Vortex Shedding- Flow over a cylinder

Vortex shedding is an oscillating flow that takes place when a fluid such as air or water flows past a blunt surface at certain velocities and Reynolds number. In this type of flow, vortices are created at the back of the body forming Von Karman Vortex Street which is a repeating pattern of swirling vortices.

Aim:

1.) To simulate the vortex shedding in both transient and steady state conditions, to find the Strouhal number for the transient flow over a cylinder.

2.) To calculate the Coefficient of Drag, Coefficient of Lift and vertex average velocity for flow over a cylinder at various Reynolds number (10, 100, 1000, 10000, 100000) using steady state solver and to analyse the effect of Reynolds number on Coefficient of Drag.

Solution:

Geometry Preparation:

• From the Ansys Workbench, Fluent model is selected and run as a stand alone module.
• Click on Geometry option, the Spaceclaim window opens
• Change the units to meter in the spaceclaim settings
• In the Spaceclaim workspace, draw a cylinder in 2D plane with diameter 2m the flow area is described from the center of the circle, to the right draw a reference line with length 20 times the diameter and on the left with length 10 times the diameter.
• The height of the flow surface is given by 10 times the diameter of the cylinder.
• Select the rectangle option and draw a rectangle enclosing the cylinder using the reference lines.
• The fill command is used by selecting the sketch and the cylinder inner portion is removed.

Mesh Preparation:

• In the meshing console, the type of meshing is changed from Quadrilateral dominant to Triangle from the method menu
• The element size around the cylinder is changed to make the circle more round by selecting sizing method and selecting edge sizing method to number of division. The number of divison given is 42.This makes the curve of the cylinder more smooth.
• The inflation layer method is then given by selecting the first layer height as 5e-3 and number of layers is assigned 12.

Inflation layer: The inflation layer is used to create thin elements along the surfaces where the velocity gradient is to be measured under no slip conditions. It creates finer mesh along the region where the gradients are to be measured instead of through out the body.It is a type of body fitted mesh

• The element size is reduced to 0.25m for finer mesh.
• The boundaries are named inlet and outlet, the cylinder walls as wall and the two bounding layers are under symmetry condition.

Quad Dominant mesh

Triangle meshing

Sizing Method

Inflation layer

Part-1

Case 1: Steady State Condition

Density (ρ): 1 kg/m^3

Viscocity (µ):0.02 kg/m*s

Velocity (u): 1m/s

Reynolds number = ρ*D*u/µ= 1*2*1/0.02

= 100

-The flow is selected as Steady state and pressure-based solver is used for this simulation.

- In physics ribbon, the viscosity model is selected as Laminar with no energy. The add material is selected and user-specified material is added with density and viscosity of air as mentioned above.

-The inlet boundary condition is selected to inlet-velocity with velocity at 1m\s and outlet as outlet-pressure with gauge pressure set at 0. The cylinder wall is set at no-slip condition.

- In the solution ribbon, the residual convergence is turned off in order to attain steady state after a number of iterations.

-In the results ribbon, a monitor point is inserted exactly at 8m away from the center of the cylinder.

- The required plots are selected from the reports ribbon like average vertex velocity, pressure and contour plot for velocity gradient.

- The simulation is initialized and run till the solution converges.

Monitor Point

Velocity contour initialization

Initial Velocity contour

Initial Pressure Contour

Case 1

Residual Plot Re=100 Steady State

Vertex Average Velocity Magnitude

Vertex Average Pressure

Case 2 : Transient State

Density (ρ): 1 kg/m^3

Viscocity (µ):0.02 kg/m*s

Velocity (u): 1m/s

Reynolds number = ρ*D*u/µ= 1*2*1/0.02

= 100

- In case 2 all the settings are similar to previous case , but the flow type is selected as transient

- After initialization, the number of time steps and time step values are given based on amount of flow time required.

Residual

Velocity Magnitude

Strouhal number:

The Strouhal number is a dimensionless number describing oscillating flow mechanisms. For large Strouhal number(order of 1), viscocity dominates the flow, for low Strouhal numbers, the quasi-steady-state portion of the movement dominates the flow.

St= f*L/U

Where,

f = Frequency of vortex shedding (hz)

L = Length of reference surface (m)

U = Free Stream velocity (m\s)

Calculation Strouhal number for transient flow, first the frequency of the oscillations are measured by using the formula

Frequency= number of cycles/ time period

The frequency is calculated from the Vertex Average Velocity graph

Number of cycles = 3

Time period = 79-55= 24 seconds

Frequency= 3/24 = 0.125Hz

To calculate Strouhal number, L= 2m, F=0.125 Hz, U=1 m/s

St= 2*0.125/1 = 0.25

Inference: From the simulations we can see that, the vortex shedding can be seen much clearly when the flow conditions are set to transient flow, this is because the shedding occurs in transient condition. The residuals in the steady flow are converged but the residuals in the transient flow are oscillating.

The Strouhal Number calculated for Transient flow is 0.25

Part 2

Case 1 :

Density (ρ): 1 kg/m^3

Viscocity (µ):0.02 kg/m*s

Velocity (u): 0.1m/s

Reynolds number = ρ*D*u/µ= 1*2*0.1/0.02

Re= 10

Scaled Residual

Vertex Average Velocity

Lift Coeffecient

Drag Coeffecient

Case 2 :

Density (ρ): 1 kg/m^3

Viscocity (µ):0.02 kg/m*s

Velocity (u): 1m/s

Reynolds number = ρ*D*u/µ= 1*2*1/0.02

Re = 100

Scaled Residuals

Vertex average Velocity

Lift Coeffecient

Drag Coeffecient

Case 3 :

Density (ρ): 1 kg/m^3

Viscocity (µ):0.02 kg/m*s

Velocity (u): 10m/s

Reynolds number = ρ*D*u/µ= 1*2*10/0.02

Re = 1000

Scaled Residuals

Vertex Average Velocity

Vertex Average Velocity

Drag Coeffecient

Case 4 :

Density (ρ): 1 kg/m^3

Viscocity (µ):0.02 kg/m*s

Velocity (u): 100m/s

Reynolds number = ρ*D*u/µ= 1*2*100/0.02

Re = 10000

Scaled Residuals

Vertex Average Velocity

Lift Coeffecient

Drag Coeffecient

Case 5 :

Density (ρ): 1 kg/m^3

Viscocity (µ):0.02 kg/m*s

Velocity (u): 1000m/s

Reynolds number = ρ*D*u/µ= 1*2*1000/0.02

Re = 100000

Scaled Residual

Vertex Average Velocity

Lift Coeffecient

Drag Coeffecient

Co-efficient of Drag :

The drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag equation in which a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag.

Cd=2F_d/ρu²A

Where,

F_d= Drag force (N)

ρ= Density (Kg/m³)

u= Flow velocity (m/s)

A= Reference area (m²)

Co-efficient of Lift:

The lift coefficient (CL) is a dimensionless coefficient that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area

CL= 2L/ ρu²S

Where

L= Lift Force (N)

ρ = Density (Kg/m³)

S= Reference area (m²)

u= Flow velocity (m/s)

Values of Cd, CI and Velocity for all cases

Case No	Reynolds Number	Co-efficient of Drag	Co-efficient of Lift	Vertex average Velocity (m/s)
1	10	3.35669	-0.00148	0.04497
2	100	1.3596	-0.03674	0.2848
3	1000	0.8837	-0.1932	7.72
4	10000	0.7269	-0.343	62.96
5	100000	0.5832	0.0418	730

Result:

1. From the steady state and transient state simulation done for Re 100 it was found that , the transient analysis gave a much better result. The residuals of the steady state converge at a point, but the residuals of transient state are oscillating

The Strouhal Number for a flow with Reynolds number 100 using Transient analysis was found to be 0.25

2. It is found from the plot for Co-efficient of drag that, the drag co-efficient reduces with increase in Reynolds number and the Lift co-efficient increases with increase in Reynolds number
3. Comparing the obtained values of drag coefficient with a standard research paper for flow over cylinder and the results are tabulated below

Reynolds Number	Obtained values of Cd	Standard Cd values from Reference paper(approx)
10	3.3566	-
100	1.3596	1.42
1000	0.8837	0.94
10000	0.7269	0.86
100000	0.5832	0.52