The aim of this test case is to validate the following parameters of incompressible steady-state laminar fluid flow through a pipe:
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.
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.
| Length | Diameter | |
|---|---|---|
| Value \([m]\) | 1 | 0.01 |
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 type | Cells in x | Cells in y | Cells in z | Number of nodes | Type |
|---|---|---|---|---|---|
| snappyHexMesh | 20 | 1600 | 20 | 341544 | 3D hex |
Fluid:
Boundary Conditions:
| Boundary type | Velocity \([m/s]\) | Pressure \([Pa]\) | |
|---|---|---|---|
| A | Inlet | Fixed Value: 0.1 | Zero Gradient |
| B | Wall | Fixed Value: 0 | Zero Gradient |
| C | Outlet | Zero Gradient | Fixed Value: 0.1 |
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.
Last updated: June 10th, 2021
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