Steady Vs Unsteady flow over a cylinder

AIM- Simulate the flow over a cylinder and explain the phenomenon of Von Karman vortex street.

INTRODUCTION

 Von karman vortex street is a repeating pattern of swirling vortices, caused by a process known as vortex shedding, which is responsible for the unsteady separation of flow of a fluid around blunt bodies. Vortex shedding will only form at a certain range of flow velocitiy and reynold number. Reynold number(Re) for a flow is a measure of the ratio of inertial to viscous forces in the flow of a fluid around a body or in a channel.

Reynold Number(Re)=`rho`vL/`mu`

where

`rho` is the density of fluid

v is the velocity of fluid

L is the characteristic linear dimension

`mu` is the dynamic Viscocity

PROCEDURE

Making the geometry

A 2D sketch was made on spameclaim with a circle at the origin with diameter of 2 meters. the inlet is 20 meters away from the centre of the circle to the left. The outlet is on the right of the circle and is 40 meters away from the centre.The length of both in inlet and outlet is 20 meters. After making the sketch "Pull" tools was used to convert the 2D sketch into a sheet.

Meshing

After making the geomerty, its was time for meshing the geometry. The elemt size size was set to 0.15m.The default mesh done by ansys was quad dominant.So I changed the mesh to Triangular. Also the was not also circle was not also a  perfect as its is very difficult to get a perfect circle.So for that edge sizing was done for the cirlce and was divided into 36 edges. 6 Inflation layer were also added around the circle. After this inlet,outlet,wall and symmetry boundries were named. All other details about the mesh are give below in the snapplets.

Figure 1- An image of the mesh

Figure 2-Details of Mesh,Method,Edge Sizing and Inflation layer.

Setup

After meshing, Fluent was open and the mesh was checked.An User defined material was cerated for the given Problem(Properties given Below). There are two parts of the problem. An monitor Point was created 8m to the left of the circle at which the velocity was calculated by using Vertex average Function. The viscous model was set to laminar are all the parts.A counter plot was created to visualize the vortex Shedding.

Figure 3- Properties of the used Material.

Part 1.1-Steady state simulation & Reynold Number(Re)=100

The inlet velocity was set to 1m/s.Number of iterations=1000. As steady State simulation is indepedent of time,stronwal number was not calulated.

Part 1.2-Transiant simulation & Reynold Number(Re)=100

The velocity and other parameter were same, but the only change was that it was a Transiant simulation with 

Now strouhal number can be calculated-

St=fD/V

where:-

f is vortex shedding frequency

D is diameter of Cylinder

V is velocity of flow

f=3/20=0.15 (From the velocity graph)

Now St=0.15`times`2/1

St=0.3 

Part 2

1) Re=10, v=0.1m/s

2) Re=100, v=1m/s

3) Re=1000, v=10m/s

4.) Re=10000, v=100m/s

5.) Re=100000 v=1000m/s

CONCLUSION

Reynold No.	Lift Coefficient	Drag Coefficient
10	0.0012161127	6.8456279
100	0.037912241	2.2124322
1000	0.30693531	1.8277082
10000	0.96680927	1.7835201
100000	1.2537591	1.8176176

As we can see from the above mentioned table with increase in reynold number the coefficient of Drag decreases and coefficient of lift increase.