Steady Vs Unsteady flow over a cylinder
STEADY VS UNSTEADY FLOW OVER A CYLINDER | VON KARMAN VORTEX STREET | CFD SIMULATION IN ANSYS FLUENT
Objective: To simulate the flow over a cylinder and capture the phenomenon of Karman vortex street.
- Simulate steady & unsteady case.
- Calculate the Strouhal Number for Re=100.
- Calculate the coefficient of drag and lift over cylinder by varying Reynolds number.
- Effect of Reynolds number on the coefficient of drag.
- Show plot illustrating vortex shedding behind the cylinder.
THEORY
Vortex - A Vortex is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved.
Vorticity - A vector that describes the local rotary motion at a point in the fluid, as would be perceived by an observer that moves along with it.
Vortex shedding - Vortex shedding is a phenomenon when the fluid flows across a bluff/blunt body, vortices are shed alternately from one side to the other, and where alternating low-pressure zones are generated on the downwind side of the structure giving rise to a fluctuating force acting at right angles to the fluid direction.
Karman vortex street - A repeating pattern of swirling vortices, caused due to Vortex shedding, which is responsible for the unsteady separation of fluid of a fluid around blunt bodies.
Reynolds number - Reynolds number is the ratio of inertial forces to viscous forces within a fluid
GEOMETRY
MESHING
Triangle dominant mesh
6 Inflation layer at the cylinder wall
Mesh metrics
Element size = 0.25m
Triangle dominant element
6 Inflation layer at cylinder wall - first layer thickness = 5e-3 m
Edge sizing - number of elements at cylinder wall = 36
Nodes= 20697
Cells = 40502
SETUP
- Pressure based solver was used as the velocity of fluids is incomparable to Mach number.
- SIMPLE solution method is used
- Laminar viscous model as Reynolds number is small
- Create a point named 'monitor point' at (8,0)
- Monitor point velocity plot will illustrate vortex shedding
Boundary Conditions
- Cylinder Wall - stationary with no-slip condition
- Gauge pressure at outlet = 0
Material properties
- Density = 1 kg/m^3
- Viscosity = 0.02 Pa.s
|
Reynold number |
10 | 100 | 1000 | 10000 | 100000 |
|
Velocity (m/s) |
0.1 | 1 | 10 | 100 | 1000 |
Output variables
- Vertex average velocity at the monitor point
- Drag and lift coefficient
- Velocity and pressure contour
- Velocity contour animation
Convergence criteria
- The solution is said to be converged if the residual plots reach a steady-state i.e. values/patterns repeats.
- The steady solution is achieved for our output variables or elsewhen we get our expected solution.
Vortex shedding plots
- Monitor point velocity plot - Velocity fluctuates in the vortex shedding.
- Lift coefficient plot - Cl will fluctuate due to pressure variation (vortices are detached and created periodically)
RESULTS
1) Unsteady simulation, Re=100
Residual plot
Monitor point velocity variation shows vortex shedding characteristics
Lift coefficient
Drag coefficient = 1.3766
Calculating frequency
Using lift coefficient plot, 140s - 160s
f = (number of cycles) / (time)
f= 1.5/20= 0.075
Strouhal number
L=Diameter=2m
U=velocity = 1m/s
St= (0.075* 2) /1 = 0.15
Strouhal number = 0.15
2) Steady simulation, Re=10
Residual
vortex shedding not observed because of low Reynolds number
Lift coefficient
Drag coefficient = 3.3251
3)Steady simulation, Re=100
Residual
Velocity variation at the point shows vortex shedding
Coefficient of lift
Coefficient of drag = 1.3345
4)Steady simulation, Re=1000
Residual
Velocity
Coefficient of lift
Coefficient of drag = 0.73215
5)Steady simulation, Re=10000
Residual
velocity
Coefficient of lift
Coefficient of drag = 0.80767
6)Steady simulation, Re=100000
Residual
velocity
Coefficient of lift
Coefficient of drag = 0.91539
Effect of Reynolds number on the coefficient of drag
|
Reynolds number |
10 |
100 (steady) |
100 (unsteady) |
1000 | 10000 | 100000 |
|
Cd (Drag coefficient) |
3.3251 | 1.3345 | 1.3766 | 0.73215 | 0.80767 | 0.91539 |
Drag coefficient vs Reynold no.
Here Drag coefficient is strictly decreasing from Re=10 to 10000
For Re=1000 to 100000, steady nature appears i.e. only small change in the drag coefficient
Conclusion
- Plots of residual, velocity, drag & lift coefficient all reach a steady-state confirming convergence of the solution.
- Fluctuation produced in monitor point velocity and lift coefficient plots confirm the capturing of vortex shedding.
- Vortex shedding is captured for both steady and unsteady simulation.
- Drag and lift coefficients have been plotted.
- Strouhal number = 0.15 is obtained for unsteady case Re=100.
- For low velocity/Re Drag coefficient is high and decreases for high Reynolds number.
- For low velocity/Re as momentum of fluid is not high enough to overcome the friction effect provided by the cylinder wall so giving high Drag coefficient value.