Week 2 - Flow over a Cylinder.
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. Create a monitor point behind the cylinder at a distance 4 times the diameter which can be used to calculate and analyze 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 a 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.
- THEORY:
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
`S_t = (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 `(c_d)` 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 `c_d` is defined as
`C_d = (2⋅F_d)/( ρ u^2 A)`
4. Co-efficient of lift:
The lift coefficient (`C_L`) 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.
`C_L -= L/(qS)=L/(1/2ρu^2S)=(2L)/(ρu^2S)`
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
6 Layers inflation
PART 1:
REYNOLDS NUMBER:
For Re = 100:
`Re=(U⋅ρ⋅D)/μ`
FLUENT SETUP:
|
SETUP |
STEADY-STATE |
UNSTEADY STATE |
|
SOLVER TYPE |
Pressure based |
Pressure based |
|
VELOCITY FORMULATION |
Absolute |
Absolute |
|
TIME |
Steady |
Transient |
|
VISCOUS MODEL |
Laminar |
Laminar |
|
MATERIAL |
User material |
User material |
|
CELL ZONES |
Fluid type: user material Density – 1 kg/m3 Dynamic viscosity – 0.02 kg/ms |
Fluid type: user material Density – 1 kg/m3 Dynamic viscosity – 0.02 kg/ms |
|
BOUNDARIES |
Velocity magnitude 1m/s
Gauge pressure – 0 pa
Condition - No slip |
Velocity magnitude 1m/s
Gauge pressure – 0 pa
Condition - No slip |
STEADY STATE
UNSTEADY STATE
Material
Cell zones
BOUNDARIES
inlet
outlet
walls
SOLUTION:
- Vertex average of velocity magnitude using surface report at a monitor point at 10m from the center of the cylinder to the right of the cylinder along the x-direction.
- Coefficient of drag and coefficient of lift reports are created using force report
- INITIALIZATION: Hybrid for steady state
The standard for unsteady state
- ACTIVITIES: contour plots of pressure and velocity and solution animation are created after initialize the solution.
- RUN CALCULATION:
For steady-state – No of iterations= 500
For transient state – Time step = 0.1
No of iterations = 500
RESULTS:
STEADY-STATE:
RESIDUAL:
This plot helps in monitoring the change in each and every convergence criterion for every time step and plots those values for every iteration or time step. This plot helps to know when convergence is achieved.
From the above plot, we can see that the solution has reached a steady state even before 500 iterations.
MONITOR POINT VELOCITY:
The above plot shows the value of vertex average of velocity magnitude at the monitor point is 0.62 m/s
CONTOUR:
VELOCITY:
youtube link
PRESSURE:
youtube link
The above contour and animation show the vortex shedding effect.
STREAMLINE:
VELOCITY:
The above animation shows the streamline flow for velocity.
PRESSURE:
The above animation shows the streamline flow for pressure.
DRAG PLOT:
The coefficient of the drag plot shows the constant value after a certain number of iterations and remains the same after that and the value is 1.367848.
LIFT PLOT:
The coefficient of the lift plot shows that it starts oscillating after some time and continues further and the value is 0.17997243.
STROHAUL NUMBER:
The strohaul number cannot be calculated for the steady state as we don't calculate the flow with respect to time.
TRANSIENT:
RESIDUAL:
This plot helps in monitoring the change in each and every convergence criterion for every time step and plots those values for every iteration or time step. This plot helps to know when convergence is achieved.
The flow is converged in 3300 iterations.
MONITOR POINT VELOCITY:
The above plot shows the value of vertex average of velocity magnitude at the monitor point is 0.27 m/s.
CONTOUR:
VELOCITY:
PRESSURE:
The above contour shows the vortex shedding effect.
DRAG PLOT:
The coefficient of the drag plot shows the constant value after a certain number of iterations and remains the same after that and the value is 1.2657366.
LIFT PLOT:
The coefficient of the lift plot shows that it starts oscillating after some time and continues further and the value is 0.018048622.
STROHAUL NUMBER:
Strohaul number = 0.01.
SUMMARY:
| CASES | REYNOLDS NUMBER | INLET VELOCITY | Cd | Cl | MONITOR VELOCITY |
| STEADY STATE | 100 | 1m/s | 1.367848 | 0.17997243 | 0.62m/s |
| TRANSIENT STATE | 100 | 1m/s | 1.2657366 | 0.018048622 | 0.27m/s |
From the above cases, we can say that in the transient case the velocity starts oscillating for the monitoring point after certain iterations and the velocity at the monitoring point is greater in the case of the steady-state case as compared to the transient case.
PART 2:
SIMULATION 1:
SIMULATION OF FLOW FOR THE STEADY STATE FOR Re = 10
Velocity calculation for Reynolds number 10,
For Re = 10:
`Re=(U⋅ρ⋅D)/μ`
`10=(U.1.2)/(0.02)`
U=0.1m/s
RESULTS:
RESIDUAL:
This plot helps in monitoring the change in each and every convergence criterion for every time step and plots those values for every iteration or time step. This plot helps to know when convergence is achieved.
MONITOR POINT VELOCITY:
From this plot we can see that for re = 10 there is no oscillations in velocity.
VELOCITY CONTOUR:
youtube link
From the contour and animation, we can see that there is no vortex shedding formation when reynolds number 10.
DRAG PLOT:
The value of cd is 3.3314425.
LIFT PLOT:
The value of cl is -0.00085925251.
SIMULATION 2:
SIMULATION OF FLOW FOR THE STEADY STATE FOR Re = 100
Velocity calculation for Reynolds number 100,
For Re = 100:
`Re=(U⋅ρ⋅D)/μ`
`100=(U.1.2)/(0.02)`
U=1m/s
RESULTS:
RESIDUAL:
MONITOR POINT VELOCITY:
The above plot shows the vertex average of velocity magnitude at the monitor point is 0.61154234
VELOCITY CONTOUR:
Youtube link
The above contour and animation show the vortex shedding formation.
DRAG PLOT:
the value of cd is 1.367848.
LIFT PLOT:
the value of cl is 0.17997243.
SIMULATION 3:
SIMULATION OF FLOW FOR THE STEADY STATE FOR Re = 1000
Velocity calculation for Reynolds number 1000,
For Re = 1000:
`Re=(U⋅ρ⋅D)/μ`
`1000=(U.1.2)/(0.02)`
U=10 m/s
RESULTS:
RESIDUAL:
MONITOR POINT VELOCITY:
The above plot shows the vertex average of velocity magnitude at the monitor point is 8.2080564
VELOCITY CONTOUR:
Youtube link:
The above animation shows the vortex shedding formation.
DRAG PLOT:
The value of cd is 0.86912317.
LIFT PLOT:
The value of cl is -0.331299.
SIMULATION 4:
SIMULATION OF FLOW FOR THE STEADY STATE FOR Re = 10000
Velocity calculation for Reynolds number 10000,
For Re = 10000:
`Re=(U⋅ρ⋅D)/μ`
`10000=(U.1.2)/(0.02)`
U=100m/s
RESULTS:
RESIDUAL:
MONITOR POINT VELOCITY:
The above plot shows the vertex average of velocity magnitude at the monitor point is 74.108414
VELOCITY CONTOUR:
Youtube link
The above animation shows the vortex shedding formation.
DRAG PLOT:
The value of cd is 0.81047329.
LIFT PLOT:
The value of cl is 0.9461438.
SIMULATION 5:
SIMULATION OF FLOW FOR THE STEADY STATE FOR Re = 100000
Velocity calculation for Reynolds number 100000,
For Re = 100000:
`Re=(U⋅ρ⋅D)/μ`
`100000=(U.1.2)/(0.02)`
U=1000m/s
RESULTS:
RESIDUAL:
MONITOR POINT VELOCITY:
The above plot shows the vertex average of velocity magnitude at the monitor point is 824.28937 m/s
VELOCITY CONTOUR:
Youtube link:
The above contour and animation show the vortex shedding formation.
DRAG PLOT:
The value of cd is 0.74380507
LIFT PLOT:
The value of cl is 0.43716453
SUMMARY:
| SIMULATION | REYNOLDS NUMBER | Cd | Cl |
| 1 | 10 | 3.3314425 | -0.00085925251 |
| 2 | 100 | 1.367848 | 0.17997243 |
| 3 | 1000 | 0.86912317 | -0.331299 |
| 4 | 10000 | 0.81047329 | 0.9461438 |
| 5 | 100000 | 0.74380507 | 0.43716453 |
From the above plot, we can say that the value of the lift coefficient keeps on increasing as we keep increasing the velocity and Reynolds number. The drag coefficient is maximum for the lowest Reynolds number and goes on decreasing.
CONCLUSION:
- 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 a cylinder is transient we are unable to observe flow separation at a low Reynolds number
- As the Reynolds number increases the coefficient of drag decreases.
- Strauhal number for an unsteady state with Reynolds number 100 is 0.01.
REFERENCE MATERIAL:
Numerical simulation of laminar flow past a circular cylinder - ScienceDirect
https://www.grc.nasa.gov/WWW/wind/valid/lamcyl/Study1_files/Study1.html
Paper Title (use style: paper title) (flowvisioncfd.com)
http://www.eng.fsu.edu/~shih/succeed/cylinder/cylinder.htm
https://en.wikipedia.org/wiki/Boundary_layer