Week 2 - Flow over a Cylinder.

Challenge 2 – External flow over a cylinder

Aim – To analyse the external flow over a cylinder, calculate the drag and lift coefficient, and observe the phenomenon of Von Karman Street for varying values of Reynolds number.

Theory and Practical Applications –

• Von Karman Street or most commonly known as vortex shedding is observed when a fluid flow over a body (external flow) and the subsequent vortices start to shed
• This phenomenon starts to occur mainly at a Reynolds number of 90-100.
• These phenomena can be found in rivers or streams as they flow past boulders, and even in the clouds as they move past mountains or islands.

Solving and Modelling Approach –

1. For analysing the external flow over a cylinder, a 2D design can be created, instead of a 3D design since the flow properties for each layer in the XY plane will be equal.
2. Since the flow over a cylinder is categorised in external flow simulations, an external control volume is required to analyse the flow around the cylinder boundary.
3. A 2D sketch was created in Ansys Spaceclaim and the “Pull” feature was used to generate a surface body for the sketch.
4. The dimensions of the control volume that were considered can be seen in the figure below.
5. After creating the appropriate geometry, a mesh was generated on the surface.
6. Since this simulation is about analysing the boundary layer of the cylinder and also the area after the cylinder, an advanced mesh is required to get accurate and precise results.
7. The mesh was created using a triangular method, edge sizing, and an inflation layer near the cylinder boundary.
8. An edge sizing of 36 was taken along the cylinder boundary, thus, each section has an angle of 10° subtended. A default growth rate of 1.2 was taken into consideration
9. An inflation layer with 6 divisions was created to accurately capture the boundary flow. Similarly, a growth rate of 1.2 was used.
10. An overall mesh sizing of 0.25m was created to obtain a highly fine mesh.
11. The meshed geometry then proceeded for setup in Ansys Fluent.

Setting up the case in Ansys Setup –

1. A pressure-based solver with absolute velocity formulation and steady-state flow was taken into consideration.
2. While analysing vortex shedding (Von Karman Street), a transient solver was used to accurately analyse each time step.
3. For simulations with Reynolds number of Re = 10, 100, and 1000, a laminar model was used since Re < 2300.
4. For simulations with Reynolds number of Re = 10000 and 100000, a K-omega SST turbulence model was used since Re > 2300.
5. A customized material with a viscosity of 0.02kg/ms was created using the create/edit materials tab and the free stream velocity was altered to vary the Reynolds number.
6. In cell zone conditions, the entire planar surface was given the properties of the customized material.
7. The named selections and boundary conditions are shown in the figures below.
8. The inlet velocity was kept as 0.1, 1, 10, 100, 1000 to get a Re = 10, 100, 1000, 10000 and 100000 respectively.
9. Since we have to calculate the coefficient of drag and lift, reference values were changed to suite this specific scenario.
10. From the results tab, a monitor point was created and the vertex average velocity at that monitor point was calculated by defining a report definition.
11. This will be helpful in calculating the Strouhal number for vortex shedding in case of a time dependent transient simulation
12. A simple scheme was used, since the coupled scheme is mainly used for compressible flows
13. A contour plot of velocity and pressure was created from the graphics option, and a solution animation was also defined for velocity
14. Hybrid initialization was done on each case and the solution was calculated for a total of 1000 iterations.
15. For transient simulations, the following values were used

• Time step size = 0.1s
• No of iterations per time step = 20
• No of time steps = 500
• Total iterations = 10,000

Reference Values –

Area = 2m²

Length = 2m

Depth = 1m

Velocity = varies according to Reynolds number

Temperature = 288.16K

Viscosity = 0.02kg/m. s

Research Papers for Validation of Values with < 5% error

• https://www.sciencedirect.com/science/article/pii/S0307904X08000243
• https://www.sciencedirect.com/science/article/abs/pii/S0142727X0700032X

1. Numerous observations can be made from the tabulation above
2. It was observed that for simulations involving Re = 10, the drag/lift coefficient and vertex average velocity plots (at monitor point), did not oscillate after a certain number of iterations.
3. For Re = 100, the coefficient of drag plot did not show any oscillations, whereas the lift coefficient and vertex average velocity plots oscillated after a specific number of iterations.
4. For all simulations with Re > 1000, the drag/lift coefficient and the vertex average velocity plots showed stable oscillations after reaching around 250 iterations.
5. It can also be observed that the lift coefficient of the cylinder for all the iterations was near to 0 since the top view of the cylinder symmetrical with 0 gravity.
6. It was also observed that the coefficient of drag reduced as the Reynolds number increased with the cylinder having a drag coefficient of 0.685 at Re = 100,000
7. Furthermore, from the vertex average velocity plots, it can be inferred that the velocity at the monitor point is around 12% less than the free stream velocity.

Part 1 - Results and Discussions – Steady and Transient case for Re = 100

Strouhal Number – 0.42 at peak magnitude

Strouhal Number = 0.374 at peak magnitude

• The K-epsilon model is accurate only for completely turbulent flows and flows that are non-separated.
• It may also cause stability issues because of stiffness
• k- epsilon model predicts well far from the boundaries (wall) and k- omega model predicts well near the wall.
• Even though it depends on Y+, an SST model is a combination of these.
• SST model used good mesh at the boundary and with wall treated usually works in most cases, but again it is problem specific.

Part 2 - Results and Discussions –

Convergence Criteria –

• For the transient simulation with a total number of 500 time steps and 20 iterations for each time step, the residuals oscillate at a constant frequency after a certain amount of iterations
• Considering the steady-state analysis at a Re = 10, the residuals do converge properly since vortex shedding is not observed at Re = 10.
• For simulations involving Re = 100, 1000, 10000, and 100000, the residuals converge by oscillating in a repeated pattern – hence convergence for these cases can be identified

Case 1 à Re = 10

• Free stream velocity = 0.1m/s
• Laminar Model used
• Iterations = 3000
• Diameter of cylinder = 2m
• Density of fluid = 1kg/m^3
• Dynamic viscosity = 0.02kg/m.s

Case 2 à Re = 100

• Free stream velocity = 1m/s
• Laminar Model used
• Iterations = 1000
• Diameter of cylinder = 2m
• Density of fluid = 1kg/m^3
• Dynamic viscosity = 0.02kg/m.s

Case 3 à Re = 1000

• Free stream velocity = 10m/s
• Laminar model used
• Iterations = 1000
• Diameter of cylinder = 2m
• Density of fluid = 1kg/m^3
• Dynamic viscosity = 0.02kg/m.s

Case 4 à Re = 10,000

• Free stream velocity = 100m/s
• K-omega SST Turbulence model used
• Iterations = 1000
• Diameter of cylinder = 2m
• Density of fluid = 1kg/m^3
• Dynamic viscosity = 0.02kg/m.s

Case 5 à Re = 100,000

• Free stream velocity = 1000m/s
• K-omega SST turbulence model used
• Iterations = 1000
• Diameter of cylinder = 2m
• Density of fluid = 1kg/m^3
• Dynamic viscosity = 0.02kg/m.s

Results and Conclusions –

• It can be observed that vortex shedding starts to occur at a Reynolds number of 100
• For simulations with Reynolds number <100, vortex shedding does not occur
• The coefficient of drag decreases slightly for every increase in Reynolds number
• Since the external body(cylinder) is symmetrical, and there is no gravity, the coefficient of lift nears 0 in all cases

Reference Research Papers –

• https://www.sciencedirect.com/science/article/pii/S0307904X08000243
• https://www.sciencedirect.com/science/article/abs/pii/S0142727X0700032X