Week 2 - Flow over a Cylinder.
AIM: To simulate the flow over a cylinder and explain the phenomenon of Karman vortex street and also to
- Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.
2. 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)
3,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 %].
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 Red range (47<Red<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.
Geometry:
A plate with the dimension of 20*60m is created using spaceclaim.
Creation of geometry and fluid domain
Converting the geometry into a surface
The final surface
Meshing
Basic Mesh a quad dominant mesh
Refining the mesh using automatic method
After changing the method to triangles and applying a sizing of 2 m
Using edge sizing with the number of divisions as 36 to create a circular edge
The mesh after applying an inflation with a first layer thickness of 5mm
Specifying 6 inflation layers for mesh refinement(body fitted mesh)
The final mesh
Creating inlet and outlet named selections
Performing mesh check
Defining the properties of the working fluid
No slip biundary condition for wall
Defining surface reports
Creating a monitor point
Performing hybrid initialization
Defining contour plots
Initial Contours of velocity magnitude
Initial Contours of static pressure
Solution methods and residual monitors
Contours of velocity magnitude after 350 iterations
Contours of static pressure after 350 iterations
Scaled Residuals
Vertex average of velocity magnitude at monitor point
Creating solution animations
Editing the computational mesh to obtain the required solution and check if vortex shedding occurs
The mesh element size of 1 m is also not accurate and hence again the mesh parameters should be altered
Vortex shedding does not occur despite increasing the iteration count and also refining the mesh. So the Reynold's number must be increased slightly as at 40 is when the flow becomes critical.
Steady state results for Reynold's number 100
Scaled Residuals
Vertex average of velocity magnitude at monitor point
Contours of velocity magnitude
Scaled residuals
Coefficient of lift plot
Coefficient of drag plot
Monitor point velocity
Contours of velocity magnitude
b. Reynolds number = 100
u = 2.5 m/s
Scaled Residuals
Coefficient of lift plot
Coefficient of drag plot
Monitor point velocity
Contours of velocity magnitude
c. Reynolds number = 1000
u = 25 m/s
Scaled Residuals
Coefficient of lift plot
Coefficient of drag plot
Monitor point velocity
Contours of velocity magnitude
d. Reynolds number = 10000
u = 250 m/s
Scaled Residuals
Coefficient of lift plot
Coefficient of drag plot
Monitor point velocity
Contours of Velocity magnitude
d. Reynolds number = 100000
u = 2500 m/s
Scaled Residuals
Coefficient of lift plot
Coefficient of drag plot
Monitor point Velocity
Contours of velocity magnitude
Transient/Unsteady state
Reynolds number = 100
u = 2.5 m/s
Scaled Residuals
Coefficient of lift plot
Coefficient of drag plot
Monitor point velocity
Contours of velocity magnitude
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 staruhal no.using ansys fluent.
1.Go to fluent solver > results > fft analyser > load lift coefficient fiel > select plot FFT
Here, x axis denotes strauhal number and y axis denotes magnitude.
2.To get the magnitude of strauhal number,
go to results > fft analyser > click on write fft to file > click on write fft.
open the file in excel and 1st coloumn denotes the frequncy and 2nd coloumn denotes strauhal number.use the command max and select 2nd row and find the magnitude of strauhal number.
Strouhal number for Re=100
Steady state
Strouhal number = 0.141
Unsteady state
Strouhal number = 0.00419
Conclusion:
1.When fluid flows over cylinder, wake region is formed next to cylinder due to decrease in pressure and recirculation of flow occures and hence flow separation occures.
2.As flow over cylinder is being transient meaning 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 varried velocity to change reynolds number. So as the reynolds no. increases coefficient of drag decreases.however after reynolds no. = 4000, flow is turbulent and hence coefficient of drag is lower.