Simulation of flow over a cylinder and explaining the phenomenon of Karman vortex street.

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.

• THEORY:

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_t=(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`(C_d)` 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 `C_d` is defined as

`C_d=(2*F_d)/(rhou^2A)`

where:

`F_d`is the drag force, which is by definition the force component in the direction of the flow velocity,

`rho` is the mass density of the fluid,

`u`is the flow speed of the object relative to the fluid,

`A` is the reference area.

4. Co-efficient of lift:

The lift coefficient (`C_L`) 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. C_L is a function of the angle of the body to the flow, its Reynolds number, and its Mach number. The section lift coefficient c_l refers to the dynamic lift characteristics of a two-dimensional foil section, with the reference area replaced by the foil chord.

where

is the lift force,

is the relevant surface area and

q is the fluid dynamic pressure, in turn, linked to the fluid density, and to the flow speed.

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.

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 0.25 m.To ensure triangular mesh, go to mesh > insert > select triangular mesh type.

3.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.

4.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

Setting up Ansys fluent :

Before opening the set up we should update the mesh. Then we should change the viscous flow to laminar

Open Materials and create a fluid that is to be used for the simulation for this case, it is air and also inputs the density and kinematic viscosity values.

Open Zones and input the inlet velocity as per the reynolds number and check if the fluid is updated.

Update the reference values which is located inside set up at the right-hand side.

Fluent details/procedure:

a. laminar model

b. fluid: Air

c. Method of discretization: Simple

d. Density/kinematic viscosity: 1/0.02

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.

h. Use hybrid initialization for steady-state and standard for transient state simulations.

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:

Pressure 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:

Pressure contour:

Unstaedy state solver:

Reynolds number = 100.

velocity = 10 m/s.

density = 1 kg/m3.

viscosity = 0.02 Pa-s.

Residual plot:

Monitor point velocity:

Coefficient of drag:

Lift Coefficient:

Velocity contour:

Pressure contour:

Strauhall 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.

for steady:-

Strauhal Number = 0.013

Strauhal Number = 0.19

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:

Pressure 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:

Pressure 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:

Pressure contour:

RESULTS

Drag and lift coefficient for different Re

Error wrt the theoretical values from the reference material:-

Strauhal Number:-

CONCLUSIONS:-

• 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.
• The Strouhal number is calculated.
• 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%.

REFERENCE:-

https://www.sciencedirect.com/science/article/pii/S0307904X08000243