4.0 Discussion
4.1 Flow Separation for Re=20 and Re=106
Flow separation

Re=20 Re=106
Figure X. Flow separation for a circular cylinder at Re = 20 and Re = 106
Flow separation for the cylinder is delayed when the Reynolds number is 106 when compared to when the Reynolds number is 20.
Looking at the boundary layer velocity profile we can see the velocity at the surface of the cylinder is zero to satisfy the no slip boundary condition. We can also see the flow momentum near the surface of the cylinder is very small due to viscous flow resistance.
When comparing the two cases, we can see that in the laminar case the flow momentum near the surface is less than the flow momentum near the surface for the turbulent case. This results into the laminar cases boundary layer flow to be more sensitive to external pressure gradients.
In our case the pressure increases in the direction of the flow resulting in a negative pressure gradient. This is known as an adverse pressure gradient. The flows in both cases now need to move against a viscous flow resistance and also a pressure force. As the flow in the laminar case is more sensitive to pressure gradients than the flow in the turbulent case, the flow will stop or reverse earlier and therefore separate earlier.
4.2 Velocity vectors for Re=1, Re=20 and Re=106
Earlier separation

Re=1 Re=20
Smaller wake region
Delayed separation
Larger wake region
Re=106
Figure X. Velocity vectors for a circular cylinder at Re = 1, Re = 20. Re = 106
Frictional drag comes from the friction between the fluid and surface of the cylinder over which it’s flowing over. Pressure drag is associated with the formation of a wake.
At a Reynolds number of 1 we can see the velocity vectors stay tangent along the entire surface of the cylinder and no separation takes place, this is known as creeping flow. This suggests at a Reynolds number of 1 the drag force acting on the cylinder is mostly made of a frictional drag. At…