Steady Vs Unsteady flow over a cylinder
Objective:
To simulate the fow over a cylinder and the process of kamran vortex street, or vortex shedding.
- Perform both steady and unsteady simulations and calculate the Strouhal Number.
- Determining the coefficient of drag and lift over a cylinder and study the effect of Reynolds number on it.
- Study of vortex shedding behind the cylinder.
Introduction:
Flow over the circular cylinder has been studied because of the variety of the applications in the industry. When the flow passes through a cylinder it observes a boundary flow phenomenon due to the boundary layer sepreation and a low pressure development behind the cylinder thus forming vortex behind the cylinder. At certain combinations of the reynolds number these low pressure region and vorteses start to oscillate behind the cylinder and this phenomenon is said to be the Kamran vortex street.
Vortex Shedding:
Pressure on the particle rises from the free steam pressure to the stagnation pressure when fluid flows towards the leading edge of the cylinder. This high pressure near the leading edge impels flow about the cylinder as boundary layers developed about both sides. This high-pressure doesn't sufficient to force the flow about the backside of the cylinder at high Reynold's number. Near the widest section of the cylinder, The boundary layer separates from the surface and forms a two free shear layer that is highly unstable. This shear layer will eventually roll into a discrete vortex and detach from the surface (a phenomenon called vortex shedding). Another type of flow instability emerges as the shear layer vortices shed from both the top and bottom surfaces interact with one another. They shed alternatively from the cylinder and generates a regular vortex pattern (the Karaman vortex street) in the wake. The vortex shedding occurs at a discrete frequency and is a function of the Reynolds number.
Given:
The 2D geometry was prepared in the ansys spaceclaim model and can be see below:
Further the body was imported for meshing and the mesh was generated in the fine category. This case is done for studying vortex shedding beacuse it can only be studied under the fine mesh category. The mesh can be seen below:
The inflation layer was set for 6 layers near the walls to create the proper shape for the walls the inflation can be seen below:
The mesh method was set to be triangular and the mesh sizing was set to be 1mm. The mesh quality was seen that the maximum number of the elements have the quality of more than 90%. The number of the nodes are 20571 and the number of the elements are 40260. The mesh quality can be seen below:
The boundaries were then named in the mesh as shown below:
Boundary Conditions:
Inlet Velocity Magnitude: 1m/s
Outlet Pressure Outlet : 0Pa
Symmetry : Symmetry
Walls: noslip
Case 1 : Steady and Transient State analysis for reynolds number 100
Steady state analysis was performed in ansys fluent
Material : User Defined
Density : 1kg/m^3
Viscosity: 0.02kg/m-s
The monitor point was also created at the distance of 8m from the cylinder to observe the process of vortex shedding. The solution was run for 450 iterations. Further the simulation was run in the laminar model. The residuals can be seen in the figure below:
The velocity contour can be seen below:
The pressure Contour can be seen below:
The average belocity at the monitor point can be seen below:
The lift at the walls can be seen below in the curve:
The drag at the walls can be seen below:
Here it can be seen that the in the residual plot at around the 450 iterations tahe residuals have gone stable. With the combination of the inlet velocity and viscosity in the velocity contours, the kamran vortex street phenonmenon can be observed. In the average velocity at the monitor point the constant sinusoidal oscillations can be observed which indictes the process of vortex shedding. In drag coefficient graph the constant drag coefficient can be observed and in the lift coefficient the constant sinusoidal oscillations can be observed which shows the changing lift directions due to the vortex shedding.
Transient Simulation
The transient simulation was run again with the same boundary conditions. Further the simulation time was set as 0.1 seconds and the the simulation was solved for 1500 timesteps. The residuals and the other results can be seen below:
Residuals
The velocity contour can be seen below:
The pressure Contour can be seen below:
The average velocity at the monitor point can be seen below:
The lift at the walls can be seen below in the curve:
The drag at the walls can be seen below:
The simulation was run for around 3000 iterations. In the residual plot constant oscillations can be observed at around 3000 iterations. In the velocity contour the constant oscillations can be observed and the vortex shedding can be observed after the time size of 0.1 seconds. At the monitor point velocity it can be seen that the velocity first drops and than starts to incrase again then starts to finally oscillate indicating the process of vortex shedding. In lift coefficient the coefficent first drops below zero and than starts to oscillate and than the amplitude of the oscillations increase and finally become constant at around 1.25. The drag coefficient shows the similar results as that of the steady state. Moreover the steady state and transient state are almost same with the final results the only difference is that in transient state we can study the change with respect to the time.
Stouhal Number
It can be important when analyzing unsteady, oscillating flow problems. The strouhal number represents a measure of the ratio of the inertial forces due to the unsteadiness of the flow or local acceleration to the inertial forces due to changes in velocity from one point to an other in the flow field.
Strouhal number is given by:`S=frac{fl}{V}`
where f is frequency of the oscillations
l is the characterstic length
v is the flow velocity
Number of oscillations in 20 seconds are almost 2
So the frequency is 2/20 .i.e. 0.1
So the strouhal number is
`S=frac{0.1*2}{1}`
Thus the strouhal number comes out to be 0.2.
Case 2 Determining the drag and lift coefficients for the various reynolds number:
Performing the steady state analysis:
- Re 10:
Material Defined User Defined:
Density: 1 kg/m^3
Viscosity: 0.2 kg/M-S
Residuals
The velocity contour can be seen below:
The pressure Contour can be seen below:
The average velocity at the monitor point can be seen below:
The lift at the walls can be seen below in the curve:
The drag at the walls can be seen below:
- Re 10:
Material Defined User Defined:
Density: 1 kg/m^3
Viscosity: 0.2 kg/M-S
Residuals
The velocity contour can be seen below:
The pressure Contour can be seen below:
The average velocity at the monitor point can be seen below:
The lift at the walls can be seen below in the curve:
The drag at the walls can be seen below:
2. Re 100:
Material Defined User Defined:
Density: 1 kg/m^3
Viscosity: 0.02 kg/M-S
Residuals
The velocity contour can be seen below:
The pressure Contour can be seen below:
The average velocity at the monitor point can be seen below:
The lift at the walls can be seen below in the curve:
The drag at the walls can be seen below:
3. Re 1000:
Material Defined User Defined:
Density: 1 kg/m^3
Viscosity: 0.002 kg/M-S
Residuals
The velocity contour can be seen below:
The pressure Contour can be seen below:
The average velocity at the monitor point can be seen below:
The lift at the walls can be seen below in the curve:
The drag at the walls can be seen below:
4. Re 10000:
Material Defined User Defined:
Density: 1 kg/m^3
Viscosity: 0.0002 kg/M-S
Residuals
The velocity contour can be seen below:
The pressure Contour can be seen below:
The average velocity at the monitor point can be seen below:
The lift at the walls can be seen below in the curve:
The drag at the walls can be seen below:
4. Re 100000:
Material Defined User Defined:
Density: 1 kg/m^3
Viscosity: 0.00002 kg/M-S
Residuals
The velocity contour can be seen below:
The pressure Contour can be seen below:
The average velocity at the monitor point can be seen below:
The lift at the walls can be seen below in the curve:
The drag at the walls can be seen below:
Disscussion:
From the above plot sit can be observed that with the change in reynolds number all the parameters change in the including the lift and drag coefficient. The table for the lift and drag coefficients can be seen below:
| Reynolds Number | Average Velocity at Monitor Point | Lift Coefficient | Drag Coefficient | Drag Vakue (Reference Paper) |
| 10 | 0.425 | 0 | 3.6 | 3.67 |
| 100 | 0.5 | 0.125 | 1.25 | 1.245 |
| 1000 | 0.7 | 0.25 | 0.75 | 0.995 |
| 10000 | 0.9 | 0.325 | 0.6 | |
| 100000 | 0.8 | 0.3 | 0.6 |
At reynolds number 10 no vortex formation can be seen in the flow. This is due to the high viscosity and low speed due to which the flow is fully laminar. Also it can be noticed that the drag coefficient is high doe to the friction generated by the fluid of higher viscosity. Also the velocity of the fluid is too low to develop the lift force. Alo there is some pressure drop behind the cylinder and due to which the velocity at monitor points first drops and then stabilises at almost half the value of inlet.
At reynolds number of 100 the vortex shedding phenomenon can be observed. The flow is fully laminar but the low pressure region can be seen oscillating behind the cylinder also known as vortex shedding. As the velocity is same but the viscosity decreases the lift force can be seen generated and the lift coeffient increases. Apart from that the drag coefficient can be seen decreasing. Due to phenomenon of vortex shedding the lift and vertex average at monitor point can be see oscillating.
At reynolds number 1000 the vortex shedding phenomenon can be observed but the phenomenon is not that smooth as that of reynolds number of 100. As the viscosity decreased the drag coefficient decreased further and the lift coeffient increased. Also the drag and and monitor graphs can be seen oscillating which indicates that the vortex shedding is still takin place.
At the reynolds number of 10000 and 100000 the flow becomes turbulent and the lift coefficient and the drag coefficient can be seen decreasing and then further stabalising in this region.