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# 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.

## Analysis Type and Mesh

Tool Type: OpenFOAM®

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).

## Simulation Setup

Fluid:

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

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.

Last updated: June 10th, 2021