The aim of this test case is to validate the following parameters of incompressible steadystate laminar fluid flow through a pipe:
The simulation results of SimScale were compared to the analytical results shown in [1]. The mesh was created with the parametrizedhexahedralizationtool on the SimScale platform.
Import validation project into workspace
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 
A uniformlyspaced 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 Steadystate (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 
Fluid:
) =10−6m2s
$={10}^{6}{m}^{2}s$
Boundary Conditions:
Boundary type  Velocity  Pressure  

A  Inlet  Fixed Value: 0.1 ms−1
$0.1\text{}m{s}^{1}$

Zero Gradient 
B  Wall  Fixed Value: 0.0 ms−1
$0.0\text{}m{s}^{1}$

Zero Gradient 
C  Outlet  Zero Gradient  Fixed Value: 0.1 Pa
$0.1\text{}Pa$

The analytical solution gives us the following equations for maximum axial velocity, pressure drop and developed radial velocity profile:
uzmax=2uzavg
$${u}_{{z}_{max}}=2{u}_{{z}_{avg}}$$
ΔP=32μLD2uzavg
$$\mathrm{\Delta}P=\frac{32\mu L}{{D}^{2}}{u}_{{z}_{avg}}$$
uz=−14μ∂p∂z(R2−r2)
$${u}_{z}=\frac{1}{4\mu}\frac{\mathrm{\partial}p}{\mathrm{\partial}z}({R}^{2}{r}^{2})$$
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 centerline 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)
[1]  Hagen–Poiseuille flow from the Navier–Stokes equations 
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