COMSOL Step-by-Step Tutorial
Expt 140 – Tank Discharge
March 4, 2013
Team 2
Joseph Duffy
Zlatko Sokolikj
Andrew Suellentrop
• This Comsol tutorial demonstrates how to
perform the velocity profile calculations using
the simplest model possible
• It utilizes the 2D axisymmetric reference
system
So we pick our space dimension to be
2D axisymmetric
And press next
We pick laminar flow
We pick laminar flow from
our physics menu
and press next
We pick Stationary Study Type
and press Finish
In the actual Exp140 Tank Discharge, our system is not stationary, yet it
is time dependent as one of our boundaries, the water level, changes. However to
make these calculations easier we assume a quasi steady state as outlined on page
16 of Exp140 Tank Discharge – Theoretical Background by Loren B. Schreiber.
That means that Comsol will perform the calculation for the velocity while the
water level is kept constant. This presents an obstacle for us as we would like to
know how the velocity profile changes as the water level drops. We can overcome
this obstacle with a feature called parametric sweep which will be covered later
down this tutorial
Before we start drawing our model we must realize the significance of
our choice of dimension. We use this geometry when our 3D model is symmetric
in both the x and y axis. What we need to draw in Comsol is a sketch which,
when rotated around the z axis 360 degrees, will give us our model
So for our model…
In the 2D axisymmetric geometry
our model looks like….
Z-axis
The tank is a 3D model that is
symmetric in the x and y coordinate
Rotated around the z axis, our model
will give us the tank in 3D
However before we start drawing
the system we need to set the
values of the parameters we are
going to use, such as density, Pipe
Diameter, Tank Diameter etc.
We right click on Global Definitions
and select parameters
To insert a parameter click on
the cell and insert the
appropriate descriptions
For more information regarding
Parameter Input, please go
through Chris Golding Intro for
Comsol
Remember to use square
brackets when plugging in the
units
In case you plan to use these
parameters for multiple
models you can save them as
text file which you can open
later on instead of having to
write them every time
In this tutorial we use the following parameters
• In this tutorial we shall use the simplest
geometry possible. We will have one rectangle
represent our tank and another one represent
our pipe
To build our first rectangle that
will represent our pipe, we
right-click on Geometry section
and select Rectangle
Remember that our model
will represent only one half
of the side section. That is
why the width of the
rectangle that is supposed
to represent the pipe has a
width of the radius
So first we need to choose what
part of our rectangle will be our
reference for its position.
We pick Corner
Therefore the corner of our
rectangle should be at (0,0)
Note*: In Comsol, whenever you
can enter a number, you can also
enter a equation using the
parameters
Therefore for width and height
we write our Dp/2 and Lp.
After we are done setting
up the rectangle, to
materialize the rectangle on
our sketch we right-click on
the Rectangle1 from the
Geometry Sections and
select Build selected
We repeat this process for
the second rectangle. The
corner of this rectangle will
be located at(0,Lp) while the
width and the height will be
(Dt/2) and Lt
We materialize the rectangle
on our sketch
The next step is to form a
union with the rectangles
we have built, merging
them together
We need input the
rectangles by selecting
them first( which will
redden the rectangle)
And then click add
We repeat this process for
the other rectangle
The objects, once included in
the union, should have the
color of blue, and should
appear in the Input Object
section
In this step, we introduce
the material that is used in
the experiment
To do that, right-click on
Materials and select Material
Make sure that this material is represented in both
domains(the rectangles), which should be colored blue
We also input the density and viscosity. We can
do this using values we know or using the
parameters we previously entered
We enter the values in the Value Column
For density we enter Rho
For viscosity we enter Rho*Mu – the product
of the kinematic viscosity and density
The next step is to select the
inlet of our system
Right click on Laminar Flow
and select Inlet
The inlet section will appear
We need to select which
wall of our system will be
the inlet. Therefore we
select the top wall and
press add
We also choose the
boundary condition
For this tutorial we choose
the pressure to be our
boundary condition and we
set it equal to our
Atmospheric Pressure
We repeat the process for the
outlet. Right click on the
Laminar Flow section, press
Outlet and select and add the
wall of the system that is to
be your outlet
We use the same boundary
condition as the inlet
Here we select the Initial Values
We select the Domain to be our rectangles
We select the Pressure to be our atmospheric
pressure
To make our calculations faster, since we know
that our velocity will be negative, we give the
velocity field a small negative number in the
z-direction
We introduce gravity to our Model
We do that by introducing the Volume Force which is
the gravitational pull on a unit of volume. The
Volume force is the Density multiplied the Earth’s
Acceleration
Right-click on Laminar Flow, and select Volume
Force. In Selection, select the domains on which this
force will act, which are our two rectangles. Also in
regards to the magnitude, input the negative product
of Density and the Earth’s Acceleration
The next step would be to
perform the calculations for
the velocity in these conditions
Right-click on the Study Section
and press Compute
Once the calculation is done
we can see that the predicted
velocity profile of the fluid is
much smaller in the tank than
in the pipe
We zoom in on the pipe
We can see that the velocity
profile in the pipe is laminar.
We can also see how the fluid
speeds up as it enters the
pipe and propagates farther
down
If we press on the Velocity3D
section we can see our model
in 3D. We can also zoom in to
get a better look at the
velocity
• Now we tackle the issue of constant boundary. To be able to
get a feel of how the velocity changes as the tank level
changes, using a constant boundary, we would have to perform
separate calculations for each level of the fluid tank. In each
calculation we would have to change the value of the
parameter that gives us our tank level. Comsol can do these
calculations all at once using a feature called parametric
sweep.
With parametric sweep we select a parameter that will change
and we choose the range in which it will change. Comsol
performs the velocity calculations for each value of the
parameter
To select Parametric Sweep
we right-click on Study and
select Parametric Sweep
Here we select the Parameter to be
changed.
First we select add…
We select the parameter that describes
our tank liquid level
In this tutorial that is Lt
And now we need to select the range
in which the parameter will be
changed.
The following window appears
* In this tutorial we chose the step method. With this method we pick a start
value(the highest level of the liquid in the tank) a stop value( the lowest level of the
liquid in the tank) and the step at which it will change. The other method is similar
with the exception that we do not choose the steps, but rather we choose the number
of values for that parameter and Comsol chooses the steps.
**Do not forget to input the units
So in this tutorial
- Our start value is the liquid level in the
beginning
- Our end value is the liquid level at the end
of the experiment
- Our step, to make this calculation short, is
0.1. Since we are decreasing our parameter
our step has to be negative, hence it is
written as -0.1. You can also choose a
smaller step size; however it will make the
calculation take longer and use up more
RAM.
- After inputting the values, press add.
After adding the values
right-click on Study and
press Compute
After the calculation is done,
we can see how the velocity
profile changes as we change
the tank height.
Select Solution 2, select the
height, and press plot .
• Now we can calculacte the average velocity
and see how it changes for each height.
𝑣 𝑑𝐴
𝑣𝑎𝑣𝑔 =
𝑑𝐴
In the geometry we are using the equation is
𝑣 × 𝑟 𝑑𝑟
𝑣𝑎𝑣𝑔 =
𝑟 𝑑𝑟
Comsol can find both the numerator and the
denominator for us and then we can use other
computational tools to calculate 𝑣𝑎𝑣𝑔.
We need to set up both integrals.
We do that by right-clicking Derived
Units in the Results section, selecting
Integration, and then selecting Line
Integration.
Now we first evaluate the numerator
- We select Solution 2 for Data set; for Parameter Selection we select From
list. Make sure all the values of the parameter are selected. Select the
Outlet as the boundary over which we integrate
- In Expression, write spf.U(the velocity profile)*r
- Select Evaluate
When the integration is complete,
the results will appear below in a
spreadsheet format. So far we
have Lt(the level in the tank) and
the integral of spf.U*r which
corresponds to our volumetric
flow rate.
Now we determine the integral in
the denominator which represents
the area
In Expression we input r, while
everything else is kept as it was
previously.
-Press Evaluate
- The new integral will appear in
the third column
- We select the whole data set
and press Copy Selection to
Clipboard.
We copy the data in an Excel Spreadsheet and find the velocity at each height by
dividing the Volumetric Flow rate by the Area, as given by the equation on the
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