Pipe Flow Simulation

OBJECTIVE:

To model and run a pipe flow simulation with an inlet Reynolds number of 100, 1000 and 10000. For each of these cases:
1. Compare the normalized velocity profiles at 85%, 90% and 95% of the pipe length.
2. Normalize the velocity profile by the inlet velocity.

SOLUTION:

The flow through pipes or pipe flow, is the branch of fluid mechanics in which the fluid flows inside a closed conduit.

The flow is controlled by:
a) Pressure gradient
b) Pipe diameter/Hydraulic mean diameter
c) Fluid properties, like density, viscosity etc.
d) Pipe roughness

The flow through pipes can be roughly categorized into laminar and turbulent flow.

Laminar flow is one in which the flow remains smooth and there is no intermixing between adjacent layers of the flow.

In Turbulent flow, the flow is not smooth and considerable intermixing between the layers can be observed.

Reynolds number (Re) is an important dimensionless quantity used to predict the flow patterns. It is defined as the ratio of inertia force to the viscous force. Laminar flow will prevail when viscous forces are larger than inertia forces. Turbulence will begin where inertia forces begin to increase and become higher than viscous forces.

Re = Inertia force/Viscous force = ρvd/µ, where
ρ – density of fluid (kg/m3)
v – velocity of fluid (m/s)
d – diameter of pipe (m)
µ - dynamic viscosity of fluid (Ns/m2)

The problem definition is to analyse the pipe flow when Re equals 100, 1000 and 10000.

Since no specific conditions are defined in the problem, the pipe dimensions of 40mm diameter, 1000mm length and 1mm thickness were taken for the analysis. Further, water was taken as the fluid. The properties of water is; density = 997 kg/m3 and dynamic viscosity = 8.9 x 10-4 Ns/m2.

Case 1: Re = 100

Re = ρvd/µ,
100 = (997 x v x 0.04) / 8.9 x 10-4
v = 0.0022 m/s

Case 2: Re = 1000

1000 = (997 x v x 0.04) / 8.9 x 10-4
v = 0.022 m/s

Case 3: Re = 10000

10000 = (997 x v x 0.04) / 8.9 x 10-4
v = 0.22 m/s

SIMULATION:

For setting up the simulation, the first step is to create a 3D model of the pipe. The pipe model created has diameter of 40mm, length of 1000mm and thickness of 1mm.
For performing the internal flow simulation, an internal mesh needs to be generated. In Solidworks, to create an internal mesh, it is necessary to for the model to be airtight or closed. This can be done using the lid feature and selecting appropriate faces at the ends of the pipe.
Further, line probs are used to study the flow at different locations in the pipe. Line sketches were created at 85%, 90% and 95% of the pipe length.

In the next step, appropriate boundary conditions were defined for the simulation. The inlet velocities were defined at one end of the pipe. For the different cases, corresponding inlet velocities of 0.0022, 0.022 and 0.22 m/s were defined. A static pressure condition with pressure of 101325 Pa was defined at the other end of the pipe model and the wall of the pipe was defined as a real wall.

In the final step, the mesh was generated. A manual mesh was generated with the number of elements in x, y and z direction as 20, 20 and 50 respectively. After setting up all the parameters the model was solved.

RESULTS:

Comparison of normalized velocity at different pipe locations

1. At L = 850mm

2. At L = 900mm

3. At L = 950mm

Comparison of normalized velocity by inlet velocity

1. Re = 100, Velocity = 0.0022m/s

2. Re = 1000, Velocity = 0.022m/s

3. Re = 10000, Velocity = 0.22m/s

The following can be inferred from the above plots:

1. At a specific location in the pipe it can be observed that as Re increases, Velocity also increases. When Re varies from 100 to 10000, the velocity increases from 0.004 m/s to 0.284 m/s.

2. For a given inlet velocity, the velocities at the different location remains almost a constant. This is because the flow has fully developed by the time it reaches each of these locations. As the flow progresses from the entry to exit, the velocity profile of the flow changes. This change is due to the formation of boundary layers. At a specific point in the pipe length the boundary layer is completely formed. The region from the entry to this point is called the entry region. Beyond the entry region, the velocity profile remains a constant. This region where the velocity remains constant is called fully developed region.