FLOW OVER CYLINDER ANSYS FLUENT

In fluid dynamics, a von Karman 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.

vortex shedding is an oscillating flow that takes place when a fluid such as air or water flows past a bluff 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 von Karman vortex street. the fluid flow past the object creates alternating low-pressure vortices on the downstream of the object. the object will tend to move toward the low-pressure zone.

When the body experiences the pressure drag during the fluid movement, then the body is said to blunt. They are said to have separated flow over a considerable portion of its layer.

the phenomenon arises under certain flow conditions which depend on the Reynolds number

Re=ρ⋅v⋅L/μ`

where Re is the reynolds number,

rho is the density of the fluid `

v is the velocity of the moving fluid

L is the characteristic length

and mu is the dynamic viscoisty or absolute viscosity

PHENOMENON EXPLANATION :

Vortex shedding happens when the equilibrium flow suffers a Hopf bifurcation and flow settles down to a new equilibrium flow, which is almost time-periodic (at Strouhal frequency). 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 Re_d range (47<Re_d<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.

PART - I

STEADY AND UNSTEADY FLOW OVER A CYLINDER FOR RE=100

GEOMETRY

THE 2D ENCLOSURE IS OF DIMENSION 60x20m and the diameter of the cylinder is 2m.

MESH

Mesh method: all triangles (second order)

number of division about the edge of the cylinder: 72

Inflation layer :

FLT=5mm

growth rate =1.2

no of layers=10

inflation Layer and the number of divisions are used to capture the circular geometry so that nodes can calculate values.

FLUENT SETUP DETAILS

MATERIAL SPECIFICATION:

air with density =1 and mu = 0.02.

VISCOUS MODEL

Laminar

BOUNDARY CONDITIONS

inlet v=1 ms-1

no slip condition for wall

and 0 gauge pressure for the outlet

Monitor point is at a distance 8 units from the origin. (origin is the centre of the cylinder)

BY SIMPLE solution method and Hybrid initialization we solve the problem.

A) STEADY CASE

RESIDUALS

MONITOR POINT

LIFT

DRAG

coefficient of drag = 2.172219

VELOCITY CONTOUR

PRESSURE CONTOURS

VECTORS

we cant find Strouhal number for steady flow condition as it represents the ratio of inertial forces due to unsteadiness of the flow or local acceleration to the inertial forces due to change in velocity in flow field.

link : https://youtu.be/lZxhg3kXkA0

UNSTEADY CASE :-

RESIDUALS

MONITOR POINT

vertex shedding frequency F can be calculated using the graph

F=3/20 [3 comes the number of cyles between 120 and 140 flow time and 20 is the difference of the flow rate (140-120)]

=0.15Hz

strouhal number :- `St=F*L/V`

where F is vertex shedding frequency

L is characteristic length or diameter

v is the velocity of the moving fluid

St=0.15*2/1=0.3

DRAG

coeff of drag=2.2581921

VELOCITY CONTOUR

PRESSURE CONTOUR

VELOCITY VECTOR

link : https://youtu.be/IBGO2I9W-rA

OBSERVATIONS AND CONVERGENCE

• From the residual plot, we can see that the flow has converged around 300 iterations in the steady case and 28000 iterations in an unsteady state.
• In the residual plot the continuity and value of X and Y become stable which means flow has converged.
• Steady flow results give the final results, while in the unsteady flow it gives results based on flow time.
• Unsteady analysis can give accurate solutions of vertices and shedding frequency and we can get intermediary results.
• When your simulation has no change on all the convergence criteria, after certain iterations or timesteps, then we can consider that the solution has reached a steady-state, i.e.., converged.
• In convergence, there is no change after some iterations or they follow the same pattern

PART II

1.)RE=10

changing velocity to 0.1 ms-1.

RESIDUALS

MONITOR POINT

DRAG

LIFT

COEFFICIENTS

VELOCITY CONTOUR

PRESSURE CONTOUR

RE=100

has been shown in part I

RE=1000

changing velocity to 10 ms-1.

RESIDUALS

MONITOR POINT

DRAG

LIFT

COEFFICIENTS

VELOCITY CONTOUR

PRESSURE CONTOUR

RE=10000

changing velocity to 100 ms-1.

RESIDUALS

MONITOR POINT

DRAG

LIFT

COEFFICIENTS

VELOCITY CONTOUR

PRESSURE CONTOUR

RE=100000

changing velocity to 1000 ms-1.

RESIDUALS

MONITOR POINT

DRAG

LIFT

COEFFICIENTS

VELOCITY CONTOUR

PRESSURE CONTOUR

RE=200

changing velocity to 2 ms-1.

RESIDUALS

MONITOR POINT

DRAG

LIFT

COEFFICIENTS

VELOCITY CONTOUR

PRESSURE CONTOUR

CONCLUSION

1. with an increase in Reynolds\'s number the drag coefficient increases.
2. flow pattern becomes unsymmetrical wrt to the axis perpendicular to the flow
3. drag force is inversely proportional to Reynolds numbers for (Re<300 where the flow is laminar after that it gets converted to turbulent ) if we change dynamic viscosity.

references: wikipedia.org

science direct research paper