Flow Simulation Through A Pipe

FLOW SIMULATION THROUGH A PIPE

AIM – Run a pipe flow simulation with an inlet Reynolds number of 100, 1000 and 10,000.

OBJECTIVES-

1. Create 3D model of pipe.
2. Run flow simulation with an inlet Reynolds number of 100, 1000 and 10,000.
3. Place line probes at 95%, 90% and 85% of the pipe length.
4. Compare the normalized velocity profile at each of these locations.

INTRODUCTION-

Flow through a pipe, a branch of fluid mechanics, is a type of liquid flow within a closed conduit. Pipe flow does not have a free surface. The behaviour of pipe flow is governed mainly by the effects of viscosity and gravity relative to the inertial forces of the flow. Depending on the effect of viscosity relative to inertia, as represented by the Reynolds number, the flow can be either laminar or turbulent.

With respect to laminar and turbulent 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 Re = ρ u D / μ = u D / ν

• ρ is the density of the fluid
• u is the flow speed
• D is the diameter of the tube
• μ is the dynamic viscosity of the fluid
• ν is the kinematic viscosity of the fluid.

A region where these forces change behaviour is known as a boundary layer. Here flow changes from laminar to turbulent.

CALCULATIONS:

Let diameter of pipe = 0.05 m

Our working fluid is taken to be water. Following table gives variation of viscosity of water with temperature.

So, let us carry out our simulation at 20°C. So, Kinematic viscosity of water ν = 1.004*10^-6 m²/s.

Case 1: Reynolds Number Re = 100. Putting values in formula we get

Inlet velocity u = 0.002008 m/s

Case 2: Reynolds Number Re = 1000. Putting values in formula we get

Inlet velocity u = 0.02008 m/s

Case 3: Reynolds Number Re = 10000. Putting values in formula we get

Inlet velocity u = 0.2008 m/s

PROCEDURE-

1. Click on New > Part. Sketch a circle of diameter 0.05 m in Front plane. Exit Sketch.
2. Clink on Extrude Boss/Base and put length 1m. Now click on Shell. Select two end faces of pipe and put thickness 0.001m. So, now we get our pipe.
3. As computational internal fluid simulation is possible only water tight geometry i.e. in enclosed pipe, we need to click on lids in Flow simulation. Select cross sectional area on both ends to apply lids. Now save the part.
4. Click on New in Flow Simulation. Use SI units. Select flow type internal.
5. Now click on Initial Global mesh and disable Automatic settings. Now put

Number of cells per X = 15

Number of cells per Y = 15

Number of cells per Z = 60

6. Now Right Click on Boundary conditions > Insert boundary conditions. Select inlet face and put inlet velocity u= 0.002008 m/s for Re= 100.
7. Again inset two more boundary conditions, one put static pressure = 101325 Pa at outlet face of pipe and other select curved face of pipe as Real wall.
8. Now click on Sketch. Select top plane. Make a line segment parallel and equal to pipe diameter at distance 0.05m from outlet face. This forms line probe at 95%length. Exit sketch.
9. Similarly create two more line sketches at distance 0.1m and 0.15m from outlet face. This forms line probe at 90% and 85% length.
10. In Results select XY plot. Select Velocity comparison as Parameter and all three line probe sketches.
11. In Results select Cut plot. Drag it parallel to front plane to desired location.
12. Click on Run. Wait for all iterations to finish.
13. Now start a New Parametric study. In input parameter select inlet velocity normal to the face.
14. In Output select Cut plot and Velocity comparison plot.
15. In Scenario vary the inlet velocity as u= 0.02008 m/s for Re= 1000 and u = 0.2008 m/s for Re= 10000.
16. Click on Run and wait for solver to finish.
17. Export the result to spread sheet and normalize it through dividing by inlet velocity.

RESULTS

Case 1: Reynolds Number Re = 100. Inlet velocity u = 0.002008 m/s

To normalize velocity profile we divide all values of velocity by inlet velocity u = 0.002008 m/s

Case 2: Reynolds Number Re = 1000. Putting values in formula we get inlet velocity u = 0.02008 m/s

To normalize velocity profile we divide all values of velocity by inlet velocity u = 0.02008 m/s

Case 3: Reynolds Number Re = 10000. Putting values in formula we get inlet velocity u = 0.2008 m/s

To normalize velocity profile we divide all values of velocity by inlet velocity u = 0.2008 m/s

EXPLANATIONS & CONCLUSIONS:

1. Velocity profile at all three line probes in all three values in almost same for all three Reynolds number as flow remain steady.
2. From Hagen Poiseuille formula for laminar flow we know velocity profile should be parabolic in nature which is evident from plots in case 1 and 2.
3. As friction between the walls slows down the liquid, we have really low values at these points almost equal to zero.
4. Similarly, the velocity has to be max at centre of pipe which is shown by each plot.
5. Cut plot at three surfaces show at while velocity profile is more readable and accurate in laminar flow than turbulent flow.