Pipe flow simulation for different Reynolds number (Re- 100, 1000, 1000) and calculating & comparing the normalized velocity at each Reynolds number

AIM- Pipe flow simulation with an inlet Reynolds number of 100,1000 and 10,000.

OBJECTIVES-

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.

REYNOLDS NUMBER- The Reynolds number is the ratio of interial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities. A region where these forces change behavior is known as a boundary layer, such as the bounding surface in the interior of a pipe. A similar effect is created by the introduction of a stream of high-velocity fluid into a low-velocity fluid, such as the hot gases emitted from a flame in air. This relative movement generates fluid friction, which is a factor in developing turbulent flow. Counteracting this effect is the viscosity of the fluid, which tends to inhibit turbulence. The Reynolds number quantifies the relative importance of these two types of forces for given flow conditions, and is a guide to when turbulent flow will occur in a particular situation.

With respect to laminar and turbuent flow regimes:

• laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion;
• turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow instabilities.

The Reynolds number is defined as-

where:

• ρ is the density of the fluid (SI units: kg/m³)
• u is the flow speed (m/s)
• D is the diameter of the tube (m)
• μ is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/(m·s))
• ν is the kinematic viscosity of the fluid (m²/s).

CASE 1 - PIPE FLOW SIMULATION WHEN REYNOLDS NUMBER IS 100.

Above picture gives the data about the velocity and total length of the pipe. Futher, at 85%, 90%, 95% we have calculated the values of the line probes where we have to find the velocities.

For the case 1 i.e., Re- 100 . the outer diameter of pipe is 80mm and inner diameter of pipe is 78mm. The velocity at inlet is 0.00114 (m/s^2). The total length of pipe is 0.468 (m).

At 85% the length of line probe is 0.397 (m).

At 90% the length of line probe is 0.421 (m).

At 95% the length of line probe is 0.444 (m).

Normalised velocity at 0.397(m)

Above is the normalised velocity graph for the line probe at 85% at the length of 0.397m .

Normalised velocity at 0.421(m)

Above is the normalised velocity graph for the line probe at 90% at the length of 0.421m .

Normalised velocity at 0.444(m)

Above is the normalised velocity graph for the line probe at 95% at the length of 0.444m .

Cut section at the inlet velocity of the pipe.

Above is the cut section diagram of inlet velocity i.e., 0.00114m/s^2 at inlet flow of pipe.

Final statment for case 1 - After plotting the velocity at each line probe we see the parabolic nature and comparing the graphs they are almost the same.

CASE 2 - PIPE FLOW SIMULATION WHEN REYNOLDS NUMBER IS 1000.

Above picture gives the data about the velocity and total length of the pipe. Futher, at 85%, 90%, 95% we have calculated the values of the line probes where we have to find the velocities.

For the case 2 i.e., Re- 1000 . the outer diameter of pipe is 80mm and inner diameter of pipe is 78mm. The velocity at inlet is 0.0114 (m/s^2). The total length of pipe is 4.68 (m).

At 85% the length of line probe is 3.97 (m).

At 90% the length of line probe is 4.21 (m).

At 95% the length of line probe is 4.44 (m).

Modal section of the pipe at 3.97m.

Above figure show the dimension of the first line probe at 3970mm.

Cut section velocity at 3.970m.

Above figure is the cut section velocity at first line probe i.e., 3970mm. The contours of velocity and mesh is seen in the cut plot and the maximum velocity is at the center and the minimu velocity at the edges. The maximum velocity is at 0.021[m/s] and minimum is 0.002[m/s].

Above is the figure of normalised veocity at 3.970m.

Modal section of the pipe at 4.21 [m].

Above figure show the dimension of the second line probe at 4.210m.

Cut section velocity at 4.210m.

Above figure is the cut section velocity at second line probe i.e., 4.210m. The contours of velocity and mesh is seen in the cut plot and the maximum velocity is at the center and the minimu velocity at the edges. The maximum velocity is at 0.023[m/s] and minimum is 0.001[m/s].

Above is the figure of normalised veocity at 4.210m.

Modal section of the pipe at 4.44 [m].

Above figure show the dimension of the third line probe at 4.440m.

Cut section velocity at 4.440m.

Above figure is the cut section velocity at third line probe i.e., 4.440m. The contours of velocity and mesh is seen in the cut plot and the maximum velocity is at the center and the minimum velocity at the edges. The maximum velocity is at 0.016[m/s] and minimum is 0.001[m/s].

Above is the figure of normalised veocity at 4.440m.

Final statment for case 2 - After plotting the velocity at each line probe we see the parabolic nature and comparing the graphs they are almost the same.

CASE 3 - PIPE FLOW SIMULATION WHEN REYNOLDS NUMBER IS 10000.

Above picture gives the data about the velocity and total length of the pipe. Futher, at 85%, 90%, 95% we have calculated the values of the line probes where we have to find the velocities.

For the case 3 i.e., Re- 10000 . the outer diameter of pipe is 80mm and inner diameter of pipe is 78mm. The velocity at inlet is 0.114 (m/s^2). The total length of pipe is 46.8 (m).

At 85% the length of line probe is 39.78 (m).

At 90% the length of line probe is 42.12 (m).

At 95% the length of line probe is 44.4 (m).

Modal section of the pipe at 39.78m.

Cut section velocity at 39.78m

Above figure is the cut section velocity at first line probe i.e., 39.78m. The contours of velocity and mesh is seen in the cut plot and the maximum velocity is at the center and the minimum velocity at the edges. The maximum velocity is at 0.168[m/s] and minimum is 0.034[m/s].

Above is the figure of normalised veocity at 39.78m.

Modal section at 42.12m

Cut section velocity at 42.12m

Above figure is the cut section velocity at seond line probe i.e., 42.12m. The contours of velocity and mesh is seen in the cut plot and the maximum velocity is at the center and the minimum velocity at the edges. The maximum velocity is at 0.202[m/s] and minimum is 0.034[m/s].

Above is the figure of normalised veocity at 42.12m.

Modal section of pipe at line probe 44.4m

Cut section velocity at third line probe i.e., 44.4m

Above figure is the cut section velocity at third line probe i.e., 44.4m. The contours of velocity and mesh is seen in the cut plot and the maximum velocity is at the center and the minimum velocity at the edges. The maximum velocity is at 0.222[m/s] and minimum is 0.034[m/s].

Above is the figure of normalised veocity at 44.4m.

Final statement at case 3- After plotting the velocity at each line probe we see the parabolic nature and comparing the graphs they are almost the same.