Week 2 - Flow over a Cylinder.
Aim:
Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street. Understanding the vortex shedding for different Reynolds numbers by changing the inlet velocities accordingly.
Objective:
1. Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100
2. 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 the Reynolds number on the coefficient of drag. [ Results should be validated with any standard literature and error should be within 5 %]
3. In both approaches, show that the flow has converged. That is, what quantities or plots need to be looked at to determine that the flow has converged?
4. Plots of the coefficient of drag and lift.
5. Plots to show vortex shedding behind the cylinder.
6. Mention the preferred material at the end of the challenge submission page.
Introduction:
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.
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 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 of overhead power line wires humming in the wind, and 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.
Reynolds Number (Re):
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.
Re = rho*V*d/Dynamic Viscosity
The range of Re values will vary with the size and shape of the body from which the eddies are being shed, as well as with the kinematic viscosity of the fluid. Over a large Red range (47<Red<105 for circular cylinders; reference length is d: diameter of the circular cylinder) eddies are shed continuously from each side of the circle boundary, forming rows of vortices in its wake. The alternation leads to the core of a vortex in one row being opposite the point midway between two vortex cores in the other row, giving rise to the distinctive pattern shown in the picture. Ultimately, the energy of the vortices is consumed by viscosity as they move further downstream, and the regular pattern disappears.
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
Co-efficient of drag:
Co-efficient of lift:
The lift coefficient (CL">CLCL) 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.
where
is the lift force,
is the relevant surface area and
q is the fluid dynamic pressure, in turn, linked to the fluid density, and to the flow speed.
PART-I
Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.
Unsteady case
Modelling:
A brief explanation to solve the flow over a cylinder
geometry
- for modelling the approach we are starting with the creation of geometry. first, we get into the geometry section where we create the geometry using the DESIGN MODULAR.
- first, we select the unit in meters as the required dimensions are given we create the geometry using the tools.
Creating the geometry by sketching using the circle and rectangle command, circle diameter of 2 m and the dimensions having 20X60m and the circle is placed 20m from the inlet.
Mesh
- first, we create the mesh by giving the element size i.e 0.25 meters.
- and we convert the quad-dominated mesh into the triangle-dominated mesh.
- we have to capture the physics at the circumference of the cylinder perfectly so we divide the circle into 36 parts.
- and then to create body-fitted mesh we are adding the inflation layers to capture the physics more clearly.
- if we are not getting the correct results for this element size, again we change the mesh size to capture the solution correctly.
- after meshing we create the named selections of boundaries.
- we gave the name to each of the faces of the boundaries.
But in the meshing nodes, the shape is more quadrilateral than the triangle so we should do this by changing the method to the triangle in the insert option.
After the geometry is loaded we should mesh it and here I used 250 mm as the elemental size.
After changing the node's shape into triangles we should improve the mesh around the cylinder by sizing in the mesh which is used to control precisely the mesh.
Then we should add inflation which is used to create a body-fitted mesh.
The method used is triangular.
The element size of the mesh is 250 mm.
Edge sizing is used around the circle with 36 'number of divisions'
And inflation used is around the circle with a first-layer thickness of 5 mm and the number of layers is 20.
And we should name the boundaries as given below
Setting up Ansys fluent
Before opening the set up we should update the mesh. Then we should change the viscous flow to laminar
Boundary Condition:
Outlet : gauge pressure = 0 Pa.
Wall: no-slip condition.
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 values.
For getting the graph of the vortex velocity we created the monitor point using the create >points > at a distance of 8 meters we create a point to which you can give any name to the point. and we can get to know about the distance where vortex shedding happens by trial and error method.
velocity plot
pressure plot
Drag
Lift
Strouhal 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 Strouhal no. using Ansys fluent.
1.Go to fluent solver > results > FFT analyser > load lift coefficient file > select plot FFT
Here, the x-axis denotes the Strouhal number and the y-axis denotes magnitude.
2. To get the magnitude of the Strouhal number,
go to results > FFT analyzer> click on write fft to file > click on write fft.
open the file in excel and 1st column denotes the frequency and 2nd column denotes the Strouhal number. use the command max and select the 2nd row and find the magnitude of the strouhal number.
CASE – 2: Simulation over the cylinder with a steady solver for Reynold numbers 10, 100, 1000, 10000, and 100000.
Open Zones and input the inlet velocity as per the Reynolds number and check if the fluid is updated.
Update the reference values which are located inside the setup on the right-hand side.
Fluent details/procedure:
a. laminar model
b. fluid: Air
c. Method of discretization: Simple
d. Density/kinematic viscosity: 1/0.05
e. Creating a monitor point behind the cylinder by selecting a point under surfaces in the results bar.
f. After creating the monitor point, create reports/plots for drag, lift, velocity wrt cylinder.
g. Create plots for the velocity at the monitor point to analyze the vortex shedding.
h. Use hybrid initialization for steady-state and standard for transient-state simulations.
1) Velocity Contour plot
Reynold numbers: 10, Velocity: 0.25 m/s.
Reynold numbers: 100, Velocity: 2.5 m/s.
Reynold numbers: 1000, Velocity: 25 m/s.
Reynold numbers: 10000, Velocity: 250 m/s.
Reynold numbers: 100000, Velocity: 2500 m/s.
2. Pressure contour plot.
Reynold numbers: 10
Reynold numbers: 100
Reynold numbers: 1000
Reynold numbers: 10000
Reynold numbers: 100000
3. Coefficient of Drag.
Reynold numbers: 10
Reynold numbers: 100
Reynold numbers: 1000
Reynold numbers: 10000
Reynold numbers: 100000
4. Coefficient of Lift.
Reynold numbers: 10
Reynold numbers: 100
Reynold numbers: 1000
Reynold numbers: 10000
Reynold numbers: 100000
Convergence
When your simulation has no change on all the convergence criteria, after certain iterations or timesteps, then we can consider that the solution has reached a steady state, i.e., converged. For CFD, RMS residual levels of 1E-4 are considered to be loosely converged, levels of 1E-5 are considered to be well converged, and levels of 1E-6 are considered to be tightly converged. For complicated problems, however, it's not always possible to achieve residual levels as low as 1E-6 or even 1E-5.
In case Re = 100 Steady state simulation, the residuals become steady but they didn't fall below 1e-4 thus we go for checking the quantity of interest which is drag coefficient, lift coefficient, and avg. vertex velocity and the above graphs show that all the quantities are in a steady state hence we can say the solution is converged.
In case Re = 100 unsteady state simulation, the residuals are steadily fluctuating but again all of them didn't fall below 1e-4 thus after checking the quantity of interest we can say that solution is converged.
Simulation Result Values
Summary Table: Cd and Cl values for the respective Reynolds number carried out for the steady state
| Case | Drag Coefficient | Lift Coefficient | Average velocity at the vertex |
| 10 | 3.3241564 | 0.00093191 | 0.042368 |
| 100 | 1.3366762 | 0.039884041 | 0.513877 |
| 1000 | 0.73401042 | 0.24294821 | 7.589774 |
| 10000 | 0.74729648 | 0.37316128 | 81.69005 |
| 100000 | 0.64683046 | 0.1398 | 784.5313 |
| Unsteady | 1.3203672 | 0.010078434 | 0.542187 |
Error with respect to the theoretical values from the reference material.
| Reynolds number | theoretical Cd | Numerical Cd | error |
| 10 | 3.5 | 3.3 | 4.77% |
| 100 | 1.4 | 1.3 | 2.5% |
Effect of Reynolds Number on Drag Coefficient(Cd):
The above-recorded data is obtained from simulation for variation in Reynolds no. . Results show that as Reynolds no. increases the drag coefficient decreases. Only for case Re = 10000 drag coefficient slightly increase by 0.01.
From the above results following can be observed:
As the Reynolds increases the coefficient of drag decreases accordingly.
The increase in Reynolds leads to the shedding of vortices from the upper and lower cylinder surface at a particular frequency. At lower Re=10, there is no formation of vortices. Vortex shedding takes place at higher Reynolds like 100, 1000, 10000, and 100000 from the above results obtained from simulation.
The transient model is appropriate for the Vortex Karman Street phenomenon as it is time-dependent.
When fluid flows over the cylinder, the wake region is formed next to the cylinder due to a decrease in pressure, and recirculation of flow occurs hence flow separation occurs.
As flow over the cylinder is being transient meaning a time-dependent phenomenon, we are unable to observe flow separation at low Reynolds no. (say 50).
In this assignment, we have kept all parameters constant and have only varied velocities to change the Reynolds number. So as the Reynolds no. increases the coefficient of drag decreases. however after Reynolds no. = 4000, flow is turbulent and hence coefficient of drag is lower.
Strauhal no. calculated for unsteady state with Reynolds no. = 100 is 0.112.
Conclusions:
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.
By plotting Power Spectral Density vs Frequency, the Strouhal number is calculated.
In the second case, five different simulations i.e (Re = 10, 100, 1000, 10000, 100000) are simulated to observe the behavior of the drag and lift coefficients by changing the Reynolds number.
In order to observe the behavior of the drag coefficients for the simulations, the velocity of the flow is varied to change the Reynolds number and the rest of the parameters are kept constant.
As we know if the Reynold number is less than 2000, then the 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.
As per the basic conditions and parameters, the results are validated from the literature.
As we refine the mesh we need to run more iterations. From the above table, it can be concluded that the error percentage is less than 5%.