FLOW SIMULATION FOR DIFFERENT VALUES OF INLET REYNOLD'S NUMBERS IN A CYLINDRICAL PIPE (using SOLIDWORKS)

AIM:

To design a cylindrical pipe and perform a flow simulation for different values of inlet Reynold's numbers using SOLIDWORKS

OBJECTIVES:

1. To place line probes at `95%`, `90%` and `85%` of the pipe length
2. To compare the normalized velocity profile at each of these locations
3. To normalize the profile by the inlet velocity

INTRODUCTION:

The Reynolds number is the ratio of inertial forces to viscous forces. The Reynolds number is a dimensionless number used to categorize the fluids systems in which the effect of viscosity is important in controlling the velocities or the flow pattern of a fluid.

Mathematically, Reynold's number can be defined as:

`N_(Re) = (rhovd)/mu = (vd)/nu`

where `rho = `fluid density

`v = `average velocity of the fluid

`d = `internal diameter of the pipe

`mu =`absolute viscosity of the fluid

` nu = mu/rho = `kinematic viscosity

Flow-through pipes are classifies into following three regimes:

1. `N_(Re) < 2000` (Laminar flow)
2. `2000 < N_(Re) < 4000` (Critical flow)
3. `N_(Re) > 4000` (Turbulent flow)

Calculations:

Given, the external diameter of the pipe = `0.05m`

the length of the pipe = `1m`

the internal diameter of the pipe = `0.048m`

density of the fluid (here, water) = `1000 (kg)/m^3`

absolute viscosity of water = `8.9 X 10^(-4) Pa*s`

• For `N_(Re) = 100`

`v = (N_(Re)*mu)/(rho*d) = 0.001854 m/s`

• Similarly, for `N_(Re) = 1000` and `N_(Re) = 10000`

`v = 0.01854 m/s` and `v = 0.1854 m/s` respectively.

PROCEDURE OF COMPLETION:

1. First, a cylindrical pipe of `0.05m` diameter and `1m` length was created. Then, a shell was made of thickness `0.002m` in the inside of the pipe.
2. Now, spearate sketches were made for different line probes at `95%`, `90%` and `85%` of the pipe length.
3. Then, under flow simulation, the inlet velocities alongwith the boundary conditions and the mesh size (along x 10; along y, 10 and along z, 78) were given. Also, the plots were also derived.
4. Then, after running the simulation for one `N_(Re)`, a new parametric study was created and the flow simulation for other subsequent `N_(Re)`s were made.

The line probes are as follows:

The parametric study is as follows:

OBSERVATIONS:

• For `N_(Re) = 100`,

At `85%` of the pipe length, the cut plot is as follows:

At `90%` of the pipe length, the cut plot is as follows:

At `95%`of the pipe length, the cut plot is as follows:

• For `N_(Re) = 1000`,

At `85%` of the pipe length:

At `90%` of the pipe length:

At `95%` of the pipe length:

• For `N_(Re) = 10000`,

At `85%` of the pipe length:

At `90%` of the pipe length:

At `95%` of the pipe length:

Now, comparing the velocities at different `N_(Re)` and at different line probes,

At `85%` of pipe length,

At `90%` of pipe length,

At `95%` of pipe length,

Now, comparing all the normalized velocity profiles:

Keywords:

• Sketch4 corresponds to `85%` of pipe length
• Sketch3 corresponds to `90%` of pipe length
• Sketch2 corresponds to `95%` of pipe length

CONCLUSION:

1. As expected, all the cut plots at their respective `N_(Re)`s show that the velocity is fairly constant through those cross-sections.
2. The individual velocity profile plots show that the velocity across the cross sections are minimum when `N_(Re) = 100` and max at `10000`.
3. While comparing the normalized velocity profiles, the max. is at `N_(Re) = 10000` and at `95%` of the pipe length.
4. This fairly proves that more the inlet velocity, at static outlet pressure, the velocity at different cross-sections will also be higher.