Laminar Flow Analysis in a Pipe

SimScale Tutorial: Laminar Flow in a Pipe

This tutorial aims to investigate the pressure drop and visualize the velocity profile in laminar flow through a pipe.

Flow Simulation Set Up

Dimensions

A cylindrical pipe with a diameter of 0.01 𝑚, and a length of 10 𝑚.

Analysis Type

Incompressible steady-state analysis.

Turbulence Model

Laminar flow

Mesh and Element Types

Three structured hexahedral meshes generated using the hex-dominant automatic algorithm, refined with a growth rate of 1.25.

Fluid : Water

Initial Conditions:

• (𝜈) Kinematic viscosity = 10^-6 𝑚²/𝑠

Velocity Profile Definition

The parabolic velocity profile through a circular pipe in a laminar flow is approximated as follows:

where 𝑢_𝑧 is the z-component of the velocity along the axis, 𝑢_{𝑧𝑎𝑣𝑔} is the average inlet velocity, 𝑢_{𝑧𝑚𝑎𝑥} is the maximum velocity that occurs at the centerline, 𝑟 is the radial distance from the centerline, and 𝑅 is the radius of the circular pipe.

Boundary Conditions

The following boundary conditions are applied to the corresponding pipe surfaces:

Face	Boundary type	Value
Inlet	Velocity inlet	Fixed value of 2×0.1×(1−(((𝑥)2+(𝑧)2)0.5/0.005)2) 𝑚/𝑠 in the y-direction
Outlet	Pressure outlet	Fixed value of 0 𝑃𝑎
Pipe Surface	Wall	No-slip

Let’s now delve into the SimScale process one step at a time for this particular problem.

Just a heads-up: The ideal way to begin is by creating a ‘New Project‘ and then importing the CAD model. However, we’ve already taken care of the steps for you, including importing the CAD model. You can get started right away with the ‘Create Simulation‘ step.

Prepare the CAD Model and Select the Analysis Type

Open a ‘New Project’ & import the CAD model

Create Simulation

Assigning the Material and Boundary Conditions

Define a Material

Define the Initial Conditions

Define Boundary Conditions

Simulation Control

• Set the ‘Numerics’ as given in the ‘FINISHED PROJECT’.

Result Control

• Now, it’s time to set up the ‘Area Average‘.
• Below ‘Result Control’, click ‘+’ next to Surface Data, and enter the following values.

• To calculate area averages and other parameters like velocity components at each probe point and record them, it’s crucial to choose the suitable probe points.
• For example, consider creating a set of points named ‘Probe Points along the Length’. Click ‘Probe Points’ and turn on the points appropriate set of points to be added to the list, and name them as ‘Probe Points along the Length’.

• Do the same for other sets.

NOTE: Please note that the example provided is just a demonstration. Refer to the Finished Project for the specific number of lists and corresponding probe points. Feel free to create your own lists tailored to your preferences. The rationale behind these selections will be explained at the end of this module.

Mesh Generation

• Click on Mesh, and Click ‘+’ next to Surface Refinement, and add the following surface refinement for the inlet, and pipe surface as given below.

Following the above, Click Generate to generate Mesh, and wait for the mesh to get generated.

NOTE: Check the Event Log below the dialogue box once the mesh is generated to check for the mesh quality before proceeding. If the mesh is not correctly generated, Simulation Run in the next stage can get terminated prematurely.

Simulation

To initiate the simulation, follow these steps:

Post- Processing

After checking the residuals, if you think it has not yet been converged, you will see the “Continue to run >>” icon, in which you can enter the end time to be your present end time and increase the maximum run time.

If not, continue by selecting ‘Post-process results.’ See below for all available post-processing options in SimScale:

• Cut Plane: Slice the domain to visualize parameters on the plane.
• Vectors: Plot vector fields to represent quantities like velocity or force.
• Contour Plot: Display scalar field data using contour lines.
• Probe Points: Insert points to extract data at specific locations.
• Particle Trace: Generate streamlines from seed faces to observe flow patterns.
• Iso Surface: Highlight regions with specific scalar values.
• Iso Volume: Highlight regions within a defined scalar value range.
• Rotational View: Inspect rotational regions by creating blade-to-blade views.
• Animation: Create animations of simulation results.
• Field Calculator: Generate new fields using predefined functions and operators.
• Compare: Visualize result fields from two different simulations side by side.

Please refer to the accompanying image to explore the full range of available options for post-processing. These options provide diverse tools for analyzing and visualizing simulation results in SimScale.

Pressure Drop

• Select ‘p’ to display the plot showing pressure values for both the inlet and outlet faces of the pipe across each iteration.
• Option 1: Click on the dropdown icon at the top-right corner to download the .csv file. Download the CSV file and observe the converged ‘p‘ values corresponding to the end time.
• Option 2: Alternatively, check the final value directly from the live plot at the end time.

Velocity Profile

The values of velocity components at various probe points, including those along the radial and axial directions of the pipe.

• The downloaded file contains precise velocity values for each probe point and iteration until the ‘end time‘.
• Utilize MATLAB/Python/any programming language you’re familiar with to plot the velocity profile using the data from the downloaded .csv files.