Flow Through Pipe

Aim:- To perform CFD of Water flow through a pipe for different Reynolds Number and observe the Normalized Flow Rate at various location.

Theory:- Flow through a pipe is governed by various laws such as Bernoulli equation and studied using parameters such Reynolds Number, Shear Stress, Velocity Profile etc.

Flow through the pipe is classified as Laminar or Turbulent according to the Reynolds Number, re

Scenario	Type of Flow
Re < 2000	Laminar
2000 < Re < 4000	Transient
4000 < Re	Turbulent

Study Objectives: - Run Pipe Flow Simulation with Inlet Reynolds Number of 100, 1000, 10000 and study Normal Fluid Velocity, normalised by the Inlet Velocity

Sl.No	Reynolds Number
Case-1	100
Case-2	1000
Case-3	10000

Obtain the data and Compare Normalised Velocity at 85%, 90% and 95% for each Reynolds Number

Mathematical Relations and Calculations:-

1. Reynolds Number, Re for a fluid flowing through a Circular Pipe is given by
   1. `Re= (ρvD)/μ`
   2. Here ρ = Density
   3. v = Fluid Velocity
   4. D = Diameter of Pipe
   5. = Dynamic Viscosity

2. Reshaping the equation for velocity we get.
   1. `v= (Re × μ)/(ρD)`
   2. In our case Re is going to vary, and other parameter are constant
      1. Taking density and Dynamic Viscosity at 20 degree Celcius
      2. Density = 997.048 kg/m³
      3. Viscosity = 8.9x10^-4 Pa.s
      4. Diameter = 38 mm = 0.038 m
   3. `v= Re ×(8.9×10^(-4))/(997.048×0.038)`
   4. `v= 2.349×10^(-5)×Re` m/s

3. Case - 1, Re = 100 ,
   1. `v= 2.349×10^(-5)×100`m/s
   2. `v= 2.349×10^(-3)`m/s
4. Case - 2, Re = 1000 ,
   1. `v= 2.349×10^(-5)×1000` m/s
   2. `v= 2.349×10^(-2)`m/s

3. Case - 3, Re = 1000 ,
   1. `v= 2.349×10^(-5)×10000` m/s
   2. `v= 2.349×10^(-1)`m/s

The calculated parameters are tabulated as

Simulation Time		0.1 sec
Step Time (Step s)		0.01 sec (10)
Pipe	Outer Dia	40 mm = 0.04 m
	Internal Dia	38 mm = 0.038 m
	Length (L)	1 m
	85% L	850 mm
	90% L	900 mm
	95% L	950 mm
Parameters	Case 1	Case 2	Case 3
Reynolds Number (Re), at Inlet	100	1000	10000
Inlet Velocity (m/s)	2.349 E-3	2.349 E-2	2.349 E-3

Study: -

A cylindrical pipe of 40 mm Outer diameter and 1 mm thickness is made, that is internal dia =38mm. For performing the CFD in Solidworks, Lids are provided at both the open ends of 1mm thick so as to avoid an error and get more accurate results

Boundary Conditions

1. Inlet Velocity – Inlet Velocity for three cases is governed by the Reynolds Number (Re)
2. Exit Pressure – Static Pressure of 101325 Pa = 1 atm
3. Real Wall – Internal wall, where water (fluid under consideration) interact with pipe is specified as the real wall.

Mesh Size

1. Circular Cross-Section
   1. X-Axis = 20 Nos.
   2. Y-Axis = 20 Nos.
2. Axial Direction, Z-Axis = 50 Nos.

Methodology:-

1. For different cases, I have performed a PARAMETRIC STUDY where the inlet velocity parameter is varied
2. The results are plotted at 85%, 90% and 95% respectively.
3. This results are exported to Excel to so as to Normalise the velocity with respect to the Inlet Velocity and plot it against the diametrical length

Results:-

Case 1 – Re = 100

In this case, the inlet velocity of the tube is set to 0.002349 m/s as calculated earlier and results are obtained at 850 mm, 900 mm, 950 mm respectively. First independent plots are made and then their combine plot is plotted.

Observation – The Reynolds Number is 100, that is a Laminar Regime enters into the pipe. Also the data points are very close to the exit, where the flow is fully developed. Therefore much deviation isn’t observed in the Actual and Normalised Velocity.

Case 2 – Re = 1000

In this case, the inlet velocity of the tube is set to 0.02349 m/s as calculated. The independent and combined plots are shown below.

Observation – Here the Reynolds Number is 1000, some-what close to Transient Range, but still in the Laminar Regime. Reynolds Number corresponding to the fluid velocity at the centre ranges in the Transient Zone. Therefore we can see a significant deviation in velocity in the plot.

Case 3 – Re = 10000

In the third case, the inlet velocity of the tube is set to 0.2349 m/s as calculated for the given pipe and Reynolds number. The independent and combined plots are shown below.

Observation – Since the Re for this case was set well above the transient range and in Turbulent Zone, we can observe the steep variation in fluid velocity from the pipe wall. Also, the velocity at the centre shows high turbulent nature and thus the parabolic profile is absent in this case.

Conclusion - It can be seen that the flow through pipe gets turbulent and deviate from parabolic velocity profile as the Reynolds number increases from Laminar to Transient and Turbulent Regime

Link to Study Result File - Aishwary Mahajan - Gdrive Flow Through Pipe