Week 2 - Flow over a Cylinder.
THEORY:
Vortex shadding:
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.
1. Flow over cylinder:
In spite of extensive experimental and numerical studies of almost over a century, flow around a circular cylinder still remains a challenging problem in fluid mechanics, where intensive investigations are continued even today to understand the complex unsteady dynamics of the cylinder wake flow. Cross-flow normal to the axis of a stationary circular cylinder and the associated problems of heat and mass transport are encountered in a
wide variety of engineering applications. Both experimental measurements and numerical computations have confirmed the onset of instability of the wake flow behind a cylinder beyond a critical Reynolds number, leading finally to a kind of periodic flow identified by definite frequencies, well-known in the literature as the Von Karman vortex street. In the case of laminar flow past cylinders with regular polygonal cross-section, the flow
usually separates at one or more sharp corners of the cross-section geometry itself, forming a system of vortices in the wake on either side of the mid symmetry plane. On the other hand, for a circular cylinder, where the point of flow separation is decided by the nature of the upstream boundary layer, the physics of the flow is much more complex than what its relatively simple shape might suggest.
2. Strouhal number:
In dimensional analysis, the Strouhal number is a dimensionless number describing oscillating flow mechanisms.
For large Strouhal numbers (order of 1), viscosity dominates fluid flow, resulting in a collective oscillating movement of the fluid "plug". For low Strouhal numbers (order of 10−4 and below), the high-speed, quasi-steady-state portion of the movement dominates the oscillation. Oscillation at intermediate Strouhal numbers is characterized by the buildup and rapidly subsequent shedding of vortices.
The Strouhal number is often given as
St=fDU'
Where,
f= frequency of vortex shedding
D= characteristic diameter of the cylinder
U'= fluid flow velocity
3. Co-efficient of drag:
In fluid dynamics, the drag coefficient (cd) 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 the drag equation in which a lower drag coefficient indicates the object will have a less aerodynamic or hydrodynamic 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 lifting airfoil or hydrofoil also includes the effects of lift-induced drag. The drag coefficient of a complete structure such as an aircraft also includes the effects of interference drag.
The drag coefficient cd is defined as
Cd=2⋅Fdρu2A
4. Co-efficient of lift:
The lift coefficient (CL) 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. CL is a function of the angle of the body to the flow, its Reynolds number, and its Mach number. The section lift coefficient cl refers to the dynamic lift characteristics of a two-dimensional foil section, with the reference area replaced by the foil chord.
CL≡LqS=L12ρu2S=2Lρu2S
where
L is the lift force,
S is the relevant surface area and
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
GEOMETRY CREATION:
The 2D geometry is created by using the above dimension then the inside cylinder is deleted in order to carry out the simulation.
MESH GENERATION:
By default Ansys creates the quadrilateral mesh of default size. We need to convert it to triangles.
METHOD:
To change the meshing method. Go to Mesh => insert => method => select face => method (triangles) => generate mesh
SIZING:
To avoid inaccuracy in the solution the sharp corners around the circle are converted into large number of edges.
To do that Go to mesh => insert => sizing => select edge => type (number of divisions) => enter 36 and generate mesh
INFLATION:
Since the flow around the cylinder is important, the inflation layer is created around the cylinder
To create a inflation layer Go to mesh => insert => inflation => select face => select edge => number of layers => enter number and generate mesh
Boundary Condition:
Outlet : gauge pressure = 0 Pa.
wall : no slip condition.
Steady state simulation:
1.Reynolds number = 10.
velocity = 1 m/s.
density = 1 kg/m3.
viscosity = 0.02 Pa-s.
Residual plot:
Monitor point velocity:
monitor point: A point is created at 8 m in x direction from the axis of cylinder to check velocity.
Coefficient of drag:
Lift coefficient:
Velocity contour:
Pressure contour:
2.Reynolds number = 100.
velocity = 10 m/s.
density = 1 kg/m3.
viscosity = 0.02 Pa-s.
Residual plot:
3.Reynolds number = 1000.
velocity = 100 m/s.
density = 1 kg/m3.
viscosity = 0.02 Pa-s.
Residual plot:
Monitor point velocity:
Coefficient of drag:
Lift Coefficient:
Velocity contour:
Pressure contour:
4.Reynolds number = 10000.
velocity = 1000 m/s.
density = 1 kg/m3.
viscosity = 0.02 Pa-s.
Residual plot:
Monitor point velocity:
Coefficient of drag:
Lift Coefficient:
Velocity contour:
Pressure contour:
5.Reynolds number = 100000.
velocity = 10000 m/s.
density = 1 kg/m3.
viscosity = 0.02 Pa-s.
Residual plot:
Monitor point velocity:
Coefficient of drag:
Lift Coefficient:
Velocity contour:
Pressure contour:
Unstaedy state solver:
Reynolds number = 100.
velocity = 10 m/s.
density = 1 kg/m3.
viscosity = 0.02 Pa-s.
Residual plot:
Monitor point velocity:
Coefficient of drag:
Lift Coefficient:
Velocity contour:
Pressure contour:
Strauhall number:
Strouhal number is a dimensionless number describing oscillating flow mechanisms.
The Strouhal number is often given as
St = f*d/u
Here,we have calculated staruhal no.using ansys fluent.
1.Go to fluent solver > results > fft analyser > load lift coefficient fiel > select plot FFT
Here, x axis denotes strauhal number and y axis denotes magnitude.
2.To get the magnitude of strauhal number,
go to results > fft analyser > click on write fft to file > click on write fft.
open the file in excel and 1st coloumn denotes the frequncy and 2nd coloumn denotes strauhal number.use the command max and select 2nd row and find the magnitude of strauhal number.
Strauhal Number = 0.112
Result:
Values of coefficient of drag and lift coefficient for respective reynolds number is tabulated as follows:
Conclusion:
1.When fluid flows over cylinder, wake region is formed next to cylinder due to decrease in pressure and recirculation of flow occures and hence flow separation occures.
2.As flow over cylinder is being transient meaning time dependent phenomenon, we are unable to observe flow separation at low reynolds no.(say 50).
3.In this assignment we have kept all parameters constant and have only varried velocity to change reynolds number. So as the reynolds no. increases coefficient of drag decreases.however after reynolds no. = 4000, flow is turbulent and hence coefficient of drag is lower.
4.Strauhal no. calculated for unsteady state with reynolds no.= 100 is 0.112.