Hagen Poiseuille Flow
Overview
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 shown in [1]. The mesh was created with the parametrized-hexahedralization-tool on the SimScale platform.
Import validation project into workspace
Geometry
A straight cylindrical pipe was chosen as the flow domain (see Fig.1.). Faces A, B and C represent the inlet, wall and outlet respectively.
| Length | Diameter | |
|---|---|---|
| Value [m] | 1 | 0.01 |
Analysis type and Domain
A uniformly-spaced hexahedral mesh was generated on the SimScale platform using the snappyHexMesh tool (see Fig.2.). It was observed that the presence of inflation layer doesn’t not significantly improve the solution.
Tool Type : OPENFOAM®
Analysis Type : Incompressible Steady-state (Laminar)
Mesh and Element types :
| Mesh type | Cells in x | Cells in y | Cells in z | Number of nodes | Type |
|---|---|---|---|---|---|
| snappyHexMesh | 20 | 1600 | 20 | 341544 | 3D hex |
Simulation Setup
Fluid:
- Water: Dynamic viscosity (ν
) =10−6m2s
Boundary Conditions:
| Boundary type | Velocity | Pressure | |
|---|---|---|---|
| A | Inlet | Fixed Value: 0.1 ms−1
|
Zero Gradient |
| B | Wall | Fixed Value: 0.0 ms−1
|
Zero Gradient |
| C | Outlet | Zero Gradient | Fixed Value: 0.1 Pa
|
Results
The analytical solution gives us the following equations for maximum axial velocity, pressure drop and developed radial velocity profile:
uzmax=2uzavg
ΔP=32μLD2uzavg
uz=−14μ∂p∂z(R2−r2)
A comparison of the velocity and pressure drop obtained with SimScale with analytical results is given in Fig.3A, 3B and 3C. Fig.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 Fig.3B, and the pressure drop along the pipe can be observed in Fig.3C.
Fig.3. Visualization of Axial velocity and pressure (A, B) and developed radial velocity profile (C)
References
| [1] | Hagen–Poiseuille flow from the Navier–Stokes equations |
Disclaimer
This offering is not approved or endorsed by OpenCFD Limited, producer and distributor of the OpenFOAM software and owner of the OPENFOAM® and OpenCFD® trade marks. OPENFOAM® is a registered trade mark of OpenCFD Limited, producer and distributor of the OpenFOAM software.