Week 2 - Flow over a Cylinder.

Aim:

To Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street.

Objective:

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

Introduction:

Vortex shading:

vortex shedding is an oscillating flow that takes place when a fluid such as air or water flows past a bluff (as opposed to a streamlined) 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 and detach periodically from either side of the body forming a Von Karman vortex street. The fluid flow past the object creates alternating low-pressure vortices on the downstream side of the object. The object will tend to move toward the low-pressure zone.

If the bluff structure is not mounted rigidly and the frequency of vortex shedding matches the resonance frequency of the structure, then the structure can begin to resonate, vibrating with harmonic oscillations driven by the energy of the flow. This vibration is the cause of overhead power line wires humming in the wind, and for the fluttering of automobile whip radio antennas at some speeds. Tall chimneys constructed of thin-walled steel tubes can be sufficiently flexible that, in air flow with a speed in the critical range, vortex shedding can drive the chimney into violent oscillations that can damage or destroy the chimney.

Reynolds Number (Re):

Reynolds number for a flow is a measure of the ratio of inertial to viscous forces in the flow of a fluid around a body.

Re = rho*V*d/Dynamic Viscosity

The range of Re values will vary with the size and shape of the body from which the eddies are being shed, as well as with the kinematic viscosity of the fluid. Over a large Re_d range (47<Re_d<10⁵ for circular cylinders; reference length is d: diameter of the circular cylinder) eddies are shed continuously from each side of the circle boundary, forming rows of vortices in its wake. The alternation leads to the core of a vortex in one row being opposite the point midway between two vortex cores in the other row, giving rise to the distinctive pattern shown in the picture. Ultimately, the energy of the vortices is consumed by viscosity as they move further downstream, and the regular pattern disappears.

Strouhal number (St):

A strouhal number is a dimensionless number describing oscillating flow mechanisms.

The Strouhal number is often given as

St = f*d/u

Where,

f is the frequency of vortex shading,

L is the characteristic length and

U is the flow velocity.

Procedure:

Geometry:

A plate with the dimension of 20*60m is created using spaceclaim.

Now, we want to simulate the effect of fluid flow over the cylinder, select the circle and delete it.

Meshing:

1. select the edges of geometry and named them inlet, outlet, wall, and symmetry.

2. Now select the body and go to mesh and click on generate a mesh with a mesh size of 190mm. To ensure triangular mesh, go to mesh > insert > select triangular mesh type.

3.To capture better results near the cylinder wall, go to mesh > inflation > select the body and edge > inflation option: 1st layer thickness >1 st layer height:5e-3 m >maximum layer:15

Solving :

1. select laminar flow inside the viscous model.

2. As we wanted to customize material property for simulation, go to materials > fluent database > select the material (air) > copy it> rename the name of the material.

Boundary Condition:

Outlet: gauge pressure = 0 Pa.

wall: no-slip condition.

Reference values:

Steady-state simulation:

1.Reynolds number = 10.

velocity = 1 m/s.

density = 1 kg/m3.

viscosity = 0.02 Pa-s.

Residual plot:

Monitor point velocity:

monitor point: A point is created at 8 m in the x direction from the axis of the cylinder to check velocity.

Coefficient of drag:

Lift Coefficient:

Velocity contour:

Pressure contour:

2.Reynolds number = 100.

velocity = 2.5 m/s.

density = 1 kg/m3.

viscosity = 0.05 Pa-s.

Residual plot:

Monitor point velocity:

monitor point: A point is created at 8 m in the x direction from the axis of the cylinder to check velocity.

Coefficient of drag:

Lift Coefficient:

Velocity contour:

Pressure contour:

3.Reynolds number = 1000.

velocity = 25 m/s.

density = 1 kg/m3.

viscosity = 0.05 Pa-s.

Residual plot:

Monitor point velocity:

Coefficient of drag:

Lift Coefficient:

Velocity contour:

Pressure contour:

4.Reynolds number = 10000.

velocity = 250 m/s.

density = 1 kg/m3.

viscosity = 0.05 Pa-s.

Residual plot:

Monitor point velocity:

Coefficient of drag:

Lift Coefficient:

Velocity contour:

Pressure contour:

5.Reynolds number = 100000.

velocity = 2500 m/s.

density = 1 kg/m3.

viscosity = 0.05 Pa-s.

Residual plot:

Monitor point velocity:

Coefficient of drag:

Lift Coefficient:

Velocity Plot:

Pressure plot:

Unsteady state solver:

Reynolds number = 100.

velocity = 2.5 m/s.

density = 1 kg/m3.

viscosity = 0.05 Pa-s.

Residual plot:

Monitor point velocity:

Coefficient of drag:

Lift Coefficient:

Velocity contour:

\

Pressure contour:

Strouhal Number:

A Strouhal number is a dimensionless number describing oscillating flow mechanisms.

The Strouhal number is often given as

St = f*d/u

Here, we have calculated Strouhal Number using Ansys fluent.

1.Go to fluent solver > results > FFT analyses > load lift coefficient file > select plot FFT

Here, the x-axis denotes Strouhal Number, and y-axis denotes magnitude.

2. To get the magnitude of Strouhal Number,

go to results > FFT analyzer> click on write fft to file > click on write fft.

open the file in excel and 1st column denotes the frequency and 2nd column denotes the Strauhal number. Use the command max and select the 2nd row and find the magnitude of Strauhal number.

Strauhal Number = 0.061586

Result:

Values of the coefficient of drag and lift coefficient for respective Reynolds number is tabulated as follows:

Conclusion:

1. When fluid flows over the cylinder, the wake region is formed next to the cylinder due to a decrease in pressure, and recirculation of flow occurs, and hence flow separation occurs.

2. As flow over the cylinder is transient meaning a time-dependent phenomenon, we are unable to observe flow separation at low Reynolds no. (say 50).

3. In this assignment we have kept all parameters constant and have only varied velocity to change Reynold's number. So as the Reynolds no. increases the coefficient of drag decreases. However after Reynolds no. = 4000, flow is turbulent and hence coefficient of drag is lower.

4. Strauhal no. calculated for unsteady state with Reynolds no.= 100 is 0.061586.