Steady Vs Unsteady flow over a cylinder

Aim : To do various simulations on the flow over a cyinder at various reynolds number

Software used : Ansys 2020 R1

Objectives:

PART-I

1. Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.

PART-II

1. Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000. (Run with steady solver)
2. Discuss the effect of Reynolds number on the coefficient of drag. [ Results should be validated with any standard literature and error should be within 5 %]

In Fluid Dynamics, a Kármán vortex street (or a von Kármán vortex street) is a repeating pattern of swirling vortices, caused by a process known as vortex shedding, which is responsible for the unsteady seperation of flow of a fluid around blunt bodies. It is named after the engineer and fluid dynamicist Theodore Von Karman, and is responsible for such phenomena as the "singing" of suspended telephone or power lines and the vibration of a car antenna at certain speeds.A vortex street will form only at a certain range of flow velocities, specified by a range of Reynolds Number(Re), typically above a limiting Re value of about 90.

Here , we have tested karman vortex street at different reynolds no like 10,100,1000,10000 and 100000

If re <100 , vortex street doesn't form. Other than that for remaing reynolds number it is formed.

Meshing Analysis:

Mesh type : Quadrilateral cells

Element Size : 0.25 m

Edge sizing : 0.05 m

Inflation : layers - 15 and thickness - 0.005 m , growth rate - 1.2

Mesh:

Mesh Closeup:

PART 1:

Comparison of steady flow and unsteady flow.

STEADY FLOW-

Re = 100

Density = 1 kg/m3

Viscosity = 0.02 kg/ms

Inlet Velocity = 1 m/s

Residual Plot:

Lift Coefficent :

Drag Coefficient:

Vertex Average of the Velocity:

Vortex Shedding contour (Velocity contour):

UNSTEADY case (or TRANSIENT case):

Time steps : 1000

Time step size :0.1

Residual PLot:

Lift Coefficient :

Drag Coefficient:

Vertex Average of the velocity:

Vortex Shedding Contour (or Velocity Contour):

Vortex shedding frequency:

f = number of cycles / time of cycles

f= 2.5/20

f=0.125

Strouhal number St=(f*L)/u

St=(0.125*2)/1

St=0.25

CASE 2:

Compring the steady flow with different reynolds number.

(1) Re = 10

inlet velocity (u) = 0.1 m/s

Residual Plot:

Lift Coefficient :

Drag Coefficient:

Vertex Average of Velocity :

Vortex Shedding Contour (or Velocity Contour):

At very slow flow in which we have neglected viscosity entirely. We can see that there is no seperation of flow and no viscous wake downstream of the cylinder.

(2) Re = 100

inlet Velocity (u) = 1 m/s

Residual Plot:

Lift Coefficient :

Drag Coefficient :

Vertex Average of Velocity :

Vertex Shedding Contour (or Velocity Contour):

We can conclude that the flow is steady and converged because curves in residuals reached the constancy.

A stable pair of vortices are formed on the downwind side of the cylinder . The flow is seperated but steady and the vortices generate a high drag on the cylinder.

(3) Re = 1000

inlet velocity = 10 m/s

Residual Plot:

Lift Coefficient:

Drag Coefficient:

Vertex Average of Velocity :

Vortex Shedding Contour (or Velocity Contour):

The flow is steady and converged because curves in residuals reached the constancy.

Flow velocity is increased so these changes we noticed :

1.The downstream vortices become unstable .

2.Vortices are seperated from the body and are alternately shed downstream .

3.The wake is very wide and generates a large amount of drag.

(4) Re = 10000

inlet velocity = 100 m/s

Residual Plot:

Lift Coefficient:

Drag Coefficient:

Vertex Average of the Velocity:

Vortex Shedding Contour (or Velocity Contour):

Flow is steady and converged because curves in residuals reached the constantancy.

The flow velocity is increased even more. Following difference occurs:

1. The periodic flow breaks down into a chaotic wake.

2. The flow in the boundary layer on the windware side of the cylinder is laminar and orderly.

3. The chaotic wake is initiated as the flow turns onto the leeward side of the cylinder.

(5) Re = 100000

inlet velocity (u) = 1000 m/s

Residual Plot:

Lift Coefficient :

Drag Coefficient :

Vertex Average of the Velocity :

Vortex Shedding Contour (or Velocity Contour):

Flow is even increased at higher velocity .(u = 1000 m/s)

The boundary layer transitions to chaotic turbulent flow with vortices of many different scales beign shed in a turbulent wake from the body.

CONCLUSIONS:

1. Drag and lift coefficient values are increased when Reynolds number is increased.

2. With increase in the reynolds number the flow is becoming more unsymmetrical.

3. Increasing velocity eventually brings the turbulent drag upto and even higher than the laminar drag value.

4. Along with this study we conclude that reynolds number below 100 does not show any Von Karmen Effect .

• Preferred Material here is Aluminium Material.