FLUID DYNAMICS STUDY OF THE CHANNEL FLOW THROUGH A CYLINDRICAL PIPE.

Theory:- When predicting or regulating the flow, F, of a gas in a system, it is important to know the relationship among flow, pressure, and dimensions of tubing. For a cylindrical, horizontal pipe (or tube or capillary) the flow, up to some critical velocity, will be "Laminar" and follow certain laws. In Laminar flow, the fluid moves in parallel layers, each with a constant velocity, but with a velocity relative to its neighbors.

The critical Renold's number for a pipe is about 2300; above this value, the flow becomes turbulent and much less predictable. For a steady laminar flow in a horizontal cylinder, the fluid velocity will describe a parabola along the tube diameter.

Laminar Re ≤ 2300 < Re Turbulent.

Goal:-

The primary goal of this study of the pipe flow is to define the fluid dynamic behavior of a fluid through a cylindrical pipe which is made by design software and analyze according to variable Reynolds Numbers at a different temperature variation.

OBJECTIVE ---

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

The objective case studies are--

• Compare the normalized velocity profile at the locations of line probes at 95%, 90% and 85% of the pipe length.
• Normalize the velocity profile by the inlet velocity.

Fluid Medium -

water

Mathematical Variables-

Reynolds Number (Re),

viscosity (μ)

density(ρ)

characteristic length (l)

velocity (V)

Units -

Dynamic viscosity (μ) - (μ) N-s/m^2 * depend on temperature

density(ρ) - 997 kilogram/meter^3

characteristic length (l) - 0.2 meter

velocity (V) - (v1/v2/v3) meter/sec

Reynolds Number (Re) - (100/1000/10000) unit.

Conditional Parameters -

Dynamic Viscosity (μ)

°C - 10 20

(μ) = 0.0013060 0.0010016

°F - 50 68

Formula -

V = Re*ρ*l / μ ;

According to Reynolds number the value of inlet velocity will change,

Case 1 - Re- 100, V1- 0.00050230692

Case 2 - Re- 1000, V2- 0.0050230692

Case 3 - Re- 10000, V3- 0.050230692

Case 1 - Re- 100.

V1- 0.00050230692 m/s.

The location of the pipe is 85% of the total length.

The location of the pipe is 90% of the total length.

The location of the pipe is 95% of the total length

The location of the flow velocity is near the pipe inlet

Conclusion - as the Reynolds number is very low, of about 100. the flow regime is laminar throughout the pipe at different locations (85%,90%,95%).

Case 2 - Re- 1000

V2- 0.0050230692 m/s.

The location of the pipe is 85% of the total length.

The location of the pipe is 90% of the total length.

The location of the pipe is 95% of the total length.

.

The location of the pipe is at the inlet of the total length.

The velocity differences of the pipe of the total length according to location.

Case 2 - Re- 10000.

V2- 0.050230692 m/s.

The location of the pipe is 80% of the total length

The location of the pipe is 90% of the total length

The location of the pipe is 95% of the total length

The location of the pipe is at the inlet of the total length.

The velocity differences of the pipe of the total length according to location.

General Study -

Conclusion -

Re - 100;

At lower Reynolds number the flow is steady and predictable. The curve of the flow regime is the same for all design point of 85%, 90%, and 95%. the flow will be laminar all over the pipe. But from the general study of the pipe flow shows that the center of the pipe flow inlet where velocity is maximum and became laminar all over the pipe. The LAMINAR flow results in a parabolic velocity profile all over the pipe.

Re - 1000;

Due to change of Reynolds number the flow velocity increases by the factor of 10. But the flow regime is the same for all design point of 85%, 90%, and 95%. the flow will be laminar all over the pipe. But from the general study of the pipe flow shows that the center of the pipe flow inlet where velocity is maximum and became laminar all over the pipe. The LAMINAR flow results in a parabolic velocity profile all over the pipe.

Re - 10000;

Because of high Reynold's number, the turbulent flow became unsteady and irregular. the flow will fluctuate continually. But the flow regime will vary from inlet to outlet. For all design point of 85%, 90%, and 95% flow became less parabolic compare to other Reynolds numbers experiments. Near the entrance of the pipe there is an irregular laminar-turbulent interface, Further downstream the wake became cone-shaped and less active with a fuzzy ill-defined interface called Relaminarization. due to which the velocity flow profile became parabolic.

As because all the design points are near to each other the flows are almost equal in nature at those points.