Flow simulation in a pipe

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.

Assumptions:

a) The pipe dimensions are assumed to be as follows:

1. Internal diameter- 36mm
2. External diameter-40mm
3. Shell Thickness-2mm
4. Pipe length-600mm
5. It is assumed that pipe for simulation is PVC and is smooth having no roughness.

b) The pipe is having static pressure of 101325 pascal.

c) The fluid flowing in pipe is water whose dynamic viscosity is 1.002 centipoise or 10^-3 ns/m2 at 293 k and whose density is 1000 kg/m3

Calculations:

Formula: Re=((ρuL)/μ)

where ρ=water density

u=inlet velocity

L=internal diameter

μ=dynamic viscosity

• Calculation of inlet velocity for flow having 100 reynolds number

100= 1000*u*(36*10^-3)/( 10^-3)

u= 0.0027777 m/s

• Calculation of inlet velocity for flow having 1000 reynolds number

1000= 1000*u*(36*10^-3)/( 10^-3)

u= 0.027777 m/s

• Calculation of inlet velocity for flow having 10000 reynolds number

10000= 1000*u*(36*10^-3)/( 10^-3)

u= 0.27777 m/s

Procedure:

A pipe of relevant size is created and flow simulation is carried out on the model. Following boundary conditions are applied

1) Calculated inlet velocity is given to pipe inlet face-lid.

2) Static pressure is given on pipe outlet face-lid

3) Wall is considered real.

A parametric study is carried to compare results and effect of velocity on pipe and various results was plotted. A animation is also carried out to see velocity profile at 100 Reynolds no.

Results:

For re=100,

Fig.1 Velocity profile at 95% of length

Fig.2 Velocity profile at 90% of length

Fig.3 Velocity profile at 85% of length

For re=1000,

Fig.4 Velocity profile at 95% of length

Fig.5 Velocity profile at 90% of length

Fig.6 Velocity profile at 85% of length

For re=10000,

Fig.7 Velocity profile at 95% of length

Fig.8 Velocity profile at 90% of length

Fig.9 Velocity profile at 85% of length

Graphs:

Velocity comparison at different pipe location & Reynolds number

Velocity at 85%

Velocity at 90%

Velocity at 95%

Normalized velocity profile by the inlet velocity at re100

Normalized velocity profile by the inlet velocity at re1000

Normalized velocity profile by the inlet velocity at re10000

Velocity profile of re100 (zoomed view)

Animations:

1)Velocity profile with axial cutplot.

https://www.youtube.com/watch?v=f2sOcn5IDMY

2)velocity profile with vertical cutplot.

https://www.youtube.com/watch?v=W1dyVpJW-EE

Conclusion:

1) High reynolds number gives high inlet velocity if other parameters are constant.

2) For re 100 velocity profile is parabolic in shape and it reaches maximum velocity at centre of circular cross section of pipe. It has a maximum speed is 0.005 m/s which is low. This result is valid for laminar flow.

3) For re 1000 velocity profile is parabolic in shape and it reaches maximum velocity at centre of circular cross section of pipe. It has a maximum speed is 0.04 m/s. This result is valid for laminar flow.

4) For re 10000 velocity profile remains saturated/ constant for certain distance along diameter. The shape of velocity is trapezoidal. It has a maximum speed is 0.29 m/s.And this result is valid for turbulent flow.

5) Velocity profile comparison at 85% , 90% and 95% of length yields almost same result for re100 which is laminar flow.

6) Velocity profile comparison at 85% , 90% and 95% of length show there is a slight increase in maximum velocity with increase in reynolds number.

7) Velocity profile along length and diameter can be seen using animation video uploaded.