FLOW SIMULATION THROUGH PIPE FOR DIFFERENT REYNOLDS NUMBER

OBJECTIVE:

To 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.

INPUTS:

Diameter of pipe : 18mm

Length of pipe : 200mm

Air density :1.2407(`kg/m^3`)

Dynamic viscosity of air (at 20 degree celcius & 1 atm pressure)`1.825*10^(-5) (N-s/m^2)`

Reynolds Number

The Reynolds number is important in analyzing any type of flow when there is substantial velocity gradient (i.e. shear.) It indicates the relative significance of the viscous effect compared to the inertia effect. The Reynolds number is proportional to inertial force divided by viscous force.

The flow is

• laminar when Re < 2300
• transient when 2300 < Re < 4000
• turbulent when 4000 < Re

Calculation of inlet velocity

Reynolds number = (rho x Velocity x D)/Dynamic visosity

By applying the above inputs and formula for reynolds number, (Ra=100,1000 & 10000)

We get,

Velocity for (Re = 100) = 0.0842 m/s

Velocity for (Re = 1000) = 0.8416 m/s

Velocity for (Re = 10000) = 8.4161 m/s

MATLAB PROGRAM TO FIND INPUT VELOCITY

%TO FIND INPUT VELOCITY FOR GIVEN REYNOLDS NUMBERS
 clear all
 close all
 clc
 
 %reynolds number formula is given by
 % re = (rho*v*d*)/mu;
 
re = [100,1000,10000]; %different reynolds number given in the question
rho = 1.2047;          %density of air in (kg/m3)
d =  0.018;            %diameter of pipe in (m)     
mu = 1.825*10^(-5);    %dynamic viscosity (N-S/m2)
v = (re*mu)/(rho*d);   %Formula to find input velocity (m/s)

THE OUTPUT OF THE PROGRAM

PROCEDURE

1. Create new part model.
2. Make circle of 18mm dia and extrude it to 200 mm.
3. Select shell, then select both face side of the cylinder and 1mm as thickness.
4. Create new sketch along length of the pipe & create a vertical line at 85% of the length and similarly for 90% ard 95% of the length.
5. Go to Flow Simulatlon, select create lid command & select end faces of the pipe.
6. Click on new in flow simulation toolbar. Right click on input data on flow simulation tree, and select general setting.
7. In Fluids, select air in gas, flow type as Laminar for first two cases and turbulent for third case and in initial conditions, temperature as 293.2 K, pressure as 101325 Pa and velocity as 0m/s.
8. Right click on boundary conditions and select insert boundary conditions. The boundary condition for inflow is the three inlet velocity at three different cases on inlet of the pipe. The boundary conditicn for wall is real wall and select inner wall of the pipe.
9. The first boundary condition for out-flow, select static pressure of 101325 Pa
10. Right click on Gloal Mesh and select edit definitions, change mesh manually, in X-direction 10, Y-direction 10, in Z-direction 50.
11. Right click on XY plot for velocity in normal to the plane direction (Z-direction) and select insert then select the 85% line sketch. Similarly, make XY plot tor 90% and 95% and similarly right click on cut plot for velocity in XY plane at distances of 85% 90% & 95% of length

outputs:

Case 1: Re = 100

1) At 85% of length

A) Cutplot at 85% of length

DESIGN POINT 1

DESIGN POINT 2

DESIGN POINT 3

2) At 90% of length

B) Cutplot at 90% of length

DESIGN POINT 1

DESIGN POINT 2

DESIGN POINT 3

3) At 95% of length

C) Cutplot at 95% of length

DESIGN POINT 1

DESIGN POINT 2

DESIGN POINT 3

CASE 2 : RE = 1000

1) At 85% of length

A) Cutplot at 85% of length

DESIGN POINT 1

DESIGN POINT 2

DESIGN POINT 3

2) At 90% of length

B) Cutplot at 90% of length

DESIGN POINT 1

DESIGN POINT 2

DESIGN POINT 3

3) At 95% of length

C) Cutplot at 95% of length

DESIGN POINT 1

DESIGN POINT 2

DESIGN POINT 3

CASE 2 : RE = 10000

1) At 85% of length

A) Cutplot at 85% of length

DESIGN POINT 1

DESIGN POINT 2

DESIGN POINT 3

CASE 2 : RE = 10000

2) At 90% of length

B) Cutplot at 90% of length

DESIGN POINT 1

DESIGN POINT 2

DESIGN POINT 3

CASE 2 : RE = 10000

2) At 95% of length

B) Cutplot at 95% of length

DESIGN POINT 1

DESIGN POINT 2

DESIGN POINT 3

Comparison of velocity in XY plot at 90% of length of design point 3 with Re = 100/1000/10000

Comparison of velocity in XY plot at 90% of length of design point 3 with Re = 100/1000/10000

Comparison of velocity in XY plot at 95% of length of design point 3 with Re = 100/1000/10000

Result- As from the above we can say that the area under the curve of Re=10000 (turbulent) is maximum in all cases. And we conclude that the area increases if velocity increases. So,Reynolds number increases as turbulence increases.