Pipe Flow Simulation with varying Reynolds number

Pipe Flow Simulation with varying Reynolds number

Objective

To compare the effects of varying Reynolds number by simulating flow in pipes. The Reynolds number is set at 100, 1000 & 10,000. The following factors are taken into account:

1. Line probes are placed at 95%, 90% and 85% of the pipe length.
2. The normalized velocity profiles are compared at the locations of the line probes.
3. The velocity profile is normalized by the inlet velocity.

Introduction

Computational Fluid Dynamics (CFD) is the process of mathematically modeling a physical phenomenon involving fluid flow and solving it numerically with the help of computing and processing power of a computer. In a CFD software analysis, the examination of fluid flow in accordance with its various physical properties such as velocity, pressure, temperature, density and viscosity are conducted. These properties need to be reviewed simultaneously in order to generate an accurate solution. A mathematical model of the physical case and a numerical method are used in a CFD software tool to analyze the fluid flow. The central mathematical description for all theoretical fluid dynamics models is given by the Navier-Stokes equations, which describe the motion of viscous fluid domains with three major equations, which are the conservation of mass, momentum and energy, respectively [1].

Theory

In this project, a few major parameters relevant to the project will be discussed in further detail

1. Reynolds number: The Reynolds number is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities [2]. It is defined by the formula:

where:

• ρ is the density of the fluid (SI units: kg/m3)
• u is the flow speed (m/s)
• L is a characteristic linear dimension (m)
• μ is the dynamic viscosity of the fluid (Pa·s or N·s/m2 or kg/(m·s))
• ν is the kinematic viscosity of the fluid (m2/s).

2. Boundary layer: It is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface [3]. The fluid's interaction with the wall induces a no-slip boundary condition (zero velocity at the wall), which increases slowly above the surface until it returns to the bulk flow velocity. The thin layer consisting of fluid whose velocity has not yet returned to the bulk flow velocity is called the velocity boundary layer.

Project Setup

For this experiment, water will be used as the working fluid. In order to run the simulations, the velocity values need to be calculated so that the inlet velocities can be entered for the varying Reynolds number. The following values are taken for the setup:

ρ: 1000 kg/m³, D (diameter): 0.04 m, µ: 1.002 x 10^-3 N.s/m².

Therefore, the calculated velocities are:

3D model

The first stage is to set up the model so that we can run the simulations. In this experiment, we will use a pipe of diameter 0.04 m. First, create a sketch on the front plane container a circle of diameter 0.04m. Extrude it to a length of 1 m, and shell it with a 0.1 mm dimension as seen in the first picture. Then, draw 3 lines at 0.85m, 0.9m and 0.95m to locate the line probes. Finally, place lids on the ends of the pipe as it is necessary to close any open gaps to be able to run the simulations. We are now ready to set up the simulation model.

Simulation setup

1. New Project: Create a new project by clicking on ‘New’ and creating a project name. Set up the following:

• Analysis type: Internal
• Working Fluid: Water
• Flow Type: Laminar and Turbulent

Leave the wall as adiabatic and don’t add any roughness to the pipe.

2. Boundary conditions:

Add the following boundary conditions:

1. Inlet velocity: Add the velocity for the smallest Re number. The others will be done in a parametric study.
2. Wall condition: The wall of the pipe is set as a real wall
3. Outlet: The outlet is set up as static pressure.

3. Mesh: The standard default contains 4 x 4 x 118 cells, which is too rough and will not create smooth results. Change the mesh settings to 20 x 20 x 100 cells, which will result in much smoother contour plots, which will be seen in the cut plots discussed in the results section.

4. Plots: In order to visualize the results, plots need to be set up. Add cut plots at 0.85m, 0.9m and 0.95m. Set the value to velocity and show the grid.

Additionally, add XY plots for the velocity at all 3 locations. Also, create an extra plot to compare the velocities for all 3 locations.

Add a transparency for the solid, and the end result will look like the below picture.

5. Parametric Study:

In order to compare the different Re numbers, we need to create a parametric study. Start by creating a new parametric study. For the input parameter, add the inlet velocity. For the output parameters, select all plots. For the scenarios, copy the first scenario 2 times, and changes the velocities per the table to match the required Re numbers. At this stage, the set up is complete.

Press the run button and let the simulations compile. The end result will look like the picture below, letting you know that the study is finished. The plots and data can be obtained from the next few tabs in the parametric study window.

Results & Discussion

A detailed discussion is provided below (right after all the plots).

Location: 85% Length, Re: 100

Location: 85% Length, Re: 1000

Location: 85% Length, Re: 10,000

Location: 90% Length, Re: 100

Location: 90% Length, Re: 1000

Location: 90% Length, Re: 10000

Location: 95% Length, Re: 100

Location: 95% Length, Re: 1000

Location: 95% Length, Re: 10,000

Velocity at 85% Length

Velocity at 90% Length

Velocity at 95% Length

Comparing all velocities at different positions

The following observations can be noted:

1. As seen in the velocity plots, for any Re number, the velocity of the flow in the middle of the pipe is higher than at the wall of the pipe. This is simply due to the presence of a boundary layer. The velocity at the wall is (approaching) zero, and it slowly climbs up till it reaches ambient conditions. However, because the flow is through a pipe, the maximum velocity is slightly higher than that of the inlet conditions. This is a little more easily visualized through the cut plots.

2. At lower Reynolds numbers (100, 1000), the velocity remains rather constant throughout the flow.

However, at higher Reynolds numbers, there appears to be a difference in velocities. This can be seen in the final plot, where the velocities at the wall appear to be different at the different line probes. While they all end up becoming the same speed in the middle of the pipe, it would appear as though the flow is being developed as the water moves along the length of the pipe.

Sources

[1] https://www.simscale.com/docs/simwiki/cfd-computational-fluid-dynamics/what-is-cfd-computational-fluid-dynamics/

[2] Wikipedia contributors. (2022, February 23). Reynolds number. In Wikipedia, The Free Encyclopedia. Retrieved 01:47, April 13, 2022, from https://en.wikipedia.org/w/index.php?title=Reynolds_number&oldid=1073588192

[3] Wikipedia contributors. (2022, March 29). Boundary layer. In Wikipedia, The Free Encyclopedia. Retrieved 01:54, April 13, 2022, from https://en.wikipedia.org/w/index.php?title=Boundary_layer&oldid=1080021986