Steady Vs Unsteady flow over a cylinder

Aim :- Numerical simulation of laminar flow past a circular cylinder.

Theory :- The given above topic mainly focuses on what happens when a laminar flow passes a circular cylinder, here my prime objective is to find out which phenomena actually happens at the wall of the cylinder. Since it would take a lot of time and cost for setup while performing the experiment to analyse the behaviour of fluid at wall of cylinder, hence I have performed numerical experiment i.e simulation for this case so that I can analyse the behaviour of fluid at the wall in short span of time.

So, here what actually I have done, I just setup the case for both steady and transient time for different reynolds number like 10,100,1000,10000,100000 respectively and analysed behaviour of fluid for all case. In order to obtain different reynolds number, I just change the viscosity of the fluid.

Finally, when I ran simulation, I found out that some vortices are being formed at the back of cylinder wall in region which is creating turbulence in the flow even though the flow in the region is laminar. However, I came to know that this phenomena is vortex shedding which happens in laminar flow. So, keeping in mind, I generated differents plots related to this concept and tried to understand that how different physical parametrs affects the vorticity behind the cylinder wall. Hence, I have dealt with such problems in this project.

In fluid dynamics, vortex shedding is an oscillating flow that takes place when a fluid such as air or water flows past a bluff (as opposed to streamlined) body at certain velocities, depending on the size and shape of the body. In this flow, vortices are created at the back of the body and detach periodically from either side of the body forming a von karman vortex street. The fluid flow past the object creates alternating low-pressure vortices on the downstream side of the object. The object will tend to move toward the low-pressure zone.

Pre-processing and solver setting :-

(i) Surface generation in spaceclaim

(ii) Mesh generation and adjustment in design-modeler

a. Mesh overview (fig 1)

b. Mesh in detail (fig 2)

Setting for mesh generation of base mesh for depicted fig 1 and fig 2

1. Setting for base mesh

2. Setting for type of mesh to be used for mesh generation

3. Setting for accurate sizing of edge(circle) in geometry

4. Setting for edge inflation in geometry as in fig 2

5. Model topology and Naming convention for boundary condition

Condition and Solver Setup in Ansys fluent

1. General setting for solver

2. Boundary condition

A. Inlet

B. Outlet

C. Wall

3. Run parameters

For steady state For transient state

Post-processed results :-

Here, I have assumed lift coefficient for both case for convergence analysis(for reynolds number 100) and what I found that in both cases magnitude of lift coefficient was oscillating which gave me information that solution have been converged because when similar pattern repeat again and again for any particular quantity on account of iteration or time-step of and it's range is in between particular maximum and minimum value then it confirms that solution has been converged.

So, here in both case, I saw that similar pattern were arising and in case of transient state, I observed that solution was converged more precisely then steady case so I could say that transient case have more convergence precision than steady case. So, I can suggest that transient case have more reliable solution then steady case.

Steady case

Transient case

1. Calculating Strouhal number when Re is 100

For Steady case

For Transient case

Here I have plotted graphs for both case and calculated the value, where I found value of strouhal number of 2 for steady case and 1.4e-2 for transient case. So, when I calculated this number for both case I got information that oscillation in magnitude is more reasonable in terms of transient case which gives more accurate value of strouhal number.

Calculating coefficient of Drag and coefficient of lift in Steady case :-

For reynolds number 10

For reynolds number 100

For reynolds number 1000

For reynolds number 10000

For reynolds number 100000

Plot showing Vortex shedding behind the cylinder using velocity contour :-

For Reynolds number 10

For Reynolds number 100

For Reynolds number 1000

For Reynolds number 10000

For Reynolds number 100000

Calculated drag coefficient and lift coefficient for different reynolds number in steady case

Reynolds Number	`C_d`	`C_l`
10	6.68	`4.8**10^(-4)`
100	270.59	34.295
1000	197898.780	`1.3148**10^6`
10000	`1.75**10^8`	`2**10^8`
100000	`1.50**10^10`	`8.0**10^9`

Here, I tabulated the drag coefficient and lift coefficient for different reynolds number and what I found that both lift and drag coefficient increases exponentially with increase in reynolds number which itself is increased exponentially in power of 10.

The tabulated form of velocity gave us information that as I would increase the reynolds number, the laminar flow would become more turbulent by creating vorticity behind the cylinder wall. It also gave information that even in laminar flow, there could be vortex shedding which could create turbulence in the region of flow. And this phenomena. We come to known as karman vortex street.