Round the Bend with SOLIDWORKS Flow Simulation

Round the Bend with SOLIDWORKS Flow Simulation

Calculating velocity changes and pressure losses in piping by hand is a thing of the past, with SOLIDWORKS Flow Simulation doing all the hard work for you! In this blog we will take a look at an S-Bend pipe with a reducer near the end and compare the results received from SOLIDWORKS Flow Simulation to the hand calculation results. The start of the pipe is 6.31m above the bottom segment, and it goes through two 45 degree bends before reaching a reducer, which linearly decreases the diameter of the pipe. The initial pipe is of diameter 1.2m and is 22.66m long before the reducer. The final piece of pipe is 0.8m diameter and is 5m long, an image of this can be seen below.

The boundary/initial conditions used for this case are: 

·     -    An inlet velocity of 10m/s ·    

    - A static pressure at the outlet of 101325Pa ·   

 -     Wall roughness of 9 micrometers ·     

-    Fluid is water set to 25°C ·     

-    K for the pipes are 9e-5 m* ·   

-      hMinor for the elbow bends are 0.13m and for the reduction section is 0.03m*

Where K is the absolute roughness of the pipe, used to calculate the major losses in the pipe and hMinor are the minor loss coefficients, which can be found online or calculated.

The mesh used in this study is a global level 6 initial level of mesh with no local refinement. This gives a total number of fluid cells of 157183, which the mesh at the outlet of the pipe can be seen below.

Using the Continuity equation, we can calculate the theoretical velocity at the end of the pipe:

Where  is the density of the fluid, A is the area of pipe, V is the velocity of the fluid and 1 and 2 represent the inlet and outlet respectively.

Plugging in the values are rearranging for the velocity at the outlet of the pipe gives us a theoretical velocity of 22.5m/s.

This is where it gets a little bit more complicated… To calculate the pressure drop across the pipe we now need to use the Bernoulli’s equation.

Where P is the atmospheric pressure,  is the density of the fluid, V is the velocity of the fluid, g is the acceleration due to gravity, h is the height of the pipe,  is the pressure head at the inlet,  is the friction losses in the pipes, is the minor losses in the pipes, where 1 and 2 represent the inlet and outlet respectively.

The only unknowns in the Bernoulli equation are the pressure head at the inlet as well as the friction and minor losses in the pipe. Using the following two equations we can calculate the losses in the pipe and sub them back into the Bernoulli equation to find the pressure head at the inlet. The pressure losses in the pipe due to friction are calculated using the following equations.

And the equation for the minor losses is,

Where f is the friction factor, L is the pipe length, D is the pipe diameter, V is the velocity of the fluid,  is the density of the fluid, Re is the Reynolds number of the flow and K is the absolute roughness of the pipe.

Calculating the major loss in both of the pipes and the minor losses in all 3 fittings we now have all the variables to sub in to the Bernoulli’s equation to calculate the pressure head at the inlet. Which, with a fluid velocity of 10m/s would be 350394.56 Pa.

Running the Flow Simulation in SOLIDWORKS only takes a few minutes and gives the following results, below are cut plots through the front plane of velocity and pressure.

Using surface parameter results on the face of the lid at the inlet and outlet of the pipe we are able to get the averaged values for pressure and velocity at the inlet and outlet. Below is a table comparing the SOLIDWORKS Flow Simulation results to the analytical results.

As you can see there is a small percentage difference between the analytical results and the SOLIDWORKS Flow Simulation results, the velocity at the outlet is very accurate, however there is a slightly larger difference at the inlet. This could be due to the mesh refinement at the inlet. If we compare the size of the mesh at the inlet compared to the outlet (below and a few images above) you can see the mesh at the inlet is coarser, which with refinement would converge on the analytical results.

Creating the geometry, setting up the flow simulation as well as meshing and running this study took under half an hour in total. Whereas the hand calculations took longer, are more laborious, introduce the opportunity for human error and are significantly less fun to use than SOLIDWORKS Flow Simulation.

 You can find more information on the Flow Simulation package along with is capabilities on our website:

https://www.solidsolutions.ie/solidworks/Simulation/Packages/Flow-CFD.aspx

By Applications Engineer Chris Boyles