Flow over cylinder

Aim:- Steady and transient flow simulations of flow over a cylinder, explain the phenomenon of Karman vortex street

PART-I

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

PART-II

• 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)
• Discuss the effect of Reynolds number on the coefficient of drag.

Expected results:-

• In both approaches, show that the flow has converged. That is, what quantities or plots can be used to determine that the flow has converged?
• Plots of the coefficient of drag and lift.
• Plots to show vortex shedding behind the cylinder.
• Mention the referred material at the end of the challenge page.

Geometry preperation

Above simulation is done on the two dimensional geometry which is constructed below

procedure

1.Drag the Fluid flow (Fluent) right side of the work bench by double click on the geometry, in space claim change the unit of length to meters by clicking space claim option in file.

2. In space claim select circle from design, draw circle of diameter 2m, choose construction line take inlet 20m from the centre of circle and 40m outlet from centre of circle.

3. 10m above and 10m below the centre of circle for symmetry.

4.After clicking on pull select the geometry then go again select and select the circle thereafter press delete.

Meshing

1.First gives the name of the edges and wall of the cylinder like inlet, outlet, symmetry an walls of the cylinder.

2. Select the mesh in element size put 0.25m after rigth click on the mesh choose select method in insert

3. in automatic method select the geometry and in method choose triangle.

4.Again right click on mesh select sizing in sizing select edge ,in type choose number of division , in number of division put 36

5. Right click on the mesh in insert select inflation , geometry select face,Boundary select cylindrical edge,Inflation option select first layer thickness,First layer height put 5e-3, Maximum layer 6 there after right click on Mesh and apply Generate Mesh.

In fluid dynamic, a Kármán vortex street (or a von Kármán vortex street) is a repeating pattern of swirling vortices, caused by a process known as vortex sheeding, 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.

Setup

Properties of fluid

Density=1 Kg/m^3

Viscosity =0.02 Kg/m-s

Initilization= Hybrid

Initial velocity condition for each case is varying here we taken K-epsilon viscous model.Monitor point was taken as 8 m behind the cylinder to monitor the change in velocity in each itration

Velocity contour at the time of inilization.

Part-I

Case1(a)

Use steadystate solver to simulate flow with reynolds number=100

Pressure velocity scheme=Simple

Number of iteration=500

Inlet velocity=1 m/s

Case1(b)

Unsteady state solver to simulate flow with reynolds number=100

Inlet velocity=1 m/s

Pressure velocity scheme=Simple

Time step=0.1

Number of time step=1500

Comparison of result of transient and steady solver

Residual plots

In case of steady state residual is not oscillating when iteration is increasing for transient state iteration increases oscillation start and fluctuation in the same patternthere fore solution will converge.

IN steady state fluctuation of velocity with respect to iteration is very slowly with respect to iteration ,for transient state solver fluctuation is more when iteration increases behind the cylinder.

Coefficient of discharge is constant for both steady and transient solver avg Cd for transient state solver is 1.3815 and avg cd for steady state solver is 1.4167.

Coefficient of lift is slightly varying for steady state ,for transient solver fluctuation is more when iteration increases oscillation an frequency both increases avg Cl for steady state solver is 0.01452.

Calculation of Strouhal number for transient state from monitor point velocity plot

The Strouhal Number is a dimensionless value useful for analyzing oscillating unsteady fluid flow dynamics problems.

The Strouhal Number can be expressed as

St = f*D / v (1)

where

St = Strouhal Number

f = oscillation frequency

D= Diameter of cylinder

v = flow velocity

The Strouhal Number can be important when analyzing unsteady, oscillating flow problems. The Strouhal Number represents a measure of the ratio of the inertial forces due to the unsteadiness of the flow or local acceleration to the inertial forces due to changes in velocity from one point to an other in the flow field.

Reference-https://www.engineeringtoolbox.com/strouhal-number-d_582.html

No of cycle =6

flow time =40s

freqyency(f)= no of cycle/flow time

= 6/40

=0.150

St = f*D / v

=0.150*2/1

=0.30

Part-II

1. For steady state solver Re=10, 100,1000,10000,100000

Residual plot for different reynolds number.

From the above residual plot we can say that when the reynolds number increased, rate of conversion is decreased for Re=10 graph decreased rapidly but in another four cases it is stable.

2.Coefficient of drag plot for different reynolds number.

From drag coefficient plot we can say that when renolds number increases drag coefficient decreases.

3.Coefficient of lift plot for different reynolds number.

For low reynolds number coefficient of lift is not fluctuating, when reynolds number increases coefficient of fluctation increases. Average coefficient of fluctuation for Re number 10 is appromixatly 0.00077, but Re number increases average coefficient of fluctuation also increases.

4.Velocity plot for different reynolds number

1. From the plot of reynolds number 10 when the number of iteration increases vortex seeding of monitor point behind the cylinder was not experienced.

2.Further when reynolds number increases for the same mesh(0.25m), and same number of iteration vortex seeding of monitor point behind the cylinder was experienced, when reynolds number increases.

3.Amplitude and frequency of the variation of velocity with respect to iteration increases when reynolds number increases.

5. Velocity contour for different reynolds number

1.For Re=10 vortex shedding was not showing therefore velocity is constant behind the cyliner.

2.From Re=100 vortex shedding was start generating, further increseas the reynolds number vortex shedding clearly visible and increases when reynolds number increases.

Observation from the above plot

Conclusion

1.Vortex shedding was observed for reynolds number increases from lower to higher value generally more than 100 reynolds number vortex obserbed.

2.For higher reynolds number coefficient of lift increases and coefficient of drag decreases form the above tabular and the plot observation.