Flow over a cylinder

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

Objective :

PART-I

• Simulate the flow with the steady and unsteady cases 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, and 100000. (Run with steady solver.)
2. 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 %]

Theory :

1. Reynolds number :

• The Reynolds number is a dimensionless number , named after Osborne Reynolds , defined as the ratio of inertia forces to viscous forces. Mathematically, it is given as:

Re=Inertia force(Fi)Viscous force(Fv)��=Inertia force(Fi)Viscous force(Fv)

i.e. Re=ρvDμ=vDν����=���

where ,

ρ = density of fluid (kg/m3)

V = velocity of fluid (m/s)

D = diameter of pipe (m)

μ = dynamic viscosity of fluid (N-s/m2)

ν� = kinematic viscosity of fluid (m2/s)

2.Strouhal number (St):

Strouhal number is a dimensionless number describing oscillating flow mechanisms.

The Strouhal number is often given as

St = f*d/u

Where,

f is the frequency of vortex shading,

L is the characteristic length and

U is the flow velocity.

St = (1*2)/1 = 2.

St=2.

• Significance :
  • The Reynolds number is used in forced convection. Forced convection is a type of heat transfer in which fluids are forced to move in order to increase the heat transfer.
  • The Reynolds number is used to predict flow patterns in different fluid flow situations. At a low Reynolds number, the flow tends to be laminar, while at a high Reynolds number, the flow tends to be turbulent.

2. Type of flow:

• Laminar flow:
  • If a fluid travels smoothly in a regular path, then flow is called laminar flow. flow is to be called laminar flow when the following conditions are satisfied:.
  • For internal flow, Re < 2000.
  • For external flow, Re < 105.
• Turbulent flow :

• If a fluid flows in an irregular path instead of regular one, then it is called as turbulent flow. The flow was to be called as turbulent flow when following conditions occurred:.
• For internal flow, Re>4000
• For external flow, Re > 5 x 105.

3. Lift and drag force:

1. When any body moves through a fluid, an intersection between the body and the fluid occurs, and this effect can be described in terms of the forces at the fluid-body interface.
2. Both shear stress and pressure vary in magnitude and direction along the surface.
3. The resultant force in the direction of the upstream velocity is termed drag (D), and the resultant force normal to the upstream velocity is termed lift (L).

3.1. Drag Force(Fd) :

• Drag force is a resistance forced which is acting opposite to the motion of the object.
• It is mathematically given as

Drag force(Fd) = CdρAV22�����22

Where ,

Cd = coefficient of drag

V = flow velocity

A = the projected area of the object w.r.t. which drag force is calculated.

ρ = density of fluid

• Drag coefficient is a dimensionless quantity used to determine the drag or resistance of an object in a fluid environment such as air ,water.

3.2. Lift force (Fl) :

• The force which is acting perpendicular to the object/body motion is called as lift force.
• It is mathematically given as

Lift force(Fl) =ClρAV22�����22

Where,

Cl = coefficient of lift.

• Lift coefficient is a dimensionless quantity which is used to determine the lift of an object in a fluid environment such as air , water.

4. Flow separation :

• When a fluid is forced to flow over a curved surface at high velocities. A fluid follows the front portion of the curved surface with no problem but it has difficulty remain attached to the surface on the back side. At sufficiently high velocities, the fluid detaches itself from the surface of body. And this phenomenon is called as flow separation.
• The location of a separation point depends upon various factors such as Reynolds number, the surface roughness, the level of fluctuation in the free stream. And it is usually difficult to predict exactly where the separation will occurs unless there are sharp corners or abrupt changes in the shape of the solid surface.

5. Von-Karman Vortex shading:

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.

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 = 100.

velocity = 1 m/s.

density = 1 kg/m3.

viscosity = 0.02 Pa-s.

D=2m

Plots:

a.Residuals

b. contour of static pressure

c.contour of velocity

d.monitor-point velocity

e. coefficient of drag

e.coefficient of lift

2. Reynolds Number = 10.

velocity = 0.1 m/s.

density = 1 kg/m3.

viscosity = 0.02 Pa-s.

D=2m

a.Residuals

b. pressure contour

c.Velocity contour

d. Monitor-point velocity

e.Coefficient of drag

f.coefficient of lift

3. Reynolds number = 1000.

velocity = 10 m/s.

density = 1 kg/m3.

viscosity = 0.02 Pa-s.

D=2m

a. Residual

b. pressure contour

c. velocity contour

d. monitor point velocity

e. coefficient of drag

f. coefficient of lift

4. Reynolds number = 10000.

velocity = 100 m/s.

density = 1 kg/m3.

viscosity = 0.02 Pa-s.

D=2m

a. Residual

b.pressure contour

c. velocity contour

d. Monitor point velocity

e. Coefficient of drag

f. coefficient of lift

5.Reynolds number = 100000.

velocity = 1000 m/s.

density = 1 kg/m3.

viscosity = 0.02 Pa-s.

D=2m

a. Residual

b. pressure contour

c.velocity contour

d. monitor point velocity

e.Coefficient of drag

f. coefficient of lift

Unsteady state simulation for Re = 100

a. residual

b. pressure contour

c. velocity contour

d.monitor point velocity

e. Coefficient of drag

f. coefficient of lift

Conclusion:

The formation of a wake region adjacent to the cylinder during fluid flow over a cylinder is caused by a drop in pressure, which leads to flow recirculation and ultimately, flow separation.

2. At low Reynolds numbers (let us say 50), we are unable to see flow separation because flow over the cylinder is a transient, or time-dependent, phenomenon.

3. The only variable we changed to alter Reynolds number in this assignment was velocity; all other parameters remained constant. The coefficient of drag therefore decreases as Reynolds number increases. however after reynolds no. = 4000, flow is turbulent and hence coefficient of drag is lower.

4. The derivative of the Stauhal number for an unstable state with Reynolds number = 100 is 2.