1. SIMULATION OF VON KARMAN STREET
IN A FLOW OVER A CYLINDER
- SALEEM MOHAMMED HAMZA (250873614)
2. WHAT IS VON KARMAN STREET?
• A fluid dynamics phenomenon
• Repeating pattern of swirling vortices caused
by the unsteady separation of flow of a fluid
around blunt bodies.
• Named after the engineer and fluid dynamist
T. Von Karman.
• Vortex formation only starts above Re>80.
• Vortex Shedding is given by Strouhal
number, 𝑆𝑡 = 𝑓𝑑/𝑈.
• For flow over cylinder St = 0.2
3. OBJECTIVE
• To simulate the flow over a cylinder for Re 103 and 104 using different turbulence
models and to compare the results and suggest the best model for this case.
• To obtain the coefficients of lift and drag and to compare it with the theoretical data
available.
• To find the Strouhal number from the simulation and to compare it with the
theoretical data available.
4. PROBLEM SPECIFICATION
• Unsteady state.
• Fluid as air of 𝜌 = 1.225 kg/m3 and 𝜇 = 1.78 x 10−5
kg/ms.
• Set diameter as 1 m for ease of calculation.
• Obtain the velocity at the inlet in order to maintain the desired
Reynolds number, i.e., 103 and 104 by using the below formula.
𝑅𝑒 =
𝜌𝑈𝐷
𝜇
5. SOLUTION DOMAIN
• A circular domain will be used for this
simulation.
• Thus, the outer boundary will be set to be 64
times as large as the diameter of the
cylinder.
• That is, the outer boundary will be a circle
with a diameter of 64 m.
7. BOUNDARY CONDITIONS
• We will set the left half of the outer
boundary as a velocity inlet.
• Next, we will use a pressure outlet boundary
condition for the right half of the outer
boundary with a gauge pressure of 0 Pa.
• Lastly, we will apply a no slip boundary
condition to the cylinder wall.
8. SOLVER SETTINGS
• SIMPLE
• Second Order Implicit
• Time Step Size
• 0.2 secs for Re = 104
• 5 secs for Re = 1000
•
• No. of Time Steps
• 400 for Re = 104
• 800 for Re = 1000
10. CD & CL PLOTS
-6.000
-5.000
-4.000
-3.000
-2.000
-1.000
0.000
1.000
2.000
3.000
4.000
0.000 500.000 1000.000 1500.000 2000.000 2500.000
Cd
Time (s)
Cd Vs Time
-0.800
-0.700
-0.600
-0.500
-0.400
-0.300
-0.200
-0.100
0.000
0.100
0.200
0.000 500.000 1000.000 1500.000 2000.000 2500.000
Cl Vs Time
Re 1000 ( k-Epsilon Model)
11. NUMERICAL RESULTS
Re 1000 (K-Omega Model)
Velocity Streamlines Velocity Magnitude
Cd Vs Time CL Vs Time
12. NUMERICAL RESULTS
Re 1000 (K-Omega SST Model)
Velocity Streamlines Velocity Magnitude
Cd Vs Time CL Vs Time
13. NUMERICAL RESULTS
Re 104 (K-Epsilon Model)
Velocity Streamlines Velocity Magnitude
Cd Vs Time CL Vs Time
14. NUMERICAL RESULTS
Re 104 (K- Omega Model)
Velocity Streamlines Velocity Magnitude
Cd Vs Time CL Vs Time
15. NUMERICAL RESULTS
Re 104 (K- Omega SST Model)
Velocity Streamlines Velocity Magnitude
Cd Vs Time CL Vs Time
16. NUMERICAL SOLUTIONS
• We can see how the lift coefficient changes with the flow time, becoming periodic
due to the vortex shedding from the cylinder.
• We can use this plot to calculate the Strouhal number of the flow, which is a ratio of
the unsteadiness in the flow to inertial forces in the flow field.
• We can calculate the Strouhal Number by calculating the frequency of the vortex
shedding from our plot.
17. RESULTS
Re Model Cd Cd Actual Cl Time period F (Hz) St No St Actual
10000
K-Epsilon 1.28015 1.00 0.00368 2.6 0.3846 0.2634 0.2
K-Omega 1.00063 1.00 0.00256 3.00 0.3333 0.2283 0.2
K-Omega- SST 1.00002 1.00 0.00048 3.20 0.3125 0.2140 0.2
1000
K-Epsilon 1.01413 1.20 0.00263 450 0.002222 0.1522 0.2
K-Omega 1.45677 1.20 0.05266 310 0.003226 0.2209 0.2
K-Omega- SST 1.28016 1.20 0.06904 335 0.002985 0.2044 0.2
19. CD VS REYNOLDS NO
0.00000
0.20000
0.40000
0.60000
0.80000
1.00000
1.20000
1.40000
1.60000
0 2000 4000 6000 8000 10000 12000
Cd
Re
Drag Coefficient Vs Re No
K-Epsilon
K-Omega
K-Omega SST
Theoretical
• We can see from the above comparison that the K-Omega SST model is the most
accurate among the three models as its value are closer to the theoretical data
available for flow over cylinder
20. DISCUSSIONS
• The simulation experiences some instabilities at the start and gradually stabilizes as
the flow develops.
• To avoid this, we can either patch the region and apply a initial condition of velocity
or run the simulation under steady state and then use this case as the boundary
condition for the unsteady simulation.
• This results in earlier vortices shedding and thus allows us to see the oscillation in the
lift coefficient vs time plot better.
• This also effectively reduces the time step size & number times steps to be run and
thus effectively capture the vortex shedding.
21. CONCLUSION
• Thus the flow over a cylinder was simulated in FLUENT 16.0 and the different
turbulence models were compared.
• The drag coefficient and the Strouhal no obtained from simulations were compared
to the theoretical data available and were found to be inline.
• It was found that the K-Omega SST Turbulence model was the most accurate and
the percentage error with the theoretical data for drag coefficient and Strouhal
number was 6% and 2% respectively which is acceptable.
