Modeling a Simple Flow in a Pipe
Goals
- Introduce you to the
basics of running a flow simulation.
- Show you how to find
information on the predicted flow.
- Introduce one hand
calculation necessary for checking flows in piping.
Preliminaries
Before starting your
first exercise, you need to make some decisions about how you are going
to organize your work. You need to store results on your UDrive
in a way that lets you find them again easily. The
method of running simulations used here drops files in directories that
don’t have meaningful names. I recommend that you create a directory
named “470” in your personal space. Immediately below that create
directories labeled “Exercises” and “Homework”. Under “Exercises”
create one subdirectory for each one that we do in class. I’ll leave
the naming convention to you. The subdirectory for this exercise could
be named “Exercise-1”, “1”,
or some variation on that theme.
Problem Definition
A 10 meter section of circular pipe consists of 5
meters that are 0.25 meters in diameter, followed by an abrupt
expansion
to a 0.353553 meter diameter for the remainder of the section (flow
area
doubles). Water flows into the test section at 20 m/s, at a
temperature of 300K. The pressure at the exit is 2.0x105
Procedure
The program that we
will use to solve this problem (and a lot of its relatives) does not
actually solve the steady state form of the flow equations. It
was designed to look at transient scenarios, and obtains a steady state
solution by running a transient long enough in time. We’ll
check to see if we’ve approached steady state later in the exercise.
The power plant
simulations in this class will be driven by the Symbolic Nuclear
Analysis Package (SNAP). The flow and heat
transfer equations in our simulations will be solved by the “TRAC/RELAP Advanced Computational
Engine” (TRACE). Before using TRACE in any computer session, you’ve got to start
something called the “Calculation Server.” Click
the Start button on your computer, and select the Programs menu. Run the mouse cursor down the list of programs until
you find “SNAP”. Select “Configuration Tool”
from
the SNAP sub-menu.
If a message box
appears saying "Attempting to connect to calculation server", click the
associated Cancel button. In the configuration
tool select the “Calculation Server” tab. Near the bottom of the
window, make certain that the drop-down menu box labeled "Code" says
TRACE. When TRACE is selected in that box, click the line above
describing the location and arguments for the executable, and finally
click the “Start Server”
button at the bottom of the window. Make a note
of
the path listed in the “Working Directory” box. That
is where you will find all subdirectories containing results of
calculations. You can close this window if you would like.
To start the exercise,
copy the file at this link to the
subdirectory that you’ve just created for this exercise. It should
appear with the file name “expansionL.inp”.
Open the file with jEdit
(found either from the Programs Menu or as a “jE”
icon on the screen). What you see in the editor
is one of several ways to pass initial and boundary conditions to TRACE. As you become more experienced, you may find that jEdit is the quickest way to
review or make very minor changes to your problem specification. For now, viewing this input file should give you
some
appreciation for the relative ease of the approach to input
construction
that we use in Exercise 2.
To run the calculation select the “Plugins”
menu, then “Snap”, and finally “Submit Calculation”. A
“Submit Calculation” window will appear. Click
the “Submit” button, then make a note of the Run Identifier in the
message window (or leave the message open while you check the job
status.
To check results of
the calculation, you can select the "Status Calculations" item seen
just
below "Submit Calculation in the previous image. As an alternative, you
can return to your Programs menu, and in the SNAP sub-menu, select “Job
Status”. In the left pane of the Job Status
window, click any “+” boxes that appear to get to a display of your
results in the right pane.
Look at the status
column. For this short calculation, it should
say
“Complete”. Click on the box containing the Run
Identifier for the job that you just completed. In
my example there are two runs listed. At this
point you should just have one job listed. More
will appear as you run more TRACE jobs. When
you’ve finished working with the results of a job, or copied its
results
to another location, you can remove it by selecting “Delete” from the
tools menu.
Now we’re going to use
the tools menu to look at results from the simulation. Click
the “View Output” item, then click “Output file”.
In the next window,
click “Points of Interest”. In the “Points of
Interest” menu select “Major Edits,”
then
click on the last line that appears (contains “trac
large edit”).
The
second line that you see should start with the phrase “problem time is”. Note that the problem was run for a 10 second
transient. The time required for fluid to flow
from the inlet to outlet is:
This
means that over 13 transit times have passed since the start of the
transient, and you would expect the solution to be well settled. You can do a quick check on steady state from
information now in front of you. Look for the
phrase “outer-iteration number is”. It should be
followed by the number one. This means that the
solution to the flow equations was found immediately. Now
look for the phrase “with fr.error of”. This is the maximum ratio of pressure change to
total
pressure during the last iteration of the time step. You
should see a very small number. In this case the
number is small enough that it probably results from round-off error in
the computer’s arithmetic.
To
get the best idea of the pressure change associated with the expansion
compare the pressure just before the expansion to that in the second
cell beyond the expansion. The slight variation
in
pressure from cell 6 to cell 7, is related
to
some subtleties in the numerical method that you don’t need to know. The slight variation from cell 1 to 2 is related to
a
boundary condition issue that we will explore in a later exercise.
For
constant density flows, pressure changes across flow area changes or
pipe bends are normally analyzed in terms of a modified Bernoulli
Equation. Let a subscript “c” denote quantities
at the area change or pipe bend, subscript “u” denote conditions
upstream of the change, and subscript “d” denote
conditions downstream of the change. The
modified
Bernoulli Equation is:
.
Tables
are available giving expressions for the loss coefficient k for various
geometries, and TRACE incorporates some of these as optional loss terms
in the momentum equation.
At
this point this exercise transitions to a short homework problem, in which you are
asked to locate some loss coefficients and check the TRACE results.