Week 2 - Flow over a Cylinder.
Aim: In this challenge we are going to Simulate the flow over a cylinder using Ansys and explain the phenomenon of Karman vortex street.
There are two parts that are to be covered in this project which are described below.
PART-I
- Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.
PART-II
- Calculation of the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000.
- The effect of Reynolds number on the coefficient of drag are discussed.
The Following are explained and shown
- 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 at the end of the challenge submission page.
karman vortex street:
As the fluid is flown over a body streamlines of fluid are developed over the body with the gradient of velocity from the streamline near the body to the one away.To start with, a stagnation point is a point in a flow field where the local velocity of the fluid is zero. Stagnation points exist at the surface of objects in the flow field, where the fluid is brought to rest by the object. stagnation point which is the point at which the fluid meets the body first .behind the body wake region is formed.The flow separation takes place depending on the surface and type of flow(turbulent or laminar).In the wake region vortices are generated. Stream length of vortices increases with increase in Renoylds number. As there is further increase the wake becomes unstable and vortex shedding is initiated. At first one of the vertices breakaway and then the second is shed because of non-symmetric pressure in the wake. The intermittently said what is us from element periodic wake of staggering what is as of opposite sign this phenomenon is called Karman vortex Street.
Reynolds number: It is a non dimensional number which describes the type of flow either laminar or turbulent.
If Re >5*10^5 Turbulent flow(external flow)
Re < 5*10^5 Laminar flow (external flow)
`Re = (rhouL)/mu`
L = length of the body
`rho`=density of the fluid flowing over the body
`mu`= Dynamic Viscosity of fluid
Coefficient of Drag:Dynamic drag is a combination of Friction drag and pressure drag .Coefficient of drag is a dimensionless number that depends on the shape, inclination, and flow conditions which affects the dynamic drag.
Coefficient of lift:Coefficient of lift is a dimensionless number that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area.
Steps followed in setting up the model
First the geometry setup (cylinder) is created in the space claim in units we need to change length to meters.
Meshing
Required size of cell is given in the mesh folder a grid size of 0.25m is used.And in the mesh definitions triangle method is selected because that mesh is enough for this problem.
Naming for all the boundaries is done.
Edge
The cylinder should be smooth enough to avoid the drag so body fitted curve is created and edges of 36 are provided.This smoothens the cylinder surface.
Inflation layer
This is created to visualize clearly what happens near the cylinder. 6 inflation layers are created.
Setup:
Opening ansys fluent
For steady state:
Steps
- Change the method to Simple ,Change the material properties to your requirement.Reference values need to be change depending upon case.
- Monitor point is created behind the cylinder from which we can plot the velocity curve.
- In the definitions we define the velocity plot,lift plot and drag plot.
- Create contours for velocity and pressure
- Initialization is done for 10 iteratons and contours for velocity and pressure are created.
- Animation is created from activites.
Steady state:
viscosity `mu`=0.02
Iterations = 500
velocity = 1(m/s)
Re =100
Residuals
Residulas
Velocity
Drag
Lift
Vector
velocity contour
pressure contour
Velocity Animation
Unsteady state:
For unsteady state:
For unsteady state we need to change the solution initialization to standard and time setting to transient and method to simple.
Transient condition is used
timesteps 3600
timestep size 0.1s
At Re 100
Residual:
Velocity
It is seen that the velocity plot repeats patterns after 200 seconds.
Lift
Vector
Velocity Contour
Pressure contour
Animation
Strohaul Number:
The Strouhal number is a dimensionless number describing oscillating flow mechanisms.The Strouhal number represents the ratio of inertial forces due to the local acceleration of the flow to the inertial forces due to the convective acceleration. At high Strouhal numbers oscillations dominate the flow while at low Strouhal numbers the oscillations are swept by the fast-moving fluid.
`St = (fD)/U`
where f is the vortex shedding frequency
D is the diameter of the sphere
U is the free-stream velocity
U = 1 m/s
f =5/(350-250)
=0.05
St = (0.05*2)/1
= 0.1
Comparing steady and unsteady state at the Re 100 with same parameters
| State | Drag | Lift |
| Steady state | 1.3303 | 0.111 |
| Unsteady state | 1.3769 | 0.266 |
Steady state:
viscosity `mu`=0.02
Iterations = 500
velocity = 0.1(m/s)
Re =10
Residuals
Velocity:
Drag
Lift
Vector
Velocity contour
Pressure contour
Animation
Pressure animation
Re = 100
Residual
Velocity plot
Drag
Lift
Velocity Vector:
Velocity contour Pressure contour
Pressure contour
Animation
Re 1000
Residuals
Velocity Plot
Drag
Lift
velocity Vector
Velocity contour
Pressure contour
Animation
Re 10000
Residuals
Velocity Plot
Drag
Lift
velocity Vector
Velocity contour
Pressure contour
Animation
Re 100000
Residuals
Velocity Plot
Drag
Lift
velocity Vector
Velocity contour
Animation
Table showing drag for different reynolds number
| Reynolds number | Drag | Lift |
| 10 | 3.332 | 0.000875 |
| 100 | 1.3303 | -0.1119 |
| 1000 | 0.7107 | 0.4066 |
| 10000 | 0.7681 | 0.661 |
| 100000 | 0.9868 | 1.886 |
The drag coefficient calculated in the simulation is compared with the research results to validate the results we got .the drag coefficient of 1.3303 is what we got in the simulation and the coefficient of drag from areserch paper is 1.3353.The error is less than 5% so the results we got are valid.
Effect of reynolds number on coefficient of drag:
Re around 1
Reynolds number has different effects on the drag coefficient at different 'Re' for reynolds number around 1 There is no boundary layer seperation and so there will be no pressure distribution and cd decreases with increase in Re.
Re `approx`10
There is aboundary layer seperation wake region is formed behind the body which increases the drag.Coefficient of drag increases with increase in reynolds number.
Re `approx` 100
The wake region becomes more predominant with more no of vortices and the vortices becomes unstable the drag coefficient increases with increase in the Re.
Re `approx`10^4
The transition to turbulent flow takes place the coefficient of drag increase with the increase in reynolds number.
Re `approx`10^6
The flow is turbulent and the coefficient of drag decreases with increase in the reynilds number this is due to the fact that the turbulence deylays the flow seperartion by stabilizing the flow.
Reference:
https://thermopedia.com/content/1216/
https://www.sciencedirect.com/science/article/pii/S0307904X08000243