Week 2 - Flow over a Cylinder.

Aim: 

Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street. 

Objective:

1.To 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.Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100. 

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 %]

4. 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?

5. Plots of the coefficient of drag and lift. 

6. Plots to show vortex shedding behind the cylinder. 

7. Mention the preferred material at the end of the challenge submission page.

Introduction:

Vortex shadding:

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

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.

 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.

The drag coefficient Cd">Cd is defined as

Cd=2⋅Fdρu2A">Cd=2⋅Fd/(ρu^2A)

where:

 Fd">Fdis the drag force, which is by definition the force component in the direction of the flow velocity,

ρ">ρ is the mass density of the fluid,

u">u is the flow speed of the object relative to the fluid,

A">A is the reference area.

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. 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.

Procedure:

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

                           

Solving :

1. select laminar flow inside the viscous model.

2.As we wanted to customimize material property for simulation, go to materials > fluent database > select the material (air) > copy it> rename the name of material.

Boundary Condition:

Outlet : gauge pressure = 0 Pa.

wall : no slip condition.

Refference values:

     

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:

      

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:

      

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:

      

Procedure to Calculate Strouhal Number:

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.

    

      Strauhal Number = 0.112

 Result:

    Values of coefficient of drag and lift coefficient for respective reynolds number is tabulated as follows: