Flow over a Cylinder.

To simulate the flow over a cylinder using steady state and unsteady state solvers.

 

l. OBJECTIVES

1. Simulate the flow of fluid over a cylinder using both Steady & Transient solvers in Ansys Fluent.

2. Determine the Strouhal number in both the Steady & Transient state simulations for Re=100.

3. Calculate the coefficient of drag and lift over a cylinder for different Re numbers (10,100,1000,10000).

4. Discuss the effect of Reynolds number on Coefficent of Drag.

ll. INTRODUCTION

1. Vortex Shedding & Von Karman Vortex Street

Vortex Shedding is an oscillating flow that takes place when a fluid such as air or water flows past a bluff(a opposed to streamlined) body at certain velocities, depending on the size and shape of body at certain velocities, depending on the size and shape of the body.

In this flow, vortices are created at the back of the body forming a Von Karman Vortex Street which is responsible for the unsteady separation of the flow of a fluid around blunt bodies. It is named after the engineer and fluid dynamist Theodore von karman.

The fluid flow past the object creates alternating low-pressure votices on the downstream side of the object. The object will tend to move towards the low-pressure zone.

If the Bluff structure is not mounted rigidly and the frequency of vortex shedding matches the reasonance frequency of the structure, then the structure can begin to resonate, vibrating with harmonic oscillations driven by the energy of the flow.

These vibations can result in the failure of many structures & mechanical components.Hence, Vortex shedding is an important factor that needs to be analysed while desiging certain bodies subjected to fluid flow.

In order to analyse the vortex shedding phenomenon, we use a dimensionless parameter called as Strouhal Number.

 

Animation of vortex street created by a cylindrical object, the flow on the opposite sides of the object is given different colors, showing that the vortices are shed from alternating sides of the object.

 

2. Strouhal Number

It is a dimensionless parameter which is used to describe oscillating flow mechanisms.

For large Strouhal numbers(i.e having order of 1 and above),viscosity dominates fluid flow. This results in a collective oscillating movement of the fluid.

For low Strouhal Number (i.e. having order of `10^-4` and below),the high-speed quasi-steady state portion of movement dominates the oscillation.

For intermidiate Strouhal numbers, The oscillations are characterized by the buildup and rapidly subsequent shedding of vortices.

The Strouhal Number is given by -

• `St=(fd)/V`

          f = Frequency of Vortex Shedding

          d = Diameter of the cylinder

          V = Flow Velocity

 

lll. PROBLEM STATEMENT

1. The flow is laminar (Re=100).

2. The flow velocity, V=1 m/s.

3. The compational domain is given below

lV. ASSUMPTIONS

As the flow velocity is given to be 1 m/s in order to obtain Reynold's Number = 100, we take -

• Density, `rho`=1kg/`m^3`
• Dynamicc Viscosity, `mu = 0.02(Ns)/m^2`

V. SPACECLAIM GEOMETRY

The computational domain is created with dimensions as given in the problem statement using Ansys SpaceClaim.                                       

 Vl. MESH

The generated ,esh has the following features -

1. Baseline Mesh: Triangular

2. Element Size: 0.25m

3. Edge Sizing: 36 divisions

4. Inflation Layer (Body Fitted Mesh):

• First Layer Thickness(First Layer Height = 0.005m)
• Number of Inflation Layers = 6
• Growth Rate = 1.2 

Generated Mesh Over The Entire Domain

A triangular baseline mesh having a mesh size of 0.25 is eslected. It is observed that at a mesh size greater than 1m, the steady state solver is unable to detect the vortex shedding phenomenon.

Generated Mesh Over The Cylinder

An edge sizing of 36 divisions is selscted in order to get appropriate circular surface.

Also, a body -fitted mesh is generated using six inflation layers having a foirst layer thickness of 0.05m and the growth rate of 1.2. This helps us to compute a more accurate solution around the surface of the cylinder, where the flow variation shall be the greatest.

 

Vll. SETUP

CASE 1: STEADY STATE

1. Solver - Steady

2. Type - Pressure Based

3. Viscous Model - Laminar

4. Material - User Material

• Density, `rho`=`1(kg)/(m^3)`
• Dyanamic Viscosity, `mu = 0.02(Ns)/m^2`

5. Boundary Conditions -

• A. Inlet - 

                Type: Velocity Inlet

                Velocity: 1m/s

• B. Outlet -

                 Type: Pressure Outlet

                 Gauge Pressure: 0 Pa

• C. wall -          Type: Wall  

                  Wall Motion: Stationary Wall

                  Shear Condition: No-Slip

6. Creating Monitor Point -

We shall generate a point to monitor the flow parameters at a distance of 4 times diameter from the centre of circle.

• Monitor Point Coordinates: (x,y) = (8, 0)

 

7. Definations-

Certain reports, contours, plots & animations need to be defined in order to analyse the simulation flow -

7.1. Vertex Average Surface Report

We shall define the Vertex Average Surface Report at the monitor point in order to analyse the flow velocity.

Since we are considering only one monitor point, the vertex average value shall be equal to the velocity value at the at point.

7.2. Contour Plots

The velocity & pressure contours are defined at the monitor point to analyse the flow parameters.

7.3. Sloution Animations

The image of the velocity contour at the monitor point are recorded after every 10 iterations. This shall help us to observe & analyse the phenomenon of vortex shedding.

 

8. Solution Methods -

• Solution Method: SIMPLE
• Initialization: Hybrid
• Number Of Iterations:1500

 

Outputs -

Residual Plot

From this plot, we can observe that the continuity residual fails to fall below the set convergence criteria of 1e-3. This is because the physics of this is supposed to sow the vortex shedding phenonmenon due to which we can expect some residuals.

Although the flow has not convergebed, since the residual plot is almost constant, we can assume tyhat the flow ahs converged.

Velocity Plot At Monitor Point

The velocity at the monitor point shiws periodic rise & fall. This is due to the vortex shedding phenomenon occouring at that point.

Velocity Contour

The velocity contour shows the Von Karman Vortex Street. In order to properly observe the vortex shedding, it is advisable to refer to the recorded velocity contour animation.

Pressure Contour

The pressure contour shows alternating low- pressure vortices on the downstream side of the object which is the expected physics of this case.

 

Strouhal Number At The Monitor Point

Using the Fourier Transform(FFT) Plot in Ansys Fluent, we can load the output data of lift magnitude at the monitor point and plot the curve for Strouhal Number.

We cannot deduce any information from this graph due the extremely small variations in the velocity magnitude at the monitor point. Hence, it is better to transform the given plot into a log plot.

Log Plot - Strouhal Number At The Monitor Point

We cannot predict the accuracy of the solution as the calculated Strouhal number is a function of frequency which is a time dependant parameter. Since, we have solved the problem using a steady state solver, we are unable to predict the accuracy of this plot.

9. UNSTEADY STATE 

1. Solver: Transient

2. Solution Methods -

• Solution Method: SIMPLE
• Initialization: Hybrid
• Time Step: 0.25s
• Maximum Number of Iterations per Time step:20
• Number of Iterations:1000

The approximate time steps was calculated by the formula-

• `Deltat approx`Cell/size/Flow Velocity `to Deltat approx 0.25s`

Note:The remaining computational parameter will remain the same as that of the steady case simulation.

3.Outputs-

Residual plot

 

From this plot, we can observe that the continuity residual fails to fall below the set convergence criteria of 1e-3. This is beacuse the physics of this is supposed to show the vortex shedding phenomenon which gives to the preiodic variations in the residual.

Although the flow has not converged, since the residuals repeat themselves after some regular intervals. Hence, we can assume that the flow has converged.

 

Velocity Plot At Monitor Point

 

Velocity Contour

 

Pressure Contour

 

Strouhal Number  VS Lift

  

 Log Plot - Strouhal Number Vs Lift

 

we have obtained a much more periodic plot as compared to the steady state Strouhal number log plot. This is because the Strouhal number is a function of frequency which is a time dependant parameter. Hence, this plot is more accurate than corresponding Steady state plot.

At Strouhal number 0.160 we find maximum lift coefficient of 0.956

 

Vlll. Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 &100000

For Re=10 there won't be any vortex shredding behind the cylinder in wake region because flow velocity is low to develop vortex street. But small amount of recirculations appears in the wake region which is symmetric about horizontal axis of the cylinder. At Re=47 oscillations are stronge enough to break one of the two vortices away from the cylinder. This is called Von Karman Vortex shedding. The vortices appears and are shed alternatively at a constant frequency. This causes system to excite and induce vibrational load. As the fluid flow over the cylinder, these vortices create low pressure zones on the downwind side of the object on alternative sides.

 

VELOCITY:

  

Re= 10                                                                                                         Re=100

 

 

 

Re=1000                                                                                                               Re=10000

 

Re=100000

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CD AND CL:

 

Re=10

 

 

 

Re=100

 

 

Re=1000

 

 

Re=10000

  

Re=100000

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VELOCITY AND PRESSURE CONTOURS

                (A) VELOCITY                                                                   (B) PRESSURE

    

Re=10

 

     

Re=100

 

  

Re=1000

  

Re=10000

 

  

 

lX. Computed data are listed in the table below:

Steady State	Drag coefficient
RE=10	3.324
RE=100	1.334
RE=1000	0.0727
RE=10000	0.7670
RE=100000	0.7032

After inspecting the plots and contours provided above, we can say that as reynolds number increases, drag coefficient decreases till Re=1000 but at Re=10000 we see a slight increase in drag coefficient and again for Re=100000 the drag coefficient decreases.

 

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X. Animation Of Vortex shedding in wake region:

Re=10

 

 

Re=100

 

Re=1000

 

Re=10000

 

Re=100000

 

Xl. RESULTS

1. For the steady state simulation, we are unable to observe any vortex shedding phenomenon at a mesh size greater than 1m, which is not case for the transient state solver.

2. For thr transient state simulation, we are unable to observe any vortex shedding phenomenon at higher time step. Hence, we are required to lower the time step, resulting in an increase in the total number of iterations required to compute the solution.

3. The increase in Re leads to shedding of vortices from upper and lower cylinder surface at a particular frequency. 

4. At lower Re=10, there is no formation of vortices. Vortex shedding takes place at higher Re like 100, 1000, 10000 & 100000.

5. The steady state solver computes the solution much faster than the transient solver.

6. The output contours, plots & animations match the trend expected from the physics of this problem. This shows that we have solved the given mathematical model correctly and have verified the results.

7. Reynolds number play an important role on the drag and lift coefficient, as reynolds number increases, drag coefficient decreases till Re=1000 but at Re=10000 we see a slight increase in drag coefficient and again for Re=100000 the drag coefficient decreases.

 

Xll. CONCLUSIONS

We can conclude that both the steady & transient state are able to simulate the expected physics of the flow under certain conditions.

However, simulating the flow using the Transient state solver is more preferable than the Steady state solver as the phenomenon of vortex shedding is a time dependent phenomenon. Thus, using the correct mathematical equations which follows the physics of the flow shall give us more accurate results.