Week 2 - 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.
OBJECTIVE:
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)
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 %]
3. 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?
4. Plots of the coefficient of drag and lift.
5. Plots to show vortex shedding behind the cylinder.
6. Mention the preferred material at the end of the challenge submission page.
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:
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
St=fDU′">St=fD/U′
Where,
f= frequency of vortex shedding
D= characteristic diameter of the cylinder
U'= fluid flow velocity
3. Co-efficient of drag:
In fluid dynamics, the drag coefficient(Cd)">(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.
4. Co-efficient of lift:
The lift coefficient (CL">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. CL is 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.
Procedure:
1.Geometry
A plate with the dimension of 20m*60m is created using spaceclaim.
2.Mesh
Now select the body and go to mesh and click on generate mesh with mesh size 0.5 m.To ensure triangular mesh, go to mesh > insert > select triangular mesh type.
After generating mesh,it is seen that size of cirle looks distoreted.
go to mesh > sizing > select circular edge > deffinition >type > no,of divisions >36.
To capture better results near 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 :6
And we should name the boundaries as given below
3.Setting up Ansys fluent
Before opening the set up we should update the mesh.
Fluent details/procedure:
a. laminar model
b. fluid: Air
c. Method of discretization: Simple
d. Density/kinematic viscosity: 1/0.05
e. Creating a monitor point behind the cylinder by selecting point under surfaces in the results bar.
f. After creating the monitor point, create reports/plots for drag, lift, velocity wrt cylinder.
g. Create plots for the velocity at the monitor point to analyze the vortex shedding.
PART1
(i) Simulate the flow with the steady case
Reynolds number = 100
velocity = 1 m/s.
density = 1 kg/m3.
viscosity = 0.02 Pa-s.
Diameter= 2 m
(ii) Simulate the flow with the unsteady case
PART2
Reynolds number = 10
velocity = 1 m/s.
density = 1 kg/m3.
viscosity = 0.2 Pa-s.
Diameter= 2 m
Reynolds number = 1000
velocity = 1 m/s.
density = 1 kg/m3.
viscosity = 0.002 Pa-s.
Diameter= 2 m
Reynolds number = 10000
velocity = 1 m/s.
density = 1 kg/m3.
viscosity = 0.0002 Pa-s.
Diameter= 2 m
Reynolds number = 100000
velocity = 1 m/s.
density = 1 kg/m3.
viscosity = 0.00002 Pa-s.
Diameter= 2 m
Result:
PART 1
Drag and lift coefficient for Re100
| Cd | CL | |
| Steady state | 1.6185626 | -0.09691378 |
| unsteady state | 2.0650898 | 0.11567776 |
PART 2
Drag and lift coefficient for different Re
| Re | Cd | CL |
| 10 | 5.4329687 | 0.0015379445 |
| 100 | 1.6185626 | -0.09691378 |
| 1000 | 1.2282405 | -0.39965945 |
| 10000 | 1.1752485 | -0.16098949 |
| 100000 | 1.1114465 | -1.0711026 |
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.
- 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 viscosity 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.
- 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.
- 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 we refine the mesh we need to run more iterations.