Flow over a cylinder

AIM

To study the external transient flow simulation over a pipe by running a baseline study and then using the cases of varying Reynolds Number.

THEORY

The Reynolds Number helps predict flow patterns in different fluid flow situations. At low Reynolds numbers, the flow tends to be dominated by laminar flow, while at high Reynolds numbers flow tend to be turbulent. Reynolds numbers are an important dimensionless quantity in fluid mechanics. The Reynolds number has wide applications, which are ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is used to predict the transition from laminar to turbulent flow and is used in scaling of similar but different sized flow situations, such as between an aircraft model in a wind tunnel and the full-size version.

The Reynolds number is the ratio od the inertial forces to viscous forces within a fluid which is subjected to relative movement due to different fluid velocities.

The flow of a fluid is transient or unsteady if its flow parameters (ie. velocity and [resssure ) are dependent not only on the position in the coordinate system used to describe the field of flow but also on time. A distinction is made between three different types of transient flow phenomena,

• Stochastically irregular phenomena eg. turbulent fluctuations
• Run-up or Run-down phenomena eg. when starting or stopping a centrifugal pump
• Periodic phenomena eg. pulsations caused by surge pumps etc.

`Reynolds Number. = ("Inertial force")/("Viscous force")`

`Re = (rho * v * d)/(mu)`

Assumptions:

1. The surface of the cylinder is smooth and roughness is considered zero
2. Effect of temperature is not considered in the study

PROCEDURE

1. Create a part file and draw a geometry of a pipe of the desired length and diameter
2. set the parameters required to set up the flow simulation study.
3. working fluid is taken as air.
4. temperature changes are neglected and pipe walls are taken as smooth
5. Transient flow and external flow is enabled and selected
6. The initial value of velocity in the x-direction for baseline study is given
7. Cut plots for pressure and velocity is retrieve4d for study after the simulation run is complete
8. Animation for pressure and velocity is obtained
9. The above steps are repeated for various other cases of Reynolds number obtained as per the problem statement.

CALCULATION & RESULT

Cylinder diameter = 0.04 m

Cylinder length = 0.10 m

Fluid= Air

Dynamic viscosity = 1.825 X 10^-5 N.S/`m^2`

Density = 1.225 kg/`m^3`

Case 1 : Baseline Simulation

The velocity of the fluid flow in x-direction is taken as 10 m/s

`Re = (rho * v * d)/(mu)`

Re = (1.225 x 10 x 0.04)/(1.825 x 10^-5)

Re = 26385.224

pressure plot:

Velocity plot:

Animation of pressure distribution :

Animation of velocity distribution:

CASE 2 : Reynolds number increased by a factor of 20%

After increasing the reynolds number by a factor of 20% the new obtained reynolds number is

Re = 31622.268

`Re = (rho * v * d)/(mu)`

31622.268 = (1.225 x v x 0.04)/(1.825 x 10^-5)

v = 11.99 m/s

the velocity obtained is used to simulate the new study.

Pressure plot :

Velocity plot:

Animation of pressure distribution:

Animation of velocity distribution:

Case 3: Reynolds number increased by a factor of 40%

After increasing the Reynolds number by a factor of 40% the new obtained Reynolds number is

Re = 36939.313

`Re = (rho * v * d)/(mu)`

36939.313 = (1.225 x v x 0.04)/(1.825 x 10^-5)

v = 14.01 m/s

the velocity obtained is used to simulate the new study.

Pressure plot:

Velocity plot:

Animation of pressure distribution:

Animation of velocity distribution:

Case 4: Reynolds number increased by a factor of 100%

After increasing the Reynolds number by a factor of 100% the new obtained Reynolds number is

Re = 52770.448

`Re = (rho * v * d)/(mu)`

52770.448 = (1.225 x v x 0.04)/(1.825 x 10^-5)

v = 20.02 m/s

the velocity obtained is used to simulate the new study.

Pressure plot:

Velocity plot:

Animation of pressure distribution:

Animation of velocity distribution:

CONCLUSION:

• With the increase in Reynolds number the velocity increases, thus the flow over the cylinder also increases.
• There isn't much of a change in pressure with varying Reynolds number ie. no large extent of changes are observed.
• The high pressures are usually at the inlet face of the pipe usually because of the obstruction to the flow encountered and it starts reaching a minimum on the opposite side of the pipe.
• The velocity variations observed from the above plots are found to be maximum near the surface of the cylinder and it's minimum at the other end where there is no contact with the surface ie. almost zero or zero at such areas.
• As we move away from the cylinder and the flow gradually develops out further and the velocity and pressure distribution starts getting constant.