Flow over a Cylinder.
Flow over a Cylinder.
AIM:
Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street. Understanding the vortex shedding for different Reynolds numbers by changing the inlet velocities accordingly. Create a monitor point behind the cylinder at a distance 4 times the diameter which can be used to calculate and analyze the vortex shedding.
Given Problem:
1.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 %]
Expected results:-
- In both approaches, show that the flow has converged. That is, what quantities or plots need to be looked at 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 (Reference Paper or Fluid Mechanics Textbook) at the end of the challenge submission page.
Theory and Explanation:
1.Flow over cylinder:
In spite of extensive experimental and numerical studies almost over a century, flow around a circular cylinder still remains a challenging problem in fluid mechanics, where intensive investigations are continued even today to understand the complex unsteady dynamics of the cylinder wake flow. Cross-flow normal to the axis of a stationary circular cylinder and the associated problems of heat and mass transport are encountered in a
wide variety of engineering applications. Both experimental measurements and numerical computations have confirmed the onset of instability of the wake flow behind a cylinder beyond a critical Reynolds number, leading finally to a kind of periodic flow identified by definite frequencies, well-known in the literature as the Von Karman vortex street. In case of laminar flow past cylinders with regular polygonal cross-section, the flow
usually separates at one or more sharp corners of the cross-section geometry itself, forming a system of vortices in the wake on either side of the mid symmetry plane. On the other hand, for a circular cylinder, where the point of flow separation is decided by the nature of the upstream boundary layer, the physics of the flow is much more complex than what its relatively simple shape might suggest.
2.Strouhal number:
In dimensional analysis, the Strouhal number is a dimensionless number describing oscillating flow mechanisms.
For large Strouhal numbers (order of 1), viscosity dominates fluid flow, resulting in a collective oscillating movement of the fluid "plug". For low Strouhal numbers (order of 10−4 and below), the high-speed, quasi-steady-state portion of the movement dominates the oscillation. Oscillation at intermediate Strouhal numbers is characterized by the buildup and rapidly subsequent shedding of vortices.
The Strouhal number is often given as
S=(f*D)/U
where f= frequency of vortex shedding
D=characteristic diameter of cylinder
U=fluid flow velocity
3.Co-efficient of drag:
In fluid dynamics, the drag coefficient(Cd)is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag equation in which a lower drag coefficient indicates the object will have a less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area.
The drag coefficient of any object comprises the effects of the two basic contributors to fluid dynamic drag: skin friction and form drag. The drag coefficient of a lifting airfoil or hydrofoil also includes the effects of lift-induced drag. The drag coefficient of a complete structure such as an aircraft also includes the effects of interference drag.
The drag coefficient Cdis defined as
Cd=(2*Fd)/(ρ*A*U^2)
where Fd=Drag force
ρ=density of fluid
A=reference area
U=fluid velocity
4.Co-efficient of lift:
The lift coefficient (CL) is a dimensionless coefficient that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity, and an associated reference area. A lifting body is a foil or a complete foil-bearing body such as a fixed-wing aircraft. CLis a function of the angle of the body to the flow, its Reynolds number, and its Mach number. The section lift coefficient cl refers to the dynamic lift characteristics of a two-dimensional foil section, with the reference area replaced by the foil chord.
CL=L/(q*S)
where L=lift force,
S=relevant surface area
q=fluid dynamic pressure, in turn, linked to the fluid density, and to the flow speed
5.Vortex Shedding:
In fluid dynamics 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 oscillation driven by the energy of the flow.
Real world Example:
1.Vortex shedding was one of the causes proposed for the failure of the original Tacoma Narrows Bridge (Galloping Gertie) in 1940, but was rejected because the frequency of the vortex shedding did not match that of the bridge.
2.A thrill ride, "VeritGo" at cedar point in sandusky,ohio suffered vortex shedding during the winter of 2001, causing one of the three towers to collapse. The ride was closed for the winter at the time.
3.In northeastern Iran, the Hashemi-Nejad natural gas refinery's flare stacks suffered vortex shedding seven times from 1975 to 2003.
Explanation:
1.Geometry creation:
Creating the geometry by sketching using the line and circle command, circle diameter of 2m and the dimensions having 20X60m and the circle is placed 20m from the inlet.Before Geometry creation change the unit of spaceclaim by File-spaceClaimoptions-units to meter.
2.Mesh creation:
After the geometry is loaded we should mesh it and here I used 0.19m as elemental size
But in the meshing nodes, the shape is more quadrilateral than the triangle so we should this by changing the method to the triangle in the insert option
After changing the node's shape into triangles we should improve the mesh around the cylinder by sizing in the mesh which is used to control precisely the mesh.
Then we should add inflation which is used to create body-fitted mesh
we should name the boundaries as given below
To name the boundaries we should select the edges and type 'n' on keyboard and when selecting two same boundaries simultaniously press ctrl while selecting.
3.Setting up Ansys fluent
Before setting up we should update the mesh. Then we have to set up some changes one by one
first:
First Go to physics and in General setting we can change the system to steady or transient,pressure based,Absolute velocity.
Then Go to the reference plane and change the valocity and viscosity
Then in viscous make it laminar
Then go to material-fluent Database-select air-copy-name it as usermaterial and select it at fluent fluid material.
Then go to zone-select fff_surface and Edit and select user material and Apply.
Then go to boundary-inlet -change velocity-Apply
Then go to solution in method - scheme-simple,initilization-hybrid for steady state and standard for unsteady,Activities-create-solution animation to create animation of contour.To create contour go to results and then contour . Before contour initialize the solution.
In solution-Defination create plot drag coefficient,lift coefficient and velocity magnitude at the votex point.(vortex point is a point 8 meter distant from the centre of the circle can be created from Result section -create at the left corner-select point -select x,y,z distant and rename it)
In solution section initialize then calculate (take 800 iteration and for unsteady take timestep as 0.1 second)
case-1
steady state:(simulate the flow with velocity 2.5m/s , Re-100 and viscosity-.05 kg/m-s)
pressure contour:
velocity contour:
residual:
velocity at the vortex point:
strouhal number plot:
Drag coefficient:
lift coefficient:
Unsteady:
(simulate the flow with velocity 2.5m/s , Re-100 and viscosity-.05 kg/m-s)
pressure contour:
velocity contour:
Residuals:
velocity at the vortex point:
strohaul number:
Drag coefficient(Cd):
lift coefficient(CL):
(TO find out strouhal number plot go
import the velocity at the vortex point file)
data table:
Re-100 | Theoratical Cd | practical Cd | Error in % | Theoratical CL | strouhal Number |
Steady | 2.7455 | 2.87 | 4.7 | -.23 | .0134 |
unsteady | 2.46 | 2.58 | 4.8 | -.1513 | .1995 |
case-2:
Finding out steady state solutions for Re-10,100,1000,10000,100000
Here viscosities will be same .05kg/m-s but velocity will differ to change the renoulds number.In each case simultanious plots are - pressure contour,velocity contour, residuals,velocity at vortex point , drag coefficient and lift coefficient.
For Re-10:
AS mentioned above plots are:
For Re-100:
Re-1000
Re-10,000
Re-100,000:
Data table:
Re | Theoretical Cd | Practical Cd | Error in % | Prectical CL |
10 | 6.56 | 6.663 | 1.52 | .0017 |
100 | 2.7455 | 2.87 | 4.7 | -.23 |
1000 | 1.63 | 1.66 | 1.84 | -0.49 |
10,000 | 1.90 | 1.89 | 0.53 | -1.2018 |
100,000 | 2.23 | 2.2197 | 0.65 | -1.46 |
conclusion:
- In the first case, the flow over a cylinder is simulated for both Steady and unsteady cases with Re=100, and with the results generated the phenomena of Von Karman Vortex Street are also observed.
- Necessary plots are plotted in order to observe that the flow is converged and the vortex shedding is happening.
- Contours are generated in order to observe the flow over a cylinder.
- By plotting Power Spectral Density vs Frequency, the Strouhal number is calculated.
- In the second case,
- six different simulations i.e (Re = 10,100,1000,10000,100000,1000000) are simulated to observe the behavior of the drag and lift coefficients by changing the Reynolds number.
- In order to observe the behavior of the drag coefficients for the simulations, the velocity of the flow is varied to change the Reynolds number and the rest of the parameters are kept constant.
- As we know if the Reynold number is less than 2000, then flow in a pipe is Laminar. Hence we use the Viscous model = Laminar.
- For Re=10, it is observed that there is no formation of vortex shedding and in the rest of the cases, it is clearly observed.
- As per the basic conditions and parameters, the results are validated from the literature.
- As we refine the mesh we need to run more iterations.
- From the above table, it can be concluded that the error percentage is less than 5%
REFERENCES:
1.https://www.sciencedirect.com/science/article/pii/S0307904X08000243
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