Steady Vs Unsteady flow over a cylinder

Aim: Simulating the flow over a cylinder

Introduction: The flow over a 2d cylinder is one of the most discussed problems in aerodynamics. The flow pattern is a function of the Reynolds number at which the flow occurs. At the trailing end of the cylinder cross section a region of low-pressure region is formed which introduces a drag force on the cylinder where as the symmetrical cross section produces minimum to no lift. The immediate adjacent layer to the cylinder remains stationary and a boundary layer is thus formed with strong viscous effects. The boundary layer separated forms a free shear layer and is highly unstable. This shear layer will eventually roll into a discrete vortex and detach from the surface

Simulation

Case 1: Steady state for Re = 100

• Geometry in space claim

• Defining boundaries

• Meshing

Element Size : 0.25 m , 40502 elements. The quality of the mesh generated is acceptable and is shown below.

• Solver Settings

2d, pressure based, Inviscid model. The boundary conditions for each named selection are specified.

Inlet Velocity = 2 m/s

Material: density 1kg/m3

Viscosity : 0.04 kg/m-s

• Results

Fig 1. Residuals at Re = 100

Fig 2. Lift plot at Re = 100

Fig 3. Drag plot at Re = 100

Fig 4. Strouhal Number at Re = 100

• The Strouhal number at Re = 100 for steady state simulation is found to be 0.0105

Case 2: Unsteady state for Re = 100

Fig 5. Residuals at Re = 100

Fig 6. Strouhal Number at Re = 100

• The Strouhal number at Re = 100 for unsteady state simulation is found to be 0.0795 for a time step size of 0.1 s.
• Although the residual plots do not provide any vision towards convergence, the repeating pattern of the lift coefficient gives us an idea regarding convergence. The coefficient of drag gets a constant value in our simulation.

• Case 3: Steady state for Re = 10

Fig 7. Residuals at Re = 100

Fig 8. Lift Plot at Re = 10

Fig 9. Drag Plot at Re = 10

Fig 10. Velocity Contour at Re = 10

• Case 4: Steady state for Re = 100

Fig 11. Velocity Contour at Re = 100

• Lift and drag coefficients at different Reynolds numbers

Sl No.	Reynolds Number	Lift Coefficient Simulation	Drag Coefficient simulation
1	10	0.00192	6.659
2	100	0.0284	2.668
3	1000	0.267	1.452

Conclusions

The following conclusions can be made from the simulation conducted.

1. The lift coefficient increases with increase in Reynolds number.
2. The drag coefficient decreases with increase in Reynolds number