Week 2 - Flow over a Cylinder.

INTRODUCTION 

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 karman vortex Shredding  . 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. We will see a common shape like cylinder in this project and analyse the vortex shedding generated around the cylindrical surface for the different values of Re number and will try to find the drag and lift coefficient ,

The variation in the velocity after its flow over the boundary of the cylinder results in a pressure drop just behind the cylinder surface in the leeward side which sucks the air around it thus creating a vortex pattern .The pattern depends on many factors like the kinematic viscosity ,Reynolds number, velocity of the flow 

In this assignment we are using air as a medium and we will seeing the variation in the vortex generation for different Reynolds numbers .   

Karman vortex shedding occurs due to the flow separation around the structures. The resulting flow resembles that observed for single cylinders when the cylinder separation is large enough. The alternate shedding of vorticity behind the structures leads to periodic pressure oscillations both in the transverse and flow directions. The oscillation frequency in the transverse direction matches the vortex shedding frequency.  

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. In the  flows characterized by a periodic motion, the Strouhal number is associated with the oscillations of the flow due to the inertial forces relative to the changes in velocity due to the convective acceleration of the flow field. Thus, an alternative definition of the Strouhal number better suited to periodic flows is given by the following expression.

SETUP

DIAGRAM

 The diagram consist of a circular boundary whose axis is normal to the surface  of air flow

Diameter=2 m

Inlet distance =20 m (from centre)

Outlet distance =40 m (from centre)

Symmetry boundary distance = 20 m

MESHING

 Element type=triangular

Element size = 0.4 m

Inflation layer = 6

Inflation growth = 1

SETUP ARRANGEMENT   

MEDIUM

 We have selected air as a medium and have assigned it a density of 1kg/m^3 and Viscosity as 0.02 ------. The medium name is given as air-new (user defined).

GRAPHS, CONTOURS AND PLOTS   

We will create a point at a distance of 10 m from the centre of the circle on the leeward side of the  cylinder. We will create graphs for the following parameters- velocity average , pressure average, drag coefficient, lift coefficient and set the residual graph. We will then generate contours for the velocity average and pressure average to see the variation in the velocity and the vortex development . To visualize the change in the velocity contour we will create solution average for the velocity contour . SIMPLECS Solver is used

CASE 1

Velocity-1m/s

Re-100

Viscosity- 0.02   

Steady State Solver (1000 Iteration) 

Velocity curve                                                                                    Pressure Curve 

    

Drag coefficeint curve                                                                  lift coefficient curve  

   

 CONVERGENCE 

   The curve converges at  200 th iteration which is visible by the curves 

 

Strouhal Number 

 We can calulate the strouhal graph by using the FFT Plot 

Note -The strohaul number cannot be calculated for the steady state as we don't calculate the flow with respect to time.

INFERENCE

·        Analysing the plots for the scaled residuals and velocity magnitude at the probe point, we can observe that the plot stabilizes at around the 200 th iteration and then the plot achieves a steady state, periodically repeating itself. Hence, we can safely conclude that the solution is converged after running for about 1000 iterations.

·        Steady State Simulation has been clearly able to detect the phenomenon, since the problem is highly nonlinear, there is no clarity about the time duration in the steady state results. While transient solution has been able to capture the phenomenon with relatively better idea of time duration. Transient simulation can be employed to get the time dependent property of the phenomenon called Strouhal Number. 

·        For Steady State Simulations, observing the residuals or any control variables can get idea about the convergence. Here, the residuals stagnated at a value also, the control point variable (velocity) at monitor point has a repeating pattern. This behaviour indicates the convergence for steady state analysis.

CASE II

Transient Based Solver   

Time Step Size=0.25 s

Time Steps= 500  

 Velocity contour                                                               Velocity curve 

 

 Pressure curve                                                         Residual curve 

  

 Drag Coefficient Curve 

 

Strouhal Number 

 The strouhal Number for th transtient annalysis was 0.025 

 PART II  

 We will now find the drag coefficient variation for the different Reynold number where we will be chang  the Velocity of the flow at the inlet based on the Reynold no 

FORMULA USED 

Re= D* U/V  

1. Re=10  

Velocity= 0.1 m/s

 Lift Coefficient                                                                                             Drag Coefficeint 

   

Value    Cl= 0.000000 

2.Re=100  

 Velocity= 1m/s 

  Lift                                                                              Drag 

  

 

 

 3. Re=1000

     Velocity= 10 m/s 

           drag coefficient                                                                        lift coefficient  

  

Covergence Curve                                                                Velocity Curve 

  

Value of Cl= -0.3849  

4.Re=10000 

Velocity at inlet=100 m/s 

Velocity Curve                                                                        Drag Coefficient Curve 

  

Lift Coefficeint Curve                                                            Convergence curve  

 

Value of Cl=  0.9461438 

5.Re=100000 

Velocity at  inlet= 1000 m/s 

Drag Coefficient                                                                                                   Lift Coefficient 

  

Covergence Curve                                                                Velocity curve 

  

INFERENCE  

With increase in Renolds number, vortex shedding is more prominent for the extreme end surfaces of cylinder. The increase in inertial against the viscous force, results in decrease in coefficient of drag (Cd). The rate of decrease in Cd for Renolds number 10 to 100 is way more drastic than after it . The reason can be the increase in randomness due to increase in the Reynould Number  

CONCLUSION   

When fluid flows over the cylinder, the wake region is formed next to the cylinders leeward side  due to a decrease in pressure, and recirculation of flow occurs hence flow separation occurs. 

As flow over a cylinder is transient we are unable to observe flow separation at a low Reynolds number of below 40 

As the Reynolds number increases the coefficient of drag decreases and increases the randomness 

Strauhal number for an unsteady state with Reynolds number 100 is 0.025 

REFERENCE 

Wikipidea 

Vortex annalysis for cylindrical boundary for different value of Reynold number