PIPE FLOW SIMULATION

AIM

To run a pipe flow simulation with an inlet Reynolds number of 100,1000 and 10,000.

THEORY

Pipe flow is a type of fluid flow within a closed conduit. Pipe flow, being confined within closed conduit, exert a hydraulic pressure on the wall of pipe. The flow is always a full flow condition where there is no free surface available. Energy in pipe flow is expressed as head and is defined by the Bernoulli equation. The pipe flow is effected by the parameters like viscosity and gravity etc. Reynolds number, which is the dimensionless number represents the flow can be either laminar or turbulent. when Reynolds number less than 2040, then pipe flow will ultimately be laminar, whereas above the critical value turbulent flow can persist. In addition, the transition between laminar flow and turbulence can be sensitive to disturbance levels and imperfections.

BASIC REYNOLDS NUMBER EQUATION

where

• ρ is the density of the fluid ( kg/m³)
• u is the velocity of the fluid with respect to the object (m/s)
• L is a characteristic linear dimension (m)
• μ is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/m·s)
• ν is the kinematic viscosity of the fluid (m²/s).

OBJECTIVE

Run a pipe flow simulation with an inlet Reynolds number of 100,1000 and 10,000.

For each of these cases do the following

1. Place line probes at 95%, 90% and 85% of the pipe length.

2. Compare the normalized velocity profile at each of these locations

3. Normalize the velocity profile by the inlet velocity.

PREREQUISITE DIMENSIONS

• Radius of the pipe = 40 mm
• Length = 500 mm
• Thickness = 1 mm
• Flow Medium: WATER
• Density of water = 1000 kg/m^3
• Dinematic Viscosity of water = 8.9 x 10^-4 Pa.s (@25 degree celcius)
  

BOUNDARY CONDITIONS

INLET CONDITION

The inlet velocities are calculated based on Reynolds number as shown below

Reynolds Number	Inlet Velocity m/s
100	.002225
1000	.02225
10000	.2225

Outlet condition

Static Pressure: 101325 Pa

Temperature: 293.2K

The wall is assumed REAL

Post Processing Data Plots after running the simulation

1. XY PLOT COMPARISION OF DIFFERENT REYNOLDS NUMBER AT DIFFERENT LINE PROBES

Design point 1 indicates Reynolds number 100

Design point 2 indicates Reynolds number 1000

Design point 3 indicates Reynolds number 1000

The below graph is calculated at 95% of length of pipe @25mm from exit

The below graph is calculated at 90% of length of pipe @50mm from exit

The below graph is calculated at 85% of length of pipe @75mm from exit

CONCLUSION FROM PLOTS (RE Reynolds number)

• Higher the Reynolds number higher will be the velocity, from the above plots green line indicates RE=10000 where the inlet velocity is .2225 units. simillarly it decreases in blue and red lin as RE decreases.
• When we compare the velocities at different line probes at particular reynolds number, the velocity decreases with increase in length as the velocity gradient is decreasing i.e (du/dy) due to boundary layer formation. Hence, the same thing goes for different Reynolds number

2. CUT PLOT COMPARISION OF DIFFERENT REYNOLDS NUMBER AT DIFFERENT LINE PROBES

CASE 1

The below contours is simulated at 95% of length of pipe @25mm from exit

RE=100

RE=1000

RE=10000

CASE 2

The below contours is simulated at 90% of length of pipe @50mm from exit

RE=100

RE=1000

RE=10000

CASE 3

The below contours is simulated at 85% of length of pipe @5mm from exit

RE=100

RE=1000

RE=10000

Conclusion

• It can be concluded that for the Reynold's Number 10,000, the flow is turbulent
• the boundary layer thickness is less compared to laminar flow @RE=100 & 1000.
• The flow reaches closer to the outlet it is seen that the velocity profile is negligbly varying.
• All the variations in velocity is happening due to boundary layer formtion as it starts from the boundary with no slop condition