Flow over a Cylinder

AIM:

To do flow simulation of external flow over a cylinder using SOLIDWORKS

OBJECTIVE:

• To do flow simulation of a baseline cylinder with external flow and then calculate the Reynolds Number.
• Run a transient flow simulation on a cylinder by increasing the Reynolds number by a factor of 20%, 40%, and 100%
• Calculate the End time of analysis with the help of Domain length and Velocity.

THEORY:

FLUID: A fluid is any substance that flows or deforms under applied shear stress or, the substance which have the tendency to flow is called as fluid.

LAMINAR AND TURBULENT FLUID FLOW:

The laminar flow is defined as the type of flow in which the fluid particles move along well-defined paths or streamline and all the streamlines are straight and parallel.

Thus, the particles move in laminas or layers gliding smoothly over the adjacent layer. This type of fluid is also called as streamline flow or viscous flow.

The turbulent flow is defined as the type of flow in which the fluid particles move in a zig-zag way, eddies formation takes place which is responsible for high energy loss.

For pipe flow, the type of flow is determined by a non-dimensional number called the Reynolds number.

With respect to laminar and turbulent flow regimes:

Laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion

Turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow instabilities.

Reynolds Number: It is a dimensionless value which is used to represent whether the fluid is laminar or turbulent. It is the ratio of inertial force to viscous force.

It is expressed by, `Re =ρu D/μ=u D/v`

Where, `ρ` is the density of the fluid; `u` is the flow speed; `D` is the diameter of the tube; `μ` is the dynamic viscosity of the fluid; `v` is the kinematic viscosity of the fluid.

Reynolds Number formula is used to determine the velocity or, diameter or, viscosity of the fluid.

CALCULATIONS:

Reynolds Number (Re) is calculated

Diameter of the cylinder = 0.02 m

Length of the cylinder = 0.05 m

Inlet velocity = 10 m/s

Density of air = 1.1845 kg/`m^3`

Dynamic viscosity of air `= 1.844 ×10^(-5) Pa.s`

`Re=(ρuD)/μ=12844.28`

Now the Reynolds Number is increased by a factor of 20%, 40%, and 100% and with that velocities are calculated

• At 20% increment Re = 15413.13 ; u = 12 m/s
• At 40% increment Re = 17981.99 ; u = 14 m/s
• At 100% increment Re = 25688.56 ; u = 20 m/s

Now simulation end time is calculated

Flow-through Time (FT) = Domain Length/Velocity ; End time = 2 * FT

Domain Length = 0.18 m

• For Re = 15413.13:- u = 12 m/s ; End time = 0.03 s
• For Re = 17981.99:- u = 14 m/s ; End time = 0.02571 s
• For Re = 25688.56:- u = 20 m/s ; End time = 0.018 s

PROCEDURE:

• Create a 3D model of a cylinder.

• Now start with the flow simulation and then click on “Wizard”, start with a new project for external flow. Select the time dependency and enter then end time according to the respective velocities as calculated above.

• Now create a finer mesh for better results.

• Now insert cut plots one for pressure and another for velocity.
• Run the Flow simulation.

RESULTS:

FOR BASELINE - VELOCITY = 10 m/s

Animation - Velocity Distribution Animation - Pressure Distribution

FOR 20% INCREASE IN REYNOLDS NUMBER - VELOCITY = 12 m/s

Animation - Velocity Distribution Animation - Pressure Distribution

FOR 40% INCREASE IN REYNOLDS NUMBER - VELOCITY = 14 m/s

Animation - Velocity Distribution Animation - Pressure Distribution

FOR 100% INCREASE IN REYNOLDS NUMBER - VELOCITY =20 m/s

Animation - Velocity Distribution Animation - Pressure Distribution

CONCLUSION:

• We can see by comparing all the pressure distributions that the range of values is quite close to each other. But the distribution area increases in front of the cylinder as the velocity increases. The maximum pressure is experienced by the cylinder at the center and its value is 101.45 kPa. From the animation it can also be seen that the distribution area of low pressure range decreases as the velocity increases. The reason behind it is that a boundary layer is generated adjacent to the surface of the cylinder, due to this boundary layer separation will occur, and a trailing wake will exist in the flow behind the cylinder. The pressure at each point on the wake side of the cylinder will be lower than on the upstream side, resulting in a drag force in the downstream direction.
• We can see by comparing all the velocity distributions that the range of values are quite close to each other and by seeing the animation the distribution area is also same in all the cases except the baseline case. As the air gets close to the cylinder its velocity begins to slow down. The fluid elements on the surface of the upstream side of the cylinder is stopped, this is called a stagnation point. Fluid elements passing either above or below the cylinder have high velocity magnitude. In the downstream region a broad wake is formed and being unstable it rolls up into vortices and are shed at regular interval.