Week 2 - Flow over a Cylinder.

Aim:

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

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 %

Introduction:

Vortex shedding:

vortex shedding is an oscillating flow that takes place when a fluid such as air or water flows past a bluff (as opposed to 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 for 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):

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 effect of fluid flow over cylinder, select the circle and delete it.

GEOMETRY

Meshing:

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

2.Now select the body and go to mesh and click on generate mesh with mesh size 0.2m. To ensure triangular mesh, go to mesh > insert > select triangular mesh type.

3.After generating mesh, it is seen that size of circle looks distorted. go to mesh > sizing > select circular edge > definition >type > no. of divisions >36.

4.To capture better results near cylinder wall, go to mesh > inflation > select the body and edge > inflation option: 1st layer thickness >1st layer height :5e-3 m >maximum layer :6

MESHED SURFACE

NAMING THE BOUNDARIES

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 material.

Boundary Condition:

Outlet: gauge pressure = 0 Pa.

wall: no slip condition.

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 x direction from the axis of cylinder to check velocity.

COEFFICIENT OF DRAG:

LIFT COEFFICIENT:

VELOCITY CONTOUR:

2.Reynolds number = 100.

velocity = 10 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 x direction from the axis of cylinder to check velocity.

COEFFICIENT OF DRAG:

LIFT COEFFICIENT:

VELOCITY CONTOUR:

3.Reynolds number = 1000.

velocity = 100 m/s.

density = 1 kg/m3.

viscosity = 0.02 Pa-s.

RESIDUAL PLOT:

MONITOR POINT VELOCITY:

COEFFICIENT OF DRAG:

LIFT COEFFICIENT:

VELOCITY CONTOUR:

4.Reynolds number = 10000.

velocity = 1000 m/s.

density = 1 kg/m3.

viscosity = 0.02 Pa-s.

RESIDUAL PLOT:

MONITOR POINT VELOCITY:

COEFFICIENT OF DRAG:

LIFT COEFFICIENT:

VELOCITY CONTOUR:

5.Reynolds number = 100000.

velocity = 10000 m/s.

density = 1 kg/m3.

viscosity = 0.02 Pa-s.

RESIDUAL PLOT:

MONITOR POINT VELOCITY:

COEFFICIENT OF DRAG:

LIFT COEFFICIENT:

VELOCITY CONTOUR:

Strouhal number:

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 no. using Ansys fluent.

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

Here, x axis denotes Strouhal number and y axis denotes magnitude.

2.To get the magnitude of Strouhal number,

go to results > fft analyser > 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 Strouhal number. use the command max and select 2nd row and find the magnitude of Strouhal number.

Result:

Values of coefficient of drag and lift coefficient for respective Reynolds number is Calculated.

Conclusion:

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

2.As flow over cylinder is being transient meaning time dependent phenomenon, we are unable to observe flow separation at low Reynold’s 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 Reynold’s no. increases coefficient of drag decreases. however, after Reynold’s no. = 4000, flow is turbulent and hence coefficient of drag is lower.

4.Strauhal no. calculated for unsteady state with Reynold’s no.= 100 is 0.112.

REFERENCE:

1. Strouhal number for cylinders Calculator | Calculate Strouhal number for cylinders (calculatoratoz.com)
2. Y+ Calculator | CFD Streamline
3. Reynolds Number calculator and velocity calculator for water pipes. (herramientasingenieria.com)