totally negligible or not present on the walls of the cylinder.But there is effect on lift coefficient on varying the Reynolds Number from 50 to 300 at a step size of 50, which we can see from the above plots.