Simulation of flow over a cylinder

ANALYSIS OF FLOW OVER A CYLINDER

INTRODUCTION

Von Karman Vortex Sreet

A Von Karman vortex street is repeating patterns of swirling vertices which are arising in the wake of flows around the blunt objects.Normally the phenomena of vortex shedding is shown on a flow over a two dimensional cylinder.The fluid flow past the object reates alternating low pressure vortices on the downstream side of the object and the object will tend to move towards the low pressure zone.

A visualisation of the vortex street behind a cylinder in air (Image source: Wikipedia)

The phenomena usually arises under certain flow conditions,expressed commonly by the dimensionless Reynolds number

CFD SIMULATION FOR A FLOW OVER A CYLINDER

PART-1:

Simulation of flow over a cylinder with steady and unsteady case.

In this case,we are going to simulate the flow over the cylinder using both steady and unsteady solver for a Reynold number of Re=100 and the Strouhal Number for Re=100 is calculated.

Geometry:

The 2-D geometry used for the simulation is shown below:

Meshing:

Meshing Element Type:Triangular

Element size : 0.25m

Inflation: First Layer Thickness

• First layer height : 5 e-003m
• Number of layers : 6
• Growth rate :1.2

Sizing: Edge Sizing

• Number of divisions:50

Number of Nodes: 20720

Number of Elements : 40520

Orthogonal Quality of Mesh : 0.968

Fluent Setup:

Material Specification: Fluid - Air

Density(kg/m3):1

Viscosity(kg/m-s):0.02

Reynolds Number,Re = 100

Physical Model : Laminar

Boundary Conditions: Inlet - Velocity Inlet (1 m/s)

Outlet - Pressure Outlet(Gauge Pressure = 0 Pa)

wall - symmetry

wall motion:stationary wall

shear condition : No slip

• A monitor point was created at a distance of 8 m from the centre of the cylinder along the x axis,for the measurement of vortex flow

Solution Method : SIMPLE

Type of Initialisation: Hybrid Initialisation

Solution:

(A) Steady Case:

A.1 Residual Plot:

• Solution converged near to 350 iterations.

A.2 Vertex Average of Velocity magnitude at Monitor point:

A.3 Drag Coefficient:

• Coefficient of Drag,Cd=2.3324

A.4 Lift Coefficient:

• Coefficient of Lift,Cl=0.05739

A.5 Vortex Shedding:

• Strouhal Number(St) is dimensionless number,describing the oscillating flow mechanism.
• Strouhal Number for the above simulation was obtained from the FFT graph in the result and the mean Strouhal number was found to be St=0.25.

(B) Unsteady case:

• Time step size : 0.1
• Time step : 1000
• Max number of iteration per timestep :20

B.1 Residual Plot:

B.2 Coeffiecient of Drag Plot:

• Coefficient of drag,Cd = 2.2469

B.3 Coefficient of Lift Plot:

• Coefficient of lift,Cl = 0.05378

B.4 Vertex average of velocity magnitude at monitor point:

Vortex Shedding frequency:f=Number of cycles/Time for cycles

= 3/20

= 0.15 Hz

We know that , Strouhal Number St = f*L/U

where, f=vortex shedding frequency

L= characteristic length over which the flow takes place

U=free stream velocity of flow

Therefore, St = 0.15*2/1

= 0.3

Observations:

• From the residuals plot as shown above we could observe that the solution converged in about 350 iterations in steady case and and for almost about 18500 iterations in the unsteady case for a timestep size of 0.1, ie the residual shows a repeating pattern after some iterations.Hence we will be able to assume that the flow has converge
• The vertex average of the velocity magnitude that was plotted shows an oscillating behaviour after certain iterations,this is due to the vortex shredding in the cylinder,thus by seeing the variations in the velocity we can confirm that the flow has converged.
• During the analysis of flow in staedy simulation ,we are not able to accurately predict the result during the intermediate phase of the flow whereas the unsteady case or the time dependent flow helps us to obtain accurate result at any time of the flow.Thus the result obtained during the unsteady simulation can bw judged as accurate about the strouhal number.

PART II:

Normally for 40<Re<100 , the laminar vortex shedding will be formed behind the cylinder due to the instability of the wake region and moreover for Re>100,the flow will be in transition from laminar to turbulent.So in the next cases some simulations were done for Reynolds number Re=10,100,1000,100000 & 1,00,000 in steady state solver only and the coefficients of drag and lift are calculated and its effect on increasing the Reynold number is analysed.

• The Reynolds number is varied by the changing the velocity of the inlet and all other parameters mentioned above like meshing remains unchanged.

Case 1.Re = 10.

Re = 10 ( `rho`=1 kg/`m^3`,L=2 m)

Since , `Re=rhouL/mu`

Therefore, u = 0.1m/s.

1.1 Residual Plot:

• The flow has converged at an iteration of 491.

1.2 Vertex average of velocity magnitude at monitor point:

1.3 Coefficient of Drag:

• Coefficient of drag,Cd=0.0647

1.4 Coefficient of Lift:

• Coefficient of lift,Cl= 0.002978

1.5 Vortex Shedding:

• For a Re = 10,we are able to note that the phenomena of vortex shedding is not taking place.The velocity almost achieves a constant value after 400 iterations.

Case 2: Re= 100

Since `Re=rhouL/mu`

u= 1 m/s.(`rho`=1 kg/`m^3`,`mu=`0.02 Pa.s)

2.1 Residual Plot:

• Flow converged almost for an iteration of 350.

2.2 Coefficient Of Drag,Cd:

• Coefficient of drag,Cd=2.3324

2.3 Coefficient of lift,Cl:

• Coefficient of lift,Cl=0.05739

2.4 Vertex average of velocity magnitude at monitor point:

2.5 Vortex Shedding:

Case 3: Re = 1000.

Here,u ie ,inlet velocity = 10m/s.

3.1 Residual Plot:

• Flow almost connverged at about 150 iterations.

3.2 Coefficient of Drag:

• Coefficient of Drag,Cd=139.75

3.3 Coefficient of lift:

• Coefficient of lift,Cl=9.006

3.4 Vertex average of velocity magnitude:

3.5 Vortex Shedding:

Note: For the next two cases , ie Re=10000 and Re=100000 ,turbulence model,ie k-omega SST turbulent model have been used for the simulations.

Case 4: Re=10,000

The inlet velocity, u = 100m/s.

`rho`=1 kg/`m^3` and `mu=`0.02 Pa.s

4.1 Residual Plot:

4.2 Coefficient of Drag:

• Coeffcient of Drag,Cd=12347.38

4.3 Coefficient of Lift:

• Coefficient of lift,Cl=6727.61

4.4 Vertex average of velocity magnitude:

4.5 Vortex Shedding:

Case 5: Re = 1,00,000:

inlet velocity,u=1000m/s.

5.1 Residual Plot:

• Flow has converged for a 100 iterations.

5.2 Coefficient of Drag:

• Coefficient of drag,Cd=1063962

5.3 Coefficient of Lift:

• Coefficient of lift,Cl=-222976.

5.4 Vertex average of velocity magnitude:

5.5 Vortex Shedding:

CONCLUSIONS:

• With an increase in the Reynolds number,the flow pattern becomes unsyymetrical w.r.t axis perpendicular to the direction of flow
• Drag force,ie the force that is exerted by the flowing fluid on the cylinder depends upon the Reynolds number of the flow.
• We can observe that when the Reynolds number is increased the coefficient of drag and lift is increased.