Flow over a cylinder

Aim:- To simulate the transient flow over a cylinder for different Reynolds number.

Theory:-

The fluid approaching the cylinder branches out and encircles the cylinder, forming a boundary layer that wraps around the cylinder. The fluid particles on the midplane strike the cylinder at the stagnation point, bringing the fluid to a complete stop and thus raising the pressure at that point. The pressure decreases in the flow direction while the fluid velocity increases. At very low upstream velocities, the fluid completely wraps around the cylinder and the two arms of the fluid meet on the rear side of the cylinder in an orderly manner. Thus, the fluid follows the curvature of the cylinder. At higher velocities, the fluid still hugs the cylinder on the frontal side, but it is too fast to remain attached to the surface as it approaches the top (or bottom) of the cylinder. As a result, the boundary layer detaches from the surface, forming a separation region behind the cylinder. Flow in the wake region is characterized by periodic vortex formation and pressures much lower than the stagnation point pressure. 

Formulas:-

                          `Re=(rho*V* D)/mu`                     `implies Re=(V*D)/nu`

Where,

`Re=`Reynolds number,                     `rho =`Density of fluid

`V=`Velocity of fluid,                         `D=`Diameter of cylinder

`mu=`Dynamic viscosity,                     `nu=`Kinematic viscosity

Calculations:-

`D= 0.02 (m)`

At temperature of 293.2K, the Kinematic viscosity of air  `nu=15.07**10^-6 (m^2/s)`

`V_1=10m/s`             `implies Re_1=(10**0.02)/(15.07**10^-6)=13271.4`

`Re_2=1.2**Re1=1.2**13271.4=15926`      `impliesV_2=12m/s`

`Re_3=1.4**Re1=1.4**13271.4=18580`      `impliesV_2=14m/s`

`Re_4=2**Re1=2**13271.4=26543`              `impliesV_2=20m/s`

Procedure of simulation:-

1.  The cylinder is modelled in Solidworks with following parameters: Diameter = 0.02 m,  Length= 0.04m.

2.  In wizard option of Flow simulation tab the parameters are set as:  Time dependent flow, Air as our fluid and Velocity is set at x axis (i.e 10, 12, 14 & 20 m/s for varying Reynold's number percentage such as 0, 20, 40 & 100). And basic mesh is created.

Results:-

For inlet velocity= 10 m/s

Pressure Distribution:

 

Velocity Distribution:

 

For inlet velocity= 12 m/s

Pressure Distribution:

 

Velocity Distribution:

 

For inlet velocity= 14 m/s

Pressure Distribution:

 

Velocity Distribution:

 

For inlet velocity= 20 m/s

Pressure Distribution:

 

Velocity Distribution:

 

Conclusion:-

We can conclude that

• Velocity is higher in the region above & below the cylinder facing the flow while the velocity at back gradually decreases creating a Wake region in the boundary layer.
• Due to Stagnation pressure at the front of the cylinder facing the flow, it has higher pressure while minimum at the back of the cylinder..
• Due to the cylindrical structure, there exists an Maximum Velocity region pointing radially outwards indicated by Red Colour in the Plots.
• The other side of the Cylinder towards exit of the flow experiences very low velocity range due to presence of obstruction indicated by Greenish Blue Colour in the Velocity Plots.
• With increase in the Reynolds Number, the inlet Velocity Increases and puts same effect on the walls of the Cylinder,  only the extent of the Flow along with range of obstruction for the flow velocity changes.