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Documentation

Validation Case: Laminar Pipe Flow

The aim of this test case is to validate the following parameters of incompressible steady-state laminar fluid flow through a pipe:

  • Velocity
  • Pressure drop

The simulation results of SimScale were compared to the analytical results obtained using the Hagen-Poiseuille equations\(^1\). The mesh was created with the parametrized – hexahedralization-tool on the SimScale platform.

Geometry

A straight cylindrical pipe was chosen as the flow domain (see Figure 1). Faces A, B and C represent the inlet, wall and outlet respectively.

pipe geometry
Figure1. Geometry of the cylindrical pipe
 LengthDiameter
Value \([m]\)10.01
Table 1: Dimensions of the pipe geometry

Analysis Type and Mesh

Tool Type: OpenFOAM®

Analysis Type: Incompressible steady-state analysis.

Turblence Model: Laminar flow

Mesh and Element Types:

A uniformly-spaced hexahedral mesh was generated on the SimScale platform using the snappyHexMesh tool (see Figure 2).

Mesh typeCells in xCells in yCells in zNumber of nodesType
snappyHexMesh201600203415443D hex
Table 2: Hexahedral mesh characteristics
snappy hex mesh used for laminar pipe flow
Figure 2. Mesh used for the SimScale case

Simulation Setup

Fluid:

  • Water:
    • \((\nu)\) Kinematic viscosity = 10-6 \(\frac{m^2}{s}\)

Boundary Conditions:

 Boundary typeVelocity \([m/s]\)Pressure \([Pa]\)
AInletFixed Value: 0.1 Zero Gradient
BWallFixed Value: 0Zero Gradient
COutletZero GradientFixed Value: 0.1
Table 3: Boundary Conditions

Results

The analytical solution gives us the following equations for maximum axial velocity, pressure drop and developed radial velocity profile:

$$u_{z max} = 2u_{z avg}$$

$$\Delta P = \frac{128}{\pi} \frac{\mu L}{D^4} Q $$

$$u_z = -\frac{1}{4\mu} \frac{\partial p}{\partial z}(R^2 – r^2)$$

A comparison of the velocity and pressure drop obtained with SimScale with analytical results is given in Figures 3A, 3B, and 3C. Figure 3A shows the developed radial velocity profile, located 60 \(cm\) from the inlet. The variation of the axial velocity along the center-line is shown in Figure 3B, and the pressure drop along the pipe can be observed in Figure 3C.

laminar flow axial velocity
Figure 3A: Visualization of Axial velocity
laminar pipe flow pressure
Figure 3B: Visualization of pressure
laminar pipe flow developed radial velocity
Figure 3C: Visualization of developed radial velocity profile

Last updated: June 10th, 2021

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