Steady / Unsteady Flow over a Cylinder.

AIM:-

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

Objectives:-

PART-I: steady-state simulation

1. Simulate the flow over cylinder using a steady-state Solver and calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000.

Part-II: Unsteady (Transient) Simulation

1. Simulate the flow over cylinder using a Transient Solver and calculate Strouhal Number, coefficient of drag and lift over a cylinder by setting the Reynolds number to 100

vortex shedding:-

vortex shedding is an oscillating flow that takes place when a fluid such as air or water flows past a bluff (as opposed to a 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 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 oscillation 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 audio antennas at some speeds. Tall chimneys constructed of thin-walled steel tubes can be sufficiently flexible that, in airflow with a speed in the critical range, vortex shedding can drive the chimney into violent oscillations that can damage or destroy the chimney.

Von Karman Street:-

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.

A vortex street will form only at a certain range of flow velocities, specified by a range of Reynolds Number(Re), typically above a limiting Re value of about 90.

Strouhal number

Strouhal number

Procedure:

Geometry:- 2 -D rectangular surface 60*20m and a hole of Dia 2 m in it.

Mesh:-

• Nodes = 20924
• Elements = 40470

I used 3 methods to generate god quality mesh

1) Triangle dominant mesh with element size = 0.25m.

2) Edge sizing 36 divisions on cylinder

3) Inflation layers

• number of layers over the cylinder = 12
• first-layer thickness = 5e-3
• growth rate = 1.2.

Quality:-

Creating named sections

Setup:

• Fluent launcher Double-precision Parallel solving with 4 solvers.
• Check the mesh & report quality.
• Setup
• General:- Type = Pressured Based, Absolute Velocity Formation & Time =both Steady and Transient.
• Models:- Viscous model:- Laminar
• Materials:- Copy air-fluid material from fluent database to create user-defined fluid with density = 1 Kg/m3, Viscosity(Kg/m-s) = 0.02 calculated from Renolds number formulae.
• Cell zone conditions:- user-defined fluid in the region.
• Boundary conditions:-
  • Cylinder wall: Stationary wall no-slip boundary condition
  • Inlet:- Velocity inlet, Absolute Velocity magnitude calculated with respect to Renolds number
  • Outlet:- Pressure outlet, Absolute Gauge pressure = 0 Pa
  • symmetry:- Symmetry
• Solution method:-
• 
• Creating a Monitor point at length = 4*Dia = 8m of the cylinder from center of cylinder towards +ve side

Report Definitions:-

Surface report

Drag & lift coefficient report:

Residual monitor:-

Reference values:-

Hybrid Initialization :

Velocity and pressure contour for animations

Solution:

For steady-state Run for 800 iterations

For Transient time calculation

V= 1m/s, L = 60 m, Time step size = 0.2 sec.

`text(Time steps = ) L/(V*text(time step size)) = 60/(1*0.2)=300`

The number of time steps should be greater than or equal to 300 in this simulation we were given 800 timesteps with maximum iterations for time step = 10

Simulation time = 800*0.2 = 160 sec

Results:-

Create XY plane

velocity contour, pressure contours, velocity streamline, velocity vector on XY Plane.

Velocity calculation:-

`V = (mu*R_e)/(rho*D) text( m/s)`

Diameter, D= 2 m

Density, `rho`= `1 text( )(kg)/m^3`

Dynamic Viscosity `mu`= 0.02 `(kg)/(m-s)`

Re = int(input('Renolds num : '))  # Renoulds number
D  = 2 # Diameter m
Rho = 1 # density Kg/m3
D_v = 0.02  # Dynamic viscosity kg/ms

V = (D_v*Re)/(Rho*D)

print('velocity = ',V, 'm/s')

Renoulds number	Velocity m/s
10	0.1
100	1
1000	10
10000	100
100000	1000

Steady State simulations:

1)

Reynolds number = 10

Velocity = 0.1 m/s

velocity animation: https://drive.google.com/file/d/1LJbwu2kXqtXa71gycsMB7m5UAMq0_t2k/view?usp=sharing

pressure animation: https://drive.google.com/file/d/1kKcpdpNRgG7-NsnHMJITdBGXqIcNMR9J/view?usp=sharing

2)

Reynolds number = 100

Velocity = 1 m/s

velocity animation: https://drive.google.com/file/d/1YFr76H9V7ctt8MX5S5zAQRR0MpgOqgcN/view?usp=sharing

pressure animation: https://drive.google.com/file/d/1Mx2Y5X4qmcDZ8obpr5x-lWyPdgs_FC0I/view?usp=sharing

3)

Reynolds number = 1000

Velocity = 10 m/s

velocity animation: https://drive.google.com/file/d/1DX_KHYSoPDmlCcmCy8tRpu1cDqxswMpO/view?usp=sharing

pressure animation: https://drive.google.com/file/d/1uaJg3JhecpdyiHcBgnAl-nmNG7i78frS/view?usp=sharing

4)

Reynolds number = 10000

Velocity = 100 m/s

velocity animation: https://drive.google.com/file/d/1OdQYwIY6crCfsR5GBcsd1RDDmxVeOwlj/view?usp=sharing

pressure animation: https://drive.google.com/file/d/1xFHcKhY7e5BKiiPkn1S7hLVYJLObiiip/view?usp=sharing

5)

Reynolds number = 100000

Velocity = 1000 m/s

velocity animation: https://drive.google.com/file/d/1fhS5RwFlF8WiMuXGLmiVSmLG2bqKnuy8/view?usp=sharing

pressure animation: https://drive.google.com/file/d/1hb58zlu_4Z_2_VK-G-fRBWj0f8qMARJF/view?usp=sharing

Transient State simulations:

1)

Reynolds number = 100

Velocity = 1 m/s

Simulation time = 100 sex with step size =0.1sec

strouhal number:

f = number of cycles/time = `1/(160-154)` = 0.166

strouhal number = `(f*L)/v` = `(0.166X2)/1`= 0.332

velocity animation: https://drive.google.com/file/d/1Pksq4a7ybgQaP9OknoOvHf8kHexL4C6o/view?usp=sharing

pressure animation: https://drive.google.com/file/d/19BWSjmQhfjgXJ5QXJEzOMqPaWZFWkn6l/view?usp=sharing

Results:-

Lift and Drag coefficient

Steady State simulation
Reynolds number	Velocity m/s	Drag coefficient	Lift coefficient
10	0.1	3.3259	0.000427
100	1	1.3365	0.1355
1000	10	1.2787	0.79
10000	100	1.10	1.176
100000	1000	1.095	1.126
Transient simulation
100	1	1.34	0.19

Conclusions:-

1. As the reynolds number increases Drag coefficient Decreases and lift coefficient increases.
2. Transient state capture more accurate vortex sheding than steady state solving.