Flow Over a Cylinder
Objective
The objective is the analysis of two-dimensional flow over a circular cylinder for different Reynold numbers and explain the phenomenon of Karman vortex street.
Introduction
Von Karman vortex street is a repeating pattern of swirling vortices, caused by a process known as vortex shedding, which is responsible for the unsteady separation of flow of a fluid around blunt bodies. A regular Karman vortex street in the wake of a cylinder is observed only in the range of Reynolds number from about 48 to 150. At lower Reynolds number, the wake is laminar, and higher Reynolds three-dimensional instabilities lead to the formation of streamwise vortex structure. In turbulent region, high degree of mixing prevents the fomation of vortex shedding.
Geometry and Dimensions
Meshing
Triangular mesh element is generated with mesh size 0.25m.
Number of nodes=20,697
Number of cell=40,502
Boundary Condition
Air flows over a circular cylinder of diameter of 2m.
Density of air`=1{Kg}/m^3`
Inlet Velocity`=1m/s`
Outlet gauge pressure`=0`
Setup
Pressure based solver is used with simple solution method. Laminar model and is used for the simulation. Monitor point is cosidered at a distance of 8m from centre of cylinder.
PART I
Case 1:- Steady state simulation
Reynold number=100
Viscosity=0.02 kg/m-s
Initialization=Hybrid
Number of iterations=500
Plot
In steady state, residual is not oscillating
Avg. Coefficent of drag=1.5
Avg. Coefficient of lift=0.025
Velocity Contour
No, vortex shedding is not observed beause it is transient process.
Case 1:- Unsteady state simulation
Reynold number=100
Viscosity=0.02 kg/m-s
Initialization=Standard
Number of time step=1600
Time step=0.1 sec
Number of iterations per time step=20
Plot
In unsteady state, solution is not coverged as residual is oscillating
Avg. Coefficent of drag=2.3
Avg. Coefficient of lift=2.5
Velocity Contour
Vortex shedding can be obeserved under unsteady simulation.
Calculation of Strouhal Number
`omega=`No of cycle/time interval=`8.5/50`
`omega=0.17`
`St={omegaD}/V`
`St=0.34`
Part II
Steady state simulation for Re=10, 100, 1000, 10000 and 100000
Number of iterations=500
Residual plot
From above graph, we can observe that simulation get converged with increase in reynolds number. For Re=10, contunity and velocity curve keep on decreasing. solution didn\'t get converged even we run for more than 1000 iterations. For Re=100, 1000, 10000 and 100000 solution get converged.
Plot of vertex average of velocity magnitude
Plot for Coefficient of drag (Cd)
Plot for lift coefficient
Obsevation from above plot
Velocity Contour
Conclusion
From above velocity contour, we can observe that no vortex shedding is possible at Re=10 becuse flow is laryer by layer and slow. vortex shedding can be observed on when Re= 100 when simulated for unsteady state. At Re=1000, three dimensional instablities restrict formation of vortex shedding. At Re=10,000 and 1,00,000 flow becomes turbulent whch prevents from vortex shedding.
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