Internal Flow Simulation in Pipe using SOLIDWORKS

Aim: To get started with Flow Simulation in Solid Works and perform the following objectives:

1. Simulating Internal flow through pipe.
2. Creating a Parametric Study by changing Reynold's No. from 100,1000 to 10000.
3. Analysing the velocity profile at 95%, 90% and 85% of pipe length.
4. Comparing the Velocity Profiles at each of above two cases.
5. Normalising the velocity profile by the Inlet Velocity.

Theory:

Liquid or gas flow through pipes or ducts is commonly used in heating and cooling applications and fluid distribution networks. The fluid in such applications is usually forced to flow by a fan or pump through a flow section.

The terms pipe, duct, and conduit are usually used interchangeably for flow sections. In general, flow sections of circular cross section are referred to as pipes (especially when the fluid is a liquid), and flow sections of noncircular cross section as ducts (especially when the fluid is a gas). Small diameter pipes are usually referred to as tubes.

We may have probably noticed that most fluids, especially liquids, are transported in circular pipes. This is because pipes with a circular cross section can withstand large pressure differences between the inside and the outside without undergoing significant distortion. Noncircular pipes are usually used in applications such as the heating and cooling systems of buildings where the pressure difference is relatively small, the manufacturing and installation costs are lower, and the available space is limited for ductwork.

Although the theory of fluid flow is reasonably well understood, theoretical solutions are obtained only for a few simple cases such as fully developed laminar flow in a circular pipe. Therefore, we must rely on experimental results and empirical relations for most fluid flow problems rather than closed-form analytical solutions. Noting that the experimental results are obtained under carefully controlled laboratory conditions and that no two systems are exactly alike, we must not be so naive as to view the results obtained as "exact".

The fluid velocity in a pipe changes from zero at the surface because of the no-slip condition to a maximum at the pipe center. In fluid flow, it is convenient to work with an average velocity `V_(avg)`, which remains constant in incompressible flow when the cross-sectional area of the pipe is constant.

Laminar and turbulent Flows

If you have been around smokers, you probably noticed that the cigarette smoke rises in a smooth plume for the first few centimeters and then starts fluctuating randomly in all directions as it continues its rise. Other plumes behave similarly (See figure 1 below). Likewise, a careful inspection of flow in a pipe reveals that the fluid flow is streamlined at low velocities but turns chaotic as the velocity is increased above a critical value. The flow regime in the first case is said to be laminar, characterized by smooth streamlines and highly ordered motion, and turbulent in the second case, where it is characterized by velocity fluctuations and highly disordered motion. The transition from laminar to turbulent flow does not occur suddenly; rather, it occurs over some region in which the flow fluctuates between laminar and turbulent flows before it becomes fully turbulent. Most flows encountered in practice are turbulent. Laminar flow is encountered when highly viscous fluids such as oils flow in small pipes or narrow passages.

The transition from laminar to turbulent flow depends on the geometry, surface roughness, flow velocity, surface temperature, and type of fluid, among other things. After exhaustive experiments in the 1880s, Osborne Reynolds discovered that the flow regime depends mainly on the ratio of inertial forces to viscous forces in the fluid. This ratio is called the Reynolds number and is expressed for internal flow in a circular pipe as

`Re = "Inertial Forces"/"Viscous Forces" = (rho*V_(avg)*D)/mu`

where `rho = "Density of the fluid"` , `V_(avg) = "average flow velocity (m/s)"`,

`D = "Characteristic length of the geometry (diameter in this case, in m)"`

`mu = "Dynamic viscosity of the fluid (Pa-s)"`

The Reynolds number at which the flow becomes turbulent is called the critical Reynolds number, `Re_(cr)`. The value of the critical Reynolds number is different for different geometries and flow conditions. For internal flow in a circular pipe, the generally accepted value of the critical Reynolds number is `Re_(cr) = 2300.`In general, Laminar and Turbulent Flows are differentiated as follows:

`Re le 2300`	laminar flow
`2300 le Re le 4000`	transitional flow
`Re ge 4000`	turbulent flow

The Entrance Region

Consider a fluid entering a circular pipe at a uniform velocity. Because of the no-slip condition, the fluid particles in the layer in contact with the surface of the pipe come to a complete stop. This layer also causes the fluid particles in the adjacent layers to slow down gradually as a result of friction. To make up for this velocity reduction, the velocity of the fluid at the midsection of the pipe has to increase to keep the mass flow rate through the pipe constant. As a result, a velocity gradient develops along the pipe.
The region of the flow in which the effects of the viscous shearing forces caused by fluid viscosity are felt is called the velocity boundary layer or just the boundary layer. The hypothetical boundary surface divides the flow in a pipe into two regions: the boundary layer region, in which the viscous effects and the velocity changes are significant, and the irrotational (core) flow region, in which the frictional effects are negligible and the velocity remains essentially constant in the radial direction.

The thickness of this boundary layer increases in the flow direction until the boundary layer reaches the pipe center and thus fills the entire pipe, as shown in figure below. The region from the pipe inlet to the point at which the boundary layer merges at the centerline is called the hydrodynamic entrance region, and the length of this region is called the hydrodynamic entry length `L_h`. The wall shear stress varies as a paraboloid shape which isalso shown in below figure.

The hydrodynamic entry length is usually taken to be the distance from the pipe entrance to where the wall shear stress (and thus the friction factor) reaches within about 2 percent of the fully developed value. In laminar flow, the hydrodynamic entry length is given approximately as `L_(h-"laminar") ~= 0.05*Re*D`

In turbulent flow, the intense mixing during random fluctuations usually overshadows the effects of molecular diffusion. The hydrodynamic entry length for turbulent flow can be approximated as `L_(h-"turbulent") = 1.359*D*"Re"^(1/4)`

The above type of flow is eferred to as Poiseuille flow and the equation for alulating the average velocity is given as `U(r)= 2*V_(avg)(1-r^2/R^2)`

So where `U(r) = "Local velocity at a distsnce r from the centre of the pipe"` when r = 0 `U(r) = 2*V_(avg)`

Before Entering into the Flow Simulation in Solid Works, here are some of the important steps which are rquired to know before doing any type of CFD simulation:

1. Forumulate the Flow Problem
2. Model the Geometry and Flow Domain
3. Establish the Boundary and Initial Conditions
4. Generate the Grid
5. Establish the Simulation Strategy
6. Establish the Input Parameters and Files
7. Perform the Simulation
8. Monitor the Simulation for Completion
9. Post-process the Simulation to get the Results
10. Make Comparisons of the Results
11. Repeat the Process to Examine Sensitivities
12. Document

To know more about this refer the document mentioned in the references.

As far know, we have defined our flow problem as Internal Flow.

Model Geometry in SolidWorks

So Based on above theory, a model of a pipe was made in SolidWorks with following Specifications:

• Diameter of Pipe(Internal diameter) = 50 mm = 0.05m
• Length of the Pipe = 1000mm = 1m

Starting Flow Simulation

Using Solid Works Flow Simulation Add-In, the tool was activated and a flow domain was set over the pipe. Some of the general settings were set through the Wizard tool in Flow simulation which were as follows:

• Analysis Type: Internal
• Fluid Used : Water
• Initial Conditions:
  • Pressure = 101325 Pa
  • Temperature = 293.2 K
• One of the important point to be noted while peforming this preliminary setup is that all the gemetries which were made for simulations must be closed, so in order to make it closed, lids were created at the inlet and outlet of the pipe.

This made a flow domain over the model which is represented as follows: Figure1- Basic Model of Pipe Figure2- Flow Domain over the pipe

Setting up Boundary Conditions:

1. Inlet Velocity = 0.0018 m/s
2. Outlet Preessure = 101325 Ps (Static)
3. Wall boundary Condition = Real wall along Pipe Surface

Mesh Generation:

Basic mesh was generated using Following settings:

• Automatic Mesh Set
  • Along X = 10 divisions
  • Along Y = 10 divisions
  • Along Z = 50 divisions

Running Baseline Simulation:

A simple trial was run in order to solve the above set calculations. The solution to the above setup was converged at 40th Iteration. The report of the Simulation is shown in the below figure:

Post Processing

Cut Plots were made along lateral and Longitudnal Directions of the pipe and Velocity Contours were generated as follows:

The boundary Layer is visible at the pipe walls which also gave an indication that the results obtained were correct.

Three Cut plots were also made to investigate the velocity variation at different Lengths which are discussed below:

• 95% Length of the pipe

It is seen that Velocity profile if parbolic.

• 90% Length of the pipe

• 85% Length of the pipe

Creating Parametric Study:

In order to check the results whether they are accurate a parametric study was done in which Reynold's Number was varied as 100, 1000 and 10000 along with the basic mesh elements.

For Calculating the Inlet Velocity, a Matlab program was made as shown:

%% CALCULATING INLET VELOCITIES FOR DIFFERENT VALUES OF REYNOLD'S NUMBER
clear all
close all
clc

% Re = (rho*V*D)/mu where Re is yje Reynold's No, rho id the density of
% working fuid, V is the average velocity , D is the diameter of the pipe
% and mu is he dynamic viscosity (All units are in SI)

Re = [100 1000 10000];
rho = 1000;  %Working fluid is water
D = 0.05;
mu = 8.9e-4;
length = 1;

V = (mu.*Re)/(rho*D)

The output Gave Following Values of Inlet Velocities:

V =
    0.0018    0.0178    0.1780

Following are the details of the Parametric Study

Based on above Parametric Study, at the three locations set above(95%, 90% and 85% of pipe length), Inlet Velocity is increased along with mesh improvement and the results are compared as shown in the below respective figures:

Velocity Profile at 95% Length

It is clear from above three cases that as Reynold,s number increases (Inlet Velocity), there is a disturbance in the velocity profile (visible in 3rd figure). We can see that the velocity profiles are parabolic in nature.

From above Figures, it is clear that the velocity profile is parabolic in first two cases as Reynold's number is less than critical Reynold's number.In case of third case where Reynold's no is 10000, the flow becomes turbulent and the velocity profile ni longer remains parabolic.

Velocity Profile at 90% Length

Same Observations were recorded at this location also. This also gave the indication that flow has become fully developed.

Velocity Profile at 85% Length

Normalised Velocity Profiles at each Sections with change in Reynold's Number

We could see that during the laminar flow the velocity at the centerline of the pipe was almost twice the inlet velocity. But as the Reynolds nuber increases and the flow changed from laminar to turbulent, the center line velocity is no more double the inlet Velocity. Also the Parabolic profile was flattened at the centre in case of turbulent flow.

The same trend were visible at 90 and 95% length of the pipe.

Conclusion

Following were the key takeaways from the above project:

1. SolidWorks can be used to simulate the internal flow through pipes with some limited settings.
2. With improving the mesh size, the plots were more refined but it also took more time to sove the calculations.
3. Velcoity profile was found to be parabolic in case of laminar flows.
4. In case of laminar flows, the average velocity of the pipe is twice the local inlet velocity in fully developed flow.

References:

1 FLUID MECHANICS-FUNDAMENTALS AND APPLICATIONS by Yunus A Cengel and JOHN M. CIMBALA

2 https://www.grc.nasa.gov/WWW/wind/valid/tutorial/process.html#document