Steady Vs Unsteady flow over a cylinder
Steady vs unsteady 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 number by changing the inlet velocities accordingly. Create a monitor point behind the cylinder at a distance 4 times the diameter which can be used to calculate and analyse the vortex shedding.
- 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 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.
- THEORY:
1. Flow over cylinder:
In spite of extensive experimental and numerical studies 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 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= (fD)/(U')`
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 (commonly denoted as: 
, 
or 
) 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 
is defined as
where:
is the drag force, which is by definition the force component in the direction of the flow velocity,
is the mass density of the fluid,
is the flow speed of the object relative to the fluid,
is the reference area.
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.
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 
.
- CONTENT:
1. Geometry:
1. Setting up geometry in SpaceClaim:
Creating the geometry by sketching using the line and circle command, circle diameter of 2m and the dimensions having 20X60m and the circle is placed 20m from the inlet.
2. Setting up the mesh in meshing:
a. After the geometry is loaded, click on Mesh at the right-sided tree, and input an element size of 0.5m.
b. After a base mesh is initiated we can refine the geometry by improving by changing the mesh from quadrilateral to triangular-shaped nodes.
c. After changing the node shape, we can improve the mesh near the cylinder and refine the shape of the circle by adding body sizing feature.
d. We can add Inflation feature which creates layers round the cylinder circle and also helps in generating accurate answers.
e. We can name the boundaries as needed accordingly such as inlet, outlet, symmetry BC and cylinder as wall.
Mesh details:
a. Element size = 0.5m.
b. All triangles method.
c. Edge sizing to give a cleaner and finer finish for cylinder while creating the mesh.
d. Inflation is to create layers of the geometry so that we can protect the cylinder geometry.
3. Setting up Fluent:
a. After the geometry is loaded in fluent, we shall set up the physics part, open viscous and choose laminar.
b. 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.
c. Open Zones and input the inlet velocity as per the reynolds number and check if the fluid is updated.
d. Update the reference values which is located inside set up at the right-hand side.
e. Calculate the number of iterations under steady-state and simulate the problem.
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 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 analyse the vortex shedding.
h. Use hybrid initialisation for steady-state and standard for transient state simulations.
i. Run the simulations for different Reynolds number as per the challenge requirement.
2. Results
Part 1: Calculating Strouhal Number for Re= 100 at steady-state and transient state simulations.
a. Steady-state:
1. Velocity and pressure contours:
2. Drag and Lift co-efficients:
3. Residuals and Velocity at monitoring point:
4. Strouhal number plot:
therefore, the Strouhal number for steady-state for Re= 100 is 0.048
b. Transient state: having a time step size of 0.1 and time steps taken/no of iterations = 500
1. Velocity and pressure contours:
2. Drag and lift coefficients:
3. Residuals and Monitor point velocity:
4. Strouhal number plot:
therefore, the Strouhal number for transient-state for Re= 100 is 0.228
Part 2: Calculate drag and lift coefficients for different numbers of reynolds numbers
a. Re = 10 , velocity(U)= 0.25m/s
1. Velocity and Pressure contours:
2. Drag and lift coefficient:
3. Residuals and velocity at monitor point:
b. Re= 100, velocity(U)= 2.5m/s
1. Velocity and pressure contour:
2. Drag and lift coefficients:
3. Residuals and Velocity at Monitoring point:
c. Re= 1000, velocity(U)= 25m/s
1. Velocity and pressure contour:
2. Drag and lift coefficients:
3. Residuals and velocity at monitoring point:
d. Re= 10000, velocity(U)= 250m/s
1. Velocity and pressure contour:
2. Drag and lift coefficients:
3. Residuals and velocity at monitoring point:
e. Re=100000, velocity(U)= 2500m/s
1. Velocity and pressure contours:
2. Drag and lift coefficients:
3. Residuals and velocity at monitoring point:
- Results and Conclusions:
1. Drag and lift coefficient values for different Reynolds number:
| Reynolds number | Drag coefficient | Lift coefficient |
| 10 | 3.313 | -0.000291 |
| 100 | 1.311 | 0.1045 |
| 1000 | 0.7616 | -0.0731 |
| 10000 | 0.7019 | 0.0715 |
| 100000 | 0.528 | 0.05531 |
2. Error wrt the theoretical values from the reference material,
| Reynolds number | theoretical Cd | Numerical Cd | error |
| 10 | 2.6 | 3.313 | 0.713 |
| 100 | 1.4 | 1.311 | 0.087 |
3. 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 is 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,
- six different simulations 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 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 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 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 number of iterations.
- From the above table it can be concluded that the error percentage is less than 5%.