Week 2 - Flow over a Cylinder.

AIM:

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

OBJECTIVE:

1. To calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 and 100000.
2. Simulate the flow with steady and unsteady case and calculate the Strouhal number for Re=100.

INTRODUCTION:

• FLOW OVER A CYLINDER:

In a spite of extensive experimental and numerical studies over a century, flow around a circular cylinder still remains a challenging problem in fluid mechanics, where intensive investigation are continued even today to understand to complex unsteady dynamics of the cylinder wake flow. Cross flow normal to the axis of stationary circular cylinder and the associated problem of heat and mass transport are encountered in a wide variety of engineering applications. Both experimental measurements and numerical computation have conformed the onset of instability of the wake flow behind a cylinder beyond a critical Reynold number, leading leading finally to a kind of periodic flow identified by definite frequencies, well-known in the literature as the Von Karman vortex street.

• STROUHAL NUMBER:

In dimensional analysis, the Strouhal number is a dimensionless number describing oscillating flow mechanisms.

For large Strouhal number (order of 1), viscosity dominates fluid flow, resulting in a collective oscillating movement of the fluid “plug”. For low Strouhal number (order of 10^-4 and below), the high-speed, quasi-steady-state portion of the movement dominates the oscillation. Oscillation at intermediates Strouhal number is characterized by the build-up and rapidly subsequent shedding of vortices.

The Strouhal number is often given as,

S_{t = fd/U’}

Where,

F= Frequency of vortex shedding

D= characteristic dimeter of the cylinder

U’= Fluid flow velocity

• CO-EFFICIENT OF DRAG:

In fluid dynamics, the drag coefficient (C_d) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in a drag equation in which a lower drag coefficient indicates the object will have a less aerodynamics or hydrodynamics drag. The drag coefficient is always associated with a particular surface area.

The drag coefficient of any object comprises the effects of the two basic contributors to fluid dynamic drag skin friction and form drag. The drag coefficient of a complete structure such as an aircraft also include the effects of interference drag.

The drag coefficient C_d is defined as,

If there is a drag equiation then write as 3 times of lift coefficient

C_d = 2. Fd/pu²A

Where,

F_d = is the drag force, which is by definition the force component in the direction of the flow velocity.

is the mass density of fluid

U = is the flow speed of the object relative to the fluid

A = is the reference area

• CO-EFFICIENT OF LIFT:

The lift coefficient (C_L) is a dimensionless coefficient that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area. A lifting body is a foil or a complete foil-bearing body such as a fixed-wing aircraft. C_L is a function of the angle of the body to the flow, its Reynolds number, and its mach number. The section lift coefficient C₁ refers to the dynamic lift characteristics of a two dimensional foil section, with a reference area replaced by the foil chord.

C_L = L/Qs = L/_1/2qu²S = 2L/qu²S

L = is the lift force

S = is the relevant surface area

q = is the fluid dynamic pressure, in turn, linked to the fluid density, and to the flow speed.

A brief explanation to solve the flow over a cylinder

1 Geometry

Creating the geometry by sketching using the line and circle command, circle diameter of 2m and the dimension having 20x60m and the circle is placed 20m from the inlet.

2 Mesh

After geometry is loaded we should mesh it and here I used 200m as elemental size

Then after we have to given name as inlet, outlet, symmetry and wall.

3 Setting up an Ansys fluent

Before opening the set up we should update the mesh. Then we should change the viscous flow to laminar.

Open materials and create a fluid that is to be used for the simulation for this case, it is air and also inputs the density and kinematic viscosity value.

Open zones and input the velocity as per the Reynolds number and check if the fluid is updated.

Update the reference values which is located inside set up at the right-hand side.

• Fluent procedure

1. Laminar model
2. Fluid: air
3. Method of discretization: simple
4. Density/kinematic viscosity:1/0.05
5. Creating a monitor point behind the cylinder by selecting point under surfaces in the result bar.
6. After creating the monitor point, create reports/plots for drag, lift, velocity wrt cylinder.
7. Create plots for the velocity at the monitor point to analyse the vortex shedding.
8. Use hybrid initialization for steady-state and standard for transient state simulations.

PART 1:

1. Simulate the flow with steady and unsteady case calculate the Strouhal number for Re=100.
   2. Simulate the flow with steady case and calculate the Strouhal number for Re=100 and velocity 2.5 m/s.

• Velocity contour
• Pressure contour
• Residual plot
• Drag coefficient
• Lift coefficient
• Velocity at monitor point

2. Simulate the flow with unsteady case and calculate the Strouhal number for Re=100 and velocity 2.5 m/s.

• Pressure contour
• Velocity contour
• Residual plot
• Drag coefficient
• Lift coefficient
• Velocity at monitor point

PART 2:

• Simulate the flow with the steady-state solver for Re=10

For Re=10, velocity=0.25 m/s

• Pressure contour
• Velocity contour
• Residual plot
• Drag coefficient
• Lift coefficient
• Velocity at monitor point

1) Simulate the flow with the steady-state solver for Re=100

For Re=100, velocity=2.5 m/s

Pressure contour

• Velocity contour
• Residual plot
• Drag coefficient
• Lift coefficient
• Velocity at monitor point

3) Simulate the flow with the steady-state solver for Re=1000

For Re=1000, velocity=25 m/s

• Pressure contour
• Velocity contour
• Residual plot
• Drag coefficient
• Lift coefficient
• Velocity at monitor point

4) Simulate the flow with the steady-state solver for Re=10000

For Re=10000, velocity=250 m/s

• Pressure contour
• Velocity contour
• Residual plot
• Drag coefficient
• Lift coefficient
• Velocity at monitor point

5) Simulate the flow with the steady-state solver for Re=100000

For Re=100000, velocity=2500 m/s

• Pressure contour
• Velocity contour
• Residual plot
• Drag coefficient
• Lift coefficient
• Velocity at monitor point

Result:

Drag and lift coefficient for different Re

Re	Cd	CL
10	3.33	-0.001555
100	1.365	-0.13
1000	0.808	-0.00839
10000	0.9876	-0.373
100000	0.937	0.833

Conclusion:

• In the first case, the flow over a cylinder is simulated for both steady and unsteady cases with Re=100, and with the results generated the phenomena of von karman vortex street are also observed.
• Necessary plots are plotted in order to observe that the flow is converged and the vortex shedding is happening.
• Contours are generated in order to observe the flow over a cylinder.

• In second case,
• Six different simulation i.e., (Re= 10,100,1000,10000,100000,1000000) are simulated to observe the behaviour of the drag and lift coefficients by changing the Reynolds number.
• In order to observe the behaviour of the drag coefficients for the simulation, the velocity of the flow is varied to change the Reynolds number and rest of the parameters are kept constant.
• If thee Reynolds number is less than 2000, then flow in a pipe is laminar. Hence we use the viscous model= laminar.
• For Re= 10, it is observed that there is no formation of vortex shedding and in the rest of the cases, it is clearly observed.