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- 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.
- 6. MESH • Mesh Quality • Aspect Ratio - 2.25882 • Minimum Edge Length – 1.57m • Growth Rate – 1.20 • Mesh Size • Level – 0 • Cells – 18432 • Faces – 37056 • Nodes – 18624 • Partitions – 1
- 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
- 9. NUMERICAL RESULTS Re 1000 ( k-Epsilon Model) Velocity Streamlines Velocity Magnitude
- 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
- 18. STROUHAL VS REYNOLDS 0.0000 0.0500 0.1000 0.1500 0.2000 0.2500 0.3000 0 2000 4000 6000 8000 10000 12000 St Re Strouhal No VS Reynold No K-Epsilon k-Omega K-Omega SST Theoretical
- 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.
- 22. THANK YOU!!!

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