Steady Vs Unsteady flow over a cylinder

Objective :-

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

PART-I

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

PART-II

1. 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.

Theory :-

In fluid dynamics, a Kármán vortex street (or a von Kármán 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. It is named after the engineer and fluid dynamicist Theodore von Kármán and is responsible for such phenomena as the "singing" of suspended telephone or power lines and the vibration of a car antenna at certain speeds.

A vortex street will form only at a certain range of flow velocities, specified by a range of Reynolds numbers (Re), typically above a limiting Re value of about 90. The (global) 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 or in a channel, and may be defined as a nondimensional parameter of the global speed of the whole fluid flow:

Re = uL/ν

where:

• u = the free stream flow speed.
• L = a characteristic length parameter of the body or channel.
• ν = the free stream kinematic viscosity parameter of the fluid, which in turn is the ratio:

v = μ/ρ

between:

• ρ = the reference fluid density.
• μ = the free stream fluid dynamic viscosity.

Strouhal number (St): It is a dimensionless number describing the oscillating flow mechanisms.

St = (f*L)/u

Where

• f = Frequency of vortex shedding.
• L = Length over which the flow is.
• u = Flow velocity.

Procedure:

Geometry:

2-D geometry is used to run the simulation. It was generated using the Spaceclaim.

circle dia = 2m

Meshing:

• Meshing element size = 0.25 m.
• Element type = Triangular.
• Sizing - Edge sizing for the cylinder wall :

No. of divisions = 36

• Inflation: First layer thickness = 5 mm.

No. of layers = 6.

Growth rate = 1.2.

Setup & Solution:

• General physics settings: steady/ transient based on the solver being used.
• Viscous model: Laminar flow.
• Material used: User material [ μ = 0.02 Kg/ m.s ; ρ = 1 Kg/ m³.].
• Boundary conditions: Inlet velocity = 1 m/s.

Outlet pressure = 0 Pa.

Wall = No slip condition.

Part I:

To simulate for Unsteady and Steady flow conditions, at Reynold’s number (Re) = 100.

Unsteady case:

No. of time steps = 950.

Time step size = 0.1

Residual plot:

Velocity plot:

Drag coefficient plot:

Lift coefficient plot:

Vortex shedding

velocity contour:

Pressure contour:

Strouhal number (St):

Strouhal number (St) = (f*L)/u

L = 2 m.

u = 1 m/s.

f = No. of cycles/time period.

= 3/20 = 0.15 Hz.

St = (0.15*2)/1

= 0.3.

Steady case:

Reference value :-

for every reynolds num we have to change the velocity value

No. of iterations = 700.

Residual plot:

Velocity plot:

Drag coefficient plot:

Lift coefficient plot:

Vortex shedding

velocity contour:

Pressure contour:

Part II:

To calculate the drag coefficient and lift coefficient at different Reynold’s numbers.

Each case's plots and contours are placed in the order of

Case 1: Re = 10 ; u = 0.1 m/s

num of iteration = 750

Scaled residual plot

Velocity magnitude plot

Pressure magnitude plot

Drag coefficient plot

Lift coefficient plot

Velocity contour

Pressure contour.

Case 2: Re = 100 ; u = 1 m/s

Already mentioned in Part I of the report.

Case 3: Re = 1000 ; u = 10 m/s.

Scaled residual plot

Velocity magnitude plot

Pressure magnitude plot

Drag coefficient plot

Lift coefficient plot

Velocity contour

Pressure contour.

Case 4: Re = 10000 ; u = 100 m/s.

Scaled residual plot

Velocity magnitude plot

Pressure magnitude plot

Drag coefficient plot

Lift coefficient plot

Velocity contour

Pressure contour.

Case 5: Re= 100000 ; u = 1000 m/s

Scaled residual plot

Velocity magnitude plot

Pressure magnitude plot

Drag coefficient plot

Lift coefficient plot

Velocity contour

Pressure contour.

Conclusion

• Increase in reynolds number also increases the drag and lift values simultaneously.
• DragForce that is exerted by the following fluid on the cylinder depends on the reynolds number of the flow .
• With increase in the reynolds number the flow is becoming more unsymmetrical.
• increasing velocity eventually brings the turbulent drag upto and even higher than the laminar drag value.

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